# Mass transported at speed of light

## Main Question or Discussion Point

You cannot acelerate an electron to the speed of light without infinite energy right? ditto for a positron. And if you succeeded, who would know. the infinite mass would cause the visible universe to disappear up its own navel.

However, an electron and a positron can annihilate to form a gamma ray (given something at this end to balance the momentum), the gamma ray can move some distance at the speed of light, encounter some thing else and split back into an electron and positron..

So the net result is that some mass has 'transported' itself at the speed of light without 'moving' at the speed of light.

How can such a subtle distinction prevent the universe from ending?

## Answers and Replies

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You cannot accelerate an electron to the speed of light without infinite energy right? ditto for a positron.
Actually it would perhaps be better to say that we do not observe an electron to move at c.
It seems to me that there is nothing in QM that prevents an electron to move at c. But since it's path is not straightforward but random, the effective speed is lower than c.
Interesting here may be to consider the Dirac equation where electrons "wiggle" at c.
But perhaps the QM experts can give a more accurate description.

Good Point

that electron disappeared....into a gamma ray.. which became ANOTHER electron..

there were 2 electrons, thus 1 electron did not travel at the speed of light

If you want to argue that somehow this 2nd electron could have been the first.. get out the heavy math graph paper

ZapperZ
Staff Emeritus
You cannot acelerate an electron to the speed of light without infinite energy right? ditto for a positron. And if you succeeded, who would know. the infinite mass would cause the visible universe to disappear up its own navel.

However, an electron and a positron can annihilate to form a gamma ray (given something at this end to balance the momentum), the gamma ray can move some distance at the speed of light, encounter some thing else and split back into an electron and positron..

So the net result is that some mass has 'transported' itself at the speed of light without 'moving' at the speed of light.

How can such a subtle distinction prevent the universe from ending?
Shouldn't you ask this the other way? You might want to consider that since the universe did not end and did not encounter the catastrophe you described, then there must be something wrong with your description.

The fact that light can travel at c but object with a mass cannot, clearly shows that light and mass are NOT identical entities! Being converted from one to the other does not make them the same thing. I can convert my paper money into a very lovely paper mache sculpture. Would you accept that as payment for your salary?

Zz.

B.E.M said:
However, an electron and a positron can annihilate to form a gamma ray (given something at this end to balance the momentum), the gamma ray can move some distance at the speed of light,
Although the energy of the gamma ray is the same as the electron, it is not the electron. Whatever properties the electron had, ceased when it was annihilated, including its mass, leaving just the energy which cannot be destroyed.

B.E.M said:
and split back into an electron and positron..
The energy may well be utilized in another electron, but it wouldn't be the same electron, just as a newspaper made from recycled newspapers can never become the original newspaper that was recycled. Universal Recycling.

B.E.M said:
How can such a subtle distinction prevent the universe from ending?
Far from ending the Universe, it may well be what keeps it ticking over.

Actually it would perhaps be better to say that we do not observe an electron to move at c.
But my point is that we are observing it to move at c. in the sense that we detect a some mass (that has rest mass) in two separate locations at two separate times, separated by ratio c.

that electron disappeared....into a gamma ray.. which became ANOTHER electron..
there were 2 electrons, thus 1 electron did not travel at the speed of light
If you want to argue that somehow this 2nd electron could have been the first.. get out the heavy math graph paper
I dont even know if a stationary electron is the same particle a second later... brb

I can convert my paper money into a very lovely paper mache sculpture. Would you accept that as payment for your salary?
Yes, so long as you can convince the banks of this 'conservation of paper money' prinicple so they are willing to convert it back for me.

B.E.M, before starting to enter the realm of more advanced physics, perhaps it wouldn't be such as bad idea if you got some kind of profound understanding of more introductory physics?

$$E = mc^2$$

That right there, is perhaps one of the most misinterpreted equations of all time by the public. Sure, you can say that mass and energy are the same, but how much does that actually make you understand?

$$s = vt$$

After all, the above equation doesn't mean that distance and velocity is them same, now does it? It isn't perhaps the best example, but it should get you on the right way.

Yes, from the special theory of relativity, that mass and energy are both but different manifestations of the same thing. But that does not mean that you can do any conversions and transformations as you please and call it whatever you want. Yes, modern scientists do not separate mass and energy in some areas of the discipline. But that doesn't mean that you can do any transformation you wish with whatever explanation you want. Yes, annihilation and pair production works, but that still doesn't mean that you can do any conversions you want for whatever reason you have in mind.

In short, it can be said to be related to the correspondence principle. New theories must be compatible with old ones in situations where they are both applicable. The correspondence principle tells us that we can still use an old theory within the realm where it works, that is, there is no point in bringing up the conservation of mass-energy when we are dealing with how much energy it takes to heat a gram of water one degree Kelvin.

It isn't as easy as just "Let's turn an electron to energy" and start using the mass of an electron with the E = mc2 formula. There are more conservation laws in the Universe besides the conservation of mass-energy, which one you have stated yourself, conservation of momentum.

