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shminux comments on Implications of an infinite versus a finite universe - Less Wrong
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"This WMAP data suggests that the Universe is infinite in extent (...)" in actuality means "as far as we know, the Universe is spatially flat, and we did not detect anything resembling spatial periodicity or an edge (domain wall), at least not yet". Don't go all Boltzmann Brains over one careless statement.
You're the phycisist (IIRC), isn't the currently favored model that there is an actual infinite number of galaxies? If so, that's what we should base our discussions on.
There are no infinities in physics, though there are many in the mathematical models it uses. The latter is because infinities actually make many concepts and calculations simpler.
This confuses me. What do you mean by "physics" besides mathematical models? You're not lapsing back to realism, are you? :)
Right, I asked myself the same question when writing my comment. I mean that infinities cannot be measured and that the current observations can be explained with infinity-free models, though sometimes not as elegantly.
Which kind of model does an instrumentalist use to guide their actions in this situation? The ones with infinities, the ones without, or a probabilistic mixture of the two kinds? It seems like you're saying just use the ones without infinities (since in either of the other two cases we do have to deal with Boltzmann brains). But how do you justify that?
In what situation? Calculus of infinitesimals is a convenient tool invented by Newton and Leibnitz to calculate planetary orbits and other things. The same can be done with differences and not differentials (and is, for numerical calculations), but requires more work. The situation is similar in most other areas. Kronecker delta is a convenient tool in physics and electrical engineering, without necessarily meaning that there is an infinitely strong and infinitely short spike of current somewhere in your circuit.
In the situation that infinite and finite cosmological models can both explain all current observations. Isn't that the topic of this thread?
The original concern was that the evidence points to the infinite universe, therefore everything imaginable happens somewhere. While this can be a fun speculation, I am merely pointing out that the evidence so far points to a very large universe, but not necessarily infinite or even close to large enough for Boltzmann brains.
That's what I argued on another site a few months ago, but how do you square that with most current reputable sources saying the universe is actually infinite?
This paper gives a lower bound of 251 Hubble spheres, but also leans towards ", the spatial extent of the Universe is infinite" (if the curvature is >=0). Nothing about "just a theoretical construct". As theoretical as all the other laws and the practical inferences we draw from them.
This paper says outright "An infinite universe is compatible with the data at a confidence level of 4.3σ."
Those were the two that came up at first glance on Google Scholar when looking for "size of the universe", they weren't cherry picked, and seemed to be follow-ups from the WMAP data.
From the last paper you linked:
The first paper only estimates the maximum curvature, not the size.
Hmm hmm, thanks. If it turns out that our current physical models imply that the universe is in fact finite, my "concerns" would go poof. You seem to be leaning towards finiteness, if so, may I ask what you base that on?
See my replies to Wei Dai.