Quantum randomness vs. dice randomness

[reilly]

Consider the following problems

1. If you were to stop, wherever you are, at three o'clock tomorrow afternoon, how many cars will you see from 3 to 3:10?

2. Why do classical and quantum approaches give identical cross sections for Coulomb scattering?

3. By what percentage will Nordstrom's(Department Store) inventory of all Nike products change over the next two weeks.?

4.If quantum and classical probabilities are different, why do they both use the concept of entropy or Shannon's information? Why can we use basic statistical and thermodynamical concepts for both classical and quantum statistics?What's different about the probability structures above - what answers are there?
Regards,
Reilly Atkinson

 

[vanesch]

What's different about the probability structures above - what answers are there?

Probabilities work the same because they are in all the cases formalisations of our ignorance, but I had the impression that the OP was about the physical origin of this ignorance: is it "unknowable" in principle, or is it just because we happen not to know (because we're too stupid, say) ?

 

[peter0302]

Consider the following problems

1. If you were to stop, wherever you are, at three o'clock tomorrow afternoon, how many cars will you see from 3 to 3:10?

2. Why do classical and quantum approaches give identical cross sections for Coulomb scattering?

3. By what percentage will Nordstrom's(Department Store) inventory of all Nike products change over the next two weeks.?

4.If quantum and classical probabilities are different, why do they both use the concept of entropy or Shannon's information? Why can we use basic statistical and thermodynamical concepts for both classical and quantum statistics?


What's different about the probability structures above - what answers are there?
Regards,
Reilly Atkinson

Again, there are two major issues here. One is determinism versus non-determinism. Any non-quantum process is deterministic at the smallest observable level. But as the process plays out over time, as vanesch said the _classical_ uncertainty in measurement propagates throughout the system and eventually it appears to behave randomly. In your example 1 and 3, both of those things are well understood deterministic processes. Every single car that passes by you between 3 and 3:10 has a human driver who is in his car driving at that exact spot for a very well known (to him!) reason. Every person who purchases shoes at Nordstrom's likewise does so for a very well defined reason.

But multiplied over vast stretches of space and time, these processes cannot be analyzed on an individual basis because they become simply too complex, so we must use statistical analysis to make any sense of them.

Quantum processes, as we've said, are non-determinisitc. You cannot look at the emission of the photon and say you understand why it happened when it did. Even in theory.

The other issue, which I consider separate, is the probabilities vs. probability amplitudes issue, which has also been talked about. You add probability amplitudes of intermediate states, which are complex numbers, and that's what causes interference. In normal statistics, you add probabilities themselves, which are real numbers, and you never get interference.

 

[vanesch]

The other issue, which I consider separate, is the probabilities vs. probability amplitudes issue, which has also been talked about. You add probability amplitudes of intermediate states, which are complex numbers, and that's what causes interference. In normal statistics, you add probabilities themselves, which are real numbers, and you never get interference.

Yes, but this is as always the same ambiguity: when you say "we add amplitudes as complex numbers and then square them" while "we don't do that with normal probabilities", then that is supposing again that those amplitudes, before we added them, evolved them etc... ALREADY represented probabilities in some way.

It is incredible how many "mysteries" one obtains that way, when assigning "probabilities" to "amplitudes" too early. From the double-slit experiment, over quantum erasers, EPR experiments, Afshar's stuff, etc... about all "paradoxes" come from considering amplitudes as some kind of probabilities before measurement. The whole "domain" of "quantum logic" arouse out of that misunderstanding

Amplitudes don't represent probabilities as long as they aren't the amplitudes of irreversibly measured pointer states. According to your favorite interpretation, they represent something physical (MWI, Bohm,...) or are just convenient calculational tools (Copenhagen,...) but they don't represent probabilities until measurement.

 

[peter0302]

Haha. I hear you. I don't mean to imply that the amplitudes have physical significance. :)

So in your favorite interpretation, what are the amplitudes? Are they the "depth" of a world?

 

[reilly]

Let's take care of interference first. Consider throwing rocks in the ocean, at the beach of course. Pick a small spot in the ocean, and ask what the probability, as a function of time, is for the water to be 1 cm, 2cm ... 10.cm above nominal sea level, similarly look at the spatial distribution of the probability of various levels. Don't forget that the norm of a complex number is a real number.

Determinism? How in the world can you say that, at the core, my example 1 is a deterministic situation? In particular, what evidence is there to support the notion that human behavior is deterministic?

The issue with Nordstrom is not that individuals make purchases under their own volition, it's how many make purchases. How's that deterministic?
Regards,
Reilly Atkinson

Again, there are two major issues here. One is determinism versus non-determinism. Any non-quantum process is deterministic at the smallest observable level. But as the process plays out over time, as vanesch said the _classical_ uncertainty in measurement propagates throughout the system and eventually it appears to behave randomly. In your example 1 and 3, both of those things are well understood deterministic processes. Every single car that passes by you between 3 and 3:10 has a human driver who is in his car driving at that exact spot for a very well known (to him!) reason. Every person who purchases shoes at Nordstrom's likewise does so for a very well defined reason.

But multiplied over vast stretches of space and time, these processes cannot be analyzed on an individual basis because they become simply too complex, so we must use statistical analysis to make any sense of them.

