Question on observer created reality

[tdunc]

gptejms

"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."

How does the 'potential' shrink the wavefunction period. I could care less what slit it goes through and the fact that its random, I already know the mechanics of that.

Ok 2-slit experiment aside. We know that in the case of a "detection area" manifested by a measuring device the wavelength of a particle(s) is reduced to no more than the width of the detection area. If the displacement of the particle is already <= the width of the detection area, is does not collapse. If it is greater than, it collapses. Supposedly. Why and How? This was a lingering question I had not answered myself in the past.


found it

"A recent paper by Keller (6) demonstrated rigorously for a propagating particle that its wave function, as an amplitude for location in space, is collapsed by any detection. Using probability theory, he proved that the probability amplitude wave for location of the ongoing quantum particle immediately following the observation becomes limited to the observation area, in other words its effective size is collapsed to that of the observation area."

"AJP 1990 Joseph B. Keller "Collapse of wavefunctions and probability densities"

I can't read it because I don't have a subscription.

 

[tdunc]

Radio antennas > collapse the wavefunction > to the area of detection - the antenna itself > limited by the speed of light. Do you have an explanation for this?

 

[gptejms]

Patrick,would you like to comment on my post #120?

 

[gptejms]

How does the 'potential' shrink the wavefunction period. I could care less what slit it goes through and the fact that its random, I already know the mechanics of that.

There are 4 points there,go through all of them and then comment.I need to see some comments on point 4,which is the most important.

"A recent paper by Keller (6) demonstrated rigorously for a propagating particle that its wave function, as an amplitude for location in space, is collapsed by any detection. Using probability theory, he proved that the probability amplitude wave for location of the ongoing quantum particle immediately following the observation becomes limited to the observation area, in other words its effective size is collapsed to that of the observation area."

"AJP 1990 Joseph B. Keller "Collapse of wavefunctions and probability densities"

I can't read it because I don't have a subscription.

I don't have a subscription either.

 

[vanesch]

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?

This is a "local realist" approach, and some people try to work it out ; for instance, the promotors of "stochastic electrodynamics" and so on. It is considered a bit "fringe" work (but that by itself doesn't matter).
The big difficulty is to make *explicit* models of what's going on, in order to obtain the same results as standard QM.
And the really nasty part are EPR situations (that's often why these people simply deny these experiments and try to find loopholes in it). They imply then always faster-than-light effects in whatever is the explicit "collapse" mechanism.
Mind you, I don't find this approach totally ridiculous - in fact my hope is that gravity does exactly this, on some level or other. But this would in any case mean a serious deviation from as well general relativity as from quantum theory as we know it.

One thing is clear, however: this approach is not completely compatible with quantum theory "all the way up".

 

[gptejms]

This is a "local realist" approach, and some people try to work it out ; for instance, the promotors of "stochastic electrodynamics" and so on. It is considered a bit "fringe" work (but that by itself doesn't matter).

The kind of local realism I am talking of is dictated by the principle of microscopic causality(i.e.nothing but the commutation property of the field at two space-time points),which is the basic feature of QFT--how can anyone doubt it?And this kind of local realism dictated by microscopic causality does not contradict EPR situations as I have already said--in EPR you don't measure the field anywhere,you are just measuring polarization at two places (which due to entanglement leads to higher correlation than expected on classical grounds).

Mind you, I don't find this approach totally ridiculous - in fact my hope is that gravity does exactly this, on some level or other. But this would in any case mean a serious deviation from as well general relativity as from quantum theory as we know it.

Don't know what you are saying here.

 

[vanesch]

The kind of local realism I am talking of is dictated by the principle of microscopic causality(i.e.nothing but the commutation property of the field at two space-time points),which is the basic feature of QFT--how can anyone doubt it?And this kind of local realism dictated by microscopic causality does not contradict EPR situations as I have already said--in EPR you don't measure the field anywhere,you are just measuring polarization at two places (which due to entanglement leads to higher correlation than expected on classical grounds).

