Question about Quantum mechanics

[randman]

I'm not sure what you're referring to.



The way that site defines "world" isn't quite the way I have been in this thread.

Obviously nothing can stop me from writing |psi> = |psi>/2+|psi>/2, or |psi>=(|chi>+|phi>)/root(2), or any one of an infinite number of other possible combinations of states that add up to |psi>. It's obviously not the case that "something goes wrong with the math" if I do so.

But as I've said several times, different terms in a superposition don't necessarily correspond to distinct "worlds" in the sense that they cannot interfere with each other. It's only when those terms correspond to states that will have extremely small interference with each other (to be a little more precise, when the Hamitonian has very small off-diagonal matrix elements in that basis) that we can say they are distinct worlds.

So when I say you should consider the initial state to be collection of worlds that later split off, that's a fine way to think about it, but you have to understand that prior to the split those worlds are really not distinct - they are just identical copies of each other and therefore can interfere (constructively in that case).

Ok, so there is a little bit of difference between the writer of that site and what you have said. The MWI as you are expressing it, you have identical "worlds" all together still until differentiated.

Arrgghh...but that still is somewhat unsatisfactory. In all the identical worlds, the photon goes from wave-like to particle-like when one measures the which-way path.

But what if the other world does not measure the which-way path?

All of the other identical worlds prior to the split would have to also measure the which-way path. The photon cannot exist as still wave-like once the which-way path is measured, right?

So the act of measurement seems to dictate a little or play a limiting factor on the choices that the identical people in the other universes can make.

That doesn't seem to be right.

As a thought experiment, say my counterpart is running the experiment and is not measuring the which-way path, but I do...... Actually just thinking of it splits the universe, I suppose....So thinking about running the experiment differently than the counterpart would cause a split in the universe?

Getting late....so MWI surmises that changes in information (interaction) cause new universes in the sense of the MWI splitting into different branches that can no longer interact.

I still think throwing out locality and causality is simpler...

 

[sol invictus]

In all the identical worlds, the photon goes from wave-like to particle-like when one measures the which-way path.

But what if the other world does not measure the which-way path?

Then it wasn't identical, so the question makes no sense.

So the act of measurement seems to dictate a little or play a limiting factor on the choices that the identical people in the other universes can make.

Nope.

Actually just thinking of it splits the universe, I suppose

It might cause a split of some kind, but it would have nothing to do with the characteristics of the particle. The particle is only affected if and when something interacts with it, such as a making measurement of its spin.

Getting late....so MWI surmises that changes in information (interaction) cause new universes in the sense of the MWI splitting into different branches that can no longer interact.

It's not the information that is relevant here, it's simply the physical interaction.

I still think throwing out locality and causality is simpler...

The page you linked to - which looks pretty good overall, by the way - has a nice rebuttal to that by analogy to the universe. As he points out, some medieval thinkers rejected the idea that stars are like the sun (rather than holes in a dome or the like) because they thought such a vast universe was too complicated.

 

[randman]

Ok, well at least then we've established that the particle can no longer be travelling in a wave-like manner in an alternate universe at that time. It does collapse into particle-like paths but via splitting universes. The thing is then, of course, the particle and everything else is now divided since what was identical is now not.

Still not getting this entirely. If a photon or electron is traveling in a wave-like pattern, but then we determine whether the which-way path so there is a splitting off, did the photon or electron travel in a wave-like pattern before we measured it or in a which-way path? MWI doesn't seem to solve the issue if you believe the particle had a definite state of either wave-like or particle-liek trajectory before the measurement.

 

[sol invictus]

Still not getting this entirely. If a photon or electron is traveling in a wave-like pattern, but then we determine whether the which-way path so there is a splitting off, did the photon or electron travel in a wave-like pattern before we measured it or in a which-way path? MWI doesn't seem to solve the issue if you believe the particle had a definite state of either wave-like or particle-liek trajectory before the measurement.

There's no issue to "solve". The wavefunction evolves in a specific way (which Vorpal illustrated a few post back, or see my post about the delayed choice quantum eraser) which fully characterizes everything.

The state of the world before the which-way measurement is

(|A>+|B>)*|0> = |A>*|0>+|B>*|0>

meaning that the photon is in a superposition of position eigenstates at locations A and B (the arms of the interferometer or the slits in the 2-slit experiment), and the detector is in neutral position 0 (it hasn't measured anything yet). Whether or not you regard those two terms as different "worlds" is a matter of taste - they do not differ in the state of any macroscopic object, so it's probably best not to think of them as distinct worlds, but it's really up to you where (and with respect to which eigenbasis) you want to draw the line.

