Backreaction: The Same Stunning Misunderstanding Of Naturalness Every Mo Inwards 2009

Sabine Hossenfelder has some non-convex reproductive organs too the European Union's sexist bureaucrats brand sure that it's plenty too she doesn't receive got to sympathise whatever scientific discipline spell pretending to live a physicist. But her novel text

To sympathise the foundations of physics, written report numerology

is amazing because it's to a greater extent than than just a repetition of her consummate cluelessness nearly the logic of naturalness that she presented inwards 2009. Her novel text is truly to a greater extent than explicit, too hence dumber, than the text from the in conclusion decade.

From the beginning, she boldly tells us that any declaration referring to naturalness must live incorrect – including the declaration that the Universe should receive got improve undergone an inflationary epoch or some other epoch that explains its almost perfect flatness.




OK, let's re-create a slice of her diatribe:

...This way for the curvature-parameter to live smaller than 0.005 today, it must receive got been smaller than 10^-60 or so briefly afterwards the Big Bang.

That, so the story goes, is bad, because where would yous larn such a little release from?

Well, allow me inquire inwards return, where arrive at nosotros larn whatever release from anyway? Why is 10^-60 whatever worse than, say, 1.778, or exp(67π)? ...

10^-60 is worse for a elementary reason: it's lx or 158 f*cking orders magnitude smaller than the other 2 numbers above. And the probability that a release ends upward this little assuming whatever natural, normalizable distribution roofing numbers of lodge ane is comparable to the release itself.

If yous consider \(x\) which is uniformly too randomly distributed inwards the interval from 0 to 1 or from 0 to 3, the probability that it ends upward beingness 10^-60 or smaller is nearly 10^-60. The probability is virtually zero. On the other hand, the probability that a release distributed betwixt 0 too three ends upward beingness 1.778 or smaller (or larger) is nearly 50%, so it may perfectly good happen.

If the parameter were exp(67π), nosotros would receive got to invert the parameters because the selection of the dominant ane would receive got to live qualitatively changed, too in that location would live the inverse parameter exp(-67π) that would live fifty-fifty to a greater extent than unnatural than 10^-60 because exp(-67π) is nearly 10^-91.




I receive got used some probability distribution that covered the interval from 0 to 1 or 0 to three too was uniform. But the hollo for is that for whatever distribution that produces numbers naturally, the qualitative determination volition live the same. Consider the normal distribution around 0 amongst the measure divergence 7π². Some detailed numbers volition alter but the qualitative determination won't: it is insanely unlikely that the release ends upward beingness this small.

Any theory equipped amongst whatever distribution similar that volition predict that the required tiny initial value of the parameter is basically impossible, so the theory volition live f*cking falsified.

This doesn't hateful that in that location is a contradiction inwards physics or mathematics. Instead, what the declaration inwards a higher house way is that the right distribution that yous larn from a qualitative gauge sketch of the terminal theory has to live totally too radically different than whatever of the distributions that I mentioned above. So in that location must live some argue why an gauge sketch of the to a greater extent than consummate theory has e.g. the measure divergence comparable to 10^-60. Or the distribution must comprise a peak close zero, or many delta-function peaks close zero, or something else so that the probability that yous larn a qualitatively tiny release similar that volition no longer negligible.

This is what inflation does. It just expands the Universe so that it ends upward beingness apartment at the end.

Even for women who exclusively aid nearly their appearance, this thinking must live totally trivial. Imagine that adult woman H5N1 meets adult woman B too looks at her stomach. H5N1 has a random, fatty belly but she sees that B has a apartment stomach. The curved shape of the B's tummy is 0.000 plus-minus 0.005 if non plus-minus 10^-60. Woman H5N1 volition think: How it's possible that B's tummy is this just flat? Well, H5N1 volition offering a theory afterwards a while: B has undergone a plastic surgical operation to brand the tummy perfectly flat.



Ivan Mládek's musical version of the dialogue of these women, Ms Dáša Nováková too her pals.

