# How did light speed become the governor of relativity?

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Hi, I hope this is the appropriate forum.. pls move if not.

I've been trying to learn how light "speed" found its way into relativity. Doing a bit of Googling, I found a Wiki reference that says Newton suggested that light and matter are interchangeable. As a layman, I can sort of understand how that could be, but not how light "speed" impacts on that. Somewhat like F=ma (or F=mv2), if I understood how light speed fits into the picture, I can then vaguely understand why E=mc2 works. Am I right in seeing F=mv2 as analogous to E=mc2?

The history of such discoveries fascinates me. I'm slowly getting some of the math, but even the basics of many relativity equations still eludes me. Be patient with me.. ;)

F=mv^2 doesn't make sense. Check the units, they don't work out.

a is not equal to v^2 in any way.

The Principle of Relativity is that you can drink coffee in an aeroplane just as normally as you are stationary on the ground. It says if we have a frame in which the laws of physics look "standard", then the laws of physics will look the same in another frame moving at constant velocity relative to the first. The Principle of Relativity implies that the laws of physics have symmetry.

Newton's laws have a symmetry called Galilean invariance which implements the Principle of Relativity.

Research in electricity and magnetism by Ampere, Faraday and others led Maxwell to formulate his equations governing electromagnetism and light. It was noticed that Maxwell's equations don't have Galilean symmetry.

Does this mean the Principle of Relativity is violated? No. Maxwell's equations have a different symmetry called Lorentz invariance or Poincare invariance. That symmetry is also consistent with the Principle of Relativity.

Although the Principle of Relativity is consistent with both Galilean and Lorentz invariance, it is not consistent with them co-existing. This led Einstein and Planck to modify Newton's laws so that they had Lorentz invariance. Galilean and Lorentz invariance are indistinguishable at low speeds, which is why we had not noticed that Newton's laws are only approximate for more than 200 years.

It is possible that Lorentz invariance is also approximate. However no experiment has yet detected its failure.

Although the Principle of Relativity is consistent with both Galilean and Lorentz invariance, it is not consistent with them co-existing. This led Einstein and Planck to modify Newton's laws so that they had Lorentz invariance. Galilean and Lorentz invariance are indistinguishable at low speeds, which is why we had not noticed that Newton's laws are only approximate for more than 200 years.
Maybe in order to close the loop on the OP's question, you should have explicitly pointed out that Galilean invariance does not have the speed of light in it whereas Lorentz invariance does.

It was noticed that Maxwell's equations don't have Galilean symmetry.
This is a huge point. It made for a huge schism in physics at the end of the 19th century, much greater than today's schism between general relativity and quantum theory. Our schism is theoretical only. While physicists don't know how to rectify general relativity and quantum theory yet, physicists have not (as far as I know) detected a direct conflict between the two. On the other hand, the conflict between Maxwell's electrodynamics and Newtonian mechanics was not just a theoretical schism. It had been directly observed in experiments and confirmed in follow-on experiments.

Because it was such a deep schism, the best minds of the time worked on rectifying the two. One approach was to view the problems as pertaining to electromagnetic radiation only. This approach led to a rather unsatisfactory theory of relativity. It isn't taught today. Einstein chose to take Maxwell's equations at face value: The speed of light is the same to all observers. This simple acceptance of the basic concept shouted out by Maxwell's equations coupled with the relativity principle (the laws of physics are the same in all inertial frames) yields special relativity.

In hindsight, special relativity was there for any of the other people working in the area to see. They didn't see it because they couldn't let go of the cherished principles of Newtonian mechanics.

A side note: in fact there is not even a theoretical schism between GR and quantum theory. Our present view is that the standard model of particle physics is only an effective theory, with QED and the Higgs sector likely to fail at a very high energies. GR can be similarly incorporated into quantum theory as an effective field theory. I'm not entirely certain, but I believe GR is expected to fail at an energy above which the Higgs sector fails, but below which QED fails. This explains why there is no conflict between GR and particle physics.

A side note: in fact there is not even a theoretical schism between GR and quantum theory. Our present view is that the standard model of particle physics is only an effective theory, with QED and the Higgs sector likely to fail at a very high energies. GR can be similarly incorporated into quantum theory as an effective field theory. I'm not entirely certain, but I believe GR is expected to fail at an energy above which the Higgs sector fails, but below which QED fails. This explains why there is no conflict between GR and particle physics.