The point is: if you try to obtain the "wave function collapse" by a dynamical process which obeys what you call microscopic causality, you should see that you then have a serious problem with EPR situations. I don't understand your remark: "are just measuring polarisation at two places, you don't measure the field" ? What else is polarization but an aspect of the field ??
But again, in QFT, the microscopic causality puts limits on the DYNAMICAL INTERACTIONS that can be present in the Hamiltonian ; they do not specify anything about what happens to the wave function, of which the collapse (if this collapse is considered real) is global and does not obey any microscopic causality. So I don't see how you are going to obtain the last one effectively based upon the first one.
The only way out (IMHO) is by keeping unitary evolution "all the way up" if you stick to microscopic causality, and to have an other explanation for the *apparent* collapse - at least if you want to stick some meaning to the wavefunction in the first place (which you don't have to in a purely epistemological view).
I really don't see how you are going to do the collapse thing unitarily (with a hamiltonian that obeys local causality). EPR for me seems to be a killer of that idea (although it is not the only one).

But I think it is even worse. As long as you accept unitary evolution, I don't see how you can get rid of the linearity that a |1> + b|2> will give you a result that is a |result_of_state_1> + b |result_of_state_2>.
And if |result_of_state_1> includes having the pointer of your voltmeter on 11V and |result_of_state_2> is having the pointer of your voltmeter on 23V, I don't see how you're going to get away with having sometimes 11 V and sometimes 23 V.

cheers,
Patrick.

 

[gptejms]

The point is: if you try to obtain the "wave function collapse" by a dynamical process which obeys what you call microscopic causality, you should see that you then have a serious problem with EPR situations. I don't understand your remark: "are just measuring polarisation at two places, you don't measure the field" ? What else is polarization but an aspect of the field ??

There is a difference:-microscopic causality implies that 'field measurements'(field intensity)' at space-like intervals can't be correlated.An aspect of the field like polarization can be--polarizations can be entangled,the field intensities themselves can't be entangled for space-like intervals.

But again, in QFT, the microscopic causality puts limits on the DYNAMICAL INTERACTIONS that can be present in the Hamiltonian ; they do not specify anything about what happens to the wave function, of which the collapse (if this collapse is considered real) is global and does not obey any microscopic causality. So I don't see how you are going to obtain the last one effectively based upon the first one.
The only way out (IMHO) is by keeping unitary evolution "all the way up" if you stick to microscopic causality, and to have an other explanation for the *apparent* collapse - at least if you want to stick some meaning to the wavefunction in the first place (which you don't have to in a purely epistemological view).

Consider the following:-

There is a source of electrons and a screen a little away.Think of this as just a field,an 'electron field'.There is no pattern on the screen.You introduce the double slit in between the source and the the screen.You have imposed certain constraints,the field gets disturbed and readjusts to 'interference pattern' on the screen--this proceeds at the speed of light(consistent with microscopic causality).Till I do not make any measurement,I think of it as just a field--in fact I am not even allowed to think of it as particles,until I make a measurement and find a particle.In fact my assertion is that only interactions are quantum,otherwise it's just a field.When I make a measurement at one of the slits and find a particle,the field again is disturbed and readjusts to 'no particle' at the other slit(if one particle comes at a time) and 'no interference effects' on the screen.Now that I have found the particle,I am allowed to talk in terms of the particle picture--and I don't see any contradictions--there is no interference pattern on the screen.

The problem arises only when you think of it as a particle incident on the double slit--you write down a|1> + b|2> and think how this collapses by unitary evolution.I say that there's no particle until you make a measurement,till then it's all a field.It's as if the measurement 'creates the particle',before that it doesen't even exist.

Jagmeet Singh

 

[Rake]

Before I begin I feel that I should state that I have only a passing amount of knowledge on the subject so if I've got something wrong let me know. My current understanding of QM is that certain atomic attributes are created through observation of these attributes. This seems to suggest that there are two values present in an observation, the observer and the reality created. So my question is what special properties does the observer possesses that allows an observation to be made. Here's what I mean, when a reality is present an observer is necessarily present. However, if an observer is present it does not neccesitate the presence of a reality. Looked at from this perspective the observer can be considered real, in that regardless of observations being made the observer always exist's and that reality only exists in relation to the observer. This would mean that the constituent parts of the observer in no way find their primary causes in the reality which the observer creates. This means that the system the observer creates finds all its values in the observer. The observer on the other hand finds none of its initial values in the system it creates. This is what troubles me the most about QM, if there is no separation between observer and observed, and the observer finds its initial values bound up within a system it creates through observation how is anything ever observed? Please help.

I don't have any amount on the subject which probably explains why I don't have any formal training. Which probably explains why I don't understand 90% of the replies, but when I read your post, these thoughts came to minf.

1)

This seems to suggest that there are two values present in an observation, the observer and the reality created."

