How observation leads to wavefunction collapse?

[Demystifier]

Is it true that the wave function describes propagation in one direction in time? But if it does describe propagation in time, then it can not give information of both initial and final states at the same time, since it propagated from one to the other in time. So there's no information of the initial state to enable a calculation of probabilities from initial to final states; the final state could have come from many different initial states. In order to determine the probability of going from initial and final states, we have to have the reverse propagation from final to initial state. Then we know both intial and final states enabling a calculation of the probability from initial to final state. Thus the wave function is multiplied by its complex conjugate to cancel out the time dependencies and get information of both initial and final states at the same instant in order to get simultaneous knowledge of both events required to "know" at some instant the probability of going from one to the other. Does this all sound right?

You might like this:
http://xxx.lanl.gov/abs/0706.4075

 

[jostpuur]

photon probability

The Klein-Gordon current (with some constants)

$$(\partial^{\mu} \phi)^* \phi - \phi^* \partial^{\mu} \phi = -2i\textrm{Im}(\phi^*\partial^{\mu}\phi)$$

vanishes for real field, and thus exists only for complex ones.

In gauge $\partial_{\mu} A^{\mu} = 0$ the Maxwell's equations are $\partial_{\mu}\partial^{\mu} A^{\nu}=0$, so the electromagnetic potential is a real four component Klein-Gordon field with postulated transformations of a four vector.

What is the probability density for photons? I have one guess: Sum of the Klein-Gordon currents for each component of $A^{\nu}$, like this

$$(\partial^{\mu} A_{\nu})^* A^{\nu} - A^*_{\nu}\partial^{\mu} A^{\nu}$$

But this does not work, because they are real fields, and the current doesn't exist! Or is this wrong kind of wave function for photon? Are they complex in quantum theory?

 

[Demystifier]

Jostpuur, you may define the complex wave function of a photon by taking the positive-frequency part of the field. See e.g.
http://xxx.lanl.gov/abs/quant-ph/0602024
especially Eqs. (3) and (5).

 

[jostpuur]

Jostpuur, you may define the complex wave function of a photon by taking the positive-frequency part of the field. See e.g.
http://xxx.lanl.gov/abs/quant-ph/0602024
especially Eqs. (3) and (5).

So the wave function is $\psi^{\alpha}\in\mathbb{C}^4$? (This was bad notation... I mean $(\psi^0,\psi^1,\psi^2,\psi^3)\in\mathbb{C}^4$)

And according to the mainstream view (that Hans de Vries has been explaining) it would be incorrect to interpret $|\psi^{\alpha}|^2$ for each fixed $\alpha$ as the probability density in similar fashion as $|\psi_1|^2$ and $|\psi_2|^2$ of a non-relativistic spin-1/2 particle?

 

[Demystifier]

So the wave function is $\psi^{\alpha}\in\mathbb{C}^4$? (This was bad notation... I mean $(\psi^0,\psi^1,\psi^2,\psi^3)\in\mathbb{C}^4$)

And according to the mainstream view (that Hans de Vries has been explaining) it would be incorrect to interpret $|\psi^{\alpha}|^2$ for each fixed $\alpha$ as the probability density in similar fashion as $|\psi_1|^2$ and $|\psi_2|^2$ of a non-relativistic spin-1/2 particle?

Yes, it is similar to the spin 1/2 case. You have to perform a sum over all components of the wave function.

 

[lightarrow]

Ok, here is my 2cents worth, As far as i have understood the following happens:

First of all never consider any particle as a particle, but rather as wave function of multiple possibilities(or locations) of that particle. But also its not the case either because after 'observation' the wave function will collapse into 1 possibility (or location) that is in its wave function, so now the wave doesn't exist but the particle exists at 1 point.

So its very important to realize that all matter isn't just physical, its a wave function at the same time. Its both n none.

So the way i understand it is this:

Imagine an electron's wave function, till now the electron doesn't exist as a particle its just a wave of possibilities. Now it WILL remain that way until something collapses the wave from a set of possibilities to just one possibility and the electron comes to existence at that point.

