Are Boltzmann Brains running Hilbert\'s Hotel? by William T. Parsons

There are some aspects of this in the literature. One paper critiques this. There are ways to non-Turing processing, and this is a discussion on interactive programming, similar to oracle Turing machines, that offers something interesting.

Cheers LC

William,

This is a valiant effort to defeat physical significance of infinities of number and extent (as of space-time and its contents). However, the aspects of infinity considered most problematic in physics are actually those regarding what could be called intensity or density of energy etc. One example is the case of the QED infinities that are handled by the suspiciously kludges of renormalization, another is the compressed singularity of GR. Ironically, the first one is caused by aspects of quantum mechanics, and the other kind might be ameliorated by QM! Your thoughts?

This surreptitious log-out is really getting annoying. I wrote the above comment, sorry. BTW thanks again for your comments at my essay. Note to any readers: my essay tries to make a true, specific contribution to physical knowledge (about why space is three-dimensional) and not just general points of principle.

Dear Conrad,

I liked much your essay, I gave it a high rate and I included it in the (second) list of best essays of my review. You seem to gather unanimity here, so I think the interesting question is: who would think otherwise (believe in physical infinity) ? You wrote in your comment that you "started out believing in physical infinity" yourself. Was it just a default position by lack of precise ideas ? Do you know any physicists having a firm belief in physical infinity ?

If I had to express a bet with respect to cosmology, I would opt for the idea of a spherical universe, that I see as the simplest and most natural way a universe can be created. Indeed, I hardly see the sense and possibility of an infinite universe (how can it start in the first place ?), and I don't believe I have clones anywhere. So, since we already verified the surprising fact that the cosmological constant is extremely small (compared to its microphysical causes) but nonzero, I see it natural to expect a similar property for the curvature of the universal "geography".

But the other question is that of the infinitely small. You seem to assume that nobody takes seriously the idea of a physical infinity in the infinitely small, as all we can measure is approximations. But I do think that there are many people whose views logically imply the existence of a physical infinity in the infinitely small, even if they are not ready to admit it. What I mean here is that they have mutually contradictory beliefs and they fail to notice the contradiction.

Precisely, I see only 3 possibly coherent views with respect to the infinitely small:

1) A digital universe, made of pixels (or the like), where continuous geometrical symmetries are only an emergent property.

2) A quantum universe, where the (usually called "paradoxical") properties of quantum physics are accepted as actually describing how things are, and finally understood as not really paradoxical since they are the solution of this other paradox : the reconciliation of continuous geometrical symmetries with the absence of actual infinity in the infinitely small. This is achieved by the fact that the continuous symmetries (such as rotations of a local object) are not acting over an actually infinite list of really distinct states, but over the continuous values of probabilities for the system to appear in one or another state if it is measured. This means to reject physical realism, as the continuity of the transition between the possibilities for 2 states to be identical or distinct, means that there is no physical reality of which state a system exactly is in. I commented this further in pages 5 and 6 of my essay.

3) A classical continuous universe, which logically means to admit an actual infinity of physically distinct possible intermediate states between 2 states. A typical example is Bohmian mechanics. Supporters of such views may hope to keep this compatible with practical finiteness, i.e. that this actual infinity only concerns the ontology that, at the same time, they wish to deny on an effective level, where it would behave as a potential infinity only. Namely, they expect the effects of the whole infinity of decimals of their "hidden variables" are not popping up in finite times. However I do not see it clear if they can really find a coherent theory satisfying that property and that would be compatible with known physics (quantum field theory). For details, see in my criticism of Bohmian mechanics, the section "Problem 2 : the nonsense of deterministic randomness".

Sorry I mistook the name, I meant William of course.

Dear William,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear Bill Parsons,

I agree that Hilbert's hotel is unphysical. But do you think that potential infinity is unphysical?

Best,

Lou Kauffman

Dear Bill,

Thank you ever so much for leaving such a positive comment about my essay.

One real Universe can only be occurring in one real infinite dimension. Unfortunately, scientists insist on attempting to measure the three abstract dimensions of height, width and depth, with completely unrealistic results. The real Universe must be infinite in scope and eternal in duration.

Gratefully,

Joe Fisher

Bill,

Your Hilbert Hotel is an esoteric location steeped in meaning. Do Boltzmann Brains have physical baggage of a type 0 civilization that restrict a Hilbert Hotel in a type 2 civilization?

My connections of mind, math, and physics are quite pedestrian in producing advances in quantum biology, DNA mapping and simulation of the BB: http://fqxi.org/community/forum/topic/2345.

Thanks for sharing your imaginative hotel.

Jim

Bill,

You are very kind, not only in being engaged in my essay but also engaging in your interest.

Quick question: Is the equation involving Gt on page 3 your work? If so, how did you derive it? Having such a meager math background, I thought it somewhat primitive but applicable, starting with a compound interest formula, the principal of dynamic growth.

On a more personal note, as a pilot, I've always respected Boeing aircraft. Did you ever work on the Triple7? A truly fantastic airplane. I worked on the military side mostly, only occasionally doing cost-benefit on the commercial side, including the 777.

Jim

I disagree with it.

Since I believe "It Takes Two Hands Clapping to Make a Noise"

-Best regards

Miss. Sujatha Jagannathan

Dear William,

Great essay! It is well-argued and well-written. You explained the difference between mathematical and physical infinity. You also gave strong arguments for how to deal with physical infinity, and I strongly agree with them and give you highest rating. I would be glad to take your opinion in my essay.

All the best,

Mohammed

Dear Bill,

What a delightful essay! You should consider moonlighting as a science writer (what is a physicist-in-residence, anyway?)

"..I reject physical infinity, for three reasons. First, mathematically, it

makes computations intractable. Second, operationally, I do not know how--even in principle--how

to observe, measure or manipulate physically infinite objects or systems. Third, conceptually, it

embodies a viciously unphysical ontology, namely, that physical constituent parts can equal each

other and the physical whole from which they derive."

These are all good reasons, but may I suggest that infinities in physical theories may have a useful role to play that is in my opinion still greatly under-appreciated: I think that at least in some (perhaps, with enough imagination, in all meaningful) cases in which they occur, they may be telling us that we are not looking at the physical situation at hand in "the right way".

The paradigm example to me is the Lorentz factor. For v=c it is infinite, and so presumably one of the unfortunate victims of your effort to eradicate its kin from physics. But what if we look at its inverse: The inverse of the Lorentz Factor tells us how much the proper time changes with respect to coordinate time. In fact, because of the mathematical form of gamma we can get it to tell us more: How much of the proper time is "projected" unto coordinate time (as I'm sure you know, one can easily see this by drawing the appropriate triangle that illustrates

[math] \tau\times(\gamma^{-2}=1- \beta^2)^{1/2}[/math]

In that case, if we take the triangle relationship seriously, gamma=1 tells us that all of the object's proper time is "projected" unto the observer's coordinate time and gamma=infinity tells us that none of it is "projected" unto the observer's coordinate time, or, in other words, that the object's proper time is orthogonal to the coordinate time if we were to assign unit vectors to the abstract plane spanned by the two time parameters . This is of course consistent with the fact that null vectors are orthogonal to time-like vectors.

Orthogonality is one of those situations which commonly involves zero and infinity, and seems to have been what lurked behind this infinity. Orthogonality is also a basic conceptual staple of physics, and so I suspect that there is something conceptually very clear and thoroughly physical behind many infinities in physics in a similar manner, but not very well recognized as such.

I'd be interested to know what you think of this argument, and whether it leads you to modify your categorical rejection of infinities in physics.

Best wishes,

Armin