# Mass transported at speed of light

ZapperZ
Staff Emeritus
Doesn't the invariant mass refer to that of the system (electron+positron) taking into account the total energy and momentum of the system ?
Say what?

Tell me the invariant mass of the electron+positron, and the photon after anhilation.

Zz.

ZapperZ said:
Tell me the invariant mass of the electron+positron, and the photon after anhilation.
The invariant mass of the electron+positron before the annihilition is equal to the invariant mass of the TWO photons after the annihiliation.

Invariant Mass is a method of basically ignoring the Mass bit by refering to the energy and momentum instead, it's not a way of cancelling out mass in the same manner as spin and charge can be cancelled out.
Adding Mass and Invariant Mass is like adding Lemons and Oranges; they're both citrus, but they're not really the same thing.

An electron has mass and invariant mass as does the positron, although when dealing with their mutual annihiliation, only the invariant mass is really relevant.

ZapperZ
Staff Emeritus
The invariant mass of the electron+positron before the annihilition is equal to the invariant mass of the TWO photons after the annihiliation.

Invariant Mass is a method of basically ignoring the Mass bit by refering to the energy and momentum instead, it's not a way of cancelling out mass in the same manner as spin and charge can be cancelled out.
Adding Mass and Invariant Mass is like adding Lemons and Oranges; they're both citrus, but they're not really the same thing.

An electron has mass and invariant mass as does the positron, although when dealing with their mutual annihiliation, only the invariant mass is really relevant.
So you are saying that photons have invariant mass, no? Can you point to me a legitimate source that claim such a thing?

Zz.

ZapperZ said:
So you are saying that photons have invariant mass, no?
I'm saying that a system of photons has invariant mass, as in the case of the two gamma rays resulting from the annihilation of the electron and positron.

http://en.wikipedia.org/wiki/Relativistic_mass" [Broken]
Even for photons, a single observer and a closed system is required for mass conservation, since photons as considered singly have zero mass, where as pairs or systems of photons moving in different directions will in general exhibit an invariant mass which is associated with the system of photons, but not with any single photon.
Hence why they must be viewed as a system.

My initial question really referred to the Relativistic Mass, incidently which both the electron and positron can be viewed as having prior to their destruction.

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ZapperZ
Staff Emeritus
I'm saying that a system of photons has invariant mass, as in the case of the two gamma rays resulting from the annihilation of the electron and positron.

Hence why they must be viewed as a system.

My initial question really referred to the Relativistic Mass, incidently which both the electron and positron can be viewed as having prior to their destruction.
I challenge your wikipedia source with http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html" [Broken]:

. By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way. But you can say that the photon has relativistic mass if you really want to. In modern terminology the mass of an object is its invariant mass which is zero for a photon.
I will also put it to you that I can go in to Wikipedia and edit out that quote. So what guarantee do you have that it will be there tomorrow?

BTW, what does "relativistic mass" have anything to do with this? The electron-positron anhilation does NOT require the electron and positron to be relativistic.

Zz.

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Ich
I really do not see why you challenge AWolf's assertion. It is definitely true.
There must be some misunderstanding.

jtbell
Mentor
I'm saying that a system of photons has invariant mass, as in the case of the two gamma rays resulting from the annihilation of the electron and positron.
One can certainly calculate the quantity $\sqrt{E_{total}^2 - (p_{total} c)^2}$ for the pair of photons, and it must equal the similar quantity for the electron and positron. But how meaningful as "mass" is that quantity for an unbound system as opposed to a bound system? One can (at least in principle) "weigh" a box with mirrored walls that contains a bunch of photons, and find that it has a greater mass than a similar box that does not contain any photons. But how does one "weigh" a system of photons that are not confined? For that matter, how does one "weigh" a system of positron + electron that are not confined or bound together?

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ZapperZ said:
Both sources agree that a photon does not have invariant mass. Find a source that refers to multiple photons viewed as a system having no invariant mass and then you'd have a valid challenge, oh, but hang on a minute, Baez does mention multiple photons.

However, modern usage defines mass as the invariant mass of an object mainly because the invariant mass is more useful when doing any kind of calculation. In this case mass is not conserved and the mass of an object is not the sum of the masses of its parts. For example the mass of a box of light is more than the mass of the box and the sum of the masses of the photons (the latter being zero).
The point about Relativistic Mass is with regards to how much of the Universe does an electron or a positron occupy. When the two are annihilated, the resulting photons do not occupy the same space.

