Why light can travel at c?

[Tiny_Explorer]

Will the existence of tachyons break relativity ? Why light doesn't have mass at most quantum level ? How to mix them up( Quantum mechanics+ Relativity )

 

[Matterwave]

Re: the title

$c$ is defined as the speed of light in vacuum.

Will the existence of tachyons break relativity ?

Define "break relativity". Tachyons would have very weird properties. They wouldn't be able to slow down to the speed of light or below. If you could observe them, they'd appear to go backwards in time in certain reference frames. Etc.

Why light doesn't have mass at most quantum level ?

Ultimately, the fact that light is massless is observed via experimentation.

If one insisted on finding a reason from theory, it would be that electroweak symmetry breaking leads to massive weak interaction bosons (W,Z) and a massless EM interaction boson, the photon. But the theory was built to explain the observation. And the details are complicated and very difficult to explain at a high school level.

How to mix them up( Quantum mechanics+ Relativity )

Quantum Field Theory

 

[Ibix]

Faster than light communication leads to causal paradoxes in relativity - search "tachyonic anti-telephone" for a simple demonstration of this.

I don't think we know why light is massless, and you can write a quantum theory where it has mass (Proca did so). We mostly use it as a test theory to put experimental upper bounds on the mass a photon could have ($<10^{-50}\mathrm{kg}$, IIRC).

We already have relativistic quantum theories - that's what quantum field theory is. What we don't have is a quantum theory of gravity.

 

[Tiny_Explorer]

Re: the title
Define "break relativity". Tachyons would have very weird properties. They wouldn't be able to slow down to the speed of light or below. If you could observe them, they'd appear to go backwards in time in certain reference frames. Etc.

According to relativity, you can't break speed of light,but tachyon does , did it break relativity ? We do not have a good experimental setup in world to find tachyon ?

 

[Ibix]

There is no evidence of the existence of tachyons, and no theories we have currently require them AFAIK. They are an intellectual exercise only.

If we ever found evidence that particles that move faster than light existed we would need to understand how relativity could co-exist with them. How that would work would depend on the actual properties of the particle.

 

[pines-demon]

Will the existence of tachyons break relativity ? Why light doesn't have mass at most quantum level ? How to mix them up( Quantum mechanics+ Relativity )

Let's improve the quality of this site. We usually ask for effort, what have you searched before? Tell us about your knowledge about the subject, do you know relativity? QFT? what do you really find puzzling, can you be specific?

 

[Dale]

According to relativity, you can't break speed of light,but tachyon does , did it break relativity ? We do not have a good experimental setup in world to find tachyon ?

What is actually forbidden is for a massive particle to travel at or faster than c, for a massless particle to travel faster or slower than c, and for a tachyon to travel at or slower than c. So tachyons work fine with the actual rule, it is just that the rule is more complicated than a simple “speed limit”.

Why do you think we would have any difficulty detecting tachyons? Most likely our failure to detect them is because they don’t exist

 

[Herman Trivilino]

Re: the title

c is defined as the speed of light in vacuum.

Well, you can change the definition to the maximum or invariant speed. Then the question becomes why does light travel at this same speed?

 

[Matterwave]

Well, you can change the definition to the maximum or invariant speed. Then the question becomes why does light travel at this same speed?

That the speed of light is invariant is a postulate of the theory of special relativity. As such, it needs no deeper explanation beyond "we observed it in the laboratory".

If one asks "why does light in particular travel at that invariant speed?" then the answer would be because light is massless and anything massless travels at that speed.

 

[Herman Trivilino]

That the speed of light is invariant is a postulate of the theory of special relativity.

The postulate is that the speed of light is independent of the speed of the source.

It follows of course that that speed must therefore be invariant.

Einstein himself was particularly interested in experimental evidence that might show that the speed of light coming from distant astronomical sources might depend on the speed of those sources. Of course, no such evidence has ever been found

Even if it were determined that the speed of light is not invariant, nothing about the theory would change. We would simply refer to $c$ as the invariant or maximum speed instead of the speed of light.

Of course it would then follow that a pulse of light is not massless.

A similar thing happened in recent decades when neutrino oscillations showed that neutrinos are not massless and therefore do not travel at speed $c$, solving the solar neutrino mystery.

 

[PeterDonis]

The postulate is that the speed of light is independent of the speed of the source.

I'm not sure that's the postulate. The formulations I've seen state it as there being an invariant speed (and light travels at that speed because anything massless does), without saying anything about the speed of the source.

