### Steven Weinberg's mistakes

Experience shows that some people likes to rewrite history and make heroes, and when Steven Weinberg died in 2021, some obituaries could not resist the temptation. In 2005, Weinberg wrote an article titled "Einstein's Mistakes". I am not Weinberg and he was not Einstein, but I will write about Weinberg's mistakes in this post.

Weinberg justified his review [1] of Einstein's mistakes in the following terms: "Perhaps most important, by showing that we are aware of mistakes made by even the greatest scientists, we set a good example to those who follow other supposed paths to truth. We recognize that our most important scientific forerunners were not prophets whose writings must be studied as infallible guides—they were simply great men and women who prepared the ground for the better understandings we have now achieved". I will not review all of Weinberg's mistakes, but only those which appear in the obituary written by Nima Arkani-Hamed: "How Steven Weinberg Transformed Physics and Physicists" [2].

Weinberg was a reductionist, as Arkani-Hamed mentions in his obituary, "he strongly believed that, armed only with the fundamental principles of relativity and quantum mechanics, the theoretical physicist can examine all phenomena in the universe — from the smallest to the largest scales". This was his first mistake. The world is multiscale and there are phenomena and laws that describe them at each level of organization of matter and that cannot be reduced to the laws and phenomena of lower levels of organization. Emergent properties are an example. Weinberg never worked on complex phenomena, so he does not know, but some of his colleagues knew better. One of them, P. W. Anderson, explained why the world cannot be described solely by elementary particle physics in his celebrated article "More Is Different" [3].

Weinberg also believed that quantum field theory was the application of quantum mechanics to fields. He was wrong. Quantum field theory and quantum mechanics are two incompatible theories. The history of quantum field theory begins when Paul Dirac quantized the electromagnetic field. Fifty-one years later, Dirac wrote a strong criticism of quantum electrodynamics, the most relevant part of which I reproduce here:

Most physicists are very satisfied with this situation. They argue that if one has rules for doing calculations and the results agree with observation, that is all that one requires.

But it is not all that one requires. One requires a single comprehensive theory applying to all physical phenomena. Not one theory for dealing with non-relativistic effects and a separate disjoint theory for dealing with certain relativistic effects.

Dirac knew that quantum field theory and quantum mechanics are incompatible. Other renowned physicists such as Evgeny Lifshitz and Lev Landau knew this also. Some textbooks on quantum field theory mention some of the differences from quantum mechanics. Weinberg wrote a book where he spread the myth that quantum fiueld theory is just quantum mechanics applied to fields. No, it is not.

Arkani-Hamed writes in his obituary that themes of unification and symmetry drove all of Weinberg's work and led to his famous breakthrough on "electroweak unification", which revealed a "hidden unity between two of the universe's four fundamental forces". Electroweak unification is a myth. There is no true unification. The electroweak theory describes two interactions, and that is the reason why there are two coupling constants and two sets of bosons in the electroweak Lagrangian density. The myth of unification has spread to students and the general public, but not all of us believe in the myth. Feynman was once interviewed by a historian of physics about the standard model and unification,

Feynman: "The standard model, standard model" (he said) "The standard model—is that the one that says that we have electrodynamics, we have weak interaction, and we have strong interaction? Okay. Yes".

Historian: "That was quite an achievement, putting them together".

Feynman: "They're not put together".

Historian: "Linked together in a single theoretical package?".

Feynman: "No".

Historian: "What do you call SU(3) × SU(2) × U(1)?".

Feynman: "Three theories" (he said) "Strong interactions, weak interactions, and electromagnetic [...] The theories are linked because they seem to have similar characteristics".

