5 ms·

The best way I've ever had it explained to me is with electron tunneling. You ask, how did the electron "jump" that potential hill, when it actually didn't have

The best way I've ever had it explained to me is with electron tunneling. You ask, how did the electron "jump" that potential hill, when it actually didn't have the momentum to do so? The answer: it didn't, it quite literally "went through" the potential hill. So you ask, well, what kind of momentum (mv^2) would allow for this "tunneling" momentum? You invariably arrive at a _negative_ moment... and thus only an imaginary velocity can fit! My intuition leads me to believe that almost some sort of other dimensional effects are at play, and our feeble math just can't accurately describe it. Perhaps it's just the nature of quantum itself, and no special dimensional consideration is needed. It's been a long time since I studied any math or physics...

tanseydavid 3y ago
Thank you for sharing this concept. I find it very illuminating.
mr_mitm 3y ago
This makes no sense whatsoever. Classical momentum is mv, not mv^2. Also, momentum is a vector and generally can't be negative. Quantum mechanical velocity is complicated as well.
whatshisface 3y ago
Momentum is mv, mv^2 is two times the kinetic energy. (Energy is real in quantum systems as well as classical ones.)
digging 3y ago
I thought quantum tunneling was due to uncertainty, allowing the position of a particle to resolve on the other side of a barrier sometimes because it is undefined before the tunneling. Are we talking about different things? Is one of us way off the mark? Or are these two angles of the same phenomenon?
lanza 3y ago
Classical mechanics are fundamentally wrong. They are low energy approximations to reality. "How did the bal go through the hill when it actually didn't have the momentum to do so" is a nonsense question because the equations of motion you are attempting to use to describe the phenomena are wrong. You can't and shouldn't try to understand QM from a CM standpoint. If you remember Taylor series expansions, this is like trying to understand `sin(x)` by looking at it's first order Taylor series expansion `x`. Your question about momentum and a potential hill is the same question as "how did the value of sin(x) start decreasing if `x` is linear?" You're using too few terms of the series expansion. The mechanisms of Newton's laws are first order terms of a proper QM solution.
- TechnicolorByte 3y ago
  Incredible analogy! The closer is a keeper: > The mechanisms of Newton’s laws are first order terms of a proper QM solution.
  - Koshkin 3y ago
    Except that this is only true when Newton's laws can be reasonably applied at all. In many (most?) quantum situations Newton's laws are completely nonsensical (while, conversely, in most classical situations QM is plain useless).
- Koshkin 3y ago
  > Classical mechanics are fundamentally wrong. All physical theories are “fundamentally wrong.” > You can’t A classical apparatus is part of the QM framework. Ergo: the commenter doesn’t know what they are talking about.
  - SideQuark 3y ago
    It is not known if all physical theories are fundamentally wrong. > A classical apparatus is part of the QM framework This sounds like nonsense. Care to elaborate, preferably with a link to a good source?
    - Zuider 3y ago
      I am not an expert, but, from listening to physicists and reading popular works, I thought they generally agreed that physics was radically incomplete. For instance, the two most powerful physical theories, Quantum Mechanics and General Relativity, contradict each other. Quantum mechanics has no explanation for what the collapse of the wave function means (it's really QM + Collapse) and it cannot account for gravity. General relativity, by contrast, assumes continuous space (which is incompatible with quantization) which leads it to predict point singularities (which is incompatible with the uncertainty principle and the Planck limit for physical distance.) As I said, I am ignorant, but someone more knowledgeable could expand on this.
user070223 3y ago
That what Carl bender talks about[0] That quantized nature is due to are ability to only measure only real values, which can be a sparse subset(Null set) placed on different sheets of the complex function, like qunatized energy levels of the electron in atoms. He also talk about research showing that exactly what happens when setting an experiment such that there is an interference which I briefly looked at a while back. [0] https://www.youtube.com/watch?v=_Sm7SNlNUOI&list=PLOFVFbzrQ49TNlDOxxCAjC7kbnorAR1MU&t=2221s https://www.youtube.com/watch?v=_Sm7SNlNUOI&list=PLOFVFbzrQ4...

tanseydavid 3y ago

Thank you for sharing this concept. I find it very illuminating.

mr_mitm 3y ago

This makes no sense whatsoever. Classical momentum is mv, not mv^2. Also, momentum is a vector and generally can't be negative. Quantum mechanical velocity is complicated as well.

whatshisface 3y ago

Momentum is mv, mv^2 is two times the kinetic energy. (Energy is real in quantum systems as well as classical ones.)

digging 3y ago

I thought quantum tunneling was due to uncertainty, allowing the position of a particle to resolve on the other side of a barrier sometimes because it is undefined before the tunneling. Are we talking about different things? Is one of us way off the mark? Or are these two angles of the same phenomenon?

lanza 3y ago

Classical mechanics are fundamentally wrong. They are low energy approximations to reality. "How did the bal go through the hill when it actually didn't have the momentum to do so" is a nonsense question because the equations of motion you are attempting to use to describe the phenomena are wrong. You can't and shouldn't try to understand QM from a CM standpoint. If you remember Taylor series expansions, this is like trying to understand `sin(x)` by looking at it's first order Taylor series expansion `x`. Your question about momentum and a potential hill is the same question as "how did the value of sin(x) start decreasing if `x` is linear?" You're using too few terms of the series expansion. The mechanisms of Newton's laws are first order terms of a proper QM solution.

TechnicolorByte 3y ago
Incredible analogy! The closer is a keeper: > The mechanisms of Newton’s laws are first order terms of a proper QM solution.
- Koshkin 3y ago
  Except that this is only true when Newton's laws can be reasonably applied at all. In many (most?) quantum situations Newton's laws are completely nonsensical (while, conversely, in most classical situations QM is plain useless).
Koshkin 3y ago
> Classical mechanics are fundamentally wrong. All physical theories are “fundamentally wrong.” > You can’t A classical apparatus is part of the QM framework. Ergo: the commenter doesn’t know what they are talking about.
- SideQuark 3y ago
  It is not known if all physical theories are fundamentally wrong. > A classical apparatus is part of the QM framework This sounds like nonsense. Care to elaborate, preferably with a link to a good source?
  - Zuider 3y ago
    I am not an expert, but, from listening to physicists and reading popular works, I thought they generally agreed that physics was radically incomplete. For instance, the two most powerful physical theories, Quantum Mechanics and General Relativity, contradict each other. Quantum mechanics has no explanation for what the collapse of the wave function means (it's really QM + Collapse) and it cannot account for gravity. General relativity, by contrast, assumes continuous space (which is incompatible with quantization) which leads it to predict point singularities (which is incompatible with the uncertainty principle and the Planck limit for physical distance.) As I said, I am ignorant, but someone more knowledgeable could expand on this.

user070223 3y ago

That what Carl bender talks about[0] That quantized nature is due to are ability to only measure only real values, which can be a sparse subset(Null set) placed on different sheets of the complex function, like qunatized energy levels of the electron in atoms. He also talk about research showing that exactly what happens when setting an experiment such that there is an interference which I briefly looked at a while back. [0] https://www.youtube.com/watch?v=_Sm7SNlNUOI&list=PLOFVFbzrQ49TNlDOxxCAjC7kbnorAR1MU&t=2221s https://www.youtube.com/watch?v=_Sm7SNlNUOI&list=PLOFVFbzrQ4...