ZapperZ
Staff Emeritus
Both sources agree that a photon does not have invariant mass. Find a source that refers to multiple photons viewed as a system having no invariant mass and then you'd have a valid challenge, oh, but hang on a minute, Baez does mention multiple photons.

The point about Relativistic Mass is with regards to how much of the Universe does an electron or a positron occupy. When the two are annihilated, the resulting photons do not occupy the same space.
Read again. When CONFINED TO A BOX, as in the photons have been localized so that you can actually measure a change in mass OF THE BOX.

For example the mass of a box of light is more than the mass of the box and the sum of the masses of the photons (the latter being zero).
Read ALL the caveats that he put in there in making sure people RESIST the temptation of putting any mass on photons, be it single or multiple.

This is still besides the point. Show me exactly what the "photon invariant mass" is.

Zz.

Hi Zapper, these dont actually contradict.
Consider two photons moving in opposite directions

Their momentums cancel in the systems rest frame, yet the system still has energy. This energy is equivalent to the system's invarient (or rest) mass even though the individual photons have no rest mass.

Ich
One can certainly calculate the quantity $\sqrt{E_{total}^2 - (p_{total} c)^2}$ for the pair of photons...
...and one is certainly allowed to call this quantity "invariant mass" of the pair of photons.

ZapperZ said:
This is still besides the point. Show me exactly what the "photon invariant mass" is.
Let me repeat myself, A photon does not have invariant mass.

What you have with the result of the electron/positron annihilation is the invariant mass of a SYSTEM OF PHOTONS. See the difference here, not one, but more than one.

My question though was not about the definition of invariant mass, but rather about the space occupied by the particles before and after the annihilation. Before the annihilation there is Relativistic Mass, but after the annihilation there is no Relativistic Mass. Spin and charge have cancelled each other out, but whatever provided the particles with their Relativistic Mass has gone, but there is nothing to explain what cancelled it out.

Ich
Before the annihilation there is Relativistic Mass, but after the annihilation there is no Relativistic Mass.
Of course there is relativistic mass. But what's the point?

Ich said:
Of course there is relativistic mass. But what's the point?
Whatever component of an electron that causes it to occupy a finite volume of space disappears when it is annihilated. The same goes for the positron.

As we have been through in some detail, the invariant mass accounts for all energy and momentum before and after the event.

The energy of the electron, which initially occupied a finite volume has collapsed in on itself to the point where it no longer occupies the same volume of space. There is nothing to account for this reduction in volume/relativistic mass.

I hope that makes a bit more sense.

ZapperZ
Staff Emeritus
Let me repeat myself, A photon does not have invariant mass.

What you have with the result of the electron/positron annihilation is the invariant mass of a SYSTEM OF PHOTONS. See the difference here, not one, but more than one.

My question though was not about the definition of invariant mass, but rather about the space occupied by the particles before and after the annihilation. Before the annihilation there is Relativistic Mass, but after the annihilation there is no Relativistic Mass. Spin and charge have cancelled each other out, but whatever provided the particles with their Relativistic Mass has gone, but there is nothing to explain what cancelled it out.
OK, let me repeat myself : what relativistic mass?

A positron and an electron does not have to be "relativistic" to cause annihilation. So what was the "relativistic mass" of electron+positron?

Zz.

Hi Guys,
Im not too concerned with the current issue. cya round.

ZapperZ said:
A positron and an electron does not have to be "relativistic" to cause annihilation.
Not exactly accurate on two points.

Firstly, a positron or electron that is completely at rest still has a relativistic mass which just happens to be equal to its invariant mass (also known as its rest mass).

Secondly, if they are both completely at rest - not relativistic - then the two of them will never be close enough to be mutually annihilated. If they were close enough to be annihiilated, then it would already have happened the moment their proximatey allowed.

So contrary to your statement, A positron and an Electron MUST be "relativistic" to cause annihilation.

Your statement actually makes no sense at all.

Hootenanny
Staff Emeritus
Gold Member
Firstly, a positron or electron that is completely at rest still has a relativistic mass which just happens to be equal to its invariant mass (also known as its rest mass).
Although I am not fond of the idea of relativistic mass, I have to say that you have a point here.
Secondly, if they are both completely at rest - not relativistic - then the two of them will never be close enough to be mutually annihilated. If they were close enough to be annihiilated, then it would already have happened the moment their proximatey allowed.

