Why does light have a finite speed?

[mfb]

none of these equations limit the speed of anything, but the don't say anything about an infinite speed also.

They do. They give the (maximal) speed of propagation of electromagnetic waves.

 

[PAllen]

Here's a reasonable derivation of light speed transmission from Maxwell's equations:

https://www.math.ucdavis.edu/~temple/MAT22C/!Lectures/10-MaxwellAndStokes-22C-S12.pdf

 

[pervect]

guys i think you miss something here.

none of these equations limit the speed of anything, but the don't say anything about an infinite speed also.

The solution to Maxwell's equations does limit the speed of light in a vacuum, and the speed at which any electromagnetic disturbances travel in a vacuum, this is well known.

I don't know why you state the contrary so often, I will assume that you are just not familiar with the proof.

The overview of the proof is this: the solution to any electromagnetic problem is a combination of "background" electromagnetic waves (which must move exactly at "c") plus the solution to the Lienard-Wiechert potentials of the charge distribution, http://en.wikipedia.org/w/index.php?title=Liénard–Wiechert_potential&oldid=612341886. Using the Lienard Wiechart potentials, one can use said potentials used to find the E and B fields themselves, in which case they are referred to "Jefimenko's equations", http://en.wikipedia.org/w/index.php?title=Jefimenko's_equations&oldid=598903545

You can find the exact expression in the Wiki quotes above, the point is that the solution for E and B depends at time and position (t,r) depends only on events within the past lightcone of (t,r), this is proved by the fact that the solution can be written as in integral of the electric and magnetic fields at the "retarded time" $t_r$.

 

[bhobba]

so how could Maxwell get an finite speed just from his equations.

Its easy.

His equations lead to a PDE that has a solution that is a wave that propagates at a finite speed eg:
http://web.mit.edu/sahughes/www/8.022/lec20.pdf

The only issue is the solution actually one nature avails itself of. And experiment says - yes.

Now from that solution it does not depend on the speed of the source. So we have a speed that is the same in any inertial reference frame. You try and catch up to such and it always moves away from you at the same speed - ergo that is the maximum speed that can be reached. As Wheeler says - forward is always forward.

Thanks
Bill

 

[lrhorer]

The fact that the speed of light is finite, like any fundamental fact of physics, comes from experimental evidence, not any theory or formula. Maxwell's equations are based on the fact that the speed of light is constant, not the other way around.

Hang on. First of all, there is a big difference between being finite and being constant. The two should not be confused, albeit far too often they are. (There's also a difference between being locally constant and universally constant.) Secondly, Maxwell did not based his formulation on the notion light or even EM waves had any particular velocity at all. It was well established before Maxwell came along the speed of light was not infinite, but he didn't take it into consideration. It was not known at all the speed of light in a vacuum was universally constant, and in fact it was assumed by everyone at the time the measured speed of light would depend on the proper motion of the observer. No one at that time even remotely dreamed there was in fact no such thing as proper motion or that the velocity of light would be absolutely constant irrespective of the frame of reference of the observer. That had to wait for 1905 to come along.

To me, the really interesting aspect of this is that when one performs the calculations for a wave based solution to Maxwell's equations, the observer dependent variables all evaporate, and one is left with a speed of propagation that is not relevant to any observer. The physicists of the day all believed Maxwell's equations to be perfectly valid, but they could not countenance the idea the speed of light could be observer independent. I submit one can hardly blame them, but their failure to understand the real nature of space and time caused them to posit and almost universally accept the perfectly incorrect notion of a luminiferous aether. When Michaelson - Morley came along, it really knocked the scientists of the day on their scholastic butts. The simple fact, however, is Maxwell's equations actually predicted the results of M-M, not the other way around. It's just that no one at the time understood the implications. In fact it took 18 years after M-M for someone to come along who actually understood how Maxwell's work predicted the results from M-M.

There are a great many people still today who cannot fathom it. I myself had no proper understanding of it as a physics undergraduate, even though I was able to perform the calculations with little trouble. I will never forget the moment when sitting in an empty classroom after the class had ended I had a very sudden epiphany. It was one of the most startling moments of my life, and in an instant the whole universe seemed to be expanding in front of me. I was dizzy and lightheaded. Had I not been sitting down, I think I should have fallen.

It's rather humorous, really, how badly the scientists of the day were mistaken, but the fact we need to remember is those people were not idiots. Not by a very long shot. Rather, they were misled by a very simple but fundamental ingrained bias of which they almost completely unaware. In short, they were making a false fundamental assumption, one which most did not even realize they were making. I feel that is an extremely important thing for every scientists to remember and take fully to heart.

