Question about Quantum mechanics

[sol invictus]

I suppose you would say the violation of local realism is only illusory due to MWI

No - "realism" is explicitly violated by MW. In this context "realism" means there is only one world, one unique result for any measurement - and that's not the case in MW. But "realism" is not the same as locality or determinism. The MWI is local and deterministic, but doesn't satisfy "realism" (which is also called "counterfactual definiteness" or some such ridiculous term).

And violating local realism seems more of an upending of what some think of as "the laws of physics" than just locality.

It's just the opposite. The fundamental laws of physics as currently understood all but require a violation of "realism", because the MWI is nothing more or less than the simplest interpretation of the quantum wavefunction predicted by the laws of physics.

 

[sol invictus]

Ok, doing some more thinking on your post. So in the 2-slit experiment, when we choose to measure the which-way path, we see the path and all the other paths are taken in other universes (presumably with people there also measuring the particle right?).

Yes, more or less.

So since the particle collapses, it does so in all the universes and there is not a universe with someone running the experiment without trying to measure the which-way path so it travels in a wave-like pattern. The interference pattern is gone for the whole multi-verse.

Is that it?

Prior to the experiment, imagine an ensemble of two worlds which exactly coincide in all respects. In each, there's an experimenter setting up a two-slit experiment with a measuring device attached to each slit.

When the particle is emitted, the two worlds begin to diverge - in one world the particle goes towards one slit, and in the other towards the other slit. However at this point the two worlds are still very "close" in the sense that they differ only due to the state of a single particle. That means that there can still be interference between them - so if, for example, the experiment had been set up so that no measurement is made at the slit, they will interfere in such a way that the pattern on the screen shows interference fringes (in both worlds, which would coincide again at that time).

But if a measurement is made at the slit, the difference between the worlds - which was a single particle's position - gets amplified enormously by interaction with the detector. From the state of a single particle differing we've gone to the states of 10^23 (or so) particles differing, for example, all the particles that make up the display of the detector, and all those in the brain of the experimenter once she sees the display. It turns out that states which differ like that have very, very little interference between them - which means that, for all practical purposes, these two worlds can never influence each other again, and are from then on completely separate.

That's why the Copenhagen interpretation works - it doesn't cause any obvious problems to throw away the world you're not part of, because it has such a tiny effect on yours.

Now here's the tricky part. You'd have to people running the same experiment and determining the which-way path and so a huge number of alternate universes with presumably the same person essentially in each of them. This suggests the act of choosing here to measure the photon one way or another then is indeed causal to whether these universes exist, hence the split.

Nope. It has nothing to do with "choice". There are really a continuum of such universes all the time, an uncountably infinite number of them, and the process we're describing as "splits" is a continuous process.

But the idea as I understand it is that those universes are already there prior to someone making the choice, which suggests a violation of causality in some sense. Either way, the universe or multiverse seems to know the choice will be made just as the photon seems to know that. The problem then remains the same unless one says the choice causes the split.

Again, no. There's no violation of causality (or locality). The "split" (into two classically distinct worlds that cannot interfere) happens only when (and where) the measurement is made.

 

[sol invictus]

Why would violation of locality make it inconsistent with special relativity?

Because in SR, space and time are mixed. A non-locality in space is a non-locality in time, from both past to future and future to past. Therefore non-locality implies acausality, which destroys not just every known law of physics, but the entire conceptual framework they are based in.

That is not one of the several "objections" discussed in the link I provided nor do I find anything about that objection elsewhere.

Well, now you have.

If you want my (unvarnished) guess as to the reason, it's because (with a few notable exceptions) the physicists that spend much of their time thinking about interpretations of QM are perhaps the worst in the field. Many of them seem not to have heard the news from the 1950s about relativistic QFT.

 

[Perpetual Student]

Because in SR, space and time are mixed. A non-locality in space is a non-locality in time, from both past to future and future to past. Therefore non-locality implies acausality, which destroys not just every known law of physics, but the entire conceptual framework they are based in.

