Calling pmb_phy

JesseM

Yes, but FAQ questions do not represent the point of view of the author, only the answers do. And see the thing about the definition of the rest mass of a composite object I added in an edit.

Aer

Who answered these questions? Was this person qualified? It would seem he is not qualified if he didn't correct the person asking the question as to what Einstein actually said.

learningphysics

Well here's another post of mine:

http://www.physicsforums.com/showpos...394#post688394

I've posted links to course notes using the same definition of inertial mass.

Aer

You are standing in very thin waters if you think this any authority in relativity.

should be "the mass of an object is the sum of all its constituents' rest masses".

Aer

One thing is for sure, the wikipedia article you linked to which was your reference for inertial mass did not define inertial mass as relativistic mass. If it is defined that way elsewhere, it is a conflict of definition.

JesseM

The top of the FAQ says "Compiled by Dr. John Simonetti of the Department of Physics at Virginia Tech." Perhaps the questions were submitted by students, I don't know. And he did correct the questioner in a way: he said "Actually, here's the way it should be said: energy and mass are related."

Just to be clear, are you claiming for sure that the inertia of a black box filled with gas won't appear to increase when the temperature increases, or are you just not certain either way?

Aer

OK - let me state that I cannot be certain, but according to mass as it is defined, the answer would be that the mass of the gas would not appear to increase.

learningphysics

Aer, this is totally wrong. Hopefully someone else will post and correct you since you won't take my posts into account.

The rest mass of an object is the (total energy of the object in the rest frame)/c^2

This need not be the sum of the rest masses of the constituent particles.

The rest frame is the frame where the center of mass of the object is at rest.

JesseM

No, not if you use the definition given by Tom Roberts, where the "rest mass" of a composite object is defined as its total energy (divided by c^2, presumably) in the center-of-mass frame. In this frame, most of the individual particles will have nonzero velocity, so their energy will be greater than just c^2 times their rest mass, it will be c^2 times their relativistic mass.

Here is another page (from mathpages.com, a pretty reliable internet resource) that says that the inertia of a composite object (its resistance to being accelerated) will be a function of its total energy, not just the energy of the rest mass of all the constituent particles: Do you have any sources to back up your claim that the inertia of a composite object is dependent only on the rest masses of its constituent particles? If not, why are you so confident about this?

Aer

Apparently you all need a little refresher course, I hope this helps.

The total energy of a particle is:

[tex]E = \gamma m c^2[/tex]

where [itex]\gamma[/itex] is the Lorentz factor, m is the particle's rest mass and c is the speed of light.

We can also write:


[tex]E = E_0 + K[/tex]

where K is the particle's kinetic energy and [itex]E_0[/itex] is the particle's rest energy. That is:

[tex]E_0 = m c^2[/tex]

The relativistic kinetic energy is then easily seen to be:

[tex]K = (\gamma - 1) m c^2[/tex]

which for [itex]\gamma[/itex] close to 1 (v << c) reduces to approximately

[tex]K = 1/2 m v^2[/tex]

the usual Newtonian expression for kinetic energy.

Aer

Very well, then his definition of "rest mass" is not the proper definition of "rest mass"

Aer

The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.

JesseM

Uh, yes, and this is the same as E=Mc^2, where M is the relativistic mass which equals gamma*m. So the total energy of a collection of particles (again, ignoring potentials--assume the particles don't interact much) is equal to the sum of their relativistic masses times c^2. Thus, if you define the "rest mass" of a composite object as the total energy in its center-of-mass frame divided by c^2, then the rest mass of a composite object will be the sum of the relativistic masses of all the particles that make it up. That brings us to the issue of whether this is in fact the standard definition of "rest mass" for a composite object: What makes you so sure? Do you have any sources that tell us how "rest mass" should be defined for a composite object made up of many individual particles which are in motion relative to each other?

And aside from the issue of definitions, that mathpages.com page confirmed that the resistance to acceleration (inertia) of a composite object will be proportional to its total energy, so the inertia of a box filled with gas will increase as the gas is heated. Do you have any source that says otherwise? Have you actually done a calculation to see how a box filled with moving objects would react to external forces? If not, why are you so confident, when multiple sources say otherwise?

JesseM

Uh, but again, we're talking about a composite object. Even in the center-of-mass frame of a box filled with moving gas molecules, most of the individual molecules will not be at rest. Unless all the molecules are moving at the same speed and in the same direction (which would be a thermodynamic miracle) there is no frame where all the molecules are at rest. And in the center-of-mass frame, the total energy of a box of gas will be the sum of the relativistic masses of all the gas molecules (assuming the energy in the walls is negligible)--do you deny this?

Aer

!! There is clearly no getting through to you. The concept of relativistic mass is not physical - it only exists in frames other than the frame of the actual object. You have an infinite number of "relativistic masses" according to your definition. What makes you think "relativistic mass" is any type of measure of "actual mass" (i.e. the weight an object would feel in a gravitational potential)?

Aer

I already did! It is the sum of all the constituents own rest masses.

Aer

If I have objects in my car moving at .9999999999999999999999999999999999999999999999c bouncing all over the place, what is the mass of my car?