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deSitter
Still in Old School


Reged: 12/09/04

Scary relativity
      #6214651 - 11/25/13 09:14 AM

Scary because there is some linear algebra here!

A square matrix as many of you know, is an arrangement of numbers that embodies in some contexts a transformation of a certain sort - for example when I rotate the coordinates in the plane,

x' = x cos a - y sin a
y' = x sin a + y cos a

This is more easily expressed (read brackets as a column vector, and parentheses as a row vector, and double brackets as a matrix with entries in "reading" order)

[x' y'] = M [x y]

where M is the square matrix [[ cos a, -sin a, sin a, cos a ]]

The determinant is the product of the diagonal entries minus that of the off-diagonal entries, here cos^2 a + sin ^2 a = 1.

OK let's introduce four basic matrices (with complex numbers as entries)

Sx = [[ 0, 1, 1, 0]]
Sy = [[ 0, -i, i 0 ]]
Sz = [[ 1, 0, 0, -1 ]]
S0 = [[ 1, 0, 0, 1 ]]

and let's make the matrix object

R = x Sx + y Sy + z Sz + t S0 = [[ z + t, x - iy, x + iy, -z + t ]]

The determinant is

|R| = (z+t)(-z+t) - (x-iy)(x+iy) = -x^2 - y^2 - z^2 + t^2.

You'll see where this is going eventually. Ask questions now.

-drl


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: Scary relativity new [Re: deSitter]
      #6214787 - 11/25/13 10:24 AM

For me, Danny, this math is over my head. I would need pictures to explain each step and a glossary (with pictures) to explain the words vector, row vector, column vector, and matrix.

BUT DO NOT DO THIS, at least at this time. Rick and Brentwood also asked you to explain the special relativity thing. It is quite likely they do understand simple math like this and I do not want to hold the three of you up. Later, perhaps y'all can draw pictures for me and stuff like that BUT NOT NOW, or perhaps, even at all.

Thank you for taking this on.

Otto


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llanitedave
Humble Megalomaniac
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Reged: 09/26/05

Loc: Amargosa Valley, NV, USA
Re: Scary relativity new [Re: Otto Piechowski]
      #6214942 - 11/25/13 11:49 AM

Sounds like a job for numpy.

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Rick Woods
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Reged: 01/27/05

Loc: Inner Solar System
Re: Scary relativity new [Re: Otto Piechowski]
      #6214978 - 11/25/13 12:08 PM

Quote:

Rick and Brentwood also asked you to explain the special relativity thing. It is quite likely they do understand simple math like this and I do not want to hold the three of you up.




It's even more likely that at least one of them has no idea what any of it means. I feel like Homer Simpson when someone talks to him, and all he's hearing is "blah, blah, blah". It may as well be runes, or the Voynich manuscript.

Is this degree of immersion in the math really necessary to create an understandable analogy for the car-headlight thing? If so, well, thanks anyway, but there's nothing here for me.


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PeterR280
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Reged: 05/27/13

Re: Scary relativity new [Re: Rick Woods]
      #6214985 - 11/25/13 12:10 PM

The Lorentz transformations would be much easier to follow.

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The Mighty Mo
professor emeritus


Reged: 10/12/13

Loc: South of North, North of South...
Re: Scary relativity *DELETED* new [Re: Rick Woods]
      #6215014 - 11/25/13 12:23 PM

Post deleted by The Mighty Mo

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brentwood
Carpal Tunnel
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Reged: 11/04/05

Loc: BC Canada
Re: Scary relativity new [Re: The Mighty Mo]
      #6215039 - 11/25/13 12:35 PM

Nothing here for me either. I can understand some of Otto's posts more!
If the answer to the question, "What does an outside observer see when a vehicle travelling at just below c puts on its headlights" can only be answered with an equation, then I would say that there is no answer, it is still an unknown.


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deSitter
Still in Old School


Reged: 12/09/04

Re: Scary relativity new [Re: brentwood]
      #6215107 - 11/25/13 01:06 PM

C'mon be patient! You have to see things before you can understand them! It's not a linear process. Ask questions!

-drl


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dickbill
scholastic sledgehammer


Reged: 09/30/08

Re: Scary relativity new [Re: deSitter]
      #6215126 - 11/25/13 01:17 PM

why do you introduce imaginary numbers?

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deSitter
Still in Old School


Reged: 12/09/04

Re: Scary relativity new [Re: dickbill]
      #6215138 - 11/25/13 01:26 PM

You'll see! It's nothing unreal - it's very real. You HAVE to be patient. It will all come down to a flag...

-drl


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choran
Carpal Tunnel
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Reged: 12/28/12

Re: Scary relativity new [Re: deSitter]
      #6215200 - 11/25/13 01:56 PM

Will the simplified version come down to solving a right triangle with sides
ct, vt, and (hypotenuse) ct' and eventually solving for t'? I've seen that approach and it is pretty understandable, but requires pics.


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brentwood
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Re: Scary relativity new [Re: choran]
      #6215224 - 11/25/13 02:08 PM

Danny,aко аз ви е поискал въпрос в България, ще можете да го разбираме без да използвате Google? Не мога да поставя си пост в Google и да се превеждат.?

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choran
Carpal Tunnel
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Reged: 12/28/12

Re: Scary relativity new [Re: brentwood]
      #6215269 - 11/25/13 02:27 PM



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deSitter
Still in Old School


Reged: 12/09/04

Re: Scary relativity new [Re: choran]
      #6215320 - 11/25/13 02:43 PM

Quote:

Will the simplified version come down to solving a right triangle with sides
ct, vt, and (hypotenuse) ct' and eventually solving for t'? I've seen that approach and it is pretty understandable, but requires pics.




Nope, 100% rigorous.

-drl


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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: deSitter]
      #6215370 - 11/25/13 03:04 PM

I haven't the math background or understanding of relativity to be able to see how this turns out. Can light be slowed down or appear slowed down from an observer's perspective at the side of the road? I have a hard time with the idea of a light beam traveling at a foot a minute or looking like it is proceeding this slowly. I thought that the light sent from the headlights would just travel at the "speed of light" as soon as turned on from the car. That it would appear instanteous from the observer in the car and from the observer at the side of the road it would also, regardless of how fast the car moved. Is there enough time and distance between the car and when the light is switched on to make it look like the light comes on before the car appears? Sorry if this sounds really stupid. I'm totally confused by it, but am hoping there will be a way to describe what actually would appear to happen for the observer at the side of the road that I can understand.

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choran
Carpal Tunnel
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Reged: 12/28/12

Re: Scary relativity new [Re: deSitter]
      #6215379 - 11/25/13 03:07 PM

Heck! Was hoping I could follow.

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Neutrino?
sage
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Reged: 12/14/09

Loc: Wasatch Front
Re: Scary relativity new [Re: deSitter]
      #6215383 - 11/25/13 03:09 PM

Tough crowd.

Quote:


You'll see where this is going eventually. Ask questions now.

-drl



SL(2,C) to SO+(1,3) to PSL(2,C) to M ?


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Rick Woods
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Reged: 01/27/05

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Re: Scary relativity new [Re: Crow Haven]
      #6215398 - 11/25/13 03:14 PM

Maya, it doesn't sound stupid to me; or else, I'm equally stupid. I can't help feeling that there must be a simple analogy that would give people like us at least a rough picture of the situation.

Danny, I appreciate your attempting to explain the whole thing, and I will follow it and try to understand. But I really hope this ends up with something on the order of "think of it like this..."
But I have no questions now, beyond "what does it mean?"


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Rick Woods
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Reged: 01/27/05

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Re: Scary relativity new [Re: brentwood]
      #6215404 - 11/25/13 03:16 PM

Quote:

Danny,aко аз ви е поискал въпрос в България, ще можете да го разбираме без да използвате Google? Не мога да поставя си пост в Google и да се превеждат.?




Brentwood, is the above what you intended to post? Looks like a lot of ASCII to me.


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: Scary relativity new [Re: Rick Woods]
      #6215414 - 11/25/13 03:20 PM

ask questions: OK; now mind you, I'm not being sassy or trying to be stupid; I just have no more familiarity with this math than I do with a language foreign to me.

What is a "square matrix"?

What do
x' = x cos a - y sin a
y' = x sin a + y cos a
mean?

And what is the meaning of these things in relation to the paradox of 1+1=1 at near light speeds?

I mean, I can do the simple equations of t=t(0) X the-square-root of 1 - v^2/c^2; the same for Length and the same for mass when mass(0) is divided by the-square-root of 1 - v^2/c^2. I can do it. I don't understand why these do what they do. I don't understand why, from the perspective of an outside observer, the combined velocity of headlight beam and the gal-in-the-spaceship-already-traveling-at-near-c is still just less than c? I would like to understand why this is the case. And as one of our colleagues here said, it would be nice if there was a real world example that explained this phenomenon; not just gave an analogical similarity like that silly higgs-boson-like-a-snow-field thing.

But, as I am writing, I am afraid I am getting to a really clear question.

Danny, even though this is special relativity and not quantum mechanics, is this an area of relativity which, like quantum mechanics, it cannot be explained with analogies from the ordinary world of fried eggs, baseball, and why the landlord can't get the furnace working?

Otto

Edited by Otto Piechowski (11/25/13 03:30 PM)


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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: Rick Woods]
      #6215431 - 11/25/13 03:28 PM

Quote:

I can't help feeling that there must be a simple analogy that would give people like us at least a rough picture of the situation.





I sure hope so, Rick.

A square matrix? Otto, I picture a square of sedimentary rock embedded with fossilized sea shells... It's bad when you haven't the math training....


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dickbill
scholastic sledgehammer


Reged: 09/30/08

Re: Scary relativity new [Re: Otto Piechowski]
      #6215434 - 11/25/13 03:30 PM

...

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brentwood
Carpal Tunnel
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Reged: 11/04/05

Loc: BC Canada
Re: Scary relativity new [Re: Otto Piechowski]
      #6215438 - 11/25/13 03:31 PM

The page of gibberish I posted above was a google translation of a couple of questions in Bulgarian. It looked all right when I posted it, but it was in Cyrillic script so maybe that's why it came through as just numbers.
The point that I was trying to make is the same as Otto's, why post in a format that is unintelligible to most on here.
That maths makes no sense to me, I can't even get enough of it to ask any questions!


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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: dickbill]
      #6215445 - 11/25/13 03:34 PM

Quote:

...




Problem is, it's pretty sad too!


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choran
Carpal Tunnel
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Reged: 12/28/12

Re: Scary relativity new [Re: Crow Haven]
      #6215452 - 11/25/13 03:36 PM

I'm no expert, but the idea is that -- by postulate --ALL observers will always measure the speed of light as the same, regardless of their state of relative motion. SO, since that number c is FORCED to remain a constant, and since
velocity=distance/time, TIME is forced to change. Two postulates (constancy of light speed, and same rules of physics in all systems moving at constant velocity relative to one another) must be accepted, and the rest follows. If you accept the postulates, you must swallow that time is dilated.
My brief summary based on what I'm sure is an incomplete understanding.

It's all quite counterintuitive and hard (impossible?) to swallow.


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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: choran]
      #6215465 - 11/25/13 03:42 PM

Wow, that isn't intuitive. Has there been any physical experimental evidence or must this remain just a result through math?

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EJN
Carpal Tunnel
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Reged: 11/01/05

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Re: Scary relativity new [Re: Otto Piechowski]
      #6215466 - 11/25/13 03:43 PM

deleted

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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: Scary relativity new [Re: Crow Haven]
      #6215474 - 11/25/13 03:49 PM

If we are correct that the-gal-traveling-in-a-spaceship-at-near-c-velocity (whom hereafter for the sake of not using these silly hyphens, we will call SpaceGalNear-c), SpaceGalNear-c turns on the headlights. It is a dark stormy misty night in the universe. SpaceGalNear-c sees the light from her headlights go out ahead of her into the misty night at the speed of light; i.e. "c".

We, who are observing her, by the side of the road, see SpaceGalNear-c traveling at near-c, and we see the headlights of her spaceship turn on. But, instead of seeing the light of her headlights zooming away in front of her at the speed of light ("c") what we see is the light from the headlights almost statically holding place just in front of her spaceship; maybe just inching ahead a small bit every second.

