Timeline for Addition of different physical quantities
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2011 at 19:57 | comment | added | AndyS | @Marek let us continue this discussion in chat | |
| Jul 17, 2011 at 19:54 | comment | added | AndyS | @Marek I'm sorry but you don't understand what addition of physical quantities means. In your example you add the teddy bears to the teddy bears (same units) and not to the bananas (different units). Your $5x+2y$ etc. is formal; it has no result. I'll stop replying to your comments now, I think my point is more than clear. | |
| Jul 17, 2011 at 19:28 | comment | added | Marek | @AndyS: you missed the point entirely. Say you have an apple and a teddy bear (so that you finally notice that this really isn't about both objects being fruits) and add another teddy bear to that. What will you have? Well, obviously one apple and two teddy bears (i.e. you have more information than just that there are three objects in the pack). As for the units, say you have units $x$ and $y$. Then surely all of the following expressions are correct $5x + 2y$, $xy$, $xy + 6y^2$. You can formalize this as a polynomial ring $K[x, y]$ or a function field but it certainly works... | |
| Jul 17, 2011 at 19:16 | comment | added | AndyS | @Marek In physics you don't just add real numbers, you add values of physical quantities (which are real numbers) with units appended to them. The operation of addition cannot be carried out if the units are not the same; that's what I proved in my post above. Trying to add bananas and apples has no physical meaning, unless you call them both fruits, in which case you're just adding fruits. | |
| Jul 17, 2011 at 18:57 | comment | added | Marek | @AndyS: as for the physical quantities, I just showed you that it can make sense in some situations. I agree though that it often doesn't make sense because often one is interested in a single quantity (like final velocity) of a certain computation and in that case it's already in the prescription of the problem that solution must have well-defined units. | |
| Jul 17, 2011 at 18:51 | comment | added | Marek | @AndyS: the structures are almost the same and there's no reason calling addition of fruits formal and addition of real numbers is according to you (I presume) non-formal while actually in reality the former is of much greater importance. You often carry with you two bananas and an apple and if you add to that three bananas, two apples and a chocolate bar, it's a perfectly natural addition operation that you perform everyday. On the other hand, real numbers have no physical meaning as one can always carry out only finite number of measurements... | |
| Jul 17, 2011 at 18:40 | comment | added | AndyS | @Marek Note how the word "formal" is used in that article. I wrote "symbolic" which is synonymous to "formal". It means that it's not really the same as addition, it just resembles it in some respects. For real physical quantities there is just no sense in adding them if they have different units. | |
| Jul 17, 2011 at 18:25 | comment | added | Marek | @AndyS: but of course there is: en.wikipedia.org/wiki/Free_abelian_group Nevertheless, the structure is weaker than that of the vector space. Vector space of dimension $n$ over a field $K$ is a free $K$-module on $n$ generators while FAG is a free $\mathbb Z$-module. | |
| Jul 17, 2011 at 15:38 | comment | added | AndyS | @Vladimir The notation for vectors you're mentioning is just symbolic; it does not mean that you're adding anything. If you define a coordinate system with the $x$-coordinate being apples and the $y$-coordinate being oranges, then a point in that two-dimensional space will define a vector (take the tail at the origin), with the $x$-component giving you the number of apples and the $y$-component the number of oranges. There is no sense in which this defines addition of apples and oranges. | |
| Jul 17, 2011 at 11:22 | history | edited | Vladimir Kalitvianski | CC BY-SA 3.0 |
added 135 characters in body
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| Jul 17, 2011 at 3:23 | comment | added | Peter Morgan | This seems to me a more-or-less reasonable suggestion, though it takes something of a leap to suggest it as Physics. There may, however, be various inequivalent extensions of the axioms of arithmetic to include what might be called "multiplication". | |
| Jul 16, 2011 at 22:16 | comment | added | Georg | The dimension of this addition is "fruit". | |
| Jul 16, 2011 at 21:45 | history | answered | Vladimir Kalitvianski | CC BY-SA 3.0 |