Double slit probability question

[PeterDonis]

I was thinking that a detection and a collapse were similar

No, they're not, because "detection" is interpretation-independent: it's something that's directly observed. "Collapse" is interpretation-dependent: some interpretations of QM have collapse, some don't, and we don't directly observe collapse, we only directly observe detection.

in case of position/momentum uncertainty a detection yields position-information and for that to be possible the wavefuntion has to collapse

Only in collapse interpretations. In no collapse interpretations (the MWI, for example), it doesn't.

 

[Nugatory]

n case of position/momentum uncertainty a detection yields position-information and for that to be possible the wavefunction has to collapse in a way that the position is known.

That cannot be right... It sounds as if you are saying that we cannot make a position measurement if there is no collapse. But we already know that quantum mechanics works just fine, for measurements of position as well as everything else, without introducing the concept of collapse.

 

[bhobba]

So you are claiming that understanding the interaction that is responsible with the momentum transfer is irrelevant in understanding the momentum transfer, right?

No - he is claiming what the formalism of QM says.

Its simple - so simple many don't get it. It took me a while to get it - but that's just because its in plain sight and you gloss over the obvious.

The formalism is a theory about observations that occur in a common-sense classical world. Whats going on when not observed - momentum transfer yada yada yada the theory is silent on.

This raises the legit issue of QM - the issue ignored by Einstein and Bohr which is why they both have issues (I won't say wrong - its simply a blemish that's best fixed - Weinberg is a bit more prosaic). How does a theory that assumes a classical world from the start explain that world. Great progress has been made in fixing that up, but some problems remain. What those issues are (the factorization problem, key theorems elucidating the problem, and other key theorems associated with decoherence - there are others as well) are (at least in part) detailed here:
https://www.amazon.com/Understanding-Quantum-Mechanics-Roland-Omnès/dp/0691004358

Thanks
Bill

 

[bhobba]

No, they're not, because "detection" is interpretation-independent: it's something that's directly observed. "Collapse" is interpretation-dependent: some interpretations of QM have collapse, some don't, and we don't directly observe collapse, we only directly observe detection.

Go to a library, or in some other way, get a copy of Ballentine.

QM is based 2 axioms - none of which includes collapse.

I know this can be confusing because some texts have it as an actual axiom - it isn't. I remember having a long 'conversation' with the author of such a book. But he remained unconvinced despite pointing him to Ballentine.

But you can take it as a given there is no collapse in the formalism of QM - I know of no expert here (and many are professors who teach it) that says so. The author of the textbook simply has not thought it through carefully enough eg there is obvious no collapse in MW - if collapse was an axiom you wouldn't have that interpretation.

Thanks
Bill

 

[PeterDonis]

QM is based 2 axioms - none of which includes collapse.

Yes, I know, but there are interpretations of QM which have "collapse" in them. I was pointing out the same thing you are: "collapse" is not part of the actual theory of QM, it's only part of certain interpretations.

 

[bhobba]

Yes, I know, but there are interpretations of QM which have "collapse" in them. I was pointing out the same thing you are: "collapse" is not part of the actual theory of QM, it's only part of certain interpretations.

Sorry - I should have made it clear - I was simply elaborating on what you said to help others reading the thread.

I don't know why, but some simply will not let go off the idea - its insidious. It was actually an axiom in a textbook

Von-Neumann gave them many moons ago:
https://en.wikipedia.org/wiki/Dirac–von_Neumann_axioms

But then you get this:
http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html

So I suppose there is a reason - sigh.

Thanks
Bill

 

[ueit]

So you are claiming that understanding the interaction that is responsible with the momentum transfer is irrelevant in understanding the momentum transfer, right?

No - he is claiming what the formalism of QM says.

Its simple - so simple many don't get it. It took me a while to get it - but that's just because its in plain sight and you gloss over the obvious.

The formalism is a theory about observations that occur in a common-sense classical world. Whats going on when not observed - momentum transfer yada yada yada the theory is silent on.

1. QM certainly takes care about momentum transfer, otherwise it would fail to correctly predict the experimental results. We know that the electron acquires momentum when passing through the slits (otherwise instead of an interference pattern you would get a point, just like in the case no barrier is present between the source and screen). We also know that momentum conservation is obeyed in QM. Nothing stops you from using a microscopic description of the barrier, write down the Hamiltonian (which would include in this case explicitly the interaction between the electron and the charged particles in the barrier) and calculate the probabilities of finding the electron in different points on the screen. It might take you some time and processing power, but in principle it could be done.

