A thought experiment of wavefunction collapse

[backward]

I propose a simple thpught experiment;
A scientist A measure the spin of an electron and finds it "up". After that he removes all evidence of his experiment and goes away, only to die in a road accident.
Another scientist, obviously unaware of the experiment done by A come and measures the spin of the same electron. Will B find the spin necessarily "up" or he will measure just any value "up" or "dpwn" with equal probability?
If the wave function collapsed by A is an objective reality, B should also measure the same value of the spin (up). Otherwise the experiment of B will be unaffected by the experiment of A, because he does not know anything about it.
Will anybody please enlighten me?

 

[DrChinese]

I hope we don't kill any scientists trying to find out!

The result for B will be as expected. There are special cases in which you can "erase" results, but this is not one of those.

 

[Charles Wilson]

The result for B will be as expected. There are special cases in which you can "erase" results, but this is not one of those.

Ummm...I not so sure, Dr. Chinese. There's a lot of information we may need in order to perform that 2nd measurement and I'm not sure it matters.
If I measure "the" electron a 2nd time, I should get a 50/50 Up or Down measurement result. There is no entanglement between the electron and any other particle that we could find. The entanglement between the electron and a posited first magnet "particle" is lost in the cross entanglements of the first magnet to the tune of 10^(Humongous) since the electron was first measured. The 2nd measurement "just" gives us a measurement: 50/50 Up or Down. If the particle is entangled now with something in the 2nd magnet, we have no way of retrieving that information either.
If we knew the 2nd measurement would give an up reading: Nobel Prize for Dr. Chinese!

CW

 

[DrChinese]

If I measure "the" electron a 2nd time, I should get a 50/50 Up or Down measurement result...

Oops, misread the post, thought we were talking about an entangled pair (I guess my mind is perpetually entangled).

In the OP case, it would depend on the nature of the first measurement. Clearly, a suitable spin observation finding "up" will put the electron in an up state, and subsequent observations will show the same thing regardless of what happens to observer A (assuming no further action to the electron). That assumes a few things about what is "suitable" but you get the idea.

 

[DEvens]

I propose a simple thpught experiment;
A scientist A measure the spin of an electron and finds it "up". After that he removes all evidence of his experiment and goes away, only to die in a road accident.
Another scientist, obviously unaware of the experiment done by A come and measures the spin of the same electron. Will B find the spin necessarily "up" or he will measure just any value "up" or "dpwn" with equal probability?
If the wave function collapsed by A is an objective reality, B should also measure the same value of the spin (up). Otherwise the experiment of B will be unaffected by the experiment of A, because he does not know anything about it.
Will anybody please enlighten me?

It depends on what you mean by "removes all evidence."

Consider: You put an electron through a spin-direction-measuring device, and it indicates "up." Then you immediately put it through a similar device. It will also indicate "up." If you then put the electron, immediately and with no other intervening interaction, through bunches of similar devices, one after another, they will all indicate "up."

An experiment has been done to this effect. If you keep banging away measuring a particular quantum state, then the first measurement is random. But every one after that is the same as the first one.

Alternatively consider: If you measure it as "up" but then let it interact with something else. Say you bounce it off a crystal with lots of electrons all at thermal energies, that is, room temperature. Say a quartz crystal. Then the spin state of the electron will not be predictable. Then it will be 50-50 up or down. Again this is experimentally verified.

So if the first guy measures it and nothing happens to it after the measurement, the second guy will measure it the same. If anything happens between the two, then it (probably) isn't predictable.
Dan

 

[mfb]

There is no way to "remove all evidence" if a human saw it. Evidence is not just something written down on paper (or a computer). It involves all the atoms in the human, the measurement device, and anything which interacted with it or the human. In other words, you get decoherence quickly.

 

[lugita15]

Here's an old post of mine that I think is relevant here:

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.

So for the OP's question, the issue is whether the measurement device really measures the spin, or whether the pointer state of measurement device simply gets entangled with the spin state of the particle. And that's largely an interpretational matter. If the former, then destroying the measurement device and any records it has made will do absolutely nothing. If the latter, then complete destruction of the device, the human who recorded it, etc., would in principle be able to reverse the effective collapse. But it would be thoroughly impractical, since as mfb noted, the decoherence time for a process involving a human being would presumably be absurdly small, so the energy required to do it in any reasonable time scale would be cosmically large.

 

[backward]

A thought experiment of wavefunction collapse

"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."

Wonderful. This has really clarified my thoughts a lot. Thanks.
As a matter of fact it was always an underlying assumption in my thought experiment that there is no decoherence during the two experiments, in which case, the result of B's experiment is "up" necessarily. The interesting point is that since B does not know anything about A's experiment, he just takes the "up" result as a random result. Of course, if he knew about A's experiment, he would expect it to be "up".
However, I am unable to visualize, as a layman, how the decoherence resulting from a measurement manifests itself as wavefunction collapse in the sense that a wavefunction composed of several pure states in the form
A*Q(1)+B*Q(2)+C*Q(3)...collapses to just Q(1), Q(2) or Q(3) with a probaility proportional to A^2, B^2 or C^
Is there a simple way to understand this without recourse to formal Mathematics? Could someone please enlighten me?

 

[bhobba]

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.

Easy - after decoherence converts it from a superposition to an improper mixed state. The question should be - why complicate your life and place it elsewhere?

A lot of water has passed under the bridge since Von Neumann did his famous analysis showing it could be placed anywhere up to and including the brain of the observer - in particular we know a lot more about decoherence. This shows the obvious and natural place to put it. Wigner, who was one of the high priests of consciousness causes collapse, when he heard of some of the early work of Zurek immediately recognized it was not required and abandoned it. I suspect he asked exactly the question - why complicate your life - immediately after decoherence is the obvious place to put the cut.

My answer to the original question, leaving aside the obvious logistics of it such as you would need to measure it immediately after the first measurement, which of course is no where near enough time for the shenanigans of dying etc to occur and the electron to remain in the laboratory, as well as matters of principle that MFB correctly noted (ie since the measuring device is entangled with the particle how you remove it without affecting the particle it is entangled with, doesn't really make sense), it will and must give up. But that is totally independent of any interpretation since it follows from the QM formalism alone.

Thanks
Bill

 

[Dr. Poounyu]

So basically, what you are asking is, if a wavefunction collapses and no one is alive to tell about it, will it bother to be collapsed? Hmm... Of course it will. Why? To a wavefunction, a human is just a large aggregate of atoms and could not care about its stupid human intentions or forgetfulness or attempt of concealment. The human observer is part of that experiment, his or her presence a contributing effector of outcome. To believe otherwise, is like like saying "Grandma has turned on the light switch to the attic light, which burned out a long time ago. But she's got Alzheimers and cannot remember turning it to the on position. If I go upstairs and put in a new light bulb, either I will see if grandma turn on the light or if I find it not turning on, conclude she never turned on the switch..." But maybe grandma threw the switch again when you were going upstairs to the attic, or maybe your light bulb is also defective. Or maybe a raccoon got in and chewed the wire to the the switch. What really is at heart of this matter is if Grandma did something, and she did: she interacted with the switch by throwing it. You not being able to find evidence for that, doesn't alter that fact, even if Grandma cannot remember.

Now... If a frog in a tropical rain forest farts and no thing is around to chemically detect it, will the gaseous flatulence cease to obey the laws of diffusion? Of course not.

Next stupid question!