Question about Quantum mechanics

[Dancing David]

That's flat-out wrong, and I already explained in detail why. As far as I can tell you completely ignored that post, so there's no point in continuing.

That is a randman discussion in a nut shell.

 

[randman]

That's flat-out wrong, and I already explained in detail why. As far as I can tell you completely ignored that post, so there's no point in continuing.

Sol, the delayed choice experiment is said to be a demonstration of Wheeler's thought experiment.

Wave-particle duality is strikingly illustrated by Wheeler's delayed-choice gedanken experiment, where the configuration of a two-path interferometer is chosen after a single-photon pulse has entered it: Either the interferometer is closed (that is, the two paths are recombined) and the interference is observed, or the interferometer remains open and the path followed by the photon is measured. We report an almost ideal realization of that gedanken experiment with single photons allowing unambiguous which-way measurements. The choice between open and closed configurations, made by a quantum random number generator, is relativistically separated from the entry of the photon into the interferometer.

http://www.sciencemag.org/content/315/5814/966.short
Another description of experiment's realizing Wheeler's thought experiment...

Wheeler realized that the observer's choice might control those variables in a test.

"If what you say is true," he said (in effect), "then I may choose to know a property after the event should already have taken place." [1] Wheeler realized that in such a situation, the observer's choice would determine the outcome of the experiment – regardless of whether the outcome should logically have been determined long ago.

"Nonsense," said the reductionists. "Rubbish," said the materialists. "Completely absurd," said the naïve realists. "Yup," said the mathematicians.

And so Wheeler's thought experiment and the predictions of quantum mechanics were brought to the laboratory for testing. [2] This is what happens.

....

In summary, we have chosen whether to know which slit the particle went through, by choosing to use the telescopes or not, which are the instruments that would give us the information about which slit the particle went through. We have delayed this choice until a time after the particles "have gone through one slit or the other slit or both slits," so to speak. Yet, it seems paradoxically that our later choice of whether to obtain this information determines whether the particle passed through one slit or the other slit or both slits, so to speak.

the original thought experiment

Does our choice "change the past"?

How long can we delay the choice? In Wheeler's original thought experiment, he imagined the phenomenon on a cosmic scale, as follows:

1. A distant star emits a photon many billions of years ago.

2. The photon must pass a dense galaxy (or black hole) directly in its path toward earth.

"Gravitational lensing" predicted by general relativity (and well verified) will make the light bend around the galaxy or black hole. The same photon can, therefore, take either of two paths around the galaxy and still reach earth – it can take the left path and bend back toward earth; or it can take the right path and bend back toward earth. Bending around the left side is the experimental equivalent of going through the left slit of a barrier; bending around the right side is the equivalent of going through the right slit.

3. The photon continues for a very long time (perhaps a few more billion years) on its way toward earth.

4. On earth (many billions of years later), an astronomer chooses to use a screen type of light projector, encompassing both sides of the intervening and the surrounding space without focusing or distinguishing among regions. The photon will land somewhere along the field of focus without our astronomer being able to tell which side of the galaxy/black hole the photon passed, left or right. So the distribution pattern of the photon (even of a single photon, but easily recognizable after a lot of photons are collected) will be an interference pattern.
5. Alternatively, based on what she had for breakfast, our astronomer might choose to use a binocular apparatus, with one side of the binoculars (one telescope) focused exclusively on the left side of the intervening galaxy, and the other side focussed exclusively on the right side of the intervening galaxy. In that case the "pattern" will be a clump of photons at one side, and a clump of photons at the other side

http://www.bottomlayer.com/bottom/basic_delayed_choice.htm


In MWI, the split universes may be internally consistent with causality after the split. However, since the choice affects the which-way path in the past as seen from the observer, if as MWI this is a purely mechanical process, the divergence of the universes must occur with entangled particles at a point earlier than the measurement. If the choice, the measurement, shows the which-way path as these experiments demonstrate, then PRIOR to the measurement, there must be divergence between the universes that would have shown the interference from the other universe or the wave-like progression.

Just positing multiple universes does not explain the splitting occurring before the measurement.

Now, I am sure MWI has an explanation but just saying there are multiple universes may explain away non-locality but I don't see how it gets around the splitting occurring prior to the measurement as delayed-choice and later experiments show.

 

[sol invictus]

Sol, the delayed choice experiment is said to be a demonstration of Wheeler's thought experiment.

Yes, I've already agreed with that.

In MWI, the split universes may be internally consistent with causality after the split. However, since the choice affects the which-way path in the past as seen from the observer, if as MWI this is a purely mechanical process, the divergence of the universes must occur with entangled particles at a point earlier than the measurement. If the choice, the measurement, shows the which-way path as these experiments demonstrate, then PRIOR to the measurement, there must be divergence between the universes that would have shown the interference from the other universe or the wave-like progression.

