Sub-particle traveling faster than the speed of light

Jack Dikian

September 2011

Today I awoke to the shocking news that CERN scientists have measured, although they are treading carefully, neutrinos to be traveling faster than the speed of light.

For those who do this type of work will know that a neutrino "little neutral one" in Italian was first postulated by Wolfgang Pauli in order to preserve the conservation of energy, conservation of momentum, and conservation of angular momentum in the decay of an atomic nucleus into a proton, an electron and an antineutrino.

Pauli theorised that an undetected particle was carrying away the observed difference between the energy, momentum, and angular momentum of the initial and final particles. A neutrino as theorized is an electrically neutral, weakly interacting elementary subatomic particle with a small but non-zero mass.

Now, it has always been assumed that neutrinos travel at the speed of light. Relativity required mass-less particles to travel at the speed of light. But for a particle to travel faster than the speed of light undermines Einstein's 1905 special theory of relativity, one of the most important pillars in modern physics. And, of course the expansion of the fabric of space-time doesn’t count here, nor “apparent" or "effective" faster than light theories in unusually distorted regions of space-time.

The early comment by most scientists has been disbelief. For example, University of Maryland physics department chairman Drew Baden called it "a flying carpet," something that was too fantastic to be believable. Indeed, CERN are asking others to independently verify the measurements before claiming an actual discovery. They are inviting the broader physics community to look at what they've done and really scrutinize it in great detail, and ideally for someone elsewhere in the world to repeat the measurements.

You see Fermilab (the other Accelerator Laboratory in Chicago) had announced similar faster-than-light results in 2007, but those came with a margin of error that undercut its scientific significance. However, Fermilab would be capable of running the tests according to Stavros Katsanevas, the deputy director of France's National Institute for Nuclear and Particle Physics Research. The institute collaborated with Italy's Gran Sasso National Laboratory for the experiment at CERN.

My immediate thought after reading the CERN press release this morning was special relativity. The second, EPR and entanglement, what Einstein called spooky action at a distance. Along with hidden variables and all. Looking at it, whilst entanglement implies instantaneous communication - there is no actual information transmitted when the entangled particles affect each other. entanglement doesn’t imply faster than light communication. We can’t affect the state the particle goes into, even though it doesn't 'decide' on its state until it is observed.

The Remarkable Theorem

Jack Dikian

September 2011

Ever since I read Flatland: A Romance of Many Dimensions by the English schoolmaster Edwin Abbott my mind turns to the idea of higher dimensions, and whether we humans have the capacity to visualize the fourth dimension. I don’t mean using time as a fourth dimension viz a viz Special Relativity – rather trying to imagine the existence of a 4-dimensional being looking back at us and our world.

Abbott‘s in his 1884 satirical novella wrote pseudonymously as "A Square", in the fictional two-dimensional world of Flatland to offer pointed observations on the social hierarchy of Victorian culture. A 3-dimensional being, of course, is could see everything in their world, and all at once.

In the same way, a 4-dmensional being looking back at us could look inside our stomach, and remove, if they want to the lunch we just had without cutting through our skin, just like we can remove a dot inside a circle (flatland) by moving it up into the third dimension perpendicular to the circle, without breaking the circle.

Then years later, I learned about Carl Friedrich Gauss and his Theorema Egregium (the remarkable theorem in Latin). How for example, can an Ant (say a 2-dimensional being) stuck on the surface of our curved world, and can’t stand back to see the curvature of our planet ever realize that the surface is curved.

The theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface. That is, curvature does not depend on how the surface might be embedded in 3-dimensional space. An absolutely amazing insight! This however only applies to curved surfaces which are 2-dimensional.

It would take a brilliant student of Gauss, Bernhard Riemann at the age of just 26 to develop and extend Gauss's theory to higher dimensional spaces called manifolds in a way that also allows distances and angles to be measured and the notion of curvature to be defined, again in a way that was intrinsic to the manifold and not dependent upon its embedding in higher-dimensional spaces. That is generalizing Gauss’ work to describe the curvature of space in any dimension. Again, how do we, non-mathematicians, visualize a curved 3-dimensional space. What encapsulates it? The genius of Riemann was to show that we don’t need to step into the fourth dimension to tell if space is curved. We can do it form the inside.

Albert Einstein, as we know, came along and used the theory of Riemannian manifolds to develop his General Theory of Relativity. In particular, his equations for gravitation are restrictions on the curvature of space. He took the mathematics of Gauss and Riemannian and used it to develop a revolutionary picture of our physical world showing that we live in the curved worlds of Gauss and Riemannian.

So we get to finally that gravity is not a pull downwards but rather an object falls following the simplest path through bend space. Of course, Einstein didn’t stop there and showed that the presence of mass that bends space.