How does energy differ from mass?

[vedder]

How is energy different from mass...?

At the risk of dumming this waaaaay down. Mass has potential, energy is potential being realized.

 

[jeff]

Originally posted by pmb
.. the issue of how to define mass is the subject of debate right now

No it isn't! Though I'm sure you'd like to think so since it would make it easier for you to convince yourself that your whole crackpot mass vs energy thing is of any importance, or even correct, which it's neither: Whether the term "relativistic mass" or "energy" is used is just personal convention and nothing more. You've built a whole philosophy on what others only argue about when they get drunk. What a complete waste of time.

Originally posted by pmb
Rest mass is an intrinsic property and it's for that reason that a particle physicist thinks only on those terms.

As I've explained to you - though to no avail - rest mass does have a special significance, but particle physicists don't pray to the "god of rest mass".

Originally posted by pmb
...the stress-energy tensor...due to Einstein...can also be called the mass-momentum tensor. People seem to constantly miss this basic fact.

And you're one of them.

 

[Tyger]

Originally posted by Tyger
Energy is related to the ability to do work against a force, while mass (inertia) is related to the change of velocity with the change of momentum. Because an object moves with the quantum mechanical group velocity of a wavegroup the inertia differs by a factor of C².

By combining QM and SR we can derive the result that objects which have energy also have the quality of inertia. This is the fundamental and simple derivation of inertia. And then rest mass is just proportional to rest energy. Part of the problem of understanding the nature of inertia is the use of the antiquated system of units with length, time and mass, because it makes mass appear to be a fundamental quality instead of being derivable.

See my post "You don't need all that junk" for a more modern system of units.

 

[pmb]

Originally posted by Tyger
By combining QM and SR we can derive the result that objects which have energy also have the quality of inertia. This is the fundamental and simple derivation of inertia. And then rest mass is just proportional to rest energy. Part of the problem of understanding the nature of inertia is the use of the antiquated system of units with length, time and mass, because it makes mass appear to be a fundamental quality instead of being derivable.

See my post "You don't need all that junk" for a more modern system of units.

You don't need quantum mechanics either. Just electrodynamics and special relativity.

Pete

 

[Tyger]

Now you've got me puzzled!

Originally posted by pmb
You don't need quantum mechanics either. Just electrodynamics and special relativity.

Pete

How do you derive the relation between mass and energy with electrodynamics and relativity?

 

[pmb]

Originally posted by Tyger
How do you derive the relation between mass and energy with electrodynamics and relativity?

The same way Einstein did. He didn't use quantum mechanics. He used electrodynamics and relativity only.

In Einstein's 1905 relativity paper, which is online here

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein considered a plane wave moving a given direction in a frame. Call this frame S'. He then transformed to a frame moving with respect to the first, call that frame S'. In that frame he related the energy of the radiation to the energy in the old frame.

In Einstein's 1905 E = mc^2 paper, which is online here

http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

Einstein considered a body at rest in S. The body emits radiation of equal energy in opposite directions; the total amount of energy of the radiation he called "L". The body remains at rest in S due to the conservation of momentum. Einstein then transforms to S' which is moving at non-relativistic velocity relative to S, and, employing the results of the paper mentioned about, argues (see E_mc2 paper above) that the difference in energy equals the difference in kinetic energy. As such this demands the the difference in kinetic energy be a result of the change in mass of the body since the change in kinetic energy is (noting that the velocity didn't change)

dK = K_i - K_f = (1/2)M_i*v^2 - (1/2) M_f*v^2 = (1/2)dM*v^2

Einstein showed that dK = (1/2)[L/c^2]v^2

Equating the two he arrives at

(1/2)dM*v^2 = (1/2)[L/c^2]v^2

or canceling like terms

dM = L/c^2

which is his 1905 E = mc^2 relation. Einstein concludes

If a body gives off the energy L in the form of radiation, its mass diminishes by L/c^2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.

Einstein's reasoning is pretty confusing. For this reason it's been criticised as being circular. However John Stachel and Roberto Torretti published a paper in the American Journal of Physics called

"Einstein's first derivation of mass--energy equivalence," Am. J. Phys. 50, 760 1982

Abstract - "It is shown that, contrary to what several authors have claimed, Einstein's first derivation of the mass–energy equivalence was logically sound, the alleged fallacy lying merely in the fact that Einstein's conclusion is entailed by, and is therefore a necessary condition of his premises."

Pete

Pete

 

[Tyger]

Originally posted by pmb
The same way Einstein did. He didn't use quantum mechanics. He used electrodynamics and relativity only.

Ah, but you see Einstein's paper did use the wave property of matter so quantum theory is implicit in it. And it's not very straight forward, where the derivation involving group velocity is.

 

[pmb]

Originally posted by Tyger
Ah, but you see Einstein's paper did use the wave property of matter so quantum theory is implicit in it. And it's not very straight forward, where the derivation involving group velocity is.