With that in mind, I would like to pose the following question:

Is c really an immutably universal constant? Clearly, for SR and GR to be at all valid, it must be constant for every inertial reference frame, but that is emphatically not the same as saying the value of c must be precisely the same throughout the spatial universe, or for that matter in time. This is an assumption I have seen made time and again, and it is not appropriate to make the assumption, even if it is found to be empirically true. Although off-topic in this forum, I submit it is also very important to ask, "If it does indeed have precisely the same value throughout the cosmos, then why is its value constant throughout all of spacetime?"

 

[Bill_K]

Is c really an immutably universal constant?

The question has no meaning. c has dimensions, therefore one can always choose units in which c = 1.
The only quantities for which we can ask this question are dimensionless combinations such as the fine structure constant.

 

[PAllen]

Its easy.

His equations lead to a PDE that has a solution that is a wave that propagates at a finite speed eg:
http://web.mit.edu/sahughes/www/8.022/lec20.pdf

The only issue is the solution actually one nature avails itself of. And experiment says - yes.

Now from that solution it does not depend on the speed of the source. So we have a speed that is the same in any inertial reference frame. You try and catch up to such and it always moves away from you at the same speed - ergo that is the maximum speed that can be reached. As Wheeler says - forward is always forward.

Thanks
Bill

Source independence follows directly from the derive wave equation. However, that says nothing about about observer independence. One common belief in the late 1800s (when the source independent consequence was well understood) was that Maxwell's equations held exactly only in the Aether frame. This did not require abandoning the POR, any more than the observation that the speed of sound in air is observer dependent - air just provides a preferred frame for waves propagating in air. This preferred frame is not fundamental, it is just a feature of 'where the air is'. Similarly, frames with CMB isotropy are not considered preferred at a fundamental level.

Before MM, the biggest anomaly in the above understanding (that I am familiar with) was stellar aberration. The observations most naturally fit a corpuscular model with light speed affected by source speed. The attempts to make it work with source independence and Aether were all very strained, and admitted as such.

 

[lrhorer]

The question has no meaning. c has dimensions, therefore one can always choose units in which c = 1.
The only quantities for which we can ask this question are dimensionless combinations such as the fine structure constant.

That was not at all the point of the question. We can adjust the units any way we like. The question is not, "Will the numeric value of c change when we use different units to express it?" That is trivial. The question is, "Having chosen our units so that a measurement of c in a lab on Earth produces the number 1, is it true a measurement of c 10 billion light-years away will produce precisely the same value?" "At the beginning of time?" "Inside a black hole?"

 

[pervect]

Source independence follows directly from the derive wave equation. However, that says nothing about about observer independence. One common belief in the late 1800s (when the source independent consequence was well understood) was that Maxwell's equations held exactly only in the Aether frame. This did not require abandoning the POR, any more than the observation that the speed of sound in air is observer dependent - air just provides a preferred frame for waves propagating in air. This preferred frame is not fundamental, it is just a feature of 'where the air is'. Similarly, frames with CMB isotropy are not considered preferred at a fundamental level.

Before MM, the biggest anomaly in the above understanding (that I am familiar with) was stellar aberration. The observations most naturally fit a corpuscular model with light speed affected by source speed. The attempts to make it work with source independence and Aether were all very strained, and admitted as such.

It's worth pointing out that the Aether frame point of view says that Maxwell's equations don't apply in a non-Aether frame. So I would say the situation is that Maxwell's equations do impose a speed limit on light, and on other interactions, as per the mathematics, when one assumes that they apply.

Thus I do have to take exception with remarks such as

none of these equations limit the speed of anything

if one believes the equations are applicable, one solves them and finds that the speed of light is constant, and that cause and effect don't propagate outside the light cone. The issue of whether one believes the equations are always applicable, applicable only in one frame, or (to complete the logical possibilities) never applicable is a different question from the above remark.

A short summary of relativity might go as follows: It was noted that Maxwell's equations were not invariant under the Gallilean transformation, therefore it was believed that they could not , in general, be correct, that they could be correct only in one particular frame.

When it was realized that the Galilean transform should be replaced by the Lorentz transform, the issue disappeared, because Maxwell's equations are invariant under the Lorentz transform.

But this is an addition to my main point, which is that if one does assume the equations are valid, they DO impose a speed limit on light, and on the propagation of cause and effect in general.

 

[PAllen]

But this is an addition to my main point, which is that if one does assume the equations are valid, they DO impose a speed limit on light, and on the propagation of cause and effect in general.

All fine except this last statement. That the wave equation for sound gives it a fixed speed with respect to air (of given temperature and pressure) in no way says anything about other speeds or cause and effect. Similarly, no such conclusion can be drawn from Maxwell's equations without additional assumptions. I again note, that Newton already had noticed that his gravitation equation was not consistent with the known stability of orbits without instant action at a distance (he proposed this reluctantly, in deferral to what Nature was saying). Thus, scientists in the late 1800s would see no reason at all to couple the speed of light to causality. They would say such an assumption is counter to empirical evidence.

