Understanding Quantum Mechanics: The Puzzle of Cutting a Pencil in MWI

[oquen]

once measurement occurs.. we are supposed to be trapped in the MWI branches.. isn't it daily objects are all in one branch (equivalent to collapse in Copenhagen).. but here's something puzzling.. when we we break a pencil.. why does it get broken? the pencil is already in one branch.. does cutting it means getting more MWI branches in our branch (you change the quantum state of the pencil)? Or is cutting a pencil means re-preparing the original the branch or quantum state?

 

[PeterDonis]

when we we break a pencil.. why does it get broken?

Because a force was exerted on it.

the pencil is already in one branch.. does cutting it means getting more MWI branches in our branch (you change the quantum state of the pencil)?

Only if there is some quantum uncertainty about how the pencil got broken. If there is, then there will be a new branch for each of the different quantum ways that the pencil could break.

 

[oquen]

Because a force was exerted on it.
Only if there is some quantum uncertainty about how the pencil got broken. If there is, then there will be a new branch for each of the different quantum ways that the pencil could break.

There is something confusing I hope you can clear up once and for all. Atyy wrote that "After wave function collapse, the time evolution of the wave function is again deterministic and governed by the Hamiltonian via the Schoredinger equation. So if you change the Hamiltonian, you will affect the evolution.". The counterpart of wave function collapse is each MWI branch. But is it not like Atyy saying that even after the MWI branch has formed, it can unform? This confused me for 2 weeks already so hope you can address this exactly now. Thanks in advance!

 

[PeterDonis]

The counterpart of wave function collapse is each MWI branch.

No, it isn't. There is no "counterpart of wave function collapse" in MWI. In the MWI, the wave function always evolves deterministically, governed by the Hamiltonian using the Schrödinger equation; it never stops doing so. Whereas in a collapse interpretation, each time a collapse happens the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again.

is it not like Atyy saying that even after the MWI branch has formed, it can unform?

No.

 

[oquen]

No, it isn't. There is no "counterpart of wave function collapse" in MWI. In the MWI, the wave function always evolves deterministically, governed by the Hamiltonian using the Schrödinger equation; it never stops doing so. Whereas in a collapse interpretation, each time a collapse happens the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again.
No.

But didn't Bohr say that whenever there was collapse, the wave function just stop being wave function? Where did Bohr say that "collapse happens when the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again".. Bohr didn't say it would start evolving again, did he?

 

[PeterDonis]

didn't Bohr say that whenever there was collapse, the wave function just stop being wave function?

No.

Where did Bohr say that "collapse happens when the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again"..

That's what "wavefunction collapse" means. It doesn't mean the wave function collapses and never evolves again. That wouldn't make sense; the system doesn't just stop evolving after a measurement.

 

[oquen]

Because a force was exerted on it.
Only if there is some quantum uncertainty about how the pencil got broken. If there is, then there will be a new branch for each of the different quantum ways that the pencil could break.

If there is some quantum uncertainty about how the pencil got broken...

in MWI, there will be a new branch
in Collapse interpretation, there will be collapse, right? If not what is the version of new branch in Collapse interpretation?

If it's collapse, then I'm right that the counterpart of wave function collapse is each MWI branch.

Maybe it's just a semantic matter. What term do you use instead of the word "counterpart" or the equivalent term to describe that if there is some quantum uncertainty about how the pencil got broken. either branching occurs in MWI or collapse occurs? I'd like the right words to use so next time i won't use a vague word "counterpart. And I'm fully aware what you said below that

In the MWI, the wave function always evolves deterministically, governed by the Hamiltonian using the Schrödinger equation; it never stops doing so. Whereas in a collapse interpretation, each time a collapse happens the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again.

 

[PeterDonis]

in MWI, there will be a new branch

In MWI, there will be one branch for each different quantum way the pencil will break. There is no "new" vs. "old" branch; none of the branches are "the same branch" as the one that existed before the pencil broke.

in Collapse interpretation, there will be collapse, right?

Yes, the pencil's wave function will collapse onto one of the possible quantum states corresponding to the different ways it could break. (This is assuming that the break counts as a "measurement", which should not be too problematic.)

If it's collapse, then I'm right that the counterpart of wave function collapse is each MWI branch.

I don't think so, but then I don't understand what you mean by "counterpart".

What term do you use instead of the word "counterpart" or the equivalent term to describe that if there is some quantum uncertainty about how the pencil got broken. either branching occurs in MWI or collapse occurs?

