Quantum Mechanics and the Nature of Determinism

[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 anyone 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?

 

[debra]

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 anyone 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!
Any comments on the above?

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

 

[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.

 

[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?

 

[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?

 

[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.

 

[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.

 

[Demystifier]

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 anyone 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?

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

 

[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.

 

[Curious6]

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.

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?

No we are not disturbing it as in the classical mechanical sense.

Are we disturbing it in a quantum sense then?

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.

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.

 

[f95toli]

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.

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.

 

[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.

 

[Demystifier]

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.

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.

Before measurement, the position and momentum are undetermined - that is the difference.

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

 

[Demystifier]

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 defined.

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

 

[malawi_glenn]

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

 

[Demystifier]

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

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.

 

[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.

 

[Demystifier]

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.

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?

 

[malawi_glenn]

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

 

[Demystifier]

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

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.

 

[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.

"True" random numbers vs. pseudorandom numbers

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." How to distinguish a "true" random number from the output of a pseudo-random number generator is a very difficult problem. However, carefully chosen pseudo-random number generators can be used instead of true random numbers in many applications. Rigorous statistical analysis of the output is often needed to have confidence in the algorithm.

Generating random numbers from physical processes

There is general agreement that, if there are such things as "true" random numbers, they are most likely to be found by looking at physical processes which are, as far as is known, unpredictable.

A physical random number generator can be based on an essentially random atomic or subatomic physical phenomenon whose unpredictability can be traced to the laws of quantum mechanics. An example of this are the Atari 8-bit computers, which used electronic noise from an analog circuit to generate true random numbers.[2] Other examples include radioactive decay, thermal noise, shot noise and clock drift. Even lava lamps have been used by the Lavarand generator.

To provide a degree of randomness intermediate between specialized hardware on the one hand and algorithmic generation on the other, some security related computer software requires the user to input a lengthy string of mouse movements, or keyboard input.

Post-processing and statistical checks

Even given a source of plausible random numbers (perhaps from a quantum mechanically based hardware generator), obtaining numbers which are completely unbiased takes care. In addition, behavior of these generators often changes with temperature, power supply voltage, the age of the device, or other outside interference. And a software bug in a pseudo-random number routine, or a hardware bug in the hardware it runs on, may be similarly difficult to detect.

Generated random numbers are sometimes subjected to statistical tests before use to ensure that the underlying source is still working, and then post-processed to improve their statistical properties.

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

 

[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!

 

[p764rds]

According to the CI the wave is non deterministic, according to some other more abstract theories the wave is deterministic.

"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?

 

[jtbell]

According to the CI the wave is non deterministic,

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

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

 

[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)

 

[The Dagda]

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

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

Are you trying to tell me the wave function is deterministic, that's fine it's just usually only people who believe in say MWI bother with such a description.

By non deterministic I mean probabilistic? Why what did you think I mean? The wave function resolves as a probability distribution of possible states, that is not what I would call deterministic in any sense of the word.

 

[enotstrebor]

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.

This is a most praise worthy comment!


[Side bar: Science is defined by webster as a ``state or fact of knowing' as appose to intuition, belief, ..."

Which ``state or fact of knowing'', the copenhagen, the many worlds, the Bohemian, the transactional, ...?]

 

[jms5631]

Are you trying to tell me the wave function is deterministic, that's fine it's just usually only people who believe in say MWI bother with such a description.

By non deterministic I mean probabilistic? Why what did you think I mean? The wave function resolves as a probability distribution of possible states, that is not what I would call deterministic in any sense of the word.

Regardless of interpretation, the unitary time evolution of the schrodinger equation is deterministic. That is not an area of debate, but forms an important substratum of quantum mechanics. Probabilities come from the outcomes of measurements which are(or appear to be for the MWI folks) probalistic. But the evolution of the wavefunction of a quanum system, which we use to derive those probabilities, is entirely deterministics, regardless of interpretational issues. You can calculate beforehand the distribution of probability for a measurement give the predictable evolution of a system, to me that is determinism in any sense that matters.

 

[The Dagda]

Regardless of interpretation, the unitary time evolution of the schrodinger equation is deterministic. That is not an area of debate, but forms an important substratum of quantum mechanics. Probabilities come from the outcomes of measurements which are(or appear to be for the MWI folks) probalistic. But the evolution of the wavefunction of a quanum system, which we use to derive those probabilities, is entirely deterministics, regardless of interpretational issues. You can calculate beforehand the distribution of probability for a measurement give the predictable evolution of a system, to me that is determinism in any sense that matters.

I agree but I was talking more broadly. Thus the confusion, of course in experiment the model is perfectly deterministic given the assumption that the wave is real, that does not lead to the conclusion though that QM is deterministic, that is an unknown.

If that is all that matters to you then you have MWI, and are no doubt happy with its conclusions, however not everyone agrees that this means QM is fundamentally deterministic nor does there seem to be experimentally any indication that it isn't "random" or at least ill defined. If you actually look up the definition of deterministic, probability is not the least of your concerns.

 

[Gokul43201]

If that is all that matters to you then you have MWI, and are no doubt happy with its conclusions, however not everyone agrees that this means QM is fundamentally deterministic nor does there seem to be experimentally any indication that it isn't "random" or at least ill defined.

What exactly is ill-defined?

 

[jms5631]

I agree but I was talking more broadly. Thus the confusion, of course in experiment the model is perfectly deterministic given the assumption that the wave is real, that does not lead to the conclusion though that QM is deterministic, that is an unknown.

If that is all that matters to you then you have MWI, and are no doubt happy with its conclusions, however not everyone agrees that this means QM is fundamentally deterministic nor does there seem to be experimentally any indication that it isn't "random" or at least ill defined. If you actually look up the definition of deterministic, probability is not the least of your concerns.

I'm sorry, but I'm not sure what you're saying or what the premise of your argument is. You seem to be mistaken in believing that stage 1 deterministic time evolution demands MWI by itself. This assuredly is not the case, and is only an interpretation of the quantum formalism. Of course measurement outcomes are probalistic, but the pre-measurement probability distribution evovles in a perfectly deterministic manner in any interpretational framework. The philosophy of quantum mechanics is without a doubt an exceedingly complex and counter-intuitive endeavor, but I think you're getting hung up on a non-problem.