I didn't say that Einstein didn't use a wave property. But that is an electromagnetic wave. I could b a radio wave or a light wave - I didn't matter.

But the wave is a classical electromagnetic wave as can be seen from the equations. No use is made nor referred to with regard to quantinization - and that's what the photon concept is all about.

Also note that the relation E = pc is a classical result derived from classical EM.

Pete

 

[jeff]

Originally posted by pmb

Rindler defines mass, for a particle with a non-zero rest mass m_o, as m = m_o/sqrt[1-(v/c)^2].

Originally posted by pmb
And as Wheeler himself says...its the active gravitational mass that generates a gravitational field - and that is not rest mass.[/i]

It's worth mentioning that though they're conceptual underpinnings differ, in GR, inertial and gravitational mass are effectively identical.

 

[pmb]

Originally posted by jeff
It's worth mentioning that though they're conceptual underpinnings differ, in GR, inertial and gravitational mass are effectively identical.

They are experimentally found to be proportional to one another and they theoretically are proportional

However they have quite different meanings and operational defintions. E.g. While the inertial mass of a particle is proportional to it's active gravitational mass - it's not that easy trying to push the universe so as to measure its inertial mass

Pmb

 

[pmb]

Originally posted by Tyger
How do you derive the relation between mass and energy with electrodynamics and relativity?

Okay. Let me try this again.

Consider a box at rest on your table top. There are particles inside. The sit on the bottom of the box and all the can do is slide on the bottom which is smooth. Think of it as a 2-dimensional gas.

I put a scale on the table and I put the box in the scale where is sits - at rest.

Initial State: All particles are motionless.

The weight of the box will then be W = Mg where M is the sum of the rest masses of the individual particles.


Now add an amount of energy of E to the box. This energy will be used to do work on the particles inside. That work changes the kinetic energy of the particles and the start moving. The weight of the box will now be the sum of the weights of all the particles. Each particles weight increases as w = mg where m = "relativistic mass" of the particle. The greater the weight the greater the measured mass of the box. This will of course be the passive gravitational mass of the particles. I could also view this a the inertial mass and that I'm accelerating the box and measuring the weight from the comoving frame. The mass I measure at that point will be the transverse mass. However the transverse mass is identical to the relavitistic mass.

It can readily be shown that the weight increase by the amount E/c^2.

That's *why* E = mc^2 in this case. And that's *why* it can be useful to think in terms of relativistic mass.

Pete

ps - This is being cross-posted to sci.physics.relativity

 

[pmb]

Originally posted by pmb
Okay. Let me try this again.

Consider a box at rest on your table top. There are particles inside. The sit on the bottom of the box and all the can do is slide on the bottom which is smooth. Think of it as a 2-dimensional gas.

I put a scale on the table and I put the box in the scale where is sits - at rest.

Initial State: All particles are motionless.

The weight of the box will then be W = Mg where M is the sum of the rest masses of the individual particles.


Now add an amount of energy of E to the box. This energy will be used to do work on the particles inside. That work changes the kinetic energy of the particles and the start moving. The weight of the box will now be the sum of the weights of all the particles. Each particles weight increases as w = mg where m = "relativistic mass" of the particle. The greater the weight the greater the measured mass of the box. This will of course be the passive gravitational mass of the particles. I could also view this a the inertial mass and that I'm accelerating the box and measuring the weight from the comoving frame. The mass I measure at that point will be the transverse mass. However the transverse mass is identical to the relavitistic mass.

It can readily be shown that the weight increase by the amount E/c^2.

That's *why* E = mc^2 in this case. And that's *why* it can be useful to think in terms of relativistic mass.

That is to say - this is why for this example. If the example was a box of photons the the collisions of the photons with the walls leads to inertia. However the cool part is that no matter how much energy you put in there's the same increase in inertial mass - the matter just uses it different to increase it's inertia.


Pete

ps - This is being cross-posted to sci.physics.relativity

 

[hey.like]

Mass and Energy was twice different idea

Mass and Energy was twice different ideas, from these ideas use first to now, but it is different in some mind deeply, it is hard.
I think the mass is gravity parameter and energy is a electric magnetic parameter. but it is eaual in mass-energy question. but the gravity and electric-magnetic was different action from common. although the unit theory try to a simple action theory, but it is hard and no right result now.
About mass and energy will be some better result in future. wait some times.

 

[hey.like]

Mass and Energy was twice different idea

Mass and Energy was twice different ideas, from these ideas use first to now, but it is different in some mind deeply, it is hard.
I think the mass is gravity parameter and energy is a electric magnetic parameter. but it is equal to in mass-energy equation. but the gravity and electric-magnetic was different action in common. although the unit theory try to a simple action theory, but it is hard and no right result now.
About mass and energy will be been some better result in future. wait some times.