So contrary to your statement, A positron and an Electron MUST be "relativistic" to cause annihilation.
Just because a particle is moving, does not mean that it is relativistic. A particle is considered 'relativistic' when it is travelling close to the speed of light, or more particularly when the kinetic energy of the particle approaches the energy corresponding to the invariant mass of the particle. I will repeat what Zz said particles and anti particles are not required to be relativistic for annihilation to occur.
Your statement actually makes no sense at all.
Actually, your statement makes no sense of all and Zz's makes a hell of a lot more sense that yours. Zz is an experimental particle physicist, so I imagine he knows what he's talk about...

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The same amount of energy exists after the annihiliation as before. $$\Delta E =c^2 \Delta m$$ is not what happened to the mass.
Of course it is :
Let the mass of the positron / electron be $$m_+$$.
Due to annihilation $$\Delta m=2m_+-0=2m_+$$

The result is a pair of photons with momenta that cancel each other (I can prove this mathematically) and with total energy:

$$\Delta E =c^2 \Delta m=2m_+c^2$$ (1)

The above should not be misconstrued in any form or fashion to mean that the resulting photons have mass. The system after annihilation has energy given by (1). This is what happened to the mass of the electron/positron pair.

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Ich
Zz claims (at least as I read it) that one is not allowed to speak of the invariant mass of a system of two photons, unless they are in a box. But one does so, and especially particle physicists really like to do so.

There are definitions what "invariant mass" and "relativistic mass" mean, so where is the point of this argument?

Hootenanny
Staff Emeritus
Gold Member
Zz claims (at least as I read it) that one is not allowed to speak of the invariant mass of a system of two photons, unless they are in a box. But one does so, and especially particle physicists really like to do so.
I am not particle physicist, so I can't really comment; however, I will ask how relevant is it to assign a 'mass' to an unbounded system [of photons]?

Zz claims (at least as I read it) that one is not allowed to speak of the invariant mass of a system of two photons, unless they are in a box. But one does so, and especially particle physicists really like to do so.

There are definitions what "invariant mass" and "relativistic mass" mean, so where is the point of this argument?
I think that the discussion got sidetracked. "Wolf" 's question was what happened to the mass.
I interpret that to mean what happened to the mass of the electron/positron pair. This makes the answer very straightforward : it turned into the energy of the resulting pair of photons. This diversion into discussing the "mass of photons", the "mass of systems of photons" , etc, is a pit snake, doesn't lead anywhere constructively.

Hootenanny said:
Zz is an experimental particle physicist, so I imagine he knows what he's talk about...
Except when it comes to invariant mass and photons, which I would have thought would have been somewhat fundemental to what he does, and that even an at rest electron would have a relativistic mass.

If a particle is moving at a velocity relative to another, then it will have a relativistic mass effected by its velocity, relative to the other. It has nothing to do with the speed of light, apart from the fact that this appears to be somewhat of a limit.

For an electron and a positron to meet and annihilate each other, one must be moving Relative to the other.

Let me rephrase the question somewhat and try to get away from definitions.

Suppose I have a container filled to capacity with an equal number of positrons and electrons. There is no room for anything else in the container. Allowing enough time, all of the electrons and positrons will pair off and annihilate each other, leaving enough room for the container to be refilled will the same number of electrons and positrons.

Why was it filled to capacity prior to the annihilation fest, and empty afterwards.

Hootenanny
Staff Emeritus
Gold Member
Suppose I have a container filled to capacity with an equal number of positrons and electrons. There is no room for anything else in the container. Allowing enough time, all of the electrons and positrons will pair off and annihilate each other, leaving enough room for the container to be refilled will the same number of electrons and positrons.

Why was it filled to capacity prior to the annihilation fest, and empty afterwards.
The container isn't empty.

Except when it comes to invariant mass and photons, which I would have thought would have been somewhat fundemental to what he does, and that even an at rest electron would have a relativistic mass.

If a particle is moving at a velocity relative to another, then it will have a relativistic mass effected by its velocity, relative to the other. It has nothing to do with the speed of light, apart from the fact that this appears to be somewhat of a limit.

For an electron and a positron to meet and annihilate each other, one must be moving Relative to the other.

Let me rephrase the question somewhat and try to get away from definitions.

Suppose I have a container filled to capacity with an equal number of positrons and electrons. There is no room for anything else in the container. Allowing enough time, all of the electrons and positrons will pair off and annihilate each other, leaving enough room for the container to be refilled will the same number of electrons and positrons.

Why was it filled to capacity prior to the annihilation fest, and empty afterwards.

After annihilation the container is "filled" with the energy of the resulting photons. I think I explained this to you about 3 times now.