Why does light have a finite speed?

[adoion]

hy,

there is nothing in Maxwells equations that would limit the speed of light.

the only way one can get light speed, is to assume that em waves solve Maxwells equations and then one gets c as the square root of something out from Maxwells equations.

the same goes for gravity waves, only observation makes one assume that space does not adjust immediately to change of mass distribution.

am i wrong in this assumption or is there something that comes out of the math, that limits light waves??

 

[HallsofIvy]

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.

 

[mfb]

The universe could have an infinite speed of light - it would have completely different physics then (because current quantum field theory would not work without special relativity), but I don't think this is an issue. We just do not happen to live in such a universe, as experiments show.

 

[adoion]

ok thanks for the answer.

but isn't it strange that as you assume wavelike solutions for his equations that you get the speed of propagation for the wave as the speed of light?

 

[mfb]

No. Why?
As HallsofIvy explained, the Maxwell equations were made to match electromagnetism. It would be strange (or just bad physics) if electromagnetic waves would not agree with the wave-like solutions of those equations.

 

[adoion]

ok thanks you guys are the best

 

[stevendaryl]

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.

It depends on what you mean by "based on". Maxwell's equations were not developed as a way of describing light--it wasn't known that light was electromagnetic. Maxwell's equations were developed as a way of describing electricity and magnetism in a unified way.

 

[stevendaryl]

No. Why?
As HallsofIvy explained, the Maxwell equations were made to match electromagnetism. It would be strange (or just bad physics) if electromagnetic waves would not agree with the wave-like solutions of those equations.

But it wasn't known at the time of Maxwell that light was electromagnetic, was it?

 

[HallsofIvy]

The question was about the fact that the speed of light is finite- that we do not instantaneously see what happens a long distance away. That was known by experimental evidence long before Maxwell's equations. Yes, you can argue that the speed with which any electromagnetic waves propagate at the speed of light (and so at finite speed) is due to Maxwell's equations but that was not the original question.

 

[phyzguy]

But it wasn't known at the time of Maxwell that light was electromagnetic, was it?

Probably you know the history, but I think it is worth reviewing it. Maxwell himself hypothesized that light was electromagnetic in nature. After adding the displacement current term to the known equations of electricity and magnetism, he realized that the equations then supported transverse waves. He calculated the speed of such waves from the known electric and magnetic constants, and found it to be roughly equal to the speed of light, which as HallsofIvy said was known empirically. Maxwell said, "We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

In my mind the fact that light "drops out" of the empirically determined equations of electricity and magnetism was one of the most fundamental syntheses in all of physics. I don't think it's true to say, as HallsofIvy did, that , "Maxwell's equations are based on the fact that the speed of light is constant, not the other way around." Maxwells' equations were developed to explain electricity and magnetism, and light (with a finite speed) "appeared" as a consequence.

 

[PeterDonis]

there is nothing in Maxwells equations that would limit the speed of light.

the only way one can get light speed, is to assume that em waves solve Maxwells equations and then one gets c as the square root of something out from Maxwells equations.

You don't *assume* that em waves solve Maxwell's equations. You *discover* that em waves solve Maxwell's equations--more precisely, they solve Maxwell's equation with zero source. You don't have to assume it; you can prove it.

the same goes for gravity waves, only observation makes one assume that space does not adjust immediately to change of mass distribution.

No, you don't assume that; you *discover* that gravitational waves solve the Einstein Field Equation--again, more precisely, they solve the source-free linearized EFE.

is there something that comes out of the math, that limits light waves??

Yes. A signal propagating at infinite speed does not solve Maxwell's Equations.

 

[HallsofIvy]

No, you don't assume that; you *discover* that gravitational waves solve the Einstein Field Equation--again, more precisely, they solve the source-free linearized EFE.

But how do you "discover" that when no one has ever even detected "gravitational waves"?

 

[UltrafastPED]

But how do you "discover" that when no one has ever even detected "gravitational waves"?

It was a discovery based on the model; Einstein (IIRC) found this solution early on. The calculations based on gravitational radiation match very well to the binary pulsars PSR B1913+16, discovered in 1974. See http://en.wikipedia.org/wiki/PSR_B1913+16

Gravitational waves have not yet been detected directly (except perhaps by the BICEP2 experiment), but are expected any time (year?) now.

So only direct verification is currently lacking.

 

[PeterDonis]

But how do you "discover" that when no one has ever even detected "gravitational waves"?

As UltrafastPED says, I meant "discover" in the sense of discovering a mathematical solution. Maxwell discovered that electromagnetic waves traveling at the speed of light were solutions of the source-free Maxwell Equations the same way.

 

[atyy]

hy,

there is nothing in Maxwells equations that would limit the speed of light.

the only way one can get light speed, is to assume that em waves solve Maxwells equations and then one gets c as the square root of something out from Maxwells equations.

the same goes for gravity waves, only observation makes one assume that space does not adjust immediately to change of mass distribution.

am i wrong in this assumption or is there something that comes out of the math, that limits light waves??