It follows of course that that speed must therefore be invariant.

How does this follow?

Einstein himself was particularly interested in experimental evidence that might show that the speed of light coming from distant astronomical sources might depend on the speed of those sources. Of course, no such evidence has ever been found

This is true, but it's not the same as the postulate being what you claim.

 

[vela]

I'm not sure that's the postulate. The formulations I've seen state it as there being an invariant speed (and light travels at that speed because anything massless does), without saying anything about the speed of the source.

In his original paper, Einstein stated the second postulate as, "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body." That's also how I recall it being stated in various intro texts.

 

[sbrothy]

I think the neutrino/photon comparison is, if not rigorous, then at least a fun thought experiment. Of course I know nothing about anything but your thread is going to keep me occupied for weeks!

Broglie’s new conceptipn of light

 

[Matterwave]

Of course it would then follow that a pulse of light is not massless.

See the second half of my post.

A similar thing happened in recent decades when neutrino oscillations showed that neutrinos are not massless and therefore do not travel at speed $c$, solving the solar neutrino mystery.

I have to be pedantic here... sorry, neutrinos were my area of research all those many years ago.

Neutrino oscillations show (squared) mass splittings. The quantities which show up in flavor oscillations are the squared mass splittings $\Delta m^2_{21},\Delta m^2_{31}$ and not the eigenmasses themselves. It is still possible that the lightest mass eigenstate is 0.

Further, the full solution to the solar neutrino problem requires the MSW effect. This is a resonance effect of adiabatic neutrino flavor transformations. Averaged vanilla (vacuum) oscillations don't account for the full deficit.

 

[Herman Trivilino]

I'm not sure that's the postulate.

See Post #12. That is also the way I remember it and it's on Page 1 of the linked source.

How does this follow?

If the speed of the light beam is independent of the speed of the source then no matter how fast the source is moving relative to you, you will observe the same speed for the light beam. All others, regardless of their speed relative to that same source, will observe the same speed for the light, too. It's the same speed for all observers. It's invariant because it doesn't vary with the speed of the observer relative to the source.

 

[PeterDonis]

In his original paper, Einstein stated the second postulate as, "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body." That's also how I recall it being stated in various intro texts.

Ah, ok, I had forgotten that last qualifier in Einstein's paper. I don't remember it being stated in Taylor & Wheeler, at least not the version I learned from many years ago, but my memory might be inaccurate; it's been quite some time since I last looked at that text.

There is a more modern approach that derives the existence of an invariant speed from considerations of spacetime symmetry. I can't remember the specific reference right now, but it's been discussed in previous PF threads. The gist of it is that spacetime symmetry considerations lead to one of two possibilities: either there is an infinite invariant speed (Galilean invariance) or there is a finite invariant speed (Lorentz invariance). That in itself does not establish, if we take the second option, that light travels at the finite invariant speed, but of course deriving that from the fact that light has zero invariant mass is straightforward. That derivation says nothing about the speed of the emitting body, nor is any such requirement necessary.

 

[PeterDonis]

It's invariant because it doesn't vary with the speed of the observer relative to the source.

No, that in itself is not enough. For example, the speed of sound is independent of the speed of the emitter relative to you (the frequency of the sound varies, but the speed does not), but it's not invariant; its speed relative to you is different depending on your speed relative to the medium in which the sound is propagating, and the medium has a definite rest frame.

 

[PeroK]

www.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Here's a derivation from first principles.

That seems a more modern approach than was possible in 1905.

 

[PeterDonis]

www.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Here's a derivation from first principles.

That seems a more modern approach that was possible in 1905.

This is the kind of derivation I was referring to in post #16.

 

[PeroK]

I think, from a logical point of view, the invariance of the speed of light is equivalent to both original postulates. Strictly speaking, in might not be possible to derive invariance from the second postulate alone. There are two postulates, in any case.

 

[Herman Trivilino]

No, that in itself is not enough. For example, the speed of sound is independent of the speed of the emitter relative to you (the frequency of the sound varies, but the speed does not), but it's not invariant; its speed relative to you is different depending on your speed relative to the medium in which the sound is propagating, and the medium has a definite rest frame.

Then I don't know. Perhaps the assumption of a lack of a medium is also required? Or perhaps it's as @PeroK says, the first postulate is also required?

 

[PeterDonis]

Perhaps the assumption of a lack of a medium is also required?

