scaramallion

I have a small question for christians and atheists alike, preferably those with a background in physics.

In QM the uncertainty principle prevents the uncertainty in two variables (such as position and momentum) from being below a certain limit which is given by;

xp >= (h bar/2)

Where x is the uncertainty in position, p the uncertainty in momentum and (h bar) is Planck's constant divided by 2pi.

My basic explanation of this is that the product of the error in position and the error in momentum must be greater than the allowable minimum (ie h bar/2). From this is can be seen that if position is known with absolute certainty (zero error) then the error in momentum becomes infinite and vice versa.

So my question is; Can God, in his infinite wisdom, know both quantities with zero error at the same time? Any comments on the particular significance of either answer is also appreciated.

eh

Nope, I suppose not. Even God, with all his magic powers, cannot know. That's because a particle simply does not posses both at the same time. So you can't measure what isn't there, and even Superman himself would be limited in this aspect.

Strawberry

Welcome to II, scaramallion! ...I'm an arts geek, so I can't answer your questions, I'm just here with the welcome wagon...

Strawberry

Marlowe

Which God would that be? Yahweh? Vishnu? Athena? You basic Deist omnipotent God? Doe sthis God need infinite wisdom - or infinite knowledge to beat the uncertianty principle?

I have always understood the UP to be somewhat an artifact of the observational apparatus, though eh's answer may be pointing out to me that I have a poor comprehension of this (so please correct me on any points where I am wrong) and the question is about quantum states ala Schroedinger's cat, which I do get as a thought experiment about probability states. Anway, I thought the reason both position and momentum cannot be known at the same time is that to know one we have to hit a particle with a photon and the photon's energy changes the other value while measuring the first (or vice versa). Presumably a supernatural entity would perhaps have some other way of divining this information and not require the value-changing photon to acquire data. So, why couldn't a god know both?

Magus55

Well, yes the Christian God would know it. There is absolutely nothing imaginable that God the Father doesn't know. Since He created the concept you're describing, why wouldn't He? He had to know it to create it. But, thats just for the Christian God, can't answer you for any others.

Dr Rick

Mythical creatures can't know anything.

Wellcome to the IIDB, scaramallion; feel free to introduce yourself in the Welcome forum if you want to.

Rick

beausoleil

Since having simultaneous precise position and momentum isn't a property of subatomic particles, even an omniscient being can't know what you ask. The 'fault' isn't in our inability to measure, it's that thinking that way is a misapplication of macroscopic ideas we have about how things behave to an inappropriate domain.

It's a bit like asking if an omniscient being could know what colour the wind is.

Jesse

This is something I wrote a while ago for another thread about whether particles could "really" have well-defined simultaneous values of things like position and momentum or whether the "fuzziness" is truly fundamental:

Although people usually focus on indeterminacy when discussing the mysteries of quantum mechanics, the real mystery is that QM poses a lot of problems for a realist view of reality, i.e. one where the properties of the world exist independently of our measurement. This is most obvious in the EPR experiments where properties of entangled particles are measured at different locations. What we find is that there are regular correlations between measurements made on particle A and measurements made on particle B which are inexplicable if we picture the particles as classical objects with definite properties that cannot communicate faster than light--this is what Einstein called "spooky action at a distance."

It is sometimes imagined that the uncertainty principle, which prevents us from knowing simultaneously the value of two noncommuting variables (like position and momentum), is just a limitation on measurement; maybe the particle has a definite position and momentum at any given time, but each time we try to measure the position it changes the particle's momentum in a random way, and each time we measure the particle's position it offsets the momentum. However, the EPR experiment shows it is much worse than that. The correlations between entangled particles are such that they cannot be explained by any picture of the world in which the particles have definite values for each noncommuting variable at every time, unless the particles can somehow communicate instantaneously so as soon as you measure one the other "knows" which property you measured and adjusts its own properties. This is the result known as "Bell's Theorem," which says that no local theory of hidden variables can explain the results of the EPR experiment.

In Huw Price's Time's Arrow and Archimedes' Point he offers a little story to help us see what's so strange about the EPR results:

This is the problem posed by the EPR experiment in a nutshell, but instead of twins we are talking about entangled particles and instead of answers to questions we are talking about measurements of the particles' "spin" along their 3 axes (there is an uncertainty relation between these spins). As the great physicist Richard Feynman said, "Nobody understands quantum mechanics…do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will go 'down the drain' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that." The weirdness of QM, and the difficulty with imagining "how can it be like than" in a way consistent with the view that reality exists before we observe it, extends to other famous experiments and thought-experiments, like the Double-slit experiment (from this page which introduces a lot of important QM concepts, including Bell's theorem) and the Schroedinger’s Cat thought-experiment. (is the cat ‘really’ alive or dead before it is measured?) But Bell's theorem and the EPR experiment show most clearly what the basic problem here is for a realist.

