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  1. We know that cosmic microwave background temperature is about 2.7K. But what temperature we will measure in space using a simple Kelvin thermometer in the shadow? Can it be lower than 2.7K?

  2. Suppose a space ship is flying in our solar system with a speed of 0.99c relative to earth. Will it measure a different temperature? Much higher? And if so, will the intense heat cause the ship itself to warm up?

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Re question 1: It's relatively simple to calculate temperatures in space because since there is no air, there is no heat conduction or convection. A body in space can only absorb heat by absorbing radiation, and can only lose heat by radiating.

The CMB behaves like a black body with a temperature 2.725K, so any body in equilibrium with it will also be at this temperature. If there are no other sources of heat your thermometer will have the same temperature as the CMB. However it's hard to achieve this. You could argue that you could shade your thermometer from the Sun, but whatever you use as a sunshade will eventually heat up and start radiating, and it will then heat your thermometer. The only way you'd get your thermometer down to 2.725K would be to put it in interstellar space or possibly even intergalactic space.

Re question 2: Travelling fast will indeed blue shift the CMB and raise it's temperature, and that will heat your ship. In principle if you travel fast enough the blue shifted CMB would vaporise your spaceship.

This actually happens to the Earth (well, not the vaporising bit!). The CMB is hotter in the direction of travel of the Earth. See http://apod.nasa.gov/apod/ap010128.html for details.

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Thanks, John. Don't you believe that ship vaporization put some strain on postulate 1 in SR? after all, there is a factor you can measure to distinguish between inertial systems: if you are in 0 speed relative to the CMBR you freeze to death. if you move relative to it, you are a toast. –  MIKE Jun 4 '12 at 7:48
    
No. After all you'd be equally vaporised if the ship was standing still and the CMB was moving at 0.99999C. The CMB looks isotropic in one particular reference frame (co-moving co-ordinates) but there's nothing absolute about this frame. –  John Rennie Jun 4 '12 at 9:20
    
Thanks. Would it be theoretically possible to built a "temperature clock" which its input will be space's temperature and its output will be the time that passed since the big bang calculated using Friedman equation and Dopller's effect? and would not 2 travelers in space at the same point and moment measure the same time exactly? And if so, what about time dilation? –  MIKE Jun 4 '12 at 18:15
    
Yes, such a clock would be easy to use. In comoving co-ordinates and assuming an FLRW metric the CMB temperature is related to the redshift by T = 2.725(1 + z), and the redshift can be calculated as a function of time (though I don't have the function to hand). If you're moving relative to the comoving frame then you'll see a dipole anisotropy in the CMB, but you can use the anisotropy to calculate your speed relative to the CMB and work back to get the temperature in the comoving frame. –  John Rennie Jun 4 '12 at 18:30
    
And what about time dilation? after all 2 observers will always measure the same time regardless of their velocity and history, isn't it so? –  MIKE Jun 4 '12 at 18:44
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