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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
C
      #5986064 - 07/23/13 01:26 PM

Recently I had been thinking about the speed of light. I believe the speed of light in a vacuum is c. 186,000 mps (c. 300,000 kps) and that this figure is represented by the symbol "C". Then, in another post, Jarad began a comment with the words, "As a practical matter, if we don't figure out a way around the hard limit of C"...." His comment caused me to get brave and post the question I have had in my mind.

Is there anything in physics which can explain why C (in a vacuum) is c. 186,000 mps and not say 1 million mps or 5 mps? Is there something about the nature of the universe, light, stuff in the universe, etc. which might explain this?

Otto


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Jarad
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Re: C new [Re: Otto Piechowski]
      #5986179 - 07/23/13 02:25 PM

Good question.

Danny can probably give a much better answer than I can. But for at least a first level answer, C is determined from 2 other physical properties of the vacuum - permeability (the magnetic constant) and permittivity (the electric constant). Wiki link

As to why those two physical constants are what they are, I can't give you an answer beyond they are built into the nature of our space-time. Maybe someone else can add a deeper insight.

Jarad


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: Jarad]
      #5986232 - 07/23/13 03:02 PM

Oh wow. I've never ever even heard of permeability and permitivity in physics.

Of course, the guy from whom I learned physics was, supposedly, fired by the Navy for building a torpedo that destroyed the sub that shot it.


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Jay_Bird
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Reged: 01/04/06

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Re: C new [Re: Otto Piechowski]
      #5986568 - 07/23/13 06:26 PM

Talk about the perils of circular reasoning...no place for that in torpedo engineering!

On a less flippant note David Bodanis "E=MC^2" might be a book you enjoy...


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Ira
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Re: C new [Re: Otto Piechowski]
      #5986570 - 07/23/13 06:26 PM

Followed the links. I am very impressed that anyone can understand it. It was sheer gibberish to me.

/Ira


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: Ira]
      #5986785 - 07/23/13 09:01 PM

No. The value could be anything. All that matters from the point of view of foundations is that it is finite, and fixed. In natural units the value is 1.

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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: deSitter]
      #5986808 - 07/23/13 09:13 PM

The important point is that C has the dimensions of speed but is not itself the speed of anything in particular. It has the dimensions of speed because it is the fundamental structural element in a more inclusive geometry that relates space to time intrinsically. The speed of light is 1. Euclidean geometry has the very same characteristic parameter but the value is imaginary, "i". In that geometry, it characterizes infinity.

-drl


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bk42
member


Reged: 01/18/10

Re: C new [Re: Ira]
      #5986837 - 07/23/13 09:26 PM

If I remember correctly, for a simple plane electromagnetic wave, you can apply Faraday's Law and show that the electric field = c times the magnetic field. Then I believe Ampere's law was used to show that the magnetic field = muXnaught X Electric Field X C X epsilon naught. Then of course the equations are set equal to each other and C is expressed as Jarad said.

This was the derivation I remember for a simple transverse plane wave though. I'm sure the actual physicists/professionals understand it and can explain it much better.


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: bk42]
      #5986900 - 07/23/13 09:51 PM

That is a side effect of relativity. In fact the relation of electric to magnetic phenomena is only clarified by relativity. You do not derive C from light. It exists independently of any particular material expression, and represents a new order in which time is not absolute. Here is a derivation.

http://membrane.com/sidd/wundrelat.txt

-drl


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Rick Woods
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Re: C new [Re: deSitter]
      #5987084 - 07/23/13 11:17 PM

FWIW, I believe it's "c", not "C".

</nitpick>


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petrus45
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Reged: 01/31/11

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Re: C new [Re: deSitter]
      #5987163 - 07/24/13 12:11 AM

Quote:

The important point is that C has the dimensions of speed but is not itself the speed of anything in particular. It has the dimensions of speed because it is the fundamental structural element in a more inclusive geometry that relates space to time intrinsically. The speed of light is 1. Euclidean geometry has the very same characteristic parameter but the value is imaginary, "i". In that geometry, it characterizes infinity.

-drl




I guess in light of this the original question might be re-formulated: Why does anything go slower than the speed of light?


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AstroGabe
sage


Reged: 01/10/10

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Re: C new [Re: petrus45]
      #5987296 - 07/24/13 02:25 AM

To answer your first question, there's no good physical reason that is known for why the speed of light is that value. It's interesting to note however that the standard definition of a meter is taken as the distance light travels in a vacuum in 1/299792458 of a second. However, if the speed of light were different than that value, the universe would be quite a different place.

