# The Conservation of Mass

If the law of conservation of mass states, in a closed system mass is never lost, how is it, when matter is annihilated, effectively creating photons (which are not considered to be matter) does this law stand true?

## Answers and Replies

G01
Homework Helper
Gold Member
The separate laws of conservation of mass and conservation of energy are not valid in relativity.

In relativity there is a combined "Law of Conservation of Mass/Energy." Mass can be converted into energy and vice versa, but the total net mass/energy in the universe remains constant.

Thus, we are allowed to create massive particles as long as we have the equivalent amount of energy present. Similarly, like in a nuclear power plant, mass can be converted into energy.

Then, why is a "vacuum" defined as the absence of matter but not of energy?

Sorry santhony, I don't think we need to go through this again.

The word vacuum refers specifically to an area of space devoid of matter. It is only meant to define a lack of matter, nothing else.

Just because they are combined as above, doesn't make them equivalent under the definition. Matter is matter, energy is energy so far as a vacuum is concerned.

If you had an area with a gas cloud of matter and anti-matter, that wouldn't be a vacuum. But, if they annihilated each other you are left with a vacuum.

There's already a four page thread on this, I don't think you need another one.

Sorry santhony, I don't think we need to go through this again.

The word vacuum refers specifically to an area of space devoid of matter. It is only meant to define a lack of matter, nothing else.

Just because they are combined as above, doesn't make them equivalent under the definition. Matter is matter, energy is energy so far as a vacuum is concerned.

If you had an area with a gas cloud of matter and anti-matter, that wouldn't be a vacuum. But, if they annihilated each other you are left with a vacuum.

There's already a four page thread on this, I don't think you need another one.
This thread is intended for serious consideration, not for people who have no questions about what some teacher or college professor told them.

I once considered myself a Christian, believing what was passed down to me, from both my parents and my church. Then, I started having unanswered questions. Questions my religion either could not answer or refused to answer. I looked for answers outside of Christianity. And, now, eventhough I have much respect for Christ, I don't think he had all the answers.

Don't make the mistake of codifying scientific definitions as religionists codify their beliefs. Eventhough everyone seems to agree with something doesn't necessarily make it right.

And, this thread is not about vacuums. It's about the conservation of mass.

Don't make the mistake of codifying scientific definitions as religionists codify their beliefs. Eventhough everyone seems to agree with something doesn't necessarily make it right.
The definition is the definition. We really don't need to go through this again. If you want a word to cover matter and energy then invent one. Vacuum is not and was never intended to be that word.

This isn't even close to religious doctrine. The definition is agreed under science and the English language (well any language - just check a dictionary). The definition of vacuum is no different to the definition of other words.

Why not question why the word matter doesn't cover energy as well? If matter doesn't cover energy then vacuum has no relation to energy because it only deals with matter.
And, this thread is not about vacuums. It's about the conservation of mass.
Then, why is a "vacuum" defined as the absence of matter but not of energy?
We spent four pages discussing exactly what you just asked in your last thread.

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photons (which are not considered to be matter)
Yet, they have mass. Using relativistic framework - mass conservation is equivalent of conservation of energy. (Sorry for such short answer, but more words does mean larger chance of writing you some nonsense :p. )

jtbell
Mentor
If you think in terms of "relativistic mass", then you can assign each of the outgoing photons a mass of E/c^2, and the total relativistic mass is the same before and after.

If you think in terms of invariant mass ("rest mass") as most physicists do, the invariant mass of the system is also the same before and after the annihilation, because it is defined via

$$m_{0(sys)} c^2 = \sqrt{E_{total}^2 - (p_{total}c)^2}$$

and the total energy and total momentum are both conserved.

However, in general, the invariant mass of a system is not the sum of the invariant masses of the individual particles that comprise the system. In this case, the invariant mass of the system of outgoing photons (remember, there must be more than one photon going out) is not zero, although the sum of the invariant masses of the individual photons is zero.

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berkeman
Mentor
We spent four pages discussing exactly what you just asked in your last thread.