1

I was looking at a video called How Hot Can It Get, and at 7:08, the host Michael states that

if an object were to reach a temperature of $1.41 \times 10^{32}$ K (planck temperature), the radiation it would emit would have a wavelength of $1.616 \times 10^{-26}$ nm (planck distance).

He then goes on to say that we don't know what would happen at that point. However, this thought brought about another question in my mind. Is there a quantum delta wavelength? Does the planck length imply that difference between two different wavelengths could not be smaller than it?

I'm thinking that one could test this by taking a beam of white light and put it through a prism to diverge it. Then from the resulting diverging light, diverged it even more with another prism, and from the result of that, diverge it even more, and so on. Alternatively, after the first prism, just go really really far away. In either case, if there is a quantium $\Delta \lambda$, one should get to a point where eventually the spectrum could be observed as non-continuous.

Qmechanic
  • 201,751
Adrian
  • 499
  • 1
    When people ask questions of the form "If the Planck length is the shortest distance, then...," the answer is pretty much always: (1) We don't really know, because we don't have a theory of quantum gravity. (2) But to the extent that we do have some inklings about quantum gravity, the Planck length is not a minimum length or a quantization of length. This is a wrong statement made in popularizations. –  Jan 10 '20 at 01:16
  • @BenCrowell, so you are saying that the planck length doesn't imply the existence of a minimum $\Delta \lambda$? Or that this isn't known at this time? – Adrian Jan 10 '20 at 01:28
  • Adrian, according to Special Relativity (SR), the Planck length is not an invariant, i.e., two observers in relative uniform motion would not generally agree that, e.g., the wavelength of some radiation is a Planck length. Obligatory link to Doubly special relativity: "a modified theory of special relativity in which there is not only an observer-independent maximum velocity (the speed of light), but an observer-independent maximum energy scale and minimum length scale (the Planck energy and Planck length)." – Alfred Centauri Jan 10 '20 at 02:49
  • Possible duplicates: https://physics.stackexchange.com/q/9720/2451 and links therein. – Qmechanic Jan 10 '20 at 03:36

0 Answers0