# Determinism vs. probability

1. Mar 14, 2004

### cripkd

I'm not a physicist, but I like these things. Have question though. After a long talk with a friend,I'm having a hard time understanding why the universe isn't deterministic. So i spent the last 3 hours reading on hawking seminars and other stuff and i think got a question who'se answer will clarify me.
I always thought that the universe was not probabilistic, but just very hard to perceive in it's true state.
So, if we consider the EPR-paradox-explained-for-kids-experiment in which we take 2 balls, a red and a blue one and 2 people, mix the balls, make each of the guys choose a ball, not look at it and separate them by 5000 miles.
Unless one of the guys looks at his ball, is each ball red and blue at once or is there a certain state of the universe, concerning that 2 balls, meaning that the color of each ball is predetermined, but just not known yet?

2. Mar 14, 2004

Staff Emeritus
Most physicists would say that it's false that the universe has "a true state" which it's just very hard to determine. If you take any of the very successful quantum theories seriously, they say that the deep truth about the universe is that it is probabilistic. The underlying reality is the quantum amplitude, which is prior to probability. Heisenberg's uncertainty is not just a failure of technology, it's real.

Whether that means the universe is indeterminate or not is another and deeper question. I don't know the answer to that one. Beware if leaping to conclusions.

3. Mar 14, 2004

### Loren Booda

What is physically deterministic proceeds between total randomness and total certainty. Determinism is actually a function of probability, i. e., the nonlocality (superluminality) of EPR's quantum effect involves a partial correlation, intermediate to the definition of classical interaction and separation.

4. Mar 15, 2004

### cripkd

LOL !
Well, it's my fault for coming here and asking this questions, because, no offense Loren , I can't get most of what you're traing to say :).
I hope I'm not offending anyone by saing this.
SelfAdjoint, but as far as what i understood from the debate around the EPR paradox , the spin of the 2 particles involved is really indefinite before we measure one of them.
So, why can't we tell, based on today's pysics, that the uncertainty principle rules that the state of a the universe is undefined before looking at one of the balls/particles. Not that I'd like that, i'm having a real crisis here :)
PS. On re-reading Loren's post i think i see what you're trying to say. Am i wrong or the EPR paradox was solved by pointing out that the 2 particles are a system and cannot be taken separatley.

5. Mar 15, 2004

### ZapperZ

Staff Emeritus
I think there is a slight misunderstanding here that is causing quite a bit of confusion.

Let's say you have something in which there are several possible outcomes. QM tells you the probability for you to get, upon measurement, each of these outcomes. It doesn't tell you exactly which one you will definitely get upon when you measure it. To some, this is an illustration of the lack of determinism in QM. This is a consequence of the nature of superposition in QM that has confounded many people.

The EPR "paradox" (I put in quotes because it isn't a paradox, really) isn't really about determinism. It is more of the illustration of non-locality and non cause-and-effect consequences of the entanglement aspect of QM. It is not the outcome of a measurement that is of concerned here, but rather the simultaneous, instantaneous determination of the state of all the entangled objects, no matter how far apart they are. This has no issues of "determinism" involved.

Zz.

6. Mar 15, 2004

### cripkd

Could someone explain this a bit more plainly? I guess i know what locality is, what entanglement is, but i don't understand the meaning of that phrase. And could someone explain also what really is the EPR paradox and why isn't it really a paradox?

7. Mar 15, 2004

### slyboy

Confused? You should be.

Confusion arises in these issues because there is ultimately no univeral agreement on how to interpret them. Quantum mechanics tells us how to calculate the probabilities of certain measurement events occuring, but it remains silent on how to interpret these probabilities.

One might suppose that the probabilities just reflect our ignorance about the true state of affairs and they could be eliminated by some deeper theory. Such theories are called 'hidden variable' theories.

However, these theories have a problem because John Bell showed that any such theory must involve influences that travel faster than the speed of light if it is to replicate the predictions of quantum mechanics. He did this by considering a generalization of the EPR experiment in which spatially separated observers can choose to measure one of several different observables on their half of an entangled pair of particles. They make this decision such that there is no time for the information about their choice to travel to the other observer before he has measured his particle unless it travels faster than light. QM says that such experiments can show correlations between the measurement results of the two parties that are not possible in such a local hidden variable theory.