OK, I'm trying to follow that argument. If we have something occurring in one space dimension, it does not necessarily affect the other two space dimensions (e.g.: if something moves in one dimension, it can be motionless in the other two.), so why could we not have some occurrence in space that has no similar effect on time?

Well, now you have.

If you want my (unvarnished) guess as to the reason, it's because (with a few notable exceptions) the physicists that spend much of their time thinking about interpretations of QM are perhaps the worst in the field. Many of them seem not to have heard the news from the 1950s about relativistic QFT.

 

[sol invictus]

OK, I'm trying to follow that argument. If we have something occurring in one space dimension, it does not necessarily affect the other two space dimensions (e.g.: if something moves in one dimension, it can be motionless in the other two.)

No, not really - there's no way to distinguish between "one" and "the other two", because a rotation turns one into another. In other words it wouldn't make sense to say that something can occur only along the x-axis, but never along the y- or z-axes. Or rather, it would only make sense if the laws of physics weren't invariant under rotations - but they are.

Same goes for space-time in relativity.

 

[Vorpal]

Edit: removed reply to PS; ninja'd by Sol.

Because in SR, space and time are mixed. A non-locality in space is a non-locality in time, from both past to future and future to past. Therefore non-locality implies acausality, which destroys not just every known law of physics, but the entire conceptual framework they are based in.

This conclusion seems either too strong or with a missing assumption. If I've a scalar field with constant-value slices forming a spacelike foliation of spacetime, then I can define (say) Newtonian gravitation with the field as the time parameter. This would break locality and allow superluminal signals, yet still be causal.

Or did you simply mean that given physics follows QFT, locality and causality are equivalent through the commutativity of spacelike separated observables? That's a bit different from non-locality implying acausality on the basis of spacetime structure alone.

 

[randman]

Sol, thanks for explaining the MWl. As I understand it then, the other world is already there and the splitting is just 2 or maybe more worlds moving apart. There isn't really a collapse from a wave-like nature to a particle-like one. It's just the photon as a particle is being interfered with by a photon that's like a particle in another universe?

For some reason, photons interact with other universes in the multiverse unless and until we measure them precisely meaning trying to determine which path it takes. We are then just measuring "our" photon then and that causes it to diverge from interfacing with the other universe's photon or other universe's photons.

Is that right?

Couple of questions though. We can also measure the interference pattern. So one universe bleeds over to the other at least in this small way and has an effect. By choosing to measure the which-way path, we cause the divergence or splitting so that the interface between the 2 or more universes separate.

So what mechanical explanation is there for the photons being connected in the first place? And what is the mechanical cause for their splitting? In other words, since we in some sense already measure the other world's photon with the interference pattern, measurement alone does not cause the splitting. It's the obtaining of specific information of the which-way path that does. Maybe that's why some talk about the many-minds interpretation.

Just doesn't seem the mechanics here play a role as much as the type of information being obtained.

Now here is the kicker. There never is a collapse of the wave function. Our photon never really travels as a wave, right? It's just interacting with another universe already in existence. So our measurement of it is just a mechanical process.

The same problem in a different way comes up then. Why does one measurement preserve the interface with the alternative universe, and another causes a divergence. Surely the physical apparatus does not do that.

In other words, how do the photons and the multiverse know whether we are determining the which-way path? The photons are not sentient, surely? And are we saying the multiverse is?

The act of measurement doesn't cause a collapse because the photon in our world was never really wave-like in the first place. MWI then doesn't resolve things in explaining the interface as a strictly mechanical causal process, imo. It seems to inject consciousness into the situation which may be needed.

Maybe you could, if you bear with me, explain how my thinking misses it here? There has to be a reason why determining the which-way path of a photon causes this divergence in the alternate universes, and there needs to be an explanation for why the photons interface in the first place. From what I understand in your explanation, there isn't a photon acting as a wave that collapses into more than one universe, nor causes those universes to be created via a split, but that the universes already exist and what we see as wave-like behavior of the photon is actually just different universes interacting with one another?