About this, we think in the same way.

 

[Mike2]

Is it true that the wave function describes propagation in one direction in time? But if it does describe propagation in time, then it can not give information of both initial and final states at the same time, since it propagated from one to the other in time. So there's no information of the initial state to enable a calculation of probabilities from initial to final states; the final state could have come from many different initial states. In order to determine the probability of going from initial and final states, we have to have the reverse propagation from final to initial state. Then we know both intial and final states enabling a calculation of the probability from initial to final state. Thus the wave function is multiplied by its complex conjugate to cancel out the time dependencies and get information of both initial and final states at the same instant in order to get simultaneous knowledge of both events required to "know" at some instant the probability of going from one to the other. Does this all sound right?

So in this view the wave function is not collapsing. Instead the wave function is combined with a wave function in the reverse direction in time in order to calculate a probability of two events separated in time, right?

 

[diegzumillo]

Hello all,
well, to start, sorry if i haven't followed all the discussion, so I'm not sure what other points were made since the first page.
i heard more than once that a single electron does not create an interference pattern, what does that mean exactly? in my understanding, the wave associated with this electron does create an interference pattern, but of course, you would have to make lots of measurements of single electrons to visualize that. even so, can't i say that a single electron does create an interference pattern?

 

[The Onion]

Hello all,
well, to start, sorry if i haven't followed all the discussion, so I'm not sure what other points were made since the first page.
i heard more than once that a single electron does not create an interference pattern, what does that mean exactly? in my understanding, the wave associated with this electron does create an interference pattern, but of course, you would have to make lots of measurements of single electrons to visualize that. even so, can't i say that a single electron does create an interference pattern?

a lot of single electrons will create an interference pattern. But 1 only will position itself in just one of the bands of the interference pattern

 

[diegzumillo]

exactly, but then my point is, what happens with photons? isn't the same thing?

 

[The Onion]

sry I am not following.

If you shoot a single electron or photon at the double stil it will interfere with itself true, and it will position itself in ONE of the interference pattern bands, but only in one. So just one particle cannot create an interference pattern on its own, you need to have a lot of single particles for the pattern to build up.

 

[RagingPineapple]

Thoughts of a total newbie:

When viewing an object, we see different wavelengths of light as colour. When we then use a monochrome camera and take a photo, the photo emerges with the colour spectrum colapsed and simplified.

Where before, we were able to differentiate hue as distinct from light intensity and the x/y location of the pixels in the image, we now cannot. We're left only with intensity and x/y (a black and white image).

This might be an interesting way of looking at the 'collapse' of particles? After all, no real collapse has occurred when taking the photograph. The colour spectrum still exists in reality, and the grass is still green. All that has happened is that the observer (camera) is not equiped to observe the full depth of reality. So the photo it produces is a simplified version of the reality being observed.

Perhaps something along those lines is occurring in the double-slit experiment? We observe, yet we cannot observe an object doing more than one thing at once, just as the camera cannot observe a pixel being both medium intensity AND red. So as the camera colapses the colours and shows just their overall intensity, we collapse all the many probabilities and show just the average of them all?


Right, I'm going to bed. Please bear in mind that the above statement is quite probably wrong.

 

[scarecrow]

Hi all

I know I raised a similar question in the thread "Wave particle duality", but it is already so full of many other questions, that I'd not be able to discuss this topic fully there.

So, in the double slit experiment, if a photon observes an electron, the interference pattern vanishes. Why is this so? What does a photon do to an electron? Also, can anybody explain to me as to how a single electron creates an interference pattern in reality? I am completely at sea as far as understanding this phenomenon is concerned. I know that in theory we have wavefunctions, but how can all the paths that can be followed by the electron, consist of one in which it passes through both the slits?

thanks
Mr Virtual

"how does observation lead to wavefunction collapse?"

Simple answer: Once you have made an observation, that means you know where the particle is. If you know where the particle is, there is no point in describing its position by a wavefunction (probability). Therefore the wavefunction collapses upon observation.

