So, Vilenkin would agree that an inflaton decay is much more likely than a Boltzmann solar system, but that you’re not actually addressing his argument.

That literally is our argument.

That’s my point. You keep citing people as if they said anything that disagrees with or undermines anything I have said, from article through all the comments.

And I keep explaining to you that you have failed at that. Because not a single one of these people said anything that disagrees with or undermines anything I have said, from article through all the comments.

Thank you for this detailed reply, Dr. Carrier.

I would just point out that Vilenkin would totally agree with you that “a Boltzmann solar system is more like the tiger and less like a spontaneous random inflation event, which only requires the assembly of a single inflaton..”

He is a big proponent of the inflaton idea. In fact, he thinks that the inflaton will continue decaying infinitely into the future, which implies that the system as a whole will never reach entropic equilibrium. So, he is totally on board on this point.

But Vilenkin was specifically referring to “the meticulous arrangement and bonding of trillions upon trillions of atoms in exactly the right arrangement so as to leave a self-sustaining solar system, planet and star, arranged just-so as to make life possible.”

That is the “Boltzmann solution”, i.e., the reduction of the entropy of the particles or molecules or atoms of the system. You even briefly touched this hypothesis in an old article of yours:

“And yes, there will inevitably be a completely random assembly of a whole working universe out to a visible horizon fourteen billion light years away that just by accident happens to look like it’s undergoing an accelerating expansion, and look like it began by a Big Bang but didn’t, and people in that world will be fooled.” (“The God Impossible”, 2012)

So, Vilenkin would agree that an inflaton decay is much more likely than a Boltzmann solar system, but that you’re not actually addressing his argument.

That is erroneous.

First, a Boltzmann solar system would not observe itself as a micro-universe. It would observe itself in a sea of cold background radiation in a seemingly flat and infinite universe.

Second, a Boltzmann solar system is actually less probable than a Boltzmann Big Bang. Vilenkin is failing to calculate the actual absurd precision and assembly of events (extreme ordering, not just entropy reversal) required for a solar system, which is not required for a Big Bang, which only requires a concentration of energy density, and is otherwise completely disordered.

Scientists and philosophers often get this wrong.

For a corrective understanding of Boltzmann phenomena see my discussion in respect to Justin Brierley and more importantly my discussion just last month in respect to Andrew Loke (look for the bit about the tiger).

A Boltzmann solar system is more like the tiger and less like a spontaneous random inflation event, which only requires the assembly of a single inflaton, not the meticulous arrangement and bonding of trillions upon trillions of atoms in exactly the right arrangement so as to leave a self-sustaining solar system, planet and star, arranged just-so as to make life possible.

And third, that’s just to get the possibility. The likelihood of life then arising (so as to make observations) is still astronomically small (see Why Life Must Be Complex (and Thus Probably Won’t Be on Mars) and Could Be a 38% Chance We Are the Only Civilization in the Known Universe).

Which means the relevant statistic is not the frequency of Boltzmann solar systems, but the frequency of biogenesis (…on up to observing civilizations, per the Drake equation, but the improbability of that is negligible at the scale of probabilities already tackled by biogenesis, making a difference of at best a few orders of magnitude, compared to dozens, so we can assume biogenesis practically entails observations to within rounding error).

The number of natural biogenesis events will vastly exceed that of Boltzmann solar systems experiencing biogenesis. Because a large enough universe to generate it by cascade (i.e. Wong-Hazen process) will generate lots of them. But indeed, even if they generated only one, that would vastly exceed the ratio for Boltzmann solar systems. Because we are multiplying two probabilities:

P(Boltzmann Big Bang) x P(biogenesis|Big Bang universe) and P(Boltzmann solar system) x P(biogenesis|single solar system).

Both probabilities are astronomically larger in the first case over the second. P(Boltzmann Big Bang) is vastly (vastly) larger than P(Boltzmann solar system), for much the same reason as Boltzmann tigers. And P(biogenesis|Big Bang universe) is vastly (vastly) larger that P(biogenesis|single solar system), because Big Bang universes generate not just one but trillions of trillions of solar systems.

So we can expect, by hundreds if not thousands or millions of orders of magnitude greater frequency, to find ourselves arising in a spontaneous Big Bang universe than in a Boltzmann solar system.

Actually, Professor Vilenkin did address that. In his 2007 book, he wrote:

“The problem with Boltzmann’s solution is that the ordered part of the universe appears to be excessively large. For observers to exist, it would be enough to turn chaos into order on the scale of the solar system. This would have a much higher probability than a fluctuation on the scale of billions of light-years that would be needed to account for the observed universe.” (Source: “Many Worlds In One”)

In other words, while a Boltzmann universe as large as ours will inevitably appear (if we accept the axioms/assumptions of the Poincaré theorem) it is extremely unlikely relative to smaller universes. Ergo, we should be observing a small universe right now. And yet, that is absolutely NOT what we observe. Ergo, it is more likely we’re not a Boltzmann fluctuation.

I’m not endorsing Vilenkin’s argument here. I’m just pointing out that he did address this potential objection.

No, Penrose outright admits quantum mechanics nullifies the key premise of the original theorem. Just as I explained. It has nothing to do with cyclical or inflationary cosmologies.

