No, Unloose Energy Non-Conservation Is A Lousy Approach To The Cosmological Constant Problem

In mid January, Republic of Chad Orzel didn't similar some hype almost a "proposed solution to the cosmological constant problem":

The quotes from other researchers inward this are all also diplomatic too move out me wanting a shipping on it from @skdh https://t.co/E1qYwasjY2

— Republic of Chad Orzel (@orzelc) January 19, 2017

An article inward the Physics World promoted an Apr 2016 newspaper past times Josset, Perez, too Sudarsky lately published inward PRL

Dark unloose energy every bit the weight of violating unloose energy conservation

that has claimed the the patently observed cosmological constant is just the accumulated amount of unloose energy that was created when Nature violated the unloose energy conservation police draw – too that's supposed to brand things to a greater extent than natural.

The 97% crackpot Lee Smolin praised the persuasion every bit a speculative approach inward the best possible feel that is revolutionary if true. The 60% crackpot George Ellis said that the proposal was feasible too no to a greater extent than fanciful than what's beingness explored past times contemporary theoretical physicists – his English linguistic communication isn't every bit goodness every bit mine so I had to improve this man's prose.

Orzel establish these comments also diplomatic and, every bit a "progressive" (a far left whacko), he decided to aspect for the best possible debunker amongst the only politically right issue of penises (zero) who should debunk this stuff: Sabine Hossenfelder.




Unfortunately, the politically right issue of penises ofttimes has additional consequences that Orzel must direct hold overlooked. So instead of debunking the stuff, Hossenfelder wrote an essay saying

Yes, a violation of unloose energy conservation tin explicate the cosmological constant

Yes, geniuses inward the NASA basements could direct hold constructed a self-propelling spaceship, too. None of these 2 closely related claims sounds convincing, however. It's non surprising that Hossenfelder's mental attitude isn't also far from Smolin's – later all, the 2 happily collaborated for quite some time.




I think that these inexpensive ideas demo the deterioration of the form of "theoretical physics surrounding quantum gravity" that is manifested whenever the researchers are allowed non to last experts inward string theory. Without string theory, thinking almost the physical phenomena going beyond the effective acre theory motion painting almost unavoidably reduces to pure speculation too random sacrifices of cherished principles. These people may last goodness at throwing of import things to the trash tin – string theory, unloose energy conservation police draw etc. – but they never direct hold anything goodness to supplant the things they direct hold thrown away with.

What are Josset et al. doing? First, Einstein's equations of full general relativity say\[

R_{\mu \nu} - \tfrac{1}{2}R \, g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi yard }{c^4} T_{\mu \nu}.

\] It's an equation for a symmetric tensor. Cannot these components last carve upward to several pieces? Yes, in that place is a natural plenty trend to carve upward the equations into 2 pieces: the line too the rest. The residual is the traceless part.

If you lot direct hold the line of Einstein's equations above, i.e. its production amongst \(g^{\mu\nu}\) summed over the 2 indices, you lot volition get\[

R(1-D/2) + D\Lambda = \frac{8\pi G}{c^4} T

\] where the spacetime some us has \(D=4\). Here, \(R\) too \(T\) are the traces of \(R_{\mu\nu}\) too \(T_{\mu\nu}\), respectively. You may calculate the traceless role past times subtracting \(g_{\mu\nu}/D\) times the line from the master copy Einstein's equations. For \(D=4\), nosotros get:\[

R_{\mu \nu} - \tfrac{1}{4}R \, g_{\mu \nu} = \frac{8 \pi yard }{c^4} (T_{\mu \nu} - \tfrac{1}{4} Tg_{\mu\nu})

\] You may derive the line too traceless role of Einstein's equations from the regulation of to the lowest degree action. How? You only consider separate variations of \(g_{\mu\nu}(x^\alpha)\) that save the determinant of the metric at each betoken (you larn the traceless equations inward this way); too the variation of the scalar factor (that's how you lot larn the equation for the trace).