2. Even if QM does not explicitly describe what the electron does at the slits you can still use logical inference. No barrier - you get a point. A barrier with a slit - diffraction pattern. A barrier with two slits - interference pattern. A barrier with no slit - nothing. What explanation do you have for this if the electron does not interact with the material of the barrier?

This raises the legit issue of QM - the issue ignored by Einstein and Bohr which is why they both have issues (I won't say wrong - its simply a blemish that's best fixed - Weinberg is a bit more prosaic). How does a theory that assumes a classical world from the start explain that world. Great progress has been made in fixing that up, but some problems remain. What those issues are (the factorization problem, key theorems elucidating the problem, and other key theorems associated with decoherence - there are others as well) are (at least in part) detailed here:
https://www.amazon.com/Understanding-Quantum-Mechanics-Roland-Omnès/dp/0691004358

[URL='https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20[/URL]

I have red this book. It is good, but I disagree with the authors on some key points (entanglement). I don't find the consistent histories approach particularly appealing.

 

[Karolus]

Only in collapse interpretations. In no collapse interpretations (the MWI, for example), it doesn't.

In 'many-worlds interpretation of Hugh Everett, (MWI) it is assumed that as, for example, when the electron is detected, its wave function continues its evolution in another universe. In other words, many universes exist (infinite ??) where the wave function evolves in every universe according to one of its possible eigenstates ... As interpretation (as high-quality scientific) seems rather philosophical ...

 

[entropy1]

No, they're not, because "detection" is interpretation-independent:

Only in collapse interpretations. In no collapse interpretations (the MWI, for example), it doesn't.

That cannot be right... It sounds as if you are saying that we cannot make a position measurement if there is no collapse. But we already know that quantum mechanics works just fine, for measurements of position as well as everything else, without introducing the concept of collapse.

If an observable has eigenstates A and B, then, by measuring, we observe (detect) either A or B. You can omit the concept of 'collapse', but each 'world' in MWI yields a single eigenvalue. Each world of MWI is compatible with collapse, though all the worlds together (in MWI) don't need it. The real world must match QM (the formalism), and therefore in every 'world' the collapse interpretation is valid, just as well as the other valid interpretations. A detection selects an eigenvalue and thus collapse is valid. That is what I ment.

 

[PeterDonis]

In 'many-worlds interpretation of Hugh Everett, (MWI) it is assumed that as, for example, when the electron is detected, its wave function continues its evolution in another universe.

No, that's not what MWI actually says. It says that when an electron is detected, the wave function of the electron becomes entangled with the wave function of the measuring device, so that both of them split into "pieces", one for each possible measurement result. For example, if we measure the electron's spin, there are two possible results, which we'll call "up" and "down", so the wave function evolution looks like

$$
\vert e \rangle \vert M \rangle \rightarrow a \vert \uparrow \rangle \vert U \rangle + b \vert \downarrow \rangle \vert D \rangle
$$

where $e$ and $M$ are the starting states of the electron and the measuring device, $\uparrow$ is the "up" state of the electron, $U$ is the "measured electron up" state of the measuring device, $\downarrow$ is the "down" state of the electron, $D$ is the "measured electron down" state of the measuring device, and $a$ and $b$ are complex coefficients whose specific values will depend on the details of the state $e$.

Notice that there is nothing here about "other universes" or "other worlds"; there is just one wave function, which happens to have two terms after the measurement (and even that is dependent on the choice of basis that we made). Calling each term a different "world" is a sort of interpretation on top of an interpretation, so to speak; you can use the MWI without ever having to think of the different terms that way.

Each world of MWI is compatible with collapse

If by "collapse" you mean "picking out one term of the wave function and ignoring all the others, even though they're still there", yes, this is true. But the usual meaning of "collapse" is "all terms but one in the wave function actually disappear". That is why it's confusing to use the word "collapse" in a context where no particular interpretation is required.

 

[entropy1]

That is why it's confusing to use the word "collapse" in a context where no particular interpretation is required.

Then, how should I call it according to you? To me a measurement is still the selection of an eigenstate.

 

[PeterDonis]

how should I call it according to you?

"Detection". That's the word you used earlier.

To me a measurement is still the selection of an eigenstate.

Not in the MWI. In the MWI all possible measurement results occur.

 

[bhobba]

1. QM certainly takes care about momentum transfer, otherwise it would fail to correctly predict the experimental results..

You are falling into the trap.

