# Why wouldn't Hubble's Law be directly in units of frequency?

Maybe using this as an example:

The energy of a particular color of yellow light is $3.44 \times 10^{-22}$ $kJ$

So if I want to find frequency of that light, I take that number, divide by $h$ and I get $5.19 \times 10^{-14}$ (or something like that) which is in what units? Hz?

What if I wanted to know the frequency of the light after travelling say 1 billion light years?

Is there a version of Hubble's Law (and parameter I'd assume) in the form of $f_\text{new} = f_\text{original} \times H_u$ where $H_u$ is a version of Hubble's Parameter in units appropriate for the units of frequency?

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"The energy of a particular color of yellow light is 3.44E-22 kJ" ::facepalm:: OK. So that's a little badly stated. Presumably the correspondent meant that the energy of a single photon was such and so. In any case we can't answer your questions (what units?) until you tell us the units of the value of $h$ you used. And once you've done that the answer should be clear, no? – dmckee♦ Feb 6 at 16:03

## 2 Answers

Really the quantity you are seeking is redshift, not the Hubble parameter. Redshift $z$ is defined by $$f_\text{observed} = \frac{f_\text{emitted}}{1+z}.$$ Now, if you want to relate redshift to proper distance $D$, you can use the Hubble relation $$H_0 D = cz,$$ which means $$f_\text{observed} = \frac{f_\text{emitted}}{1+H_0D/c}.$$ For distances large compared to $c/H_0$, this becomes $$f_\text{observed} \approx \frac{c}{H_0D} f_\text{emitted}.$$

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@mikethematrix To come to my point of view re your question, let me first make sure I interpret your question correctly. Hubble's law for the expansion of the universe states that the galaxies are receding from one another at speeds that are proportional to their distance, d, between them. Then, for two galaxies at distance d we have $v=Hd.$ Clearly the 'constant' H has units $s^{-1}$. Are you asking why could we not put $H$ in units of $Hz$ instead of having it in $s^{-1}$, probably motivated by the equation $v=\omega R$ from circualr motion and perhaps inspired by Planck's law $E=hf$?

If this is what you mean, then you need an answer that is different from that given by Chris. In my opinion, the answer in this case is, no, you cannot put $H$ in $Hz$. The reason is that Hubble's law does not describe a periodical phenomenon like in a circular motion. So the 'constant' $H$ is far more fundamental than the frequency of a periodical phenomenon. At any time t, it relates to the age of the universe:

Age of universe = $\frac 1H$.

If this is not how you meant your question, then Chris's answer is a nice answer which I have increased its vote by 1.

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