Am I seeing this correctly? From the outside of observer the light from the headlight would be almost statically standing still in front of the headlight lamp of SpaceGalNear-c?

Otto


EDIT ADDITION BY Otto

This can work, I mean whereas the light beam seems near static to the observer but normal to SpaceGalNear-c; is if SpaceGalNear-c's time has really slowed down as perceived by the outside observer; as in almost down to t= nearly 0; then it would appear to be screeching away at light speed to SpaceGal, but to us it would appear near static.

But why does the time slow down?

Otto

Edited by Otto Piechowski (11/25/13 03:59 PM)


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dickbill
scholastic sledgehammer


Reged: 09/30/08

Re: Scary relativity new [Re: EJN]
      #6215476 - 11/25/13 03:49 PM

Quote:

ALL observers will always measure the speed of light as the same, regardless of their state of relative motion



That in itself is counterintuitive, so why would we start with a counterintuitive postulate?


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: Scary relativity new [Re: EJN]
      #6215487 - 11/25/13 03:53 PM

so a square matrix is a container with 1s and 0s, whose place in the 9 positions within this container is determined by them following that formula related to i's and j's; "delta_ij = {1 if i = j, 0 if i <> j"

What does the "delta_ij" mean?

What does the "and i,j = 1 to 3" mean? I mean, what is the relevance to this statement (and i,j = 1 to 3) to the container with 1s and 0s?

Otto


EDIT ADDITION BY Otto

EJN, thank you for adding,

"If you are familiar with any programming languages,
a square matrix is a two-dimensional array with the
same numbers of rows & columns.

For example in VB,

Dim array(10, 10) as Integer


Clear as mud? "

Unfortunately, I had one class of fortran thirty some years ago. That's it. I really appreciate you trying to help me. But its over my head. Might as well be that Rosetta Stone and I have a baby's understanding of the one language.

I fear it would be a waste of your time to try to get me up to speed.

But I appreciate your trying.

Otto

Edited by Otto Piechowski (11/25/13 04:03 PM)


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choran
Carpal Tunnel
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Reged: 12/28/12

Re: Scary relativity new [Re: Crow Haven]
      #6215494 - 11/25/13 03:56 PM

One can argue endlessly about the results and what they mean, but yes, there are experiments that verify some of SR's predictions. Some that seem to contradict the predictions in Einstein's first paper on SR (Sagnac experiment, Dayton Miller experiments) are explained away due to problems/misunderstanding of the nature of the reference frame under consideration, or experimental error. It will drive you crazy, trust me, to try to understand it all. Most physicists accept SR as true. Argue against it at your own risk.

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EJN
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Reged: 11/01/05

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Re: Scary relativity new [Re: Otto Piechowski]
      #6215508 - 11/25/13 04:02 PM

deleted

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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: Otto Piechowski]
      #6215519 - 11/25/13 04:05 PM

Quote:

From the outside of observer the light from the headlight would be almost statically standing still in front of the headlight lamp of SpaceGalNear-c?






That's what comes to mind, Otto, when I try to visualize it. However, if this can happen, what is going on with light we observe from a star moving through space if we could observe it from "the side of the road" for example? Would that light also look like it was slowed down and not reaching out to infinity? Or what if we used a laser beam?

Sorry I don't know what to do with the square matrix, other than maybe using it for a good beading pattern....


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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: Scary relativity new [Re: EJN]
      #6215526 - 11/25/13 04:06 PM

OK, EJN I got that. I understand.

Danny, EJN, now that I understand (for the moment) what a square matrix is, what does the sin and cosine stuff mean, and why does it relate to the c+c=c headlight paradox?

Otto

EDIT ADDITION

I did use sines and cosines in trig once upon a time; but I taught myself trig; its been forty years; I know they have something to do with angles in a triangle; something about representing the angles numerically, maybe?

Otto

Edited by Otto Piechowski (11/25/13 04:11 PM)


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: Scary relativity new [Re: Crow Haven]
      #6215536 - 11/25/13 04:10 PM

OK, a star moving at near light speed, spits out light.

I'm thinking.

Let's imagine a quasar traveling, because of universe expansion, relative to us at say (being silly), near-c. If its light has reached us, it has also had the same amount of time to go-out sideways from us; so, though it took forever from our perspective to get to us, it has also had forever to go sidewise to our point of view.

Maybe that explains what the quasar's perpendicular-to-us light is so far away from the quasar, but the gal's headlight light isn't; it's a matter of the total time of the scenario.

?

I'm guessing.

Otto


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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: choran]
      #6215539 - 11/25/13 04:11 PM

Thanks for that info on the experiments. Yes, I don't think I'm going to be able to wrap my head around this very well, but it is interesting to try to get a bit of understanding of it.

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choran
Carpal Tunnel
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Reged: 12/28/12

Re: Scary relativity new [Re: Otto Piechowski]
      #6215554 - 11/25/13 04:14 PM

The "C+C paradox" that you refer to is simply a consequence of the first postulate: "The speed of light will always be measured at C, regardless of the state of motion of the light source, or the state of motion of the observer."
You have to accept the postulates and work from there to the consequences.
The matrices are tools used in linear algebra, (they are n x m arrays of numbers which can be manipulated and to which operations can be done). Linear algebra is a course offered a year or so after calculus, or at least that was the case when I was in school.


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The Mighty Mo
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Re: Scary relativity *DELETED* new [Re: Otto Piechowski]
      #6215558 - 11/25/13 04:16 PM

Post deleted by The Mighty Mo

Edited by The Mighty Mo (11/25/13 04:19 PM)


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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
Re: Scary relativity new [Re: Otto Piechowski]
      #6215600 - 11/25/13 04:33 PM

Quote:

OK, a star moving at near light speed, spits out light.

I'm thinking.

Let's imagine a quasar traveling, because of universe expansion, relative to us at say (being silly), near-c. If its light has reached us, it has also had the same amount of time to go-out sideways from us; so, though it took forever from our perspective to get to us, it has also had forever to go sidewise to our point of view.

Maybe that explains what the quasar's perpendicular-to-us light is so far away from the quasar, but the gal's headlight light isn't; it's a matter of the total time of the scenario.

?

I'm guessing.

Otto




"It's a matter of the total time of the scenario." That sounds reasonable...but it's hard to ignore a picture of a light beam just hanging there in slo-motion, it would be fun to see it.


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GregLee1
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Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity new [Re: Otto Piechowski]
      #6215612 - 11/25/13 04:42 PM

Quote:

If its light has reached us, it has also had the same amount of time to go-out sideways from us; so, though it took forever from our perspective to get to us, it has also had forever to go sidewise to our point of view.




I'm having a lot of trouble following much of this discussion, mostly because of a sort of omniscient observer viewpoint that is apparent here. How can I see light that is going out sideways from a distant object? Well, I can't. The light has to reach my eyeball before I can see it.


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brentwood
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Re: Scary relativity new [Re: The Mighty Mo]
      #6215614 - 11/25/13 04:42 PM

I can do thought experiments that show that time does in fact slow down at speeds approaching c. I do this with bouncing balls, light beams and with deference to the giants of the past, railway carriages. For this to work, you have to accept that c is a constant. If I really work at it, and write some of it down, I can also show the contraction in length along the direction of travel and also can see the logic of the mass increase.
The lightbeam will still leave the moving car at c, it is just that to an outside observer, the car is following closely behind.
Can you respond to this Danny without using any maths? what does the outside observer see.


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deSitter
Still in Old School


Reged: 12/09/04

Re: Scary relativity new [Re: brentwood]
      #6215647 - 11/25/13 04:58 PM

Everybody STOP thinking for a while I'll do the thinking! Just pay attention!

Believe me, this will be worth it.

-drl


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choran
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Re: Scary relativity new [Re: deSitter]
      #6215666 - 11/25/13 05:03 PM

"Everybody STOP thinking for a while."

FINALLY, something I can easily do!!

Edited by choran (11/25/13 05:04 PM)


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deSitter
Still in Old School


Reged: 12/09/04

Re: Scary relativity new [Re: choran]
      #6215686 - 11/25/13 05:12 PM

Actually, DO think about this thought experiment...

The Moon moves over the Sun. It exactly eclipses it, so that totally is a mere blink of the eye - but for that fraction of a millisecond, the Sun is covered and no light gets to Earth from its photosphere. And, this is a perfect Moon, with no bumps and a perfect sphere, likewise a perfect Sun, with no tidal bulging.

So now say the Moon acquires a large tangential speed to Earth. Naively we expect the Lorentz contraction in the direction of its motion to cause the eclipse to not happen...

That's the problem we're solving. In it are ALL the other problems of how moving things look.

-drl


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Re: Scary relativity new [Re: deSitter]
      #6215700 - 11/25/13 05:15 PM

I think I follow. The moon is moving at a near light speed so it "shrinks" in the direction of movement (perpendicular to the line connecting earth to sun). Since it shrinks, it should not cover the sun.

?


Otto


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Crow Haven
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Re: Scary relativity new [Re: Otto Piechowski]
      #6215711 - 11/25/13 05:23 PM

Otto, so does that mean that the light from the Sun would get to the observer before the Moon appears to?

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Re: Scary relativity new [Re: Crow Haven]
      #6215728 - 11/25/13 05:35 PM

Maya,

Let's let Danny drive this description. I was just trying to understand what he meant by tangential and why he said, according to what we know about SR, that the moon should never cover the sun. (Oh, in case you are wondering about that "shrink" thing, according to the popularized version of SR I learned on my own, to an outside observer looking at an object moving perpendicular (at right angle) to the observer, the length of an object moving at a near light speed, "shrinks" in the direction of the movement. According to the formula (if I remember it correctly) if an object at "rest" is 10 meters long, once it starts moving at a constant 90% the speed of light, to an outside observer it will only appear 4.36 meters long.)

Otto


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Crow Haven
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Re: Scary relativity new [Re: Otto Piechowski]
      #6215740 - 11/25/13 05:41 PM

Thanks for the explanation, Otto.

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Re: Scary relativity new [Re: deSitter]
      #6215773 - 11/25/13 06:04 PM

Quote:

Actually, DO think about this thought experiment...

The Moon moves over the Sun. It exactly eclipses it, so that totally is a mere blink of the eye - but for that fraction of a millisecond, the Sun is covered and no light gets to Earth from its photosphere. And, this is a perfect Moon, with no bumps and a perfect sphere, likewise a perfect Sun, with no tidal bulging.

So now say the Moon acquires a large tangential speed to Earth. Naively we expect the Lorentz contraction in the direction of its motion to cause the eclipse to not happen...

That's the problem we're solving. In it are ALL the other problems of how moving things look.

-drl




Now come on - we've all confessed to being ignoramuses; have some charity!
What's the Lorentz Contraction and why would we expect that? This isn't going to work unless we understand the steps leading up to the solution.


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Re: Scary relativity new [Re: deSitter]
      #6215788 - 11/25/13 06:14 PM

deleted

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Re: Scary relativity new [Re: Rick Woods]
      #6215792 - 11/25/13 06:16 PM

total confusion.

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Re: Scary relativity new [Re: dickbill]
      #6215806 - 11/25/13 06:26 PM

Quote:

Quote:

ALL observers will always measure the speed of light as the same, regardless of their state of relative motion



That in itself is counterintuitive, so why would we start with a counterintuitive postulate?




Counterintuitive doesn't bother me. But, is this what we're saying?

At rest: c = 186,000 mph relative to that (at rest) condition.

At speed (c - 1 fpm), it still goes 186,000 mph; but that's taking SpaceGirl's speed as the new "at rest" and measuring from there. At that speed, time and space are warped and compressed, and the (new) 186,000 miles are squeezed into whatever portion of the (old) one foot light can travel in one second (as measured at the near-c speed).

Would a weak analogy be one of those pictures where, when you look at it straight on, it's just a row of straight vertical lines; but when you look at it from the lower edge of the paper, the undistorted view appears?

I suspect that to make the analogy I'm looking for, you have to mix the two states, which isn't valid somehow. Like, translating the old 1-foot measure into the at-speed condition.


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Re: Scary relativity new [Re: PeterR280]
      #6215809 - 11/25/13 06:27 PM

On the positive side if you learn tensors you ill be half way there to general relativity.