Just positing multiple universes does not explain the splitting occurring before the measurement.

Now, I am sure MWI has an explanation but just saying there are multiple universes may explain away non-locality but I don't see how it gets around the splitting occurring prior to the measurement as delayed-choice and later experiments show.

See post 80, where this exact question is answered in detail. If you don't understand post 80, ask about post 80 - don't keep asking the same thing over and over while ignoring detailed answer I've already given you.

 

[randman]

Sol, as you acknowledge already, the point of the experiment is to test Wheeler's thought experiment, basically if you measure the which-way path of a photon, does that tell you what the which-way path of the photon prior to the measurement. Wheeler's idea is not so much the photon travelled more wave-like but that it's not really in any definite, discrete form at all but has the potential for form and so depending on how we measure it, that dictates what the past trajectory was; hence his participatory universe concept, right?

In Post 80, you said they just measured the photon on the arms but this is not a complete description by itself and suggests that all that is being tested is what happens after the measurement instead of seeing if the measurement does do as Wheeler's thought experiment, dictate whether the particle travelled more wave-like or particle-like BEFORE the measurement.

The earlier link contained a diagram of a more extensive later experiment and so a more complicated diagram. The diagram of an earlier experiment in the link below is from a popular article but illustrates the basic concept of the experiment nicely. It's the first diagram under the heading "How to Destroy and Revive a Light Wave."

Information rather than direct intervention destroys wavelike behaviour in an experiment done at the University of Rochester. A laser fires photons past a half-silvered mirror, or beam splitter, to two down-converters, labelled 1 and 2. These convert each incident photon into two lower-energy photons, called signals and idlers. Because the signal detector cannot tell how the signals arrived, each signal takes both routes, like a wave, generating an interference pattern at the signal detector. But the pattern can be destroyed merely by blocking idlers from down-converter 1 (dotted line). The reason is that each signal's path can now be retraced; simultaneous detection of a signal and idler indicates that both came from a photon reflected by the beam splitter into down-converter 2.

http://www.fortunecity.com/emachines/e11/86/qphil.html

The apparatus when set up so there is no means to tell which path the photon took indicates it went through "both routes", but if after the photon takes it's path we put a device in place to determine whether it took one path or both, it takes just one path even though the measurement was AFTER it went through the beam splitter.

So in MWI, how does the measurement of merely blocking the "idler" photon cause the photon to take only take one path BEFORE the measurement?

I suppose MWI would say the universe did not split before the measurement but since the split, we can now only measure one photon and so even though we determine the photon took only one path before the measurement, in reality under MWI, it took both paths (there was an interference pattern at that time). But we just cannot detect it now?

 

[sol invictus]

So in MWI, how does the measurement of merely blocking the "idler" photon cause the photon to take only take one path BEFORE the measurement?

Again, that's exactly what I explained in post 80.

According to MW, it's not true that the photon only took one path even if you block the idler photon (or one arm in my example). In one world it took one path, in the other it took the other path.

If you block the idler/arm/detect the path, you decohere the two worlds IN THE FUTURE and prevent them from interfering IN THE FUTURE and forming an interference pattern. There is no effect on anything in the past.

If you do not block the idler/arm/do not detect the path, the two worlds maintain coherence (assuming the experiment is done very carefully), and then they interfere and produce an interference pattern.

The ONLY effect of the block is on the future, and only within the lightcone - so this is a local, causal explanation for what is observed.

 

[randman]

I think I got that. Thanks. The delayed choice quantum eraser experiment cited earlier seems to suggest a different wrinkle however, but need to study it more.

http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

It seems interference can cause a which-way path to be determined (MWI split), but a wave pattern can subsequently emerge from the same photon if we obscure the ability to know the earlier which-way path. The interference though would remain so in MWI there would be a split.

So a particle in MWI can "collapse" or in MWI result in a splitting, but return to a wave pattern and another universe split again?

Why if it's mechanical, would a particle travelling in a particle-like fashion switch back to a wave-like pattern?

 

[sol invictus]

I think I got that. Thanks. The delayed choice quantum eraser experiment cited earlier seems to suggest a different wrinkle however, but need to study it more.

Delaying the choice until after the photons pass the splitter makes no difference at all in the MWI, because it's only the act of measuring/recording or not-measuring/not-recording that matters. It's only strange in Copenhagen or one of the other interpretations.

Why if it's mechanical, would a particle travelling in a particle-like fashion switch back to a wave-like pattern?

