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Isn't all of theoretical physics pure mathematics? That's the point. Well, maybe not "pure", but HUP isn't particularly "pure" either.

jfengel 5y ago
What the article means is that the Heisenberg Uncertainty Principle isn't just some problem of measurement that could possibly be overcome by better tools. Rather, HUP is a mathematical consequence of the axioms of quantum mechanics, and you won't get around it by clever technology. Only blowing up QM entirely would get around HUP -- and the results would almost certainly be less familiar, rather than more like classical mechanics. (Indeed, this is already the case: it's called Quantum Field Theory.)
- bsaul 5y ago
  hey, since you might be familiar with this: so quantum field theory is actually a departure from QM instead of its continuity ? I'm confused, i thought QM was the best thing we had regarding quantum behaviors... Also, i sometimes saw theoretical physicists talk about "quantum gravity" as if it was a solid theory (i tried to look at some presentation on the topic, but it was way beyond my level)... That made me even more confused, because i was under the impression that chord theory was the only thing we had to unify quantum mechanic and general relativity, and that it was far from accomplished... Could you (or anyone reading this) help me out of my confusion ?
  - Koshkin 5y ago
    QM alone fails to account for certain facts. QFT does this by using somewhat “weird” methods in order to bring Special Relativity and QM together. It has been working pretty well so far, and it is indeed the best we have. String Theory, on the other hand, while being a consistent theory of quantum gravity, uses a model (or models) that we may never be able to verify experimentally.
  - jfengel 5y ago
    Quantum mechanics is the low-energy case of quantum field theory. They have the same kind of relationship as Newtonian mechanics have to general relativity: a very, very different basis that just happens to have a convenient low-energy formulation, where the differences between truth and experiment are too small to be observed. Quantum mechanics can't even begin to talk about quarks. The weak and strong forces just don't exist. And they're very, very different kinds of forces from gravity and electromagnetism. It requires a completely different kind of basis, one based on fields rather than particles. As for "quantum gravity", there's a lot to unpack. There are very sound and useful theories of Quantum Field Theory in curved spacetime, such as semiclassical gravity. That's what Stephen Hawking was working on when he produced his black hole results. But those theories have limitations and aren't a full integration of quantum mechanics with gravity. Unfortunately, that seems to require yet another complete rewrite of the fundamental basis of things, such as strings or loop quantum gravity. And more unfortunately, the differences only occur at stupid high energy levels, so it's practically impossible for us to do experiments to help figure out which one is right.
Koshkin 5y ago
The difference between theoretical physics and mathematics is 1) the subject and 2) the criterion of truth.
publicola1990 5y ago
HUP is may be a physical phenomena, but the same kind of uncertainty is part of Fourier transforms which are entirely mathematical constructs. So even more intriguing than HUP, is the thing that purely mathematical constructs exibit the same sort of uncertainty as HUP. Gibbs phenomenon was initially thought by physicits to be due to defects in instruments making the measurements, but later it was unferstood to be a mathematical rather than physical characteristic.

jfengel 5y ago

What the article means is that the Heisenberg Uncertainty Principle isn't just some problem of measurement that could possibly be overcome by better tools. Rather, HUP is a mathematical consequence of the axioms of quantum mechanics, and you won't get around it by clever technology. Only blowing up QM entirely would get around HUP -- and the results would almost certainly be less familiar, rather than more like classical mechanics. (Indeed, this is already the case: it's called Quantum Field Theory.)

bsaul 5y ago
hey, since you might be familiar with this: so quantum field theory is actually a departure from QM instead of its continuity ? I'm confused, i thought QM was the best thing we had regarding quantum behaviors... Also, i sometimes saw theoretical physicists talk about "quantum gravity" as if it was a solid theory (i tried to look at some presentation on the topic, but it was way beyond my level)... That made me even more confused, because i was under the impression that chord theory was the only thing we had to unify quantum mechanic and general relativity, and that it was far from accomplished... Could you (or anyone reading this) help me out of my confusion ?
- Koshkin 5y ago
  QM alone fails to account for certain facts. QFT does this by using somewhat “weird” methods in order to bring Special Relativity and QM together. It has been working pretty well so far, and it is indeed the best we have. String Theory, on the other hand, while being a consistent theory of quantum gravity, uses a model (or models) that we may never be able to verify experimentally.
- jfengel 5y ago
  Quantum mechanics is the low-energy case of quantum field theory. They have the same kind of relationship as Newtonian mechanics have to general relativity: a very, very different basis that just happens to have a convenient low-energy formulation, where the differences between truth and experiment are too small to be observed. Quantum mechanics can't even begin to talk about quarks. The weak and strong forces just don't exist. And they're very, very different kinds of forces from gravity and electromagnetism. It requires a completely different kind of basis, one based on fields rather than particles. As for "quantum gravity", there's a lot to unpack. There are very sound and useful theories of Quantum Field Theory in curved spacetime, such as semiclassical gravity. That's what Stephen Hawking was working on when he produced his black hole results. But those theories have limitations and aren't a full integration of quantum mechanics with gravity. Unfortunately, that seems to require yet another complete rewrite of the fundamental basis of things, such as strings or loop quantum gravity. And more unfortunately, the differences only occur at stupid high energy levels, so it's practically impossible for us to do experiments to help figure out which one is right.

Koshkin 5y ago

The difference between theoretical physics and mathematics is 1) the subject and 2) the criterion of truth.

publicola1990 5y ago

HUP is may be a physical phenomena, but the same kind of uncertainty is part of Fourier transforms which are entirely mathematical constructs. So even more intriguing than HUP, is the thing that purely mathematical constructs exibit the same sort of uncertainty as HUP. Gibbs phenomenon was initially thought by physicits to be due to defects in instruments making the measurements, but later it was unferstood to be a mathematical rather than physical characteristic.