A) I don't understand QM but I don't think that reality gets "created". When you mention 2 values, the first thing that comes to my mind is the space-time co-ordinate of the observer and the s-t co-ordinate of that which is being observed. The reason this came to mind is that the only way you can observe anything, or as you say, create reality is when a photon traverses s-t to go from that which is being observed directly into the retinae of the observer. But since each photon that is absorbed into the retina of an observer at a specific s-t co-ordinate is unique then I would think that "reality" as we define it is a one-of-a-kind but slightly inaccurate snapshot of an object's past state at a precise s-t co-oridinate. My logic for this definition is based on the following:

1) Its a past representation because as it traverses s it must also traverse t

2) Its inaccurate because

a) prior to leaving the object the photon imparts a recoiling force upon it which must displace it and hence change its state by an undeterminate factor.

b) The photon gets tugged upon by gravity and who knows what else as it traverses s-t to get to your retina.

3) Its one of a kind because

a) you can never have 2 photons strike an object exactly in the same spot, at the same velocity, same approach angle, same gravitational lensing, etc...

a) Even if you could have 2 exactly the same photons You will never get 2 brains that will extrapolate the same representation.

In this context, reality is relative to the observer, which is to say that essence precedes existence. I think therefore I am.

2)

what special properties does the observer possesses that allows an observation to be made. Here's what I mean, when a reality is present an observer is necessarily present. However, if an observer is present it does not neccesitate the presence of a reality

A) By properties I would say a pair of eyes connected to a brain that can take take in photons and extrapolate.

3)

Here's what I mean, when a reality is present an observer is necessarily present.

A) As long as by reality you mean something that we observe. But even if it is not observed it must still exist. I understand that quantum mechanics says something else and so do a lot of others including Descartes, to whom I would counter: Nay Rene! Sum ergo cogito! And then maybe slap him with my glove for effect...

4)

if an observer is present it does not neccesitate the presence of a reality

A) Again I would counter that simply because the only place I would think where reality is not present is anything outside the boundaries of our universe as defined by s-t. So anything that does not have an s-t co-ordinate cannot be considered "real". This does not include any s-t region that might be causally disconnected from us due to the fact that it is receding faster than the speed of light. Imo reality does not require c to give it essence or an s-t co-ordinate even though a photon from that co-ordinate will never reach the earth. Reality simply is. Which is really just a way of saying that then s is dependent on t but independent of v...which it must be because as soon as you get v involved then we're talking about that one-of-a-kind but slightly inaccurate space-time representation of reality and not the real reality (the real reality...I made a funny!) Another argument I would make is that if an observer is present, then the observer themselves define reality. Again, this is a case where existence precedes the essence of reality and not vice-versa (i.e. sum ergo cogito)

5)

This means that the system the observer creates finds all its values in the observer. The observer on the other hand finds none of its initial values in the system it creates. This is what troubles me the most about QM, if there is no separation between observer and observed

A) Same argument. I can see why you are having trouble with it. I'm having a lot of trouble with it myself. Maybe I'm just not getting it (likely) but it seems to me like this is a case of human arrogance (unlikely because these humans are like 1000 times smarter th an me) to try to define reality through us. In this sense it almost seems like thir is a prescriptive approach rather than a descriptive one. I prefer the latter. But I have a sneaking suspicion that i am being fooled by my limited concept of reality and also not understanding what it is that QM is really saying. This is likely because I know that QM does not suggest that there is no separation between the observer and the observed because such a position goes against what that ice-berg lettuce guy said. (sorry sometimes I recall the mnemonic and not the memory which is like saying...that the...nevermind...)

 

[gptejms]

In continuation of what I wrote in post #128,let me add the following:-

In QFT,what is the role of the wavefunction?Now, wavefunction is a functional of the field--what this just does is to give you the probability density of finding a certain field value(upon measurement) at a place.You can't have a superposition of this wavefunction at two places--we don't know what meaning to assign to it.We no longer have the wavefunction of a particle which leads to the measurement problem.

Now let me come to the Schrödinger equation which gave rise to the notion of a wavefunction(of a particle).Schrödinger equation is the non-relativistic limit of the K.G. equation or the Dirac equation which are field equations.Now does the field suddenly change into a wavefunction when the velocity is sufficiently lowered i.e. v/c < < 1? Of course not,it's still a field which obeys the continuity equation.It also satisfies microscopic causality and the wavefunction is still a functional of the field.Wavefunction of a particle is a notion that leads to all the problems--it should be replaced by 'field of a particle' or particle field.