Last point and sorry to be so long, but why wouldn't we consider from the photon's vantage point travelling at the speed of light, no time elapses, and so it acts as one "now" or present system. In other words, it seems to violate causality when a present action affects it in the past from our vantage point, but in reality, it exists in sort of ever-present, timeless state. I am sure someone has considered this before but haven't seen it in the literature. Doesn't relativitypredict this?

 

[randman]

Ok, reread your post. Maybe can clarify.....sorry to go on at such length.

But if a measurement is made at the slit, the difference between the worlds - which was a single particle's position - gets amplified enormously by interaction with the detector. From the state of a single particle differing we've gone to the states of 10^23 (or so) particles differing, for example, all the particles that make up the display of the detector, and all those in the brain of the experimenter once she sees the display. It turns out that states which differ like that have very, very little interference between them - which means that, for all practical purposes, these two worlds can never influence each other again, and are from then on completely separate.

As far as the measurement at the slit, later experiments such as the delayed choice measurements do it differently and so it doesn't seem the mechanical process of measuring causes that much difference since the measurement is after the fact so to speak but you also mention the difference in the photons in the brain of the experimenter.

So as our understanding changes of something, there can be divergence from other universes where another version of us, so to speak, sees or understands something different? Kind of sounds like mysticism or an explanation of some mystical experiences....not knocking that mind you.

So what if the experimenter never looks at the results, is there still divergence?

 

[sol invictus]

This conclusion seems either too strong or with a missing assumption. If I've a scalar field with constant-value slices forming a spacelike foliation of spacetime, then I can define (say) Newtonian gravitation with the field as the time parameter. This would break locality and allow superluminal signals, yet still be causal.

You can define that as an effective theory - but if your fundamental theory is Lorentz invariant, non-locality will always imply acausality.

Or did you simply mean that given physics follows QFT, locality and causality are equivalent through the commutativity of spacelike separated observables? That's a bit different from non-locality implying acausality on the basis of spacetime structure alone.

I guess that depends on what you mean by "spacetime structure". I had in mind that the spacetime is locally Minkowski, and that the fundamental laws of physics are Lorentz invariant. I think that's what you need for my statement to hold.

 

[sol invictus]

Your posts are a bit too long for me to read carefully, randman - can you condense your questions down a bit?

As far as the measurement at the slit, later experiments such as the delayed choice measurements do it differently and so it doesn't seem the mechanical process of measuring causes that much difference since the measurement is after the fact so to speak but you also mention the difference in the photons in the brain of the experimenter.

So as our understanding changes of something, there can be divergence from other universes where another version of us, so to speak, sees or understands something different? Kind of sounds like mysticism or an explanation of some mystical experiences....not knocking that mind you.

So what if the experimenter never looks at the results, is there still divergence?

Let me be very clear - human understanding has absolutely nothing to do with anything I'm saying. The brain of the experimenter is relevant only insofar as it is a large object with many degrees of freedom. Replace all experimenters in what I said above with measuring devices, and nothing at all would change.

This whole thing about our knowledge affecting the world is complete nonsense.

 

[Perpetual Student]

No, not really - there's no way to distinguish between "one" and "the other two", because a rotation turns one into another. In other words it wouldn't make sense to say that something can occur only along the x-axis, but never along the y- or z-axes. Or rather, it would only make sense if the laws of physics weren't invariant under rotations - but they are.

Same goes for space-time in relativity.

That's very helpful, thanks -- it provides me with an intuitive sense of your point. Could you further explain how the laws of physics are invariant under rotations in space-time? Doesn't the gamma function change some aspects of the nature of physics as one moves (rotates?) from space dimensions to time?

 

[sol invictus]

I'll address a few of your questions...

Couple of questions though. We can also measure the interference pattern. So one universe bleeds over to the other at least in this small way and has an effect.

Right - when they only differ by the state of a single particle, it's probably better not to think of them as separate. In any case they can interfere with each other, and that's what gives you the interference pattern.

In other words, how do the photons and the multiverse know whether we are determining the which-way path?

The measurement affects the evolution of the wavefunction. It only affects it locally and causally, but it certainly affects it.

The photons are not sentient, surely? And are we saying the multiverse is?