Particles with mass travel slower than the speed of light since the space-time momentum four-vector cannot be a null. That's a way of saying that since space and time are interconnected, and that the energy and momentum are interconnected, then the fact that a rest mass exists, the particle travels through space and time at different rates. Essentially, the world line of the particle is constrained to be time-like.

Now, the particle obtains a mass by a breaking of a symmetry. This can be the electroweak gauge symmetry which is related to recently discovered the Higgs boson. Another symmetry is chiral symmetry, and its breaking is how a bulk of the mass if protons and neutrons (and by extension, us) is generated.

Hope this helps,
Gabe


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: petrus45]
      #5987632 - 07/24/13 10:26 AM

Quote:

Quote:

The important point is that C has the dimensions of speed but is not itself the speed of anything in particular. It has the dimensions of speed because it is the fundamental structural element in a more inclusive geometry that relates space to time intrinsically. The speed of light is 1. Euclidean geometry has the very same characteristic parameter but the value is imaginary, "i". In that geometry, it characterizes infinity.

-drl




I guess in light of this the original question might be re-formulated: Why does anything go slower than the speed of light?




Good question. For the same reason that some places in Euclidean geometry are in the foreground and attainable, and some are on the horizon and "ideal". Relativity has a similar configuration of ideal points, the "light cone" that divides space into regions that are causally connected. At any given place and time, events outside the light cone at that point cannot have had an effect on any physical process there, and cannot in turn be affected by something occurring at that point.

The speed of light is the invariant characterization of this ideal domain. The very same exists in Euclidean geometry and characterizes in turn its ideal domain.

-drl


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: AstroGabe]
      #5987713 - 07/24/13 11:25 AM

Your response Gabe reminded me of something called the Anthropic Principle (strong or weak, I forget) by a physicist whose name I think is Wheeler.

Applying it here, "c" is the speed it is because if it were not that speed, the universe as we know it with its specific set of parameters within which human sentience can exist, would not exist.

simpler: "c" is "c" because if "c" were "not-c" human sentient would not exist to ask "why is "c" "c"?"

Your response raises interesting speculation within me. It's as if your response is not the answer to my question, but is the answer to a more interesting question which is, in fact, something of an answer to my question.

Thank you.

Otto


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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: Rick Woods]
      #5987718 - 07/24/13 11:30 AM

Thank you for the correction, Rick.

Otto


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Otto Piechowski
Pooh-Bah


Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: Otto Piechowski]
      #5987735 - 07/24/13 11:47 AM

“To answer your first question, there's no good physical reason that is known for why the speed of light is that value. It's interesting to note however that the standard definition of a meter is taken as the distance light travels in a vacuum in 1/299792458 of a second. However, if the speed of light were different than that value, the universe would be quite a different place.

Particles with mass travel slower than the speed of light since the space-time momentum four-vector cannot be a null. That's a way of saying that since space and time are interconnected, and that the energy and momentum are interconnected, then the fact that a rest mass exists, the particle travels through space and time at different rates. Essentially, the world line of the particle is constrained to be time-like.

Now, the particle obtains a mass by a breaking of a symmetry. This can be the electroweak gauge symmetry which is related to recently discovered the Higgs boson. Another symmetry is chiral symmetry, and its breaking is how a bulk of the mass if protons and neutrons (and by extension, us) is generated.

Hope this helps,
Gabe


Your response Gabe reminded me of something called the Anthropic Principle (strong or weak, I forget) by a physicist whose name I think is Wheeler.

Applying it here, "c" is the speed it is because if it were not that speed, the universe as we know it with its specific set of parameters within which human sentience can exist, would not exist.

simpler: "c" is "c" because if "c" were "not-c" human sentient would not exist to ask "why is "c" "c"?"

Your response raises interesting speculation within me. It's as if your response is not the answer to my question, but is the answer to a more interesting question which is, in fact, something of an answer to my question.

Thank you.

Otto “



WHICH MEANS....oh wow....which means, though "c" is a constant in our universe, "c" is not a Law; but "not a Law" I mean "c" can in different universes be a different value.

