Mass Energy: Understanding Total, Rest and Kinetic Energies

[pmb_phy]

And mass isn't condensed energy.

Ah! Yes! Someone after my own heart. I've been saying that for a very long time. A simple countrer example is a box with a gas in it. Nothing is condensed here. The greater the kinetic energy of the gas particles the greater the mass of the box-gas system. But there is nothing condensed here to think about. And when a positron collides with an electron then its clear that it will emit radiation. However since the radiation has (relativistic mass) then the total mass of the system remains unchanged. The only converrsion going on here is the form the mass takes on.

Pete

 

[lightarrow]

As long as we talk about relativistic mass and total energy, mass and energy are equal, excepting for c^2 factor. So, in this case, it's meaningless to talk about "mass is condensed energy", since they are the same thing.

If we talk about rest mass, then it's different.

IMHO, If the photon is spatially localized with approximated dimensions greater than those of the electron and positron, we can pheraps say the energy is more "condensed" in the particles than in the radiation: in the particles energy is stored in the form of rest mass (mostly); in the photon is present in the form of electromagnetic radiation (no rest mass).

So, as pmb_phy says, it's only the form of the energy that changes.

 

[Jorrie]

Hi Jorrie

I don't know where you got the impression that I believe that relativistic mass is proportional to kinetic energy. And I never say that 'relativistic mass' is energy. If you have Rindler's 1982 intro to SR text he states that explicitly. Rindler is where I picked up on this not to well known fact.

Pete

Hi Pete,

I was originally referring to Actionintegral's reply to Pervect:

Originally Posted by pervect: "relativistic mass" is another name for energy

and Actionintegral's reply:

"I would agree with you if you replace the word "energy" with "kinetic energy" in the above phrase."

So my reply to yours was slightly confusing if the context was not clear.

But hey Pete, I think you missed that original statement by Pervect!

Regards, Jorrie

 

[actionintegral]

This is why I steer clear of questions with lots of responses!

 

[Farsight]

Ah! Yes! Someone after my own heart...

Thanks Pete. I do think loose phrases like "energy consumption" or "pure energy" cause problems for the man in the street.

 

[pmb_phy]

As long as we talk about relativistic mass and total energy, mass and energy are equal, ...

Nope. That statement has been proven wrong. In fact Einstein wrote a paper which implied it was wrong early in his carreer (~1906). See above where I explained this. The expression E = mc^2 is invalid for a neutral atomic nucleus moving in a uniform E-field. I guess I should try to calculate the difference someday as another example of where it differs.

Best wishes

Pete

 

[pmb_phy]

Hi Pete,
Originally Posted by pervect: "relativistic mass" is another name for energy

Yes. I saw that. It is an incorrect statement.

But hey Pete, I think you missed that original statement by Pervect!

I miss all of his posts since I blocked him. He kept repeating himself with the same ole comments about certain things and he absolutely refused to work out our differences in PM. I have no time or patience with people with these qualities. Note that I'm not putting pervect down. Call it a clash of personalities. I have nothing against him myself.

Best wishes

Pete

 

[pervect]

Yes. I saw that. It is an incorrect statement.
I miss all of his posts since I blocked him. He kept repeating himself with the same ole comments about certain things and he absolutely refused to work out our differences in PM. I have no time or patience with people with these qualities. Note that I'm not putting pervect down. Call it a clash of personalities. I have nothing against him myself.

Best wishes

Pete

I'll invite our moderators or other science advisors here to express there opinion about which of us is correct, if they have an opinion on the matter.

Meanwhile, I am convinced that Pete is wrong, and I've attempted to not just state this as a personal opionion, but to provide some extensive quotes and references about why I think he is incorrect.

I'm also not particularly interested in exchanging PM's with him.

This is the first I've heard that Pete has his "fingers in his ears". I'm not quite sure what do to about that, it's news to me.

I don't have any particular personal animosity towards Pete, in fact I learned quite a number of things by arguing with him over the years. But I don't feel like recent conversations with him have been very productive for either of us - they may still continue to be of some use to people learning the topic, I suppose.

 

[Farsight]

Perhaps this might be a good time for me ask you guys about the relationship between rest mass, inertia, and momentum?

 

[lightarrow]

Perhaps this might be a good time for me ask you guys about the relationship between rest mass, inertia, and momentum?

I'll give you my answer, but someone will probably not agree with it.

1. Rest mass = m. Is the body's mass in its ref. frame.

2. Inertia. If you mean "inertial mass" then it is = m/SQRT[1 - (v/c)^2].

3. Momentum (linear momentum): p = m*v/SQRT[1 - (v/c)^2].

 

[Farsight]

Thanks lightarrow. I'll go with intertial mass.

I wanted to try to get things going again with a simple viewpoint relevant to the original question. Imagine I'm at rest in space, alongside my cannonball. We can talk about its rest mass, inertial mass, and momentum quite happily. There are no issues.

Now imagine I'm moving at 10m/s past the cannonball. However in my ignorance I think I'm stationary, and the cannonball is actually moving past me. The rest mass is still what it was. But as far as I'm concerned, the inertial mass is slightly different, and momentum is very different. I can even throw in kinetic energy, and say it's got some now when it didn't previously. But the object hasn't changed at all. Not one jot. It's still sitting there, happily doing nothing. Because these things are ways of relating my velocity to my the subject. They aren't actually there in the cannonball.

 

[pervect]

Thanks lightarrow. I'll go with intertial mass.

I wanted to try to get things going again with a simple viewpoint relevant to the original question. Imagine I'm at rest in space, alongside my cannonball. We can talk about its rest mass, inertial mass, and momentum quite happily. There are no issues.

Now imagine I'm moving at 10m/s past the cannonball. However in my ignorance I think I'm stationary, and the cannonball is actually moving past me. The rest mass is still what it was. But as far as I'm concerned, the inertial mass is slightly different, and momentum is very different. I can even throw in kinetic energy, and say it's got some now when it didn't previously. But the object hasn't changed at all. Not one jot. It's still sitting there, happily doing nothing. Because these things are ways of relating my velocity to my the subject. They aren't actually there in the cannonball.

What do you mean by "inertial mass"? And why do you care, i.e. why isn't knowing the rest mass, momentum, and energy of the cannonball "good enough"?

 

[Farsight]

I didn't mean to bring it up, pervect. Blame lightarrow. I was just trying to show that there's a variety of terms that we tend to think of as being some property of the actual object. You know, what is the momentum of the cannonball? and all that. But the cannonball is just sitting there. Nothing's happened to it. It hasn't moved, changed temperature, or anything. The property isn't in the cannonball. It's in my velocity, relative to the cannonball.

 

[lightarrow]

What do you mean by "inertial mass"?

I mean the term M which is multiplied to velocity v to give linear momentum p:
p = M*v, since F = dp/dt.

 

[pmb_phy]

I mean the term M which is multiplied to velocity v to give linear momentum p:
p = M*v, since F = dp/dt.

"What do you mean by inertial mass?" is a rather odd question since the term is almost universally used to refer to what some people call "relativistic mass" or just plain "mass."

Best wishes

Pete