Re: The Universe in a Grain of Sand
From: Bjoern Feuerbacher (feuerbac_at_thphys.uni-heidelberg.de)
Date: 02/07/05
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Date: Mon, 07 Feb 2005 09:46:16 +0100
B.B. wrote:
> What follows in the next paragraph is some quotes from Brian
> Greene's "Fabric of the Cosmos". I'd like to ask a couple of
> questions. First. Is QM that incompatible with GR as the author
> claimed or do real physicists understand it better than pop-sci
> account?
One has to be careful what one actually means when one talks
about an incompatibility here. QM itself *is* compatible with
GR in the sense that one can formulate QM for curved spacetimes.
However, when one tries to apply Quantum *Theory* to gravity *itself*,
i.e. when one tries to formulate a "Quantum Gravity" theory,
*then* one runs into big troubles.
> Second. Does anyone actually believe that our entire
> universe were once smaller than the size of the atom?
The entire *observable* universe: probably yes. The *entire*
universe: no.
Notice that Greene himself talks about the *observable*
universe in the quotes below!
> This doesn't make any sense.
So what? It also does not make sense that heavy objects
fall equally fast than light one. Nevertheless, that's
also a fact.
> Quoting Brian Greene in "Fabric of the Cosmos"
>
> "Does It Matter?
>
> In practice, the incompatibility between general relativity and
> quantum mechanics rears its head in a very specific way. If you
> use the combined equations of general relativity and quantum
> mechanics, they almost always yield one answer: infinity.
Replace "Quantum Mechanics" with "Quantum Theory" here, then
I agree.
> And that's a problem. It's nonsense. Experimenters never measure an
> infinite amount of anything. Dials never spin around to infinity.
> Meters never reach infinity. Calculators never register infinity.
> Almost always, an infinite answer is meaningless. All it tells us
> is that the equations of general relativity and quantum
> mechanics, when merged, go haywire.
>
> Notice that this is quite unlike the tension between special
> relativity and quantum mechanics that came up in our discussion
> of quantum nonlocality in Chapter 4. There we found that
> reconciling the tenets of special relativity (in particular, the
> symmetry among all constant velocity observers) with the behavior
> of entangled particles requires a more complete understanding of
> the quantum measurement problem than has so far been attained
> (see pages 117-120). But this incompletely resolved issue does
> not result in mathematical inconsistencies or in equations that
> yield nonsensical answers.
Greene seems to conveniently gloss over the problems with
renormalization in Quantum Field Theory.
When combining QM with SR, or, more correctly, when
applying Quantum Theory to relativistic fields, there *also*
were infinities in the equations first. It took some very
bright physicists and about 15 years to resolve them in a
practical way (Feynman, Tomonaga and Schwinger), and even
about 20 years more for a consistent picture on what's
really going on there (Wilson).
> To the contrary, the combined
> equations of special relativity and quantum mechanics have been
> used to make the most precisely confirmed predictions in the
> history of science. The quiet', tension between special
> relativity and quantum mechanics points to an area in need of further theoretical development, but it has
> hardly any, impact on their combined predictive power. Not so
> with the explosive union between general relativity and quantum
> mechanics, in which all predictive power is lost.
And this ignores that there *are* some possibilities to
make predictions when combining QT with GR - for example,
in the semi-classical limit, Hawking derived his famous
theory that black holes can "evaporate".
[snip]
> Second, although most things are either big and heavy or small
> and light, and therefore, as a practical matter, can be described
> using general relativity or quantum mechanics, this is not true of all things.
> Black holes provide a good example. According to general
> relativity, all the matter that makes up a black hole is crushed
> together at a single minuscule point at the black hole's center.
> 7 This makes the center of a black hole both enormously massive
> and incredibly tiny, and hence it falls on both sides of the
> purported divide: we need to use general relativity because the
> large mass creates a substantial gravitational field, and we also
> need to use quantum mechanics because all the mass is squeezed to
> a tiny size.
I think it's a strange argument to say "it's tiny, therefore
we need QM!"
> But in combination, the equations break down, so no
> one has been able to determine what happens right at the center
> of a black hole.
Not at the center - but at least at the event horizon. See
Hawking's work I mentioned above.
[snip]
> To understand why, imagine, as in Chapter 10, running a film of
> the expanding cosmos in reverse, heading back toward the big
> bang. In reverse, everything that is now rushing apart comes
> together, and so as we run the film farther back, the universe
> gets ever smaller, hotter, and denser.
"smaller" has to be taken with a grain of salt here if
talking about the entire universe. It's o.k. if talking
only about the observable universe.
[snip]
Bye,
Bjoern
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