That sounds like a particle-physics view of GR as merely a field theory in Minkowski spacetime. However, a relativist's view would emphasize a curved-spacetime [with possibly nontrivial topologies], which looks Minkowskian in a small neighborhood.

What do you mean by "quantum theory" (which is distinct from "particle-physics")?

I think current formulations of "GR" and "quantum theory" have foundational differences, which is one of the reasons why Quantum Gravity hasn't been properly formulated yet.

Sorry, that "quantum theory" was my terminology. Some of ya'll get tweaked at calling the standard model etc. "quantum mechanics". To me they are all variations on the same non-classical theme, but that's perhaps because that entire part of my physics education has atrophied from lack of use. (I've been working as an aerospace engineer and systems engineer for the last 30+ years.)

That sounds like a particle-physics view of GR as merely a field theory in Minkowski spacetime. However, a relativist's view would emphasize a curved-spacetime [with possibly nontrivial topologies], which looks Minkowskian in a small neighborhood.

What do you mean by "quantum theory" (which is distinct from "particle-physics")?

I think current formulations of "GR" and "quantum theory" have foundational differences, which is one of the reasons why Quantum Gravity hasn't been properly formulated yet.

Yes, the formulation I had in mind assumes trivial spacetime topology. It further assumes that spacetime can be covered with harmonic coordinates (apparently, this assumption can be weakened if I correctly understand a comment in Weinberg's text, but I have never seen that elaborated). As I understand, there isn't observational evidence that requires one to go beyond these. I believe harmonic coordinates can penetrate the event horizon. Also, the equivalence principle can be derived in this framework, whereas minimal coupling isn't a real principle of GR, only background independence.

Sorry, that "quantum theory" was my terminology. Some of ya'll get tweaked at calling the standard model etc. "quantum mechanics". To me they are all variations on the same non-classical theme, but that's perhaps because that entire part of my physics education has atrophied from lack of use. (I've been working as an aerospace engineer and systems engineer for the last 30+ years.)

Well, I'm a biolgist, so I'm even more clueless about this. Weinberg does say that QM is more important than QFT, from which I gather he considers QFT a type of QM. In condensed matter, there is an exact equivalence between non-relativistic QM and non-relativistic QFT (roughly it's just a Fourier transform). So I think you were right on this.

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Einstein chose to take Maxwell's equations at face value: The speed of light is the same to all observers. This simple acceptance of the basic concept shouted out by Maxwell's equations coupled with the relativity principle (the laws of physics are the same in all inertial frames) yields special relativity.
How do Maxwell's equations shout out that the one-way speed of light is the same to all observers?

Hi, I hope this is the appropriate forum.. pls move if not.

I've been trying to learn how light "speed" found its way into relativity. Doing a bit of Googling, I found a Wiki reference that says Newton suggested that light and matter are interchangeable. As a layman, I can sort of understand how that could be, but not how light "speed" impacts on that. Somewhat like F=ma (or F=mv2), if I understood how light speed fits into the picture, I can then vaguely understand why E=mc2 works. Am I right in seeing F=mv2 as analogous to E=mc2?

The history of such discoveries fascinates me. I'm slowly getting some of the math, but even the basics of many relativity equations still eludes me. Be patient with me.. ;)

Actually, the speed of light is not properly named !

It should be named the "invariant speed".
And it happens that any zero-mass particle can only travel at the invariant speed.
It happens that it is also the speed of light. (photons have no mass)

Historically, light offered physicist the opportunity to discover the "invariant speed".
This is why it was called like that.
To be honest, still today, light is by far the best thing to measure this "invariant speed".
The recent FTL neutrinos story shows that quite well.
Also, very fast electrons in accelarators could be use to observe the "invariant speed", but in a much more difficult way.

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F=mv^2 doesn't make sense. Check the units, they don't work out.

a is not equal to v^2 in any way.
Oops.. I was getting confused with the formula for centrifugal force.

Actually, the speed of light is not properly named !

