Why does the which path information collapse the wave function?

[Xtyn]

I don't know if I got this right, but as far as I know, if you are able to deduce through which slit the particle went through, it behaves classically, if you have no way of deducing through which slit the particle went through, it behaves in a quantum way (interference pattern).

Now, I don't mean all that observer nonsense, I know that some people have a mystical interpretation of that, but the observer cannot be special, from my point of view.

I've read about some double slit experiments with polarized photons which I found very strange, this is an example:
http://grad.physics.sunysb.edu/~amarch/

So, why does the which path information collapse the wave function?

 

[Simon Bridge]

It actually behaves in a "quantum way" all the time.
http://arxiv.org/pdf/quant-ph/0703126]

It's just that it gets explained badly.
Sometimes the quantum mechanical result is closest to the classical particle result and sometimes it is closest to the classical wave result. But it is always a quantum mechanical result. Knowing which slit is not the same as knowing the path (which cannot be known) - and it does not "collapse the wave function", instead it prepares the system in a different wieghting of states depending on the approach to measurement.

 

[micky_gta]

Xtyn you have big brain in your head. Stop using only the left side, use everything you got. Start using the right side of your brain and answers will follow. I don't understand people that use half of their power?

Imagination is more powerful than knowledge - Einstein

http://www.ucmas.ca/wp-content/uploads/2011/04/Left_Vs_Right_Brain.gif

 

[Simon Bridge]

http://www.positscience.com/human-brain/facts-myths/brain-mythology It is not clear how the gif helps Xytyn with the question either.

I took some trouble to go look at the website ... and it asserts A "which-way" detector can be designed that in no way disturbs the photon and the same phenomenon is observed.

It is difficult to see how one can detect a photon without disturbing it.
However, the experiment proposed uses quantum entanglement ... which amounts to preparing the system in a different state to the standard double-slit experiment.

The description is structured to emphasize the wierdness of the effect.
I wonder if the same careful treatment as in the paper I linked (post #2) will help. I think, in principle, it is still the same thing ... the source + polarizers + slits-configuration is preparing the quantum state. The entanglement makes it a more complicated... in fact the weirdness is mostly entanglement weirdness. But each experiment in the list does set up the initial states differently.

The site tries to let the reader down gently at the end: We can think of the loss of interference as being due only to the fact that the photons are entangled and that the presence of the quarter wave plates changes this entanglement. The interference pattern can be brought back through the erasure measurement because of the entanglement of the photons, and the way that the presence of the quarter wave plates and polarizer changes the entanglement.

 

[DrChinese]

I don't know if I got this right, but as far as I know, if you are able to deduce through which slit the particle went through, it behaves classically, if you have no way of deducing through which slit the particle went through, it behaves in a quantum way (interference pattern).

Now, I don't mean all that observer nonsense, I know that some people have a mystical interpretation of that, but the observer cannot be special, from my point of view.

I've read about some double slit experiments with polarized photons which I found very strange, this is an example:
http://grad.physics.sunysb.edu/~amarch/

So, why does the which path information collapse the wave function?

Another way to think of it is that it restricts the available paths. There are still multiple paths, just not as many. And the restricted paths (from one slit) do not interference with the same robustness as when there are 2 slits.

 

[Xtyn]

I took some trouble to go look at the website ... and it asserts A "which-way" detector can be designed that in no way disturbs the photon and the same phenomenon is observed.

It is difficult to see how one can detect a photon without disturbing it.

I've read that pdf you linked to but I did not understand much of it, as I'm not too good at physics, I've studied something else.

I think you are right, any observation interferes with the experiment, especially on a quantum level. When I first heard of the double slit experiment with electrons I thought that the observation changed their behaviour because observation meant bombarding them with photons.

When I read about the double slit experiments with polarized photons I was a bit surprised. I don't understand polarization too well, but I do understand how vertically polarized glasses work to reflect the horizontally polarized photons which themselves are reflected off of snow, cars, roads and such things. I understand that this is how they reduce the glare. I understand 3D glasses as well.

What I don't understand is how they can change the polarization of photons. From what I understand, if they put a polarizing glass on one slit, the interference pattern disappears, but if they put another glass which "erases" the polarization, the interference pattern reappears, although I can't understand how they can "erase" the polarization.

