[ARVIND (OP)]

According to the laws of conservation of mass, mass can neither be created nor destroyed. Big bang states that the universe began with a primeval atom. So, that primeval atom must have had a definite atomic mass. So, the mass of the universe during big bang should be same as of the present universe. But, you may say that according to Einstein`s formula, E=mc²  , much amount of mass must have been converted into energy, and of course, the quantity of mass in the universe must have come down. But,there is an increase in the quantity of energy. Does this mean that the quantity of energy and the quantity of mass is in inverse proportion ?

[michi]

Not sure I entirely agree. I've never heard of a "primeval atom". What I have learned is that the universe started out in an extremely hot and dense state. No room for atoms in that kind of plasma soup…

So, in the beginning, it seems there was no mass, only energy. The mass started forming only once the universe cooled down, as far as I know. So, if anything, if you want to make a distinction between mass and energy, the energy has come down since then, seeing that some of it was converted into mass.

As far as I know, the sum of mass and energy in the universe is constant, but the ratio has varied over time. In terms of inverse proportion, I think you'd be right: if some mass gets converted into energy, there is now less energy and more mass (and vice versa).

But, at some level, the distinction seems irrelevant, seeing that Einstein told us that mass and energy are equivalent.

I don't know enough about cosmology to understand what happens to the mass that gets carried away from use progressively with the expansion of the universe. At some point, the expansion rate is greater than the speed of light, so mass (and energy) would seem to "disappear" as the expansion accelerates more and more. As far as I know, at some point, the last black holes will have evaporated and the expansion will be so great that the universe will be empty at any given point. The expansion will have cooled the universe to absolute zero and carried away all the energy and mass, so there is nothing left everywhere.

I'd appreciate hearing from people with a cosmology background on this though. My understanding is rather naive…

Michi.

[lightarrow]

According to the laws of conservation of mass,

Where did you find this law?

mass can neither be created nor destroyed. Big bang states that the universe began with a primeval atom.

An atom? Certainly not.

[Pmb]

According to the laws of conservation of mass, mass can neither be created nor destroyed.

True. In tensor notation this is as T^ab_:0 = 0 (conservation of energy and momentum)

Big bang states that the universe began with a primeval atom.

Lemaitre had the idea that the universe expanded from a dense state at R->0, which he called the Primeval Atom. This viewpoint is now thought of as being a misconception. There was nothing like a primeval atom that sat in space at any place or time. Energy could be conserved during the big bang so long as gravitational energy is taken into account.

According to the laws of conservation of mass, mass can neither be created nor destroyed.

You’re speaking about two things here. The proportionality of energy and mass and the conservation of energy. Together they lead to conservation of mass. I’m not sure this holds in general though since its only possible to define conserved energy if the geometry is time-independent.

This is a bit confusing to me since I’m not an expert in cosmology but I know that while a conserved energy cannot always be found (i.e. when the spacetime is time dependant) it seems the case that the universe came from nothing. That is to say that the total energy of the universe started off as zero as did the gravitational potential energy started off as zero too. As the gravitational potential energy decreased the mass-energy started to increase, the sum always being zero

[Pmb]

So, in the beginning, it seems there was no mass, only energy.

According to the mass-energy relationship there is a mass density for every energy density. That’s why you’ll see the term “mass density of radiation” in some cosmology texts when they’re speaking about a radiation dominated epoch of the universe.

The mass started forming only once the universe cooled down, as far as I know. So, if anything, if you want to make a distinction between mass and energy, the energy has come down since then, seeing that some of it was converted into mass.

In what sense are you using the term “mass”? Do you mean it in the sense of “inertial mass” or “proper mass”?

[Pmb]

Where did you find this law?

For lightarrow this is a rhetorical question since he already knows that this law exists. Usually when he sees or hears it he merely wants to have a debate about it.

This law can be found in many relativity texts such as Relativity; Special, General and Cosmological by Wolfgang Rindler, Oxford University Press page 110 Eq. (6.7)

No more debates on definitions, huh?? Please?

[lightarrow]

Where did you find this law?

For lightarrow this is a rhetorical question since he already knows that this law exists.

Not at all. I didn't know it, and you confirm it doesn't hold: you talked of "energy" conservation law.

Usually when he sees or hears it he merely wants to have a debate about it.

The OP wrote that he didn't want to discuss if light has mass or not. If, as you say, I merely wanted a debate, I would have provided an answer for that question  []
The point is that it's not possible to discuss about "the mass of the universe" without a precise knowledge of basic terms/concepts, and the OP it's clearly not an expert, so my intention is to teach, or to make people think about it a bit more.

[simplified]

Does radiation of photon increase mass of dark matter in space?

