top-down causation

Originally posted by KazetNagorra
I'm not talking about hidden variables. Bell's theorem rules out that (for instance) a particle has a definite momentum and position at the same time (as described by a hidden variable theory), but the absence of a definite momentum and position does not imply randomness.

But I think it does. The momentum and position are probabilistic, as opposed to deterministic.

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec14.html
"The uncertainty principle is realized when we ask the question; is our knowledge of reality unlimited? The answer is no, because the uncertainty principle states that there is a built-in uncertainty, indeterminacy, unpredictability to Nature."
(my bolding)

Originally posted by apathist
But I think it does. The momentum and position are probabilistic, as opposed to deterministic.

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec14.html
"The uncertainty principle is realized when we ask the question; is our knowledge of reality unlimited? The answer is no, because the uncertainty principle states that [b]there is a built-in uncertainty, indeterminacy, unpredictability to Nature."
(my bolding)[/b]

No, you are mistaken. Take for instance a simple particle in a box - a standard problem one learns in a course on elementary quantum mechanics. The particle is prepared in some state, and then allowed to evolve in time. At no point does the particle have a definite momentum or position, but the Schrödinger equation still describes the time evolution deterministically. Nevertheless, the uncertainty principle still applies. The author of the piece is therefore wrong that the uncertainty principle implies indeterminacy.

Originally posted by apathist
Volition is the act or an instance of making a conscious choice or decision.It is a voluntary decision. That's a standard type of definition.

And when I look up 'voluntary' it says: Done, given, or acting of one's own free will.
We are not really getting anywhere.

The definitions implicate some sort of top-down causation, don't they?
They suggest that your 'will' is responsible for certain outcomes. This is hardly anything but blatantly obvious. I disagree that it is 'top-down' causation or has anything to do with determinism vs non-determinism.
Your will obviously works by some mechanism. That mechanism may be deterministic or it may not. That mechanism may be bottom-up or top-down or a mixture of both.

The reality of course is that we are mostly quite confused about what our will actually is. To what extent is it part of our concious thought processes and to what extent unconscious? To what extent is is directly affected by hormones and other chemical effects? And to what extent can those be considered 'external influences'?

Originally posted by KazetNagorra
No, you are mistaken. Take for instance a simple particle in a box - a standard problem one learns in a course on elementary quantum mechanics. The particle is prepared in some state, and then allowed to evolve in time. At no point does the particle have a definite momentum or position, but the Schrödinger equation still describes the time evolution det ...[text shortened]... The author of the piece is therefore wrong that the uncertainty principle implies indeterminacy.

I find what you reveal here interesting and seems to tally with what I suspected but lets see if I got this straight; nothing in either the Schrödinger equation nor the uncertainty principle logically implies there exists truly random events as opposed to merely pseudo-random events in particular; they merely imply limits to your measurement and observation of the events, that is all?

Originally posted by humy
I find what you reveal here interesting and seems to tally with what I suspected but lets see if I got this straight; nothing in either the Schrödinger equation nor the uncertainty principle logically implies there exists truly random events as opposed to merely pseudo-random events in particular; they merely imply limits to your measurement and observation of the events, that is all?

I think what he said was that they don't even imply pseudo-random events and that limits to your measurements are another topic altogether ie the particles are, in fact, waves not distinct objects with a position and velocity so to talk of measuring exact position's and velocity is incoherent. Further, interactions between wave-like particles behave deterministically. The limits are not so much our measurements but our ability to carry out calculations on large numbers of particles.

Originally posted by twhitehead
... The limits are not so much our measurements but our ability to carry out calculations on large numbers of particles.

that IS pseudo-randomness.

Originally posted by humy
I find what you reveal here interesting and seems to tally with what I suspected but lets see if I got this straight; nothing in either the Schrödinger equation nor the uncertainty principle logically implies there exists truly random events as opposed to merely pseudo-random events in particular; they merely imply limits to your measurement and observation of the events, [b]that is all?[/b]

The Schrodinger equation just gives the wavefunction given some boundary conditions. It doesn't say what the wavefunction means. That is supplied by the interpretation that given some small region the probability of finding the particle in that region is given by the product of the norm of the wave function and the volume of the region.

The wavefunction of a particle that has an exact momentum is a plane wave, this is a mathematical idealization, one doesn't expect to find such a thing in nature. It is equally likely to be observed to be anywhere. Similarly a particle that is exactly at some point has a wavefunction that is a Dirac delta function. Taking the Fourier transform of this gives us a linear superposition of all possible wavelengths - the probability of measuring it to have any given wavelength, and therefore momentum, is the same as finding it with any other wavelength. So there is infinite uncertainty in its momentum, since the momentum is Planck's constant times the wavelength. For an arbitrary wavefunction the half width of the packet times the half width of the Fourier Transform of the packet is greater or equal to Planck's constant.

The probabilistic part comes from the interpretation of the wavefunction. There is empirical support for this as if one does a double slit experiment a photon at a time then they arrive at random points, but the classically expected pattern builds up over time. The uncertainty principle is a consequence of the wave nature of the particle. The particle is interpreted as being a probability wave in the Copenhagen Interpretation (there are other interpretations) so it's a little difficult to say that the uncertainty principle has nothing to do with randomness as the wavefunction is interpreted as a probability wave. However if one supports an interpretation of Quantum Mechanics, such as the deBroglie-Bohm or Everett's Many Worlds interpretations, which is entirely deterministic, then one still believes the uncertainty principle. It's just that the variation in the momentum and position measurements are not random in those interpretations.