As phyzguy and PeterDonis have pointed out - there is something that comes out of the Maxwell's equations that limits the speed of light waves.

 

[kurros]

The speed of light in Maxwell's equations is inversely related to the product of the permeability and permittivity of the vacuum (constants). So it is interesting to see what happens if one of these is taken to zero, so that the speed of light goes to infinity.

If we take the permittivity to zero, then Gauss' law gets weird. It seems to say that the tiniest electric charge would create an infinitely strong electric field. So that seems bad.

If we take the permeability to zero, it looks like nothing could ever create a magnetic field. That seems more physically plausible at least. Electric fields would never have any curl either... slightly odd but maybe it is ok, since the electric field lines radiating from point charges would be always perfectly straight.

So in conclusion, I wager that if the speed of light were infinite, there would be no magnetic fields in our universe :). Which I guess means there would be no light either :p.

 

[adoion]

As phyzguy and PeterDonis have pointed out - there is something that comes out of the Maxwell's equations that limits the speed of light waves.

yes but that's strange isn't it.

basically what the displacement current says is that a rate of change of a electric field produces a magnetic field.
the same goes for Faradays law, a change in magnetic field makes an electric field.

the thing to see here is that the consequences of changing a magnetic or an electric field are manifested immediately. that is when the magnetic field changes i get immediately a electric field of some configuration and the same goes for changes of electric fields.

the only reason why a wave would propagate at a finite speed is if there would be a delay in the creation of both of those fields.

is this what's happening?

 

[bhobba]

there is nothing in Maxwells equations that would limit the speed of light.

You are looking at it the wrong way.

The rock bottom essence of SR is symmetry, specifically the symmetries of the POR. From that alone you can derive SR:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

It predicts an invariant speed - it may be infinity - but it wasn't put in at the start, and it appears.

Now assuming this speed and the Coulomb law you can actually derive Maxwell's equations:
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm

What this means is the the constant C in Maxwell's equations is the constant C of the Lorentz equations. It represents one of the most elegant determinations of the invariant speed in the Lorentz transformations confirmed by countless experiments.

Thanks
Bill

 

[adoion]

You are looking at it the wrong way.

The rock bottom essence of SR is symmetry, specifically the symmetries of the POR. From that alone you can derive SR:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

It predicts an invariant speed - it may be infinity - but it wasn't put in at the start, and it appears.

Now assuming this speed and the Coulomb law you can actually derive Maxwell's equations:
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm

What this means is the the constant C in Maxwell's equations is the constant C of the Lorentz equations. It represents one of the most elegant determinations of the invariant speed in the Lorentz transformations confirmed by countless experiments.

Thanks
Bill

lets say you have a point charge in empty vacuum and nothing else.

this charge will have associated with it a electric field witch is present in all of space.
an magnetic field will not be present if that particle is not moving.

1. first question, moving with respect to what? and that's a really good question.

now let's say it moves with respect to your frame of reference centered in you, that is with respect to you.

if this charge now moves an infinitesimal distance in one direction, then we will have immediately a magnetic field associated with it.

the induced magnetic field will depend on the particles speed and its charge, and it must build up gradually since the particle must still use an infinitesimal amount of time to travel the infinitesimal distance it can't do it immediately.

2. is this maybe the source for the finite speed of radiation, that it can't be infinite because one would have to move an object at infinite speed to create an immediate sensible change in the field?

but then again there is also a solution to Maxwells equations with no charges and no currents.

 

[mfb]

@kurros: No magnetic fields would also make Newtonian mechanics work exactly, and we would not need special relativity. That would be a universe where the low-velocity limit of our universe is exact for all speeds.
It would also mean no mass differences from binding energy. And it would not have protons or neutrons in the way we know them. Annihilation processes would not work in the same way they work in our universe, and basically everything else in particle physics would be different as well.

 

[PeterDonis]

the consequences of changing a magnetic or an electric field are manifested immediately. that is when the magnetic field changes i get immediately a electric field of some configuration and the same goes for changes of electric fields.

The consequences of a changing magnetic or electric field are only manifested immediately *at the point where the change occurs*. The effects of the change are *not* manifested immediately at a point spatially distant from the point where the change occurs; they propagate at the speed of light.

 

[PeterDonis]

this charge will have associated with it a electric field witch is present in all of space.
an magnetic field will not be present if that particle is not moving.

1. first question, moving with respect to what? and that's a really good question.

Moving with respect to the detector that is detecting the fields. A detector at rest relative to the charge will only detect an electric field. A detector moving relative to the charge will detect a magnetic field as well.

if this charge now moves an infinitesimal distance in one direction, then we will have immediately a magnetic field associated with it.

"Immediately" at the location of the charge, yes. But if the detector is spatially distant from the charge, then it will not detect a magnetic field until a time $t = d / c$, where $d$ is the distance from the charge to the detector. In other words, the information about the change in the field due to the change in the charge's state of motion propagates at the speed of light.

but then again there is also a solution to Maxwells equations with no charges and no currents.

