A giganitc wavefuntion of the universe = determinism?

[roberto85]

A giganitc wavefuntion of the universe = determinism??

So the wavefunction offers a much more simplistic and perhaps more beautiful way to describe a system when compared to the kernel since all effects of the past history of a particle can be defined in terms of a the wavefunction. If we were to ignore everything we knew of it's history (or did not know this information) except for it's wavefunction at a particular time; we could calculate the future of the particle's evolution. All of history's effect upon the future of the universe could be obtained from a single gigantic wavefunction.

I then added after this sentence after quoting this: 'which does suggest the universe is deterministic although quantum physics tends to disagree when dealing with just one particle let alone the whole universe.'

This is taken from richard feyman's book on path integrals. Could this suggest the universe obeys determinism?? Am i right in saying this since i dotn want to be wrong about this. Please help - any input would be greatly appreciated, many thanks

Roberto

 

[roberto85]

A gigantic wavefunction of the universe = determinism??

I quote:

So the wavefunction offers a much more simplistic and perhaps more beautiful way to describe a system when compared to the kernel since all effects of the past history of a particle can be defined in terms of a the wavefunction. If we were to ignore everything we knew of it's history (or did not know this information) except for it's wavefunction at a particular time; we could calculate the future of the particle's evolution. All of history's effect upon the future of the universe could be obtained from a single gigantic wavefunction.

I then added after this sentence after quoting this: 'which does suggest the universe is deterministic although quantum physics tends to disagree when dealing with just one particle let alone the whole universe.'

This is taken from richard feyman's book on path integrals. Could this suggest the universe obeys determinism?? Am i right in saying this since i dotn want to be wrong about this. Please help - any input would be greatly appreciated, many thanks

Roberto

 

[Dick]

No, it doesn't suggest determinism any more than the unitary evolution of a wave function for a single particle suggests determinism. At some point you have to measure an observable from the wavefunction. Don't write your addition to Feynman. Look up "Copenhagen interpretation".

 

[roberto85]

No, it doesn't suggest determinism any more than the unitary evolution of a wave function for a single particle suggests determinism. At some point you have to measure an observable from the wavefunction. Don't write your addition to Feynman. Look up "Copenhagen interpretation".

Thankyou Dick, sage advice, could i perhaps write that although this statement may suggest a deterministic view of the universe but this is not true because it is contrary to the postulates of the copenhagen interpretation? I have also stated the copenhagen interpretation in this report, so it might be a nice way to link it in somehow. What would you suggest, yes or no? Many thanks

Roberto

 

[Dick]

I guess I'm not sure what Feynman was thinking about that in the quote. His path integral formulation gives an elegant way of justifying Schrodinger's equation and can be generalized to quantum field theories. But it still just gives you a way to compute future probabilities. Not future events. I think. I'm not an expert on quantum ontology. But if you know why an exact equation for the evolution of the wavefunction doesn't predict the exact future, then you know what I mean.

 

[roberto85]

I guess I'm not sure what Feynman was thinking about that in the quote. His path integral formulation gives an elegant way of justifying Schrodinger's equation and can be generalized to quantum field theories. But it still just gives you a way to compute future probabilities. Not future events. I think. I'm not an expert on quantum ontology. But if you know why an exact equation for the evolution of the wavefunction doesn't predict the exact future, then you know what I mean.

Okay so here is the paragraph i have written:

So the wavefunction offers a much more simplistic and perhaps more beautiful way to describe a system when compared to the kernel since all effects of the past history of a particle can be defined in terms of the wavefunction. If we were to ignore everything we knew of it's history (or did not know this information) except for it's wavefunction at a particular time; we could calculate the future of the particle's evolution. This remarkable fact could conceivably mean that 'all of history's effect upon the future of the universe could be obtained from a single gigantic wavefunction' \ref{FeyPI} which does suggest the universe is deterministic although the Copenhagen interpretion does suggest this is impossible. Despite the relative elegance of wavefunctions predominantly used in the Schroedinger branch of quantum mechanics; the path integral formulation offers a more intuitive understanding of the behaviour of the universe and has applications in important calculations such as Monte Carlo simulations and other emerging theories such as causal dynamical triangulation (CDT). But on the whole Schroedinger equations and Heisenberg's matrix mechanics are used more widely in general physics and we will demonstrate the equivalence of the path integral formulation to Schroedinger mechanics by deriving and transforming the former to the latter.

