Question on observer created reality

[ZapperZ]

It is the essence of the Copenhagen view, to which I do not subscribe AS SUCH. Of course, in practice, everybody who uses QM works with it this way. But I find it fundamentally disturbing that quantum mechanics somehow stops to be valid, and classical theory takes over, and that's it. I'd rather see then both theories as limiting cases of a more fundamental theory.

I should have just let this slip by, but I can't help myself. :)

Why do you find this "disturbing"? Discontinuity in understanding and discontinuity in description happens all the time. At a first order phase transition, practically all bets are off. What you used to describe in one phase simply cannot be extrapolated into the other phase. There's an abrupt discontinuity in a number of state variables. So you switch gears and adopt a different set of description and properties.

My point here is that if you live by a principle where you are disturbed by this abrupt change, then you should also be disturbed by many more phenomena than just QM-classical boundary. So are you? :)

Zz.

 

[gptejms]

I'm sorry but it just doesn't make sense.

ok,my formula applies to the transformation of a hamiltonian under a time dependent unitary transformation.

 

[gptejms]

QFT and the measurement problem

You can do this, but only if you allow for a stochastic potential. Some people work on this.

Why stochastic?Can you give the references?

I am now throwing in another idea.In terms of QFT:-the principle of microscopic causality tells you that the measurement of the field at place 1 and subsequently at place 2(time-like separated) doesen't give you the same result as measurement at place 2 first and then at place 1(non-commutation).What this implies is that when I make a measurement at place 1,I create a disturbance which travels at the speed of light and the whole field readjusts to some new values.This is precisely what is happening in the 2-slit experiment(or for that matter any other experiment)--you measure the field or find an electron at slit 1,the field readjusts at slit 2 to no electron(if one electron comes at a time) and the field at the screen also readjusts to 'no interference pattern'.

 

[vanesch]

My point here is that if you live by a principle where you are disturbed by this abrupt change, then you should also be disturbed by many more phenomena than just QM-classical boundary. So are you? :)

What is disturbing in the QM-classical boundary is that it is "slippery". It is not defined, and you cannot deduce its location (at least, according to standard QM - I'm not talking about speculative extensions). If QM, in its unitary version, applies "all the way up", it should be *in principle* possible to UNDO about just any measurement result, and have "notebooks, people and all that" interfere quantummechanically. For the moment, we are technologically only able to do that for systems of 2 or 3 photons or so.
So wherever you put physically the QM - classical boundary, it is *in principle* possible, if QM applies all the way up, to transgress it, which would then show that the QM-classical boundary is not yet reached.

What I mean is the following:

If you have a system S, in the famous state a|1> + b|2>, and you have a measurement apparatus M and we do the "pre-measurement" interaction thing a la von Neumann, we end up with
|psi> = a |1> |M1> + b |2> |M2>

Now, as long as M1 and M2 are very complicated states, which are going to stay essentially orthogonal (so that the entanglement is "for ever"), if you take a "relative observer position" to be the measurement apparatus, then you can say that the measurement apparatus has "irreversibly" recorded the result.
But if we are technologically advanced enough to subject this complicated apparatus M to such an evolution that at a certain time M1 and M2 evolve towards the same state MX (this is unitarily possible, because we can "compensate" on the system: it is in essence the INVERSE measurement interaction), then we arrive back at |psi> = (a |1'> + b|2'>) |MX>. We could now perform an experiment on the system S IN ANOTHER BASIS, and observe quantum interference.
This is the essence of a quantum erasure experiment (although all papers about it formulate it in a much more spooky way about "forgetting" and "not violating the Heisenberg uncertainty relations" etc...).
We can do it with photons and even with more sophisiticated stuff.
If we would have thought that the interaction of M with the system was a "measurement" (was the "phase transition" between quantum and classical), we would have been proven wrong, because this quantum erasure could not happen anymore. In density matrix language: once the non-diagonal elements have been set to 0 (the quantum-classical transition: the Born rule), there's no way to put them back.
There is *in principle* no indication in current quantum theory that M cannot include the laboratory, the experimenter, the solar system, the galaxy etc... (except, except... for gravity - but I stick to non-speculative, current, quantum theory). So you can push back this "quantum-classical" transition in principle to beyond "M" systems the size of our galaxy.
To do that experimentally of course would require a mind-bogglingly sophisticated technology, but there is nothing in current quantum theory (except for our ignorance of how to treat gravity) that indicates that it cannot be done in principle.
Once you've pushed back the QM-classical transition far beyond the scale of humans and laboratories, it doesn't matter anymore: we clearly have then bodystates in a superposition, of which we consciously only observe ONE term.
This infinite possible "pushing back" is not present in the thermodynamical examples of phase transitions.