I have no idea what you mean by "mechanical", so I can't answer that. As I've said multiple times, the MWI is simply the assertion that the wavefunction represents reality. The wavefunction can be a superposition of terms with relative phases, and those phases are what cause quantum interference and hence interference patterns in some measurements. However if the phase coherence is destroyed, as it is by any interaction that involves macroscopic objects that record any information, no interference will take place.

 

[randman]

However if the phase coherence is destroyed, as it is by any interaction that involves macroscopic objects that record any information, no interference will take place.

MWI came about when it was generally thought once decoherence occurred (wave function collapse in Copenhagen), it could not revert back. The idea is the measurement act causes the split and so the particle will traverse in a particle-like form.

By mechanical, I mean the physical measurement causes the collapse/splitting.

But if that is the case, how can it exhibit interference again?

It's measured. There is a split. But if we devise a way that we can no longer tell the which-way path, even though the split must have occurred, the interference reappears.

 

[sol invictus]

But if that is the case, how can it exhibit interference again?

It's measured. There is a split. But if we devise a way that we can no longer tell the which-way path, even though the split must have occurred, the interference reappears.

It doesn't "reappear". You can only see the interference pattern when you look at a histogram of a specific subset of the experimental data. If you take all of it together, it's not there. In the MWI, all you're doing is post-selecting the subset of events in which there was interference.

In other words the explanation in post 80 works perfectly - I just worked it out in detail for the specific experiment you're referring to.

 

[randman]

Trying to find some discussion on how MWI treats the quantum eraser experiment, one runs across some odd things.

Although Everett has said that people cannot feel the other branches of his Many-Worlds interpretation, Deutsch describes a gedanken experiment in which an observer can feel himself having been split into two branches that have now merged into his present branch, in the sense that, although he accurately remembers only one branch, he can infer that "... there was more than one copy of himself (and the atom) in existence at that time, and that these copies merged to form his present self.

http://www.valdostamuseum.org/hamsmith/ManyWorlds.html

Maybe some positions have more intuitive feeling behind them than one supposes? Not that the math, etc,....isn't there also, however.

 

[Perpetual Student]

s. i. :

I'm not quite clear on how you personally view the MWI version of quantum theory. Do you believe these other worlds actually exist in some tangible sense or are they merely hypothetical, ghostlike or potential existences -- whatever you think that may mean. You may have answered this question somewhere -- if so, sorry for the redundancy.

 

[sol invictus]

s. i. :

I'm not quite clear on how you personally view the MWI version of quantum theory. Do you believe these other worlds actually exist in some tangible sense or are they merely hypothetical, ghostlike or potential existences -- whatever you think that may mean. You may have answered this question somewhere -- if so, sorry for the redundancy.

Never mind what I personally believe, that isn't relevant. I would say that what defines the MWI is the assertion that the wavefunction is real - it is a direct description of reality. If so, all these worlds (at least all the decohered ones) are equally tangible and real.

 

[randman]

Sol, I don't think you are doing justice to the delayed-choice quantum eraser experiment. Edit to make this simpler. The experiment shows a photon going through a detector and still showing an interference pattern. That's interaction and should result in a MWI split.

Other photons are sent through detectors and don't show an interference pattern (a collapse).

The only difference appears to be in the 2nd example, we can know which path it took.

 

[sol invictus]

Sol, I don't think you are doing justice to the delayed-choice quantum eraser experiment.

I've read the original paper and worked out the math. It's quite trivial, and it agrees with all the results of the experiment. It also agrees with the math in the paper (although my version is simpler, since I ignored various irrelevant complicating factors like the finite width of the slits).

I've explained the math in a post you ignored, or at least failed to understand.

Can you please explain in what way I'm not doing it justice?

 

[Perpetual Student]

Never mind what I personally believe, that isn't relevant. I would say that what defines the MWI is the assertion that the wavefunction is real - it is a direct description of reality. If so, all these worlds (at least all the decohered ones) are equally tangible and real.

OK, I'll never mind what you personally believe. My (layman's) understanding of the wavefunction is that it describes the probability of something (e.g.: position) over time. In what sense is it real and a direct description of reality? Is it real in the same sense that any probability density function that describes the relative likelihood of an occurrence at a point is also real in that it realy works? Or, it is it something more tangible than that? Any probability density function is merely a function that describes the relative likelihood for some random variable to occur, but has no reality concerning the actual occurrence of any single or collection of points. How and why would the wavefunction be more "real" than that?

 

[Vorpal]

Invalidation of Bell's inequality means that physics can't both be local and contain hidden variables, meaning the wavefunction is a complete description of the physical state. I don't know how physicists test for reality in a lab, but being able to predict certain kinds of experimental results with evidence that it is impossible to do better seems like a good criterion. How 'real' you want to consider that is up to you, but if locality holds, then no theoretical description can be any 'realer'.