Why would you say that people would expect the Moon would to shrink due to the Lorentz contraction?


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Re: Scary relativity new [Re: EJN]
      #6215813 - 11/25/13 06:28 PM

Quote:


Quote:

What's the Lorentz Contraction




L = L0 * sqrt(1 - (v^2/c^2))




What does it describe?
I really am trying to get my squishy little brain around this somehow.


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Re: Scary relativity new [Re: Rick Woods]
      #6215827 - 11/25/13 06:34 PM

Re: sun/moon example, I'm betting no Lorentz "length" transformation (shortening in direction of movement), but instead a "rotation" so sphere stays a sphere. Get your popcorn, this is gonna get sticky!

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Re: Scary relativity new [Re: choran]
      #6215840 - 11/25/13 06:38 PM

First of all Special Relativity deals with inertial reference frames without acceleration or gravity. Why introduce something like an orbit if you are explaining Special Relativity? It makes it even more confusing.

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Re: Scary relativity new [Re: PeterR280]
      #6215849 - 11/25/13 06:41 PM

By the way how many years did it take Einstein to get there from Special Relativity?

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choran
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Re: Scary relativity new [Re: PeterR280]
      #6215857 - 11/25/13 06:47 PM

1905 (SR) to about 1915 (GR) I think.

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Re: Scary relativity new [Re: choran]
      #6215858 - 11/25/13 06:48 PM

And now for a musical interlude from Grace Slick & Jefferson Airplane - White Rabbit

www.youtube.com/watch?v=sxKAprtLh7M


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Re: Scary relativity new [Re: EJN]
      #6215878 - 11/25/13 06:59 PM

Yup. Rabbit Hole dead ahead!! I think when Danny gets back we're all in for it. Teacher leaves the classroom and everybody acts up. LOL

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Neutrino?
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Re: Scary relativity new [Re: PeterR280]
      #6215880 - 11/25/13 07:00 PM

Quote:

First of all Special Relativity deals with inertial reference frames without acceleration or gravity. Why introduce something like an orbit if you are explaining Special Relativity? It makes it even more confusing.




We aren't dealing with gravity, acceleration or orbits.

The set up is simple: As seen from the Earth, the Moon perfectly blocks the Sun (assuming both are circular) during an eclipse. Now, imagine the Moon now has some respectable fraction of c velocity with respect to our Earth frame. You mentioned Lorentz transformations are easy before. Applying these transformations, from our Earth, we expect there to be some contraction of the diameter of the Moon in the direction of its motion. Thus, the Moon is no longer circular.

The question is...do you still "see" an eclipse?

Edited by Neutrino? (11/25/13 07:04 PM)


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Crow Haven
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Re: Scary relativity new [Re: PeterR280]
      #6215884 - 11/25/13 07:03 PM

just confused...
Quote:

the Moon is no longer circular.

The question is...do you still "see" an eclipse?






...if it only changes size in one direction wouldn't it still be possible to be large enough to briefly eclipse the Sun????


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Re: Scary relativity new [Re: Crow Haven]
      #6215891 - 11/25/13 07:11 PM

Unbelievable! Someone asks what the Lorentz contractions are and someone answers "L = L0 * sqrt(1 - (v^2/c^2))"
I had to think what 'tangential' meant. Oh it is so difficult flapping around like a chicken when we are trying to soar like eagles! (Of course one could say that the Eagles should come down into the barnyard every now & then!)


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Re: Scary relativity new [Re: deSitter]
      #6215896 - 11/25/13 07:13 PM

I'm waiting for Danny to explain to me/us why the moon would not, not eclipse the sun in this scenario.

Danny…just ignore all the 2nd through tenth row students. I'm in the front row. I left the red apple on your desk. I'm all ears…err…eyes.

Otto


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Neutrino?
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Re: Scary relativity new [Re: choran]
      #6215900 - 11/25/13 07:13 PM

Quote:

Yup. Rabbit Hole dead ahead!! I think when Danny gets back we're all in for it. Teacher leaves the classroom and everybody acts up. LOL




I wouldn't call it a rabbit hole. It really is just a matter of when speaking of observation that we must carefully define what we mean by "see", or using "moving clocks run slow".

These guys are used in analogies without care to define what they really mean; both have stipulations that can't be ignored. Not defining them properly propagates into people saying "time slows down" and such.

Edited by Neutrino? (11/25/13 07:16 PM)


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Re: Scary relativity new [Re: Crow Haven]
      #6215908 - 11/25/13 07:16 PM

here is a similar problem you have a rod that is 10 feet long and it is traveling over a hole the is 9.9 feet long. it has a strong downpull. The rod will contract if it is moving very fast. Will it fall through the hole?

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Re: Scary relativity new [Re: Otto Piechowski]
      #6215918 - 11/25/13 07:20 PM

deleted

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Re: Scary relativity new [Re: EJN]
      #6215942 - 11/25/13 07:28 PM

Thank you for that EJN, but I don't have the correct plug-ins and do not wish to install any on this machine. Can you explain it to me in words? Otto

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Re: Scary relativity new [Re: brentwood]
      #6215949 - 11/25/13 07:30 PM

Quote:

Of course one could say that the Eagles should come down into the barnyard every now & then!



Well, the Eagles came down to Allstate Arena last month and put on a really fine concert.
Welcome to the Hotel California.


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Re: Scary relativity new [Re: EJN]
      #6215955 - 11/25/13 07:33 PM

Ok, got that, the contraction is real but we do not see it so there is still an eclipse. Thanks, Diagrams good, maths & equations not!

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Re: Scary relativity new [Re: EJN]
      #6215961 - 11/25/13 07:36 PM

With this thread, I feel like I'm in Hotel California! I just hope they'll let me leave!

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Re: Scary relativity new [Re: brentwood]
      #6215988 - 11/25/13 07:52 PM

Brentwood, I don't have the plug in to see the video. If you would, in words, why don't we (the outside observer) not see the contraction?

Otto


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PeterR280
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Re: Scary relativity new [Re: Otto Piechowski]
      #6215994 - 11/25/13 07:59 PM

you have a very long perfectly stiff rod that reaches Mars. You tap out morse code before the light signal gets there.

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deSitter
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Re: Scary relativity new [Re: Otto Piechowski]
      #6215998 - 11/25/13 08:04 PM

Quote:

I think I follow. The moon is moving at a near light speed so it "shrinks" in the direction of movement (perpendicular to the line connecting earth to sun). Since it shrinks, it should not cover the sun.

?


Otto




Yes, the eclipse happens, regardless of the state of motion of the Moon. This does not mean the Lorentz contraction is false - it means that the world is not 3D + time, it is 4D, and that new geometry has visible effects. That's what I am going to try to get across. Yes it is difficult, but as Kennedy said, we choose to go to the Moon, not because it is easy, but because it is hard!

-drl


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Re: Scary relativity new [Re: Otto Piechowski]
      #6216003 - 11/25/13 08:10 PM

deleted

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deSitter
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Re: Scary relativity new [Re: EJN]
      #6216009 - 11/25/13 08:15 PM

I hate to get off on a tangent but the length contraction is most definitely visible - it's just not a contraction in the naive sense of 3D space. The invariants live in 4D space, not 3D, and all direct reference to 3D space alone - which means all diagrams such as this - are misleading (a euphemism for wrong).

-drl


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Re: Scary relativity new [Re: EJN]
      #6216017 - 11/25/13 08:17 PM

The screen capture above shows it well. The previous shots are of the disk as it approaches us & light waves coming off various segments. It kind of made sense, but I'm still waiting to see how this ties in with those bloody headlights!
But I will be patient.


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deSitter
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Re: Scary relativity new [Re: deSitter]
      #6216027 - 11/25/13 08:24 PM

Also - VERY important - the Moon is not a disc, it is a sphere - were it a disc, the eclipse would NOT happen, and in fact, the faster that disc went, the more elliptical would become its outline. This is precisely the issue with graphical representation of relativity - the effects take place in space that is essentially 4D, and they cannot be reduced to plane descriptions - any more than any one flat map of the spherical world can be accurate in all ways.

-drl


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Re: Scary relativity new [Re: deSitter]
      #6216039 - 11/25/13 08:33 PM

I believe I understand. Thank you guys.

Lesson #2.

Oh…what did the box matrix and trig have to do with this?

Otto


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deSitter
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Re: Scary relativity new [Re: Otto Piechowski]
      #6216083 - 11/25/13 08:49 PM

We just got started. There is a long hill to climb.

-drl


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PeterR280
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Re: Scary relativity new [Re: Otto Piechowski]
      #6216084 - 11/25/13 08:50 PM

Mass and energy equivalence is real too. If an object moved fast enough would it become a black hole?

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Re: Scary relativity new [Re: PeterR280]
      #6216135 - 11/25/13 09:17 PM

Also with a disc going by the sun at relativistic speed, would it not appear that the disc is turning toward the direction of motion and block the sunlight across a perpendicular wave front? in other words, it would appear turned enough to catch the front part of the wave front.

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Re: Scary relativity new [Re: PeterR280]
      #6216138 - 11/25/13 09:20 PM

if you were riding on the disc, you would see the earth as being foreshortened and you would see your disc blocking the earth.

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deSitter
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Re: Scary relativity new [Re: PeterR280]
      #6216219 - 11/25/13 10:15 PM

Here's a poem by Schiller (pardon the impossible translation)

Threefold is the mass of space;
Restless goes it, without ceasing,
Striving lengths, into the distance,
Ever widening, all increasing,
Bottomless, sunk to the depths.

An image now to you is given:
Restless go you, always striving,
Never standing still,
If you would see the thing completed,
Unfold yourself into the breadth,
If you would fain create a world,
Then you must climb into the depth,
If you would be shown the essence.

Only persistence can lead ahead,
Only depth can lead to clarity,
And in the abyss, there dwells verity.

-drl


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Re: Scary relativity new [Re: deSitter]
      #6216253 - 11/25/13 10:28 PM

The increased mass of the moon would lens the Sun's light around it, effective magnifying the size of the Sun and preventing the eclipse. Maybe.

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deSitter
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Re: Scary relativity new [Re: GregLee1]
      #6216257 - 11/25/13 10:31 PM

Quote:

The increased mass of the moon would lens the Sun's light around it, effective magnifying the size of the Sun and preventing the eclipse. Maybe.




I would give you 3 points for creativity here. But it would be a 10 point problem.

-drl


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PeterR280
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Re: Scary relativity new [Re: deSitter]
      #6216286 - 11/25/13 10:54 PM

the important concept for the moon problem is the relative nature of simultaneity.

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Re: Scary relativity new [Re: deSitter]
      #6216313 - 11/25/13 11:21 PM

Quote:

We just got started. There is a long hill to climb.

-drl




We haven't even done that, and this thread is into its 5th page.
I don't mean to sound impatient; but can we get ON with it?


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scottk
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Re: Scary relativity new [Re: deSitter]
      #6216319 - 11/25/13 11:24 PM

Has anyone said 42?

To the original poster: is it 42?

It's 42 isn't it.


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Neutrino?
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Re: Scary relativity new [Re: deSitter]
      #6216389 - 11/26/13 12:30 AM

Quote:

Also - VERY important - the Moon is not a disc, it is a sphere - were it a disc, the eclipse would NOT happen, and in fact, the faster that disc went, the more elliptical would become its outline. This is precisely the issue with graphical representation of relativity - the effects take place in space that is essentially 4D, and they cannot be reduced to plane descriptions - any more than any one flat map of the spherical world can be accurate in all ways.

-drl




Sorry: Yes, I meant spherical. I was thinking spheres always present as a disc even at large velocities/subtended angle... that was why I was confusing circular in there.


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PeterR280
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Re: Scary relativity new [Re: Neutrino?]
      #6216430 - 11/26/13 01:35 AM

Actually if the moon were a flat disc and you were sitting on it, you would see it casting a nice round shadow. You would see a flattened earth passing through the round shadow so the eclipse should last longer than expected.

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Re: Scary relativity new [Re: deSitter]
      #6216656 - 11/26/13 08:40 AM

For being nearly two centuries before GR and SR, that poem of Schiller's is eerily prophetic.

