# Quantum Mechanical Weirdness

1. Feb 5, 2009

### Curious6

I asked these questions elsewhere but on second thought they make much more sense together.

1. If particles can move around in seemingly random ways, are they maintained within an object or is there occasional 'jumping out' of particles from within that object? By an object I mean something like a table, a person's body, a rock....is it the case that at any one time certain particles are moving out of the object and certain objects in? If anybody could give any insight on this it would be much appreciated!

2. We are not able to determine the position AND the momentum of a particle at any given time, but however, that does not mean that the particle does not have position AND momentum at any given time. Is this right? If so, then, to find out if a particle was moving 'randomly' we'd have to know whether for any given momentum and position it would move to different positions at different times. However, this is impossible because of the uncertainty principle.

Any comments on the above?

2. Feb 5, 2009

### debra

Jumping out of rocks? I suppose they could 'jump' a nano meter or so - seems like science fiction to me though.

3. Feb 5, 2009

### malawi_glenn

The thing is that the particles in quantum world don't move randomly, their position is undetermined until it is measured. A QM particle does not have a clear trajectory, as compared with a canon ball.

That is an important concept in quantum mechanics. We can't imagine or make a movie how the particles are moving, we can only draw the wave function -> the

The particle has position and momentum before the measurement, but WHICH configuration it had is meaningless to ask in QM.

It is like flipping a coin, while the coin is in the air - it has two sides, but when it lands in your hand, one side has been chosen. The difference is that if you know everything about the properties of the coin and the initial flipping force given to it, you can determine its outcome with 100% accuracy, in principle. In QM, these processes are truly random.

4. Feb 5, 2009

### Curious6

OK, thanks for the answers malawi glenn. Now, let me put this in another way. Say we have a machine that emits particles in an identical fashion. These particles pass through a slit. If at the slit we were to calculate particle number 1's momentum, we couldn't know its position because of the uncertainty principle. Now for particle 2 instead of measuring momentum we measure its exact position when it is at the slit. Given that the machine is emitting particles in an identical fashion, we could assume particle 2's momentum to be the same as the momentum calculated for particle 1, so that knowing particle 2's position would allow us to calculate where it would be next time we were to look for its position since we would know both its position and its momentum (based on our calculation of the momentum of particle 1). Anything wrong with this logic?

Last edited: Feb 5, 2009
5. Feb 5, 2009

### malawi_glenn

first of all, your slit will have a spread in position, so there is also a practical uncertainty.

Secondly, you have to know how a particles wave function evolve in time and space. You will have a wave packages with super positioned momentum and position eigenstates.

Third, how would you know that your machine produces identical fashion particles?

6. Feb 5, 2009

### Curious6

Say the slit is fashioned in such manner that it could allow only one particle to pass, and that it theoretically produces identically-fashioned particles.

Anyways, that thought experiment is just to illustrate a question I have, which is sort of unresolved. It can basically be put as follows: is the reason we can't observe a particle's position and momentum due to a particle not having a momentum and position at any given time or just because by observing it we are disturbing the particle's behavior so that we cannot know the position and momentum at the same time (e.g., by observing it we are always shedding light on it therefore disturbing it)?

Furthermore, you have said a number of times that in QM particles do not behave randomly. Do you mean that if we were to know a particle's position and momentum at the same time we could calculate its position in the next second but that there is intrinsically no way of knowing the position and momentum at the same time? Or are you saying that even if we knew a particle's position and momentum at same time we could still not predict its position in the next second?

Any comments would be much appreciated! Thanks.

7. Feb 6, 2009

### malawi_glenn

But you will obtain the single slit diffraction pattern, just as with light - due to the probabilistic nature of the particle trajectory.

You are neglecting this fact, and you also assume that only one value of position and momentum will be obtained, but that is not the case since a propagating particle will have a spread in its wave package.

No we are not disturbing it as in the classical mechanical sense. If you know math, I can send you a derivation of the uncertainty relation.

Even if we knew the particles momentum and position at a certain time, we can not predict where it would be and with what momentum the next time we want to measure. This is due to the intrinsic probabilistic nature of quantum mechanics.

8. Feb 6, 2009

### Demystifier

Have you ever heard about the Bohmian interpretation? I think you might like it. See also my blog.

9. Feb 6, 2009

### malawi_glenn

Bohm intepretation of QM is another way of doing QM. What is not taught in school is that different implications of QM exists. What we learn in school is the Copenhagen interpretation. But there are others, such as Bohn Intepretation, and multiverse model and so on.

10. Feb 6, 2009

### Curious6

What is meant by a spread in a particle's wave package? Does that basically mean the wave package contains information on both the particle's location and momentum distributed in a probabilistic way?

Are we disturbing it in a quantum sense then?

OK, I see. However, you said a number of times the quantum particles don't move randomly. This implies it moves according to a set of rules (or laws if you wish). However, since you also say in this quote that even if we knew the particle's momentum and position we could not predict its position at any future time, the conclusion one is forced to draw from that is that it's behaviour is random. Could you please clarify these statements? Thanks.

11. Feb 6, 2009

### f95toli

I think you are missing the main point here: It is not only the desciption that is probabilistic, it is the particle itself; or more specifically what would be considered to be a particle in classical physics.
The wavefunction propagates in a deterministic way so there is nothing "random" about QM as long as we do not perform a measurement, but the wavefunction is of course a distribution which is why the measurement is probabilistic.

