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 said: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?
Dickfore said:In Relativity, the term potential energy is meaningless.
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:andypandy2020 said: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.
andypandy2020 said: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?
You seem to be confused about what the term energy means. Go ahead and look up classical definition.Mueiz said: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 said: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 a good point. Potential energy pertains to a system and really cannot be attributed to an individual object within the system.Dickfore said: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.
In the theory of relativity, potential energy and mass are considered equivalent and can be converted into one another. This is represented by Einstein's famous equation, E=mc², which states that energy (E) is equal to mass (m) multiplied by the speed of light squared (c²).
Potential energy does not directly affect the mass of an object. However, when an object gains potential energy, it gains an equivalent amount of mass according to the equation E=mc². This is because potential energy is a form of energy and energy is equivalent to mass in the theory of relativity.
Yes, potential energy does increase the gravitational pull of an object. This is because, according to the theory of relativity, energy and mass are equivalent and therefore have the same gravitational effects. So when an object gains potential energy, it also gains an equivalent amount of mass, resulting in an increased gravitational pull.
Yes, potential energy can be converted into mass and vice versa. This is demonstrated by the equation E=mc², where energy and mass are interchangeable. For example, when an object falls from a higher position to a lower one, its potential energy decreases and is converted into kinetic energy. This decrease in potential energy also results in a decrease in the object's mass.
In the theory of gravity, potential energy is the energy an object possesses due to its position in a gravitational field. This potential energy can be converted into other forms of energy, such as kinetic energy, as the object moves within the gravitational field. According to the theory of relativity, this change in potential energy also results in a change in the object's mass, which in turn affects its gravitational pull.