The question is - is there any flaw in this explanation, or it is the right explanation in general language?

Let me break the explanation into two parts -

  1. Why there is a certain speed of electromagnetic waves (which happens to be $c$)?

Speed of any wave is property of the medium through which it travels. So, it is property of empty space that electromagnetic waves travel at a certain speed (no more, no less). It is a property, not a limit. If it was a limit, then light (or EM) could travel at < c through empty space. But it travels exactly at c, in empty space. So, it is a property. If you have problem with this explanation, then you should also have problem with - sound having a certain speed through air, and need to go to more basic level. If you accept a certain speed of sound, I will expect you to accept this property in case of EM waves as well. The value of this property happens to be c. (Per modern physics, the EM waves are fields that have a property that they propagate exactly at c through empty space. It is still a property, not a limit).

A lot of people are objecting to space being a medium. My questions on this is - what are ripples in space. If space can - 1. curve, 2. it can distort, 3. it can expand, 4. it can tell mass how to move, 5. it can fall into a black hole and carry light with it, why it can not be a medium?

  1. Why any material body (or, a collection of massive fields) can not move faster than $c$?

This is a direct consequence of (1) and so, turns out to be a limit. (It is limit because bodies can move at any speed as long as it does not exceed c)

Let us consider how do we increase speed of a mass - we apply a force on it. For example, we can make a standing car move by pushing it with our hands. The electrons in our hands, and the ones in the car (where we touch it) repel each other and that repulsive force causes increase in the speed of the car. Suppose you were running at your maximum speed and a car passes by you at 300 miles/hour. Can you increase speed of the car by pushing with your hands when it passes by you? Answer is no (a normal human being can not move the hands faster than 300 miles/hr). To increase the speed of a moving body, the force has to act on it faster than the speed of the moving body.

Any force we apply to accelerate a body, the force is ultimately exerted on the body as one of the fundamental forces. All the fundamental forces themselves travel at c. Just as example, electromagnetic force propagate at the same speed as EM waves i.e. c. For simplicity let us agree that all fundamental forces propagate at c as a property per (1) Therefore they can not increase speed of any material body that is already moving at a speed of c to > c.

Note that the forces have to travel faster than c through space in order to cause a speed greater than c. But we know they move at c. So even the fundamental forces become ineffective for a body that is already moving at c.

Even if the force emanates very next to the moving body, to act on the body, it has to travel through space and because the body is already travelling through space at c, the force can not reach the body through space. Even if it did (because it emanated inside the body itself), it still has to act through space and can not increase the speed of the body to more than its own speed.

The forces become ineffective in the direction of movement of the body at c. They are still effective in other directions and , so body can be slowed down etc.

Therefore, speed of propagation of fundamental forces is a property (not a limit). This property has highest value in empty space which happens to be c. And, nothing can propagate faster than the forces themselves - what will cause anything to do so? Speed of forces (a property just like speed of sound) turns out to be a speed limit for material bodies. Which should not be any mystery.

May I also comment that in particle accelerators, they use the electric/magnetic fields to accelerate the particles and obviously can not accelerate them faster than c. Even accelerating them to very close to c will be very challenging.

  • $\begingroup$ I think your main problem is that you are trying to find an explanation for relativity from a classical (19th century) point of view which perceived fields as phenomena that are being carried by some sort of matter, while in reality it's the other way around, matter is a consequence of the fields. $\endgroup$ – CuriousOne Feb 11 '16 at 7:30
  • $\begingroup$ Actually, I did not mention that anywhere, if I did indirectly, please point out where. All I am saying is the fields (forces) act on material bodies through space at c. Material bodies as we know them. They being as consequence of fields, or vice a versa, does not seem to be subject in this explanation. $\endgroup$ – kpv Feb 11 '16 at 7:38
  • $\begingroup$ You wrote "Speed of any wave is property of the medium through which it travels.", which seems you are thinking of the vacuum as a medium. That's pretty much the viewpoint which one can find in the works of Maxwell and other 19th century physicists. Only after the search of the aether turned up nothing did the opposite viewpoint establish itself. Matter fundamentally breaks Lorentz symmetry, so it does matter which comes first. Nature seems to clearly establish that there is a fundamentally Lorentz symmetric vacuum which is populated by massless and massive fields. $\endgroup$ – CuriousOne Feb 11 '16 at 7:46
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    $\begingroup$ It is classical description, so it can be old. So, seems matter as we know, is collection/combination of fields of which at least some are massive fields. The force fields act on the massive fields to accelerate them. Is it ok. If so, material bodies can be read as collection of massive fields (and may be also some mass less ones). The fact remains that a force field acts on "anything massive" to accelerate and it does so at c. And anything massive can not be accelerated to > c by something which itself acts at c. That is what I have tried to say in laymen's language. I will edit accordingly. $\endgroup$ – kpv Feb 11 '16 at 8:02
  • $\begingroup$ The point is that you don't have to go trough a loop using matter to argue that Lorentz symmetry won't allow you to accelerate beyond c. It's all there in the basic symmetry of the vacuum. That's similar to us not having to construct perpetual motion machines which we then prove to be non-working to know that energy is conserved. $\endgroup$ – CuriousOne Feb 11 '16 at 8:46


There is no "classical" explanation...

The speed of light is given by: $$ c = {1 \over {\sqrt {\mu_0\epsilon_0}}} $$

$\mu_0 = $ permeability of free space, $\epsilon_0 = $ permettivity of free space

So this simple equation shows that the speed of light depends on the ability of free space (i.e., the vaccuum) to support electric and magnetic fields. If the speed of light were markedly smaller than it actually is, (say 1000 $ms^{-1}$) then that would require magnetic and electric fields to propagate far more strongly than they do. This would have enormous consequences for the formation of atoms, for example, and the universe would be entirely different (stars and biology would probably be impossible).

And that's without considering the second point:

Relativity: the equation above says nothing about the relative speeds of observers - $c$ just depends on fundamental parameters of nature. So therefore $c$ must be the same for all observers. Once you grasp that, Special Relativity is the inescapable consequence.

So the speed of light and SR are just consequences of a couple of fundamental constants.

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    $\begingroup$ The question is not about why the limit is c. It is about why there is any limit at all? whatever it is. Calculation of c is not part of it. The question is also not about what would have happened if it was different from c. As far as I know, Relativity does not remove the limit, or changes it. Upper limit remains irrespective of whether you think relativistic or otherwise. $\endgroup$ – kpv Feb 11 '16 at 15:46
  • $\begingroup$ The explanation above does say why there is a limit... $\mu_0$ and $\epsilon_0$ define an invariant speed. The existence of an invariant speed leads to SR. SR defines a maximum speed (any speed $> c$ is unphysical). So it is all consistent. $\endgroup$ – Oscar Bravo Feb 12 '16 at 7:47

Speed of any wave is property of the medium through which it travels. So, it is property of empty space that electromagnetic waves travel at a certain speed (no more, no less).

The vacuum is not a medium. With a medium the propagation speed is related to the bulk and/or Young's modulus depending on the wave type. That's why it's a property of the medium. The vacuum does not have any moduli so your argument fails at this step.

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    $\begingroup$ Just to be on the same page, I wrote empty space, not vacuum. But I guess you mean the same. If space can - 1. curve, 2. it can distort, 3. it can expand, 4. it can tell mass how to move, 5. it can fall into a black hole and carry light with it blah blah .. it got to have some modulus - we may not know what it is, that is different issue. We know it is not ether but it may be something that we do not know otherwise how it can exhibit all the above behavior most of which get mention in GR. Am I missing something here? $\endgroup$ – kpv Feb 11 '16 at 9:41

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