B Manipulating quantities with natural units

etotheipi

I'm only really just learning how natural units work so forgive me if this seems like a silly question.

I was just wondering if someone could verify whether the following line of reasoning is valid (I will use joules instead of electron volts just so we can ignore the e conversion factor for now). I'm just going to convert say 5J into a mass.

I first set c to 1 light second per second. Then noting that $$m = \frac{E}{c^{2}}$$ I say that $$m = \frac{5J}{(1 ls s^{-1})^{2}} = 5 \frac{J}{(ls s^{-1})^{2}}$$ Though this is an ugly unit so I'll just write it as $$5 \frac{J}{c^{2}}$$ When I feel like converting back into SI units, this is equivalent to $$5 \frac{J}{(3*10^{8} m s^{-1})^{2}}=\frac{5}{(3*10^{8})^{2}} \frac{J}{(m s^{-1})^{2}}=\frac{5}{(3*10^{8})^{2}} \frac{kg m^{2} s^{-2}}{(m s^{-1})^{2}}=\frac{5}{(3*10^{8})^{2}} kg$$

The logic seems ok to me when I consider the unit to be just as important a part of the overall quantity as the numerical value preceding it and so I treat it just like a normal algebraic variable.

I guess the main point of my question is whether we can move values between the units and their numerical 'coefficients' so to speak. So something like $$300 MeV / c^{2}$$ can be rearranged to $$\frac{300}{(3*10^{8})^2} \frac{MeV}{(m s^{-1})^{2}}$$ and so on.

Related Other Physics Topics News on Phys.org

mitochan

Hello.
I guess the main point of my question is whether we can move values between the units and their numerical 'coefficients' so to speak.
It seems OK to me as in plain case,
$$300\ km/h=300\times 1000 \ m/h = 300/3600 \ km/s$$

David Lewis

If you use light-second as the unit of length, then you must also use it in your unit of energy.
[Energy] = ML2T-2
(Joule uses meter as the unit of length.)

"Manipulating quantities with natural units"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving