[MikeS (OP)]

E=mc2
"Mass–energy equivalence in either of these conditions means that mass conservation becomes a restatement, or requirement, of the law of energy conservation, which is the first law of thermodynamics. Mass–energy equivalence does not imply that mass may be "converted" to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy are both conserved separately in special relativity, and neither may be created nor destroyed. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but the precursors and products of such reactions retain both the original mass and energy, each of which remains unchanged (conserved) throughout the process."  http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

"e−+ e+ → γ + γ
When a low-energy electron annihilates a low-energy positron (antielectron), they can only produce two or more gamma ray photons, since the electron and positron do not carry enough mass-energy to produce heavier particles and conservation of energy and linear momentum forbid the creation of only one photon. These are sent out in opposite directions to conserve momentum. "  http://en.wikipedia.org/wiki/Annihilation

I can see this conserves energy but how does it conserve mass?

[simplified]

 m is kinematic mass of energy.

[JP]

A two photon system can have invariant mass while a single photon doesn't.

[Phractality]

As you have pointed out, mainstream explanations make no sense. Any explanation that does makes sense belongs in the New Theories section. You should ask your question again, there. Since this is the mainstream physics secion, I'll just refer you to the Wikipedia's own Talk section on the material you quoted.

[My own (new theory) interpretation of mass-energy conservation (which will probably be sensored by a particular over-aggressive mod)...]


Sure will be! - A particular over-agressive mod.

[Soul Surfer]

The simple fact that is that mass is NOT conserved.  It is only energy and momentum (including angular momentum) that are conserved.   The old statement found in some(out of date) textbooks that "matter cannot be created or destroyed" is now untrue and has been replaced by the conserved values described earlier in this note.

[JP]

The simple fact that is that mass is NOT conserved.  It is only energy and momentum (including angular momentum) that are conserved.   The old statement found in some(out of date) textbooks that "matter cannot be created or destroyed" is now untrue and has been replaced by the conserved values described earlier in this note.

I wonder about that now.  That's how I learned it, and I'm not about to blindly believe Wikipedia, but the wiki articles makes it clear that they're talking about invariant mass of a whole closed system.  Two photons do have an invariant mass, as lightarrow pointed out in another thread recently.  I wonder if conservation of mass does hold if you take closed systems as a whole...

[Soul Surfer]

The concept of invariant mass from the Einstein equation is really just for people who are fixated on mass as something important.  mass is best viewed as "trapped energy" and the amount of energy that is trapped defines its gravitational mass.  The same is true for space and time, these are a function of energy and momentum via the main fixed constant which is accepted as the speed of light.  In reality we should always use dimensions of energy and momentum.  but these are not very easy to use in our normal world of space time.

[MikeS (OP)]

Thanks Phrac for the link.  Very interesting.
Thanks all for comments.

If mass increases with an input of energy, as in a spring for instance.  Is this just a way of looking at it or has it ever been experimentally verified?

At the big bang all that existed was energy.  Therefore, everything in the universe is made from energy.  It follows that there must be an equation to link energy and mass (or matter).  I still don't understand why E=mc2 does not imply that energy can be turned into mass when quite obviously at some point it was.  I do understand that there is no simple conversion other than for elementary particles.

Does the total energy of the universe E = its rest mass times the speed of light squared?

[Pmb]

E=mc2
"Mass–energy equivalence in either of these conditions means that mass conservation becomes a restatement, or requirement, of the law of energy conservation, which is the first law of thermodynamics. Mass–energy equivalence does not imply that mass may be "converted" to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy are both conserved separately in special relativity, and neither may be created nor destroyed. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but the precursors and products of such reactions retain both the original mass and energy, each of which remains unchanged (conserved) throughout the process."  http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

"e−+ e+ → γ + γ
When a low-energy electron annihilates a low-energy positron (antielectron), they can only produce two or more gamma ray photons, since the electron and positron do not carry enough mass-energy to produce heavier particles and conservation of energy and linear momentum forbid the creation of only one photon. These are sent out in opposite directions to conserve momentum. "  http://en.wikipedia.org/wiki/Annihilation

I can see this conserves energy but how does it conserve mass?

The article that you quote is speaking about proper mass and that the "mass" of a system of free particles in an inertial frame then is the sum of the proper mass of all the particles in the system, which, of course,  is not conserved. However if one takes the view that "mass" is relativistic mass then mass of a system of free particles is conserved.