Now, this does not rule out determinism per se, since you can make a non-local hidden variable theory that includes fater-than-light influences. The most popular theory of this type is called Bohmian mechanics. Other possibilities include denying the possibility of free-will. If the observers really have no choice in what observable they choose to measure, then all mesurement outcomes could be decided locally at the beginning of the universe.

Such possibilities are distateful to most physicists, which is why most people say that QM is genuinely non-deterministic.

8. Mar 15, 2004

### quantumcarl

If the dudes with the balls 5000 miles apart, are both looking to see what colour their balls are in an unlit, windowless bathroom at the Chevron, the balls have no colour. The conditions surrounding the experiement are not specified. Even under Barium light the balls would be completely different colours when compared to the description imparted at the begining of the experiment. These conditions are determined by the various states found in the universe. There is no probability factor that suggests what the conditions will be when the balls are finally observed with regard to their colour. We cannot give a probability concerning the conditions unless the conditions are pre=determined by the experimentor. This points to the initiator of the experiment being the determinate source regarding the colour of each ball in question.

9. Mar 15, 2004

### pallidin

Pick me!
Just kidding.
Look, you have a 1-dollar bill and a 20-dollar bill, and you randomly mix them in a black bag.
I reach in and grab one of the bills, not looking at it, and place it in my wallet.
Another individual grabs the other, also not looking at it, and places it in his wallet.
Let's say that the chances of either having either the 1 or 20 dollar bill is 50-50.
Fair enough.
Are we to say that the actual denomination of the bill in my wallet prior to my or his inspection is indeterminate?
Well, indeterminate as far as "guessing" it's denomination, sure.
But, indeterminate as to it denominational actuality in my wallet until it is observed? Absurd!!!
Pick me again!
A coin is tossed in the air, lands on my hand, quickly covered by my other hand so as not to know if its heads or tails.
Is the coin in some quasi-state of heads/tails existance prior to my lifting the covering hand? Wow, I must, as a human observeratory posses very high powers, and surely the coin must quantum-quiver in some way prior to observational influence, as it is hard-stamped heads/tails.
I simply do not buy into the theory, perhaps because in a very curious way, the theory has NEVER been proven at all beyond mathematical constructs. Am I wrong?
Has this theory EVER been shown to actually exist(not inferred) beyond conjecture?

Last edited: Mar 15, 2004
10. Mar 16, 2004

### cripkd

My question exactly :)

11. Mar 16, 2004

### ZapperZ

Staff Emeritus
Re: Re: determinism vs. probability

I think this illustrates why there are major misconceptions on the understanding of the state of superposition in QM. Most people have this kind of impression of the quantum state before measurement - that there IS a definite state the system is in. It is just that our ignorance of it that causes us to put it into some mixture of various outcome. The flipping of a coin is usually an example (of classical probability). When you flip a coin, before you look at it, the coin is EITHER heads OR tails, but not both.

If this were a quantum system, the superposition of the various outcomes (eigenstates) would be interpreted as heads AND tails as in the coin example. The question now is, is this merely a "theory", or mathematical artifact, without any experimental verifications? No, it isn't!

Consider two hydrogen atoms. If they are separated far apart, the energy level of each one is well defined and well-described by the Rydberg states. What happens here is that the electron in each atom can be considered to be localized around each H nucleus. In other words, if you only have 1 electron to share between these two H nucleus, an electron would be at EITHER one OR the other, but not at both simultaneous. The total energy of the system is simply the sum of the individual energy of the two atoms.

Now, let's bring them closer and closer to each other until they feel the presence of each other. In mathematical terms, there are now overlap of the wavefunction due to the distortion of the potential energy field of the individual atom. Something interesting now occurs. You can no longer describe the system as being made up of two individual atoms (no suprise here), but more interestingly, the overlap of the wavefunction seems to imply (if we limit ourselves to the Copenhagen Interpretation) that an electron in the system is SIMULTANEOUSLY spreading itself over BOTH nucleus! The superposition of states here includes the superposition over BOTH locations!

