In Quantum Mechanics things travel as waves and interact as particles. Between interactions, everything is described by the Schrodinger Wave Function, which evolves to include every possible path. But at the point of an interaction the wave function must collapse to satisfy conservation rules.
Consider an electron fired at a dual slit with a phosphor screen. While traveling from the electron gun, thru the slits, to the screen, the electron is described by a Wave Function. It has no fixed position or momentum. The Schrodinger wave passes through both slits and interferes with itself on the other side. The wave function evolves into a series of lines.
But when the electron interacts with the screen it always appears as a single point. It must do so by the laws of conservation. At the interaction it must have a specific location and momentum in order for there to be conservation of charge, momentum, energy, etc.
This interaction is enough to 'collapse the wave function'. No 'observation' is required.
How does this happen? There is no localized mechanism that can possibly make this work. The conservation laws are not local restrictions. They are universal.
Please note that this is my own explanation of now QM works, and does not necessarily reflect the official position of any school of thought. It does, however, reflect the actual use of Quantum Mechanics, in that systems evolve via the Schrodinger Equation and interactions must obey conservation laws. And No, it cannot explain how entanglement works.
> In Quantum Mechanics things travel as waves and interact as particles. Between interactions, everything is described by the Schrodinger Wave Function, which evolves to include every possible path. But at the point of an interaction the wave function must collapse to satisfy conservation rules.
That would make some sense if by interaction you mean "interaction with the macroscopic environment". When small-enough quantum systems (like two particles) interact there is no collapse and the evolution is unitary.
> This interaction is enough to 'collapse the wave function'. No 'observation' is required.
How do you distinguish the interactions that 'collapse the wave function' from those who do not?
The idea that Measurement = "interaction with the macroscopic environment" is part of the Copenhagen interpretation, not a requirement of QM itself.
Aside: (Personally, I see this more as Bohr's way of dodging questions he had no answer to, and not a viable way to think about Quantum Mechanics. A better answer would have been "I don't know. Let's figure it out." But that was impossible for political reasons. Bohr was being attacked by Einstein for 's sake. He can be forgiven for adopting Ali's "rope-a-dope" tactics if he felt that Einstein was trying to destroy his entire field in its infancy. But I find "there is no quantum world" simply unacceptable.)
Now to answer your question as best I can, an interaction must collapse the wave function when it is required to fulfill a conservation rule. For example, if an electron is captured by a nucleus it becomes bound and emits a photon. This is an interaction that must conserve momentum, angular momentum, energy, and charge. Because of that, the electron can no longer be represented by a non-localized wave function. The universe must concentrate those properties down to a point in order to "do the accounting" necessary for the conservation rules.
No, I don't know how it does that. But then, NONE of the available interpretations answer that question. This indicates to me we are thinking about it wrong.
What I like about Stuckey's paper is that it adds another factor: besides conservation rules the universe seems to require that "measurements" obey the Relativity Principle (No Preferred Frame of Reference). I have yet to figure out how to incorporate that.
Is the idea of “collapsing the wave function” a requirement of QM itself? In that context, a “measurement” would be to be what you call “an interaction that must collapse the wave function”.
And your answer is simply wrong. An excited atom can emit a photon, for example, and the system will still be described by a “non-localized wave function”. It won’t even be well defined if the spontaneous emission has happened or not yet.
The evolution of a quantum system according to Schrödinger’s equation doesn’t violate conservation rules. And, in case it’s not clear, the quantum system described by the wave function in the example above is the atom-photon(-or-not) pair.
My understanding is that any kind of measurement will do, it doesn't matter how you get it. You could use photons to do the measurement but there are other ways which all have the same result.
It's a mystery how the particle "knows" (In other words, nobody knows when the wave function collapses) but one popular interpretation is that the particle exists in all states, i.e. in a pure description of reality. When any quantum system interacts with it, then it becomes entangled with the result of that measurement, branching it into a new universe (edit for clarification: a new world where it was as if it was never a wave, and it was always a particle). That's my understanding of the many-worlds theory.
That entanglement propagates across nearby particles, so it doesn't have anything to do with eyes or consciousness. If the air molecules around your body interact with the particle then that entanglement propagates through your body and places you in the new world.
Re: When any quantum system interacts with it, then it becomes entangled with the result of that measurement, branching it into a new universe. That's my understanding of the many-worlds theory.
This is a case of a simple theory that indeed models the mystery well. However, it seems "wasteful" in that it would branch into gazillion trees of reality. In Occam's Razor, does "simplicity" include quantity of "stuff" needed? Because sometimes the brute force algorithm/model is the "simplest" if we ignore quantity of stuff and time, such as bubble-sort. Bubble-sort is one of the simplest sorting algorithms known, but is inefficient from a time and resource standpoint.
