The wave function and determinism

The state of a system, indeed any system, whether that be described as being tangible ''outside'' or even the construction of the incorporeal inside, that of subjective experience should be described by a state vector, given as \(|\Psi>\). The state of a vector is the overall description of the possibilities that may arise when a collapse of the wave function has appeared. The collapse of the wave function happens upon a measurement. Observable's are resultant from measurements. Observables in the language of quantum mechanics are Hermitian Matrices which means it will produce a real number.

The definition, in totally mathematical terms right now, is given by the following.

\(<a| M^{\dagger}|b>^{*}\)

where the <a| is acting like a complex conjugate, in fact, this has been complex conjugated where all rows and columns have been interchanged. Incidently, M on <a| will give you a vector, but M and <a| after this onto |b> will give you a number. It won't give you a vector in this case, it's just a number.

So you get from \(<b|M|a>\) to the expression \(<a| M^{\dagger}|b>^{*}\) by complex conjugating it. In fact, if it is Hermitian you can now state it as

\(<b|M|a> = <a| M|b>^{*}\)

where we have just erased the conjugation dagger sign. This just means it is equal to it's Hermitian conjugate. This is the true definition of the meaning of Hermitian.

Now the wave function, the ''configuration'' of states of a system describes all possible solutions which may or may not occur for a system. A photon bouncing of a mirror does not take one path alone, in fact, will take every angle possible to account for the wave function which smears every possibility over a given region. Given a large enough region, you may even call it infinite.

And now, given all this information, I ask, what is a set of possibilities, if not the analog of such a wave function? In fact, as history goes, when phsyicists realized that a wave function existed, they believed it was a product of the mind, simply, just a way for us to catalogue the events. This subjective idea of the wave function soon diminished and we realized atleast in principle, there was something physical behind this [1]. However, if we take the basic idea of the wave function seriously, then it should not be bound to physical objects alone. That even subjective experiences may be subject to such a phenomenon as well.

Suppose that every experience is ruled by a wave of possibilities, given as \(\Psi\). This description will state that before anything has been resolved by the action of a human being, or maybe even by thought, the wave function itself will be spread among many different possibilities.

The probability of finding any one of those experiences, or thoughts or actions result in a collapse of the wave function, traditionally given by the probability postulate as

\(\mathbf{Tr} \rho = \mathcal{1}\)

The density matrix here, in case anyone jumps down my throat, is given by the unit matric which will give a Hermitian Operator, which is by definition as we have covered, an observable. The trace is simply the sum over all possible Eigenstates given as \(\lambda_i\) where \(i = (1,2...n)\).

In quantum mechanics, rather than applying matrix mechanics, we will find the probability of a system to be

\(\int_{\Omega} |\psi|^2\)

Where \(\Omega\) is our boundary [2].

The real crux of this arguement, is that consciousness, the acts of consciousness or/and the conscious acts of decisions are subject to collapses of the wave function. You could have the choice of turning two playing cards over that have been placed in front of you. Those cards will be represented by a wave function:

\(|\Psi> = \frac{1}{2}i|A> + \frac{1}{2}|B>\)

This will, not in a physical sense, but a subjective sense describe the possibilities that may arise from either state which depend on their orientation to each state in the complex plane. Upon measurement, of either playing card in the subjective subliminal sense will yeild the value upon the measurement of either card to account for the collapse of the wave function postulate.

So, it can easily be shown that somehow probabilities and the wave function generally describe the actions of choice and will have perhaps massive implications to the philosophical arguements between, determinism vs indeterminism.



[1] - I provided evidence recently that the wave function was physical when pressed by alphanumeric.

[2] - In dirac notation \(<\psi_n|\psi_m> = 0\) unless psi_m and psi_n correspond to the same eigenvectors.

 

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Pseudoscience, now? Is this one of those "take two steps back" to get forward strategies?

 

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Two steps back, hopefully at this place might mean three steps forward. The more I spend at this place, the more I am thinking this might be true! lol

 

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You know what they say, cranks of a feather....

 

James, shut up already!!

You aren't a physicist and by saying this makes no sense, you obviously can't even follow a very simple analog! :bugeye:

 

@Mister --

Have you heard the one about the pot and the kettle?

 

Indeed it is true, I have no PhD. I bet my Diploma in physics is still more than he holds however.

 

Be careful what bets you make around here, you'd be surprised who is what.

 

I'd hardly doubt it in most cases.

Most of the people round here are extraordinarily unbelievable at times, even the imagination could believe you are speaking to a cartoon character some times.

