Reason behind speed of em waves being constant

1. Aug 18, 2013

dwellexity

Do we have any understanding as to why em waves have same speed in all inertial frames?

2. Aug 18, 2013

ghwellsjr

It's Einstein's second postulate, that's why, including that they propagate in all directions in any given inertial frame at the same speed independent of the source and that speed is the universal constant for the speed of light, c.

3. Aug 18, 2013

dwellexity

yes, i know that but what i am asking is that now this postulate has been confirmed by experiments, so don't we have any separate theory to explain this postulate?

4. Aug 18, 2013

ghwellsjr

First, why would we need a separate theory to explain the postulate? The postulate is what enables us to explain our experiments.

Second, there is no experiment that confirms Special Relativity and disaffirms the competition in vogue at the time that Einstein made his postulate, Lorentz Ether Theory.

5. Aug 18, 2013

Bill_K

If we did, would you want a theory to explain that theory?

6. Aug 18, 2013

vanhees71

In fact, that the speed of em.-wave propagation is identical with the limit speed, $c$ has not deeper theoretical reason in contemporary physics, i.e., the standard model of elementary particles. In the language of QFT it's the masslessness of the photon which is an assumption in the standard model that has no deeper theoretical reason but is a very precisely measured fact about nature. The boundary for the photon mass according to the particle data booklet is $m_{\gamma}<10^{-18} \; \mathrm{eV}$.

In the framework of relativistic QFT a massless spin-1-boson, however, is necessarily described as a gauge field, if you make the usual assumptions locality, micro-causality, and boundedness of the Hamiltonian from below, leading to a Poincare covariant definition and unitarity of the S-matrix. The physics reason is that a massless particle with spin $s$ has only two polarization-degrees of freedom (e.g., in terms of helicity $\lambda \in \{\pm s\}$) but a vector representation (spin 1) of the Poincare group has three polarization-degrees of freedom, and in the realization with a vector field you have even four field degrees of freedom, and you have to get rid of the unphysical degrees of freedom. There's also a more satisfactory explanation based on the representation theory of the Poincare group, as you can read in my QFT manuscript:

http://fias.uni-frankfurt.de/~hees/publ/lect.pdf

The em. field is described within the standard model as an Abelian gauge field (based on the gauge group U(1)). In this case, you can even introduce a finite mass without violating renormalizability, using the socalled Stückelberg formulation for a massive vector field, leading to a renormalizable theory for a massive vector field if this is treated as a gauge field, i.e., only minimaly coupled to a conserved current. Also the massless limit can be taken in this formulation without running into trouble (provided infrared and collinear singularities are resummed properly).

On the other hand this means that there is no restriction from the fundamental symmetries underlying the standard model that would demand that the photon be massless.

Only for non-Abelian massive gauge fields one has to invoke the Higgs-Kibble-Guralnik-Hagen-Englert-Brout mechanism, leading to at least one additional massive spin-0 boson (the Higgs boson).

7. Aug 18, 2013

Staff: Mentor

There's no completely satisfying answer to this sort of "why" question. As Bill_K points out, even if we had a theory to explain the theory, we'd still need a theory to explain the theory that explained the theory, and so on ad infinitum. So in practice we decide to accept some things as postulates rather than following the infinite "why" chain.

Nonetheless, nature has given us some pretty strong hints that the constant speed of light is a "good" postulate, one that we can be comfortable accepting and building on. My favorite hint: you can calculate the speed at which light travels from Maxwell's laws of electricity and magnetism, and indeed this was known decades before relativity. It seems somewhat reasonable to assume that the laws of electricity and magnetism should be the same for all inertial frames (for example, we don't expect them to change with the seasons, even though the velocity of the earth and the experimenter changes by many miles a second over the course of a year), and hence that the speed of light will be the same in all inertial frames.

Of course, "seems reasonable" is somewhat in the eye of the beholder. Much of the second half of the 19th century was spent trying to develop theories that did not assume a constant speed of light yet were consistent with Maxwell's laws. The simple clean ones didn't match experimental observations; the complex ones that do match experiment contain unsatisfying and counter-intuitive assumptions and don't work as a base for further development.

8. Aug 19, 2013

tom.stoer

Historically this was Maxwell's theory of electromagnetism from which unique and invariant c follows. But today we understand this theory as one field theory build on top of SR and therefore being Lorentz covariant by construction.

So we do not have an explanation in terms of a different or more fundamental theory.

