The new theory of everything?

Chris Jeynes questions the reality of the arrow of time (the second law of thermodynamics) and how it conditions the fundamental laws of physics

The fact is that we live first and die later. This inescapable fact has not stopped physicists from toying with the idea that in reality Time’s Arrow is illusory. You see, it’s also perfectly obvious to everyone that it’s the Sun that orbits the Earth – that’s just common sense, but just because it’s “obvious” doesn’t mean it’s is “true” (everyone now knows that the Earth revolves around the Earth). Sun)!

Loschmidt’s paradox

Physicists have now firmly established two great fundamental theories: Quantum mechanics (QM)atomic physics, and General Relativity (RG), the physics of the cosmic. There is no doubt in anyone’s mind that these theories are broadly correct. The problem is that all the laws of QM and GR are time-reversible: that is, they would look the same if time went backwards – the laws seem to ignore the second law, and so it seems that the arrow of time is not basic! However, obtaining the observed thermodynamic behavior (live first and die later, not the reverse) using only the “fundamental” laws of QM and/or GR is fraught with pitfalls: this is called the Loschmidt’s paradox.

The second law and quantum gravity

Another big problem for physicists is that although QM and GR are excellent theories, they are also mutually incompatible (which assures us that something has to change). Thus, the hunt is now on for a theory of quantum gravity capable of successfully unifying the physics of the small with the physics of the large. But what if the Arrow of Time is indeed more fundamental than either (or both) of QM or GR?

Quantitative Geometric Thermodynamics (QGT)

We have established a new approach to the thermodynamics of stability by showing that the geometry of any entity incorporates the effect of the second law of thermodynamics. Therefore the The DNA molecule is right-handed because of the arrow of time: this was proven by Michael Parker in 2010 and more strictly in Appendix A of our 2019 article. Buckminsterfullerene is stable because it takes a maximum entropy form (proven in 2020). Likewise, the Maximum entropy geometry of spiral galaxies (also proven in 2019) explains their omnipresence in the Universe. Of course, these things are already known, but the thermodynamic proofs are analytical and do not depend on any other physics: there is something fundamental about QGT.

Thermodynamics of the Very Big

The famous Bekenstein-Hawking equation (BHE) specifies the entropy of a black hole (BH). It remains the only widely accepted physical formula that explicitly includes the QM and GR constants. All spiral galaxies are now thought to have a central supermassive BH (SMBH), and the QGT’s 2019 demonstration of their stability was explicitly aimed at a highly idealized ‘galaxy’ composed only of the central SMBH.

But in May 2021, we demonstrated independently (from QGT) that the BHE was just a special case of a more general holographic relationship that also applied to nuclear entities. So, now the BHE has three independent leads: from statistical mechanicsthen string theoryand now from QGT. In August 2021, we calculated the entropy production of BH and demonstrated the strange and very far-reaching result that, like energy, the production of entropy (implying dissipation) is a conserved quantity. For physicists, the idea that dissipative processes can be conservative is strange.

Thermodynamics of the Very Small

The alpha particle (4He) is also extraordinarily stable. By using our generalization of the BBB, we demonstrated (in February 2022) that when we treat alpha as a unitary entity (that there is nothing simpler), we can correctly calculate its size only from QGT and using no QM. Moreover, we also correctly calculate the nuclear sizes not only of the helium isotopes (6He, 8He – see Figure) but also of the “helium series” (4He, 8Be, 12C, 16O, 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca: these results do not seem to be available from QM).

Image: © 2021 Michael Parker

The 8He nucleus is modeled in QGT as an alpha particle with a four-neutron shell which is a holomorphic pair of holomorphic neutron pairs. See Parker et al. (2022)for the image see the newspaper Contents. The 8He nucleus has an observed material radius of 2.49 ± 0.04 fm and a material radius calculated by QGT at 2.51 fm

time is complex

QGT’s mathematical apparatus is quite heavy and very unfamiliar: unfortunately, physical simplicity always seems to come at the cost of mathematical inscrutability. We have now shown (November 2022) that time itself is most elegantly represented as a complex number. Such a formalism allows a “simple” and coherent treatment of both reversibility and irreversibility, directly addressing Loschmidt’s paradox.

This consistent treatment is more familiar than expected. When light passes through a medium, there is a “dispersion relationship” (examples are the rainbow or the spectrum outside the prism), and there can be absorption of light. Physicists manage all of this through the “refractive index,” a complex number where the “imaginary” component represents the absorption of light.

It turns out that the “dispersion relation” is entirely general, and one can treat the energy of the system and the production of entropy of the system as two sides of the same coin. This is another very far-reaching result which is also strange since although we are accustomed to considering energy as the vital quantity of physics, dissipation has always been treated as a troublesome imperfection of the system. However, we know that everything interesting in the world involves irreversibility (and dissipative processes), so it is rather comforting that these things can now be formally understood in the same way that we deal with energy.

Theory of everything

We have demonstrated that QGT can handle both quantum and cosmic scales: the second law of thermodynamics is treated as fundamental (and not as “emerging” from QM). We have shown that QGT handles irreversible systems transparently with the reversibles that have most interested physicists, showing how an entirely general treatment is both mathematically elegant and also tractable.

It is disconcerting that what looks like a theory of everything is emerging unexpectedly from a most unlikely side: thermodynamics has been considered the domain of chemists even though physicists have made important breakthroughs (Nobel Prize in Chemistry to Onsager in 1968 for his “reciprocal relations” and to Prigogine in 1977 for his ‘theory of dissipative structures’).

But our intuition about the reality of the Arrow of Time (living first and then dying) seems correct in this case: the Second Law is really fundamental.

Sharon D. Cole