Is Quantum Mechanics Deterministic or Is There an Element of Randomness?

[Nick R]

Hi, my question is simply: "Is all physical phenomena deterministic?" or said different, "Can all physical systems be predicted exactly given initial conditions?"

I am not very far into my studies in physics, but I am aware there is such a thing as the "Heisenberg Uncertainty Principal" and it has to do with an uncertainty of the state of very small particles.

Is it generally accepted by physicists that the uncertainty principal is simply modeling phenomena that we are currently unable to explain analytically or is it suspected that there is an actual randomness or a sort of divine influence in events that actually makes the future indeterminate?

 

[Mk]

vanesch has written a lot of great posts about this.

I can't find the one I was looking for, but here's one:

Randomness is of course epistemologically the lack of knowledge, but the question is in how much we could, if we wanted, in principle, fill in that lack of knowledge, and it is on this basis of principle that our different categories reside.

The first category is a pseudo-random number generator as in a computer. This is in fact a finite-state machine that is perfectly predictable, but which has low-order correlation functions which make it look like random numbers. But there's nothing "difficult" in predicting the outcome of a pseudo-random number generator: you have a finite set of outcomes, and the next outcome is determined by the previous one, an internal state (which is also taken from a finite set), and eventually an external input, also taken from a finite number of possibilities. If you know that input (say, the clock), you know the internal state and you know the previous output, then the algorithm of the finite-state machine computes the next output.
If there's no external input, then these generators are always cyclic: they go through a certain cycle of outputs, and then repeat again the same series.

The second category is "deterministic chaos". You have a deterministic system (described by, say, a hamiltonian flow), but the Liapounov exponents are positive. Now, this is much harder to predict over a longer time, simply because you need infinite precision in the initial conditions. As your precision is ALWAYS going to be finite, sooner or later the output will be sensively dependent on the "part after the comma" beyond where your precision went. So here the randomness is dependent on the inherent uncertainty by which one can measure/know a quantity which is a genuine real number. No matter how precise one knows a real number, there will always be a remaining uncertainty (even if it is after 200 digits), and in a chaotic system, this uncertainty is sooner or later blown up to a sizeable part of the phase space. So although the *dynamics* may be "deterministic", if your system is determined by a state given by real numbers, there will ALWAYS be a randomness in the initial conditions, no matter how small. It is THIS unavoidable randomness that "shows its ugly face" in chaotic processes.

The third category are quantum phenomena. Here, it is *in principle* impossible to know what will happen: the dynamics (at least, the *observed* dynamics) is random, and not deterministic. (unless this is proven false one day)

Here's another good thread:
https://www.physicsforums.com/showthread.php?t=126272

 

[Nick R]

From reading his posts I gather that physicists do not currently know or have any suspicions as to whether the randomness inherit in quantum mechanics is "reducible to ignorance" or not.

 

[madmike159]

I read something once which said once we have a theory of everything, if we knew everything about the universe at anyone time we could predict the out come. I think I read that in one of Stephen Hawking books. Surly thought the uncertainty principal would stop that from ever being true.

 

[vanesch]

From reading his posts I gather that physicists do not currently know or have any suspicions as to whether the randomness inherit in quantum mechanics is "reducible to ignorance" or not.

In the "orthodox" views on quantum theory, the randomness is irreducible. For all we know, there isn't a way to *find out* that information, even in principle, before the actual event happens. In the classical example of the Heisenberg uncertainty of position and momentum, if you know the position of a particle with a certain position, and you are going to perform a momentum measurement on it (with a minimum uncertainty, given by the uncertainty principle), then there is absolutely no way to find out what that measurement is going to give in any more precise way before you actually do it. Unless one day quantum theory is falsified/modified/..., as long as quantum theory is a good description of nature, we're stuck with it (simply because quantum mechanics runs into fundamental problems if we WERE able to find out what was going to happen). So on a quantum mechanical level, the randomness seems to be irreducible.

However, it is not because *we are not, even in principle, able to predict* that it doesn't mean that "nature doesn't knows better". This is open to discussion. Is it because we are by one or other principle unable to find out all information in nature (but if we were able to have a "gods eye view", we would be able to predict), or is "nature itself" ignorant, and is there nothing in the ontology of nature that "determines" what will actually happen ?

There are ontological models of quantum mechanics (Bohmian mechanics for instance) which have it that "nature" is perfectly deterministic, but that for some or other reason, we cannot get at that extra knowledge. There are even funnier ontological models of quantum mechanics (many world views - my favorite) which solve the issue in an even more bizarre way: nature is deterministic, and all outcomes actually happen in parallel, only, you observe just one of them (and the randomness is now displaced into which one you are going to observe, of which many world views have no deeper explanation - so at this point there IS indeed something fundamentally random, but it is not in the workings of nature, but in the nature of your subjective observation).

Nevertheless, all these views agree with the claim that it will be impossible for you to make any better predictions than are allowed by standard quantum theory.

