[math-fun] quantum theory foundational issues, my theory of how they should be resolved
From: meekerdb <meekerdb@verizon.net>
and, quite so. The 2nd law is true. It actually is a theorem of mathematics in Von Neumann's formulation of quantum mech with his defn of "entropy" (entropy increases during "measurements", stays same rest of time).
Being "a theorem of mathematics" just means it follows from some assumed axioms. Von Neumann's formulation is like decoherence theory without mentioning the environment. So it has the same weakness plus one more.
--well, I suppose I'd agree with that, but... the point is, this picture by Von Neumann of quantum mechanics, although clearly "wrong" in the sense essentially everybody agrees there must be no such thing as "measurement" really... also is clearly "right" in the sense everybody agrees that Von Neumann quantum mech agrees with every experiment. If you deny there is measurement, then this theorem shows entropy always stays the same. Which proves something is screwed up. The truth (i.e. my picture) is that entropy associated with the part of the universe we can perceive, increases. Random information swap effects occur with the other part, this causes us to perceive measurement-like effects and entropy increase. (Any observer "in the other part" who could not perceive our part would also perceive entropy increase.) The fact that I show theorem that the info once swapped "cannot come back to haunt us" means this can keep happening forever, and will keep seeming like measurement and hence entropy increase forever.
Now if the universe were to turn round and start contracting, I assure you entropy would continue to not decrease (and to increase).
If you just did a CPT transformation on the state of the universe you'd have
--no. CPT is a symmetry of flat space quantum field theories (e.g. the standard model). But, it is NOT really a symmetry of general relativity. General relativity CANNOT be solved going backward in time, it can be solved going forward in time. Situation is like the 1D heat equation, which has solutions going forward in time, but not going backward in time. (Another theorem of mathematics.) My paper explains this. I think this observation, although easy, was new.
universe that was obeying all the same laws of physics, except it was contracting - and hence the entropy would be decreasing.
--your reasoning here bogus, see above.
Of course no one living in this universe would notice this because the physical arrow of time would still point in the direction of expansion. So yes entropy increasing (on average) is a kind of tautology.
--no, it is not. And it does not just increase "on average," in Von Neumann's theorem.
If the universe started out high entropy, it would not matter either. This is a statement about enormous probabilistic "forces." It holds regardless of the shrinking or expanding of the universe which is an irrelevancy. This whole ludicrous myth was started by S.Hawking in his popular book "history of time" and even though Hawking later publicly stated that him saying this was the greatest and most humiliating error he ever made in his life, this absurd myth then attained a life of its own.
Now in my paper I cited I pointed out that general relativity DOES say something about the direction of time (unlike every other physical theory in the standard model if "measurement" is regarded as not existing). Namely, there are theorems in GR like black holes can merge but not bifurcate. But can white holes bifurcate? I think so; it is only statistically improbable because of the retarded radiation boundary condition.
--there are no white holes. Anyhow, my paper discussed this, if there were a solution describing white holes bifurcating then an observer would perceive it as black holes merging.
Efficient gravity wave emitters can exist but not absorbers. Small perturbations of the Schwarzschild metric die out with time, not grow.
That's because they radiate away energy.
--no, it is because the perturbations get absorbed into the black hole (or anyhow this seems more true description). It is actually again rather like 1D heat equation, where small ripples just die out. Not because they are "radiated away" (1D heat equation has no "radiation"). A Schwarzschild black hole is like a bell. It can "ring" with characteristic frequencies. But these frequencies are actually complex numbers, i.e. both oscillation and exponential die-out occurs. (These are called in the literature "quasimodes" of the black hole.) Every quasimode always has the imaginary part of the frequency of the right sign for die-out, not exponential growth. Similarly to the 1D heat equation where any fourier mode will die out exponentially with time, not grow. GR features a unique time-sign-direction just like the 1D heat equation. Physicists had not previously seen this, or at least the usual GR books never say so. And it is not a tautology. Now if these bell-ringing eigenmodes "radiated" energy away, then their amplitudes could not fall exponentially (which they do, everywhere, with the same e-folding time everywhere), they instead would fall like a power law. That is why I say it is a better description that the modes get absorbed into the hole. The direction of time in GR is "into" not "out of" a black hole. It thus is uniquely signed. It is highly related to the positivity of mass (and quantum field theories also agree mass is positive only, so presumably quantum gravity -- whatever that is -- which somehow merges the standard model with GR, also agrees mass positive). This discussed in my paper.