Otto


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Re: Scary relativity new [Re: Rick Woods]
      #6216937 - 11/26/13 11:02 AM

Quote:

Quote:

We just got started. There is a long hill to climb.

-drl




We haven't even done that, and this thread is into its 5th page.
I don't mean to sound impatient; but can we get ON with it?




I saw that coming yesterday, when Danny wouldn't answer our questions, and still isn't. That's why I bailed on actively participating in this...whatever it is... It could've been simply and easily answered in a couple posts several days ago in the original "Two Mirrors" thread.


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Re: Scary relativity new [Re: The Mighty Mo]
      #6217074 - 11/26/13 12:11 PM

Well I have some questions regarding the first post.

Let's say we have a 2 dimensional flat universe with a reversible Time, basically a plane where any transformation can be done in any time direction. Then we can apply the matrix transformation that drl gave us, for example the rotation. And so we got this matrix of sin and cosines and no Time member, because Time is not a part in the rotation transformation. And of course we got an important characteristic of this world: the distance between 2 points, a square root of x^2+y^2, and again no Time value because Time has nothing to do with the distance between points and the geometry of this plane.
Now my questions are:
1) Are you using the Transformation to deduce the geometry of this world? or said otherwise, what is the rational to start with a Transformation here?
why choosing a Rotation? why not a Translation or Magnification?

2)In a 3-d world, the terms are basically the same with a distance in (x^2+y^2+z^2)^1/2, the addition of Time wouldn't change that.
So why introducing Imaginary numbers, is it only to ease the calculation?
And why is a term in Time suddenly appearing in the equation? I understand it is because of Light and its invariant characteristics, but this world also contains other objects whose speed is relative to other objects. So why is this world's geometry defined by the properties of Light and not, say, the properties of a canon ball?


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deSitter
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Re: Scary relativity new [Re: The Mighty Mo]
      #6217093 - 11/26/13 12:21 PM

Well since no one seems to want to follow the math, I'll just describe what happens. Hopefully I can do that OK.

If you made an even coordinate grid on the Moon, as on a globe, then the state of motion of the Moon would finally cause great distortion of this grid as speed increased. The surface features would seem to crawl around, be more densely packed here, less so there - but the apparent shape taken by the visible globe of the spherical Moon, would always be circular. What does such a statement really mean? And not just the Moon of course - any moving sphere, regardless of its state of motion, appears spherical, but it does not appear fixed - the distribution of its surface features changes. (The spectrum and intensity of the light are also affected, but that can be ignored for now.)

In the language of geometric optics, what we see is defined by a pencil of light rays drawn backward from our pupil to the physical objects that emitted (reflected, scattered...) the light. So the real question is not directly about lengths and clocks - it is about the nature of these pencils of light, and how they are affected by the state of motion. This is a very different question than making assumptions about the "actual state" of something.

That's the question to be answered. To do so, it is necessary to get some intuition for the way geometry itself is involved. This is the most amazing fact of all science - that physical geometry itself has changed for the first time since Euclid.

-drl


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Re: Scary relativity new [Re: deSitter]
      #6217374 - 11/26/13 02:53 PM

Danny, I don't think it's a matter of folks not wanting to follow the math, it is the inability of most of us to do so. It's been 40 years since my linear algebra and calculus days, and longer since trig. In the meantime, anybody who wants to see the math in the original 1905 paper on SR can go here.
Maybe the ones that can handle the math than then ask you questions.
Good luck!

http://www.fourmilab.ch/etexts/einstein/specrel/www/
][/url]

Edited by choran (11/26/13 02:55 PM)


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Re: Scary relativity new [Re: deSitter]
      #6217376 - 11/26/13 02:54 PM

I do appreciate all the efforts here to try & get some of these concepts through to us thickies. The maths means nothing to me, I didnt even get the poem, but I did get Danny's post above about pencils of light.
I can appreciate how we have to be patient in being explained properly. I have a similar frustration, but the other way around with trying to explain the remote for the TV/PVR/Soundsystem/Cable Box. I want to explain how the whole thing works, so it is understood so you don't have to remember it all but I just get asked not to "try and explain all that, just tell me what I have to press & in what order and I'll write it down".


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Re: Scary relativity new [Re: brentwood]
      #6217400 - 11/26/13 03:09 PM

Brentwood, I believe that the heart of SR are the two postulates I posted earlier in the thread. It is the fact that the postulates force light velocity to be a constant for ALL observers that requires that time now become "dilated."

Try this rather lame, and probably wrong,example: You have pitcher throwing to a catcher. This pitcher always throws 100mph fastballs. Now, have the pitcher run at 10mph toward the catcher and throw. One would say "OK, the ball is now moving 110 mph. Or, have the catcher run toward the pitcher at 10mph. Again, most would say, "OK, the catcher will measure the ball incoming at 110 mph." SR says NO, by DEFINITION the catcher and pitcher will always measure the ball going 100mph. OK, so something's got to give, right? Since Velocity=distance/time, and since the velocity of the ball is FORCED to be 100mph, TIME is forced to become observer dependent and malleable. Now, please, everybody, don't jump on me. I'm not trying to be complete or even wholly accurate, just trying to give a sense of why SR REQUIRES time dilation as a consequence of REQUIRING that all observers measure light at a fixed C regardless of their velocity relative to the source, and regardless of the sources's velocity relative to observer. Again, once you accept the two postulates of SR, you are stuck with all the rest. The math getting to that point is tough for most of us.


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Re: Scary relativity new [Re: choran]
      #6217410 - 11/26/13 03:15 PM

Well, that's what I thought was going on when folk here started to talk about the observation being a 4D phenomena for all involved and not a 3D+time.

Otto


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Re: Scary relativity new [Re: Otto Piechowski]
      #6217455 - 11/26/13 03:38 PM

A mathematician by the name of Minkowski, who used to be Einstein's math teacher, came up with a way to represent the mathematics of Special Relativity in geometrical form by formulating a 4 dimensional geometry of spacetime. The problems of SR could be solved geometrically. Einstein viewed this as a mathematical tool but later realized that the 4D spacetime geometry was the way to solve the riddle of General Relativity. The math that Danny was showing is the ultimate way to understand Relativity. If you understand what Danny is showing, you will be on the way to understanding General Relativity but it's not easy if you don't have a grasp of the fundamentals in trigonometry, linear algebra, etc.. You have to know what sine and cosine are, you have to understand complex numbers, you have to be able to manipulate matrices.

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Re: Scary relativity new [Re: Otto Piechowski]
      #6217462 - 11/26/13 03:41 PM

The only point I was trying to get across in the earlier post is that if you, by postulate, force one thing to become a constant across all reference frames, while at the same time adding a relativity postulate (no absolute motion, all physics rules apply in reference frames in relative motion to one another) something's got to give--time. The flip side is that length must also give if length is measures by "clocks" depending on light signals to synchronize them. To get further into it, have pitcher and catcher stationary, and a guy driving by in a car doing the measurement of pitch speed. If you FORCE him to conclude that the pitch is moving at 100mph, regardless of HIS motion relative to the pitch, you can see what's going to happen to time. IT becomes relative, because velocity of ball light) is forced to stay CONSTANT.

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Re: Scary relativity new [Re: choran]
      #6217504 - 11/26/13 03:54 PM

Does this all work out the same if there are more than 4 dimensions to spacetime?

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Re: Scary relativity new [Re: Crow Haven]
      #6217512 - 11/26/13 03:58 PM

WAY beyond my pay grade! Danny and some of the others will have to tackle that one.

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Re: Scary relativity new [Re: choran]
      #6217515 - 11/26/13 03:58 PM

Choran, I do get that. I can see how there is a difference in time to different observers. As I said earlier in the thread, for many years I have used the example of bouncing balls, lightbeams and railway carriages to illustrate this.
As for the car putting on its headlights I still think to the driver, the headlights go on and the light appears to light up the way ahead as normal.
You could separate the car from the light by having a series of mirrors at right angles laid out along the path of the light and they would reflect the light back at you as the light beam passes down the line. If you say had a string of mirrors 3 million Ks long, and you were an observer many ks away, would you not see these lights light up one after another over a 10 second period? If the car was moving in the same direction, would you not see the car as well but at a slightly lower speed?


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Re: Scary relativity new [Re: Crow Haven]
      #6217526 - 11/26/13 04:05 PM

deleted

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Re: Scary relativity new [Re: EJN]
      #6217537 - 11/26/13 04:12 PM

There were some attempts at adding a fifth dimension to explain the electric and magnetic fields along the lines of what Einstein did for gravity. These were classical ideas. Of course string theory came long as a quantum theory that has many more dimensions.

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Re: Scary relativity new [Re: deSitter]
      #6217557 - 11/26/13 04:21 PM

Thank you Danny, I appreciate the reply. Your explanation is exactly how I remembered it. Yes, like the others, my trouble was that I don't understand the math. My last advanced Algebra and Calculus courses, and my last formal Relativistic Physics course, was back in 1977. And I haven't had to use any of it since. Math isn't my strong suit, but I can conceptualize and see it in my head easy enough. That's why I like summarized explanations, I fill in the blanks in my mind.

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Re: Scary relativity new [Re: brentwood]
      #6217560 - 11/26/13 04:25 PM

I'm not quite sure I understand the physical setup. SR would indeed say that the driver would measure the light from his own headlights at c. Observers in constant relative motion to the car would ALSO measure the headlight beam as moving at c. That's as far as I can go at the moment. If the answer is what would an observer in relative motion to the car measure the CAR'S speed, then you have to drag out the space-time diagrams or apply the time dilation formula.

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Re: Scary relativity new [Re: choran]
      #6217639 - 11/26/13 05:06 PM

Thanks for the info on extra dimensions everyone.

Regarding the original car and headlight problem, at least you can picture it... I'm stuck with a picture of a car, observed from the roadside, moving with the head light beam extending just a short distance in front as both car and beam move ahead (will both the car and beam of light continue to travel like this and the car never overtake the beam of light and end up ahead of it?), and if there were another car ahead of that first car could they, looking back in their mirror, not see the light or the car behind them in the dark... Wow, I haven't got this yet...

Back to chocolate chip dough ball deformation on the baking tin of life!


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Re: Scary relativity new [Re: Crow Haven]
      #6217657 - 11/26/13 05:15 PM

To a guy on the road it will not look like the headlight beam is just a short distance ahead--the beam will move away from the car at the speed of light, a constant, regardless of the speed of the car. Remember postulate one.
You cannot chase and catch up with a light beam--it will always move away from you at the speed c, a constant. That is one of the two underlying postulates of SR. According to the theory you must accept that.
That's why it's so hard to swallow for most--totally counterintuitive. Whether you are racing toward the beam, or racing away from it, its velocity relative to you is always unerringly c, a constant. That lead inexorably to the idea that time dilates, or changes, depending on reference frame.

Edited by choran (11/26/13 05:19 PM)


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Re: Scary relativity new [Re: deSitter]
      #6217663 - 11/26/13 05:19 PM

I'm going to take a guess here and say that Danny is old enough to collect social security. Being that's the case, sometimes you young whippersnappers don't understand the motivations and inclinations of us who are older; especially when it comes to something like not being fast enough, or seeming to beat around the bush, or seeming to obfuscate. So those of you can understand the psychology of someone like our friend Danny, and others in this forum, of his age; I offer for illustrative purposes only the following joke:

An elderly man was applying for a job. The young interviewer began the interview:

Interviewer: "Sir, what do you consider your greatest weakness to be?"

Elderly Person: "Honesty."

Interviewer: "I don't think honesty is a weakness."

Elderly Person "I don't give a *BLEEP* what you think." [If the key word in the elderly man's reply is censored out by our algorithmic censor; understand, the word censored does not rhyme with Frack, but it means the same.]


Personally, I like the speed this is going. It is just about perfect for me.

Otto


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Re: Scary relativity new [Re: Otto Piechowski]
      #6217669 - 11/26/13 05:23 PM

Danny's the best! We're just chewing the fat until he returns. This whippersnapper was born in the early 50s. Most of the snap is gone.

Edited by choran (11/26/13 05:24 PM)


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Crow Haven
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Re: Scary relativity new [Re: choran]
      #6217674 - 11/26/13 05:25 PM

Thanks! That's helpful, at least I can observe/see something, even if seeing isn't always knowing what's really going on.