 

[NightSwimmer]

Does the "Heisenberg Uncertainty Principal" not in any way pertain to our inability to measure a characteristic of an object without fundamentally changing the characteristic which is being measured?

I know that if I attempt to use a low impedance meter to measure a voltage across a component an electrical circuit, then I will change the impedance of the component when I attach my meter leads in parallel with said component. Regardless of the accuracy of my meter, I can't possibly obtain an accurate measurement. By using a very high impedance volt meter (which I generally do) I am able to reduce the error in my measurement -- but I can never eliminate it altogether.

Doesn't the same situation apply at the quantum level? Is that what is meant by the theoretical "Gods Eye View"? Does that refer to the ability to ascertain information about a particle without affecting the particle being measured?

 

[vanesch]

Does the "Heisenberg Uncertainty Principal" not in any way pertain to our inability to measure a characteristic of an object without fundamentally changing the characteristic which is being measured?

No. Unfortunately, many textbooks (especially intro textbooks) explain it that way, but that is making an assumption which is incompatible with the very quantum mechanical description in the first place. Probably this is done to find an analogy with situations the reader might be more acquainted with, such as the one you suggest, but the error is the following:

In order to CHANGE a characteristic, it would mean that the object HAS the characteristic. However, the quantum-mechanical description of the state does NOT allow for a simultaneous value of say, "position" and "momentum": a "position state" is made up of several momentum states, and a momentum state is made up of several position states. So there is no quantum state which corresponds to some precise position AND momentum value. So quantum-mechanically, a particle cannot be in a state where it HAS both a precise position and momentum value. It is not that the value *changes* arbitrarily, it is that it doesn't EXIST.

Upon a measurement of, say, the momentum, the quantum state has to change from a superposition of many momentum states into a state which has only one momentum state. It is this process (the famous "projection") which appears to us to be random and which is badly understood. The particle has to flip from a state in which it has "several momenta in parallel" into a single one of them. It is not that it had "a certain momentum" and then "got a random kick".

I know that if I attempt to use a low impedance meter to measure a voltage across a component an electrical circuit, then I will change the impedance of the component when I attach my meter leads in parallel with said component. Regardless of the accuracy of my meter, I can't possibly obtain an accurate measurement. By using a very high impedance volt meter (which I generally do) I am able to reduce the error in my measurement -- but I can never eliminate it altogether.

The point is that knowing the impedance of your meter, you could CALCULATE what deviation that impedance introduced, and hence correct for the error (and hence obtain a very precise measurement of the impedance).

Quantum mechanically, there's no "correction" possible.

 

[infinityanshu]

But still in Quantum mechanics you can minimize the uncertainty on account of other non-commutable observable...like "the squeezed states of light "

so I think by gathering more and more information about the behavior of the system...we can minimize the uncertainty of a particular observable on account of the other ... but yes still the Heisenberg uncertainty principle holds true...

correct me if i am wrong .. also this is my first post on PF :)

 

[Count Iblis]

According to QM, the wavefunction evolves according to a deterministic law, therefore QM is deterministic. The difference with classical physics is that an observation effectively erases information from the perspective of the observer.

This is perhaps best illustrated by a thought experiment. We place a person in an isolated room and administer a deadly poison gas that kills the person with 100% certainty within 5 minutes. So, the wavefunction of the person describes a dead person after 5 minutes.

According to classical physics we could, in principle, observe the dead person and collect enough information to be able to compute the hypothetical situation in which the person had not been killed.

According to quantum mechanics, we can still talk to the person after the 5 minutes have passed, provided we make sure the wavefunction of the contents of the box doesn’t decohere (in practice this is an unrealistic assumption). This works as follows. Asking a question to a person amounts to applying some perturbation to the Hamiltonian. Recording the answer is equivalent to measuring some observable. But in this case we want to undo the effect of time evolution since the poison was adminstered. The wavefunction evolves in time according to:

|psi(t)> = Exp(-i H/hbar t) |psi(0)>

Asking a question induces some unitary evolution Q on the wavefunction. We want to apply this to living person
|psi(0)> when given the dead person |psi(t)>

Q |psi(0)> = Q Exp(i H/hbar t) |psi(t)>

Suppose that the person was sure to give some definite answer to the question. Then Q |psi(0)> is an eigenstate of the operator, A, that corresponds to measuring the answer (the eigenvalue lambda):

A Q Exp(i H/hbar t) |psi(t)> = lambda Q Exp(i H/hbar t) |psi(t) >

And it follows that:

B |psi(t)> = lambda |psi(t)>

where

B = Exp(-i H/hbar t)Q^(-1) A Q Exp(i H/hbar t)

So, measuring the observable B when the person is dead gives the same result as asking the question and recording the answer to the person when he was alive. But if you just open the room and see the dead person lying in the ground, then you can't do this anymore. The wavefunction |psi(t)> will (effectively) collapse and information about the past will be lost.