It is at least more tangible than the Copenhagen interpretation, in which the answer to to what kind of quantum state macroscopic objects have is "we don't do that," and one instead lives with the oddity that there is no quantum state of an object that is composed of quantum particles.

You can picture the state as a vector. It's very natural for two-level systems, because the two-dimensional projective Hilbert space looks like an ordinary sphere, so one doesn't even have to worry too much about it being complex in that case.

 

[schrodingasdawg]

OK, I'll never mind what you personally believe. My (layman's) understanding of the wavefunction is that it describes the probability of something (e.g.: position) over time. In what sense is it real and a direct description of reality? Is it real in the same sense that any probability density function that describes the relative likelihood of an occurrence at a point is also real in that it realy works? Or, it is it something more tangible than that? Any probability density function is merely a function that describes the relative likelihood for some random variable to occur, but has no reality concerning the actual occurrence of any single or collection of points. How and why would the wavefunction be more "real" than that?

I've read some of the discussion but not all of it, so I apologize if I repeat anything that's been said.

I think the primary issue here is whether the wave-function is real or fictitious. By real, I suppose it is meant that there is a physical thing---an atom, molecule, or what-have-you---that really exists in some state described by the wave-function. The electron in a hydrogen atom, for instance, is really spread out in a cloud around the proton---if you believe the wave-function is real. If you don't believe the wave-function is real, but just a fiction used to predict probabilities---if you believe the observables (e.g. position, momentum, spin, etc.) alone are real, and you don't think there are hidden variables---then you would, in contrast, think that the electron not only isn't spread out in a cloud around the proton, but that it doesn't actually have a determinate position until it is measured to have one.

It's my understanding that the Copenhagen interpretation is non-realism of the wave-function, and that von Neumann's interpretation is realism of the wave-function plus a collapse postulate. In the former, a collapse postulate is needed anyway to make predictions, but collapse isn't a 'real' process since the wave-function isn't real. In von Neumann's interpretation, wave-function collapse is a real process. In either interpretation, there is the problem of what constitutes a measurement. It seems in the end to boil down to either accepting a sort of subject/object dichotomy as in some sort of idealist philosophy, or postulating that there's a certain physical scale or process where collapse occurs.

The many-worlds interpretation of course is still realist about the wave-function, but does away with collapse. It still has the appearance of collapse however, and sol invictus explained how it does this far better than I ever could. With kets and all.

 

[Dilb]

It is at least more tangible than the Copenhagen interpretation, in which the answer to to what kind of quantum state macroscopic objects have is "we don't do that," and one instead lives with the oddity that there is no quantum state of an object that is composed of quantum particles.

That's not true. By the CI (Copenhagen interpretation) a macroscopic "ordinary object" is constantly interacting with a larger environment, and therefore decoheres into non-interacting "ordinary" states. It leaves you with a bunch of probabilities (e.g. this rubber ball at rest on a flat surface is actually distributed somewhere within a femtometre of it's initial position) but whatever.

The bizarre thing about CI is what happens when something with a probability happens, e.g. P goes from 0.5 to 1. CI says that "that's what happened, project and renormalize everything", MWI says "the results have decohered and entangled themselves with the environment, so the environment (i.e. us) automatically sees a projected and renormalized result".

 

[Perpetual Student]

Is seems to me that much doubt still remains as to whether there is any reality to the wavefunction. After all, it is merely a mathematical model of something. Certainly, there is some underlying reality being modeled by the wavefunction, but what can it possibly mean to say the wavefunction itself is "real" any more than the "current-function" in terms of voltage and resistance (I = V/R) is real?

 

[schrodingasdawg]

Is seems to me that much doubt still remains as to whether there is any reality to the wavefunction. After all, it is merely a mathematical model of something. Certainly, there is some underlying reality being modeled by the wavefunction, but what can it possibly mean to say the wavefunction itself is "real" any more than the "current-function" in terms of voltage and resistance (I = V/R) is real?

That's a good question. The current function itself is, of course, a mathematical description of what's going on, but it describes something going on. There really is charge in the circuit that really is moving, though. If someone says the current is real, I would presume they mean that there really is charge moving through the circuit rather than that some Platonic form of the current variable exists out there or whatever.

Saying the wave-function is real would similarly mean that the wave-function describes something actually going on. The electron really is spread out it a cloud around that proton, for instance. I don't think anyone means that the mathematical description itself is real, any more than they'd mean that the mathematical description of current is real rather than a representation.