 

[meopemuk]

"how does observation lead to wavefunction collapse?"

Simple answer: Once you have made an observation, that means you know where the particle is. If you know where the particle is, there is no point in describing its position by a wavefunction (probability). Therefore the wavefunction collapses upon observation.

I agree with you 100%. That's the best explanation of the wavefunction collapse I've seen so far.

Eugene.

 

[scarecrow]

I agree with you 100%. That's the best explanation of the wavefunction collapse I've seen so far.

Eugene.

Thanks. I thought about this answer before going to bed last night :)

 

[diegzumillo]

ok, i can understand that too! (yay)
but to say that isn't the same thing to say that the particle was always there with that position and momentum, we just didin't know that? that is, our theory isn't complete, it gives a probability, but nature is deterministic. so a second measure would give you the same information you already had.
then what happens to that copenhagen interpretation? I've 'heard' there's a proof for it.
i'm merely asking questions here, I'm in no way an expert! total noob.. but not for long i hope! hehe :)

 

[meopemuk]

but nature is deterministic.

How do you know that? I thought that the main lesson of quantum mechanics is that nature is not deterministic.

Eugene.

 

[diegzumillo]

How do you know that?

I don't. The sentence got a little longer than i expected but, i started by saying: "but to say that isn't the same thing to say..."
so, it's not really my affirmation. it's possible, however, that i missunderstood scarecrow's explanation. then it wouldn't imply determinism.

 

[diegzumillo]

what i do know, is that we say the wavefunction collapses because when we make a second measure instantly after the first one, you get the same result.

 

[meopemuk]

what i do know, is that we say the wavefunction collapses because when we make a second measure instantly after the first one, you get the same result.

This is true if both times we measured the same observable, e.g., position. If the first time we measured position and the second time we measured momentum, then the result of this second measurement is, again, unpredictable.

In other words: in quantum mechanics even having (a maximally possible) full and complete knowledge about the prepared state of the system we cannot predict results of measurements of all observables. If you know what the system is doing now, you cannot tell exactly what will happen in the future. That's what I call "indeterminism".

Eugene.

 

[scarecrow]

what i do know, is that we say the wavefunction collapses because when we make a second measure instantly after the first one, you get the same result.

Not necessarily. The only way that will happen is if your physical observable is time-independent.

The reason the wavefunction collapses is because there's no logic behind describing a physical observable (expectation value) by a probability if it already has been observed.

Example: Right now I don't know where the position of an electron is in an atom, but I know a probability density (orbital) in which it should be. Once you somehow can see exactly where it is, it can no longer be in an orbital since the orbital is strictly a probability density. Therefore, the electron which you observed has to be a free electron obeying the laws of classical physics.

 

[diegzumillo]

ok! scarecrow's second explanation was as good as the first one, i actually understood them. i was having problem with what was defined as wave function collapse, it was wrong.
so, it has nothing to do with the measure itself (in the way i thought it had, i mean)

 

[scarecrow]

Therefore, the electron which you observed has to be a free electron obeying the laws of classical physics.

I'm not quite sure about this statement I have made...

This may be a paradox in which I have no explanation.

 

[Fra]

"how does observation lead to wavefunction collapse?"

Simple answer: Once you have made an observation, that means you know where the particle is. If you know where the particle is, there is no point in describing its position by a wavefunction (probability). Therefore the wavefunction collapses upon observation.

I agree with this too. This is the most natural explanation if you take on the bayesian interpretation. That is the wavefunction represents the observer information relative to the subject. If the information is updated, so is the wavefunction.

The dynamical equations, like schrödinger equation rather (IMHO) describes the expected evolution of this information in the lack of measurement. Any measurements must clearly interfere with the equations of dynamics.

But if there are some domains where you think the discontinuity bothers you, there is a way out. The normal description is extremely simple. You consider that you make a measurement, and then you know the answer - the questions collapses. But if you add a level of complexity, one can assign a weight to each measurement. For example, suppose you've repeated the supposedly same measurement 100 times, and it is A, then the 101 time you get B - what is more likely, that it is B or that the measurement is not to be trusted? Anyway, if one considers such a scenario the observers wavefunction will acquire a kind of inertia - resistance to revision, that basically makes it more continuous and possibly even imposes bounds on rate of change. This is speculations, but things I'm currently thinking of, and the relative probability offers as it seems many natural resolutions.