There isn't one. Both of these are interpretations, not different theories of physics. They are different ways of describing the quantum math; they are not different ways the world could be. At least, that's how it is at our current state of knowledge.

If we someday come up with a more fundamental theory to which our current QM is an approximation, it might tell us something different, but that something different might not be any of our current interpretations.

 

[oquen]

No, it isn't. There is no "counterpart of wave function collapse" in MWI. In the MWI, the wave function always evolves deterministically, governed by the Hamiltonian using the Schrödinger equation; it never stops doing so. Whereas in a collapse interpretation, each time a collapse happens the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again.
No.

Oh we forgot something. There is some problem with these lines wherein you said "Whereas in a collapse interpretation, each time a collapse happens the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again."

Before collapse, wave function is just wave function in Hilbert space, there is no electron yet... then when Bohr rule is applied, suddenly, the electron appears... but how can it "starts evolving deterministically again"... you are like saying the electron disappears again and back to pure wave function (the same one prior to collapse)?

In the double slit. After the electron is detected in the detector, its not possible to uncollapse it because it is a destructive setup where the electron is destroyed. But can you show another experiment where after the electron appears (the jumps randomly part), then when it starts to evolve deterministically again.. it vanishes back into the world of Hilbert space? I only know the following. When you measure the position of electron, it is there.. but when you shift and measure the momentum of the electron, then the position basis disappears, and momentum basis come out (so called measurement of non-commuting variables). But is there another where you didn't put it in any basis so it doesn't show any basis (in other world existing as pure ray in Hilbert space) or the "then starts evolving deterministically again.". Remember in summary:

before collapse.. wave function evolves deterministically in Hilbert space.. no particle exists
after born rule or collapse, electron suddenly appears
if it starts evolving deterministically again.. it uncollapses?? so electron vanishes again and what you have is wave function again??

 

[PeterDonis]

Before collapse, wave function is just wave function in Hilbert space, there is no electron yet

This is not correct. The electron is the wave function--more precisely, the wave function describes the state of the electron. You appear to have gotten a lot of misunderstandings by reading pop science sources about QM. You really, really need to spend some time with a good QM textbook.

you are like saying the electron disappears again and back to pure wave function

No, I'm saying your understanding of how QM works is incorrect. See above.

(the same one prior to collapse)?

No. The wave function that starts evolving deterministically again after the collapse is not the same as the wave function that evolved deterministically to the state just before collapse.

After the electron is detected in the detector, its not possible to uncollapse it because it is a destructive setup where the electron is destroyed.

No, it's not possible to uncollapse it because it has interacted with a huge macroscopic object and its state has decohered. The electron doesn't get destroyed in the detector.

can you show another experiment where after the electron appears (the jumps randomly part), then when it starts to evolve deterministically again

Sure, an example is a spin measurement. If the electron is in a superposition of spin eigenstates going into the measuring device, then (on the collapse interpretation), the measurement collapses its wave function onto one of the two spin eigenstates. But then the electron comes out of the measuring device and its wave function starts evolving deterministically again.

 

[Jilang]

But then the electron comes out of the measuring device and its wave function starts evolving deterministically again.

By remaining in the eigenstate?

 

[PeterDonis]

By remaining in the eigenstate?

In this case the spin part does, yes. But the position part, for example, will not. So there is still time evolution going on.

 

[oquen]

No, it's not possible to uncollapse it because it has interacted with a huge macroscopic object and its state has decohered. The electron doesn't get destroyed in the detector.

I'd like to know the context of your definition of "uncollapse".
Let's review and be accurate in the terms used:

Collapse = "In collapse interpretation, each time a collapse happens the wave function momentarily stops evolving deterministically and jumps randomly, then starts evolving deterministically again." (you said)

Uncollapse = what do you mean by "uncollapse" when you mentioned " it's not possible to uncollapse it because it has interacted with a huge macroscopic object and its state has decohered. The electron doesn't get destroyed in the detector."

Did you mean by uncollapse as the wave function not evolving deterministically again? So the wave function can't evolve deterministically when "it has interacted with a huge macroscopic object and its state has decohered"??

or did you mean uncollapse as system or double slit experiment not able to be in coherence again?

I know coherence in a system is not same meaning as wave function evolving deterministically. Right?

 

[PeterDonis]

I'd like to know the context of your definition of "uncollapse".

It was your word originally. I assumed that what you meant by it was something like "restore the wave function to what it was before the measurement".