9. Aug 19, 2013

CompuChip

Actually, some of those experiments predate the postulate. Michelson and Morley conducted their famous 'failed' experiment as early as 1887 which was a major reason for many physicists (notably, Einstein) to start thinking about this stuff.

10. Aug 19, 2013

tom.stoer

In general this might be true, and I think this is the impression one may get, but especially regarding Michelson and Morley there is a debate whether Einstein was even aware of this experiment!

But historically the root cause is Maxwell's theory which was established and confirmed decades earlier.

11. Aug 19, 2013

harrylin

Here you confound two different things; perhaps this is due to even some textbooks confounding them.

1. Reason behind the speed of EM waves being a constant: that's the second postulate. Einstein motivated this on the basis of Maxwell's theory: it's a basic property of waves to have a constant speed, independent of the speed of the source.

2. Why EM waves have the same speed in all inertial frames: That "constancy" between different frames is called invariance; it follows from the first postulate (called relativity principle) if one considers the second postulate as law of nature. This invariance has also been deduced from the second postulate together with conservation of energy and momentum.

SR simply starts with those things as postulates as they were suggested by experience (experiments).

12. Aug 19, 2013

vanhees71

Einstein himself once wrote that he was not aware of the Michelson-Morley result when writing up his famous paper in 1905. However, this was written some 40 years later, and it is not so clear whether Einstein remembered right, what he has read and has had in mind before writing his paper "On electrodynamics of moving bodies". In this paper he doesn't cite a single reference

Indeed, he gives a symmetry argument as a motivation for his investigation of space-time structure (translation mine):

"It is well known that Maxwell's electrodynamics, as it is interpreted today, leads to asymmetries which do not seem to be observed phenomenologically, if it is applied to moving bodies. E.g., one might think about the electromagnetic interaction of a conductor with a magnet. The observed phenomenon depends only on the relative motion between the conductor and the magnet, while according to the usual interpretation one has to strictly dependent between the different cases whether the one or the other is moving. Is the magnet moving and the conductor at rest, around the magnet an electric field of a certain value of energy is building up, which -at places where the parts of the conductor are located- produces an electric current. Is, however, the magnet at rest and the conductor moving, there is no electric field around the magnet but an electromotive force is created in the conductor, which does not correspond to an energy, but leads to the same electric currents in the conductor, provided the relative motion is the same in both cases considered."

On the other hand in the next sentence he says:

"Examples like this, and the failed attempts to measure the motion of the earth relative to the "light medium", lead to the conjecture that there are no phenomena related to the notion of absolute rest not only applies to mechanical but also to electromagnetic phenomena." (highlighting mine)

Unfortunately Einstein doesn't give a reference (BTW there are no references at all in that whole paper!) for such attempts to measure the relative motion to the ether. So we cannot say with certainty which "failed experiments" he had in mind.

13. Aug 19, 2013

harrylin

He certainly knew Poincare's "La Science et l'hypothèse" of 1902 which he appears to paraphrase there. In that book Michelson's experiment is not mentioned by name, as far as I can see; however the theoretical consequences of that type of experiments that failed to determine the motion of the Earth are discussed in detail. And in particular he mentions Fitzgerald's hypothesis, which as we know related to Michelson-Morley.

[addendum:] It's also worth mentioning that Einstein learned electrodynamics directly from Lorentz's papers, and some of Lorentz's papers happen to mention that Michelson-Morley experiment by name (others mention their repeat of the Fizeau experiment). If he saw those citations, possibly he did not pay much attention to them.

Last edited: Aug 19, 2013
14. Aug 19, 2013

ghwellsjr

The issue here and the salient point of Einstein's contribution is that time and space are relative in his theory in a manner unlike in any other previously published theory. That aspect comes out of his second postulate and is not something that can be discovered or learned or proved by any experiment. If Einstein (or anyone else) had not come up with this brilliant insight (the second postulate), then we could still be using only theories that affirmed concepts of an absolute time and absolute space and there would be nothing wrong with those theories.

15. Aug 19, 2013

vanhees71

Yes, as far as I remember right, reading Einstein's contribution to Schilpp's "Einstein, philosopher scientist" book, he mentions that he studied Lorentz. I'm not sure whether he mentioned Poincare. I have to get this book again and check.

