Just How Fast is c?

There's currently a controversy in physics circles, caused by a group in Italy that were measuring the speed of arrival of neutrinos from Cern.

To the consternation of almost everyone in the physics community, they have reported (twice now) that neutrinos travel faster than the speed of light: By the miniscule amount of 0.0000025% (approximately).

Okay, that's pretty small. But the speed of light, c, is supposed to be exactly 299,792,458 meters per second (in our terms, 186,282.397 miles per second). Also in our terms, the neutrinos are 0.0047 miles per second too fast.

It is such a concern because much of our understanding of the universe is based on the idea that the speed of light is the absolute maximum speed with which anything (material or energy) can travel. So why would neutrinos be exempt?

Well, I've wondered about this for some time: Specifically, how do we know the speed of light? Looked at objectively, our measurement is surprisingly circular:

• How do we know how fast c is? We measured the speed of photons in vacuum.
  
  • Funny thing is, we also know that the speed of photons varies all the time. The speed varies by gravitational fields and density of matter in the vicinity.
    
  • So how do we know we got the right speed? Because that's the speed we measured. Circular.
    
• We know the speed is exactly 299,792,458 meters per second. Why? Because we defined the length of the meter as the distance light travels in exactly 1/299,792,458^th of a second. Circular.
  
• From the equation E=mc², we know that a certain amount of mass equates to a certain amount of energy.
  
  • Our energy units are defined in terms of the second, and the second ties back to the speed of light. In fact, the second is defined by counting the amount of time that it takes light to make a certain number of vibrations. Circular again.
    
  • Our mass units are now defined in terms of the second. Sigh.
    
  • Even if they weren't, and we could independently measure mass versus energy, we're talking about an error in our measurement of the conversion between the two of 0.0000000000000625%. That's right: Many more zeros. Remember, the equation contains c² and so any conversion discrepancy is squared as well. (When you square a number less than one, you get a smaller number: 0.1 squared is 0.01, for example.)
    

Basically, as it stands, we have no way to confirm that our computation of c is correct. We know how fast photons go alright. But to assume c is the same? All of our measures and our definitions are circular because they all come back to one measurement that we can't test against anything else.

I've thought for some time that the speed of c is suspicious. We are told that nothing with mass can go the speed of light. Photons have energy, and therefore mass, and so why are they exempt from the rule? The stock answer I've seen for this is that photons define c, and so they must by definition go c. Circular.

What speed does the universe consider to be c? We don't know. The only definition of c we have was measured from photons, and there's no objective reason to think that photons travel at c...except that we said so. Circular.

Now, suppose for just a moment that the real value of c is just a bit more than 299,792,458 meters per second, but that our "ideal" photons aren't so ideal after all, and can't quite get up to the real speed of c.

Maybe neutrinos can get closer. We know they have much less mass than the equivalent mass-energy of the photon. Makes sense that, not being so "fat", they can go a little faster.

I guess we'll see, as more experiments come in, but it won't surprise me if neutrinos set a new limit, even if the new limit is only 0.0000025% higher.

Update 01/28/2011

I was looking for a way to clarify this in a mathematical sense. Right now there is a broad assumption that there is only one C, as in:

• E = MC²
  
• C = speed of photons in vacuum
  

Let's temporarily assign subscripts to these, so that we have:

• E = MC_E²
  
• C_L = speed of photons in vacuum
  

The problem that I see is that there is no objective proof that:

C_E = C_L

Yes, it is easy to show that they are approximately equal, as in:

C_E ≅ C_L

But approximately equal (≅) is not the same as equal (=), and cannot serve as proof for equal. Given that we are talking about a few millionths of a percentage point, experimental error actually precludes proof of the equality. Now, let's assign another subscripted C for neutrinos:

C_N = speed of travel of neutrinos

Again, there is no objective proof that:

C_E = C_N

Since we cannot prove equality of any pair of these values, then we are left with no reason to think that the relationship between photon tranvel and neutrino travel is necessarily an equality. Perhaps the relationship is:

C_L < C_N

...and if this is true, then the neutrino experiment will be validated. If that experiment is validated, then it would suggest that the real relationship is:

C_L < C_N < C_E

Wouldn't that be a surprise? Even if it is only a few millionths of a percentage difference?

Update March 07, 2012

Well, it appears that the measured overspeed is due to a bad connection. That has nothing to do with my reasoning above; it just means that most of the physics community will go back to assuming C_E=C_L.