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Q&A What if the Planck constant was exactly zero?

This question really has no answer because it is phrased in a way which doesn't actually have much meaning. As phrased, it appears as though the universe is governed by these constants, which can ...

posted 8y ago by Cort Ammon - Reinstate Monica‭  ·  edited 4y ago by HDE 226868‭

Answer
#1: Post edited by user avatar HDE 226868‭ · 2020-06-02T20:43:41Z (almost 4 years ago)
Fixed formatting.
  • <p>This question really has no answer because it is phrased in a way which doesn't actually have much meaning.</p>
  • <p>As phrased, it appears as though the universe is governed by these constants, which can be dialed this way or that by some supreme force. In this universe, we'll set Planck's constant to $6.626070040(81) \cdot 10^{−34}\;\text{J}\cdot\text{s}$, in another universe, $0\;\text{J}\cdot\text{s}$. A more meaningful approach would be to say that the universe appears to be governed by some laws, and several of those laws happen to involve ratios that are expressed as a constant. This is important because it points out a key issue with the question: there is not just one way to set Planck's constant to $0$. The mere definition of a parallel universe which is identical to ours but with $h = 0\;\text{J}\cdot\text{s}$ is insufficient to describe the parallel universe unless it is massively degenerate.</p>
  • <p>If we were to presume that the universe was nothing more than a set of equations and Planck's constant is something you can just dial down to 0, we get some strange behaviors. The first is the one that SudoSedWinifred mentioned. There is no quantization of energy in this universe. All of quantum physics immediately degenerates in messy piles of broken equations. It goes downhill from there. I don't know enough QM equations by memory, but the end result of setting Planck's constant to $0$ may cause a divide by zero in quantum mechanics, which means the universe you describe simply cannot possibly exist. Even if that isn't the case, by the Planck-Einstein equation, $E = h\cdot
  • u$, the energy of a photon is proportional to its frequency, and the constant of proportionality is Planck's constant. If Planck's constant is $0$, this equation falls apart... photons can no longer carry energy. Not only is all of quantum mechanics completely and utterly torn apart, but electromagnetics also falls apart.</p>
  • <p>So the real question is not what happens when Planck's constant is $0$, but rather what you did to make the concepts behind Planck's constant lose meaning. You could state "energy has no quantization in my parallel universe," and build up behaviors from there. However, there is a difference between declaring the Einstein-Planck equation is $E = 0\cdot
  • u$ and declaring that that equation is simply invalid and does not apply to this universe. You could also make a world where photons are incapable of carrying energy, and explore the consequences of that. In such a case, Planck energy is still a valid effect, and QM still (sort of) hobbles along, but there is simply no connection between those effects and photons.</p>
  • <p>Or you can just say "it's a parallel universe where $h = 0\;\text{J}\cdot\text{s}$," but the resulting universe is so degenerate that it wont be much fun to try to explore. It is as meaningful as "writing something on the other side of a Möbius strip." It sounds great, but doesn't actually mean anything (because a Möbius strip simply only has one side).</p>
  • <p>This question really has no answer because it is phrased in a way which doesn't actually have much meaning.</p>
  • <p>As phrased, it appears as though the universe is governed by these constants, which can be dialed this way or that by some supreme force. In this universe, we'll set Planck's constant to $6.626070040(81) \cdot 10^{-34}\;\text{J}\cdot\text{s}$, in another universe, $0\;\text{J}\cdot\text{s}$. A more meaningful approach would be to say that the universe appears to be governed by some laws, and several of those laws happen to involve ratios that are expressed as a constant. This is important because it points out a key issue with the question: there is not just one way to set Planck's constant to $0$. The mere definition of a parallel universe which is identical to ours but with $h = 0\;\text{J}\cdot\text{s}$ is insufficient to describe the parallel universe unless it is massively degenerate.</p>
  • <p>If we were to presume that the universe was nothing more than a set of equations and Planck's constant is something you can just dial down to 0, we get some strange behaviors. The first is the one that SudoSedWinifred mentioned. There is no quantization of energy in this universe. All of quantum physics immediately degenerates in messy piles of broken equations. It goes downhill from there. I don't know enough QM equations by memory, but the end result of setting Planck's constant to $0$ may cause a divide by zero in quantum mechanics, which means the universe you describe simply cannot possibly exist. Even if that isn't the case, by the Planck-Einstein equation, $E = h\cdot
  • u$, the energy of a photon is proportional to its frequency, and the constant of proportionality is Planck's constant. If Planck's constant is $0$, this equation falls apart... photons can no longer carry energy. Not only is all of quantum mechanics completely and utterly torn apart, but electromagnetics also falls apart.</p>
  • <p>So the real question is not what happens when Planck's constant is $0$, but rather what you did to make the concepts behind Planck's constant lose meaning. You could state "energy has no quantization in my parallel universe," and build up behaviors from there. However, there is a difference between declaring the Einstein-Planck equation is $E = 0\cdot
  • u$ and declaring that that equation is simply invalid and does not apply to this universe. You could also make a world where photons are incapable of carrying energy, and explore the consequences of that. In such a case, Planck energy is still a valid effect, and QM still (sort of) hobbles along, but there is simply no connection between those effects and photons.</p>
  • <p>Or you can just say "it's a parallel universe where $h = 0\;\text{J}\cdot\text{s}$," but the resulting universe is so degenerate that it wont be much fun to try to explore. It is as meaningful as "writing something on the other side of a Möbius strip." It sounds great, but doesn't actually mean anything (because a Möbius strip simply only has one side).</p>