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I've heard this pop up in a discussion with my physicist/engineer roommates, but didn't care to ask at the time. Now I'm mighty curious about it. Wikipedia doesn't really seem to say much on this issue.

From what I understand about the Uncertainty Principle, it says that there are certain properties of electrons and stuff that cannot be measured, and are therefore uncertain. Then Wikipedia (under indeterminism) states that Sir Arthur Eddington says that the Uncertainty Principle isn't really so because we can't measure these properties, but because turns out nature is indeterministic. At least that's what I took from those paragraphs. Even without my biased wording, it sounds more like an assertion than evidence.

I've also read a few things about how other scientific conventions perceive the issue, like how a ball on the peak of a perfect mound might randomly roll down in any direction, and I'm still unconvinced. My belief of determinism is generally that if you knew every single variable that existed as a factor at the very beginning and birth of the universe, you could correctly determine all properties of any individual particle at any point in time.

Could anyone provide some more background about this? Especially regarding quantum mechanics?

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You should look at a similar question I asked on the subject not too long ago. It may help clarify the confusion regarding fundamental nature of quantum physics in regards to the very idea itself being a positive claim as opposed to a "lack of knowledge" claim. –  stoicfury Sep 2 '11 at 15:27
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Thanks for pointing me to your question. At first it wasn't evident, but reading these answers brought up that question for me. –  glifchits Sep 3 '11 at 21:50
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Although the uncertainty principle was originally proposed by Heisenberg as a limitation on measurement, it's now understood to be a limitation on what there is to be known about a physical system. –  Ben Crowell Jun 5 '13 at 21:49
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6 Answers

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I thought I would give a physicists perspective here.

There are two types of evolutions in quantum mechanics: unitary (or free) evolution and measurement. Free evolution is fully reversible and deterministic; a given operator takes a specific wave functions and maps it to a specific other wave function. The uncertainty comes from the non-unitary measurement evolution.

Unfortunately, if you want to approach this problem from a realist point of view (how most people think of classical mechanics, etc) it becomes difficult to solve the measurement problem: i.e. what constitutes a measurement, where is the system and where is the measurement device? Isn't the measurement device + orginal system just a bigger system that should be undergoing unitary transformations? This question has puzzled many, with some notable (and also non-notable, crack-potty) scientists even linking measurement to the acts of conscious observers.

Most serious researchers on the foundations of quantum mechanics, usually side-step this question by taking the operationalist point of view. Tagline: "all we have is some procedures for setting up an experiment and the results of experiments". In this framework, you can derive Bell's theorem, which says that any phenomena that is both deterministic and local must satisfy the Bell inequality. Quantum mechanics violates the Bell inequality (and there has been many experiments to mostly confirm this violation, there are some technical loopholes that need to be addressed in some of the experiments). This means that you must give up at least one: locality or determinism. Since without locality it becomes impossible to talk about causality, most people prefer not to give it up, and instead give up determinism.

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Thanks for this fantastic answer! I'm only unclear what you mean by the two evolutions in quantum mechanics; are you referring to branches of opinion or distinct sub-fields within the topic? –  glifchits Sep 6 '11 at 3:01
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Thanks, I meant evolution as in a transformation of state from time t to time t + 1. –  Artem Kaznatcheev Sep 6 '11 at 3:04
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@ArtemKaznatcheev I don't see that locality is required for determinism. 'Action at a distance' makes perfect sense and is compatible with determinism, even if it seem incredible. So it isn't the violation of Bell's Inequality that makes systems non-deterministic, it is rather the statistical interpretation of the wave function presented originally by Born that is incompatible. A deterministic non-statistical interpretation has been presented by Bohm. –  adrianos Jan 6 '12 at 14:10
    
That said, there are many problems with Bohm's approach to quantum physics (e.g. see Fine's excellent book, 'The Shaky Game'). So there is nothing wrong in principle with Bell and determinism, but there are many problems with the attempts so-far to create a deterministic theory (Einstein famously failed to do so). –  adrianos Jan 6 '12 at 14:31
    
@adrianos I never said that locality is required for determinism. Read my second to last sentence; you have to give up either locality OR determinism. Most people prefer to give up determinism and keep locality. Bohm (who is linked in my answer as a realist) is a notable exception that preferred to give up locality in order to keep determinism. However, from my experience working in quantum computing, I do not feel that most practicing physicists share his views. –  Artem Kaznatcheev Apr 29 '12 at 3:57
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Quantum Physics doesn't disprove determinism.

