17 Dec 2007 10:53:04 UTC

Topic 193379

(moderation:

Just wondering. Maybe the 'speed of light limit' is a property of the space it self and not the light?

It appears that space can be curved and expand. Can it be excluded that space have mass and density?

If the 'speed of light limit' just is a property of space it self the fastest relative speed observed by a 'Third Party Observer' should be 2*sqr2.

Do any of you know what the fastest measured relative speed observed by a 'Third Party Observer' is?

I am on my way to Thailand right now for a 80 day vacation so I want to wish you all a Merry Christmas.

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## Can the 'speed of light limit' be a property of space and not th

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Merry Christmas, Tomas!

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## RE: Just wondering. Maybe

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There are constants in Maxwellâ€™s equations called the permittivity and permeability of free space (vacuum), epsilon-nought and mu-nought respectively, From these the speed of light can be deduced: c is the reciprocal of the square root of their product. IIANM epsilon-nought can be determined experimentally from Coulombâ€™s law, while the value of mu-nought is corollary to the definition of the ampere.

## RE: Just wondering. Maybe

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Hmmm ... there are a few levels of answers to this question.

- the most concrete is that when Special Relativity was formulated, one requirement was that it marry the behaviour of electromagnetic phenomena ( massless photons ) with dynamical observations ( massive particles ). In particular a material body would emit light at a speed which was independent of that body's motion & indeed the same speed for any viewpoint of observation of that emission. That is where c = the speed of light slips in to the equations, and as General Relativity derives from SR then descriptions of gravity have c as a factor. So you could strictly say that the speed of light is a property of our *measurement* of space under these schemes. At this level of description SR and GR don't actually define space and time, but prescribe comparisons between frames of reference ( what is constant & what varies & how to convert observations ), given or assuming some deeper definition of space and time. So here light has properties which we use to probe spacetime.

- on a different level now, more metaphysical if you like, is the issue of what is meant by something existing. This leads you to 'does a tree falling in a forest make a sound if no-one is there', 'is the fridge light on when you close the door', 'does Schroedinger's Cat possess an alive or dead status prior to having a peek in the box' ..... etc. The basic problem here is that we exist ( by whatever definition ) within the very thing we are attempting to describe. Not only can we not visualise 4-D space, we can't pop outside and have a look. So what underlies, often unstated, a lot of relativity discussions is some model or god's eye view which spans the situation of interest AS IF we were outside of space and time. So we imagine a photon leaving the Andromeda galaxy and scooting along in between the stars, subject to various influences like cosmic expansion, dark matter or somesuch and then firing down the pipe of some telescope or like instrument to trigger a CCD cell, say. But we do that modelling in order to then derive some connection between the recorded light as received by said 'scope and from that we deduce some happenings in Andromeda ( and between ). So here light has properties endowed upon it, so to speak, by the intervening space and we are tracking it's behaviour under that influence. You explain black holes this way - too much concentrated mass curves space, space only allows a maximum speed and the courses available for light travel are closed paths .... and so on.

So it 'depends' really .... :-)

Um... I think the phrasing is that space has matter/mass/energy contained within it - the directly measurable stuff we are familiar with. What space possesses in addition to this relies upon whatever you think is happening at really small scales. There is a lot of talk about quantum this and quantum that, foam, loops, strings, extra knotty dimensions, virtual and transient particles and the like. All very clever, self consistent even, but notably lacking in measurable confirmations. In particular String theory for all it's beauty hasn't yielded even one number to test. So while it's a not unpleasant description of things, it falls at the first hurdle by not even producing a question to be answered by experimental means.

You'd have to define that a bit better I'm afraid ... :-)

Have a safe trip!

Cheers, Mike.

NB. So I should have summarised somewhat by saying that deeper definitions of space and/or time ( in terms of what? ) would enable a better answer to your first question. It's not a practical problem so much, as people just get on with it and measure stuff. But if you're going to abstract or generalise theoretically in the future ( like melding GR with Quantum Mechanics ) then it will have to be tackled. I think Roger Penrose threw up a pure math model a decade or so ago along these lines, see 'twistors' I think ...

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## Yup, it's twistors, it was

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Yup, it's twistors, it was Roger Penrose, but 4 decades ago ( 1967 ) .... :-)

see here for instance, based on lectures he gave.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: RE: If the 'speed of

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It was a assumption based on the fact that the movement of light seams to be dependent of the movement of the light source and the case when an object is traveling infinite close to light speed along the x-axis at he same time it transmit the light beam along the y-axis.

Say that you have a third party observer that check the time the light takes to go the distance between the location where it is being emitted (x0, yo) to a detector located at x1, y1.

To me it looks like the speed of light as it is defined now is restricted to be measured along only one coordinate axis that is why a third party observer should get a different value when he observe the movement along 2 coordinate axis. So I guess that, in theory, you should be able to travel infinite close to the speed of light both along the x-axis and y-axis at the same time and emit a light beam along the z-axis and that the speed of light seen by a third party observer would have a maximum of sqr3 in that case.

Thank you Odysseus and Mike for your very interesting answers.