If there are "free" dimensions to spare out there, then the "wasteful" multi-verse model may not really be wasteful. We humans are used to thinking in terms of economic trade-offs, and a model that uses up large quantities of space/time rubs our instincts wrong.
If true, the theory means that in some universe somewhere I'm a billionaire who married a supermodel.
I think you're mixing up metaphysics and human intuition with what the math describes. The current math says there may be essentially infinite worlds created in infinite time, where yes there is least one in which you are a billionaire married to a supermodel. The only constraint is in the properties of nature (e.g. a world will never be created in which an electron has 0 spin).
However, I agree with you that it seems implausible because it implies absurd situations like, there is a world in which someone lives a life of celebrity because every time they roll some dice it always lands on 6, and every time they flip a coin it lands on heads, etc.
Even worse, many-worlds doesn't really solve the problem anyway - it still doesn't explain WHY you only observe one result, when the Schrodinger equation predicts several. That is, why can't you see the other worlds?
Don't you have the same problem in classical mechanics? Let's say you're standing at the edge of a pond, and you see waves rippling across the surface. The deviation in height of the surface of the water is described by h = cos(r + t) where r is the distance from the centre of the pond and t is the current time.
Why can you see the solution of the equation for the entire surface of the pond at once, but only for a single instant of time at any given moment?
It's not the same thing, because classical mechanics explicitly models the time - it can predict that at time T the system is in one state, and indeed when I look at a the system at time T, I see it in a single state.
Conversely, the Schrodinger equation gives an amplitude to the same particle/wave at many locations at time T. However, when you look for it at time T at all of those locations at once, you only find it in one of them. If you perform the experiment many times, you will find it at all of those locations some amount of the time. But then, if you try to use the Schrodinger equation to model movement before AND after interaction with the detector, you will not be able to find the particle at any position that doesn't match what the detector initially saw.
That is, say the Schrodinger equation predicts the particle has the same amplitude at locations X and Y. Then, after interacting with something at locations X and Y at time T1, it will have some amplitude at locations X1, X2, Y1, Y2 at time T2.
Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
Isn't the problem that you're only looking at the system in a single world W, when viewing all solutions requires viewing it in multiple worlds?
I mean, I get that time is a little different in that you will eventually experience and remember all possible solutions as you stand there watching the system, because classical time is a linear chain of events. In the multi-world case, it's a branching chain, and your experience and memories of the different solutions are stuck in their own branches.
That does make worlds weird and different from the other dimensions, but we accepted time as being weird and different from space for a very long time.
> Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
This makes total sense if it's actually a wave and the particle is merely a solution for a particular world W. The detector didn't change anything about the wave. It just coupled you to the wave system earlier, so now your branch of the many-world tree can only see the subset of solutions that correspond with whatever you detected. The only thing that has changed, though, is your ability to see the other solutions. You branched earlier, so now each branch you exist in only sees a subset of the full solution.
That said, I am not a physicist. The many worlds explanation was just the first thing that actually made sense to me about quantum mechanics. It's so conceptually simple.
That doesn't seem like a question that can be answered mathematically, does it? That's like asking, why do electrons have a spin of 1/2? Why is the speed of light 299,792,458 m/s? These are just properties of the universe.
Not really. It's the same question as the measurement problem: Schrodinger's equation predicts that a particle can exist in many places at the same time, with different amplitudes, and interact with particles in all those places. However, if we want to predict the particle's movement after it encounters a detector, we need to update the wave function to set its probability to 1 at the position of the detector and 0 everywhere else - otherwise, our predictions are measurably wrong.
Now, the question is: what causes this discontinuity in the equations of motion? Why is interaction with a detector different than interaction with another particle? Many Worlds simply reframes this problem, but doesn't get rid of it. In MWI, you would say 'the particle moves in all universes according to the wave function, until it interacts with a detector, possibly interfering with versions of itself in other universes. Then, when it encounters the detector, the world line of the detector splits - in some universes it passes the detector, in others it doesn't. However, it no longer interacts with other versions of itself,so we must update the wave function inside the universe where it passed the detector'.
> Now, the question is: what causes this discontinuity in the equations of motion? Why is interaction with a detector different than interaction with another particle?
> Many Worlds simply reframes this problem, but doesn't get rid of it.
Maybe I'm misunderstanding. It's like asking "why is there a difference between me jumping in a swimming pool and someone else jumping in it? I don't get wet when someone else is swimming." The difference is... one of you is in the pool. It's not going to spontaneously make the other person wet.
In MWI the difference is that if it interacts with a particle, you're not entangled, the particle is. If it interacts with a detector then you're entangled. So, there is no difference except for what gets entangled.
What that means is the wave function can only appear to collapse when you entangle. If some particle entangles, it will collapse for that particle and branch into a new world, but you're not in that world; for you it's still a waveform.