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Re: Scary relativity new [Re: Otto Piechowski]
      #6217683 - 11/26/13 05:31 PM



Quote:

Personally, I like the speed this is going. It is just about perfect for me.

Otto




Fine for me as well, I'm in no hurry!


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Re: Scary relativity new [Re: Otto Piechowski]
      #6217709 - 11/26/13 05:41 PM

Quote:

I'm going to take a guess here and say that Danny is old enough to collect social security.




Not yet

-drl


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Re: Scary relativity new [Re: deSitter]
      #6217737 - 11/26/13 05:59 PM

deleted

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Re: Scary relativity new [Re: choran]
      #6217906 - 11/26/13 07:14 PM

One clarification to what you said. The principle of special relativity states that the laws of physics are the same in all inertial reference frames, including Maxwell's equations. Einstein explicitly added that c is a constant based on Maxwell's equations and the Michelson Morley experiments. So if you are in an inertial reference frame, it means you are not accelerating and there are no gravitational fields.

There are no preferred inertial reference frames. It does not make sense to say you are zooming through space. There is no way of determining that you are moving through space. You can only measure your speed relative to something else. So from your perspective, light will always travel at c. If Joe is traveling at a very fast speed relative to you and he emits light from a headlight, it will be traveling at c. You will however, also see Joe moving. He may be moving very close to the speed of light so he will look like he is chasing the light beam.

Joe is also in an inertial reference frame so for him the beam of light moves away from him at c. The transformation equations allow you to make calculations in reference frames that are moving relative to you. Minkowski space lets you make the transformation as geometric calculations in spacetime.


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Re: Scary relativity new [Re: EJN]
      #6217912 - 11/26/13 07:19 PM

"To a guy on the road it will not look like the headlight beam is just a short distance ahead--the beam will move away from the car at the speed of light, a constant, regardless of the speed of the car. Remember postulate one."
If by the guy on the road, you mean someone other than the driver, how can he see the light leaving the car at c, when the car itself is almost at c. To the driver, yes, but not to an observer. If the light is 'seen' receding from the car at c and the car is traveling at almost c, then the light is seen to be traveling at almost 2c, which as we know is impossible. To the very distant observer the light is seen traveling at c, and the car falling slowly behind.
And yet Danny said this was wrong?


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Re: Scary relativity new [Re: brentwood]
      #6217978 - 11/26/13 07:57 PM

I am going to make this messy with a problem of relativity around which I could not get my mind.

Supposedly, there were two cesium atomic clocks which were perfectly aligned. One flew into orbit around the earth on the Skylab; the other stayed on earth. When the one which had been in orbit came back to earth and the two clocks were compared, the clock that had been on Skylab was a little bit behind the clock which remained on earth. This accorded perfectly with the formula T = T0 * sqrt(1 - (v^2/c^2)).

This is often used to say if a future human travels to say, a planet circling a star 10 light years away at a constant speed of 90% c, and then, after a very brief stay on that planet, returns to earth at 90% c, the traveler would have aged around 9 years but everyone he knew on earth around 20 years.

I don't get it. If as said immediately by PeterR280 "There are no preferred inertial reference frames" why would it not be the exact opposite as well; the space traveler saw the earth moving away from her at 90% c, and then "returned" to her at 90% c, all taking about 20 years; why is it not the case the traveler would have aged 20 years and the earthlings, only around 9 years.

Obviously, I don't understand what is meant by non-preferred frames of reference or even frames of references. But I don't understand this and would appreciate someone clearing it up for me.

Otto


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Re: Scary relativity new [Re: Otto Piechowski]
      #6217993 - 11/26/13 08:06 PM

Otto, I have thought this myself and all my attempts to clarify it have been unsuccessful. I didn't want to bring it up until this pesky question of the headlights has been sorted.

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Re: Scary relativity new [Re: Otto Piechowski]
      #6217997 - 11/26/13 08:08 PM

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Re: Scary relativity new [Re: EJN]
      #6218007 - 11/26/13 08:14 PM

The twin paradox is a tough one to get your arms around. If you do a search on the twin paradox there are multiple explanations. You can even get rid of the acceleration issue by assuming instant jump from one reference frame to the other to get to the solution.

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Re: Scary relativity new [Re: brentwood]
      #6218032 - 11/26/13 08:26 PM

See the two definitions in SR: 1) Light will be measured at c by all observers, regardless of the motion of source or observer. That's just something you must accept by definition. See page one of the Einstein paper I linked.
No one, regardless of their speed, or the speed of the source of light that they observe, can ever measure the speed of light as other than c. It is thus by definition. If you want to swallow SR, you have to swallow this.
No sense in arguing -- it is a postulate, axiom, or whatever you want to call it. Change that and no SR.


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Re: Scary relativity new [Re: brentwood]
      #6218047 - 11/26/13 08:32 PM

Re: Danny said it is wrong, I believe it is wrong. I've tried to explain, that by keeping c constant, the calculation of relative velocities also changes.
To get the amount of change, you have to use the formulas Danny was beginning to develop. You have to do a relativistic transformation formula in the nature of X=1/square root of 1-v2/c2. Sorry, can't type exponents and radicals on my computer.


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Re: Scary relativity new [Re: Otto Piechowski]
      #6218057 - 11/26/13 08:36 PM

Otto, I think you have inadvertently misstated the Cesium flying clock experiment. They used two clocks, flew them around the earth in two planes, one east, one west. Results: They both differed from the earth boundreference clock, but not by the same amount. Only worked when the reference clock was a hypothetical clock at the earth's center. This is at odds with the literal prediction of SR, so they backed off and said it was in incorrect reference frame, and had to resort to GR.

Edited by choran (11/26/13 08:42 PM)


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Re: Scary relativity new [Re: choran]
      #6218058 - 11/26/13 08:37 PM

Relative velocities are relative velocities.

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Re: Scary relativity new [Re: PeterR280]
      #6218067 - 11/26/13 08:39 PM

Re: twins. Einstein finally felt the need to weigh in on the twin paradox that had arisen under SR. He framed his paper as a debate between relativist and skeptic, as I recall. He wiggled about a bit and admitted that SR cannot solve the problem, but ran over to GR with gravitation being the reason for the asymmetry. That's all I can say. You can dig up the short paper and see what he had to say.

Edited by choran (11/26/13 08:58 PM)


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deSitter
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Re: Scary relativity new [Re: choran]
      #6218086 - 11/26/13 08:50 PM

(sigh) It's really a mess the way relativity is taught.

I would ignore everything you've read in the books about trying to make intuitive pictures of what is going on. There ARE pictures that are intuitive, but not the ones that circulate - the "pole in barn" file. You can ignore all that. Blank your mind.

As for acceleration accounting for the twin paradox - it's not really relevant. I have no idea why this idea circulates. The fact is, you cannot make the whole universe move in such a way as to bring a star to you while the rest of it acts just as if you were moving through it, and it had stayed put. But it doesn't matter anyway. The point is that the rules of relativity as we are discussing them are local, and they apply in those situations that really happen. We don't need to consider hypothetical cases that cannot obtain without extra input - in the case of going to the star, the source of the miraculous conspiracy. There is ample proof of relativity in the lab, that no requirement forces us to stretch it across the universe without further thought.

Again - the key point is the pencil of light rays that intersect where you are. That's what has to be understood. What we have is a new idea of connectivity regarding time - a given place is not at once connected to every other place.

-drl


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Re: Scary relativity new [Re: deSitter]
      #6218107 - 11/26/13 09:00 PM

Danny, my memory did not serve me. Just consulted the "Dialog" paper by Einstein and you are correct--he did not duck over to GR for acceleration, but explained the non-symmetry in the supposed twin paradox in terms of gravity. I've corrected my above post to reflect this.

Edited by choran (11/26/13 09:00 PM)


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deSitter
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Re: Scary relativity new [Re: choran]
      #6218120 - 11/26/13 09:07 PM

What I would also like to get across, is that ordinary Euclidean geometry is every bit as strange in its own way as is that of relativity - because it has the idea of infinity. That is the key thing that makes 4D geometry understandable intuitively, once you have re-thought 3D geometry in the same way. (And remember most of all - the 4D geometry is not the same as just adding on another leg, another "th" to width, depth, and breadth.)

-drl


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Re: Scary relativity new [Re: deSitter]
      #6218150 - 11/26/13 09:23 PM

Danny,

I don't understand the pencil thing you explained and which others said they understood. I want to understand it. Can you do it again? Please?

Otto

And by the way, when you explained the time travel delay thing, I almost shouted out; damn, I knew it. I knew it was a local practical thing about one part is moving real damn fast and all the rest are comparatively stationary.


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Re: Scary relativity new [Re: choran]
      #6218153 - 11/26/13 09:24 PM

Choran, I think we're at cross purposes here. I completely accept that c is a constant. It's very difficult to explain even very simple concepts without a diagram and the math means nothing to me. One more try, in point form.
We are at rest with respect to another vehicle that is very distant,and has its side to us with a gigantic light on the front pointing to the right.
Laid out on a stationary track in line with the beam of the light are a zillion mirrors at right angles pointing towards us.
The light is switched on. The mirrors light up in sequence. We can calculate that the light beam is traveling at c. as it takes 10 seconds to light up 3million kilometers of the track.
The vehicle then goes off to the left, accelerates to near c and as it gets to near the beginning of the track, it puts on its headlights.
We measure this speed and as we all know it again is c.
We can also see the moving vehicle and again we measure its speed and calculate it to be c-1ft per minute, so it looks as though the other vehicle is slowly falling behind it's own light beam.
You would get the same effect if the distant vehicle remained stationary and put its light on at the same instant as another vehicle flashed past on the same route at the same speed, c- 1ft pm. We would still measure the light beam at c and the speeding vehicle as c-1ftpm.
What am I missing? Why am I wrong?


Edited by brentwood (11/26/13 10:07 PM)


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Re: Scary relativity new [Re: deSitter]
      #6218154 - 11/26/13 09:26 PM

I would love to understand it, but I'm probably a hopeless case unless the math is minimal and the prose maximal.

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deSitter
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Re: Scary relativity new [Re: brentwood]
      #6218204 - 11/26/13 09:53 PM

Quote:

Choran, I think we're at cross purposes here. I completely accept that c is a constant. It's very difficult to explain even very simple concepts without a diagram and the math means nothing to me. One more try, in point form.
We are at rest with respect to another vehicle that is very distant,and has its side to us with a gigantic light on the front pointing to the right.
Laid out on a stationary track in line with the beam of the light are a zillion mirrors at right angles pointing towards us.
The light is switched on. The mirrors light up in sequence. We can calculate that the light beam is traveling at c. as it takes 10 seconds to light up 3million kilometers of the track.
The vehicle then goes off to the left, accelerates to near c and as it gets to near the beginning of the track, it puts on its headlights.
We measure this speed and as we all know it again is c.
We can also see the moving vehicle and again we measure its speed and calculate it to be c-1ft per minute, so it looks as though the other vehicle is slowly falling behind it's own light beam.
You would get the same effect if the distant vehicle remained stationary and put its light on at the same instant as another vehicle flashed past on the same route at the same speed, c- 1ft pm. We would still measure the light beam at c and the speeding vehicle as c-1ftpm.
What am I missing? Why am I wrong?
Laid out




What you are missing is the correct geometry. It is very frustrating to watch smart people go around and around because the new input that is needed is not at hand. You will get it, I promise you.

-drl


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Otto Piechowski
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Re: Scary relativity new [Re: deSitter]
      #6218243 - 11/26/13 10:12 PM

Everyone, I am going to go way out a limb;

Danny, you wrote, "ordinary Euclidean geometry is every bit as strange in its own way as is that of relativity - because it has the idea of infinity."

Are you aware how absolutely relevant and brilliant that is? OK, I'm being dramatic. But I think you have touched on something absolutely central to the evolution of western culture, much of modern technological culture, and much of the science and mathematics of modernity as well.

