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Calling pmb_phy

by Aer
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Aer
#19
Aug4-05, 10:21 PM
P: 214
Quote Quote by 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.
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
#20
Aug4-05, 10:24 PM
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P: 4,124
Quote Quote by Aer
learningphysics - based on my previous experience with you, I am going to assume you have no idea what you are talking about.

OK, I don't have to assume from memory anymore, here is a quote by you:

link to your post
NO! And I am going to assume your misunderstanding stems from reading posts/websites by pmb_phy.
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
#21
Aug4-05, 10:24 PM
P: 214
Quote Quote by JesseM
Also, in a post on this thread "Tom Roberts" describes the definition of rest mass for a composite object:
You are standing in very thin waters if you think this any authority in relativity.

the mass of an object is its total energy in its rest frame
should be "the mass of an object is the sum of all its constituents' rest masses".
Aer
#22
Aug4-05, 10:26 PM
P: 214
Quote Quote by 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.
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
#23
Aug4-05, 10:29 PM
Sci Advisor
P: 8,470
Quote Quote by 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.
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
#24
Aug4-05, 10:33 PM
P: 214
Quote Quote by JesseM
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?
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
#25
Aug4-05, 10:35 PM
HW Helper
P: 4,124
Quote Quote by 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, 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
#26
Aug4-05, 10:38 PM
Sci Advisor
P: 8,470
Quote Quote by Aer
should be "the mass of an object is the sum of all its constituents' rest masses".
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:
Another derivation of mass-energy equivalence is based on consideration of a bound "swarm" of particles, buzzing around with some average velocity. If the swarm is heated (i.e., energy E is added) the particles move faster and thereby gain both longitudinal and transverse mass, so the inertia of the individual particles is anisotropic, but since they are all buzzing around in random directions, the net effect on the stationary swarm (bound together by some unspecified means) is that its resistance to acceleration is isotropic, and its "rest mass" has effectively been increased by E/c^2. Of course, such a composite object still consists of elementary particles with some irreducible rest mass, so even this picture doesn't imply complete mass-energy equivalence.
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
#27
Aug4-05, 10:40 PM
P: 214
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
#28
Aug4-05, 10:42 PM
P: 214
Quote Quote by 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.
Very well, then his definition of "rest mass" is not the proper definition of "rest mass"
Aer
#29
Aug4-05, 10:49 PM
P: 214
Quote Quote by JesseM
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:
The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.
JesseM
#30
Aug4-05, 10:54 PM
Sci Advisor
P: 8,470
Quote Quote by 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.
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:
Quote Quote by 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.
Quote Quote by Aer
Very well, then his definition of "rest mass" is not the proper definition of "rest mass"
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
#31
Aug4-05, 10:56 PM
Sci Advisor
P: 8,470
Quote Quote by Aer
The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.
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
#32
Aug4-05, 10:59 PM
P: 214
Quote Quote by JesseM
Uh, yes, and this is the same as E=Mc^2, where M is the relativistic mass which equals gamma*m.
!! 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
#33
Aug4-05, 11:01 PM
P: 214
Quote Quote by JesseM
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?
I already did! It is the sum of all the constituents own rest masses.
Aer
#34
Aug4-05, 11:03 PM
P: 214
If I have objects in my car moving at .9999999999999999999999999999999999999999999999c bouncing all over the place, what is the mass of my car?
JesseM
#35
Aug4-05, 11:06 PM
Sci Advisor
P: 8,470
Quote Quote by 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.
It's just as physical as energy--in fact it is simply the energy divided by c^2. If you prefer, we can ignore the concept of "relativistic mass" altogether and just talk about the total energy of a composite object in its center-of-mass frame.
Quote Quote by Aer
You have an infinite number of "relativistic masses" according to your definition.
No, because the definition specifies that you're looking at things in a particular frame, the center-of-mass frame of the composite object.
Quote Quote by Aer
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)?
Again, forget relativistic mass and just talk about energy. The reason I think it's the total energy rather than the sum of all the rest masses that determines weight is because I have several sources written by experts which say that it's the total energy that determines resistance to acceleration (inertia). What makes you think that the inertia of a composite object is proportional only to the sum of the rest masses of the particles that make it up rather than proportional to the total energy of the particles that make it up, when several sources written by experts say otherwise?
Aer
#36
Aug4-05, 11:08 PM
P: 214
Quote Quote by JesseM
If you prefer, we can ignore the concept of "relativistic mass" altogether and just talk about the total energy of a composite object in its center-of-mass frame.
This is stupid, then we would just be talking about adding up the masses and kinetic energy to get the total energy.


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