Jagmeet

 

[vanesch]

In QFT,what is the role of the wavefunction?Now, wavefunction is a functional of the field--what this just does is to give you the probability density of finding a certain field value(upon measurement) at a place.You can't have a superposition of this wavefunction at two places--we don't know what meaning to assign to it.We no longer have the wavefunction of a particle which leads to the measurement problem.

No, the wavefunction is indeed a functional of the field (in the rarely used Schroedinger picture of QFT), but it gives you the probability AMPLITUDE to have a CERTAIN ENTIRE CLASSICAL FIELD CONFIGURATION.
So you can have a superposition of the kind:

a |plane wave with wavevector k> + b |sphericalwave outward from A> + ...

You can have a superposition of different fields, for instance a field that has a bump at A, and another field that has a bump at B. This is not the same as a field that has both a bump at A and a bump at B.
Now, when a measurement establishes (in the first case) that we have a bump at A, then the collapse comes down to the component in the wave function (field with the bump at B) disappearing from the wavefunction, instantaneously. This is exactly the same situation as in non-relativistic QM, so I don't see how this "resolves" the measurement problem.

Now let me come to the Schrödinger equation which gave rise to the notion of a wavefunction(of a particle).Schrödinger equation is the non-relativistic limit of the K.G. equation or the Dirac equation which are field equations.Now does the field suddenly change into a wavefunction when the velocity is sufficiently lowered i.e. v/c < < 1? Of course not,it's still a field which obeys the continuity equation.

This view (Dirac's view) is known to be misguided now - although it took until the 50ies for people to fully realize this. The Schroedinger equation is not the NR limit of the KG equation or the Dirac equation in QFT. The KG or the Dirac equation play the role of Newton's equations of motion and the Schroedinger equation remains what it is: the dynamical prescription of the wavefunction in Hilbert space (which is now constructed over field states instead of particle positions).

It also satisfies microscopic causality and the wavefunction is still a functional of the field.Wavefunction of a particle is a notion that leads to all the problems--it should be replaced by 'field of a particle' or particle field.

"Field of a particle" in QFT is the CLASSICAL FIELD. And on this classical field, one applies now "the wavefunction" over all possible classical configurations of the field. The Dirac equation is NOT the relativistic version of the Schroedinger equation, it is the classical dynamical equation of the classical field that has to be quantized. It is the CLASSICAL field evolution equation (Dirac's equation) that satisfies microscopic causality, but this classical field is NOT the wavefunction.

cheers,
Patrick.

 

[gptejms]

No, the wavefunction is indeed a functional of the field (in the rarely used Schroedinger picture of QFT), but it gives you the probability AMPLITUDE to have a CERTAIN ENTIRE CLASSICAL FIELD CONFIGURATION.

Right!Thanks,I stand corrected.

You can have a superposition of different fields, for instance a field that has a bump at A, and another field that has a bump at B. This is not the same as a field that has both a bump at A and a bump at B.

Why 'different fields'--you can have a superposition of two different field configurations,where the field is the same.

Now, when a measurement establishes (in the first case) that we have a bump at A, then the collapse comes down to the component in the wave function (field with the bump at B) disappearing from the wavefunction, instantaneously. This is exactly the same situation as in non-relativistic QM, so I don't see how this "resolves" the measurement problem.

Seems fine.But the difficulty is that this seems to violate microscopic causality(a property of any quantum field) namely that if you introduce a measurement/disturbance at A,the field at B can not get instantaneously readjusted. Before a measurement is made,the field at B could have been a bump or no bump,now it definitely is 'no bump' in zero time.

This view (Dirac's view) is known to be misguided now - although it took until the 50ies for people to fully realize this. The Schroedinger equation is not the NR limit of the KG equation or the Dirac equation in QFT. The KG or the Dirac equation play the role of Newton's equations of motion and the Schroedinger equation remains what it is: the dynamical prescription of the wavefunction in Hilbert space (which is now constructed over field states instead of particle positions).

See what I am asserting here is that the Schrödinger equation is the NR limit of the KG or Dirac field(quantum) equations--where the field is quantised.There is nothing like the wavefunction of a particle.Plus the field obeys microscopic causality.

It is the CLASSICAL field evolution equation (Dirac's equation) that satisfies microscopic causality, but this classical field is NOT the wavefunction.