/Fredrik

 

[Demystifier]

"how does observation lead to wavefunction collapse?"

Simple answer: Once you have made an observation, that means you know where the particle is. If you know where the particle is, there is no point in describing its position by a wavefunction (probability). Therefore the wavefunction collapses upon observation.

Does it mean that the particle possesses some properties that are not described by the wave function? If yes, what are these properties?

 

[Fra]

Does it mean that the particle possesses some properties that are not described by the wave function? If yes, what are these properties?

Not to speak for scarecrow but some personal comments in response to this - in the context of an extended personal and non-standard interpretation - that it is in a certain sense possible that there are things/propertis yet to be discovered that are currently unknown, and by definition we don't know what this maybe be. One can not predict the future, one can only provide an estimate of the future, based on the past.

The wavefunction by constructions describes exactly, what we think we know. What we don't know, or wether what we think we know may later need revision nonone can possibly know.

The problem may be howto understand how "we know" can be generalized to general non-intelligent systems. I think it can be done and that a systems, or particle internal state, which by definition is not entirely observable from the point of view of the environment, can still encode conditional information.

Unlike a ordinary hidden variable construction, I think the key here is that information is fundamentally relative. One does not assume or speculate about the unknown beyond what can be induced from what is known. In essence I think the proper answer should be sought after in terms of self organisation. But I think not only the particle posistion is subject of self organisation, that also applies to the reference frames, spacetimes and geometries themselves.

/Fredrik

 

[Fra]

Addition: What I wrote is inconsistent with the standard QM (unitarity etc) though. Which is why I believe that QM needs revision. The basic interpretation thouhg, still helps even in the standard QM. This way of thinking will most probably introduce gravity phenomenan all by itself, because it's required by consistency!

/Fredrik

 

[Mike2]

It's difficult to believe that the particles in a particular interaction have information about how probable it is that the interaction will occur. It either happens or it doesn't, right? I think probabilities are only something humans would be interested in. Is it fair to describe the wave function as collapsing when it is only humans who are combining the wave function with its complex conjugate to get a probability? Does the wave function cease to be a wave function simply because we arbitrarily combined it with its conjugate to get a number?

 

[arfa]

Wavefunction collapse is a postulate of QM supported by experimentation.

Wave function collapse is what happens when too many angels go dancing on one surfboard to the tune of "Wonderful, wonderful Copenhagen".

Whereas you can ask: given both the everyday observed and experimental evidence, why shouldn't quantum objects be both waves and particles while in motion?

 

[Fra]

It's difficult to believe that the particles in a particular interaction have information about how probable it is that the interaction will occur. It either happens or it doesn't, right? I think probabilities are only something humans would be interested in.

I disagree, I find it very easy to believe that particles are manifestations of statistical phenomena. It also suggest explanations for the observed complexity and self organisation in nature.

One should I think also not mix up the human language and human descriptions of nature, with nature itself. Of course particles doesn't solve equations, it doesn't think about things... it just "is".

Edit: Still of course, at some some point WE are of course part of nature too, so the distinction between our description and what it desribes are bound to converge/unite at some level. This is allowed in the view I have at least.

However, your points are probably more common in the community, and what I suggest is not yet anything mature. What really beats me is why not more work is done on this compared to all other stuff people work on.

/Fredrik

 

[scarecrow]

Does it mean that the particle possesses some properties that are not described by the wave function? If yes, what are these properties?

I'm not quite sure what your trying to get at here.

In terms of a wavefunction collapse, the particle does not suddenly have different properties or behavior after an observation.

Example: An electron is in some superposition of states a and b. At time t = 0 assume the electron is in state a and at some time later the electron can only be described by a probability density, i.e. the electron has a probability of being in one state or the other. But since it's a probability, the electron can theoretically exist in both states at the same time, e.g. 40% in a and 60% in b.