A number of different "interpretations" of quantum-mechanical weirdness have emerged over the years, with none yielding any new physical predictions (and thus being experimentally indistinguishable) but each offering a different way to conceptualize what’s "really" going on in these sorts of experiments. Here is a page which gives some good links on these various interpretations, and I’ll attempt my own summary here:

1. The Copenhagen Interpretation

Basically, the Copenhagen interpretation says that we shouldn’t worry about how what’s really going on in the first place—science can only deal with correlating and predicting the results of various measurements, but it can’t tell us anything about what goes on when we’re not looking. This is basically a logical positivist perspective, and it was preferred by Bohr.

2. "Objective Collapse" interpretation

Here the wave-particle duality is taken literally—the world exists as a wavelike potential when it’s not being observed, but somehow measurements periodically "collapse" the wavefunction into a definite state. Some versions of this suppose that it’s consciousness that does the collapsing, others suppose that an entangled system collapses once it reaches a certain limit in mass. Unlike the other interpretations, these might actually be expected to yield different predictions than orthodox QM—so far, there’s no evidence for anything like this though.

3. The Bohm-de Broglie interpretation

Bell’s theorem shows that no local hidden variable theory can explain the results of the EPR experiment, but that leaves open the possibility of a nonlocal hidden variables theory where particles can communicate faster than light. This is the route taken by Bohm and de Broglie’s interpretation. In the Ypiarian story, this would be like the twins having a psychic link which allows one to know what question the other was asked, and adjust his own answer accordingly.

4. Transactional interpretation

The EPR experiment can also be explained if you assume the future can affect the past, so that the particle’s original properties are affected by the measurements that will be made on them later, once they are separated. In the Ypiarian story, this would mean that the twin’s choices to commit or not commit various crimes would be affected by which questions they would be asked much later when they’re interrogated. This isn’t as strange as it sounds, since all the laws of physics we currently know of are time-symmetric (they look the same forwards as they do backwards) and apparently the apparent "arrow of time" emerges solely from statistical mechanics, perhaps because the universe started off in a very low-entropy state. Huw Price’s book Time's Arrow and Archimedes' Point, which I quoted from above, deals with this problem, and he favors a version of this interpretation.

5. The Many-Worlds interpretation.

This interpretation takes the mathematical formalism of QM literally and proposes that the wavefunction is all there is. This means that when I measure the state of a particle that’s in superposition, instead of "collapsing" it into a definite state, I just become entangled with it and enter into a superposition myself; basically, I "split" into two versions of myself, one of whom observes one state and another of whom observes another. In popular accounts this is sometimes explained in terms of the entire universe splitting into parallel histories all the time, but it’s a bit more subtle than that, since different "worlds" can interfere with each other and cannot be viewed as totally "parallel,’ although thermodynamics may explain the appearance of splitting through a phenomenon called decoherence. For technical reasons this interpretation preserves locality (see question 12 of the Everett FAQ), and it’s also 100% deterministic to boot (although it suggests an odd kind of subjective indeterminacy in which my first-person experience randomly chooses which split copy to become—hence a variation of this interpretation is the many-minds interpretation which deals with this issue a little more explicitly). This interpretation is seen as being the most theoretically elegant one by a number of physicists, and it seems that it is sometimes implicitly assumed in quantum cosmology, although physicists are often agnostic about whether other worlds/histories are actually "real." Many-worlds could also make sense of quantum computation, which some physicists believe can be understood in terms of the quantum computer performing different computations in different worlds and then combining the results through interference.

So, those are the various interpretations…as I said, the main problem is that none of them really gives any new testable predictions, which is a bit unsatisfying. There’s some good reason to think that a theory of quantum gravity would transform our understanding of QM somewhat, so perhaps such a theory will depend on a modified version of one of these interpretations that is testable in some way. In any case, Bell’s inequality shows definitively than no classical, realist picture of the world can explain the EPR results, so whatever the truth turns out be, it’s guaranteed to violate our cherished assumptions in one way or another (faster-than light signalling, the future affecting the past, parallel universes…take your pick!)

Answerer

How about the 'Many-Minds' interpretation?

Godot

Hell of a post up top there Jesse! (the really, really big one, I mean)

Made my brain hurt a bit though. Guess I need to brush up on my quantum mechanics some.