It should be named the "invariant speed".
And it happens that any zero-mass particle can only travel at the invariant speed.
It happens that it is also the speed of light. (photons have no mass)

Historically, light offered physicist the opportunity to discover the "invariant speed".
This is why it was called like that.
To be honest, still today, light is by far the best thing to measure this "invariant speed".
The recent FTL neutrinos story shows that quite well.
Also, very fast electrons in accelarators could be use to observe the "invariant speed", but in a much more difficult way.
This actually makes some sense to this novice.

Did Newton suggest that matter is interchangeable with light (or one can be converted to the other)? It made me think that, if that's so, then that would make light speed the "invariant speed" of matter, especially if there's no loss in the conversion. Kind of like if all the energy in a sample of matter is converted to light, then light speed represents some limit of the energy in that matter. I can't explain exactly how I think this other than it seems intuitively correct. And if so, then that would mean that the energy of a mass would be proportional to some factor of light and the size of the mass. Is that how E=mc2 came about?

Did Newton suggest that matter is interchangeable with light (or one can be converted to the other)?
You're thinking of Einstein, not Newton. And Einstein did not say that matter is interchangeable with light. He said that mass is a form of energy. Slight difference there.

What lalbatros was getting at was that a better name for the speed of light is the invariant speed of the universe. All photons must travel at c, not just the photons that happen to be in the visible range. More importantly, all massless particles must travel at c, not just photons. So calling c the speed of light is a bit restrictive. But it's the name we're stuck with.

Besides, "invariant speed of the universe" is a bit too wordy while "speed of light" is nice and succinct.

You're thinking of Einstein, not Newton. And Einstein did not say that matter is interchangeable with light. He said that mass is a form of energy. Slight difference there.
I got the info from this Wiki article:
"In 1717 Isaac Newton speculated that light particles and matter particles were inter-convertible..."
What lalbatros was getting at was that a better name for the speed of light is the invariant speed of the universe. All photons must travel at c, not just the photons that happen to be in the visible range. More importantly, all massless particles must travel at c, not just photons. So calling c the speed of light is a bit restrictive. But it's the name we're stuck with.

Besides, "invariant speed of the universe" is a bit too wordy while "speed of light" is nice and succinct.
Thanks for the clarification, it does help. :)

What I'm trying to understand, is how we got to the understanding of this "invariant speed". People have shown me λ calculations, which I've struggled to follow. I'm trying to understand the historical path. As I understand it at the moment, these steps may have been part of the journey:

1) Someone (Newton?) discovered the "inter-convertible" nature of light particles and mass particles. (How? I know of his experiments with light and prisms, but what led to his "speculation"?)
2) Sometime later, c was determined to be the max speed of anything in the universe. (How? And did it have something to do with "inter-convertibility" demonstrating max energy from matter or something of that nature?)
3) Did 1 and 2 impact on Einstein coming up with E=mc2? And is there a lay way of explaining it?

What I'm trying to understand, is how we got to the understanding of this "invariant speed".
It was determined experimentally. It was contradicting the simple Galilean transformation. So they had to find another transformation that keeps the speed of light unaffected:

This is the way I see it:
The more v, the more E (and vice versa). When v = c, and that's exactly where matter is converted to energy, v cannot go any higher and you get E = mc2.
That is not a good way to see it.

A massive object can never go at c. No matter how much energy is added to massive object (relative to some observer), that observer will never see the object moving at c. A better way to think of E=mc2 is that it is a lower bound on energy, not an upper bound. An object with zero velocity relative to some observer still has energy given by E=mc2. There is no upper bound on energy in special or general relativity.

It was determined experimentally. It was contradicting the simple Galilean transformation. So they had to find another transformation that keeps the speed of light unaffected:

The youtube video was wonderfully illustrative. The three effects made sense (shrinks moving objects, slows down moving clocks, breaks simultaneity) with the shrinking of moving objects being a great surprise.

How did they come to understand the need to keep the speed of light unaffected? Please excuse the ignorance, as I had wondered if it is a bit like how sound is compressed then stretched, like when an aircraft passes overhead, and possibly also accounts for Doppler effect.

How did they come to understand the need to keep the speed of light unaffected?
That's simply what you observe in the real world. The speed of EM-waves doesn't depend on the speed of the source. So the very same photon has the same speed in every inertial frame.
I had wondered if it is a bit like how sound
No, because sound has uniform speed only the rest frame of the medium. EM-waves have a uniform speed in all inertial frames.

