[jeffreyH (OP)]

If we have a particle freely falling in a gravitational field would it experience an increase in relativistic mass as it accelerates? If not why not?

[jeffreyH (OP)]

On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater. If we consider this to be a non inertial frame are we justified in attributing this to a gain in relativistic mass. If not why not?

[JohnDuffield]

If we have a particle freely falling in a gravitational field would it experience an increase in relativistic mass as it accelerates? If not why not?

No, because of conservation of energy, and because gravity is not a force in the Newtonian sense.  When you drop a brick, gravity converts potential energy into kinetic energy. Then when the brick hits the ground the kinetic energy is dissipated, and you're left with a mass deficit. The point to note here is that the potential energy was not stored in the gravitational field, it was stored in the brick, as mass-energy. This mass-energy is actually internal kinetic energy, which is why a radiating body loses mass. See Einstein's E=mc² paper. So when the brick is falling all that was happening is that internal kinetic energy is being converted into external kinetic energy. The sum total energy does not change, so the relativistic mass does not change either, because relativistic mass is really total energy. Instead the rest mass is decreasing as the brick falls.

On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater. If we consider this to be a non inertial frame are we justified in attributing this to a gain in relativistic mass. If not why not?

No, because the relativistic mass doesn't change, and because the mass deficit depends on gravitational potential rather than gravitational force.

* conservation of momentum p=mv means the Earth is also affected. But there's no discernible motion of the Earth. The kinetic energy KE=½mv² is not equally shared. The brick gets all bar an infinitesimal portion of the kinetic energy.

[jeffreyH (OP)]

John the second question I asked was intentionally wrong. Can you understand why?

[jeffreyH (OP)]

BTW John I'm intentionally ignoring the rubbish you typed in response to the first question. Just in case you thought otherwise.

[Bill S]

On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater.

In what sense can this be considered as an increase in mass, of any kind?

[jeffreyH (OP)]

On a planet with different gravity to earth an object will weigh more if the gravity is at the surface is greater.

In what sense can this be considered as an increase in mass, of any kind?

That is a topic I am investigating. I am having to invent some new mathematical tools to do so.

[JohnDuffield]

BTW John I'm intentionally ignoring the rubbish you typed in response to the first question. Just in case you thought otherwise.

Your response is abusive and ignorant, and it brings Naked Scientists into disrepute. My answer contained appropriate references, and was correct.

[jeffreyH (OP)]

Relativistic mass doesn't change? The rest mass is decreasing as the brick falls? And that is just two of your misconceptions. You could always go back to physics.stackexchange.com if you don't like it here. Oh sorry no you can't.

[yor_on]

Before one ask Jeffrey.
Is relativistic mass something belonging to a object, or would it be a result of circumstances?

[jeffreyH (OP)]

It is as a result of the circumstance of velocity. More precisely a change in velocity. That is acceleration. However it persist when the force is removed. So that it can be considered to be inertial.

[yor_on]

so, in a empty space, how would you measure it?

[jeffreyH (OP)]

You can't since there would be no mass present. When you ask if relativistic mass belongs to an object it is the wrong question. The change in relativistic mass is continuous and not quantised as far as I know so you cannot separate it from rest mass. Since you would have to define which part of the mass in the local frame is at rest. Usually all of it in its own inertial frame.

[yor_on]

Yea, but how would you measure a relativistic mass?
Where I get stuck is when I think of it locally.

I don't see any way to measure it.
It's in a way resembling the the problem I have with 'potential energy'. It needs a 'universe' to be defined.

[yor_on]

The problem is 'direct measurements' relative 'indirect measurements'.
If I define a 'direct measurements'' to be a result of me measuring in a 'black box'.
Then a gravitational acceleration doesn't exist.

If that doesn't exist, where does 'potential energy' exist?

The whole question makes me think of Mach universe.
If I move 'outside' then the guy in the box have to be lying, from the frame of me observing him 'gravitationally accelerating'.

[jeffreyH (OP)]

Well it is good to be thinking about it. That way new insights are gained.

[JohnDuffield]

Relativistic mass doesn't change? The rest mass is decreasing as the brick falls? And that is just two of your misconceptions. You could always go back to physics.stackexchange.com if you don't like it here. Oh sorry no you can't.

You can read about stack exchange here: Dishonest moderation on Physics Stack Exchange. And you can read about the mass deficit here: Wikipedia: binding energy:

"Classically, a bound system is at a lower energy level than its unbound constituents. Its mass must be less than the total mass of its unbound constituents. For systems with low binding energies, this "lost" mass after binding may be fractionally small. For systems with high binding energies, however, the missing mass may be an easily measurable fraction. This missing mass may be lost during the process of binding as energy in the form of heat or light, with the removed energy corresponding to removed mass through Einstein's equation E = mc²".

[jeffreyH (OP)]

Reading that shows how justified the moderators were to challenge your assertions. To suggest that Paul Dirac had no idea about the electron is pretty embarrassing for you I'm sure. If not then you are beyond help.

[jeffreyH (OP)]

You have a strange idea about the relationship between binding energy and gravity. Please explain how this 'mass deficit' comes about in your own words. So we can actually tell whether or not you actually understand the concept.

[JohnDuffield]

I've told you already. See Einstein's E=mc² paper. A radiating body loses mass because mass-energy is internal kinetic energy. This is demonstrated in extremis by electron-positron annihilation. Each is a radiating body that loses mass. All of it. When you drop an electron, it falls down because some of the internal kinetic energy is converted into external kinetic energy. Then when it hits the ground this external kinetic energy is typically radiated away. The electron mass is then less than what it was. There is a mass deficit. There's also a mass deficit when an electron is attracted to a proton to form a hydrogen atom. The hydrogen atom mass is circa 13.7ev less than the mass of a free proton plus the mass of a free electron.