All QM predicts is the outcome of observations. Whats going on when not observing its silent on.

Yes an electron going through an electric field will gain or loose momentum WHEN OBSERVED. Whats going on while in the field - who knows.

But gaining momentum when going through slits - can't follow that one. It changes direction when observed - but KE is unchanged hence the absolute value of momentum doesn't change - only direction when observed. When there are two slits you apply the principle of superposition which leads to the interference pattern - but again KE is not changed - momentum direction - yes but in a more complicated way due to the superposition.

As I said its so easy and in plain sight you ignore it. You must force yourself to NOT do that. That's all there is to it really. At all times remember - without an observation QM says nothing other than the probability of an observation if you were to do it. Now exactly how does an observation 'work'. Even defining in purely QM terms what an observation is. Start a new thread if you want to discuss that - but decoherence has shed a lot of light on it.

Thanks
Bill

 

[ueit]

You are falling into the trap.

All QM predicts is the outcome of observations. Whats going on when not observing its silent on.

Yes, but the electron is observed at the screen.

Yes an electron going through an electric field will gain or loose momentum WHEN OBSERVED. Whats going on while in the field - who knows.

Again, we are speaking about electrons that are observed.

But gaining momentum when going through slits - can't follow that one. It changes direction when observed - but KE is unchanged hence the absolute value of momentum doesn't change - only direction when observed.

Let's say the electrons coming from the source travel along Z axis, which is perpendicular on the barrier. Let's say that X is the axis connecting the slits in the plane of the barrier.

The initial momentum on X is 0, right?

When the electrons are observed they are found at some distance from the original direction, therefore they acquired some momentum on X, say mx.

So, the momentum on X has changed and momentum conservation requires that some other particle/particles acquired a momentum -mx.

When there are two slits you apply the principle of superposition which leads to the interference pattern - but again KE is not changed - momentum direction - yes but in a more complicated way due to the superposition.

It seems to me that you have a wrong idea about the momentum conservation law. Momentum is conserved as a vector. If the direction is changed, the momentum is changed. Momentum conservation requires that the total momentum on each of the three axis (X, Y and Z) remains constant. If the particle started with 0 momentum on X and ended with a non-0 momentum on X it means that some other particles acquired an opposite momentum on X.

The superposition principle cannot be a cause for the change in momentum. The cause can only be some interaction with other particles.

Andrei

 

[DrChinese]

The initial momentum on X is 0, right?

That's not correct in any particular case, as the momentum is undefined (poorly defined) in X. If it were well-defined, there would be no interference pattern building up.

 

[ueit]

That's not correct in any particular case, as the momentum is undefined (poorly defined) in X. If it were well-defined, there would be no interference pattern building up.

Interference or not, one can always determine the mean speed of the particles on any axis by dividing the distance traveled over the time taken from the emission to detection. If there is nothing between the source and screen the distance traveled on X is 0 (almost). If there is a barrier with slits you can get 0 for the central maximum but for the other fringes you will get a non-0 value.

Andrei

 

[DrChinese]

Interference or not, one can always determine the mean speed of the particles on any axis by dividing the distance traveled over the time taken from the emission to detection. If there is nothing between the source and screen the distance traveled on X is 0 (almost).

One can imagine there is something that can be calculated and labeled mean speed. But it is meaningless (no pun intended) because you still don't know where it went or what it was doing in the meantime (no pun intended here either).

Obviously uncertainty is a substantial issue as well. Making it difficult to comment about momentum in a particular direction.

 

[ueit]

One can imagine there is something that can be calculated and labeled mean speed. But it is meaningless (no pun intended) because you still don't know where it went or what it was doing in the meantime (no pun intended here either).

Obviously uncertainty is a substantial issue as well. Making it difficult to comment about momentum in a particular direction.

It does not matter what the particles are doing "in meantime". You just cannot measure a violation of momentum conservation. Think in this way:

1. The initial momentum of the particles on X (before the arrival at the slits) can be made arbitrarily small by placing the source very far away. Do you agree with this?
2. The final momentum of the particles on X has some value, proportional with the distance between the center and the last visible fringes. It cannot be arbitrarily small because in that case you would see one dot, not an interference pattern.

You can measure very accurately the time of emission, the time of detection, the position of the slits and the position of the dots on the screen. The only unknown is the time when the particle arrives at the slits, but that could also be determined by comparing the time of flight with and without the barrier in place. This gives you everything you need to determine both the initial and final momentum with any accuracy you want.