After the measurement, the state is

|A>*|a>+|B>*|b>

meaning photon is at location A and detector has measured it to be at A plus photon is at location B and detector has measured it to be at B. Those are two clearly different "worlds", because the state of the detector - a macroscopic object - is different.

If you understand that notation, it should answer all the questions you've been asking. If not, you need to learn a little bit of the math to make any further progress on this.

 

[Perpetual Student]

Could anyone guide me to a source discussing the Lorentz invariance of quantum field theory?
BTW, I have now found several sources discussing the problems with Lorentz invariance of Bohmian mechanics. I does seem to be a serious flaw.

 

[sol invictus]

Could anyone guide me to a source discussing the Lorentz invariance of quantum field theory?
BTW, I have now found several sources discussing the problems with Lorentz invariance of Bohmian mechanics. I does seem to be a serious flaw.

Any book on particle physics or quantum field theory will go into at considerable length. They're mostly pretty technical, though.

 

[orange31]

Isn't the main problem with "understanding" Qm and non-locality the attempt to visualize it, as the only way we can visualize things (4 dimensions) cannot represent the math equations (which themselves are also a representation)?

People accept that if M theory is proven, then there will be 10 or 11 dimensions, 7 of them "invisible". But we still seem to want to visualize QM as a 4 dimensional opera and it doesn't seem feasible..?

 

[Dilb]

No. The philosophical issues of QM are still a problem even when you only look at 1 or 2 dimensions. It's actually fairly easy to pile on extra dimensions in quantum mechanics, at least as far as the problems in this thread are concerned.

 

[Perpetual Student]

Any book on particle physics or quantum field theory will go into at considerable length. They're mostly pretty technical, though.

Well, I've done a little investigation and have found that the issue is quite technical and considerably beyond me.

My understanding is this (using simple layman's terms): Quantum field theory regards particles as excitations of a field (each type fundamental particle (elecron, quark, etc.) existing as the result of a particular field. The mathematics of Lorentz invariance then describes the required transformations as these excitations/particles move through space-time that is consistent with SR.

Is that a reasonably good non-technical description?

 

[sol invictus]

Well, I've done a little investigation and have found that the issue is quite technical and considerably beyond me.

My understanding is this (using simple layman's terms): Quantum field theory regards particles as excitations of a field (each type fundamental particle (elecron, quark, etc.) existing as the result of a particular field. The mathematics of Lorentz invariance then describes the required transformations as these excitations/particles move through space-time that is consistent with SR.

Is that a reasonably good non-technical description?

Yes, that's fine. The physically relevant point is that experiments done in laboratories at rest in any Lorentz frame should give identical results - in other words, there is no special Lorentz rest frame (if there was, it would constitute a preferred "direction" in spacetime) any more than there is a preferred direction in space. That invariance has been tested to extremely high accuracy in a variety of different ways.

Non-relativistic theories are formulated assuming there is a special rest frame, and their predictions therefore tend to be different in different Lorentz frames. That's the worry with Bohm.

 

[randman]

Sol, it took me a number of years looking at various experiments and reading popularized descriptions, interviews as well as peer-reviewed papers to get a handle on how the Copenhagen line of thinking explains quantum mechanics but haven't spent as much time on MWI.

In quantum teleportation, properties are said to be "teleported" in the sense of using entanglement to cause another particle to take on specific properties. MWI, as I understand it is a mechanistic theory that says an alternative universe or many of them "split off" when a particle takes on definite properties such as a which-way path (2-slit experiment above).

But how does merely affecting one particle spatially separated from another cause the entangled particle to take on specific properties? There is no physical connection between them.

As I understand it, MWI says locality cannot be violated and so the change in one particle results in a splitting of previously identical universes and so the entangled particles must have forms in respect to the particle that was messed with so to speak.

I am sure MWI has an explanation but here is my question. If we observe, say, 3 entangled particles having no definite spin, and measuring one results in a specific spin, how do the other particles know what that is to respond? This goes to my question on MWI, do the entangled particles have an indefinite spin, either this way or that, existing as a superposition before the measurement in the identical universes, or are there 2 universes so close together that really each one already has only one position so to speak and so the others do as well, but measuring causes a split because the universes cannot be identical any longer since in one we know what happened?

Hopefully, you can see the conundrum I am getting at. If MWI posits a split takes place, a further division, as a result of the wave function collapsing, then there is still a non-local effect causing the same thing with the entangled particles.

