Equivalence Principle: Mass Increase With Time?

[GRDixon]

An uncharged, isolated particle of mass m is subjected to a constant force that increases its speed relative to an IRF. Its mass presumably increases as long as the force acts. Does the mass of an identical particle, held at rest in a gravitational field also increase with the passage of time when the constraining force is equal and oppositely directed to the gravitational force?

 

[D H]

An uncharged, isolated particle of mass m is subjected to a constant force that increases its speed relative to an IRF. Its mass presumably increases as long as the force acts.

You are referring to relativistic mass, a somewhat outdated concept. The particle's intrinsic mass does not change.

Does the mass of an identical particle, held at rest in a gravitational field also increase with the passage of time when the constraining force is equal and oppositely directed to the gravitational force?

No.

 

[sylas]

An uncharged, isolated particle of mass m is subjected to a constant force that increases its speed relative to an IRF. Its mass presumably increases as long as the force acts. Does the mass of an identical particle, held at rest in a gravitational field also increase with the passage of time when the constraining force is equal and oppositely directed to the gravitational force?

I presume you mean the "relativistic mass", which is really just the energy of a particle or object scaled to mass units. More usually these days, we would say that the "mass" is an intrinsic property of something, independent of the relative velocity of an observer. Just saying "mass" alone usually means "rest mass".

The answer to your question is no. The gain in mass you refer to is the gain in energy associated with increasing speed relative to some inertial observer.

Cheers -- sylas

PS. And D H wins this round of "physicsforums snap". But it was close!

PPS. And welcome to the forums, GRDixon! Glad to have you aboard.

 

[yuiop]

In modern relativity, the mass is no longer considered to be increasing and the term "relativistic mass" is no longer encouraged. It is however reasonable to state that to an inertial observer in flat space, the kinetic energy of the accelerating particle is continuously increasing as is the the relative velocity. The inertial observer in the gravitational context is a free falling observer and to a free falling observer the particle at rest in the gravitational field is also increasing in kinetic energy and relative velocity. To an observer accelerating alongside the accelerating particle in flat space, the kinitic energy and relative velocity of the particle is not changing. To an (accelerating) observer at rest with the particle that is itself at rest in the gravitational field, the kinetic energy and relative velocity is also not changing. Looked at like that, the particle subjected to constant force in flat space is equivalent to a particle at rest in a gravitational field. Hope that helps.

 

[GRDixon]

In modern relativity, the mass is no longer considered to be increasing and the term "relativistic mass" is no longer encouraged. It is however reasonable to state that to an inertial observer in flat space, the kinetic energy of the accelerating particle is continuously increasing as is the the relative velocity. The inertial observer in the gravitational context is a free falling observer and to a free falling observer the particle at rest in the gravitational field is also increasing in kinetic energy and relative velocity. To an observer accelerating alongside the accelerating particle in flat space, the kinitic energy and relative velocity of the particle is not changing. To an (accelerating) observer at rest with the particle that is itself at rest in the gravitational field, the kinetic energy and relative velocity is also not changing. Looked at like that, the particle subjected to constant force in flat space is equivalent to a particle at rest in a gravitational field. Hope that helps.

Thanks, KEV. It definitely gave me food for thought.

 

[yuiop]

Thanks, KEV. It definitely gave me food for thought.

Thanks

If it helps any, it is worth noting in an informal sense, that the inertial observer in flat space is equivalent to the free falling observer in a gravitational field, because both observers do not feel any force acting on themselves. This was an insight Einstein had when he was trying to figure out GR, which he described in the form of the falling elevator thought experiment.

 

[Al68]

An uncharged, isolated particle of mass m is subjected to a constant force that increases its speed relative to an IRF. Its mass presumably increases as long as the force acts.

Only if you use the word mass to mean resistance to acceleration in the direction of motion.

Does the mass of an identical particle, held at rest in a gravitational field also increase with the passage of time when the constraining force is equal and oppositely directed to the gravitational force?

The object's resistance to acceleration in its direction of motion (relativistic mass) would increase with time relative to an inertial (freefall) reference frame. Which only means that its coordinate acceleration relative to an inertial reference frame would decrease with time.

 

[Naty1]

Dixon posted:

...held at rest in a gravitational field...

which has multiple interpretations...instead of posting on my own I decided to read prior posts...and #4 by KEV is better than I would have done...great answer!

that sidesteps the interpretation of Dixon's meaning...You can read in other threads about who means what regarding accelerating in a gravitational field...or being at rest in one...bottom line is that's it's all 'relative' and depends on your reference frame.