To Sympathize The Foundations Of Physics, Written Report Numerology

Numbers speak. [Img Src]

Once upon a time, nosotros had problems inwards the foundations of physics. Then nosotros solved them. That was forty years ago. Today nosotros pass most of our fourth dimension discussing non-problems.

Here is i of these non-problems. Did y'all know that the universe is spatially almost flat? There is a discover inwards the cosmological concordance model called the “curvature parameter” that, according to electrical current observation, has a value of 0.000 plus-minus 0.005.

Why is that a problem? I don’t know. But hither is the storey that cosmologists tell.

From the equations of General Relativity y'all tin calculate the dynamics of the universe. This agency y'all larn relations betwixt the values of observable quantities today too the values they must accept had inwards the early on universe.

The contribution of curved shape to the dynamics, it turns out, increases relative to that of thing too radiations every bit the universe expands. This agency for the curvature-parameter to live on smaller than 0.005 today, it must accept been smaller than 10^-60 or so briefly later the Big Bang.

That, so the storey goes, is bad, because where would y'all larn such a modest discover from?

Well, allow me inquire inwards return, where produce nosotros larn whatsoever discover from anyway? Why is 10^-60 whatsoever worse than, say, 1.778, or exp(67π)?

That the curved shape must accept had a modest value inwards the early on universe is called the “flatness problem,” too since it’s on Wikipedia it’s officially to a greater extent than existent than me. And it’s an of import problem. It’s of import because it justifies the many attempts to solve it.

The shortly most pop solution to the flatness occupation is inflation – a rapid menses of expansion briefly later the Big Bang. Because inflation decreases the relevance of curved shape contributions dramatically – yesteryear something similar 200 orders of magnitude or so – y'all no longer accept to kickoff amongst some tiny value. Instead, if y'all kickoff amongst whatsoever curved shape parameter smaller than 10¹⁹⁷, the value today volition live on compatible amongst observation.

Ah, y'all mightiness say, but clearly at that topographic point are to a greater extent than numbers smaller than 10¹⁹⁷ than at that topographic point 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 discover is null regardless of its value. So the declaration is bunk. Logical mush. Plainly wrong. Why produce I boot the bucket on hearing it?

Worse, if y'all desire to selection parameters for our theories according to a uniform probability distribution on the existent axis, too then all parameters would come upwardly out infinitely large amongst probability one. Sucks. Also, doesn’t depict observations^*.

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

If y'all accept problem seeing the trouble, allow me inquire the enquiry differently. Suppose we’d create out to stair out the curved shape parameter today to a precision of sixty digits later the point. Yeah, it’s non going to happen, but deport amongst me. Now you’d accept to explicate all these sixty digits – but that is every bit fine-tuned every bit a null followed yesteryear sixty zeroes would accept been!

Here is a different illustration for this idiocy. High liberate energy physicists yell upwardly it’s a occupation that the volume of the Higgs is xv orders of magnitude smaller than the Planck volume because that agency you’d quest ii constants to cancel each other for xv digits. That’s supposedly unlikely, but delight don’t inquire anyone according to which probability distribution it’s unlikely. Because they can’t respond that question. Indeed, depending on character, they’ll either walk off or verbalize downwards to you. Guess how I know.

Now consider for a 2nd that the volume of the Higgs was genuinely nigh every bit large every bit the Planck mass. To live on precise, let’s say it’s 1.1370982612166126 times the Planck mass. Now you’d i time again accept to explicate how y'all larn just those sixteen digits. But that is, according to electrical current lore, non a finetuning problem. So, erm, what was the occupation again?

The cosmological constant occupation is some other such confusion. If y'all don’t know how to calculate that constant – too nosotros don’t, because nosotros don’t accept a theory for Planck scale physics – too then it’s a complimentary parameter. You boot the bucket too stair out it too that’s all at that topographic point is to say nigh it.

And at that topographic point are to a greater extent than numerological arguments inwards the foundations of physics, all of which are wrong, wrong, incorrect for the same reasons. The unification of the approximate couplings. The so-called WIMP-miracle (RIP). The rigid CP problem. All these are numerical coincidence that supposedly quest an explanation. But y'all can’t speak nigh coincidence without quantifying a probability!

Do my colleagues deliberately prevarication when they claim these coincidences are problems, or produce they genuinely believe what they say? I’m non certain what’s worse, but suspect most of them genuinely believe it.

Many of my readers similar outflow to conclusions nigh my opinions. But y'all are non i of them. You too I, therefore, both know that I did non say that inflation is bunk. Rather I said that the most mutual arguments for inflation are bunk. There are skillful arguments for inflation, but that’s a different storey too shall live on told some other time.

And since y'all are amid the few who genuinely read what I wrote, y'all every bit good sympathise I didn’t say the cosmological constant is non a problem. I just said its value isn’t the problem. What genuinely needs an explanation is why it doesn’t fluctuate. Which is what vacuum fluctuations should do, too what gives ascent to what Niayesh called the cosmological non-constant problem.

Enlightened every bit y'all are, y'all would every bit good never yell upwardly I said nosotros shouldn’t assay to explicate the value of some parameter. It is ever skillful to await for ameliorate explanations for the supposition underlying electrical current theories – where yesteryear “better” I hateful either simpler or tin explicate more.

No, what draws my ire is that most of the explanations my colleagues set forrad aren’t whatsoever ameliorate than just fixing a parameter through measuring  – they are worse. The ground is the occupation they are trying to solve – the smallness of some numbers – isn’t a problem. It’s just a belongings they perceive every bit inelegant.

I thence accept a lot of sympathy for philosopher Tim Maudlin who recently complained that “attention to conceptual clarity (as opposed to calculational technique) is non business office of the physics curriculum” which results inwards inevitable confusion – non to advert waste materials of time.

In response, a pseudoanonymous commenter remarked that a tidings betwixt a physicist too a philosopher of physics is “like a ground betwixt an experienced motorcar mechanic too mortal who has read (or mayhap skimmed) a volume nigh cars.”

Trouble is, inwards the foundations of physics today most of the motorcar mechanics are repairing cars that run just fine – too and then neb y'all for it.

I am non opposed to using aesthetic arguments every bit inquiry motivations. We all accept to larn our inspiration from somewhere. But I produce yell upwardly it’s bad scientific discipline to pretend numerological arguments are anything to a greater extent than than appeals to beauty. That real modest or real large numbers require an explanation is a belief – too it’s a belief that has boot the bucket adapted yesteryear the vast bulk of the community. That shouldn’t come about inwards whatsoever scientific discipline.

As a consequence, high liberate energy physics too cosmology is directly populated amongst people who don’t sympathise that finetuning arguments accept no logical basis. The flatness “problem” is preached inwards textbooks. The naturalness “problem” is all over the literature. The cosmological constant “problem” is on every pop scientific discipline page. And so the myths alive on.

If y'all suspension downwards the numbers, it’s me against ten-thousand of the most intelligent people on the planet. Am I crazy? I sure am.

---

*Though that’s just what happens amongst bare values.