Faster than Light

Superluminality. Finally!

  1. Faster than Light
  2. Why not Discard Special Relativity?
  3. Bye Bye Einstein

CERN has published news about some subatomic particles exceeding the speed of light, according to BBC and other sources. If confirmed true, this will remove the linchpin of modern physics — it is hard to overstate how revolutionary this discovery would be to our collective understanding of world we live in, from finest structure of matter to the time evolution of the cosmos. My own anarchical mind revels at the thought of all of modern physics getting rewritten, but I also have a much more personal stake in this story. I will get to it later in this series of posts. First, I want to describe the backdrop of thought that led to the notion that the speed of light could not be breached. The soundness of that scientific backdrop (if not the actual conclusion about the inviolability of light-speed) makes it very difficult to forgo the intellectual achievements of the past one hundred years in physics, which is what we will be doing once we confirm this result. In my second post, I will list what these intellectual achievements are, and how drastically their form will have to change. The scientists who discovered the speed violation, of course, understand this only too well, which is why they are practically begging the rest of the physics community to find a mistake in this discovery of theirs. As it often happens in physics, if you look for something hard enough, you are sure to find it — this is the experimental bias that all experimental physicists worth their salt are aware of and battle against. I hope a false negation doesn’t happen, for, as I will describe in my third post in this series, if confirmed, this speed violation is of tremendous personal importance to me.

The constancy (and the resultant inviolability) of the speed of light, of course, comes from Einstein’s Special Theory of Relativity, or SR. This theory is an extension of a simple idea. In fact, Einstein’s genius is in his ability to carry a simple idea to its logically inevitable, albeit counter-intuitive (to the point of being illogical!) conclusion. In the case of SR, he picks an idea so obvious — that the laws of physics should be independent of the state of motion. If you are in a train going at a constant speed, for instance, you can’t tell whether you are moving or not (if you close the windows, that is). The statement “You can’t tell” can be recast in physics as, “There is no experiment you can device to detect your state of motion.” This should be obvious, right? After all, if the laws kept changing every time you moved about, it is as good as having no laws at all.

Then came Maxwell. He wrote down the equations of electricity and magnetism, thereby elegantly unifying them. The equations state, using fancy vector notations, that a changing magnetic field will create an electric field, and a changing electric field will create a magnetic field, which is roughly how a car alternator and an electric motor work. These elegant equations have a wave solution.

The existence of a wave solution is no surprise, since a changing electric field generates a magnetic field, which in turn generates an electric field, which generates a magnetic filed and so on ad infinitum. What is surprising is the fact that the speed of propagation of this wave predicted by Maxwell’s equations is c, the speed of light. So it was natural to suppose that light was a form of electromagnetic radiation, which means that if you take a magnet and jiggle it fast enough, you will get light moving away from you at c – if we accept that light is indeed EM wave.

What is infinitely more fundamental is the question whether Maxwell’s equations are actually laws of physics. It is hard to argue that they aren’t. Then the follow-up question is whether these equations should obey the axiom that all laws of physics are supposed to obey — namely they should be independent of the state of motion. Again, hard to see why not. Then how do we modify Maxwell’s equations such that they are independent of motion? This is the project Einstein took on under the fancy name, “Covariant formulation of Maxwell’s equations,” and published the most famous physics article ever with an even fancier title, “On the Electrodynamics of Moving Bodies.” We now call it the Special Theory of Relativity, or SR.

To get a bit technical, Maxwell’s equations have the space derivatives of electric and magnetic fields relating to the time derivatives of charges and currents. In other words, space and time are related through the equations. And the wave solution to these equations with the propagation speed of c becomes a constraint on the properties of space and time. This is a simple philosophical look on SR, more than a physics analysis.

Einstein’s approach was to employ a series of thought experiments to establish that you needed a light signal to sync clocks and hypothesize that the speed of light had to be constant in all moving frames of reference. In other words, the speed of light is independent of the state of motion, as it has to be if Maxwell’s equations are to be laws of physics.

This aspect of the theory is supremely counter-intuitive, which is physics lingo to say something is hard to believe. In the case of the speed of light, you take a ray of light, run along with it at a high speed, and measure its speed, you still get c. Run against it and measure it — still c. To achieve this constancy, Einstein rewrote the equations of velocity addition and subtraction. On consequence of these rewritten equations is that nothing can go faster than light.

This is my long-winded description of the context in which the speed violation measured at OPERA has to be seen. If the violation is confirmed, we have a few unpleasant choices to pick from:

  1. Electrodynamics (Maxwell’s equations) is not invariant under motion.
  2. Light is not really electromagnetic in nature.
  3. SR is not the right covariant formulation of electrodynamics.

The first choice is patently unacceptable because it is tantamount to stating that electrodynamics is not physics. A moving motor (e.g., if you take your electric razor on a flight) would behave differently from a static one (you may not be able to shave). The second choice also is quite absurd. In addition to the numeric equality between the speed of the waves from Maxwell’s equations and the measured value of c, we do have other compelling reasons why we should believe that light is EM waves. Radio waves induce electric signals in an antenna, light knocks of electrons, microwaves can excite water molecules and cook food and so on.

The only real choice we are left with is the last one — which is to say SR is wrong. Why not discard SR? More reasons than a blog post can summarize, but I’ll try to summarize them any way in my next post.

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