Quantum Mechanics: A Brief Overview and Explanation

[Another God]

For the few of us here who use this forum for things other than physics (strange, I know...) could someone do me a favour and please give us a brief overview of what it is that quantum mechanics really concerns itself with, and how this stuff is known?

I was asked this the other day, and wqas surprised to realize that I couldn't really answer it myself. I know there is the stuff about velocity and location of a particle, but that is about all I know, and not only do I not know it well, but I have no idea how that knowledge claim is justified.

So, please, looking for a quick rundown of 'QM' Thanks

 

[arcnets]

Another God, maybe this will help:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_Quantum_age_begins.html

 

[Another God]

Thanks alot, I'll have a read of that, and post any questions that remain

 

[Another God]

OK, that has given me a good background now, for what has happened and stuff, but it hasn't really explained any of the theoretical aspect of anything: It just says what theories were proposed and by who without really covering why or what it means. Because of that, most of it was quite meaningless to me.

So now that I have some sort of background framework, maybe someone could fill in some of the details and the meanings?

One question that comes straight to mind from that paper though, is the momentum/position issue. So often in discussion on this forum I have heard people refer to that, implying that the claim is that a particle can either have momentum, or position, neith at the same time. I mean, they imply that the uncertainty principle claim is a claim about the nature of the particle. I never liked that, but accepted that i knew nothing, and so never questioned it. This paper on the other hand states it as if it is in fact our 'measurement' of the momentum and the position which are the issues, not the momentum and position of the particle itself.

the process of measuring the position x of a particle disturbs the particle's momentum p

I have no problem accepting this sort of statement: That it is our act itself that causes the uncertainty principle, not the particle which is an eternally uncertain entity.

And the fact that it is based on us measuring either the momentum OR the position, implies to me that it may be possible to one day refine our techniques so that we can somehow measure 'the particle', and thereby gain knowledge of both momentum and position AT THE ONE MOMENT, rather than trying to measuring one, and then the other...

How far wrong am I?

 

[quantumdude]

Originally posted by Another God
One question that comes straight to mind from that paper though, is the momentum/position issue. So often in discussion on this forum I have heard people refer to that, implying that the claim is that a particle can either have momentum, or position, neith at the same time.

That is but one untestable interpretation of quantum mechanics. Another one is the one you quoted below, that the particle can have a sharply defined position and momentum simultaneously, but because of the process of measurement we cannot know them both at the same time.

I mean, they imply that the uncertainty principle claim is a claim about the nature of the particle.

No, it is a claim on the nature of measurements. The truth is that we do not--and can not--know what happens in between measurements, so either interpretation (as well as a host of other interpretations) are consistent with experiment.

I never liked that, but accepted that i knew nothing, and so never questioned it. This paper on the other hand states it as if it is in fact our 'measurement' of the momentum and the position which are the issues, not the momentum and position of the particle itself.

It's funny that it would state both interpretations without separating them, because they do in fact contradict each other.

And the fact that it is based on us measuring either the momentum OR the position, implies to me that it may be possible to one day refine our techniques so that we can somehow measure 'the particle', and thereby gain knowledge of both momentum and position AT THE ONE MOMENT, rather than trying to measuring one, and then the other...

Now this is expressly forbidden in quantum mechanics. The uncertainty principle has nothing to do with human error in experimental measurements. It's not as though you can get around the problem by being "more careful". It is a known fact that particles behave as waves. If you try to squeeze a wave into a small box to determine its position, it will diffract in such a way that its momentum will change in an unpredictable way. If you nail down its momentum precisely, you force it into a monochromatic plane wave state that extends over all space.

One way I make myself comfortable with the indeterminacy issue is by recognizing that the classical variables (position and momentum) are artifacts of our macroscopic experience. That is, we think that a particle should have a simultaneously measurable position and momentum because we are used to thinking that they should. Once one sheds the idea that position and momentum are the correct degrees of freedom in which to embed one's mindset, one can see that quantum mechanics is a deterministic theory in a different set of variables: Ψ and Ψ*, the wavefunction and its conjugate.

Now a lot of people would find this distasteful, because wavefunctions cannot be measured (they are complex-valued quantities), whereas position and momentum can be measured. They would say that nature would never be so absurd that its true, fundamental degrees of freedom are purely mathematical objects. But what are you going to do? It's not as though you can tell nature how to behave.

edit: typo

 

[slyboy]

One way I make myself comfortable with the indeterminacy issue is by recognizing that the classical variables (position and momentum) are artifacts of our macroscopic experience. That is, we think that a particle should have a simultaneously measurable position and momentum because we are used to thinking that they should. Once one sheds the idea that position and momentum are the correct degrees of freedom in which to embed one's mindset, one can see that quantum mechanics is a deterministic theory in a different set of variables: Ø and Ø*, the wavefunction and its conjugate.