[Pmb]

Not at all

My apologies lightarrow. I made an invalid assumption

Conservation of mass: Suppose we have two tardyons (i.e. particles for which v < c always) whose proper masses are U and u which go into an interaction and two particles whose proper masses are U’ and u’ come out of it. Let the inertial masses of U, u., U’ and u’ be M, m, M’ and m’. From the law of conservation of energy we have

Uc^2/sqrt(1 – U^2/c^2) + uc^2/sqrt(1 – u^2/c^2) = U’c^2/sqrt(1 – U’^2/c^2) + u’c^2/sqrt(1 – u’^2/c^2)

Cancel out c^2 to get

U/sqrt(1 – U^2/c^2) + u/sqrt(1 – u/c^2) = U’/sqrt(1 – U’^2/c^2) + u’/sqrt(1 – u’^2/c^2)

The inertial mass of U, u, U’ and u’ are M, m, M’, m’ are given by

M = U/sqrt(1 – U^2/c^2)

m = u/sqrt(1 – u/c^2)

M’ = U’/sqrt(1 – U’^2/c^2)

m’ = u’/sqrt(1 – u’^2/c^2)

Upon substitution into the above expression we obtain

M + m = M’ + m’

This equation expresses the conservation of the masses of the two particles. This argument can easily be extended to any number of particles. I do so at my website at
http://home.comcast.net/~peter.m.brown/sr/conservation_of_mass.htm

Here is a real life example using nuclear fission
http://home.comcast.net/~peter.m.brown/sr/nuclear_fission.htm

and you confirm it doesn't hold: you talked of "energy" conservation law.

You must be referring to the follow expression I posted T^ab;0. Actually that was an error. It should have read  T^{ab}_;b = 0. This is really two equations. One equation is the differential equation for the conservation of energy and the second is the differential equation of the conservation of mass. Since according to the mass-energy equivalence energy density = (mass density)*c^2 so one equation of T^{ab}_;b = 0.is a differential equation which represents conservation of mass. This is all shown on my web site at
http://home.comcast.net/~peter.m.brown/sr/energy_momentum_tensor.htm

[Pmb]

Does radiation of photon increase mass of dark matter in space?

No. Dark matter is matter which doesn't interact in any way other than gravitationally. Radition interacts with matter.

[yor_on]

But it is strange. If the universe is accelerating assuming energy to be constant, then there should be some sort of redistribution of it, shouldn't it? Or can you assume that a expanding geometry doesn't demand energy?

[yor_on]

Thinking of it, there is a redistribution that can't be ignored, isn't there? It's called (cosmological) redshift, and it is, and isn't, observer dependent. It is observer dependent in such motto that the observer always will influence the measurement, depending on its relative motion relative what is being measured, but it is observer independent in such motto that the expansion always must influence the measurements, that is if I'm thinking right here

So the light/radiation lose energy as the geometry expands. But it is a symmetry? It's another word I'm thinking of too, not that I remember it at the moment. If it now is this way, does the 'loss of energy' balance up the cost of a expansion?

[lightarrow]

Not at all

My apologies lightarrow. I made an invalid assumption

Conservation of mass: Suppose we have two tardyons (i.e. particles for which v < c always) whose proper masses are U and u which go into an interaction and two particles whose proper masses are U’ and u’ come out of it. Let the inertial masses of U, u., U’ and u’ be M, m, M’ and m’. From the law of conservation of energy we have

Uc^2/sqrt(1 – U^2/c^2) + uc^2/sqrt(1 – u^2/c^2) = U’c^2/sqrt(1 – U’^2/c^2) + u’c^2/sqrt(1 – u’^2/c^2)

Cancel out c^2 to get

U/sqrt(1 – U^2/c^2) + u/sqrt(1 – u/c^2) = U’/sqrt(1 – U’^2/c^2) + u’/sqrt(1 – u’^2/c^2)

The inertial mass of U, u, U’ and u’ are M, m, M’, m’ are given by

M = U/sqrt(1 – U^2/c^2)

m = u/sqrt(1 – u/c^2)

M’ = U’/sqrt(1 – U’^2/c^2)

m’ = u’/sqrt(1 – u’^2/c^2)

Upon substitution into the above expression we obtain

M + m = M’ + m’

This equation expresses the conservation of the masses of the two particles.

The OP talked of "conservation of mass", not "conservation of  inertial mass".

[Pmb]

The OP talked of "conservation of mass", not "conservation of  inertial mass".

The term "mass" is just an abbreviated term for "iertial mass". They mean identically the same thing. Whether the OP meant "proper mass" when he used depends on the conext in which theterm is used. Whenever one says "According to the laws of conservation of mass, mass can neither be created nor destroyed." they must be refering to the quantity m in the relationship m = p/v. Not everyone interprets the term "mass" as you do.

In case you weren't reading close enough that is why I posted the question "In what sense are you using the term “mass”? Do you mean it in the sense of “inertial mass” or “proper mass”?"

What gave you the impression that the op believes that "mass" and "inertial mass" aren't synonyms?

[lightarrow]

The OP talked of "conservation of mass", not "conservation of  inertial mass".

The term "mass" is just an abbreviated term for "iertial mass".

Not according to the main part of the physics community, but according to the minority; for most of physicists "mass" means "invariant mass" (that you call "proper mass", but which term I don't like because I don't understand the meaning for a photon, e.g.)

They mean identically the same thing. Whether the OP meant "proper mass" when he used depends on the conext in which theterm is used. Whenever one says "According to the laws of conservation of mass, mass can neither be created nor destroyed." they must be refering to the quantity m in the relationship m = p/v. Not everyone interprets the term "mass" as you do.

Ok, but I believe the concept of mass is not well understood by everyone and so I prefer to remark the problematics involved, so people is stimulated to think about it more.

What gave you the impression that the op believes that "mass" and "inertial mass" aren't synonyms?

Let's ask to him...

[Ethos_]

Assuming that mass can not be created nor destroyed, the total mass of our universe was not created at the Big Bang. It must have come from somewhere outside our present space/time capsule we call the universe. If not, then mass can be created from nothingness and this law is found suspect.