I'm not sure cross-universe communicating is necessary in the multiverse model. The splitting just resembles communication from our perspective in that it makes the probabilities look "rigged".
>>"However, it seems "wasteful" in that it would branch into gazillion trees of reality."
In a way, it could be interpreted as very efficient. Only the branches where some "measurement" is done are "calculated". I suppose the others are garbage collected at the end of time, or something like that.
And maybe it's not a tree, but a graph of universes. In the same way that a universe split in two, two universe could also fuse into one when they share the previous state. Somehow it feels like this have to be connected to reversible vs. non-reversible computation.
Ah.. it's a good feeling being a fearless dilettante.
Re: Only the branches where some "measurement" is done are "calculated". I suppose the others are garbage collected at the end of time, or something like that.
But that's adding complexity back into it. You are increasing complexity of the theory/model by adding a complex cleaner/trimmer in order to reduce the quantity of resources consumed.
If the universe is a mathematical object there being an infinity of universes isn't any more wasteful than there being an infinity of integers for example. From Occam's point of view it's simpler if all integers exist rather than there being a cap if that were even logically possible. So yeah go supermodel!
Math is a modeling technique, not a "thing". To me it doesn't make sense to say the universe "is" math. Maybe it's a machine "running" math notation (programming code), but that's not the same as it "being" math.
The universe isn't mathematical, it is explained by math, a country is not Chinese because I wrote a tour guide in Chinese about it. Infinite universes isn't really applicable here, you're thinking of a growing block universe. A simpler point is a block universe. https://en.m.wikipedia.org/wiki/Eternalism_(philosophy_of_ti...
> one popular interpretation is that the particle exists in all states, i.e. in a pure description of reality. When any quantum system interacts with it, then it becomes entangled with the result of that measurement, branching it into a new universe (edit for clarification: a new world where it was as if it was never a wave, and it was always a particle).
The two-slit experiment contradicts this. You get different results depending on when you perform the observation(s).
So the new world is a world where the particle was originally a wave, and became a particle when it was observed. Not a world where the particle was always a particle.
Yeah. On the other hand it does give decent intuition about how certain interactions would result, especially if talking about massive particles traveling much slower than light.
I remember reading an article here a while back that involved a macroscopic re-creation of the double slit experiment results, but where mere observation remained possible, because light did not sufficiently influence the substrate. In that experiment the particles were droplets traveling on top of a set of waves, working in the pilot wave fashion.
Any attempt to use anything of similar scale to the particles to observe which slit the drop went through would break the interference pattern, but mere light did not, allowing one to visually see how a pilot wave style interpretation could work, if it were not for that whole (photons travel at the speed of light, so these would need to be faster than light propagating pilot waves) thing.
Indeed it looks like flubert linked a video from an earlier study of the same basic mechanics, prior to the more recent one that included the double slit experiment replication.
You can't observe something without sending information. In order to make an observation, you must interact with whatever is being observed, so that information about the interaction can come back to you.
In the bag example above, we can observe the Australian ball and know the color of the American ball, and we cannot use this interaction in Australia to send information to America. But we cannot avoid sending information to the Australian ball when we observe it.
>> You cannot send information by merely observing something.
This is, at the least, very poorly phrased. As explained above, not only can you send information by observing something, it's impossible not to do so. The question here is where the information goes.
I assume, for the sake of my own sanity, that "observation" means the particle becomes a cause for some kind of effect, e.g. colliding with something in a way that changes the something's state. Quantum mechanics experts, please don't tell me it's weirder than that.
In many formulations, e.g. multiverse, the apparatus doing the measuring (doesn't have to be a human or anything) becomes entangled with the thing being measured. This is still not super well understood.
Particles don't know anything, but you have to interact with it in order to observe it. You have to bounce a photon off of it or something like that in order to get any information out of it.
Consider an electron fired at a dual slit with a phosphor screen. While traveling from the electron gun, thru the slits, to the screen, the electron is described by a Wave Function. It has no fixed position or momentum. The Schrodinger wave passes through both slits and interferes with itself on the other side. The wave function evolves into a series of lines.
But when the electron interacts with the screen it always appears as a single point. It must do so by the laws of conservation. At the interaction it must have a specific location and momentum in order for there to be conservation of charge, momentum, energy, etc.
This interaction is enough to 'collapse the wave function'. No 'observation' is required.
How does this happen? There is no localized mechanism that can possibly make this work. The conservation laws are not local restrictions. They are universal.
Please note that this is my own explanation of now QM works, and does not necessarily reflect the official position of any school of thought. It does, however, reflect the actual use of Quantum Mechanics, in that systems evolve via the Schrodinger Equation and interactions must obey conservation laws. And No, it cannot explain how entanglement works.