Can Moving a Hydrogen Atom by an Angstrom Alter Its Mass?

[YummyFur]

Not sure if this should be in the quantum or classical forum, but as gravity has not been shown to be quantised yet...

My question is this, seeing as there is no quantised theory of gravity yet, that would mean that if a single atom of say hydrogen residing on the surface of the Earth was moved radially away from the centre of the Earth by a single angstrom unit, then it must be theoretically possible to calculate the increase in it's mass due to it's increased potential energy. Is this correct? If so how small is this number, in approximate orders of magnitude.

If it is correct then the same must be true if instead of an angstrom unit it is moved by a mere Planck length.

 

[Jano L.]

Why do you think the potential energy of small particle in a gravitational field would change its inertial mass? I think it will not.

 

[YummyFur]

Are you suggesting that only it's gravitational mass that is increased? I just thought that potential energy manifested as mass increase, but maybe not for a subatomic particles maybe just for a system like a spring?

But the main point I wish to understand is how it can be that there is any question that gravity is quantised. I mean how can it not be, if potential energy as a result of gravity is reliant on a measurement, and this measurement must necessarily be limited by the Planck length then gravity must be quantised, must it not?

 

[Jano L.]

I think that neither inertial nor gravitational mass of the particle changes when it changes its position in gravitational field. In electrostatic field, particle has the same mass wherever it may be. It is the total mass of the whole system (source of the field) + particle that changes when the particle moves.

Do you really think that potential energy is something that gets measured? I think it is just a theoretical concept, mathematically defined to be integral of motion of equations of motion.

 

[PJC01]

I would first like to clarify that the non-quantisation of gravity is still a topic of ongoing research and debate in the scientific community. While there have been attempts to unify gravity with quantum mechanics, a complete and consistent theory has not yet been achieved.

To answer your question, yes, it is theoretically possible to calculate the increase in mass of a single atom of hydrogen if it is moved radially away from the center of the Earth by a single angstrom unit. However, the increase in mass would be extremely small and difficult to measure. This is because the gravitational potential energy of an object is directly proportional to its mass and the distance from the center of gravity. So, even a tiny increase in distance would result in a very small increase in potential energy and thus, mass.

In terms of orders of magnitude, the increase in mass due to a single angstrom unit movement would be on the order of 10^-38 grams, which is incredibly small. Moving the atom by a Planck length would result in an even smaller increase in mass, on the order of 10^-70 grams.

It is important to note that these calculations are based on classical mechanics and do not take into account the effects of quantum mechanics. In a quantum theory of gravity, the increase in mass due to a change in distance may be different. However, until a complete theory is developed, we cannot accurately predict the exact values.

In conclusion, while it is theoretically possible to calculate the increase in mass of an atom due to a change in distance, the resulting numbers are extremely small and difficult to measure. The non-quantisation of gravity remains an open and complex topic in physics, and further research is needed to fully understand its effects.