Doesn't this experiment signify that inertial frames are not equivalent?

Question

When we talk about kinetic energy of a body, it is actually the combined kinetic energies of all the atoms in that body. Now suppose a body is at rest. So its atoms would have some internal random motion and thus we can measure its temperature. But suppose it starts moving with a constant velocity $v$, so it will have kinetic energy $\frac{1}{2} mv^2$. So the kinetic energy of each atom is increased. So this means that the body will becomes hotter than earlier. But from the frame of body itself, it was at rest and thus there should be no change in its temperature although the temperature of the atoms of the ground should change.

How is this even possible? Why is temperature of the same body different when seen from two different inertial frames? Does this mean that it is not compulsory that two inertial frames are equivalent?

Note : I tried to search for a similar question on this site and I found this question and the selected answer literally seems contradicting to me and my ideas. The answer talks about all three possibilities and all the possibilities are based on pure mathematics (I guess), so I would like to know

why is there even a possibility of the temperature of a moving body to fall down or remain constant? Shouldn't it increase?

Or if I am wrong somewhere please correct me.

Please try to give a purely physical reason. It would be more appreciated since I am just a high schooler and don't understand those transformational mathematics.

Edit: I don't know why is the question closed. The question linked (as a dupe of ) , gives a wrong information that since pressure is invariant that's why temperature is invariant too. But this implies that pressure is more fundamental than temperature which is not true. So it will be helpful if the question is reopened and someone provides a proper reason for temperature invariance.

Edit 2 : In thermodynamics we can change the internal energy of a system (and thus change the temperature) by doing work on it . Then why can't the work of friction change our body's temperature ?

Answer 1

This question is based on two misunderstandings. One is regarding the nature of thermal energy and the other is regarding the equivalence of inertial frames.

First, regarding thermal energy. Thermal energy is energy which is in a large number of unknown internal degrees of freedom. The overall KE of the entire system is not part of the thermal energy because it is not an internal degree of freedom and it is not unknown. Accelerating the system as a whole does not directly imply an increase in temperature. Also, although not directly related to your question, it is important to know that thermal energy is not always kinetic energy except for ideal gasses. For other materials the internal degrees of freedom will contain other forms of energy as well.

Second, regarding the equivalence of inertial frames. Just because the quantity is different in both frames does not imply a violation of the equivalence between the frames. In order for there to be a violation it is necessary that the laws of physics be different in the two frames. If a law of physics were “moving objects are hotter” then if I had a heat bath and two thermometers and you had an identical heat bath and two thermometers then I would measure my heat bath to be cool and yours to be hot, and you would measure your heat bath to be cool and mine to be hot. The laws would still be symmetric and you could not use the discrepancy to identify a reference frame.

Answer 2

So this means that the body will becomes hotter than earlier. But from the frame of body itself , it was at rest and thus there should be no change in its temperature although the temperature of the atoms of the ground should change.

Assuming the velocity of the body is non relativistic (i.e.,much less than the speed of light), the temperature of the body should not change due to it moving at constant velocity.

Temperature is based on the random translational kinetic energy of the atoms and molecules with respect to the center of mass of the object. Movement of the center of mass at constant speed does not change the kinetic energy of the particles with respect to the center of mass.

I like to call the kinetic energy and potential energy of the center of mass the objects external energy, that is, e.g. its kinetic and gravitational potential energy with respect to an external frame of reference, such as the ground. The microscopic kinetic energy of the particles of the object with respect to the COM is the internal microscopic kinetic energy of the object. The intermolecular forces between particles are the microscopic potential energy part of the internal energy. These concepts are illustrated in the diagram below.

How is this even possible ? Why is temperature of the same body different when seen from two different inertial frames ? Does this mean that it is not compulsory that two inertial frames are equivalent ?

Again, at non relativistic speeds (where the situation gets more complex) the temperature of the same body should be the same as seen from two inertial frames. Per Einstein's relativity principle, all inertial frames are equivalent for the performance of all physical experiments. If temperatures measured on an object were different in different inertial frames, it would violate this principle.

Hope this helps.

Answer 3

Temperature is determined by the random motion of atoms or molecules within a substance. This does not change if the substance is moved or accelerated (a non- random action)(unless there is kinetic friction involved).