Originally posted by twhitehead
I think what he said was that they don't even imply pseudo-random events and that limits to your measurements are another topic altogether ie the particles are, in fact, waves not distinct objects with a position and velocity so to talk of measuring exact position's and velocity is incoherent. Further, interactions between wave-like particles behave deter ...[text shortened]... o much our measurements but our ability to carry out calculations on large numbers of particles.

No, in the Copenhagen interpretation one can measure either position or momentum with arbitrarily fine precision, at least in principle. However what one cannot do is measure both position and momentum with arbitrarily fine precision. The measurements interfere with each other. This is true with a single particle and has nothing to do with the difficulty of carrying out calculations involving large numbers of particles.

Interactions between particles do not behave deterministically. When one calculates a transition amplitude it gives the probability for a particular outcome, it does not specify the outcome.

Originally posted by DeepThought
No, in the Copenhagen interpretation one can measure either position or momentum with arbitrarily fine precision, at least in principle.

I believe that KazetNagorra is ignoring interpretations and saying that under the Schrodinger equation the particle simply does not have a definite position and momentum.
I think a good argument can be made that no interpretations are necessary. We should simply stick with what the Schrodinger equation says and stop trying to invent underlying physics that fits our mental model better but has no actual evidential basis.

Originally posted by humy
that IS pseudo-randomness.

Fair enough.

Originally posted by DeepThought
The Schrodinger equation just gives the wavefunction given some boundary conditions. It doesn't say what the wavefunction means. That is supplied by the interpretation that given some small region the probability of finding the particle in that region is given by the product of the norm of the wave function and the volume of the region.

Does a wave function have to mean something?
This is not my field of expertise, so I am just guessing here, but I believe that you can describe quantum particles as wave functions and when they interact you get a new wave function. At no point do you need to 'interpret' it or convert it to probabilities.

Originally posted by KazetNagorra
No, you are mistaken. Take for instance a simple particle in a box - a standard problem one learns in a course on elementary quantum mechanics. The particle is prepared in some state, and then allowed to evolve in time. At no point does the particle have a definite momentum or position, but the Schrödinger equation still describes the time evolution det ...[text shortened]... The author of the piece is therefore wrong that the uncertainty principle implies indeterminacy.

The Uncertainty Principle pertains to measurements. When one measures the position of the particle in the box to some precision then after the measurement the wave function is not the same as it was before the measurement, since the measurement has localised the particle to some small region whose size is determined by the precision of the measurement. The result of the measurement is stochastic, at least in the Copenhagen interpretation. It's not at all clear to me that the Uncertainty Principle does not imply indeterminacy, as it pertains to measurements rather than what the particle is doing when undisturbed.

I think this hangs on what the correct interpretation of the wavefunction is. If it's interpreted as a probability wave then the whole thing is automatically non-deterministic. In Everett's Many Worlds interpretation it may as well be since there's a copy of the observer in each World and so to each copy of the observer the result will appear random. In interpretations which attempt to retain determinism like Bohmian Mechanics it automatically is not indeterministic. Certainly historically they drew the inference that the wavefunction is probabilistic from the Uncertainty Principle. I don't think the article writer is wrong, per say, it's just that the inference is neither automatic, inferences that are not deductions never are, and it's not automatically right either.

Originally posted by DeepThought
The Uncertainty Principle pertains to measurements. When one measures the position of the particle in the box to some precision then after the measurement the wave function is not the same as it was before the measurement, since the measurement has localised the particle to some small region whose size is determined by the precision of the measurement.

Isn't it more reasonable to simply say 'interaction' rather than 'measurement'? I think the over emphasis on measurement is what leads to the ridiculous claims that conciousness must be involved.

Originally posted by DeepThought
The Uncertainty Principle pertains to measurements. When one measures the position of the particle in the box to some precision then after the measurement the wave function is not the same as it was before the measurement, since the measurement has localised the particle to some small region whose size is determined by the precision of the measurement. ...[text shortened]... utomatic, inferences that are not deductions never are, and it's not automatically right either.

Take any kind of normalized wave function, and compute the product of the standard deviation of the momentum and position operators. It will obey the Heisenberg uncertainty principle. No measurement is required for this to be the case. Evolve the wave function using some unitary operator - again, the Heisenberg uncertainty principle will be obeyed at all times, no measurement is performed, and the unitary operator describes the time evolution deterministically.

Now, if you perform a "measurement," (typically involving some interaction with a macroscopic system) then probability enters the picture. What's a "measurement," really? Does it follow from some innate randomness in nature, or is it merely an apparent randomness that is not visible due to neglecting or averaging over some microscopic details in the system? That's the million dollar question.

Originally posted by twhitehead
Isn't it more reasonable to simply say 'interaction' rather than 'measurement'? I think the over emphasis on measurement is what leads to the ridiculous claims that conciousness must be involved.

It's a little bit more tricky than that because there are some simple interacting systems which we can solve, usually using numerical tools, to arbitrary precision (i.e. they are deterministic). In his standard work on quantum mechanics for undergrads, Griffiths suggests a "measurement" should be interpreted as the slightly less vague "interaction with a macroscopic system" (see above).