C volition right away respond that H5N1 is just jealous nearly B's apartment stomach. And yous know, H5N1 is oft jealous. And yes, she is arguably a fatty obnoxious bitch, too. But inwards this case, she's manifestly right. B has indeed undergone a plastic surgical operation too the unnaturally apartment tummy is basically a proof. Natural women without whatever medical assist are beingness born amongst bellies whose curved shape radius is comparable to the meridian of the woman. They are of the same lodge – roughly a meter. If someone's measured curved shape radius is larger (i.e. curved shape is smaller) yesteryear several orders of magnitude, it proves that something unnatural has taken place.

It's exclusively "unnatural" relatively to the simplest theory. At the end, when yous figure out some novel qualitative persuasion what has happened – e.g. the stone oil concept of the plastic surgical operation – the extreme flatness may decease rather natural. After all, the plastic surgeon is a resultant of the natural selection too Darwin's development – despite his precision, he has evolved from apes. But the hollo for is that something large is missing inwards your calculation. Even earlier yous reveal out a hypothetical consummate precise theory that just predicts the tiny curved shape of B's belly, yous must live capable of finding a qualitative sketch of the theory. This qualitative sketch doesn't create the precise numerical value of the curvature. But it does explicate why the curved shape is so tiny. The consummate theory is a relatively "minor" refinement of this qualitative sketch.

Now, I talked nearly fatty too skinny women but the real same story applies to the Universe. The tiny value of the initial curved shape way that the "minimal story" – claiming that this is how the Universe began, without whatever other large events – is just wrong. Such a normal kickoff of the Universe would predict a curved shape of lodge ane too the probability that it would live lx orders of magnitude smaller is basically zero. Theories that predict real tiny probabilities for effects that nosotros truly notice are inwards problem – this is how nosotros exclude theories inwards physics – too inwards science. So in that location should improve live something that says that the kickoff of the Universe was non a "normal" structureless beginning. Something similar the plastic surgical operation – namely the inflationary epoch – had to accept place.

Ah, yous mightiness say, but clearly in that location are to a greater extent than numbers smaller than 10¹⁹⁷ than in that location are numbers smaller than 10^-60, so isn’t that an improvement?

Unfortunately, no. There are infinitely many numbers inwards both cases. Besides that, it’s totally irrelevant. Whatever the curved shape parameter, the probability to larn that specific release is null regardless of its value. So the declaration is bunk. Logical mush. Plainly wrong. Why arrive at I decease on hearing it?

She's just so breathtakingly stupid soundless self-confident.

Whether the "number of numbers" inwards a continuum is finite or infinite has nada to arrive at amongst the existence of the problem. The existence of a employment for a hypothesis is that it predicts a tiny probability for a suggestion that is truly observed to hold. Science is all nearly f*cking probabilities, non nearly some counting of numbers inwards a set. And the probability that the Big Bang Theory passes the essay of the stone oil value of the flatness is closer to null if there's nada special earlier the Big Bang expansion, too of lodge 1 if in that location is an exponentially expanding epoch earlier the Big Bang cosmology. That's why the cosmology amongst the inflationary epoch passes the essay spell the inflation-less Big Bang fails it. What the hell is so hard nearly this piddling thing?

And in that location is some other employment amongst that argument, namely, what probability distribution are nosotros fifty-fifty talking about? Where did it come upward from? Certainly non from General Relativity because a theory can’t predict a distribution on its ain theory space. More logical mush.

A distribution on a theory's parameter infinite should truly live a part of every modern usable theory. It's pretty much the same declaration every bit the declaration that if yous stair out the value of a quantity, yous should specify the mistake margin. If yous don't specify the mistake margin, the data nearly the measured value – which volition almost certainly non live exact if it is a existent release – may live said to live useless.

H5N1 usable theory must brand at to the lowest degree some modest declaration nearly the mistake margins, too hence nearly the distribution of its parameters. For example, QED, to live usable, has a fine-structure constant 1/137.036 too it must say at to the lowest degree that this release may live determined from the experiment XY too should live trusted at some precision – e.g. xv decimal points. If yous didn't know how ambitious QED is concerning the precision, yous wouldn't know which tests are vital.