What do you mean here?It's not the classical field,but the quantum field that obeys microscopic causality(commutation relations of the field).

 

[Sherlock]

The problem arises only when you think of it as a particle incident on the double slit--you write down a|1> + b|2> and think how this collapses by unitary evolution.I say that there's no particle until you make a measurement,till then it's all a field.It's as if the measurement 'creates the particle',before that it doesen't even exist.

That's how I think of it. The measurement itself is the particle. It might
be reasonable in some situations to speak of particles or waves or
whatever existing independent of measurement, but, strictly speaking,
these terms refer to recorded instrumental phenomena (and values
in formalizations associated with instrumental preparations).

Precisely what might exist, and how it might behave, in some
'quantum realm' beyond or independent of macroscopic records
is an open question. With both slits open, there's currently
no way to tell whether an assumed quantum disturbance incident
on the double-slit went through both slits or only one.

In an unambiguous usage of terms, it isn't just "as if" the photon
or electron doesn't exist until a recorded measurement creates it -- it
really *doesn't exist* in the world (beyond mathematical form) of
physical interactions until it becomes physical evidence via some
instrumental change(s).

I'm thinking of the measurement problem as a real, physical
incapability on our part. Your proposed resolution to this problem
seems to me to be a metaphysical, and not satisfactory, one.

 

[gptejms]

Now, when a measurement establishes (in the first case) that we have a bump at A, then the collapse comes down to the component in the wave function (field with the bump at B) disappearing from the wavefunction, instantaneously. This is exactly the same situation as in non-relativistic QM, so I don't see how this "resolves" the measurement problem.

Let me add here the following to what I already wrote in a part of post #132 as a response to the above.You are writing your wavefunction as a superposition of a 'field bump' at x1,t1 and a 'field bump' at x2,t1(i.e. two possible field configurations).Now your assertion is that when I make a measurement at x1,t1 and the bump appears there,the bump at x2,t1 is insatantaneously wiped off.

My assertion is that if at all you have to use your wavefunction for field superpositions,you can't use equal times at x1 and x2.At x2,the time must at least be (x2-x1)/c + t1 (in consistence with microscopic causality).

Let me repeat that the Schrödinger equation is an equation for a quantum field not for wavefunction.Wavefunction in the new picture(if I may say so) has a lesser role to play--you can't use it for superpositions in the way one did for the wavefunction of a particle.

 

[gptejms]

In an unambiguous usage of terms, it isn't just "as if" the photon
or electron doesn't exist until a recorded measurement creates it -- it
really *doesn't exist* in the world (beyond mathematical form) of
physical interactions until it becomes physical evidence via some
instrumental change(s).

I'm thinking of the measurement problem as a real, physical
incapability on our part. Your proposed resolution to this problem
seems to me to be a metaphysical, and not satisfactory, one.

Would it be ok for you if I dropped the "as if" ?!Is that the only objection?Keeping it or dropping it is just a matter of taste--stick to whatever you like,it makes no difference.

 

[vanesch]

Why 'different fields'--you can have a superposition of two different field configurations,where the field is the same.

Yes, of course I meant two different configurations of the same field (let us say, the electron field).

What do you mean here?It's not the classical field,but the quantum field that obeys microscopic causality(commutation relations of the field).

No, the classical field satisfies microscopic causality (because of the fact that the differential equation (KG or Dirac) that it obeys is Lorentz-invariant). From this, and the quantization procedure the quantum operator associated with the field value at the point (x,t), satisfies commutation relations which correspond to microscopic causality, in the Heisenberg picture. Translated in the Schroedinger picture, this means that the UNITARY evolution of the wavefunction satisfies microscopic causality. However, collapse, which is not a unitary evolution, does NOT. So you're going to have a hard time to model this collapse by a unitary evolution, and that's what I'm trying to tell you since the beginning of this thread.
The above dichotomy is simply because QFT is just another quantum theory, just like non-relativistic QM is. And the "immediate collapse" is not something that has to do anything with the specific model of the dynamics we're trying to quantize (non-relativisitic point particles in Euclidean space, or classical fields obeying relativistic equations such as Dirac or KG). It is part of the general quantum theory. Even string theory suffers from it. So it doesn't matter what conditions you impose upon the dynamics (such as Lorentz invariance, or microscopic causality, or non-interaction, or whatever you can think of).
Collapse happens in Hilbert space, not in any real 4-dim manifold on which the quantum dynamics is modeled.

cheers,
Patrick.