However, there is also conservation of charge and conservation of spin. An electron has a charge of -1, a photon has a charge of 0. An electron has a spin of +1/2, while a photon has a spin not equal to +1/2. That is why annihilation that includes an electron, must also include a positron. That way, both charge and spin is conserved. ZapperZ made a more exhaustive post on this a while back I believe, but I cannot seem to find it right now.

I accept that in some sense it may not be the same electron, but it sure looks the same. As far as I know there is no test to distinguish them. So also I suppose there is no reason we will not encounter some cream pie flying towards our face at the speed of light because at some microscopic level, maybe it is not travelling as matter at all.

(im not trying to be facious there, I actually find the thought sort of cool. Perhaps we could find a way to adjust matter so it sort of slides along at the speed of light, because in reality it is not moving, just exchanging itself with identical particles.)

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ZapperZ
Staff Emeritus
Yes, so long as you can convince the banks of this 'conservation of paper money' prinicple so they are willing to convert it back for me.
Are you willing to stake your livelyhood on this? When was the last time this has happened?

If I were running the bank, I would not, especially if the dollar bills have been pulverized. In fact, in many countries, such destruction to the currency makes it no longer of legal tender.

A photon is not identical to electron+positron. If you insist that it is, then you're doing some new physics that hasn't been formulated and verified yet. It is as simple as that.

Zz.

ZapperZ said:
A photon is not identical to electron+positron.
The mutual annihilation of an electron and a positron results in two gamma rays.

Each gamma ray contains exactly the same amount of energy as the electron or the positron and all spin and charge is cancelled out.

ah, actually I forgot about the second gamma ray.. I presume that potentially there might be only one gamma ray if something like a proton is present to balance the momentum etc? i.e an exact time reversal of a gamma ray splitting into two particles? (perhaps the second gamma ray hits the proton to transfer momentum?)

ps: I agree the banks would be hard to convince. Thus the fine print

ZapperZ
Staff Emeritus
The mutual annihilation of an electron and a positron results in two gamma rays.

Each gamma ray contains exactly the same amount of energy as the electron or the positron and all spin and charge is cancelled out.
Yes, but they are STILL not identical. One has zero invariant mass, the other do not. In particle detectors in high energy physics experiments, one has different signature than the other.

A photon is not made up of electron+positron, the same way a neutron is not made up of a proton+electron+antineutrino+others. There is a difference between the entity and the products it came from or decay to.

Zz.

You cannot acelerate an electron to the speed of light without infinite energy right? ditto for a positron. And if you succeeded, who would know. the infinite mass would cause the visible universe to disappear up its own navel.

However, an electron and a positron can annihilate to form a gamma ray

Ummm, no. It can be proven (mathematically) that the result of the positron -electron collision is TWO photons, not one. You can do that yourself by calculating the norm for the 4-vector energy-momentum for the electron-positron pair : it is greater than zero (one photon corresponds to zero).
The positron-electron annihilations produces TWO photons that travel in opposite directions.

(given something at this end to balance the momentum), the gamma ray can move some distance at the speed of light, encounter some thing else and split back into an electron and positron.
You can use the same math as above to prove that :

1. in an empty region of space a photon cannot decay into an electron -positron pair (same calculations as above)

2. the photon CAN produce an electron-positron pair in the vicinity of a nucleus. The presence of the nucleus is KEY in the creation of the electron-positron pair. So, this situation is NOT the REVERSE of the situation that created the photon in first place.
This does NOT mean that for a while, the positron-electron have travelled at c.

So the net result is that some mass has 'transported' itself at the speed of light without 'moving' at the speed of light.
No. I hope that now you understand why.

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B.E.M said:
So the net result is that some mass has 'transported' itself at the speed of light without 'moving' at the speed of light.
Maybe it helps to think sometimes in terms of relativistic- (rather than rest-)mass, which stays constant in your scenario. An electron particle cannot spontaneously accelerate toward the speed of light, because something else would need to somehow add to the electron's relativistic mass (toward infinity). However, it can spontaneously change into another form with the same relativistic mass (such as a photon with particular frequency) provided various other physical constraints are satisfied (eg. being faster, the photon has more momentum, so momentum-conservation may demand that another particle be transformed at the same time, and if both are transformed to photons then charge conservation requires the other to be a positive particle with electron mass..).

2. the photon CAN produce an electron-positron pair in the vicinity of a nucleus. The presence of the nucleus is KEY in the creation of the electron-positron pair. So, this situation is NOT the REVERSE of the situation that created the photon in first place.
...
No. I hope that now you understand why.
Hi nakurusil,
I think both of these points were dealt with. for example
ah, actually I forgot about the second gamma ray.. I presume that potentially there might be only one gamma ray if something like a proton is present to balance the momentum etc? i.e an exact time reversal of a gamma ray splitting into two particles? (perhaps the second gamma ray hits the proton to transfer momentum?)
Of course two particles at rest (0 momentum )cannot become one particle at speed of light (some momentum in some direction) without something to balance the momemtum. You don't need to talk about solving 4-vectors.
Secondly, basically everything in physics is reversable. I was assuming protons as bookends, but presumably two gamma rays can spontaniously form an electron-positron pair also.