No and no.

Last point and sorry to be so long, but why wouldn't we consider from the photon's vantage point travelling at the speed of light, no time elapses, and so it acts as one "now" or present system. In other words, it seems to violate causality when a present action affects it in the past from our vantage point, but in reality, it exists in sort of ever-present, timeless state. I am sure someone has considered this before but haven't seen it in the literature. Doesn't relativitypredict this?

The question doesn't make sense. Present actions don't affect photons in the past, and you cannot really consider the world from a photon's vantage point, it's a massless particle. If you like you can consider the world from your vantage point as you accelerate closer and closer to the speed of light, but nothing acausal happens then.

 

[randman]

The measurement affects the evolution of the wavefunction. It only affects it locally and causally, but it certainly affects it.

This is what I am getting at. In MWI, how is there a wave function? There only seems to be a wave function (writing an equation does not make it so in the physical world). What's going on are 2 or more universes interacting with each other.

If not, then the measurement causes a split into 2 universes and so there is a massive on-going creation of matter and energy.

Can't have it both ways. If there is a wave function, then new universes are created via splitting. If the universes already exist, the wave function is just an illusory concept. There are just different photons in different universes interfacing with one another.

Present actions don't affect photons in the past, and you cannot really consider the world from a photon's vantage point, it's a massless particle.

Why can't one consider time from the photon's perspective? It wouldn't be the photon's present affecting the past if the photon doesn't have a past, present and future from it's vantage point.

I know it's a massless particle, but it still travels at a certain speed.

Not being dogmatic because there must be a reason this explanation has not come up, but still not sure why it wouldn't work.

On MWI though, from what I am understanding, it seems like an effort to have it both ways: to say there is a wave-function in one universe, but there is no creation of new universes.

 

[sol invictus]

This is what I am getting at. In MWI, how is there a wave function? There only seems to be a wave function (writing an equation does not make it so in the physical world).

That's exactly wrong. The MWI is essentially the statement that we should take the wavefunction literally, at face value, as a description of "reality". Since wavefunctions can be superpositions of macroscopically distinct states (cat is alive and cat is dead), that means (if we accept this interpretation) that we must accept that reality can consist of sums of distinct "worlds".

And indeed, what one finds is that starting from a wavefunction that describes one "world", we immediately evolve into one that describes multiple worlds. It's easiest to think of this process as I said before, as the evolution of an infinite ensemble of universes (which in the case I just described start off identically and then evolve differently), but mathematically what's going on is simply the unitary time evolution of the wave function.

If not, then the measurement causes a split into 2 universes and so there is a massive on-going creation of matter and energy.

For the third time, no. The Schrodinger equation conserves energy; it is impossible for the energy to change.

Why can't one consider time from the photon's perspective?

Because photons don't have a perspective.

 

[randman]

Because photons don't have a perspective.

But we do and can imagine what time is like at the speed of light.

It's easiest to think of this process as I said before, as the evolution of an infinite ensemble of universes (which in the case I just described start off identically and then evolve differently),

This dodges the heart of my basic question on MWI. Are worlds "evolving" into new worlds, or are the other worlds already there that just happen to be exactly the same and do they share the same photon or is there a different photon per the different universe BEFORE the collapse?

Take the photon. When it travels like a wave in our world, does it go through the 2 slits at once in our universe, interfering with itself, or this just an illusion as the other universe's photon interferes with it?

Is it one photon that splits into 2 or more, or 2 photons or more all along?

If there are 2 worlds exactly identical already and one photon, but they diverge when the wave function collapses, how do you explain the divergence and the collapse happening before the measurement in the delayed choice experiments?

 

[sol invictus]

This dodges the heart of my basic question on MWI. Are worlds "evolving" into new worlds, or are the other worlds already there that just happen to be exactly the same

Start with the latter.

and do they share the same photon or is there a different photon per the different universe BEFORE the collapse?

There isn't a very clear distinction. Really, there's simply a wavefunction. In some cases that wavefunction is supported on several configurations that differ from each other in many degrees of freedom (those are truly distinct worlds), in other cases, it's supported on configurations that differ only in the state of a single particle (those can be thought of as different worlds, but you must bear in mind that they can interact - specifically, interfere - with each other).