Arkani-Hamed tells us how Weinberg reimagined quantum field theory from a different perspective and used this to study long-range forces such as electromagnetism and gravity. Well, Weinberg misunderstood both electromagnetism and gravity. My advice is that if you want to better understand those interactions, stay away from Weinberg's works. Arkani-Hamed states that from the restrictions imposed by special relativity and quantum mechanics on spin-2 particles, we can derive the equivalence principle and from there general relativity. This is another myth. General relativity is not equivalent to a spin-2 theory. Moreover, what Weinberg called a "graviton" was not really a graviton. One of the reasons quantum gravity is in its current sad state is because particle physicists like Weinberg did not understand general relativity and tried to apply quantum field theoretic methods to a metric theory that does not describe gravitation in terms of a gravitational field. A full discussion of the technical details goes beyond this post, so let me simply reproduce a recent tweet from cosmologist Will Kinney: "in general relativity, the gravitational field doesn't really exist".

Arkani-Hamed continues:

Above all, Weinberg was a great unifier. He disliked the 'Einsteinian' view of gravity as the curvature of space-time — which gives gravity a privileged position in defining the arena where all other phenomena operate — feeling that this erected an artificial barrier preventing researchers from seeing deeper connections between gravity and the rest of physics. This led him to formulate general relativity using the methods of particle physics, in the first of his many tour de force textbooks, Gravitation and Cosmology.

The problem here is that the "great unifier" did not unify anything. Weinberg misunderstood the subjects that he wanted to unify. This is why in his classic book *Gravitation and Cosmology*, Weinberg makes the bold claim that general relativity can be understood as electrodynamics and that the geometric approach is not necessary. When we review his works on the subject, we discover that he confuses an effective metric with a Riemannian metric, a geometrical deviation from a fictitious background with a true spin-2 tensor, a quadratic Ricci term with a EMT, and so on. At least Weinberg warned readers of his book: "The reader should be warned that these views are heterodox and would meet with objections from many general relativists". However, the true problem was not heterodoxy but validity. His views on general relativity are wrong.

Weinberg also confused the concepts of macroscopic and microscopic locality and, based on this confusion, he stated that the interactions of particles accessible at some energy scale must be described by an effective quantum field theory involving only these particles. In reality, those effective theories can only describe particles and their interactions in an approximated way, which is sufficient for the purposes of particle physicists, but not for scientists working on complex phenomena. This was not his only misstatement about quantum field theory, for in in his three volume set devoted to quantum field theory, Weinberg claims that quantum field theory is the only way to combine quantum mechanics with Lorentz invariance and the cluster-decomposition principle. This statement is doubly incorrect. Once, because quantum field theory is incompatible with quantum mechanics, as we saw earlier. And another, because we have been using for years in nuclear and particle physics theories that combine the three elements without being field theories.

Weinberg also worked on the infamous cosmological constant problem. This is a problem that arises when physicists take a term in one of the equations of general relativity, interpret this term as describing a vacuum, then take a quantum vacuum term from one of the equations of the standard model of particle physics, and finally link both terms in a naive way. To make matters worse, what they call a quantum vacuum is not a true emptiness, but a remnant of the fact that excitations of quantum fields are not physical particles, but rather unphysical objects called *bare particles*. After all this mess, no one would be surprised to learn that Nature's response was to turn the cosmological constant problem into "the largest discrepancy between theory and experiment in all of science". The difference between the value predicted by physicists like Weinberg for the cosmological constant and the measured value is of the order of 10¹²⁰. Yes, you read that right, it is a one followed by 120 zeros!

And what was Weinberg's solution to "the worst theoretical prediction in the history of physics"? Unable to offer a valid solution, he recurred to the anthropic principle. This is a wild card that physicists resort to when they do not know how to explain or calculate something about the universe. Anthropic reasoning cannot predict the observed value of the cosmological constant, and in fact leads to vastly different predictions of the cosmological constant.

This post contains just a sample of Weinberg's mistakes. He made additional errors regarding the H-theorem and unitarity, offered an invalid derivation of the SchrÃ¶dinger equation from an operator-valued version of the Dirac equation, and others.

## REFERENCES AND NOTES

- https://physicstoday.scitation.org/doi/10.1063/1.2155755
- https://www.quantamagazine.org/how-steven-weinberg-transformed-physics-and-physicists-20210811/
- More Is Different: Broken symmetry and the nature of the hierarchical structure of science. 1972: Science 177(4047), 393–396. Anderson, P. W.