That isn’t the case at all; why are you adding this (fictitious) requirement?
Particles don’t collapse; wave functions “collapse”. It seems every message from you to me contains this kind of problem [the confusing of mathematical objects with physical objects].
I recommend not worrying about fancier versions of the experiment until you have an understanding of the standard “simple” version. For example:
Which of the following wave functions (position basis) are “collapsed”?
A:
B:
mmmhhh…
I would say A.
Both are “collapsed”. A is collapsed in position, B is collapsed in momentum. Of course, this requires A to be “un-collapsed” in momentum, and B to be “un-collapsed” in position.
It would be much more clear if instead of saying “collapsed” we said: the object’s wave function has collapsed (changed) so that it is only composed out of a single plain wave, guaranteeing you can only get one possible result should you measure the associated variable, on the associated particle; and consequently the wave function in the conjugate basis will be a combination of every possible plain wave in that basis (typically an infinite number of them), leading to you getting a random result should you try to make a measurement associated with that basis. But instead people get lazy and say collapsed, leading to people who only read the headlines thinking a particle can collapse; or worse that there is something magical about this.
But aren’t you just shifting the mystery from “collapse” to “getting a random result”?
The outcome of the experiment is the same: the random measurement could occur at any possible position of the particle, and the detector may detect nothing. However, the detector must have somehow caused a difference. How?
What mystery you are talking about? When you measure a particle and learn something about it, we erase the previous wave function, and replace it with a wave function that corresponds to what we found.
Just like if I calculated the odds of you being dealt a royal flush of diamonds in 5 card stud (1/2598960). But if I then peeked at 4 of your cards and find the jack, queen, king, and ace of diamonds, that will cause me to erase the previous probability, and replace it with a much larger probability (1/48). It isn’t a mystery that gathering additional information about an object, can change probabilities of outcomes associated with the object. This isn’t magic.
the same as what?
What random measurement are you talking about? No one has mentioned random measurements up to this point (as far as I can tell).
A difference between what two things? I have no idea what you are talking about at this point; maybe you could start over and describe EXACTLY what exact situation/experiment you are talking about?
In the double-slit experiment, the result you obtain on the screen changes depending on the measurements you make. You get an interference pattern when no measurement is made, but two blobs if you take a measurement. This isn’t just about eliminating probabilities; we are also observing a real physical outcome.
the result on the screen; IS THE MEASUREMENT
Not only on the screen, but you can also make a measurement at the slits themselves; this is the double-slit experiment.
If you place a detector in one of the slits, you can measure where the photon/electron/whatever is passing through. This changes the result on the screen.
No that is a different experiment.
yes, because that is a totally different experiment. Different experiments can have different outcomes. This isn’t magic.
ps:
creating an electron on the side of the slit near the screen (then having it hit the screen), yields a different result than creating an electron on the far side of the slits and having it encounter the slits then hit the screen. It is a totally different experiment. So the fact you don’t get the same outcomes shouldn’t surprise anyone!
Ok, let’s move on to the double slit experiment. You mentioned that the wave function is only a mathematical construct and not something mysterious. If that’s the case, then why does it produce an interference pattern? What is the particle interfering with?
The length of the two possible paths [one though each slit] to a given location on the screen typically differ. When they are the same, the probability of finding an electron at that location is relatively large, when they differ by 1/2 a cycle, they cancel perfectly (0 probability). When they differ by a whole cycle, the probability of will be large again. In most locations they differ by some other amount, so it varies from location to location smoothly. That is where the pattern comes from.
PS: When an outcome can happen more than one way, classically we add their probability together to get the probability of the outcome. However in QM we do something slightly different. We add their probability amplitudes. Unlike actual probabilities, probability amplitudes can be negative (or even complex). This is how you can have the sum of two paths give less probability than either path by itself (with the most shocking result when the probability amplitudes cancel giving 0 probability to find an electron).
Therefore, the particle behaves like a wave, but you mentioned that the wave is only a mathematical construct. So, while the wave is a mathematical construct, it produces real, observable results.
No, particles are particles because they deposit all their momentum into a single location. The states are modeled as mathematical functions, special mathematical functions known as wave functions. The wave function encodes every thing that can be possibly known about the particle (this is why you have to change/collapse it when you learn more!). It is not physical thing (at least by Copenhagenist), it is a bookkeeping device. Not unlike a company’s financial records. Don’t confuse the company for their files. Don’t confuse a particle with the mathematical object we use to store its details.
I’m not saying the wave function is real; I’m only saying that the interference pattern we observe is real. This pattern is not expected from classical particle behavior, right?
Yes, and I already explained why: because we don’t calculate probabilities the classical way anymore. Classically to get a pattern like that, you’d need to have one of the probabilities be negative (at least some of the time), so it could cancel the other (to give you a sum of 0). But there is no such thing as negative probability, so this pattern is impossible classically. Luckily, we don’t live in a classical world, so this isn’t a problem. The classical description works pretty good when you have a huge number of objects; it gets worse and worse the smaller number of objects you work with; until eventually when you come to an experiment like this, where the predictions from classical logic conflict with measurements. That is why this experiment is so counter-intuitive; because it clashes violently with our naive assumptions about the world should work. But I assure you, the rules are simple (but weird). It isn’t magic.
PS:
Classically in a situation where a particle can pass through two paths to reach a certain location:
A)The probability of reaching the location from path A (through slit A)
B)The probability of reaching the location from path B (though slit B)
The following two relations will always be true classically:
A + B => A
A + B => B
Both of these relations are not true in general (in QM).
Well, this is magic from a classical viewpoint. Or rather, the classical viewpoint was not the full picture.
We’ll continue tomorrow
the classical view point is trash
I guess not. I recommend forgetting about the double slit experiment; there is so much bullshit posted on that topic, that the layman basically has no chance.
Concentrate your focus on the “Stern-Gerlach Experiment”; it is much simpler, yet has the same weirdness. This is the fundamental experiment that forced quantum mechanics upon us.