I know i shouldn't be asking for a prrofreading type question, but this is the only paragraph i feel slightly uncertain if i am expressing fact here. Any thoughts Dick or anyone?? Your advice on this is invaluable. I am also considering mentioning the anthropic principle because its ideology tends to lend itself nicely to the interpretation of the path integral formulation, worth a mention also? Many thanks

Roberto

 

[nomadreid]

First of all, a single wavefunction for the entire universe may be esthetically pleasing, but since there is no feasible way to formulate, let alone measure, it, one questions the utility of introducing it. But OK, once you have it, it is true that, given the computing capability, you could predict the wave function for the total history of the universe, which you can call determinism, albeit not the kind of determinism that predicts the positions and momenta of every particle -- the Heisenberg Uncertainty Principle put this possibility definitively to rest, without contradicting the wave function concept. You could predict the probabilities of the particles' positions, momenta, etc. However, this does not solve the Measurement problem. As an example, the wave function may tell you that the probability that the spin of an electron in a certain situation is 30% "up" and 70% "down", but this does not tell you which one that electron will "choose" when measured. So there remains the impossibility to extend this new determinism into the old one, no matter how extensive your wave function.

 

[roberto85]

First of all, a single wavefunction for the entire universe may be esthetically pleasing, but since there is no feasible way to formulate, let alone measure, it, one questions the utility of introducing it. But OK, once you have it, it is true that, given the computing capability, you could predict the wave function for the total history of the universe, which you can call determinism, albeit not the kind of determinism that predicts the positions and momenta of every particle -- the Heisenberg Uncertainty Principle put this possibility definitively to rest, without contradicting the wave function concept. You could predict the probabilities of the particles' positions, momenta, etc. However, this does not solve the Measurement problem. As an example, the wave function may tell you that the probability that the spin of an electron in a certain situation is 30% "up" and 70% "down", but this does not tell you which one that electron will "choose" when measured. So there remains the impossibility to extend this new determinism into the old one, no matter how extensive your wave function.

Wow, that was amazing clear, although I'm unsure if what I've now written (which i have slightly adapted from your post, which i hope you don't mind ) is correct. Here is the full paragraph I've written:

So the wavefunction offers a much more simplistic and perhaps more beautiful way to describe a system when compared to the kernel since all effects of the past history of a particle can be defined in terms of a the wavefunction. If we were to ignore everything we knew of it's history except for it's wavefunction at a particular time; we could calculate the future of the particle's evolution. This remarkable fact could conceivably mean that 'all of history's effect upon the future of the universe could be obtained from a single gigantic wavefunction' \ref{FeyPI} which does suggest the universe is deterministic although the Copenhagen interpretion excludes this possibility. For instance a single wavefunction for the entire universe may be asthetically pleasing, but since there is no feasible way to formulate, let alone measure it, one questions the utility of hypothesising it's existence. But theoretically if it was obtainable it is true that given the computing capability you could predict the wave function for the total history of the universe which is essentially determinism; albeit not the kind of determinism that predicts the positions and momenta of every particle. This is because the Heisenberg uncertainty principle precludes it's validity since it contradicts the wave function concept. You could predict the probabilities of the particles' positions, momenta, etc. but this does not solve Heisenberg's measurement problem which illuminates our limitation in precisely predicting a system's evolution, no matter how large or small the system may be.


But have i contradicted myself since i quoted Feynman: we could calculate the future of the particle's evolution.

But then i go on to say: but this does not solve Heisenberg's measurement problem which illuminates our limitation in precisely predicting a system's evolution, no matter how large or small the system may be.




