Hypothetical 'black hole'/electron atom

In summary, the conversation is about finding the mass of a black hole that would result in identical energy levels to a hydrogen atom when an electron is formed between them. The speaker is confident that they can calculate this mass using gravitational interactions instead of electromagnetic interactions, but they are struggling with the concept of quantized gravitational orbits. Another speaker reassures them that there are no complications and that the quantization only applies to the electron, not the electromagnetic field. The first speaker is relieved and thanks the second speaker for their help.
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Homework Statement


I have been asked to consider an atom formed between an electron and 'black hole' i.e. a point singularity with mass and no charge. I should find the mass of the black hole Mh such that the energy levels of this atom would be identical to the energy levels of a hydrogen atom

I'm fairly sure I can calculate a mass that would give the same energy of the n=1 orbital (13.6eV) at the Bohr radius a0 by considering gravitational rather than EM interactions, but I'm having difficulty grasping the notion of quantised gravitational orbits. Are all 'energy levels' quantised?

Cheers guys
 
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You are maybe thinking there are complications here when there aren't. When you solve schrodingers equation for the hydrogen atom, you aren't quantizing the EM field. You are only quantizing the electron. The field itself is a classical electric field. There isn't any problem replacing that with a gravitational field that generates the same inverse square potential. No need to do quantum gravity.
 
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I always end up doing that! It's the 'levels' aspect of it that threw me. Got a reasonable value out of it now, thanks Dick
 
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1. What is a "hypothetical 'black hole'/electron atom"?

A "hypothetical 'black hole'/electron atom" is a theoretical concept that combines the properties of black holes and electrons. It suggests that if an electron were to be compressed to a certain density, it could potentially exhibit characteristics similar to those of a black hole.

2. How is this concept related to black holes and electrons?

The concept of a "hypothetical 'black hole'/electron atom" is related to black holes and electrons because it combines the properties of both. Black holes are known for their extreme density and gravitational pull, while electrons are fundamental particles with a negative charge. This concept suggests that under certain conditions, an electron could behave like a black hole.

3. Is there any evidence to support this concept?

Currently, there is no direct evidence to support the existence of a "hypothetical 'black hole'/electron atom". However, some theories in physics, such as string theory, suggest the possibility of this concept. Additionally, scientists are continuously conducting experiments and observations to further understand the nature of black holes and electrons.

4. What would be the implications of this concept being proven true?

If this concept were proven true, it would greatly impact our understanding of fundamental particles and the behavior of black holes. It could also potentially lead to advancements in technologies such as quantum computing and space travel.

5. How does this concept relate to the search for a unifying theory of physics?

The concept of a "hypothetical 'black hole'/electron atom" is often discussed in the context of trying to find a unifying theory of physics, also known as the Theory of Everything. This is because it combines two fundamental aspects of physics, gravity and quantum mechanics, and could potentially bridge the gap between these two theories.

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