Friday, September 23, 2011

Faster than light Neutrinos? Not so fast!





Yes, I have read the news that a team associated with CERN and based in Switzerland, is claiming the detection of neutrinos travelling faster than light. If correct, it would indeed overturn one of the foundational precepts of modern physics: that no material object can exceed the speed of light. But the $64 question is whether it's true or a belief based on premature data. (In any case, to be accepted, the results will have to be confirmed by independent groups!)

Let's also not forget we've had these 'false starts' before. In 2007, a team at Chicago's Fermilab believed they had similar faster-than -light results only to learn subsequently their findings couldn't be taken very seriously because the margins of error were so great that they extended to the insignificant!

Earlier, in a paper appearing in the journal Nature, in July 2000, physicists at the NEC Research Institute in Princeton, New Jersey claimed to have "broken the limit set by the speed of light". They achieved this by firing a laser pulse into a glass chamber filled with a cesium (Cs) atom vapor. NEC’s Lijun Wang, in fact, insisted he’d created an experiment in which light speed was not merely exceeded by an added increment, but by a factor of three hundred! This meant that an almost identical light pulse exited the chamber and traveled about sixty feet before the main part of the laser pulse finished entering the chamber, Wang said.

Needless to say, this flouts well-known accepted axioms of causality. (Wherein causes are assumed to precede effects). The problem also was that the experiment has never been confirmed, so we take it with more or less a grain of salt.

Basically, in this new experiment, CERN fired a neutrino beam from a particle accelerator near Geneva to a lab 454 miles away in Italy. In so doing it travelled 60 nanoseconds faster than the speed of light, defined to be at 186,282 mi./sec. The CERN team calculated the margin of error at 10 nanoseconds, which made the result statistically significant. Evidenlty also, appreciating the enormity of the find, they spend months checking and re-checking their results. According to one University of Bern physicist, Antonio Ereditato:

"We have not found any instrumental effect that could explain the result of the measurement"

Maybe so, but that doesn't mean we instantly accept it. Recall the hallowed halls of science are littered with experiments that appeared to prove or show some fantastic phenomenon or violation of normal physical laws, but could never be confirmed. One of them was the claim for cold fusion, by Pons and Fleischmann in the late 90s, which would have revolutionized the energy industry. But no one could replicate it and it was later found that they had not taken into account all the experimental errors that migh have led to heat being evolved.

Recall (from the last instalment of 'Introducing Special Relativity), that by the work -energy theorem:

W = K(f) - K(i)

K(i) = 0 (u = 0)

K(f) = m(o)c^2/ [(1 - u^2/c^2)^½ ]

Where in this case, K(f) would be the kinetic energy acquired by the neutrinos en route to the lab in Italy. We assume the neutrinos start from rest, so K(i) = 0 and u = 0 at that point.

Here we would need to find the velocity, u. If one knows in advance the rest mass m(o) of the particular species of neutrino (there are three types: electron, mu and tau) than one can obtain u by using:


K(f) = (m'/ m(o))

where m' denotes the enhanced mass over m(o)

For example:

The normal rest mass of an electron = 0.511 MeV (Millions of electron volts)

Then, if the rest mass is found to be 3.25 MeV while undergoing K(f) one can find u. We have:

K(f) = (3.25/ 0.511) = 6.36x the rest mass

So: E = 6.36mc^2 = mc^2/ [(1 - u^2/c^2)^½ ]

and:

6.36 = 1/ [(1 - u^2/c^2)^½ ] or:

(1 - u^2/c^2) = 1/(6.36)^2 = 1/40.44

or: u^2/c^2 = 1 - 0.0024 = 0.9976

u = [0.9976c^2]^½ = 0.9987c

Note that even such a large increase doesn't translate into superluminal velocity for the electron. Now we know the three species of the neutrino have rest masses as follows:

Electron neutrino: less than 8 eV

Mu neutrino: less than 250 keV

Tau neutrino: less than 35 MeV

Let's just deal with the last and assume for the sake of argument m(o) = 30 MeV. Then we ask what it would have to be to even be at the speed of light.

In performing the computations one would find (and I leave this as an exercise for ambitious readers) that no matter how high the enhancement of the rest mass you cannot obtain a superluminal velocity.

Even if the tau neutrino mass had increased to 10 million MeV this would not disclose a superluminal speed. One would have:

K(f) = (10^6 MeV/ 30 MeV) = 3.33 x 10^4 the rest mass

whence:

3.33 x 10^4 = 1/ [(1 - u^2/c^2)^½ ]

or:

(1 - u^2/c^2) = 1/(3.33 x10^4)^2 = (9 x 10^-10)

u^2/c^2 = 1 - (9 x 10^-10) = 0.9999

u = 0.9999c

What would yield a superluminal speed? Well, an imaginary mass! Let's take the example of the earlier electron again, and allow an imaginary rest mass of 3.25i MeV (E.g. employing the imaginary number, i). Then:

K(f) = (3.25i/ 0.511) = -6.36i over the rest mass of 0.511 MeV

So: E = -6.36i (mc^2) = mc^2/ [(1 - u^2/c^2)^½ ]

6.36 i= 1/ [(1 - u^2/c^2)^½ ] or:

(1 - u^2/c^2) = 1/(6.36i)^2 = 1/(- 40.44)

(Since: (i)^2 = -1 )

or: u^2/c^2 = 1 + 0.0024 =

u = [1.0024 c^2]^½ = 1.0011 c

In other words, in order to have a superluminal speed, it would imply the increase in mass has to be imaginary! I.e. an imaginary value would have to be assigned to the mass, and hence to K(f).

Now, of course, the counter-relativists will simply insist that these equations derived from special relativity are all wrong.

Fine, then we await their new supra-relativistic physics to deliver the correct equations!

In the meantime we take their results as well......imaginary!

Of course, I'm not alone with this view. Evidently, University of Maryland's Chairman of the Physics Dept., Drew Baden, called it a "flying carpet" or something that was too fantastic to be believable. Until these guys at CERN show they don't require imaginary masses for the neutrino beam's trip to Italia, we have to concur!

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