Watch the beginning of the movie Troy, where the monolog begins. It speaks about the Greeks not begin able to deal with eternity. My professor, a phenomenologist, called it the Greek's "pathological concern with ephemerality". Simply (yeah, right, I know);…simply, this impossible-to-get-your-mind-around concept of infinity in geometry, was actually present in and a driving concern in the political, social, relational, emotional reality of ancient Greece…i.e. "How does one live in the now when eternity stretches on forever?" or "How do we get along when, all we are faced with is the eternal return of the same?" "How do we live, really live, when all we experience is the same-old, same-old?"

The Greeks never found a useful answer. The one they chose was fame (e.g. Achilles will only fight if fame is obtained). But fame is like ash on the tongue; it never satisfies.

Brilliant, and relevant, the nexus of the non-intuitive-concept-of-infinity in the plane euclidean geometry of greece et alia, and the impact of that concept of infinity (eternity) seeping into all aspects of Greek culture and those aspects of modern culture caught in the sway of a pathological concern with ephemerality.

Wow. I'm impressed. I never put those two together until you mentioned the non-intuitive concept of infinity found in euclidean geometry.

Otto


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brentwood
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Re: Scary relativity new [Re: deSitter]
      #6218247 - 11/26/13 10:13 PM

Ok, so what do you see? You say what I said is wrong, but how?
What geometry? this vehicle is so very far away that all the events that happen are almost in a straight line.


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deSitter
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Re: Scary relativity new [Re: brentwood]
      #6218264 - 11/26/13 10:20 PM

Please be patient. I am thinking very hard about how to present this in the right order without the benefit of symbols. To do it with words. It should be possible.

-drl


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choran
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Re: Scary relativity new [Re: deSitter]
      #6218269 - 11/26/13 10:22 PM

I think we have to wait for deSitter here. I do not believe you will measure the vehicle as traveling c-1, or anything close to it, if I understand the example, but I will certainly muck up any attempted explanation, so I'm taking the coward's way out.

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brentwood
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Re: Scary relativity new [Re: choran]
      #6218342 - 11/26/13 11:04 PM

If there were two asteroids way out there that were both the same distance from the Earth and a known distance apart and our spacecraft flew past them both and we timed it and got the speed at c-1fpm, that would be the same as in my example.
While I was typing my post above I was having second thoughts as I thought there would be some time dilation effect that would effect our observation. However if the asteroids were 3million k apart, we would time the interval at a little over 10 secs. but the driver of the car would perceive it at much less than 10secs.


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Re: Scary relativity new [Re: deSitter]
      #6218713 - 11/27/13 07:38 AM

Is the question "What would you see?"

There is a real world example of the car and beam of light; superluminal motion. In this example a jet is moving very near the speed of light and the jet is also emitting light. What you see depends on your line of sight. See this wiki for an example.

Pretend that the jet is the car and what we see is the beam of light from his headlights.

Regards,

Charlie B


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Rick Woods
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Re: Scary relativity new [Re: EJN]
      #6219174 - 11/27/13 12:04 PM

Quote:

~




?


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Rick Woods
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Re: Scary relativity new [Re: deSitter]
      #6219191 - 11/27/13 12:12 PM

Quote:

Please be patient. I am thinking very hard about how to present this in the right order without the benefit of symbols. To do it with words. It should be possible.

-drl




Bless you, my son.


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Otto Piechowski
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Re: Scary relativity new [Re: choran]
      #6219284 - 11/27/13 12:57 PM

You are correct Choran. Somewhere I had heard of, or perhaps imagined, a dual cesium clock scenario using skylab. Thank you for pointing out to me my mistake, and for telling us of the true scenario.

Otto


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choran
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Re: Scary relativity new [Re: Otto Piechowski]
      #6219725 - 11/27/13 04:07 PM

The first such experiment is called Haefele-Keating. The clocks on one plane ran slower than the earthbound clock, while the clocks on the other plane ran
faster, by a different amount. The experiment is still a little controversial, I believe. They actually published "predictions" of what would happen a while before the actual experiment. What most people did not know was they they had already performed the experiments months before, so knew what to expect. The experiment like most is not a true, isolated test of SR, due to the effects of gravity and the absence of straight-line motion, and so on. As far as I know, most tests of SR have been similarly confounded, and most if not all involve two-way measures of light speed. Obviously, given the results of H-K, the speed of light in an earthbound frame is different east versus west. See related--Sagnac effect. Again, just my layman's (probably wrong) take, but there it is for what it's worth.


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EJN
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Re: Scary relativity new [Re: choran]
      #6219832 - 11/27/13 04:59 PM

There was a young lady named Bright,
who could travel faster than light.
She set out one day, in a relative way,
and came back the previous night.


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Pess
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Re: Scary relativity new [Re: Crow Haven]
      #6219842 - 11/27/13 05:05 PM

Quote:

I haven't the math background or understanding of relativity to be able to see how this turns out. Can light be slowed down or appear slowed down from an observer's perspective at the side of the road? I have a hard time with the idea of a light beam traveling at a foot a minute or looking like it is proceeding this slowly. I thought that the light sent from the headlights would just travel at the "speed of light" as soon as turned on from the car. That it would appear instanteous from the observer in the car and from the observer at the side of the road it would also, regardless of how fast the car moved. Is there enough time and distance between the car and when the light is switched on to make it look like the light comes on before the car appears? Sorry if this sounds really stupid. I'm totally confused by it, but am hoping there will be a way to describe what actually would appear to happen for the observer at the side of the road that I can understand.




Well a photon travels at precisely 'c'. 'Slowed light is only photons traveling through a substance that absorbs and re-emits photons giving the appearance of "slower than 'c'"

But the point is, and this is important, every photon travels at precisely 'c'.

Now here is where it gets really weird. No matter from what reference frame you are in, if you measure a photon its speed will be measured at exactly 'c'.

If you stand at the side of the road and watch two trains come head-on and measure the speed of their headlights...each headlight photon will be measured traveling at precisely 'c' no matter if the trains are traveling at 0mph or 99.9999999% of 'c'

To an observer, the closure rate may be 2c, but measuring an actual photon will always give 'c'.

In fact, an engineer traveling on a train and measuring a photon emitted by his headlight will measure that photon traveling away from him at 'c' even if his train is going 99% of 'c'.

Why? Well the basic explanation is that the faster you go the more you warp space time. You effectively expand time and shrink distance.

Pesse (Tiiiiiiime..is on my side..) Mist


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deSitter
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Re: Scary relativity new [Re: EJN]
      #6219847 - 11/27/13 05:07 PM

I would like to hear some intuitive definitions of infinity, restricted however to geometric ideas. That is, it's not about integers or rational or irrational or any of the details of numerical and symbolic infinity - just that involving spatial relations.

-drl


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PeterR280
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Re: Scary relativity new [Re: Pess]
      #6219848 - 11/27/13 05:08 PM

You don't warp spacetime when you go faster.

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choran
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Re: Scary relativity new [Re: deSitter]
      #6219882 - 11/27/13 05:24 PM

How about "a plane is infinitely thin", a point is infinitely small, and an angle can be infinitely divided into yet smaller angles. Or, parallel lines will not meet even when extended into infinity.

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Crow Haven
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Re: Scary relativity new [Re: Pess]
      #6219963 - 11/27/13 06:02 PM

Well, at least I was a little bit right when it came to the speed of light always being the same. Thanks for the help, Pess!

Can space/time itself be moving, and so moving all objects within it including the light beam?


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The Mighty Mo
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Re: Scary relativity new [Re: Crow Haven]
      #6219971 - 11/27/13 06:05 PM

I'll risk showing my ignorance on this subject, but isn't what you're referring to Maya exactly what we observe in the expansion of the universe - an expansion of spacetime?

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Crow Haven
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Re: Scary relativity new [Re: deSitter]
      #6219985 - 11/27/13 06:11 PM

What I picture is something like a Mobius strip, or tube-shape used like this with further connected tubes continuing forever spiraling in every direction sort of like fractal designs do. A shape that expands in every direction forever.

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Crow Haven
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Re: Scary relativity new [Re: The Mighty Mo]
      #6219996 - 11/27/13 06:16 PM

Quote:

I'll risk showing my ignorance on this subject, but isn't what you're referring to Maya exactly what we observe in the expansion of the universe - an expansion of spacetime?




It's my ignorance! Yep, that's what I'm thinking of and how could it influence any of the objects in the problem...perhaps there's no effect? Or could even light appear to speed up even though it really can't according to "the law." I'm just wondering...


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The Mighty Mo
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Re: Scary relativity new [Re: Crow Haven]
      #6220022 - 11/27/13 06:27 PM

Nope, it wouldn't speed up, but instead of the redshift we observe from objects moving away in the expansion, we would see blueshift for objects approaching us. But we will never see a blueshift in normal observation as we're also moving away from anything "behind" us or that would be moving in our direction (from its point of reference and origin). So all we see is a redshift of everything with no definable boundary; and the frequency of the redshift denotes the distance from an object.

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Crow Haven
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Re: Scary relativity new [Re: The Mighty Mo]
      #6220029 - 11/27/13 06:31 PM

Thanks! Boy, that is one speed limit there's no way around.

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Ira
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Re: Scary relativity new [Re: Crow Haven]
      #6220164 - 11/27/13 07:44 PM

Not only can you explain it without math, but Michelson and Morley did it in their laboratory in Ohio. Perhaps the most famous experiment of all time:

http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment

/Ira

Edited by Ira (11/27/13 07:45 PM)


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choran
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Re: Scary relativity new [Re: Ira]
      #6220203 - 11/27/13 08:01 PM

You lost me there, Ira (easy to do). I thought M-M were simply trying to measure the effect of the (then posited) aether on the speed of light, reasoning that light going in the direction of the earths movement and back would go at a different speed than light moving perpendicular to the direction of the earth's movement?

You are right that M-M paved the way for Einstein's 1905 paper, because it's surprising so-called "null result" led to the conclusion that there was no "aether", and thus there was no absolute reference frame against which to measure motion. That's the importance of the experiment.

Interestingly, a later series of experiments (see Dayton Miller) up near Mount Wilson in Pasadena came up with a non-null result with a much bigger apparatus, and caused Einstein to say that if those results were correct, that relativity was in big trouble. After Miller's death the results were attributed to experimental error--temperature variations or something, I believe.

Edited by choran (11/28/13 09:38 AM)


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Otto Piechowski
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Re: Scary relativity new [Re: deSitter]
      #6220255 - 11/27/13 08:30 PM

I don't know math language so grant me some flexibility here as I attempt to put my ideas about infinity into words.

Infinity refers to a quantity to which if an additional amount were added, the size of the original quantity would not be changed. So, if an infinite length is being considered, that infinite length plus another foot would still be equivalent in size to the original infinite length without the additional foot.

Also, and this is the one that just fascinates me; one can have sets of similar type objects which contain different objects but are of the same size. For example; Set 1, Set 2, and Set 3 are all infinite and all the same size even though Set 1 is made up of all integers, Set 2 is made up of all prime numbers, and Set 3 is made up of all even numbers. They would all still have the same quantity even though it is obvious, for example, that Set 1 has all the elements of Set 2 and others.

Otto


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choran
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Re: Scary relativity new [Re: Otto Piechowski]
      #6220304 - 11/27/13 09:05 PM

We've either driven Danny bonkers and he is at this moment roaming the streets muttering about our denseness, OR he is at home cooking up one heckuva lesson plan. What's the deadline to drop the class before I flunk?
Somebody ask him if it's "pass-fail."

I remember a funny SNL skit from about 30 years ago when somebody is teaching a class of really uninterested high school students. It's the first day of school, and the guy introduces himself and starts the first lecture. Immediately a hand flies up and this girl, loudly chewing gum, says "Do we have to know this for the final?"


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TVG
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Re: Scary relativity new [Re: Ira]
      #6220338 - 11/27/13 09:30 PM

Could the detection of the Higgs field be considered a glorified example of the "luminiferous aether"? Maybe M&M just could not go small or precise enough? I could be way off base here and please explain so if I am.

Thanks to everyone contributing to this discussion so far, especially drl, I am really enjoying this.(even though I have no idea what any of you are talking about)

Todd


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GregLee1
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Re: Scary relativity new [Re: deSitter]
      #6220342 - 11/27/13 09:32 PM

Quote:

I would like to hear some intuitive definitions of infinity, restricted however to geometric ideas.




