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As a preface, I am not a physicist. I'm simply interested in abstract physics and fundamental principles of the universe and such. As such, if you can provide an answer for the layman (as non-academic and unjargonized as possible), it would be very, very appreciated so that I can actually understand it.

Everything I ever learned about physics seemed to be built off of an assumption that the universe and everything in it behaved deterministically. So it should always be a (theoretical) possibility that, given perfect knowledge of every particle and force in the universe at a given moment, we can calculate with 100% accuracy what the state of the universe will be in the next moment.

This of course assumes omniscience and unlimited computational capacity, which is why I said this is only a theoretical possibility. However, we can define our closed system to be much smaller -- say, a bottle full of nitrogen and helium -- and apply this principle more directly. And it seems like this assumption is absolutely necessary for scientific experiments to even take place or have any validity, since without this kind of determinism, the observations and the results inferred from them can't ever actually be trusted.

I don't understand quantum mechanics very well, but it seems like this theory breaks this assumption completely. From what I understand, there is no way to predict what the state of the particle will be at the next moment. The most I can know is that, given that a particle is in state A, it will next be in state B or state C. There is absolutely no way to know for sure, and the only way to find out is to observe it actually change. Furthermore, observations of this kind don't yield any insight into what other particles in state A will do.

So, in classical physics, laws used to look like this:

A -> B   [A implies B]

But with quantum physics, all of this is gone, and our laws can at best look something like this:

A -> ((B v C) v D) v E   [A implies B, or C, or D, or E, or ...]  

How does this not break everything physics is built upon? The implications of this are seriously troubling to me, and I feel like it destroys everything I thought I knew. Can anyone explain how this works in slightly lower-level terms, or show how it's still possible for the theories and laws of classical physics to hold any weight?

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closed as not constructive by dmckee Mar 7 '13 at 18:30

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My advice would be "don't tell the nature how it should behave." The universe doesn't have to conform to our naive philosophical biases. I tend to show people the following video when questions like these come up: youtube.com/watch?v=iMDTcMD6pOw . –  jld Mar 6 '13 at 21:08
    
@elfmotat Thanks for the video. I will watch it when I'm in a more appropriate environment. I think it's less "telling nature how to behave", and more "everything nature ever showed me about how it behaves is a complete lie." It legitimately kind of creeps me out that determinism is false. –  asteri Mar 6 '13 at 21:10
    
Some people see the many-worlds interpretation of quantum mechanics as preserving determinism, since there is no random waveform collapse as such in that theory; instead, the only 'random' factor is our subjective perception of which universe we are in (which isn't really random, since all other universes can ask the same question). –  kbelder Mar 6 '13 at 22:13
    
Philosophically speaking, physics tries to understand the nature behavior. It doesn't mind if the theories are deterministic or not, because at the end of the day the validity of them are subjected to experimental results. And answering your question, quantum mechanics is not a deterministic theory by the fact that it uses probability theory. –  Anuar Mar 7 '13 at 0:54
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This question and the answer seem to be more philosophical than physical, and seem to have completely ignored Bell's inequality and the limits that experimental test on it imply. –  dmckee Mar 7 '13 at 18:30

3 Answers 3

NEWTONIAN MECHANICS:

Newtonian mechanics, as expressed through Newton’s laws of motion, gave us huge confidence about our understanding of nature. We were able to calculate the motion of planets and predict their position quite accurately many years into the future, and then observed them to check they do as we have predicted. Things worked extremely well. Occasionally there were some disagreement between our predictions and observation, like the anomalies in the motion of Uranus for example. But these did not mean the Newtonian laws were wrong; we simply missed something out, and in the case of Uranus it was a planet beyond it that caused the anomalies. The physical properties of that planet were all calculated and predicted, again, using the Newtonian laws. Newtonian mechanics was so triumphant, that physicists began to believe they had discovered the holly grail of science. This however was all to change, when the same laws were applied to study the behaviour of matter at the smallest scales we knew, the atomic scale.

$QUANTUM MECHANICS:$

The application of Newtonian mechanics for the study of the atom, after it was discovered by Rutherford that atoms were like minute solar systems, was expected to produce yet more results that would be in agreement with our calculations. Lo and behold! Things went pare shaped so badly, and it became obvious that new physics was needed urgently.

We could not explain:

i) The atomic spectra,

ii) The black body radiation spectrum

iii) The photoelectric effect

iv) The wave properties of matter as displayed in the Davisson-Germer experiment.

v) We could not explain the properties of matter as we were discovering them: Superconductivity, Super fluidity and many more.

