Alternatives to Quantum Mechanics?

[Jonnyb42]

I am curious what are other theories of physics at very small scales besides quantum mechanics? Especially those that aren't probabilistic and undeterminitive, (if there are any at all!)

 

[Antiphon]

There are none.

 

[ShadowVegan]

Quantum mechanics is, by definition, physics at the smallest scale. Of course there is also nuclear physics, atomic physics, etc., but QM is the absolute smallest scale because QM revolves around quanta (which are elementary). However, there is, of course, a chance that some things we believe to be quanta (i.e. photons) are composed of something even smaller, meaning that they aren't actually quanta.
If you are just looking for other theories, there are lots of theories within QM, nuclear physics, etc. (such as string theory and other unification/quantum gravity theories), but if they deal with the smallest scale (quanta) they will be classified as QM.

 

[vanesch]

I am curious what are other theories of physics at very small scales besides quantum mechanics? Especially those that aren't probabilistic and undeterminitive, (if there are any at all!)

This is a difficult question to answer, because what some consider "another theory", others consider it as a "different interpretation of quantum theory". As you might know, although the *formalism* (that is, the calculations) of quantum mechanics give very good results, many people aren't happy with what one could call the "philosophy" behind it. So people have, over the last 80 years or so, porposed alternative *interpretations* of what the calculations mean. And in doing so, they sometimes added formal elements which aren't part of the original quantum formalism. Probably the most famous such "version" is Bohmian mechanics. Other interpretations limit themselves to re-assigning different meanings to the formal elements of quantum mechanics "as we know it" (and can hence with less doubt be called "interpretations"). The "philosophical" viewpoint of these different interpretations is vastly different, and sometimes "religious wars" are fought over them.
But as far as I know, on all "experimentable" physics, they come out the same *observational* results. That's why, if not just different interpretations (because added formal elements), they are physical theories that are equivalent to quantum mechanics (at least for all practical purposes).

In other words, on the "hard scientific" level, all these theories are empirically indistinguishable, and it is almost a matter of semantics to call them "different theories", although on the philosophical level, they are totally different, for instance on the level of "determinism", or "stochastic". There are deterministic interpretations of quantum mechanics (Bohmian mechanics for instance). There are "strict" interpretations of the existing formalism (many worlds). There are "shut up and calculate" interpretations (what there "is" is unknowable, we can only calculate what we observe)... For everybody's taste, there must be something. All of these viewpoints have some kinky points, that's probably why none of it stands out clearly above the others... but they all talk about "quantum mechanics" in some or other form, as they are observationally equivalent.

Apart from crackpot websites, I've never seen totally different theories in the same domain of applicability, without them trying to establish some kind of equivalence to quantum mechanics (at least for all practical purposes). And there's a good reason for that: the kwantitative predictions of quantum mechanics are impressively verified by experiment, so there is very little "wiggle room" without being in contradiction with observation.

In other words, no matter all philosophical and even formal difficulties sometimes, quantum mechanics works very well as a scientific theory.

 

[tom.stoer]

One should distinguish between
1) "quantum mechanics" as the formalism and
2) the application of quantum mechanics in the physics of atoms, nuclei, elementary particles (in the advanced formalism called quantum field theory) and even in string theory and quantum gravity (which is currently not a final theory but a bunch of research programs).

Regarding 2) there may be even smaller scales (below electrons and quarks) even if there is no hint why this should be the case. But there is no attempt to use something different than 1)
So Regarding 1) there is no other approach at all. What is debated is its interpretation.

 

[Jonnyb42]

Thank you everyone, I am very satisfied with the responses. I was just worried a little bit when Einstein did not like the theory, (or did he not like the philosophy?) because he was a very intuitive person. I can feel slightly more assured, since there being no other theory TO learn, (and I would be undoing quit a bit if I were to come up with some theory of my own, not to mention the vast amount of time it would take and not take advantage of all the work done already) to continue and learn quantum mechanics. So with this, I have a few more questions.

What math does quantum mechanics use? I have currently finished high school Calculus AP, (so I suppose first year college calculus,) and am prepared to learn vector calculus (and of course MUCH more afterwards). Also, which would be better to learn first, QM or General Relativity? (that probably also depends on which is more math intensive.)

Thanks again

 

[haael]

What math does quantum mechanics use? I have currently finished high school Calculus AP, (so I suppose first year college calculus,) and am prepared to learn vector calculus (and of course MUCH more afterwards). Also, which would be better to learn first, QM or General Relativity? (that probably also depends on which is more math intensive.)

QM uses linear algebra, abstract algebra, analysis, groups, tensors, spinors and topology, to name few.
GR uses only linear algebra, analysis and tensors.

GR was easier for me to understand, than QM. Plus, GR is somewhat complete, as opposed to QM, which is still under construction, a beta version of a kind.

 

[element4]

QM uses linear algebra, abstract algebra, analysis, groups, tensors, spinors and topology, to name few.
GR uses only linear algebra, analysis and tensors.

Your reply is very misleading in my opinion. For elementary QM you don't need any deep understanding of anything else than linear algebra and a little bit of functional analysis (not rigorous, and this is usually covered in introductory books). The rest you need only for more advanced aspects of QM.
(More advanced aspects of ) GR uses all the subjects you mention too, plus much more.