cheers,
Patrick.

 

[vanesch]

ok,my formula applies to the transformation of a hamiltonian under a time dependent unitary transformation.

Can't be !
Let us have for simplicity a time-independent Hamiltonian (it should be valid for that case too, right ?)

So you claim that:

H_H = U_dagger H_S U + U_dagger H_S U

(because we still have: hbar U-dagger dU/dt = U-dagger (i hbar dU/dt) = U-dagger H U)

So H_H = 2 U_dagger H_S U

However, in the case of a time-independent hamiltonian, you can easily find out that U = exp(- i hbar H_S), which commutes of course with H_S

So we find that H_H = 2 H_S ?

Expectation values of energy in the Heisenberg picture are twice as big as those in the Schroedinger picture ??

cheers,
Patrick.

 

[vanesch]

Why stochastic?Can you give the references?

Have a look at "decoherence and the appearance of a classical world in quantum theory" (by Joos, Zeh et al). The last 3 chapters (which I haven't studied in detail myself) are: 7. Open quantum systems (by Kupsch), 8. Stochastic collapse models (by Stamatescu) and 9. Related concepts and methods (by Zeh).
Look for the model of Ghirardi, Rimini and Weber (non-hamiltonian evolution) or Barcheilli, Lanz and Prosperi who build a model with "continuous approximate position measurement".

But I'm not very knowledgeable of all this stuff - I don't like the approach: it is introducing small "fudge terms" in the Schroedinger equation which aren't there in standard QM, so that the evolution is non-unitary, and then trying to find values for the free parameters so that at small scales, the effect of the terms is neglegible, and at large scales, it introduces a projection. It is not based upon some grand a-priori principle, and that's what I don't like about it.

you measure the field or find an electron at slit 1,the field readjusts at slit 2 to no electron(if one electron comes at a time) and the field at the screen also readjusts to 'no interference pattern'.

This won't work in all generality: you need faster-than-light propagation to do so. Ok, Bohm's theory does exactly this, but it has instantaneous action at a distance terms in it.

cheers,
Patrick.

 

[gptejms]

Can't be !
Let us have for simplicity a time-independent Hamiltonian (it should be valid for that case too, right ?)

So you claim that:

H_H = U_dagger H_S U + U_dagger H_S U

(because we still have: hbar U-dagger dU/dt = U-dagger (i hbar dU/dt) = U-dagger H U)

So H_H = 2 U_dagger H_S U

However, in the case of a time-independent hamiltonian, you can easily find out that U = exp(- i hbar H_S), which commutes of course with H_S

So we find that H_H = 2 H_S ?

Expectation values of energy in the Heisenberg picture are twice as big as those in the Schroedinger picture ??

cheers,
Patrick.

Why don't you use tex?The math notation you write is not so readable--e.g. what is U-dagger?