However, this does not mean the particle is physically in two places at the same time, it is only a mathematical construct to describe what has been shown experimentally.

Once the electron has been observed - at that instant the wavefunction collapses - and the electron is definitely (100% probable) in the place where it has been observed. After the observation, the electron must be described again by the wavefunction since it is not being observed anymore.

This is why there is such a thing in QM called expectation values...what do we expect (on average) to get.

 

[f95toli]

I'm not quite sure what your trying to get at here.
In terms of a wavefunction collapse, the particle does not suddenly have different properties or behavior after an observation.

That is not really correct.
There are plenty of phenomena which involves changing the properties of a system by measuring it; that is the whole idea of state preparation by projective measurements; i.e. you can prepare a quantum system in a state by measuring it in a certain way. This is a standard method in quantum information processing.

Note that these are not "statistical" properties in the classical (ensemble) sense; this method works even you are working with e.g. single ions or qubits.
There are many other examples where (indirectly) observable properties (such as Rabi splitting in cavity-QED) changes simply because you perform a measurement.

In my view many discussions tend to miss a very basic point: Real quantum systems decay whether "an intelligent observer" is looking at them (or measuring them in some other way) or not; simply because real systems are subject to dissipation. Hence, in a sense the "wavefunction collapse" picture gives you the wrong idea of what is going on: A real cat will ALWAYS be EITHER dead OR alíve; simply because the cat is too big to be in a superposition of state (or to be more precise: a system of that size will always decay very quickly since it is impossible to insulate it from external degrees of freedom); whether a human is looking at it or not obviously does not matter

 

[Mike2]

I disagree, I find it very easy to believe that particles are manifestations of statistical phenomena.

I think this shows the global nature of physics - that one interaction would depende on what many others would do. As you say, objects don't calculate probabilities. They should simply respond to only the properties of the interacting particles alone. It's hard to say that a particle has a property if another reacts to it only sometimes. But if a particle's properties are truly statistical, then this only goes to show that the laws of nature are derived from the most general principles of probabilities themselves.

What really beats me is why not more work is done on this compared to all other stuff people work on.

This would be addressing philosophical issues on the ultimate foundations of nature. That doesn't help design a better oven or car or radio, does it?

 

[Fra]

I think this shows the global nature of physics - that one interaction would depende on what many others would do. As you say, objects don't calculate probabilities. They should simply respond to only the properties of the interacting particles alone.

Yes, OTOH I guess one can say that humans only respond too, our brains simply respond to input. In a broad sense the difference is mainly a difference in complexity of multiple orders of magnitude. I don't see any problem or contradiction here.

if a particle's properties are truly statistical, then this only goes to show that the laws of nature are derived from the most general principles of probabilities themselves.

Yes, in a certain sense I think you are right. In the spirit you did that derivation. However I think there is some missing elements there even though I agree to a certain extent.

The missing part is the coupling, between orders of complexity that is also responsible for evolution (all of it, not just the biological evolution - I see no reason to make a fundamental distinction except at the level of complexity).

"truly statistical" - what exactly is that? To me it's an idealisation that doesn't quite make sense. Apparently or expected statistical or random yes, but "truly"? This is really one of the critical focus points IMO. Unless there is a proper discrimination between truly and apparent, then apparent is all we've got, and i think this distinction really does make a difference.

One can IMO not consider the statistics to be made outside the observer, whatever statistics is made, we only have at hand the information capacity of the observer. This certainly puts limits on things, these limits will most probably (IMHO at least) imply non-trivial relational dynamics.

/Fredrik

 

[Fra]

The reason I wrote "statistical phenomena" is because it seemed like a decent description, but what I really mean is statistical in the sense of bayesian expectations combined with a principle of self-organisation. In many cases, this does simplify to the standard notions of Kolmogorov probability. But the generalisation lies in that hte probability space itself, is fundamentally uncertain too. And there is couplings that leads to interesting interactions which takes us beyond the simple classical statistics.

/Fredrik