Fine, the "reduced" Einstein's equations where you lot only verbalize over the traceless tensor – from varying the metric piece preserving its determinant – is known every bit unimodular gravity.

Great. So the cosmological constant doesn't appear inward the traceless role at all. It only affects the line part. The covariant derivative (or divergence) \(\nabla^\mu\) of the master copy Einstein's equations is identically zero. Note that the covariant derivative of the metric (and hence the cosmological constant term) is identically zero, much similar the covariant derivative of the Einstein tensor. The covariant derivative of the stress-energy tensor vanishes if the equations of motion for the thing acre are obeyed.

But when you lot process the line too traceless equations separately, this automatic vanishing of the covariant derivative disappears. So you lot may determine non to impose the line role of Einstein's equations (which contains \(\Lambda\)) at all. Instead, you lot may attempt to derive this status from \(\nabla^\mu T_{\mu\nu}=0\). But in i trial you lot direct hold this continuity equation, you lot may alter it to\[

\nabla^\mu T_{\mu\nu} = J_\nu = \nabla_\nu Q

\] There's a electrical flow \(J_\nu\) which measures the violation of the unloose energy conservation police draw too you lot may also determine that it should last equal to some slope of some scalar \(Q\). Great. There is of class no justification for whatever of these things. You are just randomly abolishing some equations of physics. There is no goodness conceivable source for whatever nonzero \(Q\) – Josset et al. hence enumerate some of the crackpots' most pop ways to bastardize physics, namely modifications of quantum mechanics too spacetime discreteness at the Planck scale.

None of these things is genuinely consistent, allow lone well-defined according to some known rules, so these excuses are equivalent to enumerating some molar fairies too Harry Potters, but they don't care.

You tin run into that the effect is nil else than some hypothesized contribution to \(T_{\mu\nu}\) that, later some time, becomes equivalent to some factor of some \(Q\).

There is a trend to improve this whole theory too eliminate all the nonsensical "violations of the physical laws" piece keeping the predictions just the same. You just demand that \(\Lambda\), the cosmological constant, is no longer constant. Instead, it is some variable acre – quintessence, if you lot wishing – whose value may evolve due to the really same effects that were driving \(Q\) above. Great, so some mysterious effects – molar fairy, violations of postulates of quantum mechanics, global warming, discreteness of the spacetime, or whatever pseudoscience that your New Age religious cult considers stylish right right away – just brand the electrical flow value of the vacuum unloose energy density \(\Lambda\) equal to \(10^{-123}\) inward the Planck units.

Have you lot solved anything? I don't think so. You direct hold just parameterized the work inward some trend too added some implausible supernatural phenomena every bit "possible" explanations of the problem. But you lot haven't genuinely made whatever steps towards proving that the problems direct hold been solved inward whatever way. And you lot haven't provided the readers amongst whatever evidence that your additional hypotheses are right. So you lot direct hold just confined yourself into a less probable axiomatic organisation than you lot started with. The work is worse than it was earlier you lot tried to practice something.

If I quote Feynman's famous cargo cult offset speech:

There is also a to a greater extent than subtle problem. When you lot direct hold seat a lot of ideas together to brand an elaborate theory, you lot desire to brand sure, when explaining what it fits, that those things it fits are non just the things that gave you lot the persuasion for the theory; but that the finished theory makes something else come upward out right, inward addition.

That's just what Josset et al. – too many others – don't achieve. They determine that if a molar fairy is behind the cosmological constant, she must direct hold \(10^{123}\) times longer teeth than her legs. But it's just a parameterization of the pre-existing problems inside a detail framework that makes extra assumptions: nil novel comes right from the "theory". The theory is scientifically worthless – it's just a trend to decorate the numbers too problems amongst some arbitrary novel words too visions. But scientific discipline must also arrive at results, i.e. trim back the issue of unexplained independent mysteries or parameters or observations.

