It seems that we can get infinitely small but we will never reach a finite amount of energy that we could call the smallest amount. How can this be explained?

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    $\begingroup$ Your question is very vague, would you care to elaborate? Because in classical mechanics, for example, we can get $E = 0$, for a rest particle (defining the potential at our will). $\endgroup$ – matrp Aug 8 '16 at 20:20
  • $\begingroup$ As I know, there is no lower limit to energy, but there is for energy * time, it is the Planck-constant. $\endgroup$ – peterh - Reinstate Monica Aug 8 '16 at 20:35
  • $\begingroup$ I guess, excluding 0, you could say 1 quantum... but exactly how much energy that is depends on context and still doesn't technically have a lower bound. $\endgroup$ – Jason C Aug 8 '16 at 20:38
  • $\begingroup$ I guess this question could equally be applied to mass, space and time. It bothers me that apparently we can't see how it is possible to have "one" of anything in real life. When we talk about units of this and that, we are only able to say that in relative terms. I wonder how then we can talk about particles and quanta when there seem to not exist any such a thing. $\endgroup$ – Mehdi Aug 9 '16 at 19:01
  • $\begingroup$ Do a search for "photon rest mass" or "electromagnetic field rest mass". $\endgroup$ – CuriousOne Aug 10 '16 at 1:37

A single photon carries the energy $E=\frac{hc}{\lambda}$, where $\lambda$ is its wavelength. As wavelength increases, energy decreases. Technically speaking, there is no upper limit on wavelength, thus there is no lower limit on energy. Strictly speaking, however, a wavelength larger than the size of the observable universe would redshift to infinity before it completed even one cycle. It would practically not exist. Still, there is no true non-zero lower bound on energy.

  • $\begingroup$ Just for fun, this lower limit in today's universe ($\lambda = 14\rm\,Gly$) is $10^{-32}\rm\,eV$. $\endgroup$ – rob Aug 8 '16 at 20:30
  • $\begingroup$ @rob ..... what number is this $14~Gly$? The radius of the observable universe is approx. $45~Gly$ $\endgroup$ – Jim Aug 8 '16 at 20:32
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    $\begingroup$ It's the age of the universe $1/H_0$ in length units. I considered using your value, the radius of the comoving horizon, decided the factor of three difference was not interesting, and flipped a coin. $\endgroup$ – rob Aug 8 '16 at 20:38
  • $\begingroup$ @rob as long as you flipped a coin, I completely support your choice of wavelength $\endgroup$ – Jim Aug 8 '16 at 20:40
  • $\begingroup$ I appreciate the comments. I guess what this means is that we can only know the smallest amount we can measure now. But there is no known unit of energy in actual universe, as far as we know. $\endgroup$ – Mehdi Aug 9 '16 at 19:03

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