https://www.livescience.com/2000ato...satonce.html
This one has me stumped. If particles can be in more than one place at once then what does that say about spacetime coordinates? Are they different for each place?

https://www.livescience.com/2000ato...satonce.html
This one has me stumped. If particles can be in more than one place at once then what does that say about spacetime coordinates? Are they different for each place?
Last edited by zinjanthropos; October 7th, 2019 at 11:36 PM.
It says
"And waves occupy multiple places in space at once." in that article .
I am not sure of how that works ,but I don't have a problem with particles being waves. The only question I would have is whether "waveness" is more fundamental than "particleness" (based on our present state of knowledge.) or whether it is better to regard the condition as entirely binary
They are not actually in two places at once. Like the famous cat, they will be in one place or the other when the position is measured. But, up until that point, there is a probability that they could be in either.
This is not much different from electron orbitals, where the electron has a probability to be anywhere with the orbital (with a probability that is the function which describes the shape of the orbital) but when detected, it will be in a specific location.
Strange,,,,thanks for response. Need to clear up something....Isn’t the cat in the box thought experiment about state of cat being alive or dead and not whether there’s the probability of a cat actually in the box? Wouldn’t knowing a cat’s in the box be the result of a measurement/observation?
(just my guess) It is the same thing ,being there or being alivealthough different probabilities.
It could be there ,but dead ,or be there but alive (or having sex with itself)
Or it could be elsewhere but dead ,or be elsewhere but alive (or having sex with itself)
Anything is possible (but the idea that the act of observation magics the scenario into existence is not mainstream ,I think.not that you were bringing it up)
For the sake of this thought experiment I can’t see how one can think there’s the probability of a cat not in the box especially when you put a live cat in there to begin with. At some point one has to trust what they’ve observe, and in this case I think there has to be 100% certainty that a cat, amongst other things used for experiment, is in that box. Otherwise why bother?
If you observed the cat in the box at the outset of the experiment that does not give 100% probability that ,if you look again later it will still be there.(my opinion is just based on what I have picked up over the years so I might have got the wrong end of the stick )
You can still trust what you observed and yet this may not transfer to your next act of observation of the "same"(nothing is ever the same) scenario.
I would agree that as time passes, what was once a live cat will look nothing like a live cat in a box upon observation. So does that mean the live cat that was originally put in the box was actually something else at one time too? Could you say the entire universe was once something else and so on and so on? Is there a probability that it isn't even there? I'm not here? What good is observation then? It almost sounds like saying nothing exists....nothing being something in some broad sense. Crazy shit!!! I'm thinking this is what happens when we don't have all the information.If you observed the cat in the box at the outset of the experiment that does not give 100% probability that ,if you look again later it will still be there.(my opinion is just based on what I have picked up over the years so I might have got the wrong end of the stick )
You can still trust what you observed and yet this may not transfer to your next act of observation of the "same"(nothing is ever the same) scenario.
They are (I assume) talking about the wavefunction that describes the object. This can be used to calculate the a probability of the object being in a particular state (which includes position). The wave function is spread out (through all of space) and has its greatest amplitude at the most likely position (or positions) that the object will be detected.
The whole cat experiment was intended to show how silly it becomes when you try and apply these things on a large scale. There is an extension of the thought experiment where one person opens the box. From the point of view of other people, that person is then in a superposition of knowing the cat is dead and knowing it is alive.
I don't think it makes much sense to think of the cat being both dead and alive. But there is no way of showing that interpretation is QM is wrong.
When I see ripples in a pond am I observing particles moving up and down or the actual or semblance of vibration itself. I mean if a wave can be a particle then why can't a particle be a wave? Is it because that's the only way nature could take a life form to evolve a sense of the wave (by turning it into a particle for convenience.....simplest way) or are vibrations just particles of some kind. When I think of vibrating strings, as in string theory's most fundamental particle, I wonder if that language/description is wrong because I'm questioning what's more fundamental ...the wave or the particle, or is it 50/50? Can I have a particle without the wave or vice versa?
You are always going to struggle to apply QM to the real world.
Curiosity kills the cat.
I try to think that nothing is real. Even you are not real. Just an assembly of atoms or vibrating strings.
Just curious.....Is a 2d pixel a space? I'm moving my cursor across the screen and notice that it can appear to completely disappear or blend in with another image on the screen if lined up correctly. I don't think they are objects sharing pixels but I was wondering if it is at least analogous to superposition? Two images sharing the same pixels or space on the screen?
It depends on what is meant by "wave". If by "wave" it is meant a sinusoidal wave, then wave and particle are equally fundamental. A particle can be regarded as an entity that is at a single location in position space, whereas a wave can be regarded as an entity that is at a single location in momentum space. A notable aspect of the waveparticle duality is that wave and particle represent complementary properties that are subject to the Heisenberg uncertainty principle. But if by "wave" it is meant an arbitrary waveform, then everything is a wave, including a particle, so that a wave is more fundamental.
No. This would suggest that wave and particle are the only two possibilities, but a quantum state can be prepared in many ways that do not result in either wave or particle. For example, the entity emerging from the two slits in the doubleslit experiment is neither a wave nor a particle (it is not at a single location in either position or momentum space).
There is a onetoone relation between these two sets. Indeed, they are connected to each other via a Fourier transformation.
It is worth noting that a wavefunction is a vector in an infinitedimensional Hilbert space, and in a similar way that ordinary space has different coordinate systems, so does Hilbert space, and position space and momentum space are two of many different coordinate systems in Hilbert space. And just as one has rotations in ordinary space or Lorentz transformations in spacetime, one has integral transformations such as Fourier transformations in Hilbert space.
Position space is the "common or garden 3d,xyz space" (or 4d spacetime). Each point in position space is a direction in Hilbert space, the set of all points of position space is the set of all directions in Hilbert space. Each point in momentum space is also a direction in Hilbert space, the set of all points of momentum space is also the set of all directions in Hilbert space, but the directions are different to those corresponding to position space. However, set of all directions in Hilbert space corresponding to momentum space span the same Hilbert space as the set of all directions corresponding to position space.
Thanks for all that.It will hopefully serve for future reference.
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