Gravitational Potential of a Chargeless Particle Confined in a Box | Einstone

[einstone]

What is the gravitational potential produced by a chargeless particle confined in a box if the particle is in a stationary state ( for the nonce,in the lowest energy state)?
Thanking you,
Einstone.

 

[dextercioby]

$$V=-\frac{Gm}{r}$$,if the particle in the origin of a system of coordinates.

Daniel.

P.S.Why...?What's the "box" catch...?

 

[einstone]

Oh, I owe you an apology. It was remiss of me to have said 'a particle'
insted of a 'microparticle' in the question. I reckon the choice of a box would produce the simplest possible wavefunctions.
Thanking you,
Einstone.

 

[dextercioby]

What do wavefunctions have to do with the gravitational potential created by the same particle (and not by another body)...?

Daniel.

 

[einstone]

How is the potential at a point inside the box determined? It should depend
upon the wavefunction.
Thank you for the reply.
I'm, with great respect,
Einstone.

 

[dextercioby]

Surprise.Usually,the potential is GIVEN...The wavefunction's is computed knowing the potential and usually not viceversa.That's because you cannot know wavefunctions through other method,than solving Schrödinger's eq.which assumes knowing the potential...

Daniel.

 

[ZapperZ]

How is the potential at a point inside the box determined? It should depend
upon the wavefunction.
Thank you for the reply.
I'm, with great respect,
Einstone.

Er.. if this "wavefunction" that you are talking about is the solution to the Schrödinger equation, then you have put the tail in front of the donkey. It is the wavefuction that is dependent on the potential, NOT the other way around. You don't find the solution to the differential equation and THEN write down the differential equation. And if you look at the Schrödinger equation that you have to solve, the "V" in there IS exactly the potential. Only after you know what V is, do you get the wavefunction.

Zz.

 

[einstone]

Thank you for the replies.
Does the particle interact with its own gravitational field ( which is
present even in absence of any other potential)? If not, what is the gravitational field produced by it?
So daffy of me to have forgotten about the gravitation & thought that the particle was free! Then I went on to find the wavefunction & calculate the potential.

 

[dextercioby]

Of course,in the CLASSICAL theory of GR,just in CED,particles can interact with their own gravity field.

In the Newtonian theory,i've already told you what the potential is.

Daniel.

 

[hellfire]

What is the gravitational potential produced by a chargeless particle confined in a box if the particle is in a stationary state ( for the nonce,in the lowest energy state)?

As already mentioned, you can describe a particle inside a gravitational potential making use of the Schrödinger equation. However, if you want to describe the gravitational field or gravitational potential generated by quantum particle you have no proper equations nor a theory to do that. In chapter 14 of R. Wald's "General Relativity", a simple argument is given why this cannot work with the current physics (a "quantum" particle and "classical" gravitation): The (classical) gravitational field should spread according to the particles' wavefunction. The instantaneous wavefunction collapse would lead to a superluminal propagation of the changes of the field. To describe this properly a quantum field theory for gravitation (or quantum gravity) would be needed in which the superposition principle would be also valid for the gravitational field.

 

[einstone]

However, if you want to describe the gravitational field or gravitational potential generated by quantum particle you have no proper equations nor a theory to do that.

Good Heavens! Never mind the equations, but is there not even a consistent theory? I thought I'd solve the problem & generalise it step by step to include Relativistic Gravitation ,then Dirac's equation & ...!
How, then, do all the theories give correct answers?

 

[dextercioby]

Only as partial theories.If u want to mix gravity & Dirac fields,end up with Sugra N=1,okay,but you can do that:
1.In the free falling frame.
2.The field theory is not renormalizable under quantization,...

But of course,both Dirac & GR are perfectly valid theories,on THEIR OWN...

Daniel.

 

[ChrisAvery]

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