16. Aug 19, 2013

harrylin

His study by means of Lorentz's papers was archived in an exposition in Bern: his teacher could not find a good textbook that included the latest developments, therefore he told Einstein to use Lorentz's papers instead. His reading and discussing of Poincare's work is mentioned by Pais ("Subtle is the Lord"), based on the declarations of one of the members of the Olympia Academy. See also http://en.wikipedia.org/wiki/Olympia_Academy

And in order not to loose track of the question of the OP: Einstein motivated both postulates as being based on or supported by experimental evidence at the time of inception. In his 1905 Electrodynamics paper he mentions experiments that suggested the relativity principle; and in a 1907 paper on the relativity principle he motivates the light postulate by the success of the Maxwell-Lorentz theory to explain experiments.

Last edited: Aug 19, 2013
17. Aug 19, 2013

Staff: Mentor

Citations do make life easier for historians of science, don't they?

I believe that by the beginning of the 20th century, there was enough awareness of the awkward fit between Maxwell's electrodynamics and Galilean relativity that Einstein didn't need to spend a lot of time explaining what the problem was. His intended audience already had the necessary context, so he could just toss out a few terse paragraphs to describe the great unsolved problem of the second half of the 19th century.

18. Aug 19, 2013

rbj

i really think that the burden of explanation rests on those who would postulate the contrary.

why should the laws of nature be different for some inertial observer in comparison to another inertial observer (that happens to be moving relative to the first observer)? both have equal claim to being an observer "at rest".

19. Aug 19, 2013

nix00

In fact, we have a theory to explain this postulate, special relativity simply. The second postulate of Einstein for special relativity is a natural consequence of the others postulates (principle of relativity and causality) when considering an homogeneous and isotropic space-time : it can be shown that under these assumptions, a speed limit exists and is generally taken as c the speed of light in vacuum. I just know a book in French which shows it "relativité restreinte ; bases et applications ; cours et exercices corrigés (2e édition) Bernard Semay, Claude Silvestre-Brac".

20. Aug 19, 2013

harrylin

Please explain how the principle of relativity and/or causality are broken by Newton's mechanics.

21. Aug 19, 2013

nix00

they are not broken, they are considered also in Newton's mechanics, in a weak form.
The fact is that when you consider Newton's equations, in an absolute referential, they are invariant under the Galilean transformations, which is fine. But Maxwell's equations are invariant under Poincare transformations, from which the Galilean ones are a limit case, when you consider small velocities. The Poincare transformations are derived from the principles of special relativity, which allows one to consider electromagnetism in this framework, but without gravitation. Gravitation is simply not considered in the theory of special relativity, both theories are "unified" in general relativity.

22. Aug 19, 2013

harrylin

You talk about Maxwell's equations. Maxwell's theory is wave theory and as such it includes the second postulate as basic assumption; together with the PoR that leads to c as the limit speed. With only the PoR and causality, Newton's mechanics and ballistic light theory do not predict a limit speed. As this is definitely off topic here, I won't say more; there have been threads that explain that issue in more detail.

23. Aug 19, 2013

nix00

I am not sure to understand your point harrylin.
I was trying to answer the question by saying that naturally in an homogeneous and isotropic space-time, under the principles, it exists a maximal speed, and you get the Poincare transformations which relate two inertial frames, moving in an uniform and linear way with respect to each other.
Maxwell's equations which define the propagation of an electromagnetic wave are also invariant under the Poincare transformations (respecting the principle of relativity) and therefore the speed of a particle in one frame will be related to the speed of this same particle in the other one by these transformations. It happens that to match with the observations, the maximal speed is defined as the speed of a light-like particle : v_max=c, the speed of light in the vacuum which is constant (by the way, the speed of light in an environment depends of the properties of the environment). Therefore, any photon will travel in any inertial referential with the same max speed which is c : yes it was a postulate, but it can be explained by special relativity.
Newton's mechanics is defined such that the gravitational force will affect the linear and uniform motion and therefore will affect the laws of transformation between two inertial frames, but it never says that neither the principle of causality, neither the principle of relativity are broken : at the contrary, Newton's equations are written in the same way in any inertial referential, and two referential are related by the Galilean transformations.
It's this contradiction between Newton and Maxwell's laws and their laws of transformation (symmetry) which leads people as Einstein and Poincare to think about special relativity, which explains again, why the speed of light can be constant in each referential.

24. Aug 20, 2013

harrylin

That looks fine to me, as you now included the words "wave" and "Maxwell".

25. Aug 20, 2013

Staff: Mentor

I disagree with this as stated. The speed of light is a result of Maxwells equations, not an assumption. You seem to like historical accounts so I would think that would be clear to you from Hertz's work.