Since you are insisting on knowing the origin of this formula,I have worked it out.No,you are not in the Heisenberg picture(my mistake if I gave that impression) here--make a transformation |\psi^\prime(t)> =U(t)|\psi (t)\rangle
Differentiating the above(plus using the Schrodinger equation) you get
H^\prime(t) = U(t)H(t)U^\dagger(t) + i \hbar U^\dagger(t)\dot U(t)

 

[gptejms]

This won't work in all generality: you need faster-than-light propagation to do so. Ok, Bohm's theory does exactly this, but it has instantaneous action at a distance terms in it.

Why do you need ftl propagation?The field readjusts after the measurement at one place at the speed of light i.e. the disturbance is communicated to other places at the speed of light--for typical experimental dimensions this happens very very fast.

 

[vanesch]

Why don't you use tex?The math notation you write is not so readable--e.g. what is U-dagger?

I used to write in pure ASCII, from the good old days when news forums were pure ascii :-)

Since you are insisting on knowing the origin of this formula,I have worked it out.No,you are not in the Heisenberg picture(my mistake if I gave that impression) here--make a transformation |\psi^\prime(t)> =U(t)|\psi (t)\rangle
Differentiating the above(plus using the Schrodinger equation) you get
H^\prime(t) = U(t)H(t)U^\dagger(t) + i \hbar U^\dagger(t)\dot U(t)

This formula is right. But that's not what you were saying ! You were claiming (post 78) that in my transformation from a Schroedinger picture operator into its Heisenberg equivalent, I missed a term, when I wrote:

A_H(t) = U^\dagger(t) A_S U(t)

The above formula is part of the definition of the Heisenberg picture, so I don't see how "a term can be missing".

Now, i \hbar dU/dt = H_S(t), it is the DEFINITION of the Hamiltonian (see chapter 2 of Sakurai for instance).

From these two equations follows:
i \hbar d A_H(t) / dt = [A_H(t), H_H(t)]

with H_H the Hamiltonian in the Heisenberg picture, and given by
H_H(t) = U^\dagger(t) H_S(t) U(t)

If all H_S(t) commute for all values of t, then H_S commutes with U and hence H_H = H_S, but this is not the case in all generality.

But I didn't need this point at all. I just wanted to show that a unitary evolution operator U exists, whether you switch on a potential or not, that this allows you to go to the Heisenberg picture, and that there, by definition, the state of the system is given by a constant ket. Hence, switching on a potential doesn't affect the constant ket at all.

 

[vanesch]

Why do you need ftl propagation?

EPR situations require this, for instance. But you do not need to set up things so complicated: imagine a light beam, hitting a beam splitter, and the two resulting beams are diverging. When they are at a reasonable distance of a few meters, say, you make the thing such that you can, or cannot, "watch the photon" (say, by guiding the beam in a local detector or not) in each arm.
Next, you let the beams (with mirrors and so on) come together again, and form an interference pattern.
If you switch the arm detectors quickly enough "in and out" the beam, there's not enough time to propagate from one arm to the other to go and tell what you did. We're in the measurable 10 ns range here for a few meters distance.

cheers,
Patrick.

 

[gptejms]

But I didn't need this point at all. I just wanted to show that a unitary evolution operator U exists, whether you switch on a potential or not, that this allows you to go to the Heisenberg picture, and that there, by definition, the state of the system is given by a constant ket. Hence, switching on a potential doesn't affect the constant ket at all.

It will be nice if you can do this exercise:-show that the atom radiates in the Heisenberg picture-should be possible.
You have so far not commented on the x-part of the plane wave.

 

[gptejms]

But you do not need to set up things so complicated: imagine a light beam, hitting a beam splitter, and the two resulting beams are diverging. When they are at a reasonable distance of a few meters, say, you make the thing such that you can, or cannot, "watch the photon" (say, by guiding the beam in a local detector or not) in each arm.
Next, you let the beams (with mirrors and so on) come together again, and form an interference pattern.
If you switch the arm detectors quickly enough "in and out" the beam, there's not enough time to propagate from one arm to the other to go and tell what you did. We're in the measurable 10 ns range here for a few meters distance.