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The title of the thread makes me laugh. I keep picturing c and γ in a presedential-style debate. Each asking supporters to contribute to their campaign, running vicious adds accusing the other of ties to Newtonian physics, and having illicit relationships with coordinates, etc. Finally the election results lead to a narrow victory for c who becomes the newly-elected governor of relativity.

Hi,

I was just wondering if "in a vacuum" is an essential part of the constant, C.
If Dark matter exists, doesn't this make a vacuum something that only exists in a laboratory, if anywhere at all? If there is no vacuum then there is no constant, if there is no constant ...

or is "c" just a mathematical concept like natural e

Yes, the measurement of the speed of light must be done in a vacuum or you will get the wrong value. I have no idea what dark matter has to do with the measurement of c.

The title of the thread makes me laugh. I keep picturing c and γ in a presedential-style debate. Each asking supporters to contribute to their campaign, running vicious adds accusing the other of ties to Newtonian physics, and having illicit relationships with coordinates, etc. Finally the election results lead to a narrow victory for c who becomes the newly-elected governor of relativity.

On the contrary, support from the Newtonian camp was crucial for their election hopes. They had to guarantee local Newtonism, otherwise no deal. The Newtonists were finally persuaded that relativity was OK, but they insisted it be NIMBY (not in my back yard). An ingenious compromise was found were relativity was not in anyone's back yard. It is in everyone else's back yard.

Back to the original post, the way the invariant light speed thing came up was this. Albert Einstein was bothered because Maxwell's equations had a strange asymmetry: if you moved a magnet relative to a conductor this was treated differently from moving that same conductor in the same way relative to the magnet. Ever since Galileo there had been symmetry like this, but with electricity and magnetism it didn't work. I'm sure many found this odd, but that was the way it worked. Albert discovered that if the newly-invented Lorentz transform was applied in combination with assuming the speed of light was constant in all reference frames then the asymmetry disappeared, and electric and magnetic fields may be considered to be the same thing.

The reason the simple Galileo transform didn't work was that the electrons were moving close enough to the speed of light to make a difference. This was the first time physicists had come across something like that.

The way I see this is that if the speed of light WEREN"T invariant it would be a real mess. Consider a hydrogen atom. The proton and electron attract, but they are attracted to the past of their counterpart, to where the other was a moment before. If this were asymmetrical depending on whom is going where then it complicates the situation even more. It would be the case that if the electron is heading toward the proton then the info going one way is faster than the info going the other way. I'm not sure what would happen then, but I think it would be much more complicated then what we have now. It could be that energy wouldn't be conserved, I'm not sure, but there would be all sorts of strange asymmetries that we don't have.

Albert later proved that there is this same "speed of light" delay in gravitational force. Nowadays most physicists think this speed limit applies to almost everything.

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Hi,

I was just wondering if "in a vacuum" is an essential part of the constant, C.
If Dark matter exists, doesn't this make a vacuum something that only exists in a laboratory, if anywhere at all? If there is no vacuum then there is no constant, if there is no constant ...

or is "c" just a mathematical concept like natural e

Yes, vacuum is important. Gravity matters too, so you can't have too much of that.

As for dark matter, the idea is that it is dark because it doesn't interact with light at all. If that is true, then it won't affect the speed of light.

The value is measured, unlike e which is calculated. No one knows why the value is what it is.

my point was that dark mater has mass and dark matter is all over the universe, so there is no such thing as a vacuum in nature. If the constant "C" is dependent on a vacuum and there is no such thing as a vacuum in space then how can we call it a constant? wouldn't all equations containing "C" be variable equations since "C" is not a constant?

my point was that dark mater has mass and dark matter is all over the universe, so there is no such thing as a vacuum in nature. If the constant "C" is dependent on a vacuum and there is no such thing as a vacuum in space then how can we call it a constant? wouldn't all equations containing "C" be variable equations since "C" is not a constant?

"dark matter is all over the universe"

Maybe yes, maybe no.

my point was that dark mater has mass and dark matter is all over the universe, so there is no such thing as a vacuum in nature.
Imagine if the universe were jam packed with dark matter, or completely void of dark matter. As far as light is concerned, there would be no difference between these hypothetical extremes and the universe as it is. Light does not interact with dark matter. Your argument is a red herring.