Take the photon. When it travels like a wave in our world, does it go through the 2 slits at once in our universe, interfering with itself, or this just an illusion as the other universe's photon interferes with it?

At the level of the words you're using, I can't distinguish between those two possibilities.

If there are 2 worlds exactly identical already and one photon, but they diverge when the wave function collapses, how do you explain the divergence and the collapse happening before the measurement in the delayed choice experiments?

It doesn't happen before the measurement. Trace it through carefully - keeping all branches of the wavefunction - and you'll see that. Or if not, I can help you (but please pick the simplest experiment you think illustrates the issue you're having).

 

[randman]

in other cases, it's supported on configurations that differ only in the state of a single particle (those can be thought of as different worlds, but you must bear in mind that they can interact - specifically, interfere - with each other

)

But prior to the collapse of the particle, they don't differ but are identical, right?

In other words is the wave function relative to the one photon evolving into different preexisting universes with the one photon sharing both worlds?

Or is there just the appearance of that? And there are 2 different photons in both worlds interfering with one another?

The wave function is a mathematical description of the photon as one system. It's not based on MWI originally. If MWI is true, there is no need for the wave function as what we see is merely the interference of one photon in one world interfering with the photon in another because the worlds are so close. If they bleed together, there is no reason to assume photons act like waves and then collapse. The superposition is merely the bleeding over of other universes with their photons, right?

If you say, no, the photon is in superposition as the wave function describes, then it's not another universe interfering with the photon. It's the same photon.

If we are positing preexisting many worlds, then the apparent collapse is an illusion. It's just 2 worlds interfering with one another, not a collapse of the particle into one state.

 

[Vorpal]

Doesn't the gamma function change some aspects of the nature of physics as one moves (rotates?) from space dimensions to time?

The gamma factor is actually just the cosine of the angle between two velocity (four-)vectors, e.g., the observer's and some particle's, except the angle is imaginary, or equivalently, the trigonometry is hyperbolic.
Ordinary inner product: <u,v> = ║u║║v║ cos θ
Hyperbolic inner product: <u,v> = ║u║║v║ cosh α, γ = cosh α.
So rather than breaking anything, the gamma factor an integral part of the the rotation. Take a gander at the Lorentz transformation in terms of the angle (rapidity) α = atanh(v) = acosh(γ):

[t'] = [ γ   -γv ][t] = [ cosh α  -sinh α ][t] <--> [x'] = [cos θ  -sin θ][x]
[x'] = [-γv   γ  ][x] = [-sinh α   cosh α ][x] <--> [y'] = [sin θ   cos θ][y]

This is a straightforward analogue of Euclidean rotations. Formally, the correspondence is a rotation in the complex plane: {t = iy, α = iθ}.

You can define that as an effective theory - but if your fundamental theory is Lorentz invariant, non-locality will always imply acausality.

Given a scalar field t as previously described, say one has a four-acceleration of a particle at x orthogonal to its four-velocity, <a,u> = 0, given by:
[latex]a \propto \int\frac{t_{,\alpha}t_{,\beta}T^{\alpha\beta}(x')}{||x-x'||^3}\left[(x-x') - u\langle u,x-x'\rangle\right]\;{\mathrm d}^3x'[/latex]
with the domain of integration a slice of constant t. The density ρ = t_,αt_,βT^αβ is Lorentz-invariant, as is the domain and vector lengths, since they are determined geometrically. Since orthogonality is also a geometric, coordinate-invariant condition, I don't see how this acceleration would not be Lorentz-invariant.

I guess that depends on what you mean by "spacetime structure". I had in mind that the spacetime is locally Minkowski, and that the fundamental laws of physics are Lorentz invariant. I think that's what you need for my statement to hold.

