Determinism is now a religion.
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01-03-2014, 08:05 PM
RE: Determinism is now a religion.
(01-03-2014 06:54 PM)cjlr Wrote:  
(01-03-2014 05:50 PM)GirlyMan Wrote:  The act of observation is indistinguishable from the act of creation. Tongue

Only insofar as "creation" may be taken as "bringing into [temporary] existence a well-defined eigenstate of the system in question from among the probabilistic distribution of possible states".

Wink

Yeah, that. Tongue

As it was in the beginning is now and ever shall be, world without end. Amen.
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01-03-2014, 11:21 PM
RE: Determinism is now a religion.
(01-03-2014 04:00 PM)cjlr Wrote:  But it's also true that randomness is a consequence of the postulates of quantum mechanics. For one example consider the canonical commutation relation between position and momentum; the mathematical formalism of their relationship is directly akin to that of Fourier transforms, and as such as the precision of one measure becomes exact the other becomes an ever broader spread. Thus the expectation becomes equally likely to be any possible value...

But this only tells us how well we can make simultaneous measurements - it's the uncertainty principle stated another way. But the uncertainty principle makes no claims that what is being measured is acausal. It might be, but it might also not be - we just can't tell because it looks like it is either way.

In the case of quantum mechanics, the wave equation is defined in probabilistic terms. This is foundational to the theory, not a consequence of it. Yet even in qm, there are odd phenomena like entanglement, that suggest some sort of hidden interconnectedness.

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02-03-2014, 05:31 PM (This post was last modified: 02-03-2014 05:35 PM by GirlyMan.)
RE: Determinism is now a religion.
(01-03-2014 06:54 PM)cjlr Wrote:  Only insofar as "creation" may be taken as "bringing into [temporary] existence a well-defined eigenstate of the system in question from among the probabilistic distribution of possible states".

Wink

It's the act of realization. Realizing vs. creating. Same damn thing.

As it was in the beginning is now and ever shall be, world without end. Amen.
And I will show you something different from either
Your shadow at morning striding behind you
Or your shadow at evening rising to meet you;
I will show you fear in a handful of dust.
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02-03-2014, 06:39 PM
RE: Determinism is now a religion.
(02-03-2014 05:31 PM)GirlyMan Wrote:  
(01-03-2014 06:54 PM)cjlr Wrote:  Only insofar as "creation" may be taken as "bringing into [temporary] existence a well-defined eigenstate of the system in question from among the probabilistic distribution of possible states".

Wink

It's the act of realization. Realizing vs. creating. Same damn thing.

Well, yes, but 'creation' is such a loaded term...

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02-03-2014, 06:41 PM
RE: Determinism is now a religion.
(01-03-2014 11:21 PM)toadaly Wrote:  But this only tells us how well we can make simultaneous measurements - it's the uncertainty principle stated another way. But the uncertainty principle makes no claims that what is being measured is acausal.

Since the uncertainty principle is descriptive, it doesn't make any claims at all...

(01-03-2014 11:21 PM)toadaly Wrote:  It might be, but it might also not be - we just can't tell because it looks like it is either way. In the case of quantum mechanics, the wave equation is defined in probabilistic terms. This is foundational to the theory, not a consequence of it.

But uncertainty is a physical consequence of waveform interaction. It is not one of the fundamental postulates; it proceeds from them.

(01-03-2014 11:21 PM)toadaly Wrote:  Yet even in qm, there are odd phenomena like entanglement, that suggest some sort of hidden interconnectedness.

There's nothing "hidden" about entanglement, it's just a phenomenon which cannot occur in classical terms.

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02-03-2014, 07:56 PM
RE: Determinism is now a religion.
(02-03-2014 06:41 PM)cjlr Wrote:  But uncertainty is a physical consequence of waveform interaction. It is not one of the fundamental postulates; it proceeds from them.

The Schrodinger equation, is defined in terms of a wave function, which is itself proabilistic:

https://en.wikipedia.org/wiki/Wave_function

wiki Wrote:The state of such a particle is completely described by its wave function:

Ψ(x,t),

where x is position and t is time. This function is complex-valued, meaning that Ψ(x, t) is a complex number.

Interpreted as a probability amplitude, if the particle's position is measured, its location is not deterministic, but is described by a probability distribution. The probability that its position x will be in the interval [a, b] (meaning a ≤ x ≤ b) is:

P_{a\le x\le b} (t) = \int\limits_a^b d x\,|\Psi(x,t)|^2

where t is the time at which the particle was measured. In other words, |Ψ(x, t)|2 is the probability density that the particle is at x, rather than some other location; see probability amplitude for details.