All these problems were resolved with just one touch of the strong right hand of quantum mechanics! The new physics was not just a slight modification to Newtonian mechanics, but entirely different and counter intuitive to what we had become accustomed to with Newtonian mechanics. No longer we could talk about objective predictions of how nature was going to behave. We could only calculate probabilities, and could only talk about probabilities, and we could only predict probabilistically the behaviour of atoms, particles, properties of solids and liquids and so on.

DO WE COMPROMISE OUR KNOWLEDGE ABOUT NATURE WITH QM?

Views vary on this as it depends on how deeply one is entrenched into the philosophy of Newtonian mechanics. The point is that, calculation after calculation, observation after observation, nature is telling us that in the micro world matter behaves according to the laws of probability. We might dislike it, but let us think about this for a moment:

Do we really believe, that nature would be able to display the richness of phenomena and variation we observe around us, had the rules she follows been rigid, black and white type of “philosophy,” as we learned from Newtonian mechanics?

We all have our own views on this, so you can form yours.

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Quantum mechanics, in its essence, is deterministic. It is only measurements that give rise to problems (in the Copenhagen interpretation).

Let's compare three theories: classical mechanics, classical mechanics with random pushing/pulling (stochastical mechanics) and quantum mechanics. In classical mechanics, all laws are deterministic in nature. If $A$ gets you to $B$ and $B$ gets you to $C$, we can easily retrace our steps. We can reverse time and get back to where we started by using the same laws without any problems.

In stochastical mechanics, however, the system we want to describe at random times gets pushed or pulled randomly hard. Let's say you still go from $A$ to $B$ but somewhere between $B$ and $C$ you get a random push in a random direction and you end up in $D$. You can't just retrace your steps. So if we reverse time in stochastical mechanics, we don't necessarily get back to where we started. Determinism is broken.

In quantum mechanics, the laws are again all deterministic in nature. The laws actually look like those of classical mechanics, in an abstract sence. That's to say: $A$ gets you to $B$, $B$ gets you to $C$, maybe $C$ gets you back to $A$, deterministic. It's only measurements that cause us a headache. As long as we don't measure anything, we can simply rewind and nature will get back to its original state. Note the very important difference with stochastical mechanics: quantum mechanics is not just like classical mechanics with a random component!

So QM is deterministic as long as we don't measure anything. However, when we make a measurement (for which a completely satisfying definition doesn't really exist), we can run into problems. Because in the Copenhagen interpretation of QM, a measurement "collapses" the wavefunction, i.e. the system is forced into an eigenstate corresponding to the measuring device. This discontinuity would break determinism. There isn't a general consensus about this among physicists. Some suggest everything is still fine if we describe the measurement fully, including the wavefunctions of all the entities involved in the measurement. Some subscribe to a different interpretation of QM, like the Many-worlds interpretation, where there is no collapse of the wavefunction and therefore no discontinuity either. Others prefer not to think about it too much. (the worst way to go as a scientist in my opinion)

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Good answer, but the view that QM is deterministic and "the laws are actually very similar to those of Classical mechanics" is in not quite true. –  JKL Mar 7 '13 at 0:18
    
@John Well, the laws themselves are deterministic, aren't they? If not, QM would just be a fancy form of stochastical mechanics and "God really does play dice", to paraphrase Einstein. When we want to measure, we can only make predictions about probabilities, though one possibility is that QM becomes deterministic again if we take into account all the wavefunctions (states) of all the interacting particles (those of the measuring device as well). However, this has been a point of discussion ever since the first Solvay conference. –  Wouter Mar 7 '13 at 6:53
    
@John The sentence you mention might not be the best phrasing, I don't mean to give the impression QM is similar to classical mechanics. I'll change that. –  Wouter Mar 7 '13 at 6:56
    
The laws of quantum mechanics are laws of calculating probabilities, and uncertainties. If there is anything deterministic in QM is the probabilities we calculate by solving Schrodinger's equation. Predicting probabilities is not equivalent to predicting the future, and how exactly things will turn out like we did in Newtonian mechanics. Even if we had the most accurate Hamiltonian, we would still calculate probabilities, but they would be much more accurate. But I agree, the nature of QM is very subtle indeed. –  JKL Mar 7 '13 at 14:23

It is quite simple actually.

Quantum mechanics is DETERMINISTIC in the sense of it's laws - they are fixed and are not subject to change. Things which are not deterministic are COORDINATES , which simply means you can not measure well your parameters (but it does not mean, for example, that you can not measure well some combinations of them - like total energy of the system).

Back to your question -- there is no uncertainty of implications in QM there is only uncertainty of position.

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