In my quest to understand quantum theory and find a reasonable interpretation
I recently came across this paper (pdf!) about 'The Impossibility of Accurate State Self-Measurements' by Thomas Breuer.
It is very similar to how I think about all this.
"It is shown that it is impossible for an observer to distinguish all
present states of a system in which he or she is contained ...
[..]
As far as quantum mechanics is concerned, von Neumann assumed the theory
to be universally valid and thus was led to the measurement problem.
Bohr denied the universal validity of quantum mechanics for 'purely logical reasons',
and thereby avoided confrontation with the measurement problem.
It has often ... been suggested that self-reference problems for universally valid
theories may pose serious difficulties for a quantum mechanical description of
the measurement apparatus. The aim of this paper is to investigate these suggestions."
January 9, 2010
I think it is unlikely that a lattice gravity model will correctly describe the quantum theory of gravitation any time soon,
although the odds have improved somewhat with new results about asymptotic safety.
While such models have interesting properties, as far as I know a reasonable continuum limit has never been demonstrated.
A few days ago Simon Catterall et al. published results for a model which goes back to the simulations of
Menotti & Pelissetto, but with an additional Wilson term in the action and thus an additional coupling
parameter. They find an interesting transition for a certain threshold value of this parameter and conclude that
"It remains to be seen whether this threshold value can be thought of as a true critical value and if so
whether this critical value corresponds to a continuous or discontinuous phase transition. The latter issue is
of course a crucial issue to address in the context of obtaining a non-trivial continuum limit."
Perhaps I should dust off our lattice gravity code(s) and see what they can do on new and better hardware.
It would be a nice (but almost certainly completely useless) project for 2010...
although the odds have improved somewhat with new results about asymptotic safety.
While such models have interesting properties, as far as I know a reasonable continuum limit has never been demonstrated.
A few days ago Simon Catterall et al. published results for a model which goes back to the simulations of
Menotti & Pelissetto, but with an additional Wilson term in the action and thus an additional coupling
parameter. They find an interesting transition for a certain threshold value of this parameter and conclude that
"It remains to be seen whether this threshold value can be thought of as a true critical value and if so
whether this critical value corresponds to a continuous or discontinuous phase transition. The latter issue is
of course a crucial issue to address in the context of obtaining a non-trivial continuum limit."
Perhaps I should dust off our lattice gravity code(s) and see what they can do on new and better hardware.
It would be a nice (but almost certainly completely useless) project for 2010...
January 3, 2010
I know that some people suspect that I delete blog posts every now and then, but this is not true. As far as I can remember I never deleted anything. It is much more plausible to assume that random 'blog posts' pop up in various RSS readers (and then disappear). Let me explain.
Quantum theory is the best description of physical reality we have and its most convincing aspect is of course the proper interpretation (see also here, here and here). In order to illustrate that, physicists usually consider the gedanken experiment of Schroedinger's cat. Initially the cat is in a state |Cb> (the C stands for cat and b stands for box), which develops into a state w|Hb> + w|Ub>.
The boring Copenhagen interpretation assumes that now a miracle occurs and we can use the coefficient w to calculate the probability to find either a happy or unhappy cat in the box.
However, the modern 'many cats interpretation' does not believe in miracles and instead tells us that the wave function never collapses and therefore ...
But wait a second, if the wave function never collapses then it is wrong to begin this gedanken experiment with the |Cb> state!
Instead we have to assume that initially the state was something like a|Cb> + b|Co>, where the o now indicates a cat
outside the box (because the decision to put the cat in the box never collapsed the wave function) and this state develops into something like w'|Hb> + w'|Ub> + n1|Co1> + n2|Co2> ...
But what if initially there was a choice between a cat and a dog, what about the decision to do the experiment at all, what about McCain winning the election etc. ?
So we have to assume that the wave function really is an infinite sum ... + w|Hb> + w|Ub> + ... ,with w->0 and with everything being possible included(*), even cats and blog posts popping up in RSS feeds etc. (**)
No wonder that Stephen Hawking was reaching for his gun...
Indeed we have to face this situation again (Fatwa and all), with all probabilities different from zero, but the lottery ticket worth nothing.
I am sorry Ponder S.
(*) The idea to look at 'relative probabilities' (i.e. for whatever reason consider |Hb> and |Ub> only, ignoring all branches we don't care about) would face the problem that we have to ignore infinitely many branches which may indeed interfere with the branches we care about; Even if the coefficients are small for each one, there are infinitely many to consider...
And how would we even know what branches we should include? Do we have to consult our memories to determine which branches were initially possible (cat inside or outside the box yes, pink unicorns no)? And the memories of which branch would we use?
(**) Of course, the idea of blog posts popping up randomly would explain a whole lot about the blogosphere...
Quantum theory is the best description of physical reality we have and its most convincing aspect is of course the proper interpretation (see also here, here and here). In order to illustrate that, physicists usually consider the gedanken experiment of Schroedinger's cat. Initially the cat is in a state |Cb> (the C stands for cat and b stands for box), which develops into a state w|Hb> + w|Ub>.
The boring Copenhagen interpretation assumes that now a miracle occurs and we can use the coefficient w to calculate the probability to find either a happy or unhappy cat in the box.
However, the modern 'many cats interpretation' does not believe in miracles and instead tells us that the wave function never collapses and therefore ...
But wait a second, if the wave function never collapses then it is wrong to begin this gedanken experiment with the |Cb> state!
Instead we have to assume that initially the state was something like a|Cb> + b|Co>, where the o now indicates a cat
outside the box (because the decision to put the cat in the box never collapsed the wave function) and this state develops into something like w'|Hb> + w'|Ub> + n1|Co1> + n2|Co2> ...
But what if initially there was a choice between a cat and a dog, what about the decision to do the experiment at all, what about McCain winning the election etc. ?
So we have to assume that the wave function really is an infinite sum ... + w|Hb> + w|Ub> + ... ,with w->0 and with everything being possible included(*), even cats and blog posts popping up in RSS feeds etc. (**)
No wonder that Stephen Hawking was reaching for his gun...
Indeed we have to face this situation again (Fatwa and all), with all probabilities different from zero, but the lottery ticket worth nothing.
I am sorry Ponder S.
(*) The idea to look at 'relative probabilities' (i.e. for whatever reason consider |Hb> and |Ub> only, ignoring all branches we don't care about) would face the problem that we have to ignore infinitely many branches which may indeed interfere with the branches we care about; Even if the coefficients are small for each one, there are infinitely many to consider...
And how would we even know what branches we should include? Do we have to consult our memories to determine which branches were initially possible (cat inside or outside the box yes, pink unicorns no)? And the memories of which branch would we use?
(**) Of course, the idea of blog posts popping up randomly would explain a whole lot about the blogosphere...
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