Do Wavefunctions Include All Possible Outcomes?

[ZapperZ]

What bothers me is when people say when something has a really low probability of happening, it's saying it's not going to happen at all. Clearly it COULD.

Not if the probably if it happening has a time period on the scale of the age of the universe! Then such a consideration of that happening is unrealistic.

Zz.

 

[Jarwulf]

Personally, I don't like infinity, and there is a belief (for me a hope), that what may seem like an infinite range, is actually finite. Consider ther Planck Length and a finite/bounded universe as a limiting facttor on time/distance, or more practical restrictions such as causality that might limit future options.

I don't know I think a buffet would be a lot cooler with an infinite variety of food.

 

[jambaugh]

What bothers me is when people say when something has a really low probability of happening, it's saying it's not going to happen at all. Clearly it COULD.

Ultimately such a statement itself is uncertain, and a matter of the probability that the theory, which you are using to predict what CAN and CAN'T happen, is correct. At some point a probability becomes so small as to be less than the probability that all the experiments confirming the theory being used were accidentally way off the mark.

When you say "Clearly it COULD", how do you know? To what probability are you correct in your assertion?

Finally we may be ignorant of the impossibility of some event and thus we speak of it as something which "COULD" happen in the sense that we are unable to eliminate to exactly zero the probability of it happening. The statement is not one of actual possibility but a statement of our lack of infinite knowledge. It is important to identify if this is the case in what you are saying.
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The above is all general concerns and context for the question at hand. The actual analysis assuming QM is correct, is this. When we speak of the wave-function for a quantum and the small probability of it "jumping to LA", we are really speaking of the small probability that it "was in LA all the time." so to speak...excepting the issue of what it means to say where it is or was at all in the absence of measurement.

It is more instructive to get down to cases. First in the non-relativistic case, you observe a quantum in NYC, at time t1. You write down a wave-function (a delta function) for its position given this knowledge. If you immediately observe its position again you will find it in NYC with probability 100% and LA with exactly 0%. You then evolve the wave-function for an interval of time so that at time t2 there is a finite small probability it will be observed in LA.

You haven't a clue as to its momentum and thus its velocity (which can be arbitrarily high in the non-relativistic setting) and so you cannot say that it couldn't be traveling so fast as to reach LA by the time t2 that you then observe it there. No teleportation involve here, simply the quantum having a very very small probability of moving very fast.

Now take the relativistic case. you observe a quantum in NYC, at time t1. You write down a wave-function (a delta function) for its position given this knowledge. You haven't a clue as to its momentum and thus its velocity (which must be less than c in the relativistic setting). If you then evolve the wave-function it will not exceed the speed of light in its propagation of probability. It is impossible to observe it in LA until it has had time to propagate there at some velocity < c. However once enough time has passed you have the same situation as before.

However some may misinterpret the point of maximum probability of a wave-function for an actual position of the corresponding quantum. In that case there is a finite probability that a later observation will find the actual quantum a distance greater than ct away from this peak. It is a surprise, not a sudden jump.

QM does not say we will see sudden jumps as implied by the term "teleportation" but rather explains that when we only look at discrete times we can only see a discrete series of positions i.e. jumps (but not sudden ones). In between looking we predict what might be seen (and how likely) with wave-functions.

Note: My analysis is based somewhat on my choice of interpretation (Orthodox CI) and others may describe the nature of the reality of the situation differently based on their interpretation. However I would point out that in the end all the other interpretations agree with the above in so far as actual observations[/] is concerned because that's what QM predicts.

A final note. The phrase "quantum teleportation" has a distinct meaning not to be confused with the above described phenomena. It has to do with copying a quantum system completely (and necessarily destructively) by using an auxiliary system. Just as we shouldn't confuse "quantum cloning" with actual copying genetic material, we shouldn't confuse "quantum teleportation" with actual instantaneous jumping from point A to point B. These are romantic choices of terminology for more mundane actual phenomena.