In my opinion one should start with some linear algebra and then grasp the elementary aspects of QM. At this level QM is mostly conceptually difficult, while for GR there might be some subtleties connected to the math and confusion might arise without any understanding of Riemannian geometry. Not to mention that one should also know SR before studying GR.

Plus, GR is somewhat complete, as opposed to QM, which is still under construction, a beta version of a kind.

What makes you say that? If there is any such opinion, it's probably the other way around. QM is much more tested experimentally in various extremes and situations than GR.

 

[alxm]

Well, there aren't any known instances where quantum mechanics fails, which means we don't need an alternative. We could of course have a simpler theory, but this is very difficult, because quantum mechanics is in fact quite simple.

Not simple in terms of mathematics, no. But simple in terms of relying on very few basic assumptions (postulates). It's not simple in the sense that it's easily intuitive to humans, and it's not simple in the sense that the math are simple.

But those two latter concerns don't count because they're anthropocentric; they're a matter of our opinion. Nature is not under any obligation to make things easily understandable by humans!

QM has in fact been simplified (as in, reduced to fewer and more basic postulates) since it was first formulated. E.g. 'Spin' was originally a postulate, but is now known to be a consequence of special relativity.

Of course, then there also are alternatives: QM was not the first theory developed to explain QM phenomena! For instance, there's the Bohr model of the atom - which is not simpler in terms of relying on fewer assumptions, but simpler in mathematical terms.

There's also the field of chemistry - and the rules of chemistry are largely simplifications of quantum mechanical results and properties. The structure of the periodic table, the octet rule, orbital hybridisation, etc. Quantum chemistry is an expanding field, but few chemists solve the Schrödinger equation when they do theory - nor do they need to; their approximate models work well enough most of the time.

 

[DJsTeLF]

E.g. 'Spin' was originally a postulate, but is now known to be a consequence of special relativity.

I'm intrigued by this statement. Could you perhaps take a moment to explain how or point me to an appropriate reference?

 

[vanesch]

What math does quantum mechanics use? I have currently finished high school Calculus AP, (so I suppose first year college calculus,) and am prepared to learn vector calculus (and of course MUCH more afterwards). Also, which would be better to learn first, QM or General Relativity? (that probably also depends on which is more math intensive.)

In fact, GR and QM are totally different subjects. As QM has much more applications (like chemistry!), I would go for QM first, and leave GR for later idle moments :-)

However, before being able to grasp somewhat seriously QM, you must first have a solid grasp of advanced aspects of classical, Newtonian mechanics, which you probably haven't seen.

Now, if you want to get a conceptual head start of quantum mechanics, go for Feynman's lectures volume 3. It is an a-typical introduction to QM, which might seem strange, but it gives you a very good idea of quantum mechanics without the full machinery and maths. And it IS serious.

(and BTW, read the first two volumes also, they are worth their weight in gold).

 

[element4]

I'm intrigued by this statement. Could you perhaps take a moment to explain how or point me to an appropriate reference?

The Poincaré group is the group of all symmetries in SR (translations, rotations and Lorentz boosts). Particles can be classified as representations (irreducible for elementary particles) of the Poincaré group. If you know some group theory (Lie groups and representation theory minimum) I can find some references for you.

But loosely speaking it turns out that these (irreducible) representations can be classified by their mass and something called a Little group.
1. For particles with $$m^2 > 0$$ (massive particles) the little group is SU(2), which physically is nothing but spin (s= 0, 1/2, 1, 3/2...).
2. For $$m^2 = 0$$ (massless particles) the little group describes helicity.
3. The last possibility is $$m^2 < 0$$ (tachyons), for which I don't remember the Little group.

 

[tom.stoer]

I'm intrigued by this statement. Could you perhaps take a moment to explain how or point me to an appropriate reference?

element4 already responded to that.

One can show that the structure group of spacetime is (loosely speaking) SO(3,1) ~ SU(2)*SU(2). And from these two SU(2) factors one can derive spin with integer and half integer values. The integer values already follow from the SO(3) rotation group in three dimensions, but the half-integer values came as a surprise (and Pauli was attacked by his teacher Sommerfeld introducing factors of 1/2 to explain the Hydrogen spectrum; Sommerfeld was afraid that sooner or later Pauli would introduce 1/3 etc. spoiling quantization at all :-)

 

[tom.stoer]

But loosely speaking it turns out that these (irreducible) representations can be classified by their mass and something called a Little group.
1. For particles with $$m^2 > 0$$ (massive particles) the little group is SU(2), which physically is nothing but spin (s= 0, 1/2, 1, 3/2...).
2. For $$m^2 = 0$$ (massless particles) the little group describes helicity.
3. The last possibility is $$m^2 < 0$$ (tachyons), for which I don't remember the Little group.

In addition to 2. there are for $$m^2 = 0$$ the so-called continuous (or infinite) helicity states w/o any quantization. I still have to figure out why they are unphysical.

 

[tom.stoer]

... For elementary QM you don't need any deep understanding of anything else than linear algebra and a little bit of functional analysis (not rigorous, and this is usually covered in introductory books). The rest you need only for more advanced aspects of QM.

...

QM is much more tested experimentally in various extremes and situations than GR.

I fully agree. QM - especially its application to atoms, nuclei and elementary particles - all based on the same principles and math - have been tested over decades w/o any hint for any physics not compatible with QM.

The only open issue is harmonization of quantum field theory with general relativity to quantum gravity.