Gravity Thought Problem

[Jim Lundquist]

If you create a theoretical closed system consisting of an electron and a positron, I assume that both the particles have mass. If they have mass, then each must have a corresponding gravitational component. If the positron, on the other hand has an “anti-gravity” component, then the net gravity of the system would be zero, because there would be no attraction between the particles. However, if the net gravity of the system is >0 and you induce a low-energy collision of the electron and positron, annihilating the mass of the particles and creating gamma ray photons, what happens to the gravity in the system? If you extrapolate this experiment to use an object the size of Earth and made of matter and an object the size of Earth made of anti-matter and they have no gravitational attraction, then what of the gravitational space-distortion that this “positive Earth” object would normally exhibit in an open system?

 

[jedishrfu]

Both particles have a mass of the same magnitude.

The positron even though its described as being anti-matter doesn't have a negative mass aka anti-gravity component, it just has a positive charge.

https://en.wikipedia.org/wiki/Positron

Since the particles are annihilated, the gamma ray photons are created and the mass of the system has been transformed into the energy of the photons.

 

[Nugatory]

If you create a theoretical closed system consisting of an electron and a positron, I assume that both the particles have mass.

They do. You can google for "electron mass" to see how much - not a lot, but some.

If they have mass, then each must have a corresponding gravitational component.

Again, they do indeed have some gravitational attraction. It is a good exercise to calculate how much it is and compare with the strength of the electrical attraction between them - it turns out that gravitational force is enormously weaker, so much less so that we can completely ignore it in all calculations of the behavior of the system.

If the positron, on the other hand has an “anti-gravity” component

It doesn't. Antimatter and matter both attract gravitationally; It's not like electricity where like charges repel and unlike charges attract.

If...you induce a low-energy collision of the electron and positron, annihilating the mass of the particles and creating gamma ray photons, what happens to the gravity in the system?

Nothing - it's still there. A sealed box containing a positron and an electron weighs exactly as much as the same sealed box containing the gamma radiation from the annihilation of the two particles, and has exactly the same gravitational influence. The same principle would apply to a systenm containg two earth-sized masses, one of matter and one of anti-matter.

 

[Jim Lundquist]

They do. You can google for "electron mass" to see how much - not a lot, but some.

Again, they do indeed have some gravitational attraction. It is a good exercise to calculate how much it is and compare with the strength of the electrical attraction between them - it turns out that gravitational force is enormously weaker, so much less so that we can completely ignore it in all calculations of the behavior of the system.
It doesn't. Antimatter and matter both attract gravitationally; It's not like electricity where like charges repel and unlike charges attract.

Nothing - it's still there. A sealed box containing a positron and an electron weighs exactly as much as the same sealed box containing the gamma radiation from the annihilation of the two particles, and has exactly the same gravitational influence. The same principle would apply to a systenm containg two earth-sized masses, one of matter and one of anti-matter.

If gamma radiation (photon) has no mass, how could there be a conservation of gravity? Would this be considered source-less gravity?

 

[sophiecentaur]

how could there be a conservation of gravity?

There would be conservation of Momentum (which is the number one conservation Law). I don't think there is any reason why gravity would have to be conserved - despite the intuitive feeling about it.

 

[jtbell]

If gamma radiation (photon) has no mass, how could there be a conservation of gravity? Would this be considered source-less gravity?

The mass of a collection of objects/particles does not in general equal the sum of the masses of the individual objects/particles. The individual gamma-ray photons each have zero mass, but their energy nevertheless contributes to the mass of the system of box + photons.

Also note that in general relativity, energy and momentum are the "source" of gravity, via the stress-energy tensor. Mass is one way that energy can enter into this, but there are other forms of energy also.