If you'd like, I can send you the following article in PDF format

Does nature convert mass into energy?, Ralph Baiellein, Am. J. Phys. 75(4), April 2007

Abstract - First I provide some history of how E = mc2 arose, establish what "mass" means in the context of the context of this relation, and present some aspects of how the relation can be understood. Then I address the question, Does  E = mc2 mean that one can "convert mass into energy" and vice versa?

[JP]

The concept of invariant mass from the Einstein equation is really just for people who are fixated on mass as something important.  mass is best viewed as "trapped energy" and the amount of energy that is trapped defines its gravitational mass.  The same is true for space and time, these are a function of energy and momentum via the main fixed constant which is accepted as the speed of light.  In reality we should always use dimensions of energy and momentum.  but these are not very easy to use in our normal world of space time.

I tend to agree.  Relativistic or invariant masses can be described in terms of energy and momentum, so energy and momentum conservation seem, to me at least, to be fundamental. 

It's interesting, though, that conservation of mass still holds.  It's more interesting that in order for conservation of mass to hold, you have to use invariant mass of a system, which leads to some odd situations.  For example, the invariant mass of two photons together is non-zero, despite the fact that the invariant mass of each photon is zero!  This is how positron-electron annihilation into two photons can conserve invariant mass. 

[Pmb]

The concept of invariant mass from the Einstein equation is really just for people who are fixated on mass as something important.  mass is best viewed as "trapped energy" and the amount of energy that is trapped defines its gravitational mass.  The same is true for space and time, these are a function of energy and momentum via the main fixed constant which is accepted as the speed of light.  In reality we should always use dimensions of energy and momentum.  but these are not very easy to use in our normal world of space time.

I tend to agree.  Relativistic or invariant masses can be described in terms of energy and momentum, so energy and momentum conservation seem, to me at least, to be fundamental. 

It's interesting, though, that conservation of mass still holds.  It's more interesting that in order for conservation of mass to hold, you have to use invariant mass of a system, which leads to some odd situations.  For example, the invariant mass of two photons together is non-zero, despite the fact that the invariant mass of each photon is zero!  This is how positron-electron annihilation into two photons can conserve invariant mass. 

Careful. That only holds for free point size objects. E.g. if there is a block which is subject to external forces then invariant mass for the block itself is meaningless.

[simplified]

The concept of invariant mass from the Einstein equation is really just for people who are fixated on mass as something important.  mass is best viewed as "trapped energy" and the amount of energy that is trapped defines its gravitational mass.  The same is true for space and time, these are a function of energy and momentum via the main fixed constant which is accepted as the speed of light.  In reality we should always use dimensions of energy and momentum.  but these are not very easy to use in our normal world of space time.

Yes.And even 'free' photon is trapped by gravitation of universe.It limits speed of photon.

[JP]

The concept of invariant mass from the Einstein equation is really just for people who are fixated on mass as something important.  mass is best viewed as "trapped energy" and the amount of energy that is trapped defines its gravitational mass.  The same is true for space and time, these are a function of energy and momentum via the main fixed constant which is accepted as the speed of light.  In reality we should always use dimensions of energy and momentum.  but these are not very easy to use in our normal world of space time.

I tend to agree.  Relativistic or invariant masses can be described in terms of energy and momentum, so energy and momentum conservation seem, to me at least, to be fundamental. 

It's interesting, though, that conservation of mass still holds.  It's more interesting that in order for conservation of mass to hold, you have to use invariant mass of a system, which leads to some odd situations.  For example, the invariant mass of two photons together is non-zero, despite the fact that the invariant mass of each photon is zero!  This is how positron-electron annihilation into two photons can conserve invariant mass. 

Careful. That only holds for free point size objects. E.g. if there is a block which is subject to external forces then invariant mass for the block itself is meaningless.

How so?

[Pmb]

Careful. That only holds for free point size objects. E.g. if there is a block which is subject to external forces then invariant mass for the block itself is meaningless.

How so?

Suppose the box is square with each side having length L. Let two photons be emitted from opposite sides. Then the invariant mass has one unique value for all time. However, if you use a frame moving parallel to the photons then, due to simultaneity effects, the photons are not emitted at the same time and the box it was emitted from has three different values, not two like it did from the rest frame of the box. This happens since the system is now a box whose energy and momentum had three different values.

If the box is under stress then the stress will add to the momentum. If the momentum is parallel to the velocity then it will affect the energy and momentum is perpendicular to the stress then it doesn't have an effect. Do a mere rotation of the box will change its invariant mass.