What Quantum Physics does do is significantly complicate the task of arguing for determinism.

Put in the simplest possible terms, the Uncertainty Principle indicates that: 1) our observation of an event has a significant effect on the event, and 2) it is impossible for a single observation to observe all relevant properties of an event. This means that any argument for determinism can no longer have simple recourse to the notion of observation.

So, when you say:

My belief of determinism is generally that if you knew every single variable that existed as a factor at the very beginning and birth of the universe, you could correctly determine all properties of any individual particle at any point in time.

you instantly run into trouble, because we can't know every single variable that existed as a factor at any point in time (including the initial state) through any type of observation.

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but what does the ability to observe the factors involved have to do with it being deterministic? Even if there were no way under the laws of physics to observe the variables necessary to deterministically reconstruct the current state of existence, there can still exist a hypothetical being unbound by the laws of physical that possesses omniscient knowledge without observation of any kind, and such a being could deterministically know future state. –  Davy8 Sep 2 '11 at 22:41
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Does the Uncertainty Principle state that only OUR observations have effects on the event, or that all possible observations would have? Is it impossible that ever any new technique is invented to measure the 'real' events? –  bonifaz Sep 2 '11 at 22:41
    
It's my understanding that determinism doesn't require the ability to gain the knowledge of every aspect of the universal state, but simply states that given the assumption that all state was known (regardless of whether it would be possible to gain such knowledge) that any future state could be derived from that information without deviation. –  Davy8 Sep 2 '11 at 22:43
    
I don't think that arguments that depend upon beings unbound by the laws of physics are going to be of much help in arguing how the universe (with its concomitant laws of physics) works. In terms of the broader question, I personally find the whole "free will vs determinism" debate singularly uninteresting and tiresome for two reasons: 1) it is *impossible to come up with a probative argument in either direction, for reasons indicated by Wittgenstein on rule-followin, and 2) it makes absolutely no difference in terms of anything that follows. –  Michael Dorfman Sep 3 '11 at 11:08
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@stoicfury: I still believe in an ethical subject, regardless of free will. I said that it makes absolutely no difference, because it certainly appears to us that we have free will, so it is incumbent for us to live as if we had free will; if, in actuality, this view is mistaken and our decisions were all pre-determined, nothing has changed-- we have acted precisely the way we would have, regardless. –  Michael Dorfman Sep 5 '11 at 13:09
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Once we start using a scientific method, that is, observing nature in order to learn what is really happening, we are already assuming a determinism of some kind, that there are strict rules about how nature works. So it understandable to assume that all our rules about nature are lock-step, undeviating. And if they're not, that's just a failure of effort, to work past the feeble approximations to get to a final exact solution. (use any grade school science here, biology, sociology, physics, etc.). All probabilistic distributions of measurements of natural phenomena are expected to be artifacts of experimental error, not part of nature, and that better experiments would eventually narrow the distribution to a single determined point.

Under the mathematics of Newtonian mechanics, this is a reasonable strategy to pursue.

It just turns out that under investigation of certain physical phenomena, sub-atomic particles, it was experimentally found that even when the experiments were adjusted to the extent that there was -no- variability in the input data (control of single particles), there was still a probability distribution on output of the system. That is, things that we metaphorically think of as discrete particles still act as though they have a probabilistic distribution. There is no determining the outcome exactly, nature has inherent distributions that are not artifacts of the experiment. (I am describing the two slit experiment). Something that we think of as a single particle can have properties that are inherently indeterminate.

At certain scale levels (very small), you really -can't- know, given initial velocity and mass, the end position of the actual particle (or set of particles).

It's not so bad as all that, because we still can quantify that lack of knowledge with a probability distribution.