 

[sol invictus]

Think of entanglement as defining a set of worlds - one in which particle A is spin up and particle B spin down, and another in which particle A is down and B is up. Then measuring A and finding (say) spin up guarantees that particle B is spin down, because it determines that you're in the first "world" and not the second. Particle B doesn't need to "know" about the results of the measurement, and there is no non-locality. The same sort of explanation works for all types of entanglement.

If you would just look at my last few posts (prior to the exchange with PS), you'll see that written out explicitly in standard quantum bra-ket notation, which is much better than the imprecise words above.

 

[randman]

Sol, I got that. The math describes what happens if MWI is true, but it doesn't show why exactly.

Entangled particles are by definition consistent as the math shows. But the math doesn't show how that happens; hence my point. One says it's just the evolution of the wave function but is the wave function physical?

As one particle "evolves", the entangled particles either evolve as well non-locally or the past history of the universe is changed violating causality since in order for there to be consistency, the particles must have definite spin PRIOR to the measurement.....seems to me.

 

[randman]

The only way I see MWI working is if we think of the universes as not splitting off but merely our perspective on what we can see in the Multiverse. Measuring a particle causing the split does not make sense, at least to me.

 

[steenkh]

The only way I see MWI working is if we think of the universes as not splitting off but merely our perspective on what we can see in the Multiverse.

That is also how I have understood it. There is no splitting off.

Measuring a particle causing the split does not make sense, at least to me.

No we just live in a world where the measurement gives one result, whereas in another world, it would give another result. We may interpret it as a split because the two worlds were identical up to this point.

 

[randman]

That is also how I have understood it. There is no splitting off.


No we just live in a world where the measurement gives one result, whereas in another world, it would give another result. We may interpret it as a split because the two worlds were identical up to this point.

I hear ya but many MWI advocates say they do split off. The splitting off thing doesn't appear to be so worked out among advocates of Many World theories.

One problem with saying they don't split off is the idea that we can then see a part of a nearly identical world, but it's not exactly identical in the sense that we are just seeing the particle as it exists in both worlds until measurement.

 

[sol invictus]

I hear ya but many MWI advocates say they do split off. The splitting off thing doesn't appear to be so worked out among advocates of Many World theories.

It's perfectly well "worked out". The ambiguity arises from trying to use English words to describe something they are extraordinarily ill-suited for, while not being able to use math (since you don't seem to understand it).

"One says it's just the evolution of the wave function but is the wave function physical?"

The wave function is "physical" in the MWI in the sense that it is regarded as directly representing reality.

"As one particle "evolves", the entangled particles either evolve as well non-locally or the past history of the universe is changed violating causality since in order for there to be consistency, the particles must have definite spin PRIOR to the measurement....."

I've already explained at least four different times why that's not true. I don't know how to explain it any better.

If you want, the particles do have definite spin both before and after the measurement, but there are two worlds, one where they have one spin and one where they have the other.

The only effect of the measurement is that it decoheres the two worlds - it almost perfectly prevents the wavefunction from interfering between the two branches - it makes them two classically distinct worlds. But that's an entirely local and causal process.

 

[randman]

ETA to shorten the post. The math describes what physically occurs then.

The delayed-choice experiments suggest that detecting something at a later point, "B", dictates or shows the which-way the particle went at an earlier point "A". The choice was delayed but we still discovered the which-way path PRIOR to the measurement, at least that's the claim.

So in MWI, the split or divergence would have to be retroactive time-wise, imo. The decoherence includes Point A despite the measurement being at Point B.

Must be an explanation though for MWI theorists....

 

[sol invictus]

The delayed-choice experiments suggest that detecting something at a later point, "B", dictates or shows the which-way the particle went at an earlier point "A". The choice was delayed but we still discovered the which-way path PRIOR to the measurement, at least that's the claim.

So in MWI, the split or divergence would have to be retroactive time-wise, imo. The decoherence includes Point A despite the measurement being at Point B.

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.

 

[PixyMisa]

ETA to shorten the post. The math describes what physically occurs then.

The delayed-choice experiments suggest that detecting something at a later point, "B", dictates or shows the which-way the particle went at an earlier point "A". The choice was delayed but we still discovered the which-way path PRIOR to the measurement, at least that's the claim.

So in MWI, the split or divergence would have to be retroactive time-wise, imo. The decoherence includes Point A despite the measurement being at Point B.

You get into exactly that kind of problem when you think about Quantum Mechanics in classical terms. So don't do that.