## Wednesday, February 04, 2009

### Relativistic phobia

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.

So it is not too surprising that many people still have serious psychological problems with the postulates of quantum mechanics, even though they have been known to be correct for more than 80 years.

Special relativity has been around for more than 100 years. It doesn't challenge our most basic assumptions about "reality" of things. Puppets have created movies that explain these crisp and clear ideas to children in the kindergartens - like the video above. But this science is still sufficiently difficult for most people - including most physics fans - which is why most of them are still hoping that special relativity will go away. As we will see, their hope is based on a complete denial of all relevant experimental input as well as a misinterpretation of all newer theories, beginning with general relativity.

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.

If we choose a freely-falling system of coordinates to describe physics, the rules of special relativity must hold in the most direct sense: we must literally be back in special relativity. The equivalence principle, a basic postulate of general relativity, is saying nothing less than that. General relativity allows regions to be glued into curved spacetime manifolds but the small patches must follow the same conditions as they did in special relativity.

So even though general relativity is newer than special relativity, it is probably special relativity - the older part of relativity - that is so hard to swallow. Why is it so?

Well, special relativity has changed our understanding of space and time. It has unified them. Similar basic statements have been said many times. But I want to be slightly more specific in uncovering the psychological framework that leads people to deny relativity more than 100 years after its discovery. What is so difficult is that the Lorentz group of symmetries is noncompact and it can relate - i.e. fully predict - the results of experiments with arbitrarily short objects. You know, when you boost an object, Lorentz contraction may shrink it 1,000 times or more. Still, this shorter object must follow the same physical laws - or trivially transformed ones - as ordinary, long objects.

This is so difficult for most people to swallow simply because most people are imagining spacetime in brutally non-relativistic ways. For example, they imagine space to be made out of "pixels" of one kind or another. If we get to very short distances, the new, perhaps discrete, architecture of space should become manifest, they think. Well, it does, but only if the short distances are carefully defined in a relativistic manner.

If we simply boost a one-millimeter ant so that the Lorentz factor is 10^{35}, the ant will become shorter than the Planck length in our reference frame. There's absolutely nothing wrong with it and the ant will locally follow the same laws of physics and biology as it does in the ordinary world. Relativity guarantees this equivalence.

Indeed, it would be impossible to reproduce this prediction with a pixelated model of the Universe - either space or spacetime - that so many people are imagining. Distances are not really shrinking in their imaginations. They are still imagining absolute distances between objects which is why they also think that new, short-distance effects occur whenever coordinate distances drop below a new threshold.

But no new phenomena may ever occur in the real world just because (and when) the coordinate distances drop below such a threshold and when the contraction is a result of an ordinary boost. Such new physical phenomena would violate relativity because relativity requires the boosts to be unobservable.

So I think that the psychology behind the anti-relativistic attitude is completely analogous to the anti-quantum zeal we have discussed previously. Those people simply want to defend their fundamentally non-relativistic picture of the world where distances and times are absolute, they don't shrink or expand, and the simultaneity of events may be decided objectively, absolutely - or at least the differences between the times, lags, and distances as seen by different observers can never become large. If these lags and differences are small enough, all these changes are marginally compatible with the people's feelings.

But in the real world, these changes may become arbitrarily large. The Lorentz factor can be an arbitrarily high real number. The more extreme phenomena we consider, the more incorrect the non-relativistic ideas about the world become. Those people believe something completely different: they believe that the old-fashioned ideas about space and time will return when we consider, sometime in the future, more extreme elementary events than we did before. The analogy with the anti-quantum zealots should be obvious.

The relativistic phobia leads those people to promote various non-relativistic ways to imagine the real world. Needless to say, such a non-relativistic picture is pretty much ruled out by experiments at the very moment when someone mentions it. So these anti-relativistic people are inventing all kinds of irrational fairy-tales why the disagreement between their theories and the observations could be OK, and so on. For example, without a glimpse of a rational reason, they claim that manifestly non-relativistic theories will be approximately relativistic.