Has an experiment of above nature been done?I find this idea so appealing--do a measurement at one place and the quantum field readjusts everywhere else within some time dictated by the velocity of light(and this arises naturally out of the commutation properties of the quantum field(microscopic causality))--I don't feel like giving it up!But yeah EPR is non-local,there may be other non-local experiments too--are QM(non-rel.) and QFT in contradiction here..?Is the principle of microscopic causality being violated in such experiments..??

 

[gptejms]

But yeah EPR is non-local,there may be other non-local experiments too--are QM(non-rel.) and QFT in contradiction here..?Is the principle of microscopic causality being violated in such experiments..??

Answering my own question--in EPR situations you are just measuring the polarization--so the principle of microscopic causality doesen't come in in any way.The other experiment where you detect a photon in one of the arms and there is not enough time for the other arm to know what you did--well you have made a measurement of the field at one of the arms--now your contention is that the message can't go fast enough to the other arm to readjust to 'no photon'--but that's not required.After all you look at the screen,see that the interference pattern is destroyed and then conclude positively that the photon passed through one arm only--for the message to pass to the screen to readjust the field to 'no interference pattern',there is enough time.

 

[vanesch]

It will be nice if you can do this exercise:-show that the atom radiates in the Heisenberg picture-should be possible.

It surely is very difficult if you want the full treatment in QFT, for many reasons. The physical picture behind it is the the E-fields in the right transition mode(s) in QFT are non-zero even in vacuum (the expectation values of the squares of the amplitudes of these modes are not zero), and it is the interaction of the electon of the atom with these modes that makes that the stationary states of the atom when calculated, taking purely into account the coulomb interaction with the nucleus, are NOT stationary states anymore when taking into account the dynamical EM field (as a quantum field). As such, the atom will get entangled with the EM field, and the transition amplitude for doing so can be calculated perturbatively, but in all these calculations, approximations are made. Even this treatment is quite complicated, and I'm not aware of a "frontal attack" of the problem in full, non-perturbative QED.
Nevertheless, there ARE calculations of the rate of decay of excited atoms following the idea I outlined very roughly above, and as far as I know, they fit with observations. I don't have references handy as such, but some stuff on this must be found in Mandel and Wolf in their "bible" on quantum optics, I'm sure.

You have so far not commented on the x-part of the plane wave.

I did, in post 81.

Incoming "plane wave" for t<t0 (free hamiltonian)

At t1 < t0, the incoming wave is exp(i k x), so solving for the time evolution in the Schroedinger picture with the free hamiltonian, will give us a time dependence which is:

exp(i k x) exp(- i omega t)
up to t = t0.
Note that for the free hamiltonian, the plane wave exp(i k x) is a stationary state.

So at t = t0, the wavefunction is exp(i k x - i omega t0).
Now, the potential is switched on, but this doesn't immediately change the wavefunction which is supposed to evolve continuously.

So simply said, for t>t0, we have to solve the Schroedinger equation with the new hamiltonian, with as a starting wave function, exp(i k x - i omega t0).
But note now that this function of x is not a stationary state anymore, so this time, the time evolution will not simply add a phase factor.
A way to solve this, is to expand exp(i k x - i omega t0) in the Hermite-Gauss functions (the new stationary states), so you will find:

exp(i k x - i omega t0) = a H0(x) + b H1(x) + c H2(x) + ...
(where H0, H1, etc... are the new stationary states)

The time evolution will now do the following thing:

at t = t2 > t0, we have that the wave function equals:

psi(x) = a H0(x) exp(-i E0 t2) + b H1(x) exp(- i E1 t2) + c H2(x) exp(- i E2 t2) ...

This will of course now not take on the aspect any more of a plane wave.

cheers,
Patrick.

 

[vanesch]

are QM(non-rel.) and QFT in contradiction here..?