I came up with a hypothesis for this. If on one slit there is something that modifies the particle in some way, the particle does not "recognize" itself, therefore, it does not interfere with itself. Maybe it's just nonsense, but I'm trying to make sense of this.

 

[Simon Bridge]

It is nonsense. You won't be able to get a decent handle on it without the physics so it is probably worth spending some effort on that paper. Don't get intimidated by all the symbols - treat them as a kind of shorthand.

The paper puts the source+slits in a box that prepares the initial state of the wavefunction describing the position and momentum of the particle. Try to see "which path" changes the initial state by physically changing the preparation.

The result of looking carefully at the QM is that the idea that the particle somehow "interferes with itself" is not needed. Interference is the result not the process.

 

[nonequilibrium]

The way I understand it, it's not the information that collapses the wavefunction, rather its the process that got the information. After all, if you have information about that system, that implies you interacted with the system through a measurement, well it's (among other things) this interaction that is responsible for collapse.

 

[Xtyn]

The way I understand it, it's not the information that collapses the wavefunction, rather its the process that got the information. After all, if you have information about that system, that implies you interacted with the system through a measurement, well it's (among other things) this interaction that is responsible for collapse.

Yes, I think so too. But there are some strange things about those double slit experiments with polarized photons. For example, it doesn't matter if you polarize the photons, they will still give an interference pattern. The problem appears when each slit polarizes them differently. You can see the link in my first post.

 

[Xtyn]

The result of looking carefully at the QM is that the idea that the particle somehow "interferes with itself" is not needed. Interference is the result not the process.

But how do you get an interference pattern if the particle does not interfere with itself? I'm talking about shooting one particle at a time. It's not like multiplying a single-slit experiment by two, it's totally different.

 

[San K]

Yes, I think so too. But there are some strange things about those double slit experiments with polarized photons. For example, it doesn't matter if you polarize the photons, they will still give an interference pattern.

Perhaps no phase difference is created here.

The problem appears when each slit polarizes them differently. You can see the link in my first post.

Perhaps a phase diffrence is created here.

 

[Mark M]

But how do you get an interference pattern if the particle does not interfere with itself? I'm talking about shooting one particle at a time. It's not like multiplying a single-slit experiment by two, it's totally different.

You're still thinking of a particle in Newtonian terms. In quantum mechanics, the probability that a certain path is taken by a particle is determined by it's wavefunction. The wavefunction evolves like a classical wave, and so we will expect to see the particles fill out an interference pattern.

 

[Simon Bridge]

But how do you get an interference pattern if the particle does not interfere with itself? I'm talking about shooting one particle at a time. It's not like multiplying a single-slit experiment by two, it's totally different.

You can easily get an interference pattern without interference... at least the classical version from HS optics. eg. You can sketch one freehand.

What these experiments reveal is that the notion that something interferes with something is not correct. So we update that idea, that model, with something more powerful. The trouble is that it involves concepts that are hard to visualise intuitively. We end up trying to describe it in the old terms we already know are wrong, so it doesn't work properly and you get confused.

 

[al onestone]

You all need an introduction to the information interpretation of quantum mechanics, but I don't have time to give you one today. Look it up in Zeilinger's work.

However, I will answer your question briefly; The which-path information of any quantum mechanics experiment does "collapse the wavefunction" or "reduce the state vector" simply because the preparation of the system at the point in time of observation is such that an amount of information which would tell you one of many eigenstates (paths) of the superposition (which is expected to be maintained for a "coherent" superposition) is known to be the definite state/path(or at least a smaller subset of states of the original superposition).

I know what you're wondering, why does it depend upon knowledge of? It doesn't, it depends upon "in principle knowledge of". As long as you could in principle make the measurement that gives you the knowledge of.

And it depends upon "in principle knowledge of" for the simple reason (that the other commentors will not illude to for interpretational differences) that the system itself IS information. The system IS "in principle knowledge of" for Quantum Mechanical systems.

 

[vanhees71]

I have never understood, why on needs the "collapse of the state" for the interpretation of quantum theory. It makes only trouble, as has been pointed out by EPR a long time ago. We only need Born's rule to interpret the meaning of the (pure or mixed) states (Minimal Statistical Interpretation).