 

Sciforums? Welcome to the Mickey Mouse Club.

 

i believe james has a phd.

 

Not in physics he doesn't.

James, what is your PhD in if indeed, you have one?

 

@Mister --

If this is your "changed" behavior I'd hate to see what you acted like in the past.

 

A PhD in physics... are you serious James. I always had you more as a ''math'' man to be honest. No seriously, is it physics you hold a PhD in?

 

Anyway, I'd like to challenge this. How is the post got a ''touch of nonesense'' in there?

The collapse related to consciousness idea has been going around for a while.

''"Consciousness causes collapse"

The involvement of consciousness in the collapse of the wave function has been summarized thus:

The rules of quantum mechanics are correct but there is only one system which may be treated with quantum mechanics, namely the entire material world. There exist external observers which cannot be treated within quantum mechanics, namely human (and perhaps animal) minds, which perform measurements on the brain causing wave function collapse.[18]

This interpretation attributes the process of wave function collapse (directly, indirectly, or even partially) to consciousness itself. Specifically, a non-physical mind is postulated to be the only true measurement apparatus.[18]

Henry Stapp has argued for the concept as follows:

From the point of view of the mathematics of quantum theory it makes no sense to treat a measuring device as intrinsically different from the collection of atomic constituents that make it up. A device is just another part of the physical universe... Moreover, the conscious thoughts of a human observer ought to be causally connected most directly and immediately to what is happening in his brain, not to what is happening out at some measuring device... Our bodies and brains thus become...parts of the quantum mechanically described physical universe. Treating the entire physical universe in this unifed way provides a conceptually simple and logically coherent theoretical foundation...[27]

The consciousness causes collapse interpretation was Wigner's motivation for introducing the "Wigner's friend" thought experiment by asserting that collapse occurs at the first "conscious" observer. Wigner believed that consciousness is necessary for the quantum mechanical process. See Consciousness and measurement. There are other possible solutions to the Wigner's friend thought experiment, however, which do not require consciousness to be different from other physical processes. See, Consciousness and Superposition.

Very technically, the interpretation identifies the non-linear probabilistic projection transformation which occurs during measurement with the selection of a definite state by a mind from the different possibilities which it could have in a quantum mechanical superposition. In other words, the idea is that creatures' minds somehow cause microscopic-scale probabilities to become reality.''

http://en.wikipedia.org/wiki/Consciousness_causes_collapse#.22Consciousness_causes_collapse.22

 

Good grief, is a branch of this gypsy topic still hanging around in this forum, too?

The increased popularity of decoherence since the '80s has surely undermined dependence upon wave function collapse as well as the consciousness factor. However, in some of the consequences of this trend (Tegmark's quotes further below), experience and the brain memory available to a specific body apparently still sneak their way into having a role: The "why" of seeming to be aware of only one outcome, and of time flowing (the subjectivity of the latter an issue which one usually finds thrashing about in special and general relativity). Zurek, of course, utilizes decoherence while even practicing agnosticism about "Many Worlds", deeming that this interpretation is not a necessary accoutrement to his work, as well straddling the fence in regard to completely discarding traditional collapse.

Max Tegmark . . . In the 1920s physicists explained away this weirdness by postulating that the wave function "collapsed" into some definite classical outcome whenever someone made an observation. This add-on had the virtue of explaining observations, but it turned an elegant, unitary theory into a kludgy, nonunitary one. The intrinsic randomness commonly ascribed to quantum mechanics is the result of this postulate. Over the years many physicists have abandoned this view in favor of one developed in 1957 by Princeton graduate student Hugh Everett III. He showed that the collapse postulate is unnecessary. Unadulterated quantum theory does not, in fact, pose any contradictions. Although it predicts that one classical reality gradually splits into superpositions of many such realities, observers subjectively experience this splitting merely as a slight randomness, with probabilities in exact agreement with those from the old collapse postulate.

[...] All possible states exist at every instant, so the passage of time may be in the eye of the beholder--an idea explored [...] and developed by physicist David Deutsch of the University of Oxford, independent physicist Julian Barbour, and others. The multiverse framework may thus prove essential to understanding the nature of time.
--from Scientific American article back in the early 2000s, Parallel Universes

 

I don't argue that decoherence exists, in fact, I made a post on this recently.. Observe:

http://www.sciforums.com/showthread.php?t=111280

I don't think humans are special in that we alone can deflate the wave of possibilities, my arguement is that our measurements are still an analog to the collapse of the wave function. My OP is in fact, completely analog.

 

And the multiverse is wack. I hold the same contentions as Smolin on this case.