Now, the ONLY time you can talk about the particle having a definite position or momentum is when you perform a measurement; when you are NOT measuring these quantities are simply not definied; from a mathematical point of view the particle does not HAVE a position or momentum; the particle is really just a "quantum mechanical object" which evolves in time.
Hence, the main issue here is that there is no such thing as a classical particle in QM.

12. Feb 6, 2009

### malawi_glenn

f95toli made many good points.

The thing is that "random motion" is that one can think that the particle has a well defined trajectory, but randomly oriented. The thing in QM is that concept of trajectory is meaningless - the particle only has a definite position and momentum when you have measured it. Before measurement, the position and momentum are undetermined - that is the difference.

So the concept of random path is not accurate enough, the 'path' that a quantum particle will take when going from A to B is the sum of ALL paths, each path weighted by the exponential of the action (time integral over the lagrangian) -> the quantum particle takes all possible paths "at once". Asking WHICH of these paths the particle took, is meaningless to ask.

Now regarding your first question in your last post, the wave function in position space will evolve with time when it propagates towards the slit. That is my things as the two slit interference pattern occurs, the particle location "spreads" in as it evolves in time.

2nd) It is hard to tell, what one does is that measurement of a quantity A on state |psi> will make that state collapse into state which is an eigenstate to that operator for A. And since the position (A) and momentum (B) operator does not commute (AB - BA is not zero), one can derive the uncertainty relation.

13. Feb 9, 2009

### Demystifier

What you say here is in contradiction with what you said previously, that "Bohm interpretation of QM is another way of doing QM". In the Bohm interpretation, the concept of trajectory is not meaningless and particle has a definite position and momentum even when you do not measure them.

Undetermined by what? By experiment? By theory? By nature itself?

Last edited: Feb 9, 2009
14. Feb 9, 2009

### Demystifier

Defined by what? By measurement? By theory? By nature itself?

Last edited: Feb 9, 2009
15. Feb 9, 2009

### malawi_glenn

When I talk about QM, I do it in Copenhagen interpretation.

16. Feb 9, 2009

### Demystifier

That's fine. But then, when you say something that strongly depends on the interpretation, it is fair to specify what interpretation do you have in mind. It is very important to distinguish the interpretation-independent claims from the interpretation-dependent ones. Especially in discussions on quantum mechanical weirdness.

17. Feb 9, 2009

### malawi_glenn

The paradigm is Copenhagen interpretation, so these things aren't even mentioned in standard textbooks on QM (e.g Sakurai etc.) It is claims from outside the paradigm which needs further cautions and specifications.

18. Feb 9, 2009

### Demystifier

Of course, standard textbooks do not say that QM is weird or that it is not weird. So if someone asks about the weirdness of QM, don't you think that one should step out form the textbook paradigm?

19. Feb 9, 2009

### malawi_glenn

wierd is perhaps not the best word, counter-intuitive is most likley the wording used in textbooks.

20. Feb 9, 2009

### Demystifier

Maybe you are right. But in my opinion, only the interpretation-dependent claims (if any) in standard textbooks are counterintuitive.

Example:
If a textbooks says that a probability of a result of a measurement is given by some equation, such a claim is neither interpretation-dependent nor counterintuitive.
But if it says that without measurement particles do not have positions, such a claim is both interpretation-dependent and counterintuitive.

21. Feb 9, 2009

### The Dagda

According to the CI the wave is non deterministic, according to some other more abstract theories the wave is deterministic. Me I go with the consensus, but it may be wrong, who knows?

There's a fine line between random and non deterministic. So fine that you could theoretically use a quantum computer to produce random results rather than the usual pseudo random results of your average PC. In this case though we could probably settle for the term probabilistic, but potentially infinitely probabilistic.

If x can be a number between negative infinity and infinity then if it quacks like a duck. That said we have ways of means of getting pesky infinities into manageable boxes, whether that is actually a trick or it is reflective of what is going on who knows? It's all a matter of interpretation and for the most part is a philosophy of science issue. The only reason CI stands out is because it has at least some indirect experiments working for it, but again the implications of these are subject to a never ending discussion on what "really" is.

http://en.wikipedia.org/wiki/Random_number_generator

Last edited: Feb 9, 2009
22. Feb 10, 2009

### Curious6

I've been away a couple of days from these forums and received a number of very interesting replies on my questions. Thanks to everyone for helping shed light on this issue!

23. Feb 10, 2009

### p764rds

"There are two principal methods used to generate random numbers. One measures some physical phenomenon that is expected to be random and then compensates for possible biases in the measurement process. The other uses computational algorithms that produce long sequences of apparently random results, which are in fact completely determined by a shorter initial value, known as a seed or key. The latter type are often called pseudorandom number generators.

A "random number generator" based solely on deterministic computation cannot be regarded as a "true" random number generator, since its output is inherently predictable. John von Neumann famously said "Anyone who uses arithmetic methods to produce random numbers is in a state of sin."

Isn't it possible to produce random numbers to a defined number of decimal places?? And in practice - say collisions - to how many decimal places must a state be defined, or are there windows?

24. Feb 10, 2009

### Staff: Mentor

What do you mean, specifically, by "the wave is non deterministic?"

Given the QM wave function of a system at some initial time $t_0$, $\Psi(x, t_0)$, the time-dependent Schrödinger equation uniquely determines the wave function at later times, $\Psi(x,t)$, until we make a measurement of some quantity and the system is not in an eigenstate of that quantity.

25. Feb 10, 2009

### malawi_glenn

One can say that in CI the only thing that is deterministic is the evolution of the probability distribution (i.e. the wavefunction)

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