I don't see what's wrong with the above, so I guess I'm confused about the statement "the fundamental laws of physics are Lorentz invariant." ... Come to think of it, I might be conflating:
(1) Lorentz-invariance of laws ~ "an isolated experiment gives the same result in every inertial frame."
(2) Lorentz-invariance of laws ~ "physical quantities given by laws are Lorentz-invariant."
The Newtonian gravity example seems to follow the latter but not the former.

(I apologize if that's the kind of thing that's obvious to physicists, but I honestly didn't realize that those two are inequivalent until now. Or is there anything else I'm missing?)

 

[sol invictus]

The wave function is a mathematical description of the photon as one system. It's not based on MWI originally. If MWI is true, there is no need for the wave function

You need to back up several steps, because that's completely wrong. It's the opposite of the truth.

Look, let me try to summarize the different interpretations of QM. First off, they are all interpretations of QM. As such, their basic mathematical structure is very similar. In all of them there is a wavefunction (usually denoted by the Greek letter psi), and a differential equation (the Schrodinger equation) that psi satisfies. The diff. eq. tells you how psi evolves in time given what it is at some initial time.

The interpretations differ primarily in what meaning they assign to psi. Here are three examples:


Many Worlds: psi describes reality.

pros: simple, local, causal, deterministic, and consistent with all known experiments.

cons: requires accepting that states like (cat is dead)+(cat is alive) can describe reality (i.e., there can be "many worlds"), and requires that collapse on to multiple near-classical states is a prediction of the Schrodinger equation (but there is now considerable evidence for this).


Copenhagen: psi is a probability distribution on the results of measurements

pros: consistent with all known experiments

cons: non-deterministic, non-local (but in a harmless way), doesn't define "measurement", requires non-unitary (in fact non-linear) extra dynamics to project onto the state corresponding to the result of the measurement


Bohm: psi is an incomplete description of reality

pros: deterministic

cons: non-local (in a very dangerous way), complicated, ad hoc extra structure added for no evident reason other than prejudice

 

[sol invictus]

Given a scalar field t as previously described, say one has a four-acceleration of a particle at x orthogonal to its four-velocity, <a,u> = 0, given by:
[latex]a \propto \int\frac{t_{,\alpha}t_{,\beta}T^{\alpha\beta}(x')}{||x-x'||^3}\left[(x-x') - u\langle u,x-x'\rangle\right]\;{\mathrm d}^3x'[/latex]
with the domain of integration a slice of constant t. The density ρ = t_,αt_,βT^αβ is Lorentz-invariant, as is the domain and vector lengths, since they are determined geometrically.

I'm not sure what "slice of constant t" means. But certainly you can write down laws of physics that depend on derivatives of your "clock scalar". If your clock scalar has the kind of profile I think you have in mind (it depends on t only in some specific Lorentz frame), then the solutions to those laws will not be Lorentz invariant, in the sense that experiments at rest in different Lorentz frames will give physically different results. A closely related example is being immersed in a fluid, or for that measuring the dipole moment of the cosmic microwave background of our universe.

I don't see what's wrong with the above, so I guess I'm confused about the statement "the fundamental laws of physics are Lorentz invariant." ... Come to think of it, I might be conflating:
(1) Lorentz-invariance of laws ~ "an isolated experiment gives the same result in every inertial frame."
(2) Lorentz-invariance of laws ~ "physical quantities given by laws are Lorentz-invariant."
The Newtonian gravity example seems to follow the latter but not the former.

(I apologize if that's the kind of thing that's obvious to physicists, but I honestly didn't realize that those two are inequivalent until now. Or is there anything else I'm missing?)

Generally one requires neither of those, although it's closer to (1). Lorentz invariance of laws really means that the laws are derivable from a Lorentz invariant action principle. It usually also means that experiments done carefully enough, at short enough distance or at high energy energy, will satisfy (1).

The kind of breaking of Lorentz invariance you see when you look around you and notice that the room you're in isn't rotation invariant is called "spontaneous", and it's par for the course - indeed, every non-vacuum solution to the laws of physics breaks at least some part of Lorentz invariance (more or less by definition of "vacuum"). So you certainly cannot require (2) - for example, rather than the acceleration consider the trajectory. Any trajectory at all breaks Lorentz invariance.