# Temperature and observer velocity

• Iraides Belandria
In summary, some investigators, including Einstein and Planck, have found expressions relating temperature and the velocity of an observer, such as T=To[Square root(1-U2/C2)]. However, this raises the question of how temperature, a thermodynamic property, can depend on the observer's velocity. Tolman's book suggests this relationship, but it is not clear how it aligns with the definition of a thermodynamic property. Further research and clarification is needed on this topic.
Iraides Belandria
Some investigators, including Einstein and Planck, have found expressions relating temperature and the velocity of an observer . ¿ How is it possible if temperature is a thermodynamic property independent of trajectory and time?

Which expressions are you referring to?

U haven't read Tolman's book,have you ? I've reccomended it to you in another thread on a similar topic...

Daniel.

dextercioby said:
U haven't read Tolman's book,have you ? I've reccomended it to you in another thread on a similar topic...

Daniel.

Dear dextercioby, I have read Tolman´s book . Tolman suggest that T=To[Square root(1-U2/C2)]. However, ¿ How is it possible that temperature depends on the observer velocity if temperature is a thermodynamic property ?. By definition, a thermodynamic property only depends on the state of the system and it is independent of velocity.

I don't think temperature is frame dependent. A fast cold brick is still a cold brick. It doesn't heat up just because it is going fast.

James R said:
I don't think temperature is frame dependent. A fast cold brick is still a cold brick. It doesn't heat up just because it is going fast.

I agree with you, but the equation presented in Tolman´s book suggests that temperature decreases for a frame moving at a certain velocity. When velocity tends to the velocity of light, the temperature is zero, according to above mentioned equation. Although, I am not sure, Einstein and Planck derived a similar equation, too. ¿What do you think, about it?

James R said:
I don't think temperature is frame dependent. A fast cold brick is still a cold brick. It doesn't heat up just because it is going fast.

suppose the brick is glowing dull red, if observed at rest

and now suppose the brick is approaching you at 3/5 speed of light.

wouldnt the thermal glow from the brick be doppler shifted?

so wouldn't the light coming to you from the brick seem a lot hotter?

But do we call the brick hotter because the thermal glow from it is hotter? I suppose it comes down to definitions of what is something's temperature, operationally------how do you plan to measure it etc.

I would not try to respond to anyone who didnt have a URL to some source and an exact page reference so that one could easily see exactly what he was talking about

it depends, IMO, on context so he has to provide a link to something definite online, some definite paragraph or sentence on some webpage.

Last edited:
I'd like to see the derivation of the equation by Einstein and/or Planck before commenting further.

Just a thought here, since some of the moleculus of a body could be moving in the direction opposite to the direction of motion of the body, the relative velocities would cancel out to some extent and would appear to you at a lesser temperature. Is that right?

## 1. What is the relationship between temperature and observer velocity?

The relationship between temperature and observer velocity is known as the Doppler effect. As an observer moves towards a source of heat, the perceived temperature will increase due to the compression of the wavelength of the heat waves. Similarly, if an observer moves away from a source of heat, the perceived temperature will decrease due to the stretching of the wavelength.

## 2. How does the Doppler effect affect temperature measurements?

The Doppler effect can affect temperature measurements by altering the perceived temperature based on the relative motion between the observer and the heat source. This can lead to inaccurate readings if not taken into account. However, modern instruments are designed to compensate for the Doppler effect, resulting in more accurate temperature measurements.

## 3. Can temperature be measured accurately while in motion?

Yes, temperature can be measured accurately while in motion as long as the Doppler effect is taken into account. By using modern instruments that are designed to compensate for the effect of observer velocity, temperature can be measured accurately regardless of an observer's motion.

## 4. How does the speed of the observer affect the perceived temperature?

The speed of the observer can affect the perceived temperature based on the direction of their motion relative to the heat source. If an observer moves towards a source of heat, the perceived temperature will increase, whereas if they move away from the source, the perceived temperature will decrease. The faster the observer's velocity, the more significant the effect will be.

## 5. What other factors can affect temperature measurements besides observer velocity?

Besides observer velocity, other factors that can affect temperature measurements include atmospheric conditions, altitude, and the type of material being measured. These factors can impact the amount of heat energy being transferred and can affect the accuracy of temperature readings. Additionally, human error and instrument calibration can also play a role in temperature measurement accuracy.

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