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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 The old statement found in some(out of date) textbooks that "matter cannot be created or destroyed" is now untrue and has been replaced by the conserved values described earlier in this note.

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." ...sorry, you cannot view external links. To see them, please REGISTER or LOGINI can see this conserves energy but how does it conserve mass?

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?

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.

Quote from: Soul Surfer on 12/09/2011 08:14:26The 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.

Quote from: JP on 12/09/2011 16:39:30Quote from: Soul Surfer on 12/09/2011 08:14:26The 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.

QuoteCareful. 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?

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.

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.

It all goes back to 'energy' doesn't it, and as 'gravity' is coupled to mass and then those photons can be defined to have a mass, we now have a circumstantial chain pointing to 'energy' as the origin of 'gravity' too, which makes sense. With the exception of me thinking of it as coupled, not generated as in 'created' by mass. to me it's more of something 'sticking' to 'it all' SpaceTime that is, including 'energy' As a geometry defining energy relative the observer sort of, and always local. Even though intrinsically invariant those light quanta's then can be seen as a summation of 'gravity', changing relative the observers position in SpaceTime.

But what do you mean by "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."?

That if we redefine the closed system to also in-cooperate the 'photons' sources, the atoms, you will find a same invariant mass, no matter the 'rotations' you apply on them by your position relative them? And then it is the observer too, he must always be included right?

So in that case, there is no difference between that system and a planet?The mass (of the two photon system) will now be invariant, no matter what rotations you apply on it.

What I really mean here is that it is the observer that defines the result. And that without the observer those two photons should have only one path. Would you agree to that or do you see it differently? As I see it all such descriptions always include a observer, and it is that thought up observer that will define the outcome. And this is more of philosophy possibly, but it is a 'presumption' for describing anything, and very important in SpaceTime, well, as I see it. Weird stuff ==

It's not a perfect description, you might assume that SpaceTime, even without observers, will have a independent 'reality', a little as I did with those photons path, relative each other. And if you do you define SpaceTime as being of a 'objective quality', independent from any observer, simultaneously with it being described from observer frames of reference. If you do that you introduce one 'SpaceTime background' that we might call 'original', but invincible to us, as what SpaceTime we see always will be defined from our 'rotation' / 'frame of reference'. But it is about what SpaceTime really 'is', as I see it.

Either all things in SpaceTime is 'observers', observing SpaceTime differently from their own frame of reference, all of it locally. Or we have a SpaceTime that has a 'objective reality', hidden from our observations. It's hard to see how it can be both to me. In the first case we have radiation and gravity keeping it together, presenting us the 'wholeness' that we all think us to see when looking out in the universe. But all of it defined locally. In the second? What is HUP? Is that a sign of how QM defines a universe, and, why do statistics work?

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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.

"In QM, the observer's measurements must physically change the object being measured."Is that the way you see HUP JP? That it is the 'physical' interference that creates it?

Well, any 'wave function' has to be metaphysical

You can't 'measure' on that and define it 'unchanged'. But I wondered as you wrote physical change And that sounded as a 'physical chain reaction' I measure and my measurement change its state by 'interfering' physically with what I try to observe. It's a question of indeterminacy isn't it?

It's nice reading this But what is a distance, and what is 'time'. You need the arrow to get a 'distance', and then you need 'statistics' to prove a 'motion'. Or you can exchange 'statistics' for 'history'. So I'm not sure if there is so much differing QM from macroscopic phenomena. If the 'distance' mesaured is a result of the observer relative SpaceTime, and the 'time' he measures for other frames also is a result of his 'motion/mass/energy/gravity'?We take too much for granted I think.