So, if you claim that momentum does not change at the slits it means that you have observed a violation of momentum conservation.

 

[DrChinese]

It does not matter what the particles are doing "in meantime". You just cannot measure a violation of momentum conservation. Think in this way:

1. The initial momentum of the particles on X (before the arrival at the slits) can be made arbitrarily small by placing the source very far away. Do you agree with this?
2. The final momentum of the particles on X has some value, proportional with the distance between the center and the last visible fringes. It cannot be arbitrarily small because in that case you would see one dot, not an interference pattern.

You can measure very accurately the time of emission, the time of detection, the position of the slits and the position of the dots on the screen. The only unknown is the time when the particle arrives at the slits, but that could also be determined by comparing the time of flight with and without the barrier in place. This gives you everything you need to determine both the initial and final momentum with any accuracy you want.

So, if you claim that momentum does not change at the slits it means that you have observed a violation of momentum conservation.

I never said you could measure a violation of momentum conservation. But I certainly reject the idea the particle is flying in a straight line like a little billiard ball, because we would see no interference if that were the case. How momentum might vary when we are not watching is unknown.

On the other hand, you cannot measure the initial position accurately AND expect to know much about initial momentum. Ditto with ending q and p.

 

[Ostrados]

It does not matter what the particles are doing "in meantime". You just cannot measure a violation of momentum conservation. Think in this way:

1. The initial momentum of the particles on X (before the arrival at the slits) can be made arbitrarily small by placing the source very far away. Do you agree with this?
2. The final momentum of the particles on X has some value, proportional with the distance between the center and the last visible fringes. It cannot be arbitrarily small because in that case you would see one dot, not an interference pattern.

You can measure very accurately the time of emission, the time of detection, the position of the slits and the position of the dots on the screen. The only unknown is the time when the particle arrives at the slits, but that could also be determined by comparing the time of flight with and without the barrier in place. This gives you everything you need to determine both the initial and final momentum with any accuracy you want.

So, if you claim that momentum does not change at the slits it means that you have observed a violation of momentum conservation.

Initial momentum is unknown and it is not 0 at x=0 how did you assume that?! And you can't know if it is small either.

You are thinking about particles as projectiles, as if they are billiard balls. Photon for example can never be standing still by have 0 momentum at x=0.

 

[ueit]

Initial momentum is unknown and it is not 0 at x=0 how did you assume that?! And you can't know if it is small either.

You are thinking about particles as projectiles, as if they are billiard balls. Photon for example can never be standing still by have 0 momentum at x=0.

I have defined X axis to be in the plane of the barrier, perpendicular on the direction of propagation of photons. The photons are not standing still but virtually all of their momentum is on Z.

All particles that arrive to the slits will have, by design, almost 0 momentum in the plane of the slits if the source is far away (the Sun for example). The distance traveled by the photons in 8 minutes is at most one half the distance between the slits, witch should be of the order of mm or smaller.

I am not assuming the particles are billiard balls, in fact I see this assumption as the most important misconception (unfortunately shared by Feynman himself) that stands against a logical understanding of this experiment. However, momentum in QM is still measured by repeated position measurements. This is how momentum is determined in particle accelerators. In our case the first position is given by the location of the source, and the second by the location of the slits.

Andrei

 

[ueit]

I never said you could measure a violation of momentum conservation. But I certainly reject the idea the particle is flying in a straight line like a little billiard ball, because we would see no interference if that were the case. How momentum might vary when we are not watching is unknown.

On the other hand, you cannot measure the initial position accurately AND expect to know much about initial momentum. Ditto with ending q and p.

You seem to imply that uncertainty principle does not let you know the position and momentum at the same time. This is a common misconception Heisenberg himself tried to fight. By performing a position measurement on a particle in a momentum eigenstate you can find out both position and momentum the particle had at the moment of measurement. The catch is that, following the position measurement, the momentum changed and you cannot predict its path.

Andrei

 

[DrChinese]

You seem to imply that uncertainty principle does not let you know the position and momentum at the same time. This is a common misconception Heisenberg himself tried to fight. By performing a position measurement on a particle in a momentum eigenstate you can find out both position and momentum the particle had at the moment of measurement. The catch is that, following the position measurement, the momentum changed and you cannot predict its path.

That interpretation of events would not be shared by everyone. I would say it could have a well defined momentum eigenstate at T=0 and a well defined position at T=1. But I would not agree it was in known p and q eigenstates at the same T=1, nor at any point in time.

 

[PeterDonis]

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