 

[PeterDonis]

coherence in a system is not same meaning as wave function evolving deterministically. Right?

I don't know because I don't know what you mean by "coherence".

 

[oquen]

I don't know because I don't know what you mean by "coherence".

coherence means there is interference in the phase like in double slits.. phase which decoherence descrambles.. I am getting everything you said now when you mentionted "No, it's not possible to uncollapse it because it has interacted with a huge macroscopic object and its state has decohered."

Prior to this thread. I thought when wave function collapses, it no longer evolves. This is why I have a hard time trying to visualize the classical world in quantum substrate. But now I could.

So let's take collapse interpretation.. when we see classical object like metal pin. It is not collapsed. But the wave function still evolves deterministically.. so we can imagine the metal pin with its different atoms and molecules wave function collapsing momentarily.. stops evolving deterministically and jumps randomly, then starts evolving deterministically again all in random as well as interacting with the environment... Right? All of this is in so called mixed state. And all this creates the decoherence.

I always wondered if decohered metal pin means it is collapsed.. so it is not. And if you confirm all the above.. then I have understood the basic.. and thank you!

 

[PeterDonis]

coherence means there is interference in the phase like in double slits..

Ok. This is actually a somewhat non-standard use of the term "coherence", but it will do for this discussion.

when we see classical object like metal pin. It is not collapsed.

Yes, it is. A classical object like a metal pin contains so many atoms and so many interactions that it is constantly decohering itself. So on the collapse interpretation, it is constantly collapsing itself (or "measuring itself" if you want to associate collapse with "measurement"). In other words, the deterministic wave function evolution using the Schrödinger equation that works well for describing a small quantum system like an electron simply doesn't work for describing a large classical object like a metal pin.

 

[oquen]

Ok. This is actually a somewhat non-standard use of the term "coherence", but it will do for this discussion.
Yes, it is. A classical object like a metal pin contains so many atoms and so many interactions that it is constantly decohering itself. So on the collapse interpretation, it is constantly collapsing itself (or "measuring itself" if you want to associate collapse with "measurement"). In other words, the deterministic wave function evolution using the Schrödinger equation that works well for describing a small quantum system like an electron simply doesn't work for describing a large classical object like a metal pin.

Before I make statements. I read as much in the physicsforums archive as possible But Nugatory said the following in one of the threads:

"When you see chairs and tables and other macroscopic objects, they are not "collapsed" - their state is a mixture that can only be described with a density matrix, and it is neither a pure state nor an eigenstate of any physically interesting operator.

The macroscopic object has an enormous number of internal degrees of freedom and therefore an enormous number of accessible states, and it moves at random among them. It just so happens that the overwhelming majority of those states are ones in which the object is located within a few atomic diameters of one position, so that's where we'll find it."

Guys. Peterdonis said classical object like metal pin is collapsed. Nugatory said classical object wasn't collapsed. So hope others to give the arguments and who is really right.

 

[PeterDonis]

Peterdonis said classical object like metal pin is collapsed. Nugatory said classical object wasn't collapsed.

You are taking both statements out of context. When taken in proper context, both Nugatory and I are saying the same thing.

In this thread you were asking if classical objects could be described by a wave function evolving deterministically or not--the latter corresponding to "collapsed". The answer is "not"--classical objects cannot be described by a wave function evolving deterministically. In fact they can't be described by a wave function at all; see below.

I haven't seen the thread from which you are quoting Nugatory--for future reference, whenever you presume to quote someone you should always give a link and use the PF quote feature--but I strongly suspect that in the context of that thread, "collapsed" meant "can be described by a wave function as if it had just been measured and is therefore in an eigenstate". In that context, a classical object is not collapsed, because it can't be described by a wave function as if it had just been measured and is therefore in an eigenstate--because, as Nugatory said, it can't be described by a wave function at all. It has to be described by a density matrix.

Why does a classical object have to be described by a density matrix? Because, as Nugatory said, it has an enormous number of states and moves at random among them. Or, to put it another way, it is constantly decohering itself--because moving at random between an enormous number of states just means the atoms in the object are constantly interacting with each other, decohering each other: which is what I said. In other words, Nugatory and I were just describing the same thing in different ways.

hope others to give the arguments and who is really right.

We are both right. You are confused not because our answers were inconsistent, but because you are using a bad conceptual framework to ask questions in the first place. You need to spend some serious time studying a QM textbook so you can develop a better conceptual framework. In the meantime, this discussion has gone on long enough and this thread is closed.