Is part of the evidence for superposition that entangled particles are never found in similar states when their wavefunction is collapsed? Does it follow that If they weren't connected, we would expect to see some statistical frequency of similarity of states as well?

Edited July 6Jul 6 by StringJunky

In an undetermined state, like spin, the odds of getting one result is 1/2.

If I measure one particle and get a result and then measure another, it will be in a given spin state half the time

But in entanglement, the odds of getting the result is 1 or 0, depending on the correlation you have in how you prepared the entanglement.

39 minutes ago, swansont said:

In an undetermined state, like spin, the odds of getting one result is 1/2.

If I measure one particle and get a result and then measure another, it will be in a given spin state half the time

But in entanglement, the odds of getting the result is 1 or 0, depending on the correlation you have in how you prepared the entanglement.

Right, thanks.

For two particles to be quantum entangled, two conditions need to be satisfied:

(1): The states of the two particles are correlated. That is, the state of one particle depends on the state of the other particle.

(2): The combined state of the two particles is a quantum superposition.

If only (1) is satisfied, the two correlated particles may be classical particles (eg billiard balls). Or it may be the result of measuring an entangled pair of particles, causing the quantum superposition to "collapse" (Copenhagen interpretation). If only (2) is satisfied, the particles are individually a quantum superposition, and therefore the combined state of the two particles is also a quantum superposition, but the two particles are completely independent of each other, perhaps because they are in different galaxies.

It is worth noting that an arbitrary two-particle state is most likely to be an entangled state. However, the entangled states usually encountered in entanglement experiments are special entangled states, not the run-of-the-mill arbitrarily chosen entangled two-particle states. (In mathematical terms, the Hilbert space of the two-particle states has a higher dimensionality than the Hilbert space of the corresponding non-entangled two-particle states.)

I think it is worthlooking more deeply into the words

superposition, entanglement ,collapse and measurement

The key to this is understanding how these work and the fact that the maths contains solutions that are always there but are not or can never be implemented.

Comparison with non quantum superposition is also helpful.

Thanks for posting this @StringJunky

Interesting stuff.

Is the twin slot experiment also, almost directly, evidence of superposition. (We just can't see it right?)

Showing the effects of said superposition projected into the multiple slots they create on the other side.?

3 hours ago, Imagine Everything said:

Thanks for posting this @StringJunky

Interesting stuff.

Is the twin slot experiment also, almost directly, evidence of superposition. (We just can't see it right?)

Showing the effects of said superposition projected into the multiple slots they create on the other side.?

I think so.

Thank you @StringJunky

It's a very odd but also very very interesting scenario isn't it.

Sorry if went slightly OT, didn't mean to take anything away from your original post.

On 7/6/2025 at 11:20 PM, StringJunky said:

Is part of the evidence for superposition that entangled particles are never found in similar states when their wavefunction is collapsed? Does it follow that If they weren't connected, we would expect to see some statistical frequency of similarity of states as well?

First the bolded bit is not accurate.

I did say in my previous post that it is worth looking into the difference between entanglement and superposition and the connection between the two as well.

I suggest a good way to do this is to study the difference between electtron spin resonance and nuclear magentic resonance spectroscopy.

Both cases provide what I consider the most rock solid examples of entanglement as a result of superposition, but the Pauli exclusion principle only applies to ESR.

Edited August 29Aug 29 by studiot