See also: A dynamical inconsistency of Hořava gravity. The authors show that the lapse function must vanish at infinity and consequently also everywhere, for generic configurations, i.e. all constraints are second-class, unless new ugly constraints are added (and they probably make a long-distance limit converging to general relativity impossible).
As I learned from seeing hundreds of visitors to various articles about Hořava-Lifshitz gravity on this blog, Zeeya Merali wrote an article for Scientific American,
To make sure that we don't think that the title is an isolated typo, exaggeration, or an error, the absurd statement in the title is repeated many times in the article. The subtitle says
Buzz about a quantum gravity theory that sends space and time back to their Newtonian rootswhile the first sentence that follows asks:
Was Newton right and Einstein wrong?Well, when it comes to the questions about the behavior at speeds that are comparable to the speed of light, the answer is a resounding No. I consider this fact to be an elementary insight that should be known to all intelligent high school students who are interested in physical sciences.
Special relativity has been found by Einstein's pure thought, by reconciling theoretical principles found by other means, but since 1905, it has been confirmed by many remarkably accurate direct experiments, too. There's no empirical doubt that when it comes to the essence of space and time and their relationships, Einstein was more right than Newton. This insight can't really be "unlearned". Ever.
Can we at least wake Einstein up and ask him what he thinks?
Well, he didn't tell us much but he would if he could. ;-) But it's OK, people only care whether Einstein is smiling, anyway.
One might speculate that in unobservable contexts, relativity breaks down in some way, and maybe even Newton's picture of space and time gets restored. Except that there's obviously no experimental justification for such speculations and all such speculations are both unmotivated as well as living on the edge of being inconsistent with the observations, to say the least.
Of course, one may always speculate that things are inherently different than they look. However, in science, there should exist at least valid theoretical reasons for speculations. And those mentioned in Scientific American definitely fail to be valid. The third paragraph presents the problem of quantum gravity as follows:
... Instead [Einstein] argued that time is another dimension, woven together with space to form a malleable fabric that is distorted by matter. The snag is that in quantum mechanics, time retains its Newtonian aloofness, providing the stage against which matter dances but never being affected by its presence. These two conceptions of time don’t gel.Well, this is surely not the case. There exists absolutely nothing in quantum mechanics that would dictate time to be "aloof".
Fully quantum theories where time is exactly as unified with space as relativity dictates have been used to describe the reality since the early 1930s. Quantum Electrodynamics was gradually joined by many other quantum field theories: the Standard Model is the most complete theory of all non-gravitational forces and particles we have observed so far and it is a fully relativistic theory. It's simply not true that there exists a contradiction between quantum mechanics and relativity. This much has been understood for 80 years and I am sure that Petr Hořava knows that.
In fact, relativity reinforces quantum mechanics, especially its postulates. The EPR phenomena imply that the wave functions must be interpreted probabilistically and no "mechanical" picture has to be looked for. Such a mechanical picture would physically violate the rules of relativity but the actual quantum field theory doesn't violate them at all.
In fact, it is not even true that there is a contradiction between quantum mechanics on one side and the "tighter" unification of space and time as prescribed by general relativity. All the vacua of string theory are specific counterexamples of such a statement about inconsistency but I don't really need to go that far. The ultraviolet divergences that appear in the loop calculations of quantized theories of gravity don't prove any inconsistency of the underlying principles (unless there are anomalies in a specific effective field theory). As we know from other quantum field theories, the infinities only mean that the field theories are effective and inaccurate at short distances. The quantum phenomena work perfectly at long distances, e.g. in the semiclassical approximation of general relativity, which is why quantum mechanics can't be incompatible with the basic principles and symmetries that define the long-distance behavior of general relativity.
So this problem - of the incompatibility of the basic principles of relativity and quantum mechanics - surely doesn't exist, so it is scientific nonsense to look for the "solution" to this non-existing problem.
"I’m going back to Newton’s idea that time and space are not equivalent."Is that a real quote? Well, that's pretty bad to mentally return 300 years back in time, in contradiction to a century of existing measurements of space and time, and without having a glimpse of an alternative valid empirical or theoretical evidence. But a part of the proposition about the "return" isn't even true.
Newton has never had an "idea that time and space were not equivalent". Instead, the non-equivalence of space and time looked like an obvious thing to everyone, including Newton (and to all of us, before we learn relativity), so that he wasn't thinking about this question at all. There have been no ideas in this direction until 1905 when a patent clerk had the idea that space and time had to be treated as inseparable entities whose properties are linked by symmetries. Einstein was the first person who had any idea about the unity or non-unity of space and time.
At low energies, general relativity emerges from this underlying framework, and the fabric of spacetime restitches, he explains.Well, general relativity doesn't and can't emerge from a fundamentally non-relativistic starting point, as we have discussed previously, but this is more technical a discussion.