No, not at all, but even experimented particle physicists let themselves mislead by this apparent conflict, and that's because they are less used to make the distinction between the unitary dynamics (say, the properties of the hamiltonian), and quantum superposition.
The unitary dynamics in QFT satisfies the SR light cone conditions, in that observables (which are function of spacetime parameters) which are on spacelike intervals, commute. This prevents a DYNAMICAL interaction that is FTL.
However, nothing stops you from considering superpositions of states which ENTANGLE parts of the fields which are spacelike separated. As such, there can be no DYNAMICAL influence, but all the EPR like stuff still remains valid in QFT. But QFT is so complicated already with all Feynman integrals, renormalization schemes and so on, that these situations are rarely considered. Moreover, in typical particle physics experiments, one works from the beginning to the end in the momentum basis, so there are usually no "quantum interference" experiments (you need to change basis to observe quantum interference) done in that domain ; so QFT as usually practiced, usually "looks" very classical. But the whole machinery is there, even if not used !

I'll try to think up a simple "analogy".
Consider the free non-relativistic hamiltonian of 2 particles. We could think of an equivalent of "relativity" that forbids us to have dynamical interaction between the two particles (instead of between spacelike separated parts of quantum fields). This would be formalized by imposing commutation between all observables that relate to particle 1 and all observables that relate to particle 2 in the Heisenberg picture. So as long as we work with product states (in the Schroedinger picture) we remain in product states.
But this doesn't stop us from considering entangled states ! And then suddenly we do find EPR like correlations between both. Is this incompatible with our imposed absence of dynamical interactions between both ?
No, it is just a property of the quantum theory.
In the same way, the absence of dynamics between different, spacelike separated parts of a quantum field do not forbid you to have them entangled, and as such find EPR correlations between them.

cheers,
Patrick.

 

[tdunc]

good thread ;)

gptejms

Did you answer Zappers question or did I miss that? I was about to ask the same thing. What is the nature of this potential? - That is introduced. There are only 2 things you could say, I want to here you say what.

vanesch #94

The QM - Classical boundary solution lies with the wavefunction(s) amplitude of a given construct. Mass is explicitly related to this function, such that the less mass an "object" has the greater the potential wavelength attributes and thus the greater the probability of P and M. Once you reach a certain density of a collection of wavefunctions in a given construct - more mass - the "object" ceases to have a QM wavefunction when considering in context of a whole object. It is at the size of molecules and compound atoms that the wavefunction amplitude of the whole decreases to a point where the molecules probability of location is almost certain.

Ask yourself, could a neutron for example, qualify for wavelengths attainable by photons based on its mass alone? I think not, and the reason being because its mass does not allow it such degree of freedom. It has as it is, a well defined position because of its larger mass and any change in momentum is bounded by such mass.

The question is, a what point when mass equals near zero does the wavelength have almost unlimited wavelength potential? The photon of course, radio waves are extremely large and qualify as one of the least massive objects we know of. Going up several notches to gamma rays we see that its wavelength amplitude is far more focused - a more well defined position, reason being because it has more mass but instead in the form of "energy" as found in Einstiens famous mass energy equations.

Now that I've said that, when we talk about measurements on massive objects we know that it has Already a well defined almost absolute position, not quite so in the QM world as things evolve more rapidly then we are able to observe them. There is no such thing as a collapse of the wavefunction in the classical macro world, because the wavefunction is already collapsed (reduced) to a point where it effectivly has none. Interference can't be considered because interference requires the interference of wavefunctions of individual particles, when an object doesn't Have a wavefunction ... you get the idea. Covalent bonds are the process by which atoms collectively combined their individual normal mode wave resounaces to form a new wavefunction as a compound atom, a superposition perhaps but not in the normal sense.

 

[gptejms]

It surely is very difficult if you want the full treatment in QFT, for many reasons. The physical picture behind it is the the E-fields in the right transition mode(s) in QFT are non-zero even in vacuum (the expectation values of the squares of the amplitudes of these modes are not zero), and it is the interaction of the electon of the atom with these modes that makes that the stationary states of the atom when calculated, taking purely into account the coulomb interaction with the nucleus, are NOT stationary states anymore when taking into account the dynamical EM field (as a quantum field).

