Relativity & Gravity: Does Potential Energy Increase Mass?

[andypandy2020]

As it is quite often shown, when an object is moving, it's kinetic energy causes an increase in its effective mass in accordance with E=mc^2.
When considering other "forms" of energy, such as gravitational potential energy, does this also cause an increase in effective mass, albeit very small?

 

[Dale]

Hi andypandy2020, welcome to PF

As it is quite often shown, when an object is moving, it's kinetic energy causes an increase in its effective mass in accordance with E=mc^2.
When considering other "forms" of energy, such as gravitational potential energy, does this also cause an increase in effective mass, albeit very small?

What you are describing here is called "relativistic mass" and it is no longer in common use amongst modern physicists. Physicists usually reserve the term "mass" to mean the "invariant mass".

 

[andypandy2020]

Ok that's fine.

What I was getting at though was that if there is an increase in an object's mass when its GPE increases, then would this not increase its GPE further? This, however, cannot be right, and so it would imply that for some reason GPE does not contribute to invariant mass.

 

[Dickfore]

In Relativity, the term potential energy is meaningless.

 

[andypandy2020]

In Relativity, the term potential energy is meaningless.

Why is that, surely an object in a field must have potential energy, and then why wouldn't this contribute to its invariant mass? Even if this term is very small why does it not cause a problem of the mass and potential energy growing?

 

[Dickfore]

Potential energy is a function of the relative distance between two particles. Since the distance is not a relativistic invariant, we cannot uniquely assign a potential energy function. Remember that the gravitational potential energy of a body near the Earth's surface is actually the potential energy of the system body-Earth and depends on their mutual separation.

 

[Dale]

What I was getting at though was that if there is an increase in an object's mass when its GPE increases, then would this not increase its GPE further? This, however, cannot be right, and so it would imply that for some reason GPE does not contribute to invariant mass.

I wouldn't go so far as to say that GPE is meaningless. In a stationary spacetime you can certainly make a potential that reduces to the Newtonian potential in the appropriate limit. However, in general GPE and even mass are difficult to define in GR. Here is a link that goes over some of the issues:

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

 

[Mueiz]

As it is quite often shown, when an object is moving, it's kinetic energy causes an increase in its effective mass in accordance with E=mc^2.
When considering other "forms" of energy, such as gravitational potential energy, does this also cause an increase in effective mass, albeit very small?

No .. Potential Energy is not a true property of the object ..it is just a mathmatical trick to make the law of concervation of energy valid locally by taking the work which will be done in the future as a property of now. This is true in both Newtonian and Relativistic Mechanics

 

[K^2]

No .. Potential Energy is not a true property of the object ..it is just a mathmatical trick to make the law of concervation of energy valid locally by taking the work which will be done in the future as a property of now. This is true in both Newtonian and Relativistic Mechanics

You seem to be confused about what the term energy means. Go ahead and look up classical definition.

At any rate, while actual potential might be a bit difficult to define in GR, especially in time-dependent metric, the rest mass of an object definitely does change with position of the object. Under linearized gravity, where GPE is fully meaningful again, this mass change corresponds perfectly to potential energy change.

 

[Mueiz]

You seem to be confused about what the term energy means. Go ahead and look up classical definition.

At any rate, while actual potential might be a bit difficult to define in GR, especially in time-dependent metric, the rest mass of an object definitely does change with position of the object. Under linearized gravity, where GPE is fully meaningful again, this mass change corresponds perfectly to potential energy change.

This is true for a system of density of particle but not for single object
To an object in a point-moment in space-time there is no potential energy

 

[Dale]

Remember that the gravitational potential energy of a body near the Earth's surface is actually the potential energy of the system body-Earth and depends on their mutual separation.

This is a good point. Potential energy pertains to a system and really cannot be attributed to an individual object within the system.