The questions this raises then are

(1) why does "c" remain a constant in any given universe; for example, in our universe it has been a little under 14 billion years,

(2) does "c" as the value it is in our universe, have to exist as that value, for any universe to exist?


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: Otto Piechowski]
      #5987755 - 07/24/13 12:00 PM

Otto, I hate be belabor the point, but C=1 - its measured value is an artifact of units of measurement. It doesn't change because it's not a dynamic aspect of the world such as perhaps the gravitational constant. If it has a certain value somewhere, then by analytic continuation of the 4-d manifold, it has the same value everywhere.

If you are asking why it is so large relative to human time scales, then that is a question without an answer.

-drl


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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: deSitter]
      #5987819 - 07/24/13 01:04 PM

Before I go forward with my question, Danny; may the recent cold fusion reaction demonstration help provide the results for which you, and perhaps all of humanity, hope!

As to my ramblings on "c"...thank you for bringing your physicist's eye to the question. Though I am not able to understand even your, I am sure it is a, simple response, I sense you are correct.

Could you please attempt a further response; in words hopefully simple enough for me to comprehend, why in our universe is "c" (in a vacuum) equal to c. 186,000 mps and not, say 5 mps or a million mps?

Otto


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: Otto Piechowski]
      #5987830 - 07/24/13 01:13 PM

You are asking why it is large on human scales. There is no answer. If say a being existed with an extent as large as a galaxy, its organization would be far different than ours.

-drl


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sirchz
super member


Reged: 09/21/09

Re: C new [Re: Otto Piechowski]
      #5987871 - 07/24/13 02:00 PM

Quote:

Recently I had been thinking about the speed of light. I believe the speed of light in a vacuum is c. 186,000 mps (c. 300,000 kps) and that this figure is represented by the symbol "C". Then, in another post, Jarad began a comment with the words, "As a practical matter, if we don't figure out a way around the hard limit of C"...." His comment caused me to get brave and post the question I have had in my mind.

Is there anything in physics which can explain why C (in a vacuum) is c. 186,000 mps and not say 1 million mps or 5 mps? Is there something about the nature of the universe, light, stuff in the universe, etc. which might explain this?

Otto




I think the short answer is that our current theories are unable to explain why the fundamental constants are what they are.


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: sirchz]
      #5987889 - 07/24/13 02:12 PM

True, but C, like Planck's constant, is not on the same footing as dynamical constants such as the electron mass and the gravitational constant. All the parameters in the Standard Model are dynamical constants.

-drl


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Jarad
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Re: C new [Re: deSitter]
      #5987911 - 07/24/13 02:28 PM

So basically you are saying that in General Relativity, the other constants that contain units of distance or time are defined relative to C. So the question isn't why is C ~3x10^9 m/s, but why is the electron so small, gravity so weak, etc.

Jarad


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deSitter
Still in Old School


Reged: 12/09/04

Re: C new [Re: Jarad]
      #5987987 - 07/24/13 03:22 PM

Yes that's a legitimate question - see Dirac's "Large Numbers Hypothesis".

The explanation of C is quite rigorous because both Euclidean and Minkowskian geometry are examples of "affine geometries" in the sense of projective geometry. Every metric geometry can be embedded in projective geometry by positing within it the ideal domain. If the metric geometry has an indefinite signature and is degenerate, the characteristic constant is real. That is the case with relativity.

The explanation of Planck's constant is not yet at hand in so categorical a way, but many (raises hand) expect a similar geometric and invariant-theoretic derivation some day. In practice, both C and h are set to 1 to simplify calculations. They can always be restored at the end.

-drl


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PhilCo126
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Re: C new [Re: deSitter]
      #5988082 - 07/24/13 04:31 PM

C = Celeritas ( Latin for "speed" )

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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: PhilCo126]
      #5988707 - 07/24/13 11:21 PM

Truly, I appreciate all the discussion that is going into this. But, is it possible for one of you to do a "Jarad" or a "Dave" and put these thoughts into even simpler words for me to begin to understand them. Why is c~3x10^9 m/s in our universe now and seemingly, for most of its current history? Why can't it be larger or smaller? Thanks guys (and gals?) Otto

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llanitedave
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Re: C new [Re: Otto Piechowski]
      #5988794 - 07/25/13 12:22 AM

Danny's reference to the value of c being '1' is spot on. It's the fundamental constant of the universe, not an arbitrary value. That's why he called it the "natural" value. If the number seems arbitrary to us, it's because we are simply using the wrong perspective. It's humanity, and our own length and time scales that are arbitrary, not the geometry of spacetime.