Not QFT,I wanted to see it in the Heisenberg picture of non-rel. QM.Anyway, the points you have raised are good.

The time evolution will now do the following thing:

at t = t2 > t0, we have that the wave function equals:

psi(x) = a H0(x) exp(-i E0 t2) + b H1(x) exp(- i E1 t2) + c H2(x) exp(- i E2 t2) ...

This will of course now not take on the aspect any more of a plane wave.

All this you've said earlier.My question was this:-the x-part of the plane wave is exp(ikx)-you decompose it into a sum of Hermite Gauss functions--this sum remains as such no matter how much you evolve it--so in your picture the momentum i.e. hbar k remains conserved--should it be?
Another thing:-the t part is exp(-i omega t)--you can't decompose a single frequency plane wave in terms of plane waves of other frequencies.

 

[gptejms]

I'll try to think up a simple "analogy".
Consider the free non-relativistic hamiltonian of 2 particles. We could think of an equivalent of "relativity" that forbids us to have dynamical interaction between the two particles (instead of between spacelike separated parts of quantum fields). This would be formalized by imposing commutation between all observables that relate to particle 1 and all observables that relate to particle 2 in the Heisenberg picture. So as long as we work with product states (in the Schroedinger picture) we remain in product states.
But this doesn't stop us from considering entangled states ! And then suddenly we do find EPR like correlations between both. Is this incompatible with our imposed absence of dynamical interactions between both ?
No, it is just a property of the quantum theory.
In the same way, the absence of dynamics between different, spacelike separated parts of a quantum field do not forbid you to have them entangled, and as such find EPR correlations between them.

That's right.
Let me add that one has to give a mechanism/reason for the entanglement, which exists at the start(in an EPR experiment).And since it's just the polarization that's being measured,there's no violation of microscopic causality anyway(see my earlier post).

 

[seratend]

All this you've said earlier.My question was this:-the x-part of the plane wave is exp(ikx)-you decompose it into a sum of Hermite Gauss functions--this sum remains as such no matter how much you evolve it--so in your picture the momentum i.e. hbar k remains conserved--should it be?

Before asking to the others, you should pay attention to what is written since the beginning (i.e. make an effort). If you do not want to accept/understand the mathematical results of more than 100 years of developpment in QM it will be difficult for you to make valid claims/interpretations.

Look at what Patrick has written in its post #104. This is a basic QM application. For example think on what the energy of a free particle is and what the energy of particle with a potential that depends on time is as well as the cost to have a pure plane wave at t=0 (for example think with the Heisenberg view).

Seratend.

 

[gptejms]

Before asking to the others, you should pay attention to what is written since the beginning (i.e. make an effort). If you do not want to accept/understand the mathematical results of more than 100 years of developpment in QM it will be difficult for you to make valid claims/interpretations.

I think you are the one who needs to pay attention to what is written--have you understood what's being discussed or what I asked vanesch--make an effort!If you do that you'll understand that no mathematical result of more than 100 years is being challenged.

 

[seratend]

I think you are the one who needs to pay attention to what is written--have you understood what's being discussed or what I asked vanesch--make an effort!.

I make an effort. Reread and try to understand post #104 by yourself. If you make an effort to understand what is written, your question about the momentum should be answered.

Seratend.

 

[gptejms]

Perhaps my using the word plane wave in the following has caused confusion.In post #107 I wrote:-
Another thing:-the t part is exp(-i omega t)--you can't decompose a single frequency plane wave in terms of plane waves of other frequencies.

Read this as:-
Another thing:-the t part is exp(-i omega t)--you can't decompose a single frequency sinusoid in terms of sinusoids of other frequencies.

Right,seratend?

