Recent news reports from the world of science indicate one team working in a particle accelerator has clocked neutrinos traveling slightly faster than lightspeed. They are begging other teams to confirm or disprove this result independently, as is proper and normal in the business of science.

Commentators and experts have been weighing in on what such a result might mean, if confirmed to be true. “Everybody” points at Einstein (specifically his 1905 Special Theory of Relativity) to say that there is a speed limit these neutrinos seem to be violating. It’s either/or, not both.

Speed limit? That is an interpretation of Einstein’s theory, not a result. It is a very old interpretation, and I personally disagree with it. Here’s why:

In Einstein’s original 1905 paper, he sets up and solves the equations that describe the appearance of object A to an observer in reference frame B, moving at some relative but constant velocity V, when seen by light photons traveling at vacuum lightspeed c.

He did this for speeding subatomic particles, just like those neutrinos. Others since have extended the theory to large objects.

The theory postulates that c is a value which all observers measure as the same, no matter their motion, which really is something actually experimentally demonstrated with certainty. The theory’s mathematical results (sometimes called the Lorentz-Fitzgerald contraction equations) describe the object’s mass, dimension, and rate of time passage:

M = Mo/√(1-V^2/c^2) where M is what is seen and Mo is the resting value at V = 0

L = Lo*√(1-V^2/c^2) where L is what is seen and Lo is the resting value at V = 0

T = To*√(1-V^2/c^2) where T is what is seen and To is the resting value at V = 0

For these, M is the object’s mass, L its dimension in the direction of travel, and T is its local rate of time flow. Lateral dimensions are unaffected by V.

If one plugs a V greater than vacuum lightspeed c into these equations, the results are not real numbers, when a real-number result is what one seeks, being the only result that has meaning in the context of this problem. For almost a century now, the common interpretation has been that the not-real result means it is not possible to travel at speeds V exceeding vacuum lightspeed c. This is the origin of the common statement about “Einstein’s speed limit”.

When solving formulas in any branch of science and engineering, there are always fundamental assumptions about the problem, even if they are unspoken. Getting a not-real result with a modeling equation can nearly always be traced back to violating a fundamental assumption, even if it is not obvious.

Why should not-real results from Einstein’s theory be any different? What was his fundamental assumption that we violate when we plug in V greater than c in those equations?

Remember, the equations describe the appearance of object A to an observer in reference frame B. That presupposes that observer B can actually see object A (there it is!)

At V greater than c, we get a non-real result, which most likely simply means observer B cannot see object A, since we assumed he could. This interpretation is based on all those other experiences with formulas and problem-solving, and getting real versus not-real results.

When you think about it, how could observer B see object A traveling so fast? Object A is traveling faster than the photons with which observer B sees. The same sort of observational thing happens with supersonic aircraft: you cannot hear them coming because the sound waves by which you hear don’t arrive until much later.

Now, is the moving object A really heavier, shorter, and moving slower in time, or does he just look that way? How do you tell? You have to bring object A back to rest in observer B’s frame of reference.

Once the relative velocity V is back to zero, the equations say mass, length, and rates of time flow look completely normal and quite equal to both object A and observer B.

And furthermore, it does not matter who was really moving: V is relative only (that’s in part where the name of the theory came from).

Yet, somebody’s time flow rate really was slower. Their clocks (which are totaling devices, not rate of flow devices) will disagree. This is an experimentally validated and very certain result. Special Relativity does not resolve that problem, which is often called the Twin Paradox.

It is Einstein’s 1915 work on General Relativity that provides the answer: whoever did the accelerating to V and then back to zero is the one who experienced less total accumulated passage of time. Yet, his sense of time flow was entirely normal, to him, throughout the journey! This is the direct consequence of speed of light, not rate of time flow, being constant for all observers.

Could object A be observed if it were flying faster than light? To me, the equations say “no” with the not-real result; remember that they were derived on the assumption the object can be observed.

Could object A actually travel faster than light with respect to reference frame B? That’s a very good question! If the not-real result actually just means he cannot be seen, then that same not-real result says nothing about whether he can actually fly that fast!

So, that’s my maverick interpretation: Einstein says nothing about an actual speed limit. I seem to stand alone in this. But I always did like shouting from the corner that the Emperor has no clothes.

But, if I am right, we actually can travel faster than light, given sufficiently powerful technology. But, navigation will be hell if we see by photons, because the entire universe becomes unobservable!

We’re going to need some additional theory!

Update 12-21-11

The December 2, 2011 issue of “Science” (volume 334 issue 6060) has an interesting “News Focus” article on pages 1200-1201. This magazine is the peer-reviewed journal published by AAAS. The article title is “Where Does the Time Go?” and its topic line is “Superluminal Neutrinos”. There is now a lot of effort at a lot of places to either replicate the experiment or de-bug the procedures OPERA used to produce its faster-than-light results. Depending upon those outcomes, this result may never be explained. But this kind of activity is exactly what should be going on. The process of doing science really works.

The article describes the experimental concept as a simple timing across a fixed distance, although the elements of accomplishing that are not that simple. These are pulses of neutrino creation at one location correlated as pulses of neutrinos received at another location. Timing is by speed-of-light corrected GPS measurements, and by electrical transmission speed corrections in all the equipment. They are looking at how much the graphs of these pulses overlap.

One item questioned in the article is the GPS calibration, which really wasn’t done often enough. Countering the notion of miscalibrated GPS is the systematic time shift required to correct the calculated neutrino speed downward, when a more randomized error would be expected.

In the sixth paragraph (on page 1200) is an assumption the OPERA scientists made about the location where the neutrinos get created, of about a km delay. That assumption should be investigated. While the article says the error associated with it is “small”, it is a small effect we are arguing about (around 60 nanoseconds of time over a distance of about 700 km).

If it were a surveying error, the article says it would have to be on the order of 18 meters, which is not really credible. To me, this points right back to the creation-delay assumption.

It has been my engineering experience that 90+% of assumptions made are faulty or inappropriate. That why I suggest investigating assumptions first, or at least very high up on the priority list.

The other assumption that should be investigated is the interpretation of special relativity implying a speed limit, as discussed above. While not a popular topic in the physics community, it should still be done.

I would be delighted if the neutrinos were actually faster than light, and we needed some new theory. That would be a real breakthrough, and no telling where it might lead.

GW

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