3 ms·

(Disclaimer: I don't know Special relativity, so I might make mistakes that betray that fact ;) We are certainly in agreement about the facts of the matter :)

by maggit 12y ago

(Disclaimer: I don't know Special relativity, so I might make mistakes that betray that fact ;) We are certainly in agreement about the facts of the matter :) The thing I find unsatisfying is specifically the phrasing "Newtonian mechanics breaks down". Breaks down how? Breaks down why? "There is a regime (...), which is determined by the Planck constant." to me reads like, and I am adding color here for effect, "The governor has decreed that on Mondays, Quantum Mechanics shall be in effect. All other days are to be executed with Newtonian mechanics only, except when Max Planck has a belly ache!" You make it look like QM is a special case of NM, while in reality, QM describes all the phenomena that NM does, not the other way around; NM is a special case of QM. I'm trying to explain it that way instead: Quantum mechanics is correct. Always, always, always[1] use Quantum mechanics!!! Newtonian mechanics is obsolete! [1]: Well, this is where my lack of knowledge about Special relativity comes in. PS: Did you know that in specific circumstances you can use these much simpler formulae instead: (...), and the error is within these totally acceptable bounds: ... ? PPS: Did you know that these simplified formulae were already known under the silly name "Newtonian mechanics"? The more you know! :) The reason that I am adding it as a comment is not to correct you -- you are already right -- but to maybe help other readers. QM vs NM did not sit right with me until I understood that NM's equations actually fall out of QM's equations in specific, nameable, circumstances :)

hawkice 12y ago
> Quantum mechanics is correct. Always, always, always use Quantum mechanics!!! Newtonian mechanics is obsolete! Okay, so when we talk about use we are talking about tools. A lot of the tools we got from Newtonian mechanics are pretty reasonably accurate. If I see a ball bounces 3 feet when I drop it from 5 feet up, there's no reason to use anything particularly fancy to guess how high it will bounce if dropped from 10 feet. These are simpler tools I can use, and they may not be great (gravity is weaker at ten feet, for instance, so it's clear I'd be wrong to some extent, forget my ignoring just about every pertinent detail of the ball), but it works. Right tool for the job doesn't need to be fancy. > You make it look like QM is a special case of NM, while in reality, QM describes all the phenomena that NM does, not the other way around; NM is a special case of QM. Quantum Mechanics is continuous and differentiable at all points, including in descriptions of e.g. mass. To make Newtonian Mechanics a special case, you'd (at the very least) have to put some gnarly integrals in place of almost every variable in your formulas. They don't _really_ agree, one isn't a subset of another. One is an approximation (and not even specifically of Quantum Mechanics, just an approximation of things-seen-on-earth, some of which have compelling quantum mechanical stories, some of which, like gravity, don't). And sometimes approximations are useful.
rotorblade 12y ago
> The thing I find unsatisfying is... I suppose my use of the word "regime" is unconventional. What I mean is a "parameter regime", or "for a certain range of a parameter". For example, for the range in which \hbar is much smaller than one (in some units), this is the "parameter regime" in which QM and Newtonian mechanics agree quite/indistinguishably well. And for the range in which \hbar is close to one, "Newtonian mechanics breaks down", in the sense that QM effects are large -- i.e. where Newtonian mechanics is no longer a good approximation to QM. > Quantum mechanics is correct. Always, always, always[1] use Quantum mechanics!!! Newtonian mechanics is obsolete! I would not agree with phrasing it like that, and it is indeed Special relativity (or a part of it). If quantum mechanics makes Newtonian mechanics (NM) "obsolete", then what does that imply for Special relativity (SR)? QM makes corrections to NM with the parameter \hbar. SR makes corrections to NM with v/c (velocities you make experiments at over speed of light). So say that we are doing a mechanics experiment on our desk (say dropping something on a spring, or whatever). And we go with your "always use QM", it would take a long time to write down what happens, the same (although a bit faster) if we were to go with "always use SR". Before you start writing down what is going on for that experiment, you make an assumption/approximation of which range of parameters is relevant for you. An apple dropped on a spring bed would not have relevant corrections from QM nor SR. > The reason that I am adding it as a comment is not to correct you -- you are already right -- but to maybe help other readers. Absolutely! Thats is also my goal in discussing these things. I do not always know how to make them "popular"/less technical, so I'm very interested in hearing other ways of explaining it.
- maggit 12y ago
  > If quantum mechanics makes Newtonian mechanics (NM) "obsolete", then what does that imply for Special relativity (SR)? Ah. That's unsatisfying :) It would be super satisfying to have one coherent theory of everything. [1] Why hasn't anybody thought of that before? ;) [1]: And then, again, it is of course useful to have efficient ways to work within subsets of the grand theory, such as NM.

