If an electron falls into a black hole. How can the Heisenberg uncertainty princ

Question

If an electron falls into a black hole. How can the Heisenberg uncertainty principle hold? The electron has fallen into the singularity now so it has a well defined position which means that it doesn't have a well defined momentum? Furthermore, the electron can't have a well defined position in space because space eigenkets are unphysical. It's momentum must certainly cause it to move.

Another question, Can one calculate the amount of new mass(the relativistic mass) that the black hole acquire after quantum particles fall in the singularity?

Doesn't this mean that the electron can't be described by a wave packet at the singularity of the black hole? If we want quantum mechanics to be applicable inside a black hole,the wavefunction should leak outside right ?

Explanation / Answer

I guess you have in mind something like a Schwarzschild black hole? An electron falls into the event horizon, and the laws of general relativity deem that it will eventually make its way to the singularity. It's important to remember that the theorems which predict the existence of the singularity are predicated on classical i.e non-quantum general relativity. When Planck-scale quantum effects are modelled, it may not be appropriate to talk of singularities any more. There is no general agreement on how to handle this at the present time.

However, even if the Schwarzschild singularity does exist in the form predicted by GR, it is difficult to talk about application of the uncertainty principle there. The problem is that, at the singularity, time ends - the time experienced by the infalling electron comes to a stop. Lack of ability to perform time derivatives makes it rather problematic to talk of the electron's momentum at the singularity.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.