Quantum processes, as we've said, are non-determinisitc. You cannot look at the emission of the photon and say you understand why it happened when it did. Even in theory.

The other issue, which I consider separate, is the probabilities vs. probability amplitudes issue, which has also been talked about. You add probability amplitudes of intermediate states, which are complex numbers, and that's what causes interference. In normal statistics, you add probabilities themselves, which are real numbers, and you never get interference.

 

[ThomasT]

Quantum processes, as we've said, are non-determinisitc. You cannot look at the emission of the photon and say you understand why it happened when it did. Even in theory.

Not to be nitpicky , but to say that quantum processes are nondeterministic "even in theory" is superfluous and for that reason can be a bit confusing. How the processes of quantum theory might approximate the processes of nature is the problem.

In the same vein, saying that quantum processes are truly random is also superfluous if truly is intended to refer to the relationship between quantum theory's calculational framework and natural processes.

Applying quantum theory to the analysis of natural process we have it that no deeper understanding of nature than a statistical one is allowed by the principles of the theory.

But these principles didn't arise from an understanding of the deep nature of reality. The point of departure for the quantum mechanical representation is the behavior of the instruments and materials used in experiments.

We can't scientifically argue whether the nature of reality is deterministic or nondeterministic.

So, if your pronouncements regarding determinism and randomness are intended to refer to quantum theory, then I wholeheartedly agree with you. However, if they're intended as statements regarding the nature of reality, then I don't. I took them to be the latter, and if I've made a mistake by doing so, then I apologize.

 

[vanesch]

Haha. I hear you. I don't mean to imply that the amplitudes have physical significance. :)

So in your favorite interpretation, what are the amplitudes? Are they the "depth" of a world?

For sure they are NOT always equivalent to probabilities. Sometimes they are (when they have something to do with observation), sometimes not. That's the point.

 

[reilly]

vanesch -- Under what circumstances is a QM amplitude equivalent to a probability? I'm assuming you are referring to something other than the norm of the amplitude.
Regards,
Reilly

For sure they are NOT always equivalent to probabilities. Sometimes they are (when they have something to do with observation), sometimes not. That's the point.

 

[vanesch]

vanesch -- Under what circumstances is a QM amplitude equivalent to a probability? I'm assuming you are referring to something other than the norm of the amplitude.

A set of quantum amplitudes (that is, the components of the state vector as seen in a certain basis) gives rise to a set of probabilities (namely, the norms squared of those amplitudes), whenever the state vector describes an irreducible measurement, and the basis chosen is the pointer basis (or the measurement basis).

The probabilities are those of (potential) observation of the result.

I say, potential, because one might not bother to look at the result, but which is nevertheless irreversibly recorded somewhere.

This is not interpretation-related.

As an MWI-er, I take this probability to be entirely on the side of the observer: it is not the probability of one or the other thing "happening", but it is the probability of the observer observing one or the other thing. But this is of course interpretation-related.

 

[FredKJohnson]

I came across your forum while I was looking into randomness. Shaking dice in a cup is not a deterministic system, it is chaotic. Think of Kepler's three body problem or the physics of weather systems. Modeling dice shaken in a cup involves second order differential equations. A small error in the initial state is magnified. Providing someone isn't cheating trying to control the dice. Also you must assume the dice are balanced cubes within good tolerances such as certified casino dice. The randomness is very good.

 

[Fenderplayer]

I came across your forum while I was looking into randomness. Shaking dice in a cup is not a deterministic system, it is chaotic. Think of Kepler's three body problem or the physics of weather systems. Modeling dice shaken in a cup involves second order differential equations. A small error in the initial state is magnified. Providing someone isn't cheating trying to control the dice. Also you must assume the dice are balanced cubes within good tolerances such as certified casino dice. The randomness is very good.

I think it is a deterministic model. You can masure the positions of the dice in the cup, the shape and inside diameter of the cup, the size and weight of the dice on each side, air resistance, the hardness of the surface upon which they are thrown, vectors, etc, ad nauseum... and come up with a mathematical model to predict the outcome. So maybe chaos is deterministic. Q-randomness is truely random because, so far, specifice locations, predictions are not yet possible. These discussions remind me of the debates between Einstein & Bohr. In time, when unified field theory is truly resolved, perhaps Q-randomeness will cease to exist. ?

 

[FredKJohnson]

I think it is a deterministic model. You can masure the positions of the dice in the cup, the shape and inside diameter of the cup, the size and weight of the dice on each side, air resistance, the hardness of the surface upon which they are thrown, vectors, etc, ad nauseum... and come up with a mathematical model to predict the outcome. So maybe chaos is deterministic. Q-randomness is truely random because, so far, specifice locations, predictions are not yet possible. These discussions remind me of the debates between Einstein & Bohr. In time, when unified field theory is truly resolved, perhaps Q-randomeness will cease to exist. ?

Sure you can define the initial state conditions, never said you couldn't. Say you have five dice in the cup playing poker dice. You shake it, they start banging against each other and the walls of the cup. It makes the Kepler three body problem simple but I suppose you have a solution for that. If so I'd be going to Sweden to pick up a prize. This is more like attempting to model the physics of weather patterns. The perturbations start to build in any model of it pretty fast. You have a hope perhaps that randomness will be resolved. That's different than having the math to do it. Any model for this would be non-linear. Good luck!