Your input has been so helpful, could you please clarify this last point, thankyou so much

Roberto

 

[Dick]

What is the Feynman reference? It sounds like what he is talking about a wavefunction that includes the observer as well as the observed, so there is no place for a 'measurement'. That gets tangled up with the whole 'interpretation of quantum mechanics' problem. Which I don't think anybody really understands, especially not me. It's more of a paradoxical thought experiment than anything that really illuminates how QM works. I think few people would agree that means the universe is deterministic. But I don't think anybody could really tell you why not. If you are not comfortable with the reference, just leave it out. It looks like you have a lot else to discuss. I think Feynman also once said something like, 'if you think you understand quantum mechanics, you are wrong.' I guess I don't know what the anthropic principle has to do with QM.

 

[roberto85]

What is the Feynman reference? It sounds like what he is talking about a wavefunction that includes the observer as well as the observed, so there is no place for a 'measurement'. That gets tangled up with the whole 'interpretation of quantum mechanics' problem. Which I don't think anybody really understands, especially not me. It's more of a paradoxical thought experiment than anything that really illuminates how QM works. I think few people would agree that means the universe is deterministic. But I don't think anybody could really tell you why not. If you are not comfortable with the reference, just leave it out. It looks like you have a lot else to discuss. I think Feynman also once said something like, 'if you think you understand quantum mechanics, you are wrong.' I guess I don't know what the anthropic principle has to do with QM.

The reference comes from the book - quantum mechanics and path integrals by Feynman and Hibbs. The reference is at the top of page 58. I have been discussing this with another PF member on a separate thread and we come round to this conclusion (although I am still clarifying it with the said poster):

So the wavefunction offers a much more simplistic and perhaps more beautiful way to describe a system when compared to the kernel since all effects of the past history of a particle can be defined in terms of a the wavefunction. If we were to ignore everything we knew of it's history except for it's wavefunction at a particular time; we could calculate the future of the particle's evolution. This remarkable fact could conceivably mean that 'all of history's effect upon the future of the universe could be obtained from a single gigantic wavefunction' \ref{FeyPI} which does suggest the universe is deterministic although the Copenhagen interpretion excludes this possibility. For instance a single wavefunction for the entire universe may be asthetically pleasing, but since there is no feasible way to formulate, let alone measure it, one questions the utility of hypothesising it's existence. But theoretically if it was obtainable it is true that given the computing capability you could predict the wave function for the total history of the universe which is essentially determinism; albeit not the kind of determinism that predicts the positions and momenta of every particle. This is because the Heisenberg uncertainty principle precludes it's validity since it contradicts the wave function concept. You could predict the probabilities of the particles' positions, momenta, etc. but this does not solve Heisenberg's measurement problem which illuminates our limitation in precisely predicting a system's evolution, no matter how large or small the system may be.

here is a link to the thread, please excuse my multiple posts in other PF sections, i was unsure where to ask this question:

https://www.physicsforums.com/showthread.php?p=2515143#post2515143

Moderator's note: Threads have been merged.

 

[nomadreid]