 

[mr.smart]

i have been pondering the wave function myself. in particular; the idea that once an observed particle is no longer observed, does it become a probability wave again?

if it remains "solid" then this would explain why the chair does not posses the probability of falling apart spontaneously. presumably the wave function collapsed when the wood was first cut and now ,as a hard piece of wood, it responds to the physical reality classically.

if however, once an observed particle becomes again un-observed, it become a wave function again, then the chair does posses the probability to fall apart, but only if you stop looking at it.

is there an excepted answer to this one... could Schroedinger's cat come back to life if we closed the box?

 

[StevieTNZ]

When you say "Clearly it COULD", how do you know? To what probability are you correct in your assertion?

Finally we may be ignorant of the impossibility of some event and thus we speak of it as something which "COULD" happen in the sense that we are unable to eliminate to exactly zero the probability of it happening. The statement is not one of actual possibility but a statement of our lack of infinite knowledge. It is important to identify if this is the case in what you are saying.

Nope, I'm referring to a probability for a physical state to actualise (extracted from the wave function), and someone saying it has a really really low probability of occurring that its practically not going to occur, I would think is wrong. For example, say I have 2% probability for sitting on this chair, and 98% for turning the TV off and walking out of the house. Even though it looks more probable that the turning off of the TV is going to occur, there is the possibility for me to go sit on the chair.

 

[Meader]

Nope, I'm referring to a probability for a physical state to actualise (extracted from the wave function), and someone saying it has a really really low probability of occurring that its practically not going to occur, I would think is wrong. For example, say I have 2% probability for sitting on this chair, and 98% for turning the TV off and walking out of the house. Even though it looks more probable that the turning off of the TV is going to occur, there is the possibility for me to go sit on the chair.

But with inanimate objects don't they have a 100% chance of not moving if they are already not moving?

 

[mr.smart]

unless there was a freak wind or an Earth quake.. then it would move... i guess random events have to be figured into the probability calculation. so there would be a slight chance of it moving.

 

[StevieTNZ]

But with inanimate objects don't they have a 100% chance of not moving if they are already not moving?

Not sure, but I guess I'm making a point regarding probabilities for two 'events', not one.

 

[jambaugh]

Nope, I'm referring to a probability for a physical state to actualise (extracted from the wave function), and someone saying it has a really really low probability of occurring that its practically not going to occur, I would think is wrong. For example, say I have 2% probability for sitting on this chair, and 98% for turning the TV off and walking out of the house. Even though it looks more probable that the turning off of the TV is going to occur, there is the possibility for me to go sit on the chair.

The critical issue is how you can make such a statement, how one determines the truth/falsehood, or likelyhood of truth of the statement, and thereby the meaning of the probability quantity.

I can speak of an absolutely deterministic dynamic system in probabilistic terms. "The (classical) particle has probability p of being found in this particular cube of space over this interval of time." These probability statements then relate back to my uncertainty in the initial conditions and in the dynamic environment.

In another setting, one may infer a particular theory of deterministic outcomes and base that theory on empirical data. The lack of infinite samples of data mean we have a certain probability that the theory is incorrect. Hence absolute statements which are 100% certain if the theory is true (a conditional probability) are say 99.999% certain given that is the probability that the theory is true given the available data.

Now take a 99.999% certain theory and make a probabilistic prediction of an outcome based on that theory which, if the theory is true would be 99.999999999% likely. Since the uncertainty in the validity of the theory outweighs the uncertainty predicted by the theory, the statement in the context of that theory is essentially equivalent to an absolute statement.

All statements about physical events are conditional probabilities. Sometimes the conditions are explicit and sometimes implicit. It is too damned inefficient to be totally explicit and so we speak in abbreviated terms. One can never make any statement about physical events which is 100% certain (unless the statement is trivial i.e. tautological). There is always the chance that say QM is wrong, or SR, or GR. There is always the small chance that all the beautiful experiments confirming our various theories happened to have all the random errors align so as to skew the theory instead of being averaged to zero.

However we use that language of absolutes to say it is certain to the degree that the risk of acting as if the statement were true is minuscule relative to the uncertainty of the context. We push that small uncertainty back one or more meta-levels under the rug of infinite regress.

