Wave Function Collapse in Quantum Mechanics: Understanding Probability

[blumfeld0]

Hello. In QM we can determine the probability of any event ocurring given the wavefunction. Once we actually take a measurement the particle 'picks' a state to be found in.
so my question is how do we know a priori that the particle is in two or more states at the same time before we make a measurement
thank you
blumfeld0

 

[ZapperZ]

Hello. In QM we can determine the probability of any event ocurring given the wavefunction. Once we actually take a measurement the particle 'picks' a state to be found in.
so my question is how do we know a priori that the particle is in two or more states at the same time before we make a measurement
thank you
blumfeld0

Because you can make a measurement of an observable that does not commute with the position operator. You can measure the energy, or momentum, etc. In some cases, you will find a measurement that can only be explained if the particle are in a superposition of an observable. An electron are in a superposition of locations to be able to produce the bonding-antibonding bonds in H2 molecule, or a supercurrent is in a superposition of current directions to be able to produce the energy gap measured in the SQUID experiments of Stony Brook/Delft experiments.

By measuring the non-commuting observable, you do not destroy the superposition of other non-commuting observables. Yet, you can still get the effects due to it.

Zz.

 

[blumfeld0]

I understand a little better. I guess my only problem now is that I don't understand what it means to commute? What does it mean physically?
thanks

blumfeld0

 

[wangyi]

Commute means the two operators concerned have so many common eigenstates that these states forms a complete set. This physically mean the two measurment makes no difference when one performs before or after the other.

i hope it can be of help:)

 

[CarlB]

I think the best way to understand the Bell inequality and why it implies that the world is a bit stranger than classical mechanics can invision is to count up the probabilities yourself, establish the inequalities, see that they are reasonable, and then stand in awe on realizing that the experiment has been made and the inequalities are not observed.

A short description of the issue is that there are correlations between the two measurements that eliminate the possibility of there not being a sort of communication between the two measurements that must travel faster than light. The communication cannot be used to transfer information, it's just in the correlations.

If the correlation were as simple as, for example, one guy always getting a "heads" when the other guy gets a "tails" and vice versa, it could be explained by simply supposing that a single coin was flipped earlier and then copies with opposite results "built into" them were handed out. But the correlation is not this simple. It's complicated in that it involves three different ways the coin can be flipped, and each of the two measurers can choose to measure the coin independently in those three ways. So it is only the overall correlations for all the possible ways the experiment can be run that are contrary to common sense.

Hey, if it were obvious, it wouldn't have sat around undiscovered in QM for so many decades. I think it's stunning that basic physics like this can date so recently. Makes it kind of exciting, doesn't it.

The math for this is not that bad. Try this link:
http://en.wikipedia.org/wiki/Clauser_and_Horne's_1974_Bell_test

Note, the above Wikipedia article is being disputed. The people disputing the accuracy of the information in the above link have little relevance to the thought of mainstream physics at this time. In addition, not that it matters, I think they're wrong too, and I'm hardly a big fan of the standard interpretation of QM.

Carl

 

[Ratzinger]

so my question is how do we know a priori that the particle is in two or more states at the same time before we make a measurement

In qm it's about ensembles, i.e. large number of particles all in the same state. The exact state is prepared again and again, and what happens after measurement can only be described statistically. That's an experimental fact.

In order to predict this statistical behavior, qm assumes all particle of the ensemble to be the same superposed state before measurement.

A quantum state before measurement is truly probabilistic, no hidden variables. What the reality of this superposition is, our classical minds can't tell, but it gives the right statistical prediction of what we measure.