This is what makes tunnelling possible. It's not just the interactions or our inability to measure multiple parameters simultaneously, it's foundational to the math.

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02-03-2014, 08:19 PM
RE: Determinism is now a religion.
(02-03-2014 07:56 PM)toadaly Wrote:  
(02-03-2014 06:41 PM)cjlr Wrote:  But uncertainty is a physical consequence of waveform interaction. It is not one of the fundamental postulates; it proceeds from them.

The Schrodinger equation, is defined in terms of a wave function, which is itself proabilistic:

https://en.wikipedia.org/wiki/Wave_function

wiki Wrote:The state of such a particle is completely described by its wave function:

Ψ(x,t),

where x is position and t is time. This function is complex-valued, meaning that Ψ(x, t) is a complex number.

Interpreted as a probability amplitude, if the particle's position is measured, its location is not deterministic, but is described by a probability distribution. The probability that its position x will be in the interval [a, b] (meaning a ≤ x ≤ b) is:

P_{a\le x\le b} (t) = \int\limits_a^b d x\,|\Psi(x,t)|^2

where t is the time at which the particle was measured. In other words, |Ψ(x, t)|2 is the probability density that the particle is at x, rather than some other location; see probability amplitude for details.

This is what makes tunnelling possible. It's not just the interactions or our inability to measure multiple parameters simultaneously, it's foundational to the math.

What I said was that uncertainty relations are not fundamental, which they're not (they're consequential to the postulates). The degree to which a necessary consequence is considered to be contained in a given premise is perhaps a little abstruse; a bottom-up construction of quantum theory does not so begin. An uncertainty relation is a consequence of non-commuting interactions. The foundation of quantum theory is "everything is wave functions", which has nothing to do with randomness per se. "A multiple-valued wave function admits of single-valued measurement outcomes" introduces the concept when certain interactions are considered; "simultaneous knowledge of exclusive parameters is impossible" complements it - and has physical meaning insofar as increasing knowledge of certain parameters causes a loss in knowledge of other parameters.

If I know a particle's position then I simultaneously know that - according to every present theory and every known observation - other properties (ie momentum) are unknown and 'random' in - and this is key - a precisely known way, which I can physically and coherently account for (what is the Fourier transform of a delta function?).

So to say "but is it really random?" is not a particularly useful question. According to everything we know? Yes, it damn well is.

You'd not be the first to object on the grounds that "but I don't like randomness"; just look at ol' Einstein. But looking for secret determinism has been fruitless for over 80 years. I'd even argue that the very idea of determinism and perfect knowledge/prediction are only historical artifacts of our (pretty useful on the African savannah but entirely inadequate for modern science) macroscopic physical intuition.

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02-03-2014, 11:56 PM
RE: Determinism is now a religion.
(02-03-2014 08:19 PM)cjlr Wrote:  So to say "but is it really random?" is not a particularly useful question. According to everything we know? Yes, it damn well is.

You'd not be the first to object on the grounds that "but I don't like randomness"; just look at ol' Einstein. But looking for secret determinism has been fruitless for over 80 years. I'd even argue that the very idea of determinism and perfect knowledge/prediction are only historical artifacts of our (pretty useful on the African savannah but entirely inadequate for modern science) macroscopic physical intuition.

I have no problem accepting the idea of apodictic randomness, I just don't see how such a conclusion can be drawn unless it's possible to ellimitae the possibility of hidden variables that might account for observed randomness. Maybe there's some proof I'm not aware of that extends beyond local hidden variables.

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03-03-2014, 11:29 AM
RE: Determinism is now a religion.
(02-03-2014 08:19 PM)cjlr Wrote:  So to say "but is it really random?" is not a particularly useful question. According to everything we know? Yes, it damn well is.

That was another one of the instructor's main points. Randomness is relative and intrinsically subjective. Random for whom?

[Image: randomness2.png]

[Image: randomness1.png]

As it was in the beginning is now and ever shall be, world without end. Amen.
And I will show you something different from either
Your shadow at morning striding behind you
Or your shadow at evening rising to meet you;
I will show you fear in a handful of dust.
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03-03-2014, 12:35 PM
RE: Determinism is now a religion.
(02-03-2014 11:56 PM)toadaly Wrote:  I have no problem accepting the idea of apodictic randomness, I just don't see how such a conclusion can be drawn unless it's possible to ellimitae the possibility of hidden variables that might account for observed randomness. Maybe there's some proof I'm not aware of that extends beyond local hidden variables.

Yes. You can't prove an absolute negative.

That doesn't preclude all available data leaning a certain way!

Notwithstanding that there's no a priori reason to assume or even allow for determinism itself, besides naive physical intuition...

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