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GregLee1
professor emeritus


Reged: 07/21/13

Loc: Waimanalo, HI
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
Carpal Tunnel
*****

Reged: 12/28/12

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
professor emeritus


Reged: 07/21/13

Loc: Waimanalo, HI
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
professor emeritus


Reged: 10/12/13

Loc: South of North, North of South...
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
sage
*****

Reged: 01/31/11

Loc: SW Ohio / N Ky.
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
Carpal Tunnel
*****

Reged: 12/28/12

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
Humble Megalomaniac
*****

Reged: 09/26/05

Loc: Amargosa Valley, NV, USA
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
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
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
Carpal Tunnel
*****

Reged: 12/28/12

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
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
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
Carpal Tunnel
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Reged: 12/28/12

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
Pooh-Bah
*****

Reged: 05/27/13

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

We should bring back phlogiston.

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choran
Carpal Tunnel
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Reged: 12/28/12

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
professor emeritus


Reged: 07/21/13

Loc: Waimanalo, HI
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
Carpal Tunnel
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Reged: 12/28/12

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

Phlogiston! Love it!

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Crow Haven
Pooh-Bah


Reged: 01/09/09

Loc: Oregon USA
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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choran
Carpal Tunnel
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Reged: 12/28/12

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
sage
*****

Reged: 01/31/11

Loc: SW Ohio / N Ky.
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
Pooh-Bah
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Reged: 05/27/13

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
Pooh-Bah
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Reged: 05/27/13

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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