Mass transported at speed of light

[Ich]

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

 

[jtbell]

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?

 

[AWolf]

I challenge your wikipedia source

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.

From your Baez link
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]

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.

 

[B.E.M]

Hi Zapper, these don't 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.

 

[AWolf]

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 canceled each other out, but whatever provided the particles with their Relativistic Mass has gone, but there is nothing to explain what canceled 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?

 

[AWolf]

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]

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 canceled each other out, but whatever provided the particles with their Relativistic Mass has gone, but there is nothing to explain what canceled 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.

 

[B.E.M]

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

 

[AWolf]

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]

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 traveling 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...

 

[nakurusil]

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.

 

[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]

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]?

 

[nakurusil]

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.

 

[AWolf]

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 fundamental 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]

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.

 

[nakurusil]

Except when it comes to invariant mass and photons, which I would have thought would have been somewhat fundamental 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.

 

[AWolf]

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

Filled or Full ?

As the photons have no mass, they are considerably smaller than the original occupants of the container. Could more positrons/electrons be added to the contents of the box ?

 

[AWolf]

The container isn't empty.

Is it still full ?

 

[nakurusil]

Filled or Full ?

As the photons have no mass, they are considerably smaller than the original occupants of the container. Could more positrons/electrons be added to the contents of the box ?

Your initial question was answered many posts ago, now you seem to generate a new set of questions just for the reason that you refused to accept the obvious answer to your initial question (what happened to the mass of the positron/electron pair).

I will answer your new question nevertheless, without doing calculations because you seem to ignore them:

1. The box was initially filled with matter.
2. After annihilation it is filled with the energy of the resulting photons.
3. Without doing the necessary calculations, it is not possible to add any more massive particles into the box because the process of adding even one more particle would require infinite energy. I will let you prove that to yourself, it is an interesting exercise. You will need to use math.

You'd be hard pressed to find a box strong enough not to explode in your face.

The answer has nothing to do with "As the photons have no mass, they are considerably smaller than the original occupants of the container. ". It is a nonsense to even attempt to talk about the
size of the photon (there is another thread going on about this).

 

[AWolf]

Your initial question was answered many posts ago, now you seem to generate a new set of questions just for the reason that you refused to accept the obvious answer to your initial question (what happened to the mass of the positron/electron pair).

Your answers, including this one, all refer to the mass becoming energy. The mass was already energy before the annihilation.

it is not possible to add any more massive particles into the box

The box no longer contains any massive particles. The electrons and positrons, which have a radius of 2.8179 × 10−15m, no longer exist.
All that is contained in the box are photons which are dimensionless.

Now even I can do the math for that

n * volume of an electron/positron != n * 0​

 

[nakurusil]

Your answers, including this one, all refer to the mass becoming energy. The mass was already energy before the annihilation.

Try reading more carefully.

The box no longer contains any massive particles. The electrons and positrons, which have a radius of 2.8179 × 10−15m, no longer exist.
All that is contained in the box are photons which are dimensionless.

Now even I can do the math for that

n * volume of an electron/positron != n * 0​

Not the right math. Try again.

 

[Mute]

Your answers, including this one, all refer to the mass becoming energy. The mass was already energy before the annihilation.

And the chemical energy in a battery is still energy when it has been converted into electrical energy and heat, but the forms of energy are not equivalent.

The box no longer contains any massive particles. The electrons and positrons, which have a radius of 2.8179 × 10−15m, no longer exist.
All that is contained in the box are photons which are dimensionless.

Now even I can do the math for that

n * volume of an electron/positron != n * 0​

You're using the "classical electron radius", though, which is just an estimate of the electron's radius based on classical physics alone. Quantum mechanically, the electron is a point particle of zero size, so

n*volume of an electron/positron = 0​

 

[jtbell]

The electrons and positrons, which have a radius of 2.8179 × 10−15m,

Where did you find that number? All I've ever seen has been upper limits on the size of an electron or positron. These simply indicate the limitations of whatever experimental technique was being used. That is, "if the electron has finite size, it must be less than this amount, otherwise we would have detected it."

For example, http://arxiv.org/abs/hep-ph/0002172, which gives an upper limit from an experiment at LEP, of 2.8 \times 10^{-19} m.

 

[AWolf]

And the chemical energy in a battery is still energy when it has been converted into electrical energy and heat, but the forms of energy are not equivalent.

In line with that, the energy of the electron/positron is still energy when it is converted to that of a couple of photons, but the form has changed.

Bare in mind that orbiting electrons can absorb/emit photons when changing shelves to increase/decrease their energy levels, so the form of the energy must be fairly compatible.

Except here there is no chemical reaction. The other properties of each particle cancel each other out.

The form of the energy changes without the addition of any energy or other particulate property. One moment it has mass, the next it doesn't (please note all previous posts about invariant mass - let's not go there again).

------------------------

When dealing with electrons/positrons annihilation, the only way to calculate the transition to gamma rays is using invariant mass. The reason for this is because if you don't use invariant mass, then the equation doesn't balance. The reason it won't balance is because on one side of the equation you have relativistic mass and on the other side you do not. To say that the mass was converted to energy takes you away from using invariant mass and into using relativistic mass which it appears to be quite widely agreed that you can't do. Relativistic Mass cannot be used to calculate the outcome of this process because photons have none and any reference to E=MC^2 is using the wrong math.

The reason that invariant mass must be used is because there is currently no method of manipulating Relativistic Mass into anything else. Sure, you can use E=MC^2 to determine the amount of energy your playing with, but that's as far as you can take it.
Whatever it is that is the root cause of, or at least has a part to play in Relativity is lost at the moment an electron/positron pair is annihilated. The requirement to add increasingly more energy to these particles to get them to travel at ever higher velocities no longer applies.
Whatever was preventing those particles from traveling at the speed of light was removed when the energy became photons, in fact traveling at the speed of light suddenly became mandetory.