Anyway, the point is that we seek as much determinism as possible in science (that is what the form of scientific laws follows, but it can turn out that nature doesn't always comply. But really, science has determined enough for us to put people on the moon, make smallpox extinct, and have auto-answer phone-menus for our banks, that a little sub-atomic non-determinism is livable. We certainly -do- know something about the particle

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And frankly, the newtonian determinism isn't so great philosophically. Sure there's the Lagrangian 'if you had the 3d position/velocity (6 coords), you could determine the course of all later events', except that (forgetting getting the initial data), the simulation on a calculating machine would require a larger universe than the actual universe it is simulating. O solving that system algebraically is currently impossible. There -is- a symbolic solution to the n-body problem but its convergence to a numeric solution is terribly slow. So even Newtonian mechanics has its determinism problems. –  Mitch Sep 2 '11 at 13:59
    
But of course (to comment on my comment well after the event, Newtonian mechanics is the start of modern determinism despite my niggling comment) because of the at least conceptual exact solvability... er not solvability... but ability to be simulated. –  Mitch Sep 5 '11 at 22:14
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The Uncertainty Principle is not directly problematic for determinism; it just says you can't measure your states that accurately. You could always assume that the states were there, but you just couldn't measure them. Einstein preferred this view, and together with Podolsky and Rosen devised a paradox that would show that uncertainty is not fundamental. Unfortunately for Einstein, the experiments delivered the seemingly paradoxical result, showing that uncertainty is fundamental and determinism, if true, is not local. (Actually, it even shows that causality is not local.)

But the more telling blow to determinism is the success of entangled/superimposed states that are stochastically collapsed under certain conditions. The double-slit experiment is the most famous of these, but it's really Bell's inequality and experiments (that failed) to confirm it that made determinism look like a bad model of reality. The experiments are too technical and detailed to describe here, but so far Bell's inequality has been routinely violated, and hence, there is no room for a deterministic model where the relevant state stored locally. (Of course, a computer simulation with all state stored globally can reproduce anything, in principle, but that doesn't make it a parsimonious way to explain results in physics.)

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virtual -1 because of "violation of Bell's inequality". Note that Bell's inequality is something that local-and-deterministic theories have to obey. Quantum mechanics violates Bell's inequality, please be careful with your terminology to avoid common misconceptions. –  Artem Kaznatcheev Sep 5 '11 at 17:17
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@Artem Kaznatcheev - Sorry, said it backwards. Fixed now. Thanks for catching that. –  Rex Kerr Sep 5 '11 at 17:26
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The problem is the clear equivocation on the word "determined". Just because a quantum fluctuation for example, is not sufficiently caused or causally determined that does not mean the event was not determined in a sense that the event was "fixed" due to existing tenselessy on a four-dimensional space-time block (the B-Theory of time). If the future is "fixed", then even if there is no sufficient cause for a certain event it still had to be the case due to having a fixed position on The Block. Therefore, even if something is no CAUSALLY determined, it could still be determined in a sense of having a "fixed" position in an objective timeless reality; with temporal becoming only being an illusion.

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Heisenbergs uncertainty principle introduced indeterminancy into modern physics, whereby modern I mean Physics from the Italian Renaissance. It was already introduced into the Physics of the Greek atomists as the clinamen which they regarded as an irreducible randomness associated with an atom (they argued it was neccessary in order to get atoms to interact).

It was originally introduced by Heisenberg as an irreducible perturbation on a minute particle. That is the randomness was seen as epistemalogical. The question turned into whether this was in fact epistemological or ontological. That debate is still current today.

For example Quantum Mechanics interpreted under consistent histories it is in fact ontological, as Bohmian Mechanics it is epistemological (but notably locality has to be given up).

In classical mechanics one can determine a trajectory of a particle precisely in spacetime, and this is reversible. In quantum mechanics one can determine the trajectory of a probability wave of the particle exactly and this is reversible. But on an interaction this probability wave collapses to a specific value known to both particles. After this point the trajectory is no longer reversible - how can it be when probability & possibility has collapsed to the known? This state then begins to evolve again.

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