Exploring the Relationship Between Schroedinger and Bohm's Quantum Mechanics

[Rothiemurchus]

There is a thread I opened on sci.physics.research about "solitons and water waves"
which has a link to the use of the Schrödinger equation in showing how water waves
take energy from one another.Apparently nobody thought the equation would work on this scale.There's not a lot of detail but I think you'll find the thread as a whole interesting.

 

[humanino]

I will agree with you when gravity is quantized using standard qft!

That is certainly not going to happen !
QM & QFT are two things. We know QFT failed with regard to gravity. Still QM must and will hold. You are confusing.

 

[humanino]

What you don't realize is that QM is a framwork much more general than when applied to a particular field. All the relevant theories attempting to quantize gravity today are very close to success, and none of them ever even tried to change QM. They have to fit in it. Don't tell me that is the reason why they did not successeded yet.

 

[Rothiemurchus]

The addition of a quantized electromagnetic field to Dirac's theory is qft isn't it?
And isn't Dirac's theory standard QM plus rest mass?

 

[humanino]

No it is not.

 

[humanino]

Dirac theory emerge from an attempt to have a relativistic Schrödinger equation, that is describe a (EM) chargeless particle respecting the Klein-Gordon equation, but without the plague of negative probability. You can have a classical Dirac equation, and then quantisize it.

 

[humanino]

The addition of a quantized electromagnetic field to Dirac's theory is qft isn't it?

It is a QFT. The formalism applies to any field.

 

[Rothiemurchus]

I should have said rest energy , mc^2.

Marlon:
Once the concept of wave-function was constructed , the idea of intensity was used as the probability of finding a particle on a certain position.

Rothie M:

A water wave would have a greater amount of mass, at one single space co-ordinate (e.g an x co-ordinate), for a bigger wave amplitude.
Can't the wavefunction be like this in reality - can't it represent a lot of particles that exist together simultaneously?
Perhaps an electron likes to surf on these waves - the higher waves
attracting it the most?

 

[humanino]

But the Schrödinger equation has a mass parameter ! Even : you cannot apply the Schrödinger equation to a massless particle, which is relativist, since the mass term is in a denominator !

 

[humanino]

The problem was to respect the Klein-Gordon p^2+m^2=E^2

tex is not working girht now !?

 

[nrqed]

The schroedinger equation is an inspired postulate - it cannot be derived

I agree with you.

Well, it's true that the Schroedinger equation can be "derived" from other considerations but whenever you trace back the steps, you always end up at a point which is an educated (clever) guess. Some start from postulating the quantum brackets starting from classical Poisson brackets, some start from directly replaing E and p by operators acting on this (weird and nonclassical) wavefunction, etc. But there is always an educated guess at the beginning. Quantum mechanics cannot be derived from classical physics so it absolutely require some smart guessing. Of course, it works great so that makes the guess very convincing.

But F=m a could also be said to be an educated guess. As are all fundamental principles of physics. There's nothing wrong with this.

Pat

 

[humanino]

Rothiemurchus : there is plenty of literature on the web, especially here on this site.
Again :
Please follow Zz advice. Otherwise this site would grow indecently. Use the search function. You cannot search more than once in 5 minutes.

 

[humanino]

This discussion is becoming ridiculous. Are you guys flattering your ego or what ? You seem not even to listen to the precious informations Zz gave you. This is not fair.

 

[humanino]

But F=m a could also be said to be an educated guess. As are all fundamental principles of physics.

Pat this is simply wrong ! The law of attraction is an educated guess. F = m a is merely a definition of what a force is !

 

[marlon]

But gravity could be the downfall for standard QM..

That is very untrue for the simple reason that QM is not trying to describe gravity. Gravitational effects are not included in QM and even the QFT from the Standard Model because at the atomic scale, they are negligible...

regards
marlon

 

[marlon]

Pat this is simply wrong ! The law of attraction is an educated guess. F = m a is merely a definition of what a force is !

I agree with Humanino.
Just look at history : how did Newton come up with the connection between F and a ? He just found out experimantally that F = ma, he did not guess this...

regards
marlon

ps : also, indeed I think this discussion is more about personal opinions and so on...Let's stick to the facts QM is the best theory for atomic scaled-events, backed up by many many experimental evidence...POINT FINAL

regards
marlon

 

[Haelfix]

You know, a lot of this depends on how you want to axiomatize your system. Non relativistic Quantum mechanics does have a rigorous mathematical interpretation that is self consistent, but I does not start from the Schroedinger equation right from the get go, or indeed even where the paper in post #2 starts from.