Im not claiming a flaw in physics here.

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Maybe it helps to think sometimes in terms of relativistic- (rather than rest-)mass, which stays constant in your scenario. An electron particle cannot spontaneously accelerate toward the speed of light, because something else would need to somehow add to the electron's relativistic mass (toward infinity). However, it can spontaneously change into another form with the same relativistic mass (such as a photon with particular frequency) provided various other physical constraints are satisfied ..
Thats reasonable: rest mass is not that fundamental, Im really just looking for a way at looking at this that makes in clear why there is a hard way and and easy way to move mass and information between two points.

btw.. I have always assumed that energy that stays in one place acts like rest mass. Is this true? For example if you had two photons bouncing in opposite directions (so zero momentum) inside a massless mirrored box then it would act like a stationary piece of mass. If you tried to push this box up to the speed of light, the wavelength of the photon opposing your travel would aproach infinity while the other would redshift towards zero.

If true, this could be a good thought-example of how restmass is just a configuration.

Hi nakurusil,
I hope you are at least slightly embarrassed when you re read this thread and realise both of these points were dealt with. for example
Not at all, you understood zilch from what I tried to explain to you.

Of course two particles at rest (0 momentum )cannot become one particle at speed of light
The positron - electron entering annihilation DO NOT have zero momentum, what gave you the idea?

You don't need to talk about solving 4-vectors.
You don't "solve" 4-vectors, one uses them in order to calculate relevant information in solving the problem. I was going to give you the detailed solution, now I am glad that I didn't waste my time typing it up for someone who would not appreciate it.

Secondly, basically everything in physics is reversable. I was assuming protons as bookends, but presumably two gamma rays can spontaniously form an electron-positron pair also.
But the situation that you chose (positron-electron annihilation in vacuum) is not reversible as I have just showed you. You will not get a photon to produce an electron-positron pair UNLESS there is a nucleus present. I was going to ask you to calculate why this is true but based on your previous answers it is clear that you wouldn't know where to start.

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Hi Nakurusil,
Sorry for being snippy before. I had just edited my post slightly to remove that first line. I think that line was the real cause for this disagreement.

I think these misunderstandings here must be based on subtle misswordings. Generally what you say makes sense but I am not making the claims you think I am.

apologies again for ruining this beautiful friendship. :)

When the electron and positron are annihilated, spin and charge cancel each other out and the total energy at the end is the same as before, but what happens to the mass ?

The two gamma rays produced have no mass, so what has happened to it ?

ZapperZ
Staff Emeritus
When the electron and positron are annihilated, spin and charge cancel each other out and the total energy at the end is the same as before, but what happens to the mass ?

The two gamma rays produced have no mass, so what has happened to it ?
But isn't that the point that I brought up to counter your argument? One has no invariant mass, the other does!

Nothing happened to the mass. The requirement that we account for mass not "disappearing" comes from the old conservation of mass law. While that works in many instances, we now know that the more general conservation law is the conservation of mass+energy, i.e. as in $E + mc^2$, not just mass alone or energy alone.

So if you consider that more generalized law, then there's no more asking about where the mass went.

The fact that there is a conversion from one to the other means that the original entity is not the same as the final entity (or else, why bother with a "conversion" in the first place). Water and ice are not identical entity even when both are made up of the same "thing". So if something that we know as simple as a process that undergoes a first order phase transition can be different, we certainly can say that a more profound and complicated conversion between mass and energy should be even MORE different.

Zz.

When the electron and positron are annihilated, spin and charge cancel each other out and the total energy at the end is the same as before, but what happens to the mass ?

The two gamma rays produced have no mass, so what has happened to it ?
But they have energy, remember $$\Delta E =c^2 \Delta m$$ ? This is what happened to mass.

But they have energy, remember $$\Delta E =c^2 \Delta m$$ ? This is what happened to mass.
The same amount of energy exists after the annihiliation as before. $$\Delta E =c^2 \Delta m$$ is not what happened to the mass.

I was going to say 'isnt mass equivalent to energy'? but I just read on wiki that this statement is not popular now as it leads to confusion between invarient mass and the less popular 'relativistic mass'

http://en.wikipedia.org/wiki/Mass_in_special_relativity" [Broken]

quote form the article:
Another way of expressing this idea is that if released energy is allowed to remain in a system (for example, as heat, or even trapped radiation), this energy will be measured as, and included in, the ordinary "rest" mass of the system (that is, this energy still contributes to the inertia of the system and its gravitational field).

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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.
Since you know, there is no point in explaining to you. Based on your initial question, it is clear that you don't know. If you really want to learn, ponder on the $$\Delta$$

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ZapperZ said:
But isn't that the point that I brought up to counter your argument? One has no invariant mass, the other does!
Doesn't the invariant mass refer to that of the system (electron+positron) taking into account the total energy and momentum of the system ?