Understanding Thermal Radiation and the Uncertainty Principle

[Meson080]

remember that when a crystal is cooled to absolute zero, the atoms don't stop moving, they still jiggle. Why? If they stopped moving, we would know where they were and that they had zero motion, and that is against the uncertainty principle. We can't know where they are and how fast they are moving, so they must be continually wiggling in there!

thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation.

Isn't the above two statements contrary?

From Feynman's quote, the atoms must be wiggling even at absolute zero. Thus we can expect the generation of electromagnetic radiation even at absolute zero. In contrast, according to wikipedia, generation of electromagnetic radiation is possible only if the matter has temperature greater than absolute zero.

 

[Orodruin]

That moving charges generate EM radiation is a classical concept and at T=0 QM effects will be at work and everything will be in the ground state. By definition, no energy can be emitted from the ground state simply because there is no lower energy state for the system to go to. It is the same reasoning that stops the hydrogen atom from breaking down. If classical thinking would be applied as in "the electron moves around the proton" then it would radiate and eventually lose all its energy. Instead, a hydrogen atom in the ground state will not be able to radiate photons.

 

[Nugatory]

Isn't the above two statements contrary?

The wikipedia statement is incomplete. Moving charged particles emit radiation only if they can also reduce their energy by slowing down (because energy is conserved, and the radiation carries some energy away, the energy left behind must less than what we started with). If we're already at the lowest possible energy level, we can't radiate because we can't further reduce our energy.

The Feynman statement is also incomplete, as no object can be cooled all the way down to absolute zero. We can get very close, but not all the way there (to see this, think about how we cool anything to a given temperature; we expose it to something even colder. There's nothing colder than absolute zero). Thus, there's always some minuscule amount of thermal radiation from the object; and the energy loss from this radiation is balanced by energy gain from equally minuscule radiation coming in from our equally cold surroundings.

 

[HallsofIvy]

You are making a fundamental logical mistake. The statement "if A then B" says that if A is true then B is true. It does NOT say what happens if A is not true. In particular, "B" may be true even when "A" is false.

The statement "All matter with a temperature greater than absolute zero emits thermal radiation" says what happens if the temperature is greater than absolute zero. It does NOT say anything about what happens at absolute zero which what Feynman's statement is about.

 

[Meson080]

Be Cool alone!

To see this, think about how we cool anything to a given temperature; we expose it to something even colder. There's nothing colder than absolute zero

From the below source, I disagree that, to cool anything to a given temperature, we need to expose it to something even colder.

MIT team achieves coldest temperature ever-Sept 11, 2003

At such low temperatures, atoms cannot be kept in physical containers, because they would stick to the walls. Furthermore, no known container can be cooled to such temperatures. Therefore, the atoms are surrounded by magnets, which keep the gaseous cloud confined. "In an ordinary container, particles bounce off the walls. In our container, atoms are repelled by magnetic fields," explained physics graduate student Aaron Leanhardt.
For reaching the record-low temperatures, the MIT researchers invented a novel way of confining atoms, which they call a "gravito-magnetic trap." As the name indicates, the magnetic fields act together with gravitational forces to keep the atoms trapped.

 

[Travis_King]

Those guys use a method of laser/Doppler cooling, which also has a lower limit on how much energy/momentum it can force the atom to lose by emitting photons (called the Doppler cooling limit). I'm not sure if the lower limit of the method MIT used is calculated using the same Doppler cooling limit, or if there are other factors involved, but there you go.

 

[Meson080]

Lets fly with Hallsoflvy!

You are making a fundamental logical mistake. The statement "if A then B" says that if A is true then B is true. It does NOT say what happens if A is not true. In particular, "B" may be true even when "A" is false.

The statement "All matter with a temperature greater than absolute zero emits thermal radiation" says what happens if the temperature is greater than absolute zero. It does NOT say anything about what happens at absolute zero which what Feynman's statement is about.

Sorry, it is difficult to understand your "understanding" with the present bunch of words given. It will be useful for everyone, if you can increase the clarity. Everyone, atleast me will be waiting.

 

[Jano L.]

Isn't the above two statements contrary?

From Feynman's quote, the atoms must be wiggling even at absolute zero. Thus we can expect the generation of electromagnetic radiation even at absolute zero. In contrast, according to wikipedia, generation of electromagnetic radiation is possible only if the matter has temperature greater than absolute zero.

For physics, in general good textbook is much more reliable than articles on Wikipedia. In this case, however, there is no problem with either statement. The quote from the Wikipedia only says that thermal radiation requires non-zero temperature. The movement Feynman talks about is called zero-point motion and hypothetical radiation it produces does not need to be thermal. There is a theory - stochastic electrodynamics - where similar radiation - the zero-point radiation - is not thermal, but has invariant temperature-independent character.

 

[Meson080]

By definition, no energy can be emitted from the ground state simply because there is no lower energy state for the system to go to.

Moving charged particles emit radiation only if they can also reduce their energy by slowing down (because energy is conserved, and the radiation carries some energy away, the energy left behind must less than what we started with). If we're already at the lowest possible energy level, we can't radiate because we can't further reduce our energy.

The movement Feynman talks about is called zero-point motion and hypothetical radiation it produces does not need to be thermal.

Nugatory and Orodruin seems to be arguing that, the radiation (not mentioned properly whether it is thermal or not) can't be emitted.

On the other hand, Jano L seems to be arguing that, the radiation ("hypothetical", but not thermal) is emitted.