A moderately technical posting about the flaws of Bohmian mechanics was followed by a sociological text about anti-quantum zeal. So it is natural to complete the commutative diagram and supplement the text about the Lorentz symmetry and computational universes by a sociological essay about the relativistic phobia. Here it is.

**The 20th century revolutions**

The quantum revolution has had a more profound conceptual impact on our understanding of the real world than relativity. We were forced to abandon determinism and the very idea that objects had well-defined, unique properties before they were observed. Evolution has trained us to understand a classical limit of the real world only because it was sufficient to hunt the deers and to eat bananas, besides other pleasures of life.

As we have mentioned previously, many people think that the constraints of special relativity were relaxed by general relativity. But just the opposite is true. General relativity doesn't deny special relativity: it generalizes it. General relativity demands that in all regions of spacetime that are much shorter than all the curvature radii, the rules of special relativity must hold.

**Approximate Lorentz invariance**

High energies. Curvature length is comparable to the Planck length. Here we don’t expect a smooth geometry. The space-time is expected to be distorted and gravity is important. Space-time is not locally flat and GR breaks down. Why do you expect Lorentz invariance to hold here?You can feel the unlimited self-confidence of ignorance in those statements.

This is not science. Correct theories that are compatible with the observations - quantum field theory and a theory based on relativistic strings, string theory - exist and the conventional empirical criteria of science force us to abandon the theories that are incompatible with observations, regardless of our prejudices.

So why do we expect Lorentz invariance to hold? Well, because we have experimentally observed it to hold in this world. And if the symmetry were only true approximately, it would be extremely likely that the violations from Lorentz symmetry would grow bigger, not smaller, at longer distances.

You know, Petr Hořava may have considered a non-relativistic theory at the Planck scale that could flow to a relativistic theory at long distances. But he only needed to adjust a few parameters because he only considered gravity. If he added other particles and forces and if he imposed no symmetry constraints at the Planck scale, he would need hundreds of parameters to be fine-tuned in order to obtain a relativistic limit at long distances. The top speed of every particle and every bound state would have to be adjusted to the same "c".

Approximate Lorentz symmetry in complicated enough systems can never emerge "by chance" and the only known sensible reason why Lorentz symmetry holds so extremely accurately in complex enough systems is that it actually holds exactly. If you find new mechanisms by which (approximately) Lorentz-invariant physical laws may emerge out of a Lorentz-breaking (or at least not manifestly Lorentz-invariant) starting point, it will be interesting.

But you must actually find this result and the required evidence. Only once you have found it, it becomes interesting. If you first try to argue that it is interesting and you hope that someone will find a justification later, you are a victim of a wishful thinking. Your reasoning has surely nothing to do with science because you completely seem to ignore the scientific evidence.

Needless to say, Giotis is not the only person who promotes these anti-relativistic preconceptions. A reader named Jerzy, who might actually be Jerzy Lewandowski, wrote pretty much equivalent words:

The obvious problem concerning Lorentz transformations relates to the fact that the Lorentz group is not compact. This means that we boost photon, say, to any energy you like, for example Planck energy, and on the other hand it is widely expected that at the Planck scale something dramatic happens. But perhaps this argument is misleading? By the same token, since the group is non-compact we will never be able to check Lorentz invariance experimentally.Well, there is obviously no "problem" caused by the non-compactness of the Lorentz group. The non-compactness is a fact and if Mr Jerzy sees it as a problem, it is his psychological problem, not a scientific problem.

The statement that one cannot check Lorentz invariance experimentally is simply stunning, especially if the guy above is Dr Lewandowski. What the hell does he think that those 100+ years of tests of special relativity have been doing? Well, we cannot make "arbitrarily large boosts". But in the same way, we cannot make "arbitrarily small rotations", to check the rotational symmetry with respect to angles comparable to 10^{-60}.

No experiment in the world can measure and verify statements for "all values" of parameters and "absolutely accurately".

These folks, instead of admitting the very possibility that their expectations about spacetime could be wrong, are eager to say literally anything - including the statement that relativity cannot be experimentally verified. That's also why the preprint servers are still being flooded with manifestly wrong and incoherent theories of deformed, distorted, doubled, or otherwise crippled relativities. These people want to preserve their prejudices in the very same way as the believers who were running the Inquisition did. Their enterprise has nothing to do with the scientific method.

## snail feedback (2) :

What annoys me a little bit is that some phycicists seem to confuse mathematical models with the reality that they model.

For instance, the fact that some aspect of physical reality can be modeled by the mathematical structure known as a Minkowski space does not mean that reality

isa Minkowski space, any more than the fact that the time-fluctuating sea levels across the surface of lake Chaplain can be modeled as an abstract 4-dimensional surface (or, equvalently, a scalar field on an abstract 3-space) means that the lakeisa 4d surface or a 3d object.I think such confusion between reality and mathematical machinery describing it is what some SR-sceptics are reacting to.

And no, reality is not a 4-d manifold with a funny metric varying as described by GR either.

It's just a model, describing observations. Just as the Hilbert space/operator/wave function model known as QM is.

But I guess you already know this far better than I can express it.

Greetings, ragnar

Dear Luhn,

one can of course distinguish "reality" and "models" or "theories" as two different things. One can imagine that theories are living "on the paper" or in a "fictitious Platonic world of ideas" while the real world lives "elsewhere".

Still, the reality follows some laws, and the theories often describe these laws faithfully. And special relativity is follows by Nature - both the "Nature in the models" and "Nature in reality" - very dogmatically.

So I don't really understand what can be valuable or deeply true about the statement that the reality is "not" a four-dimensional space with the Minkowski signature.

It is a four-dimensional Minkowskian space - at least as much as the world at one moment is a Euclidean-signature geometry (Riemannian or approximately Euclidean).

So the reality is both a four-dimensional spacetime following the laws of Riemannian geometry whenever geometry and time measurements are large and make sense - as well as your other example.

The reality also is - completely exactly - a set of states in the Hilbert space with operators on it. I really don't understand why would a sensible person familiar with physics ever say that it is *not*. It is surely "isomorphic" to these things, and you happened to pick two examples that are almost certainly valid absolutely exactly.

So the only way how I can interpret your statements that the reality must be something different and theories are "only models" blah blah blah is a general hatred against mathematics and all science based on mathematics.

But science and Nature are based on mathematics whether someone likes it or not. The "are" mathematics.

Well, the opposite opinion is surely a driving force behind all phobias of the scientific type - whether they're against quantum mechanics, evolution, relativity, string theory, or anything else.

Yes, I strongly oppose these phobias and their unifying sentiment. The world *is* a Hilbert space with Hermitean operators, and the world *is* a set of events on a Minkowskian background. The only conceivable purpose of saying that it is not the case is to understate both the importance and accuracy of physics.

Best

Lubos

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