In the original version by Einstein, yes, I think something like that was implicitly being assumed.

The more modern derivation from spacetime symmetries, as in the reference @PeroK gave, also requires that no medium is present when you get to the point of deriving that light moves at the invariant speed because it's massless. But there the assumption of no medium being present has an obvious role, because we already know light in a medium doesn't move at the invariant speed, so we're not expecting our derivation to apply when a medium is present.

 

[Matterwave]

www.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Here's a derivation from first principles.

That seems a more modern approach than was possible in 1905.

One thing (not necessarily a bad thing) with physics proofs is they always depend somewhat on some shared concepts and definitions. So, pinpointing the exact "these are the assumptions / postulates" is always a bit tricky.

From reading that paper, I see the following 3 postulates (maybe not everyone agrees with me):

1. All inertial reference frames are equally valid (often called "the principle of relativity").
2. (Minkowski) Spacetime is homogenous (invariant under translations). In order to deduce the transformations are linear (and can be expressed as matrix eqns for example).
3. (Minkowski) Spacetime is isotropic (same in all directions) in order to assert $\gamma_{-v}=\gamma_v$.

The rest seems like algebra to me. So the claim of the paper, in my own words, is that homogeneity and isotropy of spacetime can be used as substitutes for the postulate of the constancy of the speed of light.

But notice 2 additional things:

1. The proof leans on group structure. This is a mathematical assumption. I'm ok with reading only the physical assumptions, but not everyone would read it like me.
2. The proof does some extra work to get to $a=-c^2$ to get back the actual Lorentz transformations.

I don't think it's universal that such a set of postulates is regarded as "deeper" or "better". The fact of the matter is we observe light speed to be constant/invariant via experimentation.

 

[Herman Trivilino]

In the original version by Einstein, yes, I think something like that was implicitly being assumed.

I remember reading a journal article many years ago where the author discussed why Einstein wrote the second postulate in that weaker form, but I don't recall the details.

 

[Nugatory]

In his original paper, Einstein stated the second postulate as, "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

I believe that the Einstein's statement of the postulates shouldn't be considered a question for physicists but instead for historians - history of science is an interesting and important discipline, but it's not the same discipline as the science itself. "Independent of the motion of the source" is jarring to the modern ear, so much so that even with his own words under our nose we might assert that that's not the second postulate. But at the end of the 19th century it provided the explicit rejection of Galilean relativity (by rejecting Galilean addition of velocities) that was needed at the time.

 

[Dale]

I believe that the Einstein's statement of the postulates shouldn't be considered a question for physicists but instead for historians

Indeed, the seminal author of some theory has the first word on the theory, not the last. Subsequent authors can and should improve on it.

On the other hand, it is reasonable for a person to cite the original. So while I personally also wouldn’t put the “independent of the source” part in either, I think @Herman Trivilino is justified in doing so.

 

[javisot]

What source exists for light in a vacuum?

 

[Herman Trivilino]

What source exists for light in a vacuum?

The sun?

 

[Herman Trivilino]

I believe that the Einstein's statement of the postulates shouldn't be considered a question for physicists but instead for historians - history of science is an interesting and important discipline, but it's not the same discipline as the science itself.

Agreed. But to see how his 2nd Postulate leads to the invariance of $c$ seems an exercise in physics itself, and even if it is only of historical interest, perhaps it can lead to a deeper understanding of the physics.

So let me give it another try. The speed of light in a vacuum is independent of the speed of the source. So regardless of how the source moves relative to an observer, the observer will measure $c$ for the speed of light. If we now invoke the 1st Postulate we can claim that the above scenario is equivalent to saying that regardless of how the observer moves relative to the source, the observer will measure $c$ for the speed of light.

Now, why Einstein chose to word his 2nd Postulate the way he did is perhaps purely of historical interest, but I seem to recall that there is some physics in there. But that's just a vague recollection. In Einstein's theory the invariance of $c$ is a conclusion rather than an assumption. Thus making it easier to verify experimentally? Or perhaps making it easier to justify theoretically?

 

[PeterDonis]

perhaps it can lead to a deeper understanding of the physics.

I think a deeper understanding of the physics comes from looking at a more modern derivation based on spacetime symmetries, such as @PeroK referenced. This shows that Einstein's 2nd postulate was really not necessary; you can get to the existence of an invariant speed which must be independent of the speed of the source without having to just assume any of those things a priori. In other words, his formulation, while it worked fine at the time, is not the most parsimonious formulation.