Von Neumann's text is probably where you want to start.. But ultimately, its the nice properties of the the Wiener measure that makes things work out.

There are still mysteries though, particularly when you jump into relativistic material. There you have to axiomatize completely differently, and in a non intuitive way, in order to have any hope for progress... And unfortunately, there is still a lot that needs to be done, it is by no means a full theory yet.

I mean, I could just as well take as a postulate that classical Hamiltonian mechanics is correct.. And then, indeed, I can *derive* Newtonian physics as an isomorphism between theories.

 

[Rothiemurchus]

Marlon:
That is very untrue for the simple reason that QM is not trying to describe gravity.

Rothie M:

In the real world all physical processes take place in the presence of gravity -
qm must depend on gravity and therefore in some sense describe it (gravity can be put into the potential energy term of the Schrödinger equation but because it is very weak compared to EM it is not, but that does not describe reality - just a useful approximation to it).

Humanino:
But the Schrödinger equation has a mass parameter ! Even : you cannot apply the Schrödinger equation to a massless particle, which is relativist, since the mass term is in a denominator !

Rothie M:
You are talking about an infinity here?
But even a photon might have a small mass - people are trying to
determine what it is.



I would like to emphasize that the only problem I have with QM is that nobody has ever justified squaring the amplitude of the wavefunction to get a probability.
There could be something fundamental underlying why this is the right thing to do.

Using the rubber sheet analogy for spacetime in GR:
If I stretch the sheet it would gain potential energy.
Could the Schrödinger wavefunction be a measure of the amplitude of the stretching
of spacetime with an electron most likely to be where the stretching is greatest
(which for a hydrogen atom would be close to the proton at 0.52 Angstroms).

 

[nrqed]

Pat this is simply wrong ! The law of attraction is an educated guess. F = m a is merely a definition of what a force is !

Yes, I agree with you. My mistake.

Pat

 

[nrqed]

I agree with Humanino.
Just look at history : how did Newton come up with the connection between F and a ? He just found out experimantally that F = ma, he did not guess this...

I agree with Humanino too and just posted something saying so. But I am surprised by your statement that Newton found F=ma experimentally. I'd love to see something more specific about this (what experiment did he actually use? What was his reasoning?)

ps : also, indeed I think this discussion is more about personal opinions and so on...Let's stick to the facts QM is the best theory for atomic scaled-events, backed up by many many experimental evidence...POINT FINAL

To a certain extent, it's true that there is some subjectivity. It does not mean that it is not a useful and worthwhile line of discussion. Of course, we could all follow the "shut up and calculate" approach but I don't think that's a good attitude. It's good that Einstein did not have this attitude. Or Bell or Feynman etc etc.
Pat

 

[nrqed]

You know, a lot of this depends on how you want to axiomatize your system. Non relativistic Quantum mechanics does have a rigorous mathematical interpretation that is self consistent, but I does not start from the Schroedinger equation right from the get go, or indeed even where the paper in post #2 starts from.

Von Neumann's text is probably where you want to start.. But ultimately, its the nice properties of the the Wiener measure that makes things work out.

There are still mysteries though, particularly when you jump into relativistic material. There you have to axiomatize completely differently, and in a non intuitive way, in order to have any hope for progress... And unfortunately, there is still a lot that needs to be done, it is by no means a full theory yet.

I mean, I could just as well take as a postulate that classical Hamiltonian mechanics is correct.. And then, indeed, I can *derive* Newtonian physics as an isomorphism between theories.

Very true and very interesting. Thanks for your input.

Regards

Pat

 

[ZapperZ]

Marlon:
That is very untrue for the simple reason that QM is not trying to describe gravity.

Rothie M:

In the real world all physical processes take place in the presence of gravity -
qm must depend on gravity and therefore in some sense describe it (gravity can be put into the potential energy term of the Schrödinger equation but because it is very weak compared to EM it is not, but that does not describe reality - just a useful approximation to it).

Take note that the quantum effects of gravity HAS been verified for at least a couple of years already![1]

Humanino:
But the Schrödinger equation has a mass parameter ! Even : you cannot apply the Schrödinger equation to a massless particle, which is relativist, since the mass term is in a denominator !

Rothie M:
You are talking about an infinity here?
But even a photon might have a small mass - people are trying to
determine what it is.



I would like to emphasize that the only problem I have with QM is that nobody has ever justified squaring the amplitude of the wavefunction to get a probability.
There could be something fundamental underlying why this is the right thing to do.