Now a lot of people would find this distasteful, because wavefunctions cannot be measured (they are complex-valued quantities), whereas position and momentum can be measured. They would say that nature would never be so absurd that its true, fundamental degrees of freedom are purely mathematical objects. But what are you going to do? It's not as though you can tell nature how to behave.
[\QUOTE]

I agree with the spirit of what you are saying, but I think you have been rather simplistic.

In what sense are you regarding the wavefunction as a dynamical variable? Are you saying that it is an objective property of the real world? I am much more of the opinion that it is a state of knowledge that we have about a physical system.

There is a sense in which the wavefunction can be measured - if one has a number of copies of identically prepared physical systems. This is known as quantum state tomography, and is becoming an increasingly important tool for quantum information and computation experiments. However, the fact that you need an infinite number of copies of the system to determine the wavefunction precisely leads me to regard it as being analogous to a probability distribution over dynamical variables rather than being a dynamical variable itself.

Now, classical probability distributions can be interpreted in two ways:

1) They tell us about the relative frequencies of outcomes we can expect (the classical approach).

2) They encode states of knowledge, or states of belief (Bayesian approach).

Analogous approaches to quantum states have been proposed, mainly in the relative frequency interpretation, but I believe that the Bayesian approach has the possibility to clear up a lot of the thorny issues in the foundations of quantum theory (See Chris Fuchs paper - "Quantum foundations as quantum information (and only a little more)" available on the quant-ph arXiv http://www.arXiv.org/quant-ph/ ).

 

[quantumdude]

Originally posted by slyboy
In what sense are you regarding the wavefunction as a dynamical variable?

In the sense that it has a definite time evolution governed by the Hamiltonian.

Are you saying that it is an objective property of the real world?

No, because wavefunctions are mathematical contrivances to begin with. The quantum field theoretic description of the world has already supplanted the quantum mechanical description. I am saying that the wavefunction is a dynamical variable within the theory.

There is a sense in which the wavefunction can be measured - if one has a number of copies of identically prepared physical systems. This is known as quantum state tomography, and is becoming an increasingly important tool for quantum information and computation experiments.

No one can measure a wavefunction. This is a simple consequence of the fact that global gauge transformations lead to identical physics. That is, Ψ is equivalent to Ψe^-iα.

Analogous approaches to quantum states have been proposed, mainly in the relative frequency interpretation, but I believe that the Bayesian approach has the possibility to clear up a lot of the thorny issues in the foundations of quantum theory (See Chris Fuchs paper - "Quantum foundations as quantum information (and only a little more)" available on the quant-ph arXiv http://www.arXiv.org/quant-ph/ ).

I have that paper, but have not read it. I'll get to it at some point.

 

[Another God]

Most of those last two posts meant nothing -> Very little to me, but I can get the idea of dropping our idea of momentum and position in terms of the macroworld.

I am reading a book atm, although it had nothing to do with me starting this thread, it i largely based on QM stuff, and so coming to understand QM stuff better will allow me to be more critical of what is being said in the book: it's called The Field by Lynne McTaggart, and it is all about the Zero Point Field. I'm only a few chapters into it, and it has so far claimed that scientists have explained Gravity, F=ma, Homeopathy, and how biological molecules communicate. And while I feel like the author isn't the best (Journalistic and quite biased), I can't deny the scientific work, so I am intrigued.

 

[CodeComplete]

I too have just started reading the same book (I got it for X-mas).

I don't pretend to understand all the theories behind the Zero Point Field (ZPF) but don't virtual particles have a corresponding virtual anti-particle and so preclude the harnessing of 'free' energy as it all equates back to zero?

Are the theories of the physics of ZPF accepted or is it something that the new age spiritual groups have grasped upon as their proof for for all things psychic etc. ?

 

[Another God]

Apparently, the key is to harness both the positive and the negative, thereby setting up an alternating current. The one counter claim that I have heard against the idea sofar though, is that it can't be done because the frequency is too low. You wouldn't be able to get any real power out of it.

Thats what I understood anyway...

 

[Another God]

Getting back on topic, I think I have a good enough basic conception of Qm (ie: The stuff that everyone knows), but I am now interested in moving into some more practical knowledge. I am already starting to simply read the threads here (that is always a good way to learn stuff), but are there any good tutorial-esque sites around that can help someone make their way into the Qm world?

I am even willing to start relearning Maths...

 

[selfAdjoint]

I just googled on tutorial, quantum mechanics and found several. Rather tha my choosing one for you, why don't you do the google and pick the one that fits your needs. Although a lot of them have animated apps to illustrate things, you don't want to limit yourself to tutorials that only do that. You would probably learn more than you know know, but you wouldn't improve your ability to understand the LaTex conversations on these boards. A one dimesion of space plus time simplified model done with math is your best bet.