Hořava likens this emergence to the way some exotic substances change phase. For instance, at low temperatures liquid helium’s properties change dramatically, becoming a “superfluid” that can overcome friction.Except that phase transitions restore symmetries at short distances (or higher energies and temperatures) and break them at long distances (or lower energies and temperatures). The opposite behavior can only arise with an accidental symmetry, and an accidental Lorentz symmetry has to be hugely fine-tuned if the effective theory is supposed to contain dozens of apparently Lorentz-invariant fields as needed in the Standard Model. Moreover, an O(1) first-order breaking of the Lorentz symmetry at the Planck scale is ruled out by Fermi.
So far it seems to be working: the infinities that plague other theories of quantum gravity have been tamed, and the theory spits out a well-behaved graviton.Except that it also spits an unwanted scalar mode, a pathologically odd number of dimensions in the phase space, plus infinitely many unknown parameters from its being strongly coupled which really restore the whole problem of the naively quantized general relativity. Charmousis et al. have shown that these problems are completely universal, stem from the very breaking of the spacetime diffeomorphism invariance in Hořava's theory, so they almost certainly can't be fixed by any "small improvements" of the theory.
The Scientific American article continues with lots of ambitious applications of the proposed theory. The theory is said to predict a "bounce" instead of a Big Bang - something that the proponents consider to be a virtue, for reasons that seem non-existent in the realm of rational arguments. Also, the theory should replace dark matter as well as dark energy by its own corrections. No one cares that the existence of dark matter distributions that are independent from the visible matter has been pretty much established. No one cares that the equation of state of dark energy has been checked to agree with the relativistic cosmological constant, too.
All these people must think it's great to address these ambitious questions without paying much attention to the question whether the theory actually agrees with the observations of elementary phenomena that have been known for centuries. Some physicists seem to have a huge irrational bias: any theory that predicts "something new" or that "differs" from the established theory is automatically a source of excitement for them. In reality, almost every such a deviation implies that the new theory is instantly falsified, so a "random new physical effect" predicted by a new theory should mostly be a cause for concern, not happiness, unless proven otherwise.
So in the article in Scientific American, they just briefly mention a paper that implies that even ordinary rules of gravity in the Solar System break down whenever some time-dependence is brought to the game because the additional pathological scalar degree of freedom actually satisfies a first-order differential equation in time. It is found to lead to bad instabilities. The centers of stars can't even be static - surely a detail. Petr was also heard as saying:
When I proposed this, I didn’t claim I had the final theory. I want other people to examine it and improve it.By the way, this quote referred to an improvement by Blas, Pujolas, and Sibiryakov. It has been shown unphysical - because cubic couplings diverge at long distances (although the quadratic ones may be fine) and kill hopes of an accidental Lorentz symmetry - by Papazoglou and Sotiriou one week ago. Scientific American doesn't mention this result (maybe just because it's too new). But be sure that every other "improvement" will share the same fate. Their problems are not in details but in the very general assumptions of Petr.
Back to the quote above. Well, some physicists may prefer citations from hundreds of papers that try to change the shape of the "wooden earphones" over admitting the obvious fact - for no citations - that the cargo (in this case, gravitational phenomena in our Universe) has nothing to do with these wooden earphones. ;-)
At the very end, Gia Dvali is cited as the only physicist who "remains cautious" because he thinks that all such Lorentz-breaking theories have to lead to "unwanted side effects". Still, he also diplomatically says that a hypothetical theory without such unwanted side effects "has to be taken very seriously". This sentence is largely vacuous because the Lorentz violation itself is an unwanted side effect (for various reasons that can be explained in detail) so a theory building on such an assumption simply can't be free of unwanted side effects.
Do you think that real physicists such as Witten, Seiberg, Strominger, Vafa, Polchinski, Gross etc. think it's a promising proposal? Why do you really think that they don't work on it? Do you think that Scientific American asks such questions or does it prefer to paint a completely distorted picture of the reality because it knows that there will always be many readers who just don't like relativity and who will appreciate anything that kicks into Einstein's butts? ;-)
I find these growing populist pressures on science - and efforts to gain influence by offering hopeless theories via the people who don't really know what they're doing - disturbing. Unfortunately, we seem to be entering the era of bandwagons whose being a bandwagon (and having the potential to attract a sufficient number of usually intellectually limited supporters) is their greatest virtue.
Moreover, it seems that physical sciences are more vulnerable to these developments. Have you heard that a large group of biologists started to study a theory that returns their field to the creationist rules? Do you know what would be the difference between the creationist situation and the present "returning non-relativistic roots of physics"? The difference is just 46 years - from the publication of The Origin of Species to Special Relativity.
And that's the memo.