Using the rubber sheet analogy for spacetime in GR:
If I stretch the sheet it would gain potential energy.
Could the Schrödinger wavefunction be a measure of the amplitude of the stretching
of spacetime with an electron most likely to be where the stretching is greatest
(which for a hydrogen atom would be close to the proton at 0.52 Angstroms).

This is where I clearly said early in this thread that QM has a set of postulates.[2] Most of these postulates assign a PHYSICAL meaning to certain mathematical operations! However, it is incorrect to think that the wavefunction as a real, physical wave. This is one of the most popular misconception of QM. Other than the fact that the wavefunction itself is complex, the wavefunction sits in a "configuration space", not in real space (except for a single-particle special case).

This hypothesis of assigning a part of the wavefunction to the location of an electron borders on an unverified personal theory. Unless we be careful, that will cause this whole thread to be dumped into the Theory Development section, which will end my participation (that may not be such a bad thing to some people).

Zz.

[1] V.V. Nesvizhevsky et al., Nature v.415, p.297 (2002).
[2] http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qm.html

 

[humanino]

Rothie M:
You are talking about an infinity here?
But even a photon might have a small mass - people are trying to
determine what it is.

I am not talking about infinity.

There are not many things we know with such an accuracy as the vanishing of the photon mass. Who is seriously trying to show that it is non-zero ? QED relies on a gauge theory which is not broken and for which the mass of the boson is zero. For all purpose the mass of the real photon is experimentally and theoretically zero in physics today.

Of course, something very nice about this mass, is that although introducing a mass term spoils the gauge invariance, you can still do it in the calcultaions and set it to zero in the end of the day. There are non-trivial reasons for the gauge invariance to be recovered.

We are not having a very constructive discussion here. All of us agree on the fact that QM is mysterious at some point, when you think about it. Yet it is working perfectly fine. All the rest is speculations so far unfortunately. I wish thise speculations could lead somewhere.

 

[vanesch]

But I am surprised by your statement that Newton found F=ma experimentally. I'd love to see something more specific about this (what experiment did he actually use? What was his reasoning?)

He used an apple tree
His reasoning went like "aaauw"

cheers,
patrick.

 

[nrqed]

He used an apple tree
His reasoning went like "aaauw"

cheers,
patrick.

You are right but that's the "experiment" he used to discover the universal law of gravitation, not F=ma...

Pat

 

[Rothiemurchus]

Humanino:
We are not having a very constructive discussion here. All of us agree on the fact that QM is mysterious at some point, when you think about it. Yet it is working perfectly fine.

Rothie M:
Yes it works fine.But perhaps finding out why it works could be a useful thing to know.

ZAPPER Z:
it is incorrect to think that the wavefunction as a real, physical wave. This is one of the most popular misconception of QM. Other than the fact that the wavefunction itself is complex, the wavefunction sits in a "configuration space", not in real space (except for a single-particle special case).

Rothie M:
In Bohm's theory it is not incorrect to think of the pilot wave as a physical wave.

The magnitude of the wavefunction squared in standard qm is real even if the wavefunction itself is complex.This is of interest because in the analogy with the intensity of a light wave both the amplitude squared and the amplitude are real numbers.The analogy isn't that good is it?

 

[bd1976]

hmmm...

Again, this is an objection based on a matter of tastes.

Secondly, when you say something is "conceptually difficult", what does that mean? I know of MANY things which I found to be "conceptually difficult" to comprehend until I actually learned about those things. Then they became conceptually easy to understand! Are we basing it on intuition? If so, then this isn't a valid foundation to use since our intuition changes with our accumulated knowledge! So when you say something is conceptually difficult, how would you know the problem isn't with you or your understanding of it?

First of all I think that quantum mechanics as a theory is fundamentally different to other physical theories. Yes its true that sometime you gain knowledge ideas become easier to understand, however I think that qm is an example of completely the opposite the more knowledge you gain the more challenging the conceptual problems become. I'm sure there’s a quote from Schrödinger that goes something like - anyone who claims to have understood qm hasn't understood it at all!

First of all there's the problem of measurement. QM is a theory based around "measurements". However what a "measurement" actually is not understood!

Secondly there is the problem of instantaneous information exchange - violating the principle of relativity! Now since there is no experiment which can preformed that violates relativity it has to be said that such a conflict is a serious cause for alarm.

Finally there is the problem of complex numbers. Now don't get me wrong complex number theory is (in my humble opinion) the most beautiful piece of mathematics I have ever encountered. However that doesn't get over the "pie" problem. Integers are whole pies, rational numbers allow for slices of pies.. but what is a complex pie? The answer is that there is no such thing! Complex numbers have no physical correspondence. So here we have a theory where the main object - "the wave-function" has no physical meaning at all and that does separate qm from the other theories in physics.

