Is Mass Really Condensed Energy

pmb_phy

Since relativity considers energy and mass to be the same thing then I ask you on what do you base this assertion?
That is the energy of the gravitational field. I was speaking about the energy/mass of matter.

In any case I was responding to your comment
When I posted my assertion that mass is a well defined quantity I had in mind the mass of a particle (i.e. inertial mass), not a general definition of mass which encompasses all of GR (i.e. active and passive gravitational mass.

In any case I now understand what you meant when you said that mass is not conserved and I therefore have no more questions to ask you so I will bow out here so that this thread doesn't drone on about mass/energy conservation. Seems like many threads get sidetracked with conversations like this and end up donminating a thread. I don't wish to contribute to that in any threads, hence my bowing out. Thanks.

Garth - If you recall, we discussed your comments in the past ad nauseum and I understand that you have a different opinion on that point so I see no reason to go over the same discusssion again. Thanks.

Pete

gijeqkeij

Probably we say the same things in different words. Let me rephrase: you can't actually distinguish in GR between mass, energy, energy of gravitational fields. That why you can't have in GR a proper energy conservation law... so mass and energy can't be well defined in GR.
gijeqkeij

actionintegral

I would be interested in learning the definition of mass. Please post it.

pmb_phy

It depends on what you mean by "mass." There are several meanings to the term: inertial mass (aka relativistic mass), proper mass, active gravitational mass and passive gravitational mass.

Inertial mass - The quantity m such that mv is a conserved quantity in elastic collisions. m is a function of speed, i.e. m = m(v).

Proper mass - For a tardyon m₀ = m(0). For a luxon m₀ = 0.

Active gravitational mass - That which is the source of a gravitational field.

Passive Gravitational mass - That which a gravitational field acts on.

For a detailed definition please see

http://www.geocities.com/physics_world/mass_paper.pdf

Pete

pervect

I am basically with gijeqkeij and Garth on this issue, as long-time posters will probably be aware.

The way I describe mass in GR is not that there is no defintion, it is rather that there is no single definition. There are many different defintions of mass in GR, some of the more comon are

ADM mass, Bondi mass, and Komar mass. The first two are applicable in asymptotically flat space-times, and differ on how they handle energy in gravitational radiation. The last is applicable in any static space-time.

Other posters have talked briefly about other sorts of mass (such as Dixon mass), which I want to learn more about someday.

See

http://www.physicsforums.com/archive.../t-110905.html

for some past discussion.


If the space-time is neither static nor asymptotically flat, there is no general definition of mass in GR, just as there is no general definition of energy.

pmb_phy

I was speaking about conservation of energy, not momentum. One would never assume that a quantity such as momentum is a constant of motion when it is moving in a gravitational field. The law of conservation of momentum applies only to those particles on which no force is acting. I.e. in Newtonian gravity a particle falling in the Earth's gravitational field (as observed by someone sitting on its surface) will measure the energy to be constant and yet the momentum will constantly changing when in free-fall. However since this is a static field then the energy of such a falling particle will be zero.
Actually its a geometric property when external 4-forces are zero. The equation div T = 0 is a geometric statement, i.e. independant of spacetime coordinates. It is easily found by calculating in a locally Lorentzian frame. So while its true that energy is frame dependant it is not true that the Law of conservation is frame dependant. Its sort of like measuring proper mass. It is measured when the particle is at rest in a locally Lorentzian field. If one is evaluating the energy from a freely-falling frame in a curved spacetime then the field will be time independant and such a field is non-conservative.

Its not as if the GR community calls this "local" energy-momentum conservation for nothing Garth. They state it that way for a reason.
3-momentum is not vector subtracted from energy since one is a tensor of rank zero while the other is a tensor of rank one. The meaning of the equation you speak of (i.e. the T^0u_u = 0 equation) is a conservation equation which states that energy entering a small enclosed surface will equal the rate at which energy passes through the surface which is the rate at which energy decreases from external to the surface. Plus you can't add 4-vectors which are located at different events in spacetime. That is a violation of the rule for adding vectors. In any case, when the energy for a single particle in free-fall in a static g-field is calculated then the energy (E ~ P ₀) it will be a constant of motion, i.e. conserved.

When one speaks of conservation laws one must take into account the specific example and see if it matches the condition postulated in the law. I.e. in that case "momentum" is rarely conserved since the law states that "The momentum of a free particle is conserved" and therefore you must take into account forces acting on a particle. Likewise the energy of a particle in a field is not constant unless the potential is time-independant, i.e. a conservative field.

Pete

s8iva

How would you explain black holes? I would like to think of mass and energy as states of existence which are not binary and rather a spectrum therefore providing the possibility of having a state that has both mass and energy.
Interestingly there is a Sanskrit verse "aapOHO vaa idhagum sarvam viswaa bhuthaanyApa". Sarvam viswaa means entire universe and aapoho means water. The gist of it roughly tries to suggest that entire universe is made of water. I found the meaning quite curious and happened to have a study at the literature. I was surprised to find what the folks were hinting at. The verse tries to suggest that entire universe existed in a liquid state. This liquid was churned and and from it arose time. I am assuming here the entire energy was churned to a single point of infinite energy to create a big bang which created time too.

I am astonished at the quality of thought that existed in these folks from the BCs with absolutely no equipments to verify even their basic theories.