My question goes from Phys.SE where people advised me to ask my question here.

I always learn in maths and physics when something is a constant in an equation we have to put it before which varies. Some days ago I just thought about it.

When you say a function is linear you say something like, let $f$ be a linear function such as $f(x)=ax$. ...

Now, why, when we say the energy is a linear function of the mass we write, $$E=mc^2$$

Instead of, $$E=c^2 m$$ because light speed is a constant.

Is this something aesthetic, does Einstein wrote it like that and then everybody does? Why don't we respect the convention when we do relativity?

My question is more general because if we look closely to GR equations when there are product terms with the speed of light then the speed of light is always the second. For example we also write $$E^2=m^2c^4+p^2c^2$$ which should be written as $$E^2=c^4m^2+c^2p^2$$

And there are many others.

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    $\begingroup$ Momentum is written $p=mv$ since, for a given particle, mass in constant and momentum is proportional to velocity. Also, for kinetic energy, $KE=\frac 12mv^2$ for similar reasons. So we got used to writing mass before velocity, especially when the velocity is squared. We just continue that pattern for Einstein's equation. I don't have references for this, so I write this as a comment. $\endgroup$ Apr 22, 2017 at 0:26
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    $\begingroup$ This seems to fall way, way below any reasonable level of significance or intrinsic interest. This is history of science and math, not trivia of science and math. In any case, relativists today normally work in units where c=1, so they aren't writing factors of c at all. $\endgroup$
    – user466
    Apr 22, 2017 at 22:48
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    $\begingroup$ @BenCrowell sorry to distrub you... $\endgroup$
    – ParaH2
    Apr 22, 2017 at 22:55
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    $\begingroup$ This is not the greatest question we ever had, but in my opinion it does not deserve two downvotes. We always considered questions about historically formed notational conventions as on-topic. $\endgroup$
    – Conifold
    Apr 24, 2017 at 22:57
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    $\begingroup$ @Conifold well this is not the best question I ever asked too. But I thought people would have been more open-minded. I'm not asking about (and I really don't care) how we write this equation today with (c=1) I'm just asking something which happened in the past and why it was like this. As I say sometime in the kingdom of blind the one-eyed man is king. $\endgroup$
    – ParaH2
    Apr 24, 2017 at 23:11

1 Answer 1


In his 1905-1907 papers Einstein derived the equation $E = m c^2 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ for a mass moving at speed $v$. So $mc^2$ is a constant, and the variable is $v$.


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