On 7/29/2013 8:34 AM, Warren D Smith wrote:
From: meekerdb <meekerdb@verizon.net>
and, quite so. The 2nd law is true. It actually is a theorem of mathematics in Von Neumann's formulation of quantum mech with his defn of "entropy" (entropy increases during "measurements", stays same rest of time). Being "a theorem of mathematics" just means it follows from some assumed axioms. Von Neumann's formulation is like decoherence theory without mentioning the environment. So it has the same weakness plus one more. --well, I suppose I'd agree with that, but... the point is, this picture by Von Neumann of quantum mechanics, although clearly "wrong" in the sense essentially everybody agrees there must be no such thing as "measurement" really... also is clearly "right" in the sense everybody agrees that Von Neumann quantum mech agrees with every experiment.
If you deny there is measurement, then this theorem shows entropy always stays the same. Which proves something is screwed up.
Not in Everett's interpretation. Entropy always stays the same, but you split up so you can only see part of the multiverse. You can't see the correlations with the rest of the multiverse so you think the entropy has gone up.
The truth (i.e. my picture) is that entropy associated with the part of the universe we can perceive, increases. Random information swap effects occur with the other part, this causes us to perceive measurement-like effects and entropy increase. (Any observer "in the other part" who could not perceive our part would also perceive entropy increase.) The fact that I show theorem that the info once swapped "cannot come back to haunt us" means this can keep happening forever, and will keep seeming like measurement and hence entropy increase forever.
Now if the universe were to turn round and start contracting, I assure you entropy would continue to not decrease (and to increase). If you just did a CPT transformation on the state of the universe you'd have --no. CPT is a symmetry of flat space quantum field theories (e.g. the standard model). But, it is NOT really a symmetry of general relativity. General relativity CANNOT be solved going backward in time, it can be solved going forward in time. Situation is like the 1D heat equation, which has solutions going forward in time, but not going backward in time. (Another theorem of mathematics.) My paper explains this. I think this observation, although easy, was new.
universe that was obeying all the same laws of physics, except it was contracting - and hence the entropy would be decreasing. --your reasoning here bogus, see above.
Of course no one living in this universe would notice this because the physical arrow of time would still point in the direction of expansion. So yes entropy increasing (on average) is a kind of tautology. --no, it is not. And it does not just increase "on average," in Von Neumann's theorem.
If the universe started out high entropy, it would not matter either. This is a statement about enormous probabilistic "forces." It holds regardless of the shrinking or expanding of the universe which is an irrelevancy. This whole ludicrous myth was started by S.Hawking in his popular book "history of time" and even though Hawking later publicly stated that him saying this was the greatest and most humiliating error he ever made in his life, this absurd myth then attained a life of its own.
Now in my paper I cited I pointed out that general relativity DOES say something about the direction of time (unlike every other physical theory in the standard model if "measurement" is regarded as not existing). Namely, there are theorems in GR like black holes can merge but not bifurcate. But can white holes bifurcate? I think so; it is only statistically improbable because of the retarded radiation boundary condition. --there are no white holes. Anyhow, my paper discussed this, if there were a solution describing white holes bifurcating then an observer would perceive it as black holes merging.
Efficient gravity wave emitters can exist but not absorbers. Small perturbations of the Schwarzschild metric die out with time, not grow. That's because they radiate away energy. --no, it is because the perturbations get absorbed into the black hole (or anyhow this seems more true description).
It is actually again rather like 1D heat equation, where small ripples just die out. Not because they are "radiated away" (1D heat equation has no "radiation").
A Schwarzschild black hole is like a bell. It can "ring" with characteristic frequencies. But these frequencies are actually complex numbers, i.e. both oscillation and exponential die-out occurs. (These are called in the literature "quasimodes" of the black hole.) Every quasimode always has the imaginary part of the frequency of the right sign for die-out, not exponential growth. Similarly to the 1D heat equation where any fourier mode will die out exponentially with time, not grow.
GR features a unique time-sign-direction just like the 1D heat equation. Physicists had not previously seen this, or at least the usual GR books never say so. And it is not a tautology.
Now if these bell-ringing eigenmodes "radiated" energy away, then their amplitudes could not fall exponentially (which they do, everywhere, with the same e-folding time everywhere), they instead would fall like a power law.
How so? If the rate of radiation is proportional to the amplitude then the energy loss rate will decay exponentially. How do you get a power law?
That is why I say it is a better description that the modes get absorbed into the hole.
OK. The interior is the future at the event horizon. Brent
participants (2)
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meekerdb -
Warren D Smith