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We say the cosmic microwave background radiation “has a temperature” of 2.7K.

Does this mean it has a temperature in the way we say the air around a warm lightbulb has a temperature of 120° or in the sense that the mix of electromagnetic waves given off by the lightbulb are like those emitted by a blackbody at 3000K?

Is the temperature of the electromagnetic field at some point in space the temperature “of the space” in which the field exists, or the temperature of a black body that would emit the spectrum of the EM field in the space if the blackbody were there at that moment.

I hear people speak as if the first, but I think they mean the second. Yes?

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  • $\begingroup$ CMB spectrum corresponds to a black-body radiation of temperature of $2.7\,\text{K}$ degrees. So, second definition. In addition to that I want to notice that ideal empty space (ideal vacuum) can't have any temperature, or in other words empty space temperature would be $0 \,\text{K}$ degrees. If you get temperature of any object greater than zero degrees of Kelvins, this means that your object is not an empty space. $\endgroup$ May 15, 2020 at 15:04

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It means the mix of electromagnetic waves "given off" by the CMB (really: "that constitute the CMB") are like those emitted by a blackbody at 2.7K.

Temperature is a property of an ensemble of particles (photons in this case, could be air molecules, or even virtual particles) but not of space itself.

Yes, people speak as if the first but mean the second.

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