There are a couple of points which I think you did not quite get in your rephrasing, although I am not sure, since the referent of "it" is not always clear. So forgive me if I repeat myself a bit.
First, in your phrasing the reader could infer, or perhaps you imply, that Heisenberg's Uncertainty Principle (HUP) contradicts the concept of the wave function. If so, this is very, very false. Let me rephrase them. They are both talking the same language of probability distributions. That is, we are referring to probability distributions of measurements. (Bell's Theorem showed that these probabilities are ontological, not epistemological.) The HUP says that if you have two quantities which are complements to one another (for example, position and momentum -- or any quantity and its change), then the standard deviations of the two corresponding probability distribution curves will multiply together to give a product less than a certain constant. The wave function, on the other hand, talks about a single distribution curve, and shows how energy will change the distribution curve over time. The two concepts work well together. So get rid of or rephrase your sentence about there being a contradiction.
Next, and very importantly, it is incorrect to say "all effects of the past history of a particle can be defined in terms of a the wavefunction". The wave function gives only probabilities. It does not say what the measured positions and momenta of the particle was, is, or will be.
Feynman was indeed trying to get across the idea of a new type of determinism. But since most people still understand determinism in the old sense, it would be unwise to say that the wave function represents "essentially" determinism. (Feynman introduced the concept of a universal wave function to make the argument cleaner, in the same way that thermodynamics talks about hypothetical closed systems.) The new determinism says that knowing a universal wave function at one moment we could predict this universal wave function at any time -- except for one caveat, known as the Measurement Problem. The Measurement Problem is not Heisenberg's; he didn't think it up. The Measurement problem is why measurement causes the wave function to go from the probability predicted by the wave function to certainty. (Classically, this is the "collapse" of the wave function, by Everett this is where different worlds split, and there are other interpretations. The Decoherence interpretation faces the reality of the absence of a universal wave function, and posits the interactions of local wave functions. But all these interpretations face the same Measurement problem.) There is no way to predict from the wave function what a particular measurement will give. Hence, the HUP destroyed the classical determinism, and the new determinism is not quite perfect, even if there were a universal wave function.
In any case, it is possible that you and Feynman are using the phrase "the future of a particle's evolution" in two different ways. Feynman was considering the particle in its indeterminate state, and the evolution was from one probability distribution to the next as energy is exchanged. Note the word "indeterminate": for Feynman, this state IS the particle. That is, this is the antithesis of the classical determinism. Feynman was famous for his "shut up and calculate" attitude: a particle IS a probability distribution, so if you can calculate the probability of a particle's position, that is deterministic enough for Feynman.
The wave function is far from simplistic. It is, in its fullest expression, both very complex and very rich. I am not sure what the "kernel" is that you are referring to.
I hope this helps. Keep asking; it is a tricky subject.

 

[roberto85]

There are a couple of points which I think you did not quite get in your rephrasing, although I am not sure, since the referent of "it" is not always clear. So forgive me if I repeat myself a bit.
First, in your phrasing the reader could infer, or perhaps you imply, that Heisenberg's Uncertainty Principle (HUP) contradicts the concept of the wave function. If so, this is very, very false. Let me rephrase them. They are both talking the same language of probability distributions. That is, we are referring to probability distributions of measurements. (Bell's Theorem showed that these probabilities are ontological, not epistemological.) The HUP says that if you have two quantities which are complements to one another (for example, position and momentum -- or any quantity and its change), then the standard deviations of the two corresponding probability distribution curves will multiply together to give a product less than a certain constant. The wave function, on the other hand, talks about a single distribution curve, and shows how energy will change the distribution curve over time. The two concepts work well together. So get rid of or rephrase your sentence about there being a contradiction.
Next, and very importantly, it is incorrect to say "all effects of the past history of a particle can be defined in terms of a the wavefunction". The wave function gives only probabilities. It does not say what the measured positions and momenta of the particle was, is, or will be.
Feynman was indeed trying to get across the idea of a new type of determinism. But since most people still understand determinism in the old sense, it would be unwise to say that the wave function represents "essentially" determinism. (Feynman introduced the concept of a universal wave function to make the argument cleaner, in the same way that thermodynamics talks about hypothetical closed systems.) The new determinism says that knowing a universal wave function at one moment we could predict this universal wave function at any time -- except for one caveat, known as the Measurement Problem. The Measurement Problem is not Heisenberg's; he didn't think it up. The Measurement problem is why measurement causes the wave function to go from the probability predicted by the wave function to certainty. (Classically, this is the "collapse" of the wave function, by Everett this is where different worlds split, and there are other interpretations. The Decoherence interpretation faces the reality of the absence of a universal wave function, and posits the interactions of local wave functions. But all these interpretations face the same Measurement problem.) There is no way to predict from the wave function what a particular measurement will give. Hence, the HUP destroyed the classical determinism, and the new determinism is not quite perfect, even if there were a universal wave function.
In any case, it is possible that you and Feynman are using the phrase "the future of a particle's evolution" in two different ways. Feynman was considering the particle in its indeterminate state, and the evolution was from one probability distribution to the next as energy is exchanged. Note the word "indeterminate": for Feynman, this state IS the particle. That is, this is the antithesis of the classical determinism. Feynman was famous for his "shut up and calculate" attitude: a particle IS a probability distribution, so if you can calculate the probability of a particle's position, that is deterministic enough for Feynman.
The wave function is far from simplistic. It is, in its fullest expression, both very complex and very rich. I am not sure what the "kernel" is that you are referring to.
I hope this helps. Keep asking; it is a tricky subject.