Yes, because, as you noted in a previous post, changes in the fields themselves produce changes in the fields: a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. But again, the information about these changes propagates at the speed of light. In fact, that's what an EM wave propagating at the speed of light *is*: information about changing fields.

 

[X338]

I'm not sure the op's question was answered, but there's a hypothesis based on a paper published by European researchers last year that it's the quantum vacuum that determines the speed of light.

Basically as photons travel from point A to point B they have to interact with the virtual particles in their the way (kind of like a person on a crowded sidewalk) and while traveling they're continually absorbed and re-emitted by those virtual particles. And as a result have a certain speed in a vacuum, in this case c.

Paper link: http://arxiv.org/abs/1302.6165

 

[bhobba]

if this charge now moves an infinitesimal distance in one direction, then we will have immediately a magnetic field associated with it.

Relativity is actually the origin of the magnetic force as shown by the fact relativity and coulombs law determines Maxwell's equations. But even aside from that simply consider a current. From relativity and length contraction its charge density in a moving frame is greater so a moving charge feels an extra force. This is the magnetic force and where it comes from.

The induced magnetic field will depend on the particles speed and its charge, and it must build up gradually since the particle must still use an infinitesimal amount of time to travel the infinitesimal distance it can't do it immediately.

is this maybe the source for the finite speed of radiation, that it can't be infinite because one would have to move an object at infinite speed to create an immediate sensible change in the field?

You have put the cart before the horse. Relativity is a theory about space-time geometry. Obviously that is more fundamental than EM effects - its the very stage physical phenomena take place in. Its symmetry properties determines the Lorentz Transformations and its geometry - that's the import of the link I gave on its derivation from group theory which is the natural language of symmetry. It is that geometry (specifically 4 dimensional space-time geometry) that determines the properties of EM fields including the existence of magnetic fields.

Its not talked about much these days but there was once this very influential program called the Erlangen program:
http://en.wikipedia.org/wiki/Erlangen_program

Its ramifications are still being felt in physics to this day. In fact Einstein, although he probably didn't really realize it at the time, was really the first to place geometry and symmetry at centre stage in physics.

Thanks
Bill

 

[bcrowell]

Yep, bhobba has it right -- took the words out of my mouth :-)

 

[bhobba]

Yep, bhobba has it right -- took the words out of my mouth :-)

Its surprising to me why people still don't get that one.

I can only presume its from not reading the modern literature.

To that end I recommend the book I learned it from by Rindler:
https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20

Thanks
Bill

 

[kroni]

I forgot the name of the book i read, i don't have pointers but Einstein prove that an infinite speed of light imply that the causality is not respected. So if you want causality you need a finite speed of light. Why 300000km\s ? it's another problem.

 

[mfb]

An infinite speed of light does not respect causality in special relativity. Causality with an infinite speed of light would be fine if we would live in a Newtonian universe.

 

[adoion]

guys i think you miss something here.

Maxwells equations are supposed to output the speed of light just from the assumption that his equations hold, Maxwell did get the speed of light from his equations and then connected this to the speed of light and not the other way around.

the first one tells how electric fields are generated from static charge.

second one says how magnetic fields are generated from static current, that is they are not created at all since there are no static currents.

third one says how electric field is created from a changing magnetic field

forth one says how magnetic fields are created from currents of charge and from a changing electric field.

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

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

there must be some damping or delay mechanism for an finite speed to be applicable to light.

if you take sound waves for example why does sound have finite speed?

 

[PeterDonis]

none of these equations limit the speed of anything

You are leaving out a crucial factor: all of these equations are equations relating the fields and charges/currents at the same event in spacetime. That's why no "speed" is apparent to you in the equations: the charges/currents are determining the fields at the same spacetime point, so the concept of "speed of propagation" has no meaning.

But suppose I want to know the effect of charges/currents at spacetime point A, on the fields at spacetime point B, which is separated from A. Then it's not sufficient just to look at Maxwell's Equations at one point; I have to come up with a solution that applies to the entire region of spacetime between A and B. But the charges/currents can be *changing* in that region, so just looking at the equations on the assumption that the charges/currents are fixed isn't enough. You have to come up with *functions* on spacetime, describing the charge/current distribution and the fields, that satisfy Maxwell's Equations at *every* point in spacetime (or at least in the region of spacetime you're interested in).

And in the process of doing all that, you will find that changes in the charges/currents at one point of spacetime do not instantly affect the fields everywhere else; the effects of those changes propagate through spacetime at the speed of light. No extra ingredient has to be added to Maxwell's Equations for this to happen; it happens automatically when you look for solutions using the process I've described above.

The general term for the process I've been describing is "solving the initial-value problem". Unfortunately I can't find a good quick reference online, but I believe it's discussed in the major textbooks on electrodynamics.

 

[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."