  • (1) Two parallel lines meet only at infinity (the horizon line in a perspective drawing).
  • (2) The focus adjustment of a camera is at a maximal distance when at infinity.
  • (3) A smoothly curving line is made up of an infinity of straight line segments, each infinitely short.
  • (4) Fractals have infinite perimeters (e.g., ideal coastlines).



Edited by GregLee1 (11/27/13 09:52 PM)


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choran
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Re: Scary relativity new [Re: TVG]
      #6220345 - 11/27/13 09:33 PM

I don't know enough to answer, but I do know that Einstein sort of slipped the aether back in for GR, but not the traditional aether. I read something once that was interesting--a theory that says the "aether" is just the local gravitational field. 'Course, I'm the only one that seems to like the idea.

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GregLee1
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Re: Scary relativity new [Re: Otto Piechowski]
      #6220430 - 11/27/13 10:20 PM

Quote:

Infinity refers to a quantity to which if an additional amount were added, the size of the original quantity would not be changed.



An illustrative cartoon: Hilbert's Hotel .


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The Mighty Mo
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Re: Scary relativity new [Re: choran]
      #6220581 - 11/28/13 12:09 AM

Choran,
My guess is Danny's off and getting ready for tomorrow. Maybe he's got family he's getting together with, I don't know him personally.

New challenge, I dare anyone to try contemplating and dwell on SR and GR after filling up on turkey and such, and posting intelligent your revelations here tomorrow. That is without your head hitting the keyboard for that after dinner nap.

As for me, I'll be sleeping... And might not ever make it to my computer tomorrow. Happy Thanksgiving all.


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petrus45
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Re: Scary relativity new [Re: deSitter]
      #6220686 - 11/28/13 02:16 AM

Quote:

I would like to hear some intuitive definitions of infinity, restricted however to geometric ideas. That is, it's not about integers or rational or irrational or any of the details of numerical and symbolic infinity - just that involving spatial relations.

-drl




Intuitive I can do. Complicated math looks impressive, but being a layperson in math I have no way of testing whether or not it means anything, or is rather purposed mainly to establish credibility for a later proclamation.

Anyhow this discussion is extremely entertaining, I'd like to play the game. Here's my intuitve two cents:

Geometry has to do with points, curves, lines and shapes, viz. boundaries. Infinity by definition has no boundary. Therefore infinity has no geometry. I think this applies regardless of whether we're talking about 3D or 4D, since even 4D geometric concepts, such as a "light cone" involve establishing boundaries. Any kind of "metric," whether of time or space, involves measuring boundaries. Infinity is the opposite of a boundary. This leaves us without a geometric definition of inifinity that means anything. Hence the need for a mathematical explanation to discuss the topic.

But here I'm back at the nub of the problem: I don't understand what all the math means. It has to be explained in words somehow for me to understand it.


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choran
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Re: Scary relativity new [Re: The Mighty Mo]
      #6220927 - 11/28/13 09:04 AM

Yes, HAPPY THANKSGIVING, all, and to all of our troops who are not home with families today.

Edited by choran (11/28/13 09:41 AM)


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llanitedave
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Re: Scary relativity new [Re: choran]
      #6221227 - 11/28/13 11:37 AM

It's very possible to be infinite but bounded. Think of a ray or plane that begins on a point in space. There is a definite boundary beyond which that shape cannot extend in a particular direction. However, it is infinite in the other direction.

Fractals is another good example. They have strict mathematical boundaries. Yet those boundaries can scale to infinity.


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Crow Haven
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Re: Scary relativity new [Re: Ira]
      #6221686 - 11/28/13 03:18 PM

Quote:

Not only can you explain it without math, but Michelson and Morley did it in their laboratory in Ohio. Perhaps the most famous experiment of all time:

http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment

/Ira




Thanks for posting that great link, Ira!

As new methods of testing are developed I think it's still interesting to keep checking on the results concerning the idea of an "aether"...although the previous experiments have ruled it out and things seem to function on the large scale as described.

I guess that's just because I like the idea of it even though the evidence so far isn't there. I'll accept the results until proven otherwise though.

I also read the article about the quantum Cheshire cats .... now that is really wild!

Everyone have a nice day!


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choran
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Re: Scary relativity new [Re: Crow Haven]
      #6221743 - 11/28/13 03:42 PM

Google Dayton Miller experiments. He built a huge contraption up near Mt. Wilson and his results contradicted M-M. The results were discredited after his death. Very interesting story there!

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Crow Haven
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Re: Scary relativity new [Re: choran]
      #6221873 - 11/28/13 04:22 PM

Thanks for the suggestion! I only had time to read one that google produced on ether-drift and it's fascinating how so many results were considered yet decided against it. I think I'll keep an open mind about it!

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choran
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Re: Scary relativity new [Re: Crow Haven]
      #6221933 - 11/28/13 04:46 PM

That's exactly what I try to do--take it all with a grain of salt. Some theories are like the weather: Don't like it? Fear not, it will change tomorrow (or in 50 years). Epicycles were around for, what, 1000?

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PeterR280
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Re: Scary relativity new [Re: choran]
      #6221948 - 11/28/13 04:52 PM

We should bring back phlogiston.

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choran
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Re: Scary relativity new [Re: PeterR280]
      #6221964 - 11/28/13 05:03 PM

Here's an interesting one. Imagine an railroad train in outer space, maybe 10 cars long, coming at earth, but not straight at us, but maybe a 20 degree angle or so, so we can see all the cars, not just the locomotive. Let's say this train is huge, like a light year per car or something.

Now we look in the telescope, and see a train. But the light reaching our eye did not leave all parts of the train at the same time, obviously. If there was just one quick light pulse, we would receive the light from the locomotive first, then a year later the light from the first car, etc
BUT assume it's not a pulse, but that the train is lit up. Then the image we see is composed of light from the last car when it crossed point X, and the front of the train when it passed point X. So the train car in the back would look closer than it really is. Seems that the train wouldn't look like it looks in an earthly perspective, with the last train looking smaller than the locomotive. This isn't even a relativistic effect, I think, but just a function of the light taking different times to reach us from different parts of the long train.

Edited by choran (11/28/13 05:05 PM)


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GregLee1
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Re: Scary relativity new [Re: Crow Haven]
      #6222018 - 11/28/13 05:33 PM

Quote:

I guess that's just because I like the idea of it even though the evidence so far isn't there. I'll accept the results until proven otherwise though.



It struck me the other day that "Doc" Smith, i.e., E. E. Smith the science fiction writer, might turn out to be essentially right about the ether and subether. His idea was that the ether has a granular structure, with large particles set in vibration to transmit electromagnetic radiation, then with smaller particles in the interstices of the large particles, which could be set in motion to transmit radiation of new sorts. This was the subether. Subetheric radiation could be used for secure communications and to make nifty destructive ray guns. I think there was also a sub-subether, with even tinier particles.

This is like the contemporary theory that the universe started with just one dimension, then developed a second and finally a third dimension. The third dimension is like "Doc" Smith's subether, because supposedly it is required to transmit a special form of radiation, gravity waves. When we can detect gravity waves, it is proposed, we will find a frequency cut off corresponding to the time when the early universe first developed a third dimension.

Phys Rev Focus has a popular article on the theory I mentioned.


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choran
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Re: Scary relativity new [Re: PeterR280]
      #6222039 - 11/28/13 05:42 PM

Phlogiston! Love it!

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Crow Haven
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Re: Scary relativity new [Re: choran]
      #6222134 - 11/28/13 06:37 PM

Quote:

Phys Rev Focus has a popular article on the theory I mentioned.




Gravitational waves -- yes! Great article on the LISA experiment. Years of patience required, but I'll be looking forward to hearing what is discovered. The whole dark energy thing I don't get, it seems unsatisfying.

Sci-fi writing contains some interesting ideas.


Quote:

We should bring back phlogiston.




I had to look that up. Phlogiston/Anti-phlogiston...
Well, I'd say one thing for it, it seemed to make sense to a lot of people at the time, and paved the way for other ideas and better experiments. I look at it as an example of what future testing methods can reveal even when older ideas and test results hold sway.


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Re: Scary relativity new [Re: brentwood]
      #6222498 - 11/28/13 10:50 PM

Very probable that your question was misunderstood. Just played the sacrificial lamb and went to Physicsforum.com and posted what I think you asked. Your understanding was confirmed, assuming that the observer and the driver are in the same reference frame. If the TRACK, however, is moving with respect to observer, then relativistic velocity addition formula has to be utilized and the car will be measured at going substantially less than the driver measures his own velocity.

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petrus45
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Re: Scary relativity new [Re: llanitedave]
      #6222664 - 11/29/13 01:02 AM

Quote:

It's very possible to be infinite but bounded. Think of a ray or plane that begins on a point in space. There is a definite boundary beyond which that shape cannot extend in a particular direction. However, it is infinite in the other direction.

Fractals is another good example. They have strict mathematical boundaries. Yet those boundaries can scale to infinity.




But you seem to be saying the defined part of the geometry is *not* infinite. Rather, "it is infinite in the other direction." This is consistent with my point, which is that defined geometric points, lines and shapes are finite, to the extent they are defined. To the extent a ray, a plane, or a spiral fractal pattern are "infinite" they have no geometry which defines the *end boundary* of the shape - only the beginning or the middle. To the extent there is no end boundary, there is no geometry.


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PeterR280
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Re: Scary relativity new [Re: petrus45]
      #6222926 - 11/29/13 07:51 AM

Geometry describes how lengths and measures work in our world. The criticism of Euclidian geometry involves Euclid's 5th postulate the says parallel lines never meet. You can extend them indefinitely and they will never meet. How can you ever know if that is a true statement of our physical world?

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PeterR280
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Re: Scary relativity new [Re: PeterR280]
      #6223142 - 11/29/13 10:48 AM

Physical world means our physical reality, not just Earth.

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Re: Scary relativity new [Re: petrus45]
      #6225954 - 11/30/13 09:13 PM

Quote:

Quote:

It's very possible to be infinite but bounded. Think of a ray or plane that begins on a point in space. There is a definite boundary beyond which that shape cannot extend in a particular direction. However, it is infinite in the other direction.

Fractals is another good example. They have strict mathematical boundaries. Yet those boundaries can scale to infinity.




But you seem to be saying the defined part of the geometry is *not* infinite. Rather, "it is infinite in the other direction." This is consistent with my point, which is that defined geometric points, lines and shapes are finite, to the extent they are defined. To the extent a ray, a plane, or a spiral fractal pattern are "infinite" they have no geometry which defines the *end boundary* of the shape - only the beginning or the middle. To the extent there is no end boundary, there is no geometry.



That's one way of looking at it. Note, though, that for any geometric shape, whether plane, ray, line, or fractal such as the Mandelbrot set, there is no point within the geometric coordinate system that is undefined. Every point is explicitly defined to be either within the set or outside of it.

Another cool thing about the Mandelbrot set is that even though it has an infinite perimeter, it has a finite area. So it's both bounded and infinite.


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Re: Scary relativity new [Re: llanitedave]
      #6236000 - 12/05/13 06:52 PM

Quote:

Another cool thing about the Mandelbrot set is that even though it has an infinite perimeter, it has a finite area. So it's both bounded and infinite.




I am not a mathametician, but my understanding is a mandelbrot set can have a finite upper limit on area, but no finite lower limit. Thus, effectively, it does not have a defined geometric boundary as to how small the pattern can get. To the extent it has a defined upper limit on area, it is not infinite since there is a boundary. Thus it would not be an exception to the propositon that infinity does not have a geometry.


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Re: Scary relativity new [Re: petrus45]
      #6236037 - 12/05/13 07:17 PM

The lack of lower limit of area is what plagues General Relativity.

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petrus45
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Re: Scary relativity new [Re: PeterR280]
      #6236405 - 12/05/13 11:20 PM

Quote:

The lack of lower limit of area is what plagues General Relativity.




I was reading back through some of the prior entries, namely the following:
- The thought experiment with the speedy moon eclipsing the sun, despite the Lorenz contraction.
- The idea that the concept of infinity is something "strange" in Euclidian geometry.