Okay, i think I've cleared up that paragraph now, i actauly quoted feynman wrong, i wrote wavefuntion instead of just function which i think refers to an amplitude. The kernel is the same as a propagator in the path integral formulation and this paragrap was meant to explain how the kernel requires information specified at all points over a particle's path whereas an amplitude (or wavefunction? oh no I am confused haha ) doesn't require so much information to be specified and so it notationally neater. Here is my next and hopefully final attempt at writing something true to fact:

So the wavefunction offers a much more simplistic way to describe a system when compared to the kernel since all effects of the past history of a particle can be defined in terms of a single function. If we were to ignore everything we knew of it's history except for it's wavefunction at a particular time; we could calculate the future of the particle's probabilistic evolution. This means that 'all of history's effect upon the future of the universe could be obtained from a single gigantic wavefunction' \ref{FeyPI} which conveys a probabilistic determinism of the universe. A single wavefunction for the entire universe may be asthetically pleasing, but since there is no feasible way to formulate, let alone measure it, one questions the utility of hypothesising it's existence. But theoretically if it were obtainable it is true that given the computing capability you could predict the wave function for the total history of the universe which is essentially quantum determinism and not a classical determinism that specifies the positions and momenta of every particle. You could predict the probabilities of the particles' positions and momenta and thus knowing a universal wave function at one moment we could predict this universal wave function at any time. The reason why classical determinism is prohibited by quantum theory is because a particle is always in an indeterminate state until a measurement is made and causes wavefunction collapse so the particle evolution we describe is that from one probability distribution to the next as energy is exchanged. As profound as this idea seems there is one caveat known as the measurement problem which is why measurement causes the wave function to go from the probability predicted by the wave function to certainty. A famous example that demonstrates the peculiarity of wavefunction collapse is that of the paradoxical Schrodinger's cat thought erxperiment. The explanation of wavefunction collapse still remains unresolved as to why or even if it really occurs and there are several theories which attempt to answer this question although none have yet provided a testable hypothesis to prove their validity.

Your input on the matter has been astoundingly helpful and so rewarding in that you have awakened me to much about quantum physics. I knew i made the right choice choosing to study physics, thanks - oh and if there are errors here still, please let me know

Roberto

 

[nomadreid]

That looks a lot better :-) However, I think you meant "simpler" instead of "simplistic".
Also, your phrasing might be clearer if, instead of writing that you are comparing the wavefunction to the propogation kernel, that you are comparing the Schrödinger's equation and the path integral formulation.
Quantum mechanics is fun, assuming one stays sane, which isn't always easy. :-)

 

[roberto85]

That looks a lot better :-) However, I think you meant "simpler" instead of "simplistic".
Also, your phrasing might be clearer if, instead of writing that you are comparing the wavefunction to the propogation kernel, that you are comparing the Schrödinger's equation and the path integral formulation.
Quantum mechanics is fun, assuming one stays sane, which isn't always easy. :-)

Great, glad that is sorted, thanks again for all your help. I am now stuck on another thing though... I am desperately trying to find some literature on the harmonic oscillator which is described by the path integral formulation and does not use dirac notation. Something as simple as possible woud be great. Sakurai is in dirac notation and feynmans book asks the reader to solve the problem itself rather than explicitly describing it. Do you know anywhere i can find this?? preferably an online source, thanks

Roberto

 

[nomadreid]

Try this:
http://www.iop.org/EJ/article/0305-4470/34/12/101/a112l1.html

 

[roberto85]

Try this:
http://www.iop.org/EJ/article/0305-4470/34/12/101/a112l1.html

That does look pretty understandable but it does contain too many terms I am unfamiliar with and would take too long for me to introduce each term into this paper. I may have to leave the harmonic oscillator out completely although I am sure i will be penalised for this. I may be able to retrieve something from feynman and Hibbs but it is going to be rather sketchy. Thanks for your help anyway

Roberto