Approximate Lorentz invariance

In the real world, it is never possible to experimentally verify a principle completely universally or completely accurately. However, experimenters may improve the limits on new phenomena. They may deduce from their observations that if a new phenomenon violates a principle, the coefficient that measures the strength (or frequency) of the new phenomenon must be smaller than a certain small number. The smaller such a number is, the less room one has for theories that fundamentally disagree with the principle.

When the number becomes really small, all experimentally allowed theories can be imagined as tiny perturbations of a theory that satisfies the principle exactly. In these cases, any viable theory that rejects the principle must be able to generate the right limit in which the principle totally holds. Of course, when no violation of the principle is known, the limiting theory is more realistic, simpler, and more interesting than the original theory itself.

The limits on Lorentz-violating effects are extremely constraining. The Tevatron is boosting protons and antiprotons so that their rest mass, 1 GeV or so, expands to 1 TeV, by a factor of "gamma=1,000". The baryons' speed is therefore close to 0.9999995 of the speed of light. Lorentz symmetry and other consequences of special relativity still seem to hold according to all the observations. There are more refined ways to measure more concrete terms in the Lagrangian that would violate the Lorentz symmetry but I don't want to discuss them here.

For "gamma=1,000", everything still seems perfectly relativistic. You might think that the number "gamma=1,000" overstates how far relativity works. Can we talk about some angles in the Minkowski spacetime? Sure, we can. Because of the mixed signature, the relevant angular variable is actually a hyperbolic angle "phi", also called "rapidity". We have "cosh(phi)=1,000" which means "phi=7.6". Note that the letter "h" in "cosh" is the only new detail that was absent in the Euclidean space. OK, I hope you don't want me to calculate that "phi" is really 7.600905. So many zeroes. :-) Feel free to check that "tanh(phi)=0.9999995", the correct velocity.

The number "phi=7.6" is much smaller than a "1,000" but it is the counterpart of the ordinary angles in the Euclidean space, expressed in rads. In the Euclidean space, "7.6" would be more than needed for a full revolution. In the Minkowski space, the angles are not periodic so there is no full revolution. But it is a huge angle, anyway. Because the physical phenomena still respect special relativity, it is very obvious that special relativity simply cannot "fundamentally break down" for "finite hyperbolic angles".

Now, every theory that fundamentally and naturally confirms the "non-relativistic prejudices" of those people is instantly ruled out. Lorentz invariance holds so well and so universally that if you invent a fundamentally non-relativistic theory, you must first show that it has an exact relativistic limit, and you may pick this limit instead of your original theory because if it is a new theory, it is more important, more simple, and more consistent with the experiments, anyway.

I think that the people who don't care about the agreement with the tests of relativity at this point have simply abandoned the scientific method and despite my being a realistic optimist, I see no reason to expect that they will ever return to it. The gigantic gap between them and the empirical reality is all but guaranteed to increase in size. For example, look at a question that a reader called Giotis asked David Berenstein:
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.

The Gentlemen has certain, uhm, expectations. They completely contradict all of our experimental and theoretical knowledge about the fundamental structure of space and time. But this Gentleman promotes his expectation by the words "it is expected". And in between the lines of a useless, infinite discussion, he makes you sure that no amount of evidence would ever convince him that his expectation is just wrong and one must simply study different theories than his preconceived ones.

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.

He also says that "it is widely expected" that when [coordinate] distances decrease to the Planck scale, something dramatic happens. Well, as all students who deserved their A in undergraduate classes of relativity expect, nothing new will happen at all when a system is boosted so that [coordinate] distances decrease close to or below the Planck length. As we've known since 1905, boosts don't do anything to the fundamental laws of physics. Get used to it, Mr Jerzy.

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".

But that doesn't mean that science cannot make progress by the usual method, i.e. the falsification of wrong hypotheses. The experiments that have been done are enough to falsify all fundamentally non-relativistic theories much like they are enough to falsify all the rotationally non-invariant theories. Whether a group is compact or non-compact is just a technicality. If you parameterize the boosts by the velocity, "v/c=tanh(phi)", then this parameter - velocity - is actually more compact than it used to be in non-relativistic physics: it always goes between -1 and +1.

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.

And that's the memo.

1. 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 is a 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 lake is a 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

2. 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