What I am able to crib together from all of this is the following:
- All of our empirical knowledge about the universe is limited by Euclidian geometry, i.e. the shapes and measurements we can see, hear, touch, etc.
- Euclidian geometry has mainly to do with finite boundaries.
- "Infinity" is a misnomer; for it simply means non-finite. It is a self-definition in the negative, but which actually has no free standing quality. As soon as we reach into "infinity" and measure a piece of it, it enters the realm of "known" and therefore ceases to be "infinite." Infinity is simply the unknown.
- Somewhere beyond where Euclidian geometry reaches its boundary, relativity allows us to "know" certain realities of the universe by mathematical deduction - realities that perhaps would otherwise be termed "infinite" or "unknowable" - realities we will never observe empirically (as in the moon experiment, in which we cannot actually "see" the curvature of spacetime around the moon though it may be there right before us), because the limits of what we can empirically observe is bound by our ability to perceive light, and spacetime is "self correcting" relative to our perception.


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Re: Scary relativity new [Re: petrus45]
      #6237088 - 12/06/13 10:58 AM

Th mathematical models allow you to do "thought" experiments that you could never do in real life. It was called "Gedunken" experiments in Einstein's time to test the theory. You can come up with paradoxical situations which may indicate a problem with the theory and then solve the appearant paradox with the mathematical model to show that it is valid.

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Re: Scary relativity new [Re: petrus45]
      #6237310 - 12/06/13 12:47 PM

Quote:

"Infinity" is a misnomer; for it simply means non-finite. It is a self-definition in the negative, but which actually has no free standing quality.



There have been plenty who agree with you:

Quote:

Finitism is a philosophy of mathematics which accepts the existence only of finite mathematical objects. The finitist philosophy of mathematics is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects like infinite sets are accepted as legitimate mathematical objects existing in some Platonic universe of mathematics.




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Re: Scary relativity new [Re: GregLee1]
      #6248192 - 12/12/13 12:36 AM

Did we ever resolve the headlight thing?

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Re: Scary relativity new [Re: Rick Woods]
      #6248433 - 12/12/13 07:48 AM

Not yet! Choran did go on a physics forum and they did confirm what I had been saying and did report as such on here. There was no comment IIRC from our resident 'Brain Trust'!
It appears that when those of us that do not fully understand this stuff ask questions on Relativity, those that do understand think we are challenging it.
Nothing could be farther from the truth. I fully accept that c is always c. The headlight thing is just an anomaly.
If you can measure the speed of a car, in the same reference frame as you, at .9c, and the car puts on its headlights you will measure the speed of the light coming from the headlights as c. As seen by an observer, again in the same reference point as you, but a distance away and the car moving across your view, not away or towards you, it will APPEAR that the light is leaving the car at .10c!
The light is moving across your point of view say from left to right at c, while the car is following behind at .9c.
We were told that this was wrong, but we would eventually understand why it was wrong. Still waiting!


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Re: Scary relativity new [Re: brentwood]
      #6248495 - 12/12/13 08:38 AM

Quote:

If you can measure the speed of a car, in the same reference frame as you, at .9c, and the car puts on its headlights you will measure the speed of the light coming from the headlights as c. As seen by an observer, again in the same reference point as you, but a distance away and the car moving across your view, not away or towards you, it will APPEAR that the light is leaving the car at .10c!
The light is moving across your point of view say from left to right at c, while the car is following behind at .9c.



The conditions are impossible simply because you can only observe light that reaches you. Not light that "is moving across your point of view". You're thinking of yourself as an omniscient observer who can somehow sense the true positions of things in a way that is independent of physical processes. But there are no such relativistic observers.


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Re: Scary relativity new [Re: GregLee1]
      #6248606 - 12/12/13 09:34 AM

A series of sensors along the path of the light that put a flag up when hit by the light. We could see the flags going up one by one and be able to calculate the speed of light from that.
Light activated garden gnomes that do cartwheels when hit by the beam.
And of course I have to add that the sensors & the gnomes are in the same reference frame as ourselves!


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Re: Scary relativity new [Re: brentwood]
      #6248632 - 12/12/13 09:46 AM

Quote:

We could see the flags going up one by one ...



What do you mean "see"?


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Re: Scary relativity new [Re: Otto Piechowski]
      #6248719 - 12/12/13 10:33 AM

Quote:

Infinity refers to a quantity to which if an additional amount were added, the size of the original quantity would not be changed. So, if an infinite length is being considered, that infinite length plus another foot would still be equivalent in size to the original infinite length without the additional foot.



If you add a finite length at the beginning of an infinite ray, I suppose the length of the ray would not be changed, but if you added it at the other end, I think the length would be changed. And if the amount you add is infinite, also, the size may be changed, as when you add the real numbers to the rational numbers, obtaining the reals, since there are more reals than rationals.


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PeterR280
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Re: Scary relativity new [Re: GregLee1]
      #6248768 - 12/12/13 10:55 AM

Cantor tried to categorize infinities into sets and came up witha hierarchy of infinities. For example, he showed that there are more irrational numbers than there are whole numbers. For example, if you count all the possible rational and irrational numbers between zero and one, there are more numbers than the entire set of whole number.

If you match 1 with .1 and 2 with .11 and 3 with .111, etc.. You can assign a decimal fraction of just 1s with all the whole numbers and still have many more infinities of decimal fractions between 0 and 1. There is some controversy over his number theories of infinities


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Re: Scary relativity new [Re: GregLee1]
      #6248978 - 12/12/13 12:37 PM

Quote:

Quote:

We could see the flags going up one by one ...



What do you mean "see"?



Well you know how when you 'see' your next door neighbour putting up his flag, well its like that except you are farther away!


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Re: Scary relativity new [Re: brentwood]
      #6249160 - 12/12/13 02:12 PM

Quote:

Well you know how when you 'see' your next door neighbour putting up his flag, well its like that except you are farther away!



I don't need to be concerned with relativistic effects when I'm watching my neighbor. What I'm trying to get at is that, in my opinion, you're not playing by the relativity rules when you describe your experiment without giving a physical account of how you make your observations of these flags. I guess light would have to pass from a flag to your eye, and that would take some time to happen?

By the way, did you see the post earlier in the thread from Charlie B giving a reference to this account of superluminal motion? I think this answers the headlight question.

Edited by GregLee1 (12/12/13 02:34 PM)


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Re: Scary relativity new [Re: GregLee1]
      #6249240 - 12/12/13 02:33 PM

Yes I understand that it does take time for the light to reach us, and yes I did assume that this is happening quite some distance away, so far in fact that all the events are happening in the same direction, so there is no shifting of angles of view. I suppose you could have the ship fly through a gas that would change colour when hit by light. You would then 'see' the gas change when the light hit it, but then of course the speed of light is not quite c because it is no longer a vacuum.
So again you 'see' the car travelling at .9c, and you somehow 'see' the light it shines ahead as c, so it 'looks' as though the light is leaving the car at .10c.


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Re: Scary relativity new [Re: Rick Woods]
      #6249369 - 12/12/13 03:41 PM

Quote:

Did we ever resolve the headlight thing?



I thought that Charlie B resolved it with his reference to superluminal motion.


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Re: Scary relativity new [Re: GregLee1]
      #6249489 - 12/12/13 04:56 PM

Quote:

Quote:

Did we ever resolve the headlight thing?



I thought that Charlie B resolved it with his reference to superluminal motion.




No just the opposite. Superluminal motion seems to show light from quasars travelling at >c, where as 'Brentwood's Paradox' seems to show <c.
So how about dem headlights?


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Re: Scary relativity new [Re: brentwood]
      #6249560 - 12/12/13 05:28 PM

Quote:

No just the opposite. Superluminal motion seems to show light from quasars travelling at >c, where as 'Brentwood's Paradox' seems to show <c.
So how about dem headlights?




Not what it said. The jet is moving close to c, the light from the jet is moving at c. The apparent motion of the jet is superluminal at the correct angles.

Regards,

Charlie B


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Re: Scary relativity new [Re: Charlie B]
      #6249962 - 12/12/13 09:47 PM

Ok, I'll rephrase it. (phew!) Superluminal motion has to do with STL , Brentwood's Paradox talks very roughly about APPARENT Slower than light.
So what about those headlights?


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Re: Scary relativity new [Re: brentwood]
      #6249977 - 12/12/13 09:55 PM

Quote:

So what about those headlights?



They're halogen with Sylvania 9003 bulbs.



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Re: Scary relativity new [Re: brentwood]
      #6250381 - 12/13/13 07:24 AM

Quote:


Quote:

So what about those headlights?


They're halogen with Sylvania 9003 bulbs.




The light from the headlights are moving at c, but the white Sylvania 9003 bulbs are blue shifted if coming at you and red shifted if moving away. There is no case where the light moves faster than c in any reference frame.

Charlie B


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Re: Scary relativity new [Re: Charlie B]
      #6250471 - 12/13/13 08:57 AM

Quote:

Quote:


Quote:

So what about those headlights?


They're halogen with Sylvania 9003 bulbs.




The light from the headlights are moving at c, but the white Sylvania 9003 bulbs are blue shifted if coming at you and red shifted if moving away. There is no case where the light moves faster than c in any reference frame.

Charlie B




See what I mean? As soon as someone asks a question about Relativity, it is immediately thought that the basic premise of Relativity, c is a constant, is being challenged. So by a car doing .9c and putting on its headlights, the light is going to shoot away from the car at 1.9c. I think that we all agree that this does NOT happen. Light leaves the car at c.
What I am asking is that if an observer were standing off to the side and the car went past you some distance away, and you could somehow see the light and measure its speed at c, and the car's speed at .9c, it would LOOK as though the light was leaving the car at .10c! Because of the time dilation, the car driver would see nothing different, to him the light would still be streaking away from him at c.
Apparently this is wrong, the geometry is wrong, or the way the observer 'sees' is wrong, but no one will explain it!
I did read somewhere that a physicist wrote "I am no longer going to try and teach Relativity to those who cannot be bothered to learn it" or something like that!


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Re: Scary relativity new [Re: brentwood]
      #6250584 - 12/13/13 10:06 AM

You are right Brentwood you would see a relative velocity of .1c between the car and light beam. The car would however see the light as leaving at c.

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Re: Scary relativity *DELETED* new [Re: brentwood]
      #6250591 - 12/13/13 10:09 AM

Post deleted by The Mighty Mo

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PeterR280
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Re: Scary relativity new [Re: The Mighty Mo]
      #6250601 - 12/13/13 10:13 AM

Mighty Mo. If the car were stationary and you accelerated would things look any different? Who would age slower?

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Re: Scary relativity new [Re: PeterR280]
      #6250610 - 12/13/13 10:18 AM

Sorry Peter, I deleted my post above, as I realized it was saying the same thing as you and Brent. If you were the one that was accelerated, and not the car, WRT the rest of the universe, then it would be you, the observer, that would age more slowly as time will slow down for you. But you won't realize it until you stop, everything would appear normal for you while you're "moving".

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Re: Scary relativity new [Re: The Mighty Mo]
      #6250656 - 12/13/13 10:37 AM

Thank you Peter and Mo for taking the time to read what I was saying. I think I'll treat myself to a chocolate biscuit & an Irish Coffee!

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Re: Scary relativity new [Re: brentwood]
      #6251123 - 12/13/13 03:17 PM

Quote:

What I am asking is that if an observer were standing off to the side and the car went past you some distance away, and you could somehow see the light and measure its speed at c, and the car's speed at .9c, it would LOOK as though the light was leaving the car at .10c!




I think that I'm not clear. The car would appear to be moving at 0.9 c, if not moving toward or away from you. The light would be emitted from the car and would be and appear to be to be moving at c. Light is not a particle that, like a bullet, can be shot from the car with a difference in velocity. It always moves at c and always appears to move at c. You cannot see the car and light as separate entities. Remember you see the car by light as well, which implies that your seeing the car and the light from the headlight would be by light leaving the car at the same time.

Regards,

Charlie B


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Re: Scary relativity new [Re: Charlie B]
      #6251222 - 12/13/13 04:09 PM

Well you could say that the car flashed its lights once and it would still work, the car has a light on it so you can see it. The 'lump' of light from the headlights is moving through space at c, while the car is seen to be at .9c. The RELATIVE speed of the light and the car is .10c, so you could say that it LOOKS as though the light is leaving the car at .10c. To the driver of the car though it looks normal, the headlights are lighting up the way ahead.

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