## Regarding the conversion of kinetic energy to mass

According to the theory of relativity, in the case of two particles of mass m and kinetic energy k colliding, the mass of the two particles together after the collision is greater than the sum of the two particles. It is claimed that thus the kinetic energy is converted to mass. How is this so? What kind of mass appears? In what form is this mass?
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 Mentor I think that depends on the specific particles involved. If you have a >1.1 MeV photon colliding with a nucleus then the extra mass can be in the form of an electron-positron pair. If you have two lumps of clay then the extra mass will typically be in the form of heat.

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 Quote by DaleSpam I think that depends on the specific particles involved. If you have a >1.1 MeV photon colliding with a nucleus then the extra mass can be in the form of an electron-positron pair. If you have two lumps of clay then the extra mass will typically be in the form of heat.
I agree with the first part of that, but heat is NOT mass!

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## Regarding the conversion of kinetic energy to mass

 Quote by HallsofIvy heat is NOT mass!
A hot object has more energy in its rest frame than a cold object. This increases the timelike component of the object's 4-momentum and therefore also increases the norm of the 4-momentum. The norm of the 4-momentum is proportional to the mass. Heat may not be mass exactly, but adding heat increases the mass of an object.

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 Quote by DaleSpam A hot object has more energy in its rest frame than a cold object. This increases the timelike component of the object's 4-momentum and therefore also increases the norm of the 4-momentum. The norm of the 4-momentum is proportional to the mass. Heat may not be mass exactly, but adding heat increases the mass of an object.
I agree with you that an increase in temperature will result in an increase in the invariant mass of an object. However, heat is not temperature and we should always maintain a clear distinction.

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 Quote by Hootenanny I agree with you that an increase in temperature will result in an increase in the invariant mass of an object. However, heat is not temperature and we should always maintain a clear distinction.
You are absolutely correct, I was unclear.

 Heat may not be mass exactly, but adding heat increases the mass of an object.
So it increases mass how though? WHat is the form of this mass? The electron-positron pair? How does this hapen? Where does the electron and positron come from?

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 Quote by Stellar1 So it increases mass how though? WHat is the form of this mass? The electron-positron pair? How does this hapen? Where does the electron and positron come from?
Higher temperature basically just means the molecules have a higher average velocity in their random movements, and so this makes the object harder to accelerate (i.e. it requires more energy) in the same way that it's harder to accelerate individual objects moving at a significant fraction of c in your frame. Basically this is a consequence of the fact that the higher the velocity, the greater the increase in energy for a given incremental increase in velocity, according to the equation:

$$E^2 = m^2 * c^4 + p^2 * c^2$$

...where p is the object's relativistic momentum, $$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$

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 Quote by Stellar1 Where does the electron and positron come from?
They come from the energy of the photon. An electron has a mass of 511 keV, so if a single photon has an energy of at least twice that, or just over 1 MeV, then it has enough energy to convert to the mass of two electrons by e=mc^2. However, a photon is uncharged, so for charge conservation it is necessary to produce an electron and a positron instead of two electrons.

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 Quote by DaleSpam They come from the energy of the photon. An electron has a mass of 511 keV, so if a single photon has an energy of at least twice that, or just over 1 MeV, then it has enough energy to convert to the mass of two electrons by e=mc^2. However, a photon is uncharged, so for charge conservation it is necessary to produce an electron and a positron instead of two electrons.
But Stellar1's question was in reference to your statement about heat increasing mass...the fact that two lumps of clay become more massive when some of their kinetic energy is converted into heat which raises their temperature has nothing to do with the creation of new particles.

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 Quote by JesseM But Stellar1's question was in reference to your statement about heat increasing mass...the fact that two lumps of clay become more massive when some of their kinetic energy is converted into heat which raises their temperature has nothing to do with the creation of new particles.

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