I know Sean Carroll as some years ago I read his beautiful lectures on general relativity that become a book. Some years later I started to read his blog and this I do also today. Sean touched a lot of arguments in physics during these years but the most important for me are those about arrow of time and reality forming (measurement problem in quantum mechanics). These two matters are strongly linked and their understanding represents a great achievement in physics and this explains why a lot of ink, paper and digital data have been spent around the world. Sean has written an article on this on Scientific American (see here). Contrarily to some wisdom around this problem is really deep as there is no reason on Earth to accept environmental decoherence and multi-universe interpretation as the ultimate answers that finally do not grant any answer to a simple fact. This fact was explained to me quite simply by Giorgio Careri. Careri has been a professor of mine at department of physics of “La Sapienza” in Rome. A day I was walking to the new building of the department (Fermi building) together with some other students when we met him going into the opposite direction. I do not remember the reason why we started to talk but he said something I am still here to remember:”One of the deepest question physics should answer is why, having a four dimensional space-time, we can move backward and forward and we can stop in three of these dimensions but not in time?”. Currently an answer is still lacking being at the root of our understanding of how reality forms and the way it forms.

Horacio Pastawski is a researcher working at University of Cordoba in Argentina and has carried out with his a group a lot of relevant work that can be traced back on the most important archival journals in physics and on arxiv as well. Horacio’s group has found an answer to this matter through NMR experiments. The point can be traced back to the Boltzmann and Loschmidt controversy. In order to answer to the criticism of Loschmidt claiming that as all laws of mechanics are reversible one should conclude that H-theorem is false, Boltzmann put forward the so called Stosszahlansatz (molecular chaos hypothesis) to conclude that indeed H-theorem is right. Boltzmann’s hypothesis is purely statistical and being this true Boltzmann is right. So, the understanding of arrow of time passes through an explanation of Boltzmann’s Stosszahlansatz that we currently lack. But in 1998 Horacio’s group performed an NMR experiment with a complex molecule, ferrocene and cobaltocene, where they showed that an intrinsic instability appears in the thermodynamic limit provoking irreversibility (see here). This shows that Boltzmann is right and this also explains why we observe irreversibility all around in the macroscopic limit. Of course, this result met skepticism in the community and they had severe difficulties to get their paper published on an archival journal notwithstanding no flaw is appearing in their experimental procedure. Anyway, they published their results on Molecular Physics and Physica A and so these are part of scientific literature. But their results received an unexpected confirmation on PRL quite recently in a different perspective as these authors were trying to understand decoherence in quantum computation.

We see that thermodynamic limit plays a central role in our understanding of reality and this matches fairly well with the observed fact that macroscopic objects behave classically and gives also a satisfactory understanding of Boltzmann’s hypothesis that would be completely missing accepting acritically environmental decoherence and multi-verse.

If one looks at the velocity four-vector for a particle parametrized by its proper time, then the rate of “change” of the coordinates is:

with

We can see that in its own rest-frame, the particle has vanishing rate of change of the spatial coordinates, but a constant rate of change in the temporal coordinate. It seems that the rate of change of the temporal coordinate cannot be made to vanish since .

Can we boost to a frame where vanishes? The Lorentz transformation implies

which does not seem to be very consistent…

This is what special relativity tells you. Does general relativity gives something else? How can quantum mechanics help? And what’s up with massless particles traveling at the speed of light?

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