Also, if there is something like a collapse of the state, how do you define it precisely and more importantly how can one verify it experimentally?

 

[Maui]

You can easily get an interference pattern without interference... at least the classical version from HS optics. eg. You can sketch one freehand.

What these experiments reveal is that the notion that something interferes with something is not correct. So we update that idea, that model, with something more powerful. The trouble is that it involves concepts that are hard to visualise intuitively. We end up trying to describe it in the old terms we already know are wrong, so it doesn't work properly and you get confused.

What is this more powerful idea?

 

[Mark M]

What is this more powerful idea?

That it's meaningless to speak of the location of the particle prior to the observation. Instead, you describe the evolution of a complex wave, a wavefunction, that represents probability amplitudes. This wave evolves like a classical wave (not through space, but through complex Hilbert space), causing probability amplitudes to interfere, changing with time. The fact that some amplitudes are negative, some are positive, and some are complex gives rise to interference.

 

[Maui]

That it's meaningless to speak of the location of the particle prior to the observation. Instead, you describe the evolution of a complex wave, a wavefunction, that represents probability amplitudes. This wave evolves like a classical wave (not through space, but through complex Hilbert space), causing probability amplitudes to interfere, changing with time. The fact that some amplitudes are negative, some are positive, and some are complex gives rise to interference.

It's very dubious if the mathematical amplitudes are interfering. It's rather the underlying "stuff" that the amlitudes represent that is interfering. The fact that physics has currently no concept(and name) to describe the very basic constituent of the universe, hardly makes it unreal. The situation is somewhat embarassing indeed.

 

[Mark M]

It's very dubious if the mathematical amplitudes are interfering. It's rather the underlying "stuff" that the amlitudes represent that is interfering. The fact that physics has currently no concept(and name) to describe the very basic constituent of the universe, hardly makes it unreal. The situation is somewhat embarassing indeed.

The amplitudes represent possible locations of the particle, not some kind of 'stuff'.

How? Quantum mechanics makes predictions that have been verified to ridiculous accuracy, what's so embarrassing? It's arguably the most successful scientific theory to date.

 

[Maui]

The amplitudes represent possible locations of the particle, not some kind of 'stuff'.

That's your impression of it. I don't agree or find it in any way rational to think that possible locations of a particle(not the particle itself, but it's possible locations!) can leave an interference pattern on the screen of a double slit experiment. In this respect at least, the BI makes a lot of sense.

How? Quantum mechanics makes predictions that have been verified to ridiculous accuracy, what's so embarrassing? It's arguably the most successful scientific theory to date.

When did i question its accuracy? And what does it have to do with what the amplitudes represent?

 

[San K]

That it's meaningless to speak of the location of the particle prior to the observation.

it's not meaningless, though I have heard many people/physicists say that, for similar phenomena, on this forum

i think it could be better rephrased as:

we don't know, we don't understand as to
what is happening at the "physical" level,
what is happening in reality
and this could be a futuristic research area

however we are able to mathematically model it very well and make some select predictions. for example: how the wave functions evolves in time and space

It's very dubious if the mathematical amplitudes are interfering. It's rather the underlying "stuff" that the amlitudes represent that is interfering. The fact that physics has currently no concept(and name) to describe the very basic constituent of the universe, hardly makes it unreal.

agreed

 

[bahamagreen]

There seems to be some confusion here about what it means to perform a measurement... Classical thinking assumes an object with existential objective attributes that may be measured. Quantum thinking might be easier to grasp with an analogy...

In Fourier analysis, a complex wave form may be interpreted as a combination of simple sine waves with various amplitudes, frequencies, and phases, and this set of sine waves may be recombined to produce the original wave form. Using the sine wave as the building block is like choosing what you want to measure of the wave form.

But, Fourier analysis does not require that the sine wave be used, you could use a cosine wave, or square wave, or triangle, ramp, or even any other wave form... even an irregular shaped weird one. Sine waves are used because the math is easier, but any wave can be used as the fundamental building block or "seed" or "point of view" to run the analysis...

The result you get will be determined by the initial choice of wave form to be applied as the "seed". To say it another way, the result of the measurement does not exist UNTIL the choice of the wave form to be applied in the analysis has been selected. The original wave form does not have these results (attributes) independent of and until the choice (seed wave) is selected - attributes only become existential and objective within the context of having selected a particular building block wave form with which to decompose the original complex wave.