See “The Nature of Space and Time,” Stephen W. Hawking and Roger Penrose, Scientific American 275.1 (July 1996), pp. 60-65. Penrose: “quantum field theory might ‘smear’ out the singularities of general relativity in some way,” “there must be small quantum fluctuations in the initial state and thus…the hypothesis that the initial Weyl curvature is zero at the initial singularity is classical,” not quantum mechanical, and Penrose explains both this point (precise locations cease to exist below the Planck scale) and that gravity stops working below the Planck scale owing to quantization of the gravitational field (and thus true singularities cannot form on present physics) in his 1991 paper “What does the Big Bang tell us about quantum gravity?” He there proposes “new physics” to get singularities back; but that’s back to speculation.

As Wikipedia puts it, unless gravity is not quantized (defying quantum mechanics by making gravity fundamentally different than every other force and energy vector), “there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter” which violates the key premise in the Hawking-Penrose theorem that gravity continues working at all scales (see gravitational singularity); and “our usual picture of continuous commutative spacetime breaks down at Planck scale distances,” violating another of the key premises in the Hawking-Penrose theorem, that spacetime remains continuous to all scales (see quantum spacetime). Penrose has never disagreed with either conclusion; he has proposed speculative ways around them, but that’s just, again, speculation, and that he has to speculate ways around them is itself an acknowledgment of them.

I don’t wish to be nitpicky here, but Penrose didn’t admit his theorem is false. To my knowledge, he still thinks the theorems hold if the assumptions are correct. The only thing here is that he proposed his cyclic cosmology to get rid of the singularity by eliminating matter from the big bang. In other words, in his model, there is no matter density at the big bang, and for singularities to form, high density particles must be present. I’m sure Penrose will admit his CCC model is still speculative and so, the singularity theorems still hold — even though Inflation seems to violate the strong energy condition of the classical theorems. But Penrose doesn’t think Inflation is true.

Regarding String Theory, George Ellis et al. criticized it in their paper:

“Cosmological inflation and its realization within QG and, in particular, in string theory, was reviewed in [240]. Examples of string inflation include brane and axion inflation. There are also string inspired effective field theories. Since string theory is considerably more constrained, some effective field theories that are apparently consistent at low energies do not, in fact, admit ultraviolet QG completions (leading to improved predictivity). However, there are indications that it might not be possible to embed simple inflationary models in string theory [239, 240]…. In particular, there are well-known no-go theorems for the existence of stable de-Sitter vacua in critical string theory [239]. This is a real problem for inflation should string theory be the final theory of QG.”

Theoretical Cosmology (pp. 47, 48)

Regarding your argument that singularities can’t form because at the Planck length there is no definite position, I didn’t find any paper arguing this is the case. The only “article” where this was briefly discussed in the Hawking popular web page where he discusses the singularity is eliminated because of the Heinsenberg principle.

Further, there are people who argue gravity doesn’t have to be quantized like other fields (so perhaps there is no real graviton).

Sheers.

That doesn’t matter to the point. The only way to “get singularities back” is to invent some new physics. Nothing Plebanski says reverses that fact. At most all he is saying is that new physics could get them back. Which is only trivially true. Hence this is just a speculation. It is not a statement about current science.

Maybe you don’t understand what he means by “the collection of models of matter”? He’s referring to models of matter before quantum mechanics was fully extended to singularity theorems (he’s talking about 1973, the year of the Hawking-Penrose theorem; not later, when Hawking and Penrose admitted the theorem is false). In other words, he is saying one could have deduced singularities from their working models of matter without relativity; but that’s all moot, because that model of matter he’s talking about has since been proved false. Now we know matter does not exist below a certain scale, nor do bosons, particularly gravitons. Thus, once you get matter shrunk to below the scale at which even gravitons function, gravity stops working. Consequently, matter cannot continue collapsing. No singularity. Additionally, below a certain scale, location does not even properly exist anymore, i.e. an object can only be smeared out over an area. There is no meaningful sense in which points of location in space exist below a Planck length; consequently, singularities are logically impossible. Unless there is something we don’t know about sub-quantum-scale physics. Hence, some new physics. But the most promising new physics, e.g. string theory, shores up this conclusion, rather than bypassing it (string theory entails a geometric bounce will occur before any singularity can form). So he needs to posit some truly alien physics not even presently plausible. That’s as speculative as speculation gets.

Though I don’t think he’s really even saying that. The Plebanski quote appears to be discussing the past history of physics. Not present physics.

That’s correct, Dr. Carrier. But Plebanski acknowledges that quantum effects may eliminate the singularity. However, it seems you’re focusing on the wrong argument. The argument is that General Relativity is just one assumption of the singularity theorems. The central assumption, according to Plebanski, is “the collection of models of matter.”

So, it seems to me that if we follow this reasoning, even if General Relativity is modified by a quantum gravity theory, singularities will still be inevitable because matter itself will continue the same!

That there are hypothetical ways to maybe have singularities is not relevant to the question of what we know. Right now what we know is quantum mechanics (not relativity) renders singularities impossible. Any speculation about how to get them back with some sort of as-yet-undiscovered laws of physics is just that: speculation.

And they admit this: these speculative new physics “have not, so far, been shown to describe any actual astrophysical situation.”

Exactly.

Sorry, my fault!

In the 2nd quote, the physicist wrote: “but their very existence proves that singularities are an inevitable part not of relativity as such, but of the collection of models of matter defined by the assumptions of the singularity theorems.”

He is basically saying General Relativity is just an assumption of the singularity theorems. He claimed there are solutions of GR which do contain singularities and this (I don’t know how) shows the Hawking-Penrose theorems do not require GR; singular states are “inevitable” consequences of the “collections of models of matter.”

What do you think about that? Remember this is not from some dishonest apologist or silly creationist website; it is from a physics textbook.