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#1 Otto Piechowski

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Posted 23 July 2013 - 12:26 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

#2 Jarad

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Posted 23 July 2013 - 01:25 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

#3 Otto Piechowski

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Posted 23 July 2013 - 02:02 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.

#4 Jay_Bird

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Posted 23 July 2013 - 05:26 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...

#5 Ira

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Posted 23 July 2013 - 05:26 PM

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

/Ira

#6 deSitter

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Posted 23 July 2013 - 08:01 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.

#7 deSitter

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Posted 23 July 2013 - 08:13 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

#8 bk42

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Posted 23 July 2013 - 08:26 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.

#9 deSitter

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Posted 23 July 2013 - 08:51 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

#10 Rick Woods

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Posted 23 July 2013 - 10:17 PM

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

</nitpick>

#11 petrus45

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Posted 23 July 2013 - 11:11 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


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

#12 AstroGabe

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Posted 24 July 2013 - 01:25 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

#13 deSitter

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Posted 24 July 2013 - 09:26 AM

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

#14 Otto Piechowski

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Posted 24 July 2013 - 10:25 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

#15 Otto Piechowski

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Posted 24 July 2013 - 10:30 AM

Thank you for the correction, Rick.

Otto

#16 Otto Piechowski

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Posted 24 July 2013 - 10:47 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?

#17 deSitter

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Posted 24 July 2013 - 11:00 AM

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

#18 Otto Piechowski

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Posted 24 July 2013 - 12:04 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

#19 deSitter

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Posted 24 July 2013 - 12:13 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

#20 sirchz

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Posted 24 July 2013 - 01:00 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


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

#21 deSitter

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Posted 24 July 2013 - 01:12 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

#22 Jarad

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Posted 24 July 2013 - 01:28 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

#23 deSitter

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Posted 24 July 2013 - 02:22 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

#24 PhilCo126

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Posted 24 July 2013 - 03:31 PM

C = Celeritas ( Latin for "speed" )

#25 Otto Piechowski

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Posted 24 July 2013 - 10:21 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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