Wikipedia:Reference desk/Archives/Science/2024 June 23

= June 23 =

I'm looking for useful physical formulas of the form:
$$X_{total}=X_{initial}+X_{additional}$$

Where the $$Xs$$ are physical properties of the same type (e.g. of energy, or of electric charge, and likewise).

Those physical properties don't have to be denoted by the same letter in the formula.

They should be denoted by not more than three letters, excluding indices if needed.

The indices: "total", "initial", "additional", mentioned above, don't have to be mentioned in the formula, either. They should be understood, though, from the standard meaning of the letters/indices mentioned in the formula. Therefore, formulas of the type $$E_{total}=E_{potential}+E_{kinetic}$$ should be ignored, because none of those Es (=energies) is usually interpreted as "initial".

"Initial" can also mean "basic".

HOTmag (talk) 10:59, 23 June 2024 (UTC)
 * What about integrations, eg the amount of electric charge on an object = integration over time of the current flowing through a surface that encloses the object.? (+ initial charge) Graeme Bartlett (talk) 11:21, 23 June 2024 (UTC)
 * I even avoid simpler formulas, e.g. of the type $$X_{total}=X_{initial}+YT, $$ not to mention $$X_{total}=X_{initial}+\int Ydt.$$ HOTmag (talk) 12:05, 23 June 2024 (UTC)
 * Is Mass–energy equivalence one of the "useful" formulas by your definition, as applied to the Parker Solar Probe? Mike Turnbull (talk) 14:19, 23 June 2024 (UTC)
 * Your example uses too many letters. I must use three only (the Xs), and all of them should be of the same type, as indicated above. HOTmag (talk) 16:03, 23 June 2024 (UTC)
 * That's a distinction without a difference. Just call it X_displacement if the letters Y and T offend you. DMacks (talk) 21:30, 23 June 2024 (UTC)
 * Why can YT offend me? Because it also means YouTube? HOTmag (talk) 06:59, 24 June 2024 (UTC)
 * "Where the $$Xs$$ are physical properties of the same type" - they have to be for the equation to make sense. see Dimensional Analysis. i can't off hand think of a non trivial equation that is simple enough for your requirements. weight_today=weight_yesterday+change_in_weight_per_day? Greglocock (talk) 22:16, 23 June 2024 (UTC)
 * They have to be [of the same type], for the equation to make sense: Yes, of course. I'd only wanted to exclude hypothetical examples meaning eg: "What I like to talk about = energy + electric charge". Admittedly, it's only a hypothetical example, because it does not reflect any useful formula, whereas what I need should be a useful formula, as indicated in the title. This requirement also excludes your last suggestion. HOTmag (talk) 06:59, 24 June 2024 (UTC)
 * How about $$m = m_0 + \delta_m$$ from bare mass? --Amble (talk) 02:35, 24 June 2024 (UTC)
 * Yes, this is a good example. Anything else? HOTmag (talk) 06:59, 24 June 2024 (UTC)
 * See equations under Equation_of_time such as "EOT = GHA - GMHA" and following. Also see $$h_{\alpha \beta} = g_{\alpha \beta} - \eta_{\alpha \beta} \,.$$ and following at Post-Newtonian expansion. In general, this type of equation comes up when you're trying to split a difficult problem into a larger part, which can be exactly solved, and a smaller part, which can be treated as a perturbation. --Amble (talk) 17:10, 24 June 2024 (UTC)
 * Thank you. To me, the time formulas are better than the Post Newtonian expansions, because I need precise equations rather than approximations. HOTmag (talk) 18:20, 24 June 2024 (UTC)
 * Does it have to be symbolic, or does this count: "When the voltage is increased by 100 volts, the new voltage will be 150 V + 100 V = 250 V"? --Lambiam 06:52, 24 June 2024 (UTC)
 * As indicated in the title, the example should be a useful formula, so yes it has to be symbolic. HOTmag (talk) 06:59, 24 June 2024 (UTC)