by maggit 12y ago

hawkice 12y ago

> Quantum mechanics is correct. Always, always, always use Quantum mechanics!!! Newtonian mechanics is obsolete! Okay, so when we talk about use we are talking about tools. A lot of the tools we got from Newtonian mechanics are pretty reasonably accurate. If I see a ball bounces 3 feet when I drop it from 5 feet up, there's no reason to use anything particularly fancy to guess how high it will bounce if dropped from 10 feet. These are simpler tools I can use, and they may not be great (gravity is weaker at ten feet, for instance, so it's clear I'd be wrong to some extent, forget my ignoring just about every pertinent detail of the ball), but it works. Right tool for the job doesn't need to be fancy. > You make it look like QM is a special case of NM, while in reality, QM describes all the phenomena that NM does, not the other way around; NM is a special case of QM. Quantum Mechanics is continuous and differentiable at all points, including in descriptions of e.g. mass. To make Newtonian Mechanics a special case, you'd (at the very least) have to put some gnarly integrals in place of almost every variable in your formulas. They don't _really_ agree, one isn't a subset of another. One is an approximation (and not even specifically of Quantum Mechanics, just an approximation of things-seen-on-earth, some of which have compelling quantum mechanical stories, some of which, like gravity, don't). And sometimes approximations are useful.

rotorblade 12y ago

> The thing I find unsatisfying is... I suppose my use of the word "regime" is unconventional. What I mean is a "parameter regime", or "for a certain range of a parameter". For example, for the range in which \hbar is much smaller than one (in some units), this is the "parameter regime" in which QM and Newtonian mechanics agree quite/indistinguishably well. And for the range in which \hbar is close to one, "Newtonian mechanics breaks down", in the sense that QM effects are large -- i.e. where Newtonian mechanics is no longer a good approximation to QM. > Quantum mechanics is correct. Always, always, always[1] use Quantum mechanics!!! Newtonian mechanics is obsolete! I would not agree with phrasing it like that, and it is indeed Special relativity (or a part of it). If quantum mechanics makes Newtonian mechanics (NM) "obsolete", then what does that imply for Special relativity (SR)? QM makes corrections to NM with the parameter \hbar. SR makes corrections to NM with v/c (velocities you make experiments at over speed of light). So say that we are doing a mechanics experiment on our desk (say dropping something on a spring, or whatever). And we go with your "always use QM", it would take a long time to write down what happens, the same (although a bit faster) if we were to go with "always use SR". Before you start writing down what is going on for that experiment, you make an assumption/approximation of which range of parameters is relevant for you. An apple dropped on a spring bed would not have relevant corrections from QM nor SR. > The reason that I am adding it as a comment is not to correct you -- you are already right -- but to maybe help other readers. Absolutely! Thats is also my goal in discussing these things. I do not always know how to make them "popular"/less technical, so I'm very interested in hearing other ways of explaining it.

maggit 12y ago
> If quantum mechanics makes Newtonian mechanics (NM) "obsolete", then what does that imply for Special relativity (SR)? Ah. That's unsatisfying :) It would be super satisfying to have one coherent theory of everything. [1] Why hasn't anybody thought of that before? ;) [1]: And then, again, it is of course useful to have efficient ways to work within subsets of the grand theory, such as NM.