- #1

mSSM

- 33

- 1

I have the following two equations, where [itex]\lambda=\lambda(t)[/itex]. I am not so sure about [itex]S[/itex] (which is somewhat my problem):

[tex]\frac{\mathrm{d}S}{\mathrm{d}t} = \left( \frac{\mathrm{d}\lambda}{\mathrm{d}t} \right)^2[/tex]

Which is supposed to mean:

[tex]\frac{\mathrm{d}S}{\mathrm{d}\lambda} = \frac{\mathrm{d}\lambda}{\mathrm{d}t}[/tex]

Now, I thought that what is essentially being done there is multiplying the first equation such that we get:

[tex]\frac{\mathrm{d}S}{\mathrm{d}t}\frac{\mathrm{d}t}{\mathrm{d}\lambda} = \frac{\mathrm{d}\lambda}{\mathrm{d}t}[/tex]

But if I now assume that:

[tex]\frac{\mathrm{d}S}{\mathrm{d}t}\frac{\mathrm{d}t}{\mathrm{d}\lambda} = \frac{\mathrm{d}S}{\mathrm{d}\lambda}[/tex]

doesn't that in turn mean that [itex]t[/itex] is a function of [itex]\lambda[/itex]? Mathematically this seams sounds (to me), but physically this does not make so much sense, if [itex]t[/itex] is the time.