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Mister T
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Reged: 02/01/08

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Re: C new [Re: Otto Piechowski]
      #5989055 - 07/25/13 06:56 AM

Light travels at the speed light travels

299,792,458 m/s or 186,282 mi/s are values we have calculated relative to the units we have chosen as our standards.

On Greezledorp III, c = 42 fremulangs/quiszzenferfulmops

(roughly translated Gleezledorpese is a VERY complex and nuanced language)

If you want to know the physical parameters that enable/confine c to it measured value, you will have to go to a planet where they have a much more advanced understanding of Wave-icle Physics than we do.

probably a planet where they kids have Large Hadron Colliders sitting in their closets collecting dust because they are bored with them....


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Otto Piechowski
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Reged: 09/20/05

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Re: C new [Re: Mister T]
      #5989062 - 07/25/13 07:07 AM

Everyone,

Thank you.

(If there is more to say, by all means say it.)

Otto


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sirchz
super member


Reged: 09/21/09

Re: C new [Re: Otto Piechowski]
      #5989634 - 07/25/13 02:03 PM

Quote:

Why is c~3x10^9 m/s in our universe now and seemingly, for most of its current history? Why can't it be larger or smaller?




Questions of why are dangerous territory. Rather than discussing "c", the speed of light, most discussions I've seen revolve around the fine structure constant. Alpha is a measure the electromagnetic interaction, which is quite important. I'm not an expert in this, so I'll stop and simply refer you to the links below for more information, especially the Economist article.

Economist Article on the Fine Structure Constant
Wikipedia - Fine Structure Constant


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petrus45
sage
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Re: C new [Re: AstroGabe]
      #5993863 - 07/27/13 11:11 PM

Quote:

Particles with mass travel slower than the speed of light since the space-time momentum four-vector cannot be a null. That's a way of saying that since space and time are interconnected, and that the energy and momentum are interconnected, then the fact that a rest mass exists, the particle travels through space and time at different rates. Essentially, the world line of the particle is constrained to be time-like.




Gabe: I'm not particularly well-versed in the shop talk on these issues, but it seems like you're saying one of the qualities of things that have "mass" is that they travel at some speed slower than "c." Is this "slowing" below "c" what actually confers mass? I've heard this "mass-conferring" issue has something to do with the Higgs Field and the Higgs-Boson. I'm picturing a big net slowing light particules down at which point they convert into mass. I'm sure this is ridiculously crude for those who understand the math, but is this image in any way useful in visualizing these concepts?


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jhayes_tucson
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Re: C new [Re: Otto Piechowski]
      #5993968 - 07/28/13 12:41 AM

Quote:

Truly, I appreciate all the discussion that is going into this. But, is it possible for one of you to do a "Jarad" or a "Dave" and put these thoughts into even simpler words for me to begin to understand them. Why is c~3x10^9 m/s in our universe now and seemingly, for most of its current history? Why can't it be larger or smaller? Thanks guys (and gals?) Otto




The universe is full of constants and the value of 'c' (in a vacuum) is one of them. It is something that we measure; like the value of Planck's constant or the value of 'G' (the gravitational constant.) It is what it is. Physics is a search for fundamentals and there may be a way to compute some of these constants from more fundamental models one of these days but as far as I know, 'c' is still considered a constant value.
John


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AstroGabe
sage


Reged: 01/10/10

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Re: C new [Re: petrus45]
      #6017540 - 08/10/13 12:31 PM

Hi Peter,
Yes, if a particle has mass it must necessarily travel with a velocity less than the speed of light. Your analogy isn't far off.
I wrote a quick article for our club last year that has a similar analogy and a bit more explanation of its importance. Starting on pg 4:

http://www.rasastro.org/newsletters/RAS%20Newsletter%20Fall%202012.pdf

Gabe


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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: AstroGabe]
      #6017545 - 08/10/13 12:34 PM

What a nice elegant explanation of what causes things to have mass! Thank you, Gabe. Otto

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PeterR280
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Re: C new [Re: sirchz]
      #6018270 - 08/10/13 09:29 PM

Maxwell's equations give solutions to electromagnetic wave equations. they also imply that the speed of light is a constant but it wasn't until Einstein that c was recognized as the speed limit of the universe. The number c is just that. There is nothing in physics now that predicts that speed from other constants. Who knows in the future.

