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Suppose a mercury thermometer is prepared such that its bulb is in contact with a heat source at temperature T. The length of the responding mercury column is L. Now, imagine that the bulb defines the origin of coordinates of a lab frame such that the thermometer lies on its x-axis with +L as the coordinate of the column end. A relativistic observer moving along the x-axis measures the length of the column Evidently, that observer would measure the Lorentz contracted length L/gamma, and thus, relative to an identical thermometer set-up in his frame, would infer a temperature Tob = T/gamma.

However, from a purely thermodynamic point of view, the temperature of one body cannot be registered by another (say a thermometer) unless those bodies are in a thermal contact that allows a small amount of heat to be absorbed by the thermometer. Moreover, starting from its first contact with the thermometer, the reading cannot occur until thermal equilibrium is established.

It thus seems that the thought experiment above is the wrong set-up because the bulb of the observer thermometer must be dipped into the lab frame heat bath as it goes by. Assuming a big lab system so that enough time has passed for the two systems to come into thermal equilibrium, they would be at the same temperature.

In other words, the temperature is a Lorentz scalar, and as noted above, this means that the Boltzmann constant transforms as kob = k(gamma)

Also noted above, if ice freezes at 273 K in the lab frame, and it appears to freeze at, say, 273/gamma in the observer frame, there's a paradox-one resolved by appeal to thermodynamic postulates.

Suppose a mercury thermometer is prepared such that its bulb is in contact with a heat source at temperature T. The length of the responding mercury column is L. Now, imagine that the bulb defines the origin of coordinates of a lab frame such that the thermometer lies on its x-axis with +L as the coordinate of the column end. A relativistic observer moving along the x-axis measures the length of the column Evidently, that observer would measure the Lorentz contracted length L/gamma, and thus, relative to an identical thermometer set-up in his frame, would infer a temperature Tob = T/gamma.

However, from a purely thermodynamic point of view, the temperature of one body cannot be registered by another (say a thermometer) unless those bodies are in a thermal contact that allows a small amount of heat to be absorbed by the thermometer. Moreover, starting from its first contact with the thermometer, the reading cannot occur until thermal equilibrium is established.

It thus seems that the thought experiment above is the wrong set-up because the bulb of the observer thermometer must be dipped into the lab frame heat bath as it goes by. Assuming a big lab system so that enough time has passed for the two systems to come into thermal equilibrium, they would be at the same temperature.

Apparently the temperature is a quantity that evolves into a Lorentz scalar through the establishment of thermal equilibrium.

Suppose a mercury thermometer is prepared such that its bulb is in contact with a heat source at temperature T. The length of the responding mercury column is L. Now, imagine that the bulb defines the origin of coordinates of a lab frame such that the thermometer lies on its x-axis with +L as the coordinate of the column end. A relativistic observer moving along the x-axis measures the length of the column Evidently, that observer would measure the Lorentz contracted length L/gamma, and thus, relative to an identical thermometer set-up in his frame, would infer a temperature Tob = T/gamma.

However, from a purely thermodynamic point of view, the temperature of one body cannot be registered by another (say a thermometer) unless those bodies are in a thermal contact that allows a small amount of heat to be absorbed by the thermometer. Moreover, starting from its first contact with the thermometer, the reading cannot occur until thermal equilibrium is established.

It thus seems that the thought experiment above is the wrong set-up because the bulb of the observer thermometer must be dipped into the lab frame heat bath as it goes by. Assuming a big lab system so that enough time has passed for the two systems to come into thermal equilibrium, they would be at the same temperature.

As noted above, if ice freezes at 273 K in the lab frame, and it appears to freeze at 273/gamma in the observer frame, there's a paradox-one resolved by appeal to thermodynamic postulates.

Suppose a mercury thermometer is prepared such that its bulb is in contact with a heat source at temperature T. The length of the responding mercury column is L. Now, imagine that the bulb defines the origin of coordinates of a lab frame such that the thermometer lies on its x-axis with +L as the coordinate of the column end. A relativistic observer moving along the x-axis measures the length of the column Evidently, that observer would measure the Lorentz contracted length L/gamma, and thus, relative to an identical thermometer set-up in his frame, would infer a temperature Tob = T/gamma.

However, from a purely thermodynamic point of view, the temperature of one body cannot be registered by another (say a thermometer) unless those bodies are in a thermal contact that allows a small amount of heat to be absorbed by the thermometer. Moreover, starting from its first contact with the thermometer, the reading cannot occur until thermal equilibrium is established.

It thus seems that the thought experiment above is the wrong set-up because the bulb of the observer thermometer must be dipped into the lab frame heat bath as it goes by. Assuming a big lab system so that enough time has passed for the two systems to come into thermal equilibrium, they would be at the same temperature.

In other words, the temperature is a Lorentz scalar, and as noted above, this means that the Boltzmann constant transforms as kob = k(gamma)

Also noted above, if ice freezes at 273 K in the lab frame, and it appears to freeze at, say, 273/gamma in the observer frame, there's a paradox-one resolved by appeal to thermodynamic postulates.

Suppose a mercury thermometer is prepared such that its bulb is in contact with a heat source at temperature T. The length of the responding mercury column is L. Now, imagine that the bulb defines the origin of coordinates of a lab frame such that the thermometer lies on its x-axis with +L as the coordinate of the column end. A relativistic observer moving along the x-axis measures the length of the column Evidently, that observer would measure the Lorentz contracted length L/gamma, and thus, relative to an identical thermometer set-up in his frame, would infer a temperature Tob = T/gamma.

Suppose a mercury thermometer is prepared such that its bulb is in contact with a heat source at temperature T. The length of the responding mercury column is L. Now, imagine that the bulb defines the origin of coordinates of a lab frame such that the thermometer lies on its x-axis with +L as the coordinate of the column end. A relativistic observer moving along the x-axis measures the length of the column Evidently, that observer would measure the Lorentz contracted length L/gamma, and thus, relative to an identical thermometer set-up in his frame, would infer a temperature Tob = T/gamma.

However, from a purely thermodynamic point of view, the temperature of one body cannot be registered by another (say a thermometer) unless those bodies are in a thermal contact that allows a small amount of heat to be absorbed by the thermometer. Moreover, starting from its first contact with the thermometer, the reading cannot occur until thermal equilibrium is established.

It thus seems that the thought experiment above is the wrong set-up because the bulb of the observer thermometer must be dipped into the lab frame heat bath as it goes by. Assuming a big lab system so that enough time has passed for the two systems to come into thermal equilibrium, they would be at the same temperature.

As noted above, if ice freezes at 273 K in the lab frame, and it appears to freeze at 273/gamma in the observer frame, there's a paradox-one resolved by appeal to thermodynamic postulates.