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Universal speed of light when not in a vacuum ?


geordief

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Suppose we have a medium which limits the speed of light to some constant speed -a fraction of c ,10% as an example.(ie c/10)

 

Will any observer in this medium ,in any inertial frame of reference see light in this medium moving at this same speed?

 

Is it possible to extend the question to an observer outside the medium -an observer in a vacuum for example ,again moving wrt the light source at a constant rate?.

 

 

As usual ,I hope my question "makes sense" and is interesting.

 

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No. but this light will be subject to the addition of velocities theorem. For example, Assume one frame is at rest with respect to the medium and sees two light beams moving to the left and right. It will measure both as moving at 0.1c relative to itself. Now assume we have another frame moving to the right at .09c.It will measure the light moving to the left as moving at 0.188 c relative to itself and the light moving to the right as moving at 0.1009 c relative to itself. The separation speed of the two beams will be .2c in the first frame and 0.198c in the second. c is the invariant speed of the universe, and you can only have one. One reason is that the invariant speed of the universe is automatically the speed limit for the universe.

 

Don't put too much importance to light itself. The important thing is the speed c. Light is only important in that it travels at c in a vacuum, which makes it convenient to use when discussions dealing with Relativistic effects.

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Don't put too much importance to light itself. The important thing is the speed c. Light is only important in that it travels at c in a vacuum, which makes it convenient to use when discussions dealing with Relativistic effects.

definetely important advice,

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Within a material in which light travels at v, all observers will see light at v and not at c.

I'm open to being corrected but velocity of light can only be c, in a vacuum, but speed of light doesn't have to be, because v is a vector with a directional component. In a medium, 'velocity of light' will become 'speed of light'.

 

Speed is the distance travelled by an object where as, velocity is distance traveled by an object per unit time in a particular direction. Speed is a scalar quantity where as velocity is a vector quantity.

https://www.enotes.com/homework-help/whats-difference-between-speed-velocity-296735

Edited by StringJunky
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Within a material in which light travels at v, all observers will see light at v and not at c.

If you read Janus' reply (post#2)I think you will see that this is not the case

 

"Now assume we have another frame moving to the right at .09c.It will measure the light moving to the left as moving at 0.188 c relative to itself and the light moving to the right as moving at 0.1009 c relative to itself. "

 

I think that I understood that response correctly....

 

It is only really the speed limit c which is the same for all (inertially moving ) observers although the relativistic addition of velocities does apply to all values of "v" . -and also in all mediums apparently.

Edited by geordief
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I thought Janus was calculating speeds as a fraction of c in a simple mathematical way.

 

There was no implication that that anything might actually travel at c in anything other than a vacuum

 

Hope I understood your point correctly.

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We use c as it represents an invariant constant. One not just the speed of light in a vacuum but more more importantly the speed of information exchange. Its literally the speed limit for any possible interactions. Including inside a medium, no particle exchange can occur faster than c. All observers will measure information exchange as the same. This is true even if there are no photons included in the system being modelled.

Edited by Mordred
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We use c as it represents an invariant constant. One not just the speed of light in a vacuum but more more importantly the speed of information exchange. Its literally the speed limit for any possible interactions. Including inside a medium, no particle exchange can occur faster than c. All observers will measure information exchange as the same. This is true even if there are no photons included in the system being modelled.

 

You wouldn't have any more to say about that with you I opened a question on that subject on Stack Exchange but am not sure I got satisfaction

 

http://physics.stackexchange.com/questions/206505/the-speed-of-information.

 

 

I think I understand it is the geometry of spacetime that causes this speed limit...

 

Can any more be said?

Edited by geordief
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This is the most accurate response on that site. Information in QM is specifically to quantum numbers. Though the Shannon portion is relevant its not quite what were talking about.

"The notion of "information" is actually crucial to the notion of the relativistic speed limit cc. In particular, the transfer of "information" is a necessary condition for a causal link between two events. The mathematical properties of the Lorentz transformation are such that if the time order of two events are timelike, i.e. a signal travelling at speed cc or less can reach one to the other in one inertial frame, then the order that those two events happen in is the same for all inertial observers: even though those observers may disagree on the time between the events, the sign of that interval is the same. Therefore, no causal link propagating at cc or less can have its direction in time reversed simply by a change of inertial frame.

If, however, information could travel at a speed greater than cc, it could be a causal link between two events that have spacelike separataion. The order of such events does depend on frame: some observers would see the effect coming before the cause! Since we believe this is impossible, we therefore conclude that faster than light signalling must be impossible. This is the very reason why physicists conclude that the maximum signalling speed, or maximum information propagation speed, must be c"

Yes the speed limit can be viewed accurately as a result of spacetime. Let me double check but if I recall Rindler does an excellent job detailing the speed limit. If I recall correctly I"ll post those details. If I remember correct his example didn't involve light itself

OK the Rindler example wasn't quite the way I recall but still appropriate.

 

lets start with

[latex]\gamma=\gamma(v)=\frac{1}{(1-v^2/c^2)^{1/2}}[/latex]

 

which denotes the Lorentz factor.

 

the transforms being

[latex]\acute{x}=\gamma(x-vt), \acute{y}=y, \acute{z}=z, \acute{t}=y(t-vx/c2)[/latex]

 

when v=c the Lorentz factor becomes infinite, and v>c leads to imaginary values of the Lorentz factor. This is the first indication that shows the relative velocity of two observers must be less than c. Since finite coordinates in one frame must correspond to finite coordinates in any other frame. This also indicates that no particle can move superluminally relative to an inertial frame. Consider for example a case where a signal or process event A causes an event B where information is assumed to be superluminal. U>c. relative to some frame S. We choose coordinates in S so that these events both occur on the x axis and let their time and distance separations be [latex]\Delta>0, \Delta x>0[/latex]

 

then in the usual frame [latex]\acute{S}[/latex] we have [latex]\Delta\acute{t}=\gamma(\Delta t-\frac{v\Delta x}{c^2})=\gamma\Delta t(1-\frac{vU}{c^2)}[/latex]

for a v that satisfies [latex]c^2/U<v<c[/latex] we would then have [latex]\Delta\\actute{t},0[/latex]. Hence there would exist an inertial frame in which b precedes A. In which cause and effect would reverse and the signal is considered to travel in the opposite spatial direction. This would violate causality.

 

The rest of his examples involve numerous causality violations.

 

page 73 Rindlers "Relativity (Special,General and Cosmology) second edition. Hope that helps better understand the quoted section

Edited by Mordred
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