 

[vanesch]

Let me add here the following to what I already wrote in a part of post #132 as a response to the above.You are writing your wavefunction as a superposition of a 'field bump' at x1,t1 and a 'field bump' at x2,t1(i.e. two possible field configurations).Now your assertion is that when I make a measurement at x1,t1 and the bump appears there,the bump at x2,t1 is insatantaneously wiped off.

My assertion is that if at all you have to use your wavefunction for field superpositions,you can't use equal times at x1 and x2.At x2,the time must at least be (x2-x1)/c + t1 (in consistence with microscopic causality).

No, this is not the case. The superposition (in a fixed reference frame) is at equal times.
Let us call f1(x,y,z) = N1 exp(-(x^2 + y^2 - 81) ), the field config 1 at t = t1 (bump around circle in xy plane of radius 9)
and f2(x,y,z) = N2 exp(-(z^2 - 141)), the field config 2 at t=t1. (bump around z = 12)

Both field configurations correspond to orthogonal kets in Hilbert space, which we denote by |1> and |2> respectively.

I can now have the quantum field, at t=t1, in the state a|1>+ b|2>

If I measure now at t=t1, that the particle was around z=12, then suddenly the state of the quantum field collapses into |2>.

It doesn't even matter what is the time evolution (the dynamics) of the quantum field, and what conditions (such as microcausality) it satisfies, because this only relates to how the state |1> will evolve from t1 to t2, and how the state |2> will evolve from t1 to t2 (and as such, we know also how the above state a|1> +b|2> will evolve).
For instance, it might be that the evolved |1> will not be a single classical field configuration anymore at t2, but can be now a superposition of classical field configurations (this is highly probable, if the field configurations are "spiked" and we cannot apply the classical evolution equations: QFT effects are then visible). BUT ALL THIS HAS NOTHING TO DO with the projection postulate, which acts upon the quantum state at a given time.

Let me repeat that the Schrödinger equation is an equation for a quantum field not for wavefunction.Wavefunction in the new picture(if I may say so) has a lesser role to play--you can't use it for superpositions in the way one did for the wavefunction of a particle.

Well, I'm sorry but you have it completely backwards here (at least in standard QM). The Schroedinger equation - which is just as valid in QFT as in ordinary QM - is the evolution equation of the wavefunction (= the quantum state of the system) in Hilbert space. However, except for the single 1-particle non-relativistic QM case, the Schroedinger equation IS NOT an equation of a field over the spacetime manifold.

cheers,
Patrick.

 

[gptejms]

No, the classical field satisfies microscopic causality (because of the fact that the differential equation (KG or Dirac) that it obeys is Lorentz-invariant). From this, and the quantization procedure the quantum operator associated with the field value at the point (x,t), satisfies commutation relations which correspond to microscopic causality, in the Heisenberg picture. Translated in the Schroedinger picture, this means that the UNITARY evolution of the wavefunction satisfies microscopic causality. However, collapse, which is not a unitary evolution, does NOT. So you're going to have a hard time to model this collapse by a unitary evolution, and that's what I'm trying to tell you since the beginning of this thread.

Ok,so in QFT,in the Schrödinger picture the field has the same status as the spatial coordinates of a wavefunction in NR quantum mechanics.The field is classical,and you may superpose different field configurations.

 

[gptejms]

Well, I'm sorry but you have it completely backwards here (at least in standard QM). The Schroedinger equation - which is just as valid in QFT as in ordinary QM - is the evolution equation of the wavefunction (= the quantum state of the system) in Hilbert space. However, except for the single 1-particle non-relativistic QM case, the Schroedinger equation IS NOT an equation of a field over the spacetime manifold.

Look at it this way--you have the K.G. or the Dirac (quantum)field equations to begin with.Now you go on reducing the velocity till v/c <<1.How does the quantum field now change into a wavefunction?At what point does the transition occur?I am asserting that it remains a quantum field--the wavefunction even in the NR limit is a functional of the field.

 

[vanesch]

Look at it this way--you have the K.G. or the Dirac (quantum)field equations to begin with.Now you go on reducing the velocity till v/c <<1.How does the quantum field now change into a wavefunction?At what point does the transition occur?I am asserting that it remains a quantum field--the wavefunction even in the NR limit is a functional of the field.