 

[vanesch]

Once you reach a certain density of a collection of wavefunctions in a given construct - more mass - the "object" ceases to have a QM wavefunction when considering in context of a whole object.

That is not standard QM. It may very well be right, but you have a whole lot of stuff to explain.

Ask yourself, could a neutron for example, qualify for wavelengths attainable by photons based on its mass alone? I think not, and the reason being because its mass does not allow it such degree of freedom. It has as it is, a well defined position because of its larger mass and any change in momentum is bounded by such mass.

Well, here's for example already a difficulty in exactly the thing you cite. Just at the other side of my office, there's a small angle neutron scattering machine, which produces interference patterns in neutron scattering due to density correlations over several micrometers. So clearly the neutron behaves as a quantum object at least over these distances.
We have quantum states of neutrons in a gravitational potential (ultracold neutrons), which extend over several tens of micrometers too.

And then there are of course collective quantum phenomena, such as superfluids, which have macroscopic masses.

It's not so easy to define a classical-quantum boundary!

cheers,
Patrick.

 

[gptejms]

good thread ;)

gptejms

Did you answer Zappers question or did I miss that? I was about to ask the same thing. What is the nature of this potential? - That is introduced. There are only 2 things you could say, I want to here you say what.

The potential will depend on what measuring device you are using,what is the nature of the interaction etc.I don't want to introduce an ad-hoc potential and do a calculation--any potential would alter the wavefunction(and disturb the interference pattern)-we need a potential that shrinks the wavefunction to span one slit only and the potential should be realistic.The case I was considering was Heisenberg's microscope at one of the slits--so photons are interacting with the electron.The crudest way to formulate this could be to take the potential to introduce random kicks in time i.e. be a sum of delta functions in time(Sum_i V_i delta(t-t_i) where t_i 's are randomly distributed--may be V_i 's could be given some spatial dependence(?).Frankly I don't have a good model for this.

It's better to take recourse to QFT so that you are in a fully quantum scenario.A consequence of this is discussed in my earlier post titled 'QFT and the measurement problem'.Briefly--when you make a measurement say at one slit, you create a disturbance that travels at the velocity of light to other places and the field readjusts to new values corresponding to what is observed-no interference pattern at the screen.

 

[gptejms]

ok vanesch I've just read what you wrote in post #104--I withdraw my question.

 

[tdunc]

vanesch

Standard QM is not something that I am known for ;) I have a whole lot to explain do I? Sounds familiar..

Your examples did not contradicted my concept.


gptejms # 114

Well I was more concerned When and Where the "measurement" as you define it takes place, exactly before or after or at the 2-slit, knowingly or not. Or in another case you could have considered, as some do, the 2-slit to Be the measurement and measurement tool. Clearly though if you were to subject the particle to a measurement - a measuring device, you could do this at Any point, the results will be quite different mind you, that's why I wanted to clairify, but it all depends what concept of behavior you are trying to convey that we don't already know? Or what theory are you promoting, there's plenty of them.

"Briefly--when you make a measurement say at one slit, you create a disturbance that travels at the velocity of light to other places and the field readjusts to new values corresponding to what is observed-no interference pattern at the screen."

Right so? You are trying to convey that the collapse of the wavefunction is at the speed of light correct?

What if I said though that the speed of a photon moving forward - c, is not the same as the speed at which a photon oscillates? Because that is afterall the varible that will collapse, not the forward speed varible. Oh it Could be, but what says that it is? I can imagine that if I throw a baseball that wobbles slightly up and down as it goes, is the speed of the wobble (call it its wavefunction) the speed of forward propagation? no

What I might say though _for the time being_ is that the collapse of a photons wavefunction is Limited by the speed of light so that we can avoid any what if senerios that deal with very large spaces and superluminal collapse.

 

[vanesch]

That's right.
Let me add that one has to give a mechanism/reason for the entanglement, which exists at the start(in an EPR experiment).

