Regarding the conversion of kinetic energy to mass

[Stellar1]

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?

 

[Dale]

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.

 

[HallsofIvy]

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!

 

[Dale]

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.

 

[Hootenanny]

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.

 

[Dale]

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.

 

[Stellar1]

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?

 

[JesseM]

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, $$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$

 

[Dale]

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.

 

[JesseM]

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.

 

[Dale]

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.

Stellar1's question had two parts. You answered the part about how thermal energy made an object more massive, so I answered the part about new particles. That is why I quoted only the specific part of his question that I was answering. Your comments about thermal energy and inertia were concise and complete; I didn't have anything useful to add on that subject.

 

[JesseM]

Stellar1's question had two parts. You answered the part about how thermal energy made an object more massive, so I answered the part about new particles. That is why I quoted only the specific part of his question that I was answering. Your comments about thermal energy and inertia were concise and complete; I didn't have anything useful to add on that subject.

I don't disagree with any part of your answer, but I interpreted Stellar1's question differently. In response to your comment "Heat may not be mass exactly, but adding heat increases the mass of an object", Stellar1 wrote: "So it [i.e. heat] increases mass how though? WHat is the form of this mass? The electron-positron pair?" When Stellar1 asked "what is the form of this mass" I thought the question was still about the mass added through heat, and that Stellar1 was confused, thinking that the mass added through heat was in the "form" of an electron-positron pair.

 

[Dale]

I thought the question was still about the mass added through heat, and that Stellar1 was confused, thinking that the mass added through heat was in the "form" of an electron-positron pair.

Hi Stellar1, just to be clear, the form of the extra mass will be different for different kinds of collisions. The high-energy photon creating an electron-positron pair was an example where new massive particles could be created. The thermal energy in the lumps of clay was a completely separate example where no new massive particles were created, but the inertia of the system was increased by the increased temperature.

 

[Shackleford]

Heat is one of two modes of energy transfer; the other being work. Heat is not energy.

 

[Dale]

The photons also have momentum and energy, so a "photon gas" has inertia and therefore mass. In this case the extra inertia would be due to the fact that the blue-shifted photons striking the rear of the accelerating cavity would have more momentum than the red-shifted photons striking the front.