If the constant "C" is dependent on a vacuum and there is no such thing as a vacuum in space then how can we call it a constant? wouldn't all equations containing "C" be variable equations since "C" is not a constant?
This too makes no sense.

The value is measured, unlike e which is calculated. No one knows why the value is what it is.
Just a small nitpick. No one knows why the value of the fine structure constant is what it is. We know exactly why the value of c is what it is. The value of c is what it is because of our choice of units.

How do Maxwell's equations shout out that the one-way speed of light is the same to all observers?

Yes, if you know how to listen. All you have to do is cast them in the form of the wave equation.

Einstein chose to take Maxwell's equations at face value: The speed of light is the same to all observers. This simple acceptance of the basic concept shouted out by Maxwell's equations coupled with the relativity principle (the laws of physics are the same in all inertial frames) yields special relativity.
How do Maxwell's equations shout out that the one-way speed of light is the same to all observers?
Yes, if you know how to listen. All you have to do is cast them in the form of the wave equation.
It is my understanding that Maxwell used his equations to derive a solution with a wave speed equal to the speed of light which led him to suggest that the propagation of light relative to the absolute rest state of the ether could be determined by a suitable experiment with enough precision, so he obviously missed the shouting coming from his own equations that the speed of light is the same to all observers.

After it was determined that no such experiment could be done no matter what the precision, Einstein lumped Maxwell's equations in with his first postulate, the relativity principle, and coupled that with his second postulate, that light propagates at c to produce his Theory of Special Relativity. He even stated that these two postulates were "apparently irreconcilable" which doesn't sound like shouting out to me.

It is my understanding that Maxwell used his equations to derive a solution with a wave speed equal to the speed of light which led him to suggest that the propagation of light relative to the absolute rest state of the ether could be determined by a suitable experiment with enough precision, so he obviously missed the shouting coming from his own equations that the speed of light is the same to all observers.

After it was determined that no such experiment could be done no matter what the precision, Einstein lumped Maxwell's equations in with his first postulate, the relativity principle, and coupled that with his second postulate, that light propagates at c to produce his Theory of Special Relativity. He even stated that these two postulates were "apparently irreconcilable" which doesn't sound like shouting out to me.

One man's shout is the other man's whisper.

How do Maxwell's equations shout out that the one-way speed of light is the same to all observers?
Yes, if you know how to listen. All you have to do is cast them in the form of the wave equation.
It is my understanding that Maxwell used his equations to derive a solution with a wave speed equal to the speed of light which led him to suggest that the propagation of light relative to the absolute rest state of the ether could be determined by a suitable experiment with enough precision, so he obviously missed the shouting coming from his own equations that the speed of light is the same to all observers.
Maxwell was listening to too much shouting coming from elsewhere, "All wave phenomena require a medium. Everyone knows that!" and "The universe obeys Galilean invariance. Everyone knows that!", to hear the shouting from his own equations. One last bit of shouting is that physicists at Maxwell's time much preferred dynamics over kinematics. Special relativity is very much a kinematics theory.

For Maxwell to have derived special relativity he would have had to ignore all that shouting from elsewhere. Physicists in the latter part of the 19th century thought they were on the verge of a complete dynamical description of the universe. Ignoring the "Everyone knows that" type of shouting and back-stepping to a mere kinematics description was too much for the physicists of Maxwell's time, including Maxwell himself.

But in hindsight, it is still conceivable that Maxwell could have done this. He could have, for example, looked at just how ludicrous his concept of a luminiferous aether truly was (a non-solid that somehow supports transverse waves and somehow doesn't interact with ordinary matter) and saw how it was contradicted by the known phenomena of the aberration of light.

But in hindsight, it is still conceivable that Maxwell could have done this. He could have, for example, looked at just how ludicrous his concept of a luminiferous aether truly was (a non-solid that somehow supports transverse waves and somehow doesn't interact with ordinary matter) and saw how it was contradicted by the known phenomena of the aberration of light.
Yes, it is conceivable that Maxwell could have derived special relativity, if he hadn't died at such a young age, but he needed more than his equations. He needed Einstein's second postulate, which is not derivable from his equations, they were already covered in Einstein's first postulate and fully compatible with Lorentz's Ether Theory. That's my only point.