Please address any comments on complex numbers inthis thread Integral

 

[humanino]

You guys are addressing here questions which we would like to have an answer to. So please, discuss here and find it. I don't have it. In the meantime, if you could find a simple geometrical TOE, don't hesitate, I'd be glad too. Ho, and elixir of long life would be fine as well.

 

[ZapperZ]

First of all there's the problem of measurement. QM is a theory based around "measurements". However what a "measurement" actually is not understood!

But we CONTINUE to study it. However, this doesn't detract from the validity of QM because it only states what CAN be measured. The mechanism of a measurement (if there is any) is part of something QM can't say unless one has a clear definition and idea of what to look for. QM can't make up things out of the air simply to satisfy something that may or may not be there.

And lest we ignore one important thing: there is ALSO a measurement problem in classical mechanics. Think about it. What you measure will depend on how accurately you measure it. At some point, the accuracy of your measurement will bump into the quantum regime. If you don't believe me, look at the diffraction from a single slit. It only APPEARS that what you measured gave you a "good" value because of the coarseness of your measurement.

Secondly there is the problem of instantaneous information exchange - violating the principle of relativity! Now since there is no experiment which can preformed that violates relativity it has to be said that such a conflict is a serious cause for alarm.

Strangely enough, EVERYONE who works in the field that does this EPR-type study, finds no such alarm. This is because for there to be a violation of SR, there has to be a TRANSFER of information via a continuous displacement over space from one location to another. QM indicates that there is no such thing! There is no info flowing from one location to another in an entanglement measurement. If there is, wouldn't you think this is widely mentioned in physics journals already and highly debated, considering this would cause two MAJOR physics principles (Relativity and QM) to be at odds with each other? If you read ALL the EPR-type papers, be it theoretical or experimental (any paper by Anton Zeilinger would suffice), in NONE of them are there any claims of superluminal transfer of information.

Finally there is the problem of complex numbers. Now don't get me wrong complex number theory is (in my humble opinion) the most beautiful piece of mathematics I have ever encountered. However that doesn't get over the "pie" problem. Integers are whole pies, rational numbers allow for slices of pies.. but what is a complex pie? The answer is that there is no such thing! Complex numbers have no physical correspondence. So here we have a theory where the main object - "the wave-function" has no physical meaning at all and that does separate qm from the other theories in physics.

Then you must also have major problems in accepting electrical engineering, classical E&M, etc. So why are we picking on QM alone?

Zz.

 

[nrqed]

...
Strangely enough, EVERYONE who works in the field that does this EPR-type study, finds no such alarm. This is because for there to be a violation of SR, there has to be a TRANSFER of information via a continuous displacement over space from one location to another. QM indicates that there is no such thing! There is no info flowing from one location to another in an entanglement measurement. If there is, wouldn't you think this is widely mentioned in physics journals already and highly debated, considering this would cause two MAJOR physics principles (Relativity and QM) to be at odds with each other? If you read ALL the EPR-type papers, be it theoretical or experimental (any paper by Anton Zeilinger would suffice), in NONE of them are there any claims of superluminal transfer of information.


Zz.

First, let me thank you for your input in this thread.

I agree with what you are saying, but I must still admit that I do feel very uneasy about this entanglement stuff. I know that no information, in the ordinary sense, is transfered, but still there *is* a correlation between the measurements. I know that my position is not a popular one among physicists but I am deeply dissatisfied with the conventional point of view that there is nothing bothersome there and that if one is wondering about whether "something" is exchanged (maybe in some way that would require a rethinking of spacetime), then that person either does not understand the formalism or is a crackpot.



I guess that maybe we should simply say "our formalism is consistent and it agrees with experiments so let's just accept that our comprehension has reached its limits (as opposed to our ability to do calculations) and let's stop asking certain types of questions". But it's hard for me to accept. These EPR type experiments are, imho, the most intriguing and mind blowing aspects of modern physics and I am suprised that most physicists just go "that's neat and strange but we "understand" what's going on, it's all in the formalism. let's move on to other things". I, on the other hand, can't help feeling that I am missing something. That's there something more to the story. Of course, I am not saying that I'll be coming up with a new revolutionary theory, I am just saying that I find it amazing how other people find it easy to accept this aspect of the theory.


Regards,

Pat


(PS:In his book on QFT, Weinberg defines the cluster decomposition principle as the principle that says that "distant experiments yield uncorrelated results. " Well, one should probably define more clearly what "uncorrelated results" means but it would seem that Bell type experiments would violate this principle!)