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llanitedave
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Re: C new [Re: PeterR280]
      #6018284 - 08/10/13 09:48 PM

No discussion on c is complete without referencing the definitive book on the subject:

K & R



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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: llanitedave]
      #6018309 - 08/10/13 10:25 PM

Not nice Dave.

But funny.

Otto


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scopethis
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Re: C new [Re: Otto Piechowski]
      #6018752 - 08/11/13 10:35 AM

doesn't the Universe have to expand faster than c?

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GregLee1
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Reged: 07/21/13

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Re: C new [Re: scopethis]
      #6019031 - 08/11/13 01:15 PM

Quote:

doesn't the Universe have to expand faster than c?



In my very partial understanding, it's the space part of the universe that expands faster than c, not any material. This is from a tutorial article at The Physics Forums :

Quote:

The material that emitted the light which we are currently receiving as CMB is now at a distance from us of 45 billon LY. The light managed to get here in slightly less than the age of the expansion which is 13.7 billion years. The material was much closer to us when the light started its journey. It didn't break any speed laws. Yet it seems to have come all the way across the balloon surface to us from a point which is now 45 billion LY away. This might strike you as paradoxical but it isn't really. The balloon analogy shows you how light can cover enormous distances in less than the expansion age.





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GregLee1
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Re: C new [Re: Otto Piechowski]
      #6019193 - 08/11/13 02:52 PM

Quote:

(1) why does "c" remain a constant in any given universe;




Does it? As it happens, just yesterday I caught part of an interview (on Morgan Freeman's Science Channel series) with a physicist telling about his alternative to Inflation. Rather than the uniformity of the universe being due to exchange between its parts when it was small (before Inflation), the early exchanges were possible because c was small (and there was no inflation). Sorry, I didn't get the name.


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PeterR280
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Re: C new [Re: GregLee1]
      #6019987 - 08/11/13 11:59 PM

Maybe the universe stays the same size and the "constants" change over time.

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EJN
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Re: C new [Re: llanitedave]
      #6020038 - 08/12/13 12:34 AM

Quote:

No discussion on c is complete without referencing the definitive book on the subject:

K & R






Does this mean that if faster-than-light travel were possible,
it would be C++ ?



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llanitedave
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Re: C new [Re: EJN]
      #6020139 - 08/12/13 02:12 AM

Unless, of course, the universe is interpreted.

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Otto Piechowski
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Reged: 09/20/05

Loc: Lexington, KY
Re: C new [Re: llanitedave]
      #6020652 - 08/12/13 12:12 PM

It might have been drl, but refresh my memory if this is wrong.

Didn't he say what Greg and Peter have been saying, that inflation may not have happened, and maybe its the constants which are changing? Something like that?

Otto


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scopethis
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Re: C new [Re: Otto Piechowski]
      #6020703 - 08/12/13 12:38 PM

that would seem to truly uphold the Relativity Theory, that everything is relative to the viewer...

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Qwickdraw
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Re: C new [Re: Jarad]
      #6021273 - 08/12/13 05:09 PM

Quote:

Good question.

Danny can probably give a much better answer than I can. But for at least a first level answer, C is determined from 2 other physical properties of the vacuum - permeability (the magnetic constant) and permittivity (the electric constant). Wiki link

As to why those two physical constants are what they are, I can't give you an answer beyond they are built into the nature of our space-time. Maybe someone else can add a deeper insight.

Jarad




Of course ad nauseum, you can now ask yourself, self, why than is the magnetic constant the electric constant at the values they are? I suppose you can kick this down the road as long as you can maintain your sanity.


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llanitedave
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Re: C new [Re: Qwickdraw]
      #6021894 - 08/12/13 11:15 PM

If the constants are changing, they'd all have to change in sync with one another, which in a practical sense means they aren't changing.

Otherwise, the values of the weak force and the strong force would also be changing. Atoms might be possible in some eras but not others, stellar characteristics and reactions would change over time, and there would be no continuity to the cosmos.

On the contrary, we have firm evidence that the constants of nature which affect matter as we know it have been constant for at least 1.7 billion years on Earth, from among other things studying the products from the Oklo fission events. The fact that type 1A supernovae appear identical throughout the history of the observable universe is also pretty strong evidence in favor of constant constants.


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