Recent content by Demystifier

Today I learned that Terry Rudolph, the R from the famous PBR theorem, is a grandson of Erwin Schrodinger and his mistress. https://en.wikipedia.org/wiki/Terry_Rudolph

I have not studied the papers in detail, but at a first look the critique looks much more plausible.

If the Hamiltonian has a continuous spectrum, then, in the canonical ensemble with non-zero temperature, any given energy has non-zero probability density, but zero probability.

You are right that any state with definite energy has zero probability in that sense. But there is nothing wrong with that conclusion. We are talking about thermal equilibrium, i.e. thermal states in a canonical ensemble, while states with definite non-zero energy are not thermal states, so in...

I think there were a few, but I can find only this one: https://www.physicsforums.com/threads/quantum-mechanics-myths-and-facts.143045/

I joined this forum soon after writing this paper, so this is how I have chosen my name. :smile:

Under a coordinate transformation ##x^{\mu}\to x'^{\mu}=f^{\mu}(x)##, the two metrics transform as $$g'^{\alpha\beta}=\frac{\partial x'^{\alpha}}{\partial x^{\mu}} \frac{\partial x'^{\beta}}{\partial x^{\nu}} g^{\mu\nu}$$ $$\bar{g}'^{\alpha\beta}=\frac{\partial x'^{\alpha}}{\partial x^{\mu}}...

How did you verify this? They do transform as tensors under coordinate transformations, but their indices are not raised and lowered in the usual way. Which is understandable, because when you have two metrics, there is an ambiguity should one raise the indices with ##g^{\mu\nu}## or...

Is this something like a white hole?

My confusion stems from the following. The Bardeen metric significantly deviates from the Schwarzschild only for small ##r##, close to ##r=0##. And yet, global properties significantly deviate from the Schwarzschild even for larger ##r##, e.g. close to ##r=2M##. How to understand that? What do I...

I believe there is no such quantity, because you study a variation of the object that defines the covariant and contravariant components.

Does it shed some light on the information paradox?

That's because tunneling is a consequence of superposition. For example, suppose that at time ##t## the particle can tunnel from the left to the right, through a barrier in the middle. This means that the wave function at ##t## is nonzero both at the left and at the right, i.e. the wave...

3. is just a definition of the dual tensor, i.e. the rule how to raise indices in the same world. In 2. you try to compare quantities from two different worlds.

No, the number of degrees of freedom is not directly related to the size of the system. It is more directly related to the number of particles. See also https://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)