The problem here is that if you try to actually make a measurement of the position of an electron in this system, you will cause a "collapse" of the superposition. The outcome then will only show that the electron is either localized at one, or the other. However, there is more than one way to skin a cat... <pun intended since this is identical to the Schrodinger Cat-type state>

Now, we can test the various consequences of such description. One clearest consequence is that, since the wavefuction has a "phase", you end up having what is known as bonding and antibonding states. What is even more interesting is that there is an energy difference between these two states. (Please remember that the emergence of these two states only occur if the wavefunction contains the superposition described earlier.) Since the energy observable (operator) is non-commuting with the position observable, a measurement of the energy state does NOT collapse the position superposition, i.e. it maintains the scenario where an electron are at BOTH locations simultaneously.

Well, guess what? The energy gap between the bonding and antibonding states in H2 molecule is WELL-KNOWN. In fact, chemists have known about this even way before QM was invented. They just did not have a clear explanation for such phenomena till QM came along. This is simply just one example of the "reality" of quantum superposition. It shows that the strange state of a quantum system isn't merely a reflection of our ignorance of the system - there REALLY is a mixture of various outcomes simultaneously. A particle CAN be in several places at one time (superposition of locations). A photon CAN pass through two slits at one time (superposition of path). And get this, a current can flow in BOTH directions at one time (superpostion of current states), as shown in the various SQUIDS experiments.[1]

These, and many other experimental observations, have shown that such things are more than just "theory".

Zz.

[1] J.R. Friedman et al., Nature v.406, p.43 (2002).

12. Mar 16, 2004

### slyboy

Of course, no-go theorems are notoriously difficult to get right because you have to consider all possible alternatives and you are bound to leave some loopholes open. However, Bell's theorem does show that you either have to abandon this idea for quantum systems OR you have to include an influence that travels faster than the speed of light in your theory. Which one you choose is largely a matter of whether you prefer determinism or locality in your physical theories. Physicists tend to prefer locality because it is very difficult to reconcile a faster-than-light influence with relativity. Bohmian mecahnics, which is a theory of this type, is notoriously difficult to construct in a relativistic setting compared with standard quantum field theory. This doesn't mean you should give up the approach if you are very attached to determinism and indeed several physicists are still working in this direction.

However, there is also another difficulty with determinism in quantum theory, which is a phenomenon called contextuality. This was first proved by Kochen and Specker and is rather difficult to prove compared to Bell's theorem. The content is essentially this:

Suppose you have a system on which you have a choice of making many different measurements. Some of the measurements may include common outcomes. For example, suppose the measurement outcomes are given by perpendicular coordinate axes in 3-dimensional space (e.g. measuring a spin component of a spin-1 particle). One possible measurement would be to measure whether you are pointing along the x-axis, y-axis or z-axis. Another one could be obtained by rotating the previous measurement in the x-y plane, but both measurements have a common outcome, namely the z-axis.

In a deterministic theory you would like to say that all the outcomes of all the measurements were determined as soon as the system was prepared. However, the Kochen-Specker result shows that to be consistent with QM, the value assigned to a particular outcome must depend on which measurement I made. For example, whether or not I am pointing along the z-axis depends on whether I measured x vs y vs z or the rotated version.

To illustrate how weird this is, let me give a more down to earth analogy. Suppose there is a buffet from which I have already chosen whether to eat meat fish or cheese. Classical physics says that there is an answer to the question "Did I choose cheese?". it is simply either true or false. In particular, the answers to the questions "Did I choose cheese, as opposed to meat?" and "Did I choose cheese, as opposed to fish?" are the same when all three are available. Quantum physics says that the answers to these two questions can be different, i.e. even if meat, fish and cheese are all available at the buffet, I can't assign a truth value to the statement that I chose cheese without qualifying the question with an alternative.

This need for such a qualification is what is meant by the term contextuality. It is one of the weirdest aspects of quantum mechanics and presents a severe obstacle for deterministic approaches to quantum theory. Of course, Bohmian mechanics is contextual as well as being non-local, so you can go down that route if you choose to do so.