It's a trick :-) In fact, it turns out that the wave function in the QFT Hilbert space (which can be identified with the Fock space), when reduced to the 1-particle subspace of Fock space, satisfies the same equation as the classical field. But you can already see the difference, for instance in the case of a real classical field: the field is supposed to be real, and the resulting NR Schroedinger equation gives you complex 1-particle wave functions! Another way to see it is: how does your field reduce to the wave function of TWO PARTICLES ? The field is function of (x,t) and the wave function is function of (x1,x2,t).

There is just a "mathematical coincidence" of the wave function equation (Schroedinger equation) in the 1-particle case and the classical field equation to have the same form. Of course there are reasons why this is so, but it is not because the equations are the same, in this particular case, that the *objects* (classical field over 4-manifold vs. wavefunction in hilbert space) are the same.
But people who get confused are in good company: it took until the 50ies for people to realize the difference.

 

[gptejms]

No, the classical field satisfies microscopic causality (because of the fact that the differential equation (KG or Dirac) that it obeys is Lorentz-invariant).

By microscopic causality,I had loosely meant the commutation relation for the field at two spacetime points itself.I've just checked Bjorken and Drell for the definition of microscopic causality:-it says 'the condition of vanishing of the commutators for all space-like intervals,no matter how small,is referred to as the condition of microscopic causality".For a classical field the above should be satisfied for all intervals--I hope that is what you mean by microscopic causality for classical fields.

 

[gptejms]

It's a trick :-) In fact, it turns out that the wave function in the QFT Hilbert space (which can be identified with the Fock space), when reduced to the 1-particle subspace of Fock space, satisfies the same equation as the classical field. But you can already see the difference, for instance in the case of a real classical field: the field is supposed to be real, and the resulting NR Schroedinger equation gives you complex 1-particle wave functions! Another way to see it is: how does your field reduce to the wave function of TWO PARTICLES ? The field is function of (x,t) and the wave function is function of (x1,x2,t).

Can you elaborate on the above--it's not quite clear to me.

 

[vanesch]

By microscopic causality,I had loosely meant the commutation relation for the field at two spacetime points itself.

Yes, that is correct, but only makes sense in the Heisenberg picture of course, where the fields are Hilbert space operators, parametrized over the spacetime manifold.
The meaning behind it is of course that the value at one (x,t) point cannot be influenced by the value at another spacetime point (x2,t2) if the interval is spacelike. In the quantum version, this comes down to a condition on commutators, in the classical version, this comes down on a condition on the Green's function (propagator).

For a classical field the above should be satisfied for all intervals--I hope that is what you mean by microscopic causality for classical fields.

No, it wouldn't of course make sense to talk about commutators of the classical fields. What I meant was that the value of a classical field at an event (x1,t1) can only depend on initial values of the classical field which are within its past light cone ; which puts a condition on the Green's function. This is exactly what is re-worded in the quantum language.
I'm a bit out of my depth here, but I'd guess (someone correct me if I'm wrong) that the classical version of microscopic causality can be reformulated as Poisson brackets vanishing over spacelike intervals.

cheers,
Patrick.

 

[gptejms]

Let's stick to Bjorken and Drell's definition of microscopic causality.

The interesting part is the non-zero commutator for time-like separations.
Measuring a field at spactime point 1 and then at spacetime point 2 does not give you the same result as measuring it first at point 2 and then at 1.I interpreted this in one of my earlier posts as due to the fact that when you make a measurement at 1(or 2),you create a disturbance which travels to 2(or 1) at the speed of light and readjusts the field there.Do you agree with this interpretation?You don't as we'll see below.In my model(the above interpretation) there's nothing instantaneous.A measurement at 1 can't instantaneously establish a field value at 2.

In your model when you make a measurement at 1,a certain field configuration is established in the whole of space(not just at 2)at once--of course it has some prob. attached with it.So when you measure at 1,you get some value 'a' and the value at 2 say 'b' is automatically established.If you do the reverse,that is measure at 2 you get some value 'c' which establishes the value at 1 say 'd'.So the disturbance model is out.Well yours is the official picture,can't overrule it--even though I find the disturbance model less disturbing!

 

[vanesch]

Can you elaborate on the above--it's not quite clear to me.

I will try to find a reference...

cheers,
Patrick

 

[vanesch]

The interesting part is the non-zero commutator for time-like separations.
Measuring a field at spactime point 1 and then at spacetime point 2 does not give you the same result as measuring it first at point 2 and then at 1.

