Quantum statistics vs classical reductionism

Quantum statistics vs classical reductionism
Ezekiel
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#61 - Quote - Permalink
Posted Feb 19, 2013 - 3:38 AM:

Numan wrote:
The world turns out to be real, after all! But it is a real world that is very, very weird!
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Makes perfect sense to me.

In the 1990s a physicist called Lucien Hardy proposed a thought experiment that makes nonsense of the famous interaction between matter and antimatter—that when a particle meets its antiparticle, the pair always annihilate one another in a burst of energy. Dr Hardy's scheme left open the possibility that in some cases when their interaction is not observed a particle and an antiparticle could interact with one another and survive. Of course, since the interaction has to remain unseen, no one should ever notice this happening, which is why the result is known as Hardy's paradox.

Numan
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#62 - Quote - Permalink
Posted Feb 19, 2013 - 11:33 AM:

'

Thank you, Ezekiel, for mentioning Hardy's work, which throws into high relief a salient feature of quantum mechanics which many people miss.

Quantum mechanics is often explained as a theory of probabilities and statistics, but this is very misleading. In statistics, you never have negative probabilities (for how can you have a probability of less than zero?), and certainly not probabilities that are complex numbers!!

But complex probability components are the bread and butter of quantum mechanics.

Hardy's Paradox and "new physics" beyond the "Copenhagen Interpretation"

A specific Lorentz-Invariant interpretation of Spacetime is implied, and the main contender for this theory is Wheeler-Feynman Absorber Theory....

This involves waves propagating from the future with waves propagating in the present "mixing" and creating our "particle" reality as a "sum of complex-wave quantum interferences".

...this is a departure from the "quantum fuzziness" of the past which involved "concrete real particles" whose existences were always positive probability contributions (inner products with real values).

Negative particle probabilities are now an observed reality, indicating an alternative interpretation to so called "particle" phenomena, as spatial and temporal complex waves interacting in spacetime, in order to resolve the obvious retrodiction anomalies that are actually measured....

[In the standard interpretation of Quantum Theory] the probabilities can never be negative and they must "add up". What we have are negative probabilities and they "add up". The negative probabilities are logical impossibilities in probability theory, clearly this is not a probability theory ... it is "something else".

emphases added
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Numan
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#63 - Quote - Permalink
Posted Feb 20, 2013 - 10:40 AM:
Subject: More Impossible than Impossible !
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Here is a diagram of Hardy's original proposed experiment, which involved electrons and positrons, rather than photons :



The brown cylinders are detectors; the gray disks are mirrors; the blue disks are interferometers ("beam-splitters"). An electron and a positron (anti-electron) are introduced into the system at the same time. Each particle goes through an interferometer and is split into two quantum states; one state represents the particle travelling along the outer pathway, the other state represents it travelling along the inner pathway. If the particles travel the inner pathway, they reach an "annihilation area". If both electron and positron travel the inner pathways, they may annihilate each other and will not affect the detectors. It is also possible that they will survive their "close encounter", but in that case, their quantum states will have been "disturbed".

The electron can only be detected at C- and D-, the positron only at C+ and D+. Near their associated detectors, each particle will encounter another interferometer. If the two states of each particle have been undisturbed, they cause Detector C to register an impact. If a quantum state has been disturbed, Detector D registers an impact.

Quantum Mechanics predicts probabilities for various outcomes: a probability for mutual annihilation, and probabilities for various combinations of detectors firing simultaneously:

1: C+ and C-
2: C+ and D-
3: C- and D+
4: D- and D+


It is the combination D- and D+ that causes the trouble. There will be a well-defined percentage of cases where D- and D+ fire simultaneously. The outer-arm quantum states are always undisturbed; therefore, if Detector D- registers an impact, the inner-arm electron state must have been disturbed, and that can only occur if it is 100% certain that the positron was in the "annihilation area". Likewise, if Detector D+ registers an impact, the inner-arm positron state must have been disturbed, and that can only occur if it is 100% certain that the electron was in the "annihilation area". If both Detector D- and Detector D+ are activated, it is 100% certain that both the electron and the positron were in the "annihilation area" at the same time. But this means that they would have annihilated each other, and none of the detectors would have been activated!

But both D- and D+ were activated!! This is the heart of the contradiction.