 

[yoda jedi]

QM does imply that one thing could in principle be in two different places at the same time, even macroscopic objects. so there are theories that try to explain away such possibility, like GRW

http://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory


from

Phys. Rev. D 34, 470–491 (1986)
Unified dynamics for microscopic and macroscopic systems



An explicit model allowing a unified description of microscopic and macroscopic systems is exhibited. First, a modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics. This dynamics also allows a description of the evolution in terms of trajectories. To set up a unified description of all physical phenomena, a modification of the dynamics, with respect to the standard Hamiltonian one, is then postulated also for microscopic systems. It is shown that one can consistently deduce from it the previously considered dynamics for the center of mass of macroscopic systems. Choosing in an appropriate way the parameters of the so-obtained model one can show that both the standard quantum theory for microscopic objects and the classical behavior for macroscopic objects can all be derived in a consistent way. In the case of a macroscopic system one can obtain, by means of appropriate approximations, a description of the evolution in terms of a phase-space density distribution obeying a Fokker-Planck diffusion equation. The model also provides the basis for a conceptually appealing description of quantum measurement.

there is a newer version, full relativistic.

FQXi’s Most Courageous Postdoc prize winner 2011
Daniel Bedingham.
October 5, 2010
http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.2774v2.pdf
http://www.springerlink.com/content/h06783vh08853088/

..."In this article we have outlined a framework for describing the evolution of relativistic quantum systems which consistently explains the behavior of both microscopic and macroscopic systems. To do this the model incorporates quantum state reduction into the standard state dynamics in a way which is not only covariant and frame independent, but also objective, naturally diferentiating between systems of diferent scale and adjusting its effect accordingly. In this way the model offers a potential unifcation of quantum and classical sectors"...


----
"he was nominated for this award by quantum physicist Philip Pearle, Emeriti at Hamilton College in Clinton, New York. He noted that he have solved an issue that had plagued other physicists working on relativistic dynamical collapse theory for a decade."


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[yoda jedi]

QM does imply that one thing could in principle be in two different places at the same time, even macroscopic objects. so there are theories that try to explain away such possibility, like GRW

http://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory


from

Phys. Rev. D 34, 470–491 (1986)
Unified dynamics for microscopic and macroscopic systems



An explicit model allowing a unified description of microscopic and macroscopic systems is exhibited. First, a modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics. This dynamics also allows a description of the evolution in terms of trajectories. To set up a unified description of all physical phenomena, a modification of the dynamics, with respect to the standard Hamiltonian one, is then postulated also for microscopic systems. It is shown that one can consistently deduce from it the previously considered dynamics for the center of mass of macroscopic systems. Choosing in an appropriate way the parameters of the so-obtained model one can show that both the standard quantum theory for microscopic objects and the classical behavior for macroscopic objects can all be derived in a consistent way. In the case of a macroscopic system one can obtain, by means of appropriate approximations, a description of the evolution in terms of a phase-space density distribution obeying a Fokker-Planck diffusion equation. The model also provides the basis for a conceptually appealing description of quantum measurement.

Right and now full Relativistic:

Relativistic State Reduction Dynamics
Daniel J. Bedingham, Imperial College London.
October 5, 2010

http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.2774v2.pdf
http://www.springerlink.com/content/h06783vh08853088/

..."In this article we have outlined a framework for describing the evolution of
relativistic quantum systems which consistently explains the behavior of both
microscopic and macroscopic systems. To do this the model incorporates quantum
state reduction into the standard state dynamics in a way which is not only
covariant and frame independent, but also objective, naturally dierentiating
between systems of dierent scale and adjusting its eect accordingly. In this
way the model oers a potential unication of quantum and classical sectors"...



-----
FQXi’s Most Courageous Postdoc prize winner 2011.
..."was nominated for this award by quantum physicist Philip Pearle, emeritus at Hamilton College in Clinton, New York. He noted that you have solved an issue that had plagued other physicists working on relativistic dynamical collapse theory for a decade"...


.