Re: [OT] Quantum physics question.

David Canzi -- non-mailable wrote:
In article <5di3bhF35b2h9U1@xxxxxxxxxxxxxxxxxx>, Rolf <rolf@xxxxxxxx> wrote:
[quoting Robert B. Laughlin:]
"Thus Newton's legendary laws have turned out to be emergent. They are not
fundamental at all but a consequence of the aggregation of quantum matter
into macroscopic fluids and solids - a collective organizational phenomenon.
They were the first laws to be discovered, they brought the technical age
into existence, and they are as exact and true as anything we know in
physics - yet they vanish into nothingness when examined to closely.
Astonishing as it may seem, many physicists remain in denial. To this day,
they organize conferences on the subject and routinely speak about Newton's
laws being an "approximation" for quantum mechanics, valid when the system
is large - even though no legitimate approximation scheme has ever been
found.



I find it difficult to think Laughlin making an outright false statement
here, so I am still waiting to see if I can get a clearer understanding of
what excatly the qoute means.

Two possible interpretations of what Laughlin is trying to say
stand out for me.

In quantum mechanics, quantities such as a particle's position
and momentum are probability density functions rather than exact
values. If the law of conservation of momentum exists at this
level, it might have to take a different form: the mean of the
probability density function of the sum of the momenta of two
interacting particles is the same after they interact as it was
before they interacted. The conservation of momentum we observe
in billiard balls would follow from this. If this is what Laughlin
is saying, it doesn't seem all that interesting.

Sadly for Laughlin this is the case. Momentum is a conserved quantity in Quantum Mechanics. It is a result of Noether's theorem: the fact that it does not matter where in space an experiment is performed implies that momentum (and energy, if you consider time as a dimension of space -> energy and momentum are related to each other in the same way as time and space) is conserved.

In particular, it is possible to measure momentum exactly (you'd lose all spatial information due to the Heisenberg uncertainty principle -> you might get an idea why Noether's theorem works the way it does); in this "picture" momentum is a conserved quantity.

What would be more interesting is if the law of conservation of
momentum didn't exist at all at the quantum level, even in the
fuzzy form I described above, but conservation of momentum at
macroscopic scales emerged statistically from large numbers of
particle interactions at the quantum scale that routinely VIOLATED
the law of conservation of momentum.

This would not work. Statistical mechanics works by virtue of the fact that collisions between atoms are elastic, i.e., conserve energy and momentum. Besides, if energy and momentum would not be conserved on a microscopic level, it would be possible to construct a perpetuum mobile, since not all processes are of a statistical nature. E.g., the photoelectric effect (which is due to an interaction between photons and electrons on the quantum level) would be either a source or a "sink" of energy if photon-electron interaction in QED did not conserve energy and momentum. In the first case you have a free source of energy; in the second case you'd also have a free source of energy by considering the reverse process.


The excerpts you've quoted don't make it clear which of these
two interpretations Laughlin intends (or if in fact he means
something else entirely), but this is talk.origins, and there
are people here who would like a version of physics that allowed
God's nano-tweezers to manipulate the universe without violating
its fundamental laws.


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