[yor_on]

Very nice question Pmb

That's what I'm starting to wonder too. Why does the geometry have such an effect, or in this case the observers definition of the geometry? Is it real, and what does it mean? Geometry and gravity are weird subjects, as is energy

[JP]

Actually, the geometry makes something clearer.  The fundamental quantity in SR for a particle is its four-vector, which describes it's momentum (3 components: px,py,pz) and energy (1 component, E).  You could write this vector as (px,py,pz,E) if you wanted.  Like any other vector, this has a direction in 4D space-time and a length.

You can describe changing the speed of your reference frame with respect to this particle as a rotation of the vector, which rearranges the components, but keeps the length constant. 

Any definition of mass is going to be based around getting a single number out of this four-vector.  Since it has four numbers, there are multiple ways to do this.  The invariant mass is the length of the four-vector, while the relativistic mass is the E-component of the vector.

It's then obvious why the invariant mass is invariant for a single particle: its four-vector doesn't change length by changing reference frames.  And the relativistic mass change, since the E-component of it can change length as the vector rotates.

[yor_on]

A very nice description JP, but how do you relate it to a two photon system? But yes, E must change depending on the geometry, as we can see when something 'falls out'. But the idea of two photons getting a mass is slightly weird, from several points of view. First of all, how do you define them as a system? It must become a closed system right, and can you do that in reality? There is also the point of them on their own being mass less, so the reason they get a mass must be their geometry if so, or is there some other factor involved here.

Assume that SpaceTime is a closed system, also assume that photons 'propagate' in SpaceTime. Then you must have spontaneous mass being created and disappearing. Wonder if there is some way to test that?

[JP]

A very nice description JP, but how do you relate it to a two photon system? But yes, E must change depending on the geometry, as we can see when something 'falls out'. But the idea of two photons getting a mass is slightly weird, from several points of view. First of all, how do you define them as a system? It must become a closed system right, and can you do that in reality? There is also the point of them on their own being mass less, so the reason they get a mass must be their geometry if so, or is there some other factor involved here.

Well, you first have to decide how to define the mass of a system of many particles.  The two usual options are:
Invariant mass: sum up the energy-momentum 4-vectors of all the particles and take the length of the result.
Relativistic mass: sum up the 4-vectors and only take the energy part.

The invariant mass is still invariant if you change speed, since rotation doesn't change the length of a vector.  Relativistic mass isn't invariant if you change speeds, since the particle energy changes. 

So, for the 2 photon system, what do you get?  Let's say you have two photons of equal energy traveling in opposite directions in your reference frame.  If you compute the sum of their 4-vectors, you get only an energy component: (0,0,0,2E), if E is the energy of a single photon.  (The momenta are equal and opposite, so adding them gets you zero.)  Both the relativistic and invariant mass in this reference frame are equal to 2E.

If you change to another inertial reference frame, the photons will Doppler shift and might rotate their directions of travel.  The invariant mass is still 2E, since changing speeds doesn't change the length of the 4-vectors.  The invariant mass does change, however, since it only depends on the energies, which are free to Doppler shift.

To use either concept for much, you need to know that you have a closed system, since if energy or momentum isn't conserved, the sum of the 4-vectors isn't conserved and either type of mass could change.  If energy and momenta are conserved, then both types of mass should be conserved so long as your reference frame doesn't change.  (And invariant mass is conserved even if it does.)

[JP]

And that brings me to a disagreement with Pmb's point above and a defense of invariant mass.  Pmb said that if you have two photons being emitted, then the invariant mass takes on three values in some reference frames due to the photons not being simultaneously emitted.  This is true because it's not a closed system over time.  If you compute the invariant mass including the atoms which will emit the photons, then invariant mass has one value at all times, no matter what reference frame you're in.

And this is why invariant mass is particularly useful.  If you have a closed system in which energy and momentum are conserved in particle interactions, then invariant mass should be conserved. This simplifies a lot of equations, especially in particle physics, where the particle decay satisfies conservation of energy and momentum, and where changing reference frames can be very useful to finding particles.

[yor_on]

By 'If you change to another inertial reference frame, the photons will Doppler shift and might rotate their directions of travel.' you mean that the photons will be found to have a different direction relative me, but relative themselves still traveling in the opposite direction, right?

But why would they Doppler shift? Ahh, okay, you mean that they might come towards me, or from me, depending on where I am in relation to them. And then we would have a different 'invariant mass' for them, depending on my geometry relative theirs. It's very interesting that one, if I now got it right

Relative themselves they do not change their order though, it's me as the observer that change their 'energy' relative where I am, if I got it right? Not that strange but still, very very thought provoking as it is about the geometry, not about the photons 'trajectories' as described by themselves, relative each other.

And that is weird :)Although explainable as you just did.
Thnx, & very nice JP. I will have to think about this one more.