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Topic: All our demons (Read 4305 times) |
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Mickey1
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All our demons
« on: Oct 5th, 2013, 2:34pm » |
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Let us recall Laplace’s demon, or intelligence, that knows the mass, location and velocity of all particles:
“for such an intellect, nothing would be uncertain and the future just like the past would be present before its eyes” (Wikipedia). The same source also informs us (on the same subject) that
“The Heisenberg Uncertainty Principle states that exact measurements of positions and momentum cannot be known, together, with more than a given precision.”
You note perhaps that in this formulation, Wikipedia assumes, indirectly, that all particles have exact positions and momentum. Our problem is that while the quantities exist (in Wikipedia’s formulation – endless other interpretations are possible), we can’t ascertain them. They are therefore not operational or constructible.
Let us now move to a similar mathematical demon or intellect. Just as its counterpart in physics it knows just about all there is to know - in mathematics. This means for one thing, that it knows all the real numbers, and all sets of real numbers . You can imagine the following Q&A
Q: Does an upper bounded set has a least upper bound?
A: Yes.
Q: how did you reason here?
A: I didn’t. I checked all bounded sets and noted that they did all have an upper bound. The answer is evidence-based.
You may note that there is some similarity here, between the two scenarios. All the numbers cannot be individually constructed by humans, i.e. by a finite sequence of instructions, just as the simultaneous position and moment cannot be constructed as an outcome of an experiment.
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Nursejim
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Re: All our demons
« Reply #1 on: Oct 5th, 2013, 10:47pm » |
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A moment, and thusly all time in general, simply does not exist. Time is feeble construct of the human mind. What we consider time is only a repeating rhythm such as in music and how great a symphony does the universe play! The sun I see with my own eyes transcends time. It exists now and the future and past. BUT alas there is no time..... there only IS. The star I see a million light years away IS my reality, not my past. Momentum can never be truly determined according to quantum mechanics. Some say the second law of thermodynamics contradict demon theory. Chaos theory anyone? Can all possible outcomes exist in the same space and the same lack of time?
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towr
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Re: All our demons
« Reply #2 on: Oct 6th, 2013, 8:45am » |
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on Oct 5th, 2013, 2:34pm, Mickey1 wrote:“The Heisenberg Uncertainty Principle states that exact measurements of positions and momentum cannot be known, together, with more than a given precision.”
You note perhaps that in this formulation, Wikipedia assumes, indirectly, that all particles have exact positions and momentum. |
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I don't note that, since it isn't implied. I note only that it speaks of measurement and not of any underlying truth or reality. If a particle has neither, you also couldn't (hopefully) measure both with more than a given precision (and if you could, there would definitely be something very wrong with your measurements as you'd be measuring something that we just presumed doesn't exist).
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rmsgrey
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Re: All our demons
« Reply #3 on: Oct 7th, 2013, 5:52am » |
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Quantum Mechanics goes further than saying that you can't measure both position and momentum to arbitrary precision at the same time - it actually makes verified predictions based on the assumption that there isn't an underlying reality where both are well-defined exact values that we just can't access - quantum tunneling, where one solid object passes through a solid barrier, works because the position of the object while it passes through the barrier is not an exact value - offering a third possibility for Schroedinger's Cat - alive, dead, or escaped...
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Mickey1
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Re: All our demons
« Reply #4 on: Oct 7th, 2013, 2:39pm » |
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“The Heisenberg Uncertainty Principle states that exact measurements of positions and momentum cannot be known, together, with more than a given precision.”
I must admit as I look back on Wikipedia’s text that it is somewhat strange: exact measurements of positions and momentum “cannot be known” (?), I take it that “measurement” here is understood as values resulting from a measurement, which then cannot be known (?). Nevertheless I admit that I have to make my own point rather than attributing anything to Wikipedia:
First I take a particle interpretation such as presented by Michael Audi (Interpretation of Quantum Mechanics Audi M (1973), The University of Chicago Press), Born and others. This is choosing a minority point of view. Secondly, I then a proceed with my demon.
Let me make two comments QM relations, i) system behavior as noted in experiments, is solid enough, ii) QM as a theory is not in itself - although often confused with - reality. Schrödinger’s cat just shows us some peculiarities in the interpretation of the theory, there is nothing wrong with reality. On her way home my wife speculate if I have made fish or steak for dinner, she doesn’t know and must assume a reality model, or a wave form with both possibilities. There is no need to bother the poor cat. Also, there are a plethora of QM interpretations, but this is the first time I have seen one with particles on route, gradually sliding through the coulomb potential barrier. I imagine anything is possible as long as you can’t see it, just like the cat.
My other comment was about the knowledge of the mathematical demon which I find far more interesting, (the other demon was just an introduction) but perhaps physicists are more interested in mathematical puzzles and vice versa.
I play the violin but I have always admired the pianists playing so many notes at the same time.
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