The paradox can be solved only if the probability is -1 for the case of both particles taking the outer pathway! This means that it is more of an impossibility than impossible!

"...a region with a negative number of photons (a hole blacker than black) would have interesting temperature and pressure, I guess."

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Motorcycle5
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#64 - Quote - Permalink
Posted Feb 22, 2013 - 2:58 PM:

Numan wrote:
The universe thus has no absolute history, but, within limits, is the summation of very many alternate histories.


By 'very many' do you mean infinite? Or are you just shy to use the 'I' word.

Can I take it as read that since we are made of the same stuff as the universe that we ourselves have no absolute history? --and I'm not complaining; I'd give anything to have not actually sat through the Ice Capades when I was a child.
Numan
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#65 - Quote - Permalink
Posted Feb 23, 2013 - 12:45 PM:
Subject: World without End?
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Motorcycle5 wrote:
By 'very many' do you mean infinite? Or are you just shy to use the 'I' word.

Can I take it as read that since we are made of the same stuff as the universe that we ourselves have no absolute history? --and I'm not complaining; I'd give anything to have not actually sat through the Ice Capades when I was a child.

I am very shy of using the "I" word. First, I suspect that Nature abhors infinities -- just as much as mathematics delights in them.
Second, I think that there are a finite number of bits of information in the causally-connected, observable universe out to the Event Horizon -- and I suspect that I know just how many bits there are.

Yes, I think that we ourselves have no absolute history -- though I am agnostic as to whether these histories differ significantly. Even if they do, you might check your delight by considering that "you" may be required to sit through the immense number of all possible variations of the Ice Capades.

If the Histories of the Universe are many and significantly different, this resembles the Many Worlds Hypothesis. I differ from the usual interpretation by thinking that these histories are not ontologically equal, but differ as to to their "reality". I conceive vast numbers of them to be vague and ill-defined -- scarcely universes at all. Perhaps there is a single Universe that is supremely Real -- the state of the Jello Block Universe when it has "finally" ceased to vibrate. In that case, all other universes, in their differing degrees of reality, are more or less approximations of the Reality to which they approach asymptotically. In this case, all these universes may be something like a halo of light surrounding the One, True Universe, something like more or less vivid Dream Universes, fading off into the outer Darkness (Well, I did admit that I like Plotinus).

In my more mawkish moments I imagine the One True Universe as the state of ultimate harmony, "where even the grass is enlightened".
However, my perverse imagination then cannot help imagining that this heavenly universe "instantly" suffers a quantum collapse of annihilation as a part of the dynamics of the much vaster realm of which it is an atomic fragment.

Anyway, I present this fantasy as a possibly original solution to the Problem of Evil. It has always struck me as odd that people do not seem to regard the pain they suffer in dreams to be as terrible as the pain they suffer in waking life. Is it because they sense the irreality of dreams? Is it because the dream-pain fades away into an indistinct perception? Is it because the experience of the waking-state is so much more intense than the dream-state that it overwhelms the dream-pain by its superior vividness?

Perhaps that is the way the Dream-Universes appear to the observers in the Real Universe. Perhaps the "you" [if such there be] in the Real Universe perceives the "you" in this dream-universe, but knows how vague, ghostly and unreal you are.

Anyway, it might form the basis for a science-fiction novel.

("Actually", an approximation appears in the novel The End of Eternity, by Isaac Asimov)
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Numan
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#66 - Quote - Permalink
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Posted Feb 24, 2013 - 12:27 PM:
Subject: Here today and gone tomorrow -- and gone yesterday and gone today
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I am very suspicious of the notion of elementary particles as stable entities.

I tend to regard the Block Universe, from Big Bang to its Ultimate Fate, as something like a supersaturated gas, with elementary particles forming and dissolving in a law-like fashion (like droplets in the gas) which creates the illusion that they may have a continuous existence and definite trajectories.

From this point of view, it is interesting that, given a reasonable particle density and universal particle temperature, the average occupation number of a generalized particle turns out to be precisely the exponential of the fine-structure constant (times a geometrical factor).

Of course, the actual occupation numbers of the real particles, like protons and neutrons, differ from this idealized, general figure, but only slightly, and in a lawful fashion, involving number densities, degrees of freedom, momentum and so on.

This, I think, is the key meaning of the fine-structure constant -- a vital component measuring the information content of the Universe.
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