 

[lrhorer]

Similarly, no such conclusion can be drawn from Maxwell's equations without additional assumptions.

Absolutely, including ones that were not known through either empirical or hypothetical means at the time.

I again note, that Newton already had noticed that his gravitation equation was not consistent with the known stability of orbits without instant action at a distance (he proposed this reluctantly, in deferral to what Nature was saying).

I often reflect upon this. One could claim that Newton's courage failed him while Einstein's didn't. (After all, making a highly controversial statement does require a reasonable amount of courage at some level.) Yet the fact is Newton had neither the mathematical, empirical, nor theoretical means at his disposal to take the hypothesis to its eventual conclusion. Had he not made what was in effect a simplifying assumption, he might never been able to put it all together. Principia might never have happened.

Thus, scientists in the late 1800s would see no reason at all to couple the speed of light to causality. They would say such an assumption is counter to empirical evidence.

And they would have been absolutely correct, but completely mistaken. We should never, ever hold our breaths until such time as we have discovered everything there is to measure.

 

[Bill_K]

That was not at all the point of the question. We can adjust the units any way we like. The question is not, "Will the numeric value of c change when we use different units to express it?" That is trivial. The question is, "Having chosen our units so that a measurement of c in a lab on Earth produces the number 1, is it true a measurement of c 10 billion light-years away will produce precisely the same value?" "At the beginning of time?" "Inside a black hole?"

You can't be serious. This is, indeed, trivial.

Define your unit of length by the wavelength of H-alpha. Use c = 1 to define your unit of time. Not just on Earth, everywhere, and for all time. Every measurement of c in this system of units will produce precisely the same value, c = 1.

 

[nixed]

The Maxwell equations, formulated from the known properties of magnetism and of electricity, had propagating electro magnetic wave solutions. The equations predicted the speed of these waves on the basis of known (experimentally measured) magnetic and electrical properties of space ( the permeability and the permittivity). This predicted speed happened to coincide with the known (experimentally measured) speed of light. Hence the deduction that light was an electromagnetic wave described by the Maxwell equations. That the speed of light should be a fundamental constant for all observers was only subsequently discovered by experiment. (Michelson Morley) It was not anticipated from theory and was astonishing at the time.

 

[Phy_enthusiast]

funny way to look at its answer is that speed of light is a constant due to modern physics.

 

[MikeGomez]

funny way to look at its answer is that speed of light is a constant due to modern physics.

That is funny, and maybe true, but if the speed of light were not constant, then physicis would be a lot more difficult than it is.

 

[aabottom]

Here's some quotes from Einstein's 1905 paper, "ON THE ELECTRODYNAMICS OF MOVING
BODIES".

"... and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

...

"In agreement with experience we further assume the quantity
(2AB)/(t'-t)=c,
to be a universal constant—the velocity of light in empty space."

 

[PhilDSP]

The physicists of the day all believed Maxwell's equations to be perfectly valid, but they could not countenance the idea the speed of light could be observer independent. I submit one can hardly blame them, but their failure to understand the real nature of space and time caused them to posit and almost universally accept the perfectly incorrect notion of a luminiferous aether. When Michaelson - Morley came along, it really knocked the scientists of the day on their scholastic butts. The simple fact, however, is Maxwell's equations actually predicted the results of M-M, not the other way around. It's just that no one at the time understood the implications. In fact it took 18 years after M-M for someone to come along who actually understood how Maxwell's work predicted the results from M-M.

It could be worth spending some time to get to know the actual history. It sounds like you've been the recipient of some major disinformation. First of all, one of the first to understand and re-formulate the Maxwell equations (Maxwell died before his theory could really start to be understood), Oliver Heaviside, showed that an electron's field becomes compressed the faster it travels in relation to the measuring device until at the speed of light it becomes infinitely thin. And remember that George Fitzgerald originated the idea and published it in 1889 that lengths become compressed in the direction of travel relative to an emitter. You should also be aware that Henry Poincare effectively published most of SR with a slightly different expression but with more mathematical detail years before 1905.

P.S. An excellent long review of Maxwell's life and contributions is at

http://www.encyclopedia.com/topic/James_Clerk_Maxwell.aspx

"In classical optics Maxwell’s theory worked a revolution that is now rarely perceived. A popular fiction among twentieth-century physicists is that mechanical theories of the ether were universally accepted and universally successful during the nineteenth century, until shaken by the null result of the Micheslon-Morley experiment on the motion of the Earth through the ether. This little piece of textbook folklore is wrong in both its positive and its negative assertions."