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Added the bump function to clarify the type of evolution of Planck's constant
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Guillaume Laporte
Guillaume Laporte
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We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why macroscopic objects mostly obey laws of classical mechanics and that quantum effects are only seen at small scales.

So let's say we start with a quantum mechanical system that evolves at first with a value of zero for Planck's constant (In this case it at first obeys classical mechanics). Then we slowly increase it over time. The objects in the system will still look like they obey classical mechanics when the constant is very small, but not zero. (They all look like macroscopic objects)

How does branching in the many-worlds start to occur if you keep the constant very small like this (if it does)?

And suppose there are many worlds, branches, what happens to the universe if you let the constant go to zero?

Edit : As more indication of the question: take the value of Planck's constant $h(t)$ to follow the bump function over time; and consider the beginning and the end of the bump. $$ h(t) = \begin{cases} e^{-\frac{1}{1-t^2}} & \text{for } -1 < t < 1, \\ 0 & \text{otherwise}. \end{cases} $$

(I know it's funny to call it a constant if you move it around.. but consider it as a Gedankenexperiment)

It would be fun to have an answer using the path integral formalism; since I like it a lot (it's mostly the only thing I am using now). And I don't mind a very math-heavy answer since I have a good background in mathematical physics.

We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why macroscopic objects mostly obey laws of classical mechanics and that quantum effects are only seen at small scales.

So let's say we start with a quantum mechanical system that evolves at first with a value of zero for Planck's constant (In this case it at first obeys classical mechanics). Then we slowly increase it over time. The objects in the system will still look like they obey classical mechanics when the constant is very small, but not zero. (They all look like macroscopic objects)

How does branching in the many-worlds start to occur if you keep the constant very small like this (if it does)?

And suppose there are many worlds, branches, what happens to the universe if you let the constant go to zero?

(I know it's funny to call it a constant if you move it around.. but consider it as a Gedankenexperiment)

It would be fun to have an answer using the path integral formalism; since I like it a lot (it's mostly the only thing I am using now). And I don't mind a very math-heavy answer since I have a good background in mathematical physics.

We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why macroscopic objects mostly obey laws of classical mechanics and that quantum effects are only seen at small scales.

So let's say we start with a quantum mechanical system that evolves at first with a value of zero for Planck's constant (In this case it at first obeys classical mechanics). Then we slowly increase it over time. The objects in the system will still look like they obey classical mechanics when the constant is very small, but not zero. (They all look like macroscopic objects)

How does branching in the many-worlds start to occur if you keep the constant very small like this (if it does)?

And suppose there are many worlds, branches, what happens to the universe if you let the constant go to zero?

Edit : As more indication of the question: take the value of Planck's constant $h(t)$ to follow the bump function over time; and consider the beginning and the end of the bump. $$ h(t) = \begin{cases} e^{-\frac{1}{1-t^2}} & \text{for } -1 < t < 1, \\ 0 & \text{otherwise}. \end{cases} $$

(I know it's funny to call it a constant if you move it around.. but consider it as a Gedankenexperiment)

It would be fun to have an answer using the path integral formalism; since I like it a lot (it's mostly the only thing I am using now). And I don't mind a very math-heavy answer since I have a good background in mathematical physics.

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Qmechanic ♦
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Guillaume Laporte
Guillaume Laporte
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What happens to branching in the Many-Worlds Interpretation of quantum mechanics in the limit when Planck's constant goes to 0?

We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why macroscopic objects mostly obey laws of classical mechanics and that quantum effects are only seen at small scales.

So let's say we start with a quantum mechanical system that evolves at first with a value of zero for Planck's constant (In this case it at first obeys classical mechanics). Then we slowly increase it over time. The objects in the system will still look like they obey classical mechanics when the constant is very small, but not zero. (They all look like macroscopic objects)

How does branching in the many-worlds start to occur if you keep the constant very small like this (if it does)?

And suppose there are many worlds, branches, what happens to the universe if you let the constant go to zero?

(I know it's funny to call it a constant if you move it around.. but consider it as a Gedankenexperiment)

It would be fun to have an answer using the path integral formalism; since I like it a lot (it's mostly the only thing I am using now). And I don't mind a very math-heavy answer since I have a good background in mathematical physics.