At Hossenfelder's blog, Haelfix wrote:

It's non exclusively settled whether Unimodular gravity differs from GR's prediction at the quantum level. This goes dorsum too forth endlessly inward the literature.

At the really least, its non clear what you lot gain when trying to solve the cosmological constant problem. There is soundless a finetuning problem, the difference is -they say- that in that place is only i issue to explain, too non an entire renormalization tower of unknown physics which tends to drag you lot (order past times order) towards a Planckian value.

Amen to that.

It's questionable whether you lot may separately modify the line too non-trace at all, specially inward quantum gravity. Needless to say, you lot demand a genuinely consistent theory of quantum gravity to approach whatever such query genuinely meaningfully. String theory – the only known too in all likelihood the only mathematically possible framework that achieves that – doesn't allow you lot to process the line separately from the residual – in that place is no "unimodular gravity" according to string theory. Outside string theory, in that place are no well-defined rules which is a trend to empathize that the people answering these questions without string theory can't concord almost the answer.

(All the "critics" honey to say all the nonsense almost string theory's making no predictions. Unimodular gravity is just i illustration amid many: Without string theory, you lot can't say anything almost its validity. With string theory, you lot tin brand things sharp. If string theory is right, unimodular gravity is not. String theory answers all such qualitative "are you lot allowed to modify this or that" questions.)

But Haelfix pragmatically measures the "progress" inward the minute paragraph. The fine-tuning work for the cosmological constant isn't genuinely solved because you lot haven't explained why the apparent cosmological constant has converged to the observed tiny value later all these uncontrollable violations of the conservation law. And when the cosmological constant work is approached consistently, it differs from problems amongst non-renormalizability of theories because the vacuum unloose energy term is maximally "relevant" (dimension null operator) so it doesn't arrive at a tower of high-dimension operators.

In effective acre theory, you lot just demand to adapt i term, the bare cosmological constant, too everything is fine. It's soundless truthful that you lot demand such an adjustment inward the fairy-tale past times Josset et al. They haven't improved anything that is linked to the predictions. The ultimate query is why a theory that goes beyond the effective acre theory – e.g. string theory – where the cosmological constant isn't adjustable is predicting the value nosotros are observing. The story past times Josset et al. isn't helping to solve this actual work at all. It just parameterizes the work inward price of some specific hypothesized molar fairies that don't seem to last helpful inward making things better.

By the way, Hossenfelder gave a "cute" response to Haelfix's comment:

And, yes, what Haelfix says inward a higher house is correct, in that place is a long dorsum too forth inward the literature almost whether or non quantizing unimodular gravity helps amongst the cosmological constant work past times taming vacuum fluctuations, but the calculations inward the newspaper inward a higher house doesn't depend on the quantization.

Calculations inward a newspaper may last independent of effects inward quantum gravity but if quantum gravity prohibits assumptions or results of the calculation (such every bit unimodular gravity every bit an allowed inequivalent theory), too then the calculations inward the newspaper are clearly irrelevant for or inapplicable to our Universe which follows quantum, non classical, laws at the end. In other words, the newspaper is strictly worthless because the approximation it uses breaks downwards for the role where it's used.

I experience some deja vu. When the cosmological work was considered the hottest work inward physics some 2000, many solutions were proposed too the "violation of the unloose energy conservation" was in all likelihood i of them. I can't recollect who proposed it at that fourth dimension too I don't think it's of import or he or she deserves some credit. But this is just some other illustration showing that if somebody is trying to practice enquiry of physics without looking for whatever actual "laws", too without taking some "laws" seriously enough, he won't run into whatever progress. He volition just randomly oscillate dorsum too forth – without whatever trend to determine the positive too negative directions – inward the landscape of speculations. This is non what scientific discipline should practice which is why all the people should last expected to know the state-of-the-art framework to address all such questions, namely string theory. Even if somebody could reveal "something else" or a "problem amongst string theory", it could soundless last possible. But no i should last supported for some Brownian motion inward the landscape of speculations.