How does energy differ from mass?

[Ring]

Originally posted by pmb

However I was not referring to the mass of the system. I was describing what it means when it is said that "mass is converted into energy". And it's almost universally agreed upon that it means that the sum of the masses of the constituent particles changes.

I agree that many texts, for the sake of simplicity, use this definition. But according to the most universally accepted definition of mass m²= E² - p²this is patently untrue. What this entails is the redefinition of the system in the middle of the stream. If you're consistent in defining the system then the mass does not change and it cannot be converted to energy.

You're referring to something else - the conservation of mass. It's a subtle point. It's the form of the composition of the system that undergoes conversion. And this goes to the notion that rest mass is a form of energy

I must disagree. Mass and energy are not things they're properties of a system. If you are consistent in defining your system and include all the products of the interacting particles then the mass and energy remain the same. If you don't do this then, as I said, your changing horses in the middle of the stream.

 

[pmb]

Originally posted by Ring
I agree that many texts, for the sake of simplicity, use this definition.

They don't do it for the sake of simplicity. They do it because that's what they think is the best way to explain/describe it. Entire papers get published just on that very notion.

But according to the most universally accepted definition of mass m ...

You mean the way it's used at Fermilab? See
http://www.fnal.gov/pub/inquiring/q.../accel_obj.html
http://www.fnal.gov/pub/inquiring/questions/angelo.html
http://www.fnal.gov/pub/inquiring/q..._speed_add.html
http://www.fnal.gov/pub/inquiring/m...ght_page16.html

Can you tell me how you got the impression that what you use is the most universally accepted definition?

What this entails is the redefinition of the system in the middle of the stream. If you're consistent in defining the system then the mass does not change and it cannot be converted to energy.

I disagree. It's not even a generally meaningful definition.

I must disagree. Mass and energy are not things they're properties of a system.

Did I ever say that they were things? No. I did not. I said that the form changed. I explained all that in detail above. It basically means that the composition of a system changes. See "Spacetime Physics - Second Edition," Taylor and Wheeler, page 248-249. In particular - see the section "Use and abuse of the concept of mass" - see page 249

"Thus part of the mass of the *constituents* has been converted to energy; but the mass of the *system* has not changed."

As I said - that is the meaning of "covert mass to energy"

And I wouldn't say that Taylor and Wheeler are sloppy or that they're too lazy to be 100% precise (though I don't always agree with them - they are precise!)


Pete

 

[elas]

I recently posted in another forum quotation from three recent books by leading physicist each of which clearly stated that "we do not know what are mass, charge or any of the other peculiar properties of particles".
My own view is on my website and is, as far as I am aware, the only proposal that explains the origin of mass and links force, mass and radius. (According to the experts there has been no explanation for the peculiar mass/radius ratios of atomic elements).
There surely is little point in trying to explain the relationship between energy and mass unless you first define what causes mass to exist.

 

[pmb]

Originally posted by marcus
We have trolls come here with fringe views of what "mass" means that say different things but this is destructive because
it undermines the conventional common language.

On second read it seems, from our past conversations, that you think I'm one of these trolls? If so then you've misunderstood. When I see something I believe is incorrect I speak up - the fact that you repeat it all the time means I speak up all that time. That's not being a troll - that means I have a different opinion than you do and I state what I think.

Comments like you post give the false impression that everyone who is a physicists does not use the term "mass" to refer to light. Well I'm a physicist and I do so there's one data point. But it was Einstein who proved this to be true - it has to be true for the "center of mass theorem" to hold true. That was the purpose of his 1906 paper in fact.

And your comment "fringe view" is quite wrong if you're referring to relativistic mass. This is something that can be found in most relativity textbooks in one form or another. MTW is a good example.

Let me give you a better example: Wolfgang Rindler is one of the more prominent authorities in relativity today. He published another book in 2001 called

"Relativity: Special, General and Cosmological," Rindler, Oxford Univ., Press, (2001)

Rindler defines mass, for a particle with a non-zero rest mass m_o, as m = m_o/sqrt[1-(v/c)^2]. He addresses photons on page 120

According to Einstein, a photon of frequency f has energy hf, and thus (as he came to realisze several years later) a finite mass hf/c^2 and a finite momentum hf/c.

The same is true for

"Introducing Einstein’s Relativity," D’Inverno, Oxford Univ. Press, (1992)

"Basic Relativity," Mould, Springer Verlag, (1994)


Let me ask you this - would you find it surprising that the term "mass density of radiation" is used throughout cosmology? Saying that "light has no mass" without clarifying can be misleading. Especially if you don't want to give the person you're talking to a distorted view of what actually is. For example: A particle physicists might say "light has no mass" but a cosmologist will speak of the term "mass density of radiation."

Would it surprise you to find cosmologists referring to the "mass density of radiation"? Try searching the internet of that phrase.

And as Wheeler himself says in
pup.princeton.edu/sample_chapters/ciufolini/chapter3.pdf

its the active gravitational mass that generates a gravitational field - and that is not rest mass.

Then there are texts like "Classical Electrodynamics," which has a problem - find the center of mass for an EM field (second ed - page 617)

Pete

 

[elas]

As an amateur I am aware that a theoretical mass for the photon was reported in Scientific American in the early 80's.
I am also aware that almost every book on particle physics, written for the layman; contains a statement to the effect that there is no answer to the question "what is mass or charge?"
The London 'Daily Telegraph' for Sat. 26 July 2003 carries a report on yet another conference to decide whether the impasse in Relativity (and by implication astro-physics) can be resolved by the introduction of Anti-gravity or Vacuum.
It seems that your confidence in current theory is not shared by those at the highest level (which does not mean that they are right, but merely that they dissagree).
My own support for a vacuum theory is up for discussion on a separate forum.
Surely it is time to realize that there is room for considerable improvement in our understanding of how things work and firm opinions should await solutions to current problems.

 

[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.