QM measurement is similar in that the attributes don't really exist until the measurement is performed. The experimental preparation of the system is essentially making a choice of how one is going to interrogate the object and creates a set of results that do not exist independently within the object apart from being interrogated from a selected perspective.

 

[San K]

The original wave form does not have these results (attributes) independent of and until the choice (seed wave) is selected - attributes only become existential and objective within the context of having selected a particular building block wave form with which to decompose the original complex wave.

well illustrated bahamagreen and agree (broadly)

QM measurement is similar in that the attributes don't really exist until the measurement is performed.

On the other hand...could we say that - all the attributes (all the possible choices) exist until measurement is performed?

 

[lugita15]

I don't know if I got this right, but as far as I know, if you are able to deduce through which slit the particle went through, it behaves classically, if you have no way of deducing through which slit the particle went through, it behaves in a quantum way (interference pattern).

Now, I don't mean all that observer nonsense, I know that some people have a mystical interpretation of that, but the observer cannot be special, from my point of view.

Here's an old post of mine that you may find interesting:

The reason there is still disagreement as to what constitutes measurement is that it makes no experimental difference according to quantum mechanics. The way QM works under the Copenhagen interpretation is that you have to split the world into two parts, the “observer” or measurement device, and the “observed” or the particles you’re measuring.

The measurement device is assumed to behave classically. The particles in the observed system are in a superposition of states described by the wave function which keeps evolving until it interacts with the classical measurement device. The question is where to draw the line. You could consider a photon to be the observed system and an atom to be the measuring device, but you can also consider the photon-and-atom system as in a superposition of states, and take a Geiger counter to be the measurement device. So there is this von-Neumann chain, going from elementary particles to Geiger counters to human beings, and we have to decide where to cut it off.

Von Neumann proved in his famous "Bible" of QM that regardless of where you cut the chain, you would get the same experimental results. But he argued that wherever you cut the chain you have things made out of particles on each side of the cut, so there’s no principled way to place the cut in the middle. So he decided that you should place the cut between the human mind and the human body, because he believed that the mind is non-physical. Hence "consciousness causes collapse" was born. Nowadays, the most popular view is decoherence, where there is no real collapse, it's just that when you have a large number of particles in the environment interacting with the system, the wave function becomes smeared out and looks like it has collapsed. So decoherence gives us a reasonable place to cut the chain, when the number of particles involved reaches a critical number so that interference effect become negligible.

 

[bahamagreen]

well illustrated bahamagreen and agree (broadly)

Well, I'm not so sure I didn't mangle something about Fourier in the process, but the analogy seems about right.

On the other hand...could we say that - all the attributes (all the possible choices) exist until measurement is performed?

Maybe all the attributes can be thought to "exist" in some kind of statistical "potential" space until a particular one is made manifest by measurement... in a sense both are sort of created by either potential measurement (calculation) or actual measurement (experiment), but I see a difference between a potential attribute and an actualized attribute... more than just the difference between being at a point in time before or after having made the measurement.

 

[StevieTNZ]

Here's an old post of mine that you may find interesting:

AGAIN I refer you back to the PDF I emailed you.

 

[audioloop]

That it's meaningless to speak of the location of the particle prior to the observation. Instead, you describe the evolution of a complex , a wavefunction, that represents probability amplitudes. This evolves like a classical wave (not through space, but through complex Hilbert space), causing probability amplitudes to interfere, changing with time. The fact that some amplitudes are negative, some are positive, and some are complex gives rise to interference.

First, coordinates (position) respect to ?
Second, without position there is no displacement, no speed, no velocity.
and in any case momentum implies position.

 

[Simon Bridge]

momentum implies position

We usually infer a change in position has occurred. You cannot know the position from the momentum or the momentum from the position. In addition, the more we know about position, the less we can know about momentum and vice versa.

Mark M was referring to the need to discipline our thought to what we can know about something rather than speculate about what cannot be known. We have no way of knowing how the particle got from source to detector ... if we did know it's position at some intermediate stage than we would have detected it there and it would not have reached the detector which is a logical contradiction.

