DaleSpam said: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.
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.HallsofIvy said:heat is NOT mass!
DaleSpam said: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.
You are absolutely correct, I was unclear.Hootenanny said: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.
Heat may not be mass exactly, but adding heat increases the mass of an object.
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:Stellar1 said: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?
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.Stellar1 said:Where does the electron and positron come from?
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.DaleSpam said: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.
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 said: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.
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.DaleSpam said: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.
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.JesseM said: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.
The relationship between kinetic energy and mass is described by Albert Einstein's famous equation, E=mc^2. This equation states that mass and energy are equivalent and can be converted into each other. Kinetic energy, which is the energy an object possesses due to its motion, can be converted into mass and vice versa.
Kinetic energy can be converted into mass through a process called pair production. This occurs when a high-energy photon, such as a gamma ray, interacts with matter and produces a pair of particles, typically an electron and its antiparticle, a positron. The total energy of the particles produced is equivalent to the energy of the original photon, converting the energy into mass.
According to Einstein's equation, any form of kinetic energy can be converted into mass. This includes energy from the motion of particles, such as in particle accelerators, or from the motion of larger objects, such as in nuclear reactions. However, the amount of mass produced will depend on the amount of kinetic energy being converted.
The conversion of kinetic energy to mass is significant because it demonstrates the relationship between energy and matter, and it is a key concept in understanding the fundamental laws of physics. It also has practical applications, such as in nuclear energy and medical imaging technologies like PET scans.
According to Einstein's equation, there is no theoretical limit to the amount of mass that can be produced from kinetic energy. However, in practical applications, there are limitations based on the amount of energy available and the efficiency of the conversion process. Additionally, the production of large amounts of mass can have significant consequences, such as in the formation of black holes in extreme astrophysical events.