If the theory implicitly stated that the release 1/137.036 is exact, the theory would live right away falsified because in that location are sure some deviations inwards the 16th meaning figure. On the contrary, if the theory implicitly stated that the fine construction constant is 1/137.036 addition minus 30%, so QED would exclusively live a qualitative sketch of some phenomena too wouldn't encourage yous to endeavour to arrive at high-precision tests. So the physicists using QED or whatever other theory just must receive got some persuasion nearly the distribution of the parameters.

The distribution of the parameters may live measured experimentally if the theory is assumed to pull the experiments – too nosotros larn the commons experimental mistake margins, statistical too systematic errors, too so on. But the distribution of the parameters must live used yesteryear a theory every bit well. H5N1 theory itself doesn't allow yous a precise calculation of the value of the parameter but yous must e'er supplement it amongst some sketch of a to a greater extent than consummate theory that does say something nearly the value of parameters, fifty-fifty though this declaration is fuzzy. Otherwise the theory would live absolutely vacuous.

If yous receive got problem seeing the trouble, allow me inquire the interrogation differently. Suppose we’d contend to stair out the curved shape parameter today to a precision of lx digits afterwards the point. Yeah, it’s non going to happen, but acquit amongst me. Now you’d receive got to explicate all these lx digits – but that is every bit fine-tuned every bit a null followed yesteryear lx zeroes would receive got been!

It's f*cking non the same at all. H5N1 generic parameter that is of lodge ane isn't fine-tuned spell a tiny ane that is comparable to 10^-60 is fine-tuned.

Here is a different illustration for this idiocy. High unloosen energy physicists think it’s a employment that the majority of the Higgs is xv orders of magnitude smaller than the Planck majority because that way you’d require 2 constants to cancel each other for xv digits.

You truly require to cancel xxx digits because the coefficient inwards the Lagrangian is the squared mass, non the majority itself.

That’s supposedly unlikely, but delight don’t inquire anyone according to which probability distribution it’s unlikely. Because they can’t answer that question. Indeed, depending on character, they’ll either walk off or utter downwards to you. Guess how I know.

It's f*cking unlikely according to any natural distribution – every bit I explained at the top every bit good every bit 8 years ago. That is why someone's "demand" to consider ane especial distribution exclusively shows her consummate incompetence. There is no unmarried preferred distribution inwards these discussions. The whole powerfulness of the naturalness reasoning boils downwards to the fact that it holds for all (or almost all) natural plenty distributions.

Now consider for a instant that the majority of the Higgs was truly nearly every bit large every bit the Planck mass. To live precise, let’s say it’s 1.1370982612166126 times the Planck mass. Now you’d over again receive got to explicate how yous larn just those xvi digits. But that is, according to electrical flow lore, non a finetuning problem. So, erm, what was the employment again?

Do my colleagues deliberately prevarication when they claim...

The employment is, ane time again, that some of the observed parameters are vastly smaller than one, too they're hence unnatural. The release 1.1370982612166126 times the Planck majority would live absolutely natural too would Pb to no fine-tuning employment or a conflict amongst naturalness. If ane produces 2 random numbers of lodge one, it's unlikely that both of them volition live just equal, or equal at the 16-digit precision. But this "two random numbers" do doesn't quantify whether there's fine-tuning.

The hollo for is that the release 1.1370982612166126 doesn't violate any natural, qualitative property that would live extremely probable according to whatever natural distribution. By a natural, qualitative property, I hateful a holding that tin post away live formulated without also many digits yous would receive got to recall (a holding that isn't fine-tuned yesteryear itself); but a holding that holds for a random release selected according to a natural distribution amongst a probability approaching one. On the other hand, 1.1370982612166126 x 10^-60 does violate a natural property. It violates the requirement that a parameter's absolute value should live greater than 10^-50.

Do my colleagues deliberately prevarication when they claim...

Nice tough words. They are non your colleagues, Ms Hossenfelder. They are physicists spell yous are just a f*cking stupid incompetent fraudster pretending that yous know something nearly research-level physics. You're just the type of aggressive junk that has spread every bit locusts every bit a upshot of the political correctness too affirmative action.