Hello, On Mon, Feb 20, 2012 at 9:54 PM, Harold E. <[email protected]> wrote: > On 20 fév, 12:44, Sergiu Ivanov <[email protected]> wrote: >> >> I'm far from being an expert in this field, so my questions arise >> rather from curiosity than from some serious background >> considerations: what uses do you envision for this feature of >> recovering the right constant? > > The use of constants as units is in the heart of theoretical physics, > since in some way it emphases the unification of several concepts. I > will use the example of special relativity: Einstein found the formula > E = mc², which means that the mass and the energy are exactly the same > thing and that we do not need to distinguish between these two > concepts, because if in some formula you use one concept, you can > immediately replace it with the other with the help of this formula. > The same happen for space and time (one can see this with the > Lorentz's transformation formula).
Aha, I think I've read about this approach to introducing units before; your explanation brings up some vague memories in my head. > Then, even if we do all the computations without writing explicitly > these constants, it's useful to write them at the end for several > reason: > 1. We are not accustomed to these units, because the value of > quantities are very different than the one of our daily experiences (v > = 0.3 c = 100000 km/s, v = 100 km/h ~ 10⁻¹⁰), and a formula will > generally "speak" us better if we can see these fundamental constants. > 2. Because of (1), our usual unit systems are very different, and so > it is easier for experiences and many other things to be able to > convert. > 3. Again because of (1) when you learn special relativity and so on, > you prefer to keep these factors. I see, this is clear. >> On the other hand, recovering the constant requires quite a bit of >> analysis of the environment. For example, in a certain environment, I >> may use E to denote something different from the total energy. > > Yes of course, here this formula was only an example. The idea to > recover the right factors are for example to say that in the left > side, the unit is J.c⁻², and in the right side it's kg. So we can > extract the good factors. If we don't have this possibility, we can > also say that "I want that this formula has the dimension X", which is > useful if people don't want to take in account the constants at the > beginning. Going back to your original idea of manipulating units as vectors, finding the necessary factors is equivalent to solving vector equations with cross-products and to solving matrix equations (to some extent), right? To me, it looks like implementing units with a sufficiently generic approach may give you support for constants as units almost for free. If the user can define their own base and derived units, then they may just choose another basis and specify how units are derived. If you can fully have custom units, you can surely have constants as units. Another impression of mine is that having custom units is actually the right way to go towards the goal of having constants as units. I guess you have thought of these things yourself already, so I'm just dumping my reasoning for the sake of providing a point of view. > No problem, I posted this message with this goal! I hope that my > explanations help you. There is a very good article of Jean-Marc Lévy- > Leblond on this topic (www.springerlink.com/content/ > kh1n15r56q0682v8/), but more on the philosophical point of view. Yes, your explanations made the whole thing much clearer to me, thank you for your effort! :-) (and sorry for my slow response) Sergiu -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