I'm sorry, but interchanging event (x1,t1) and (x2,t2) if t1 < t2 doesn't place suddenly the "second event before the first one". It is tricky to say what it means to "measure first at point 2" (which is an event, with a time coordinate!). So interpreting exactly what it means for NON-commuting observables at timelike separated events is tricky !
In fact, one usually talks about non-compatible observables AT EQUAL TIMES (in a certain reference frame). Time-like separated events are never at equal times in any frame, so it's going to be tricky.
It is in fact more instructive to say that space-like separated events have COMMUTING field operators - indeed, space-like separated events can be made equal-time events in a certain reference frame, and if you work in that frame, you can say that these field operators are dynamically independent.

I interpreted this in one of my earlier posts as due to the fact that when you make a measurement at 1(or 2),you create a disturbance which travels to 2(or 1) at the speed of light and readjusts the field there.Do you agree with this interpretation?You don't as we'll see below.In my model(the above interpretation) there's nothing instantaneous.A measurement at 1 can't instantaneously establish a field value at 2.

But entangled field states CAN be entangled at space-like separated events, and they do have space-like separated Bell-violating correlations. So this "field propagation" won't do. And it doesn't have to, in fact, because it is NOT the dynamics of individual field configurations that is at hand here (which have dynamics that is constrained by special relativity), but THE CHOICE BETWEEN DIFFERENT FIELD CONFIGURATIONS which is mastered by the quantum state (the wave function, if you want).

In your model when you make a measurement at 1,a certain field configuration is established in the whole of space(not just at 2)at once--of course it has some prob. attached with it.So when you measure at 1,you get some value 'a' and the value at 2 say 'b' is automatically established.If you do the reverse,that is measure at 2 you get some value 'c' which establishes the value at 1 say 'd'.So the disturbance model is out.Well yours is the official picture,can't overrule it--even though I find the disturbance model less disturbing!

Yes, except that the "disturbance model" doesn't explain EPR situations, which are supported by experiment as well as theory !

cheers,
Patrick.

 

[vanesch]

I will try to find a reference...

Indeed, not many QFT books mention this, so I went through Peskin, Zee, Stone, Ryder to no avail, but Brian Hatfield, "Quantum Field theory of point particles and Strings" has a very illuminating chapter on it in the beginning (chapter 2).

cheers,
Patrick

 

[gptejms]

I'm sorry, but interchanging event (x1,t1) and (x2,t2) if t1 < t2 doesn't place suddenly the "second event before the first one". It is tricky to say what it means to "measure first at point 2" (which is an event, with a time coordinate!). So interpreting exactly what it means for NON-commuting observables at timelike separated events is tricky !

No.The second part is hypothetical--a hypothetical observer at t2,disturbance going back in time followed by an observation at t1.Indeed,it's hypothetical,but it conveys the idea.

There's a footnote in Bjorken and Drell which says Bohr and Rosenfeld made a detailed analysis of the physical meaning of the commutation relations in terms of physical measurement in some obscure journal in 1933,and also in Phys. Rev,78,794(1950).Can you get hold of this---if yes,I'll be obliged if you can send me a copy.

Yes, except that the "disturbance model" doesn't explain EPR situations, which are supported by experiment as well as theory !

We have discussed EPR,polarizations can be entangled but not field intensities at space-like intervals.The former is not forbidden by the time-like commutator(I don't know what to call it,after reserving the term microscopic causality for space-like intervals,a la Bjorken & Drell!)

 

[gptejms]

Indeed, not many QFT books mention this, so I went through Peskin, Zee, Stone, Ryder to no avail, but Brian Hatfield, "Quantum Field theory of point particles and Strings" has a very illuminating chapter on it in the beginning (chapter 2).

Thanks,but I am right now in a place where we get no physics books or journals.Kindly illuminate me on the contents of the illuminating chapter!

 

[vanesch]

We have discussed EPR,polarizations can be entangled but not field intensities at space-like intervals.The former is not forbidden by the time-like commutator

I don't see why you make a difference between "intensities" and "polarizations" ? I mean, if we're talking about a vector field, then, can the x-component at A be entangled or not with the 45-degree component at B or not ? And can the x-component at A be entangled with the x-component at B ? And can the x-component at A be entangled with the y-component at B ?
Can the +45 component at A be entangled with the -45 component at A ? And at B ?