The idea that anything is "travelling every possible path" at the same time, tends to lead to sloppy thinking and should be avoided. We can use information about the available paths to make predictions about the kinds of things we are likely to observe but that does not imply anything about what is happening.

What we are doing with these experiments is probing what is actually happening "at the physical level" (in so far as that phrase can mean anything at all). We do not have a classical picture for what happens at this level... the fundamental level of individual particles.

Perhaps StevieTNZ will share that PDF with the rest of us? ;)

 

[Mark M]

First, coordinates (position) respect to ?
Second, without position there is no displacement, no speed, no velocity.
and in any case momentum implies position.

The first point doesn't make sense. Second, that isn't how quantum mechanics works. As I said, it's meaningless to speak of any of those observable properties prior to measurement. We describe those observables with the wavefunction. We then describe the evolution of the wavefunction with Schrodinger's equation, in which the time evolution of the wavefunction is determined by the Hamiltonian of the system.

The problem is, is that you're still thinking in Classical terms to describe a quantum phenomenon.

 

[lugita15]

Perhaps StevieTNZ will share that PDF with the rest of us? ;)

Attached is the PDF. Here is my description of it from an old post of mine:

A thought experiment in Ghirardi's "Sneaking a look at God's Cards" purports to provide a means of empirically distinguishing between actual wavefunction collapse and decoherence. (In fact Ghirardi apparently makes a bolder claim, that this is an empirical test of the Copenhagen interpretation!). Here's how it works: if A is the observable whose eigenstates form the pointer basis of an apparatus, Ghirardi proposes to perform a measurement on an observable Z of the apparatus which is incompatible with A. Does anyone know whether such an experiment has been performed? In practice our apparatus has a position pointer basis, because we have to read off the position of the pointer, so we would have to somehow perform a momentum measurement of the apparatus pointer or something.

 

[audioloop]

On the other hand...how we can say that - all the attributes (all the possible choices) exist until measurement is performed?

then the reality is omni-existent

 

[Simon Bridge]

then the reality is omni-existent

In so far as "omniexistent" means" exists everywhere" then this would be correct, yes: reality is everywhere. If that's not what you mean then you'll have to clarify this use of the term.

I actually liked The following question from Audioloop, in responce to Mark_M's it's meaningless to speak of any of those observable properties prior to measurement, showing up in the email notification, but it seems to have been deleted:

[If] then, position does not exist, and consecuently(sic) without position there is no displacement, how can exist a trajectory then ?

A single classical trajectory, indeed, has no fundamental existence... however, we see trajectories all the time, for instance: in bubble chambers. The answer is that the classical trajectory shown in such things exists on average as an emergent phenominon due to many small interactions. You'll notice that the bubble trajectory has a width ... i.e. an uncertainty in the particle's position over time? However, it's still meaningless to speak of the particle's position prior to measurement. The trajectory shown is the result of many successive measurements. That's how you see it.

So the next step in the inquiry is to place a 2-slit experiment in a bubble chamber (or appropriate analog) isn't it? Then you can follow the rough trajectories from source to screen. ;)

 

[audioloop]

In so far as "omniexistent" means" exists everywhere" then this would be correct, yes: is everywhere. If that's not what you then you'll have to clarify this use of the term.

I actually liked The following question from Audioloop, in responce to Mark_M's it's meaningless to speak of any of those observable properties prior to measurement, up in the email notification, but it seems to have been deleted:A single classical trajectory, indeed, has no fundamental existence... however, we see trajectories all the time, for instance: in . The answer is that the classical trajectory shown in such things exists on average as an emergent phenominon due to many small interactions. You'll notice that the bubble trajectory has a width ... i.e. an uncertainty in the particle's over time? However, it's still meaningless to speak of the particle's prior to measurement. The trajectory shown is the result of many successive measurements. That's how you see it.

So the next step in the inquiry is to place a 2-slit experiment in a bubble chamber (or appropriate analog) isn't it? Then you can follow the rough trajectories from source to screen. ;)

and have a direction, it don't go to anyplace, nor does it come from all places.

 

[Maui]

If you place just one detector behind one of the slits(A and B, say you place the detector behind A) and shoot one electron and the detector doesn't register anything, it means you 'collapsed' the wavefunction without interacting with the electron in any way(complementairy requires that the electron went through the other). The information of the which path collapsed the wavefunction without interaction.