That mechanism (to obtain the entangled state from the start) is obtained by dynamical interaction when the two subsystems WERE interacting. Interaction (hamiltonian interaction) causes entanglement of the system.
When the subsystems get separated, they cannot interact dynamically anymore, but their global state is still entangled.
The interaction with a measurement apparatus can be seen exactly in the same way (it is the von Neumann "pre-measurement interaction").

cheers,
Patrick.

 

[gptejms]

gptejms # 114

Or what theory are you promoting, there's plenty of them.

I am not promoting any theory here.I can tell you what my train of thought has been during this thread:-

1.Measurement is akin to introducing a potential which shrinks the wavefunction to one or the other slit--it's definitely 'one slit'(no interference pattern) now,my conscious knowledge of it is not important.It's just that when I go to observe,it's revealed to me that the particle went through this particular slit--I may go after 10 years to make an observation that there is no interference pattern and that the particle went through this particular slit.This does not mean that the particle was in a superposition of two slits all this while.Now one may ask how the potential shrinks the wavefunction sometimes to slit 1 and at other times to slit 2--well the potential has an element of randomness in it.The merit of this scheme is that measurement is explained via QM/unitary evolution itself.

2.Then to be in a fully quantum scenario,I thought why not look at this problem from the QFT aspect.There, from the principle of microscopic causality,it becomes clear that measurement at one place introduces a disturbance which causes the field at other places to readjust to new values within a time dictated by the velocity of light.This at least tells you that the so called collapse can't be at superluminal speeds.EPR is not in contradiction with this because you are not measuring the field,you are just measuring the polarizations which are correlated due to the entanglement.But one case stands out:-say you have a single particle in a box,you put a partition in the box,take one half to Pluto,keep the other half on earth,make a measurement on Earth and find the particle.Now microscopic causality tells me that this information is not instantaneously passed on to Pluto--the field there will readjust to 'no particle' after some time gap.But if an observer on pluto makes a measurement before that,can he still find the particle?--I leave that unanswered.

3.Does the above i.e. microscopic causality solve the measurement problem.No,it doesen't.Now the wavefunction is a functional of the field.There is still a chance for the particle to be in this or that slit!Now I do not know enough QFT to introduce another field to interact with the particle field and to see what that leads to.I hope the QFTists here can shed some light on that.

 

[gptejms]

That mechanism (to obtain the entangled state from the start) is obtained by dynamical interaction when the two subsystems WERE interacting. Interaction (hamiltonian interaction) causes entanglement of the system.
When the subsystems get separated, they cannot interact dynamically anymore, but their global state is still entangled.

Agree with this part.

 

[gptejms]

Continuing with what I wrote to tdunc,here's point 4

4. In point no. 1,I said that the potential has an element of randomness in it.Now coming to QFT,the quantum field by its very nature is stochastic--the result of a measurement at one place has a probability attached with it.So let's use that to our advanatge--when I make a measurement at one of the slits,I sometimes find the electron and sometimes don't(in which case it's at the other slit)--this is exactly what the stochastic potential(in point no. 1) was supposed to do!

So I think a satisfactory picture is this:-if you don't make any measurement what-so-ever,it's better to think just in field terms--the two slits cause a field readjustment at the screen to form the interference pattern.When you make a measurement at one of the slits,the field is again disturbed and readjusts to 'no electron' at the other slit and 'no interference effect' on the screen.

It's just field all the way,only measurements/interactions are quantum.Appearance of the interference pattern by introduction of the two slits,the disturbance/destruction of this pattern by introducing the measurement device at one of the slits is just 'field readjustments' that proceed at the speed of light.I think it's not even justified to say that the electron passed through both slits--you can talk of 'an electron' only when you make a measurement at one of the slits and when you do that,there is no interference pattern.Remember complementarity--it's a perfectly sound principle.Think of the whole thing as just field readjustments(measurement or no measurement) and it's even better.

What do you all say to the above?