Why aren't state-reduction theories refuted by diffraction experiments

[James MC]

Spontaneous collapse theories like GRW postulate that elementary particles have a 10 to the -16 probability per second for spontaneously collapsing in the position basis, where the collapse function involves multiplication by a Gaussian. Entanglement then guarantees that macroscopic objects are effectively always collapsed. Measurement problem solved.

But hold on: consider the double-slit experiment: the electron to be fired at the slits is forever entangled with the continually collapsing electron gun! So shouldn't the shot-out electron be constantly collapsing as it travels towards the slits? But then GRW entails that there can never be interference patterns!

Okay there must be some simple solution to this. Here's my attempt at a solution, do let me know your thoughts...

The electron gun (g) is itself in a superposition since its components are all Gaussians. So simplify the gun superposition to just two of its high amplitude components (i.e. two distinct points where its Gaussian peaks):

#|x1-x100>g + #|x2-x100>g

which means that the gun is in a position superposition of two x-axis ranges.

Now separate out the electron it's about to fire:

#|x1-x100>g|x100>e + #|x2-x101>g|x101>e

...so that the electron is in a superposition of being at 100 and 101 (on the x-axis), and is entangled with the gun.

Okay now the gun fires:

(#|x1-x100>g(#|x100>e + #|x101>e)) + (#|x2-x101>g(#|x101>e + #|x102>e))

Boom!

(#|x1-x100>g(#|x100>e + #|x101>e + #|x102>e)) + (#|x2-x101>g(#|x101>e + #|x102>e + #|x103>e))

Just look at that electron wave function spread as if it wasn't entangled with the gun!

And because the two slits are at x104, the electron can go through them both...

#|x1-x100>g|x104>e + #|x2-x101>g|x105>e

But then start spreading out again, interfere, then collapse somewhere on the screen.

I think that must be how it works?

 

[Jazzdude]

There's not really a reason to assume that the gun is entangled with the beam in the first place. It's much more like |gun>|beam> and the beam part evolves in the experiment independently. It then only gets entangled with the detector (i.e. the single atoms in the screen).

Cheers,

Jazz

 

[James MC]

There's not really a reason to assume that the gun is entangled with the beam in the first place. It's much more like |gun>|beam> and the beam part evolves in the experiment independently. It then only gets entangled with the detector (i.e. the single atoms in the screen).

The beam and the gun are entangled simply because they interact.

 

[StevieTNZ]

If your scenario is indeed the case (the electron gun and electrons are entangled), then no interference pattern would be seen. However, an interference pattern appears. Because of this, what you say is refuted.

This is because the electron gun provides us with no which way information on what slit the electron took.

 

[James MC]

If your scenario is indeed the case (the electron gun and electrons are entangled), then no interference pattern would be seen. However, an interference pattern appears. Because of this, what you say is refuted.

Do you have an argument for this claim? In the original post, I suggested how an interference pattern would be seen despite the entanglement!

This is because the electron gun provides us with no which way information on what slit the electron took.

How does this answer the question about state reduction theories? If the electron gun collapses the electron beam then the electrons won't be in a (roughly equal) superposition of going through both slits in the first place. The question is how state reduction theories deal with this.

 

[StevieTNZ]

All I can say is, I know what I want to say. Its putting it into words that make sense to everyone so they understand exactly what I'm saying.

I think you've framed state reduction theories in the wrong experiment to see if they're valid or not.

 

[James MC]

All I can say is, I know what I want to say. Its putting it into words that make sense to everyone so they understand exactly what I'm saying.

I think you've framed state reduction theories in the wrong experiment to see if they're valid or not.

The question I've asked is neither grossly technical nor obscurely philosophical, it is a straightforward question about how spontaneous collapse theories that entail continued gun/beam entanglement explain interference patterns. I think I gave the correct answer in the first post but am interested to see if others agree. Please don't continue commenting here unless you are willing to provide constructive feedback.

 

[Jazzdude]

The question I've asked is neither grossly technical nor obscurely philosophical, it is a straightforward question about how spontaneous collapse theories that entail continued gun/beam entanglement explain interference patterns. I think I gave the correct answer in the first post but am interested to see if others agree. Please don't continue commenting here unless you are willing to provide constructive feedback.

I think you are greatly mistaken. The feedback you got was very constructive. Your exposition however was cryptic, uses notation that is not explained and in general does not contain any rigorous argument, at least none I can see. You main step isn't even motivated in any way.

Cheers,

Jazz

 

[James MC]

I think you are greatly mistaken. The feedback you got was very constructive. Your exposition however was cryptic, uses notation that is not explained and in general does not contain any rigorous argument, at least none I can see. You main step isn't even motivated in any way.

Cheers,

Jazz

I expected responders to at least have some knowledge of state reduction theories (which entail that the electron and the gun are forever entangled but become less and less correlated post emission). If one finds something cryptic or unsupported one only needs to ask about it.

 

[StevieTNZ]

I'll give this answer a go:

I gather that by now, someone would have realized that if we see the interference pattern as predicted by QM, and this was in violation of predictions of state reduction theories, then this would be known - those theories would be thrown out the window.

My guess is your calculation/scheme is not accurate or appropriate to model and test the validity of such theories.

 

[James MC]

Thanks but I've now run the issue past a physicist. The feedback was that my proposed solution in my original post is the correct solution to this problem for state reduction theorists, and that what's confused other posters is probably the unexplained use of '#' for amplitudes and x1-x100 for position range.

 

[StevieTNZ]

Which physicist did you run your calculation by? If indeed you say your calculation is correct, then it has profound implications for how to solve the measurement problem.

 

[James MC]

http://arxiv.org/abs/1007.2906

Why do you think it has profound implications for the measurement problem? I didn't think any physicist took seriously the idea of position eigenstates (due to momentum incompatibility), I thought it was standard to think of Jazzdude's |gun>|beam> example as unphysical? The solution is then just that the electron disperses in each component of the gun superposition. My (admittedly non-standard) formalism above was only an attempt to make that idea more precise.

 

[StevieTNZ]

Either your example is correct (which you say it is), and predicts something other than QM.
If so, and QM predictions are found, state reduction theories are no longer tenable.

This reduces what we can turn to, to solve the measurement problem.

 

[James MC]

"And predicts something other than QM"? Please can you put more detail into your posts, otherwise I can't evaluate them!
What does "QM" predict? Are you saying it predicts collapses to position eigenstates? In that case "QM" was refuted long ago (when we realized the implication collapse to position eigenstates has for momentum i.e. experimentally disconfirmed violations of energy conservation).

 

[StevieTNZ]

By QM prediction I mean the interference pattern found. QM predicts that.

 

[James MC]

Yes. So do state reduction theories. By the method I describe in the original post.

 

[meBigGuy]

"So shouldn't the shot-out electron be constantly collapsing as it travels towards the slits? But then GRW entails that there can never be interference patterns!"

I think that assumption is broken. There cannot be interference patterns if the "particles" are not in the same state when they "combine" after the two slits. Nothing about the gun/particle entanglement make the particle states different after the 2 slits.

The particle is only collapsing to the extent it is entangled with the gun.

 

[StevieTNZ]

I guess I got confused by the title of this thread: "Why aren't state-reduction theories refuted by diffraction experiments" as if its a question, when really your OP is about how state reduction theories deal with the interference pattern.

Maybe the title "Why state-reduction theories aren't refuted by diffraction experiments" would be have been more appropriate.