Eise Posted March 9, 2018 Posted March 9, 2018 21 hours ago, studiot said: Why is inductance measured in Henries in the MKS system and centimetres in the cgs system Why is EMF measured in voltage in the MKS system and ergs in the cgs system since they are different physical quantities? I assume that even in the cgs-system, adding inductances and lengths, or EMFs and ergs does not make sense... For those who understand what it is all about (I do not quite), the Wikipedia article about the cgs system describes it all.
Strange Posted March 9, 2018 Posted March 9, 2018 9 minutes ago, Eise said: I assume that even in the cgs-system, adding inductances and lengths, or EMFs and ergs does not make sense... Quite. As previous examples have shown, being dimensionally consistent is a necessary but not sufficient requirement for an equation to be complete/useful. But if it isn’t dimensionally consistent then we know it is incomplete or wrong. Incomplete can be OK. It can be a useful shortcut, like the chemistry example earlier or e=mc2. As long as you know it is incomplete.
studiot Posted March 9, 2018 Author Posted March 9, 2018 13 hours ago, Bender said: Mathematically, you can work with dimensions as if they are variables that don't have a value (or can have any value, if you want). Works great. Yes you have emphasised my point that the Mathematics and the Science can be separated. So if you like you can add another separation by introducing a system of dimensions. Just as in the flower, fruit and veg market you have the horticultural system, the system of weights and measures and the Mathematics (usually simple arithmetic). All are quite independent of each other. 13 hours ago, Bender said: Mathematically, you can work with dimensions as if they are variables that don't have a value (or can have any value, if you want). Works great. Both expressions are true for all values of y. I really don't understand this. What is y?
Carrock Posted March 9, 2018 Posted March 9, 2018 12 minutes ago, Strange said: But if it isn’t dimensionally consistent then we know it is incomplete or wrong. Incomplete can be OK. It can be a useful shortcut, like the chemistry example earlier or e=mc2. As long as you know it is incomplete. e=mc2 is dimensionally consistent...
studiot Posted March 9, 2018 Author Posted March 9, 2018 3 minutes ago, Carrock said: e=mc2 is dimensionally consistent... Where did he say it wasn't? He said it was incomplete. 35 minutes ago, Eise said: I assume that even in the cgs-system, adding inductances and lengths, or EMFs and ergs does not make sense... Indeed any more than adding the two distinct quantities both with the dimensions L2MT-2 makes sense, as I already noted before.
Carrock Posted March 9, 2018 Posted March 9, 2018 (edited) 16 minutes ago, studiot said: Where did he say it wasn't? He said it was incomplete. It is a complete description of rest mass. Momentum etc is not included. As there is no universal equation of everything, every equation is incomplete in that sense. e=mc2 is not a shortcut in finding the equivalent energy of a mass at rest. You could add 0 momentum and 0 unicorns and 0volts/second if you wish. Edited March 9, 2018 by Carrock added third example
Strange Posted March 9, 2018 Posted March 9, 2018 (edited) 10 minutes ago, Carrock said: It is a complete description of rest mass. Momentum etc is not included. As there is no universal equation of everything, every equation is incomplete in that sense. That is pretty much my point. 10 minutes ago, Carrock said: e=mc2 is not a shortcut in finding the equivalent energy of a mass at rest. You could add 0 momentum and 0 unicorns if you wish. And that is what I meant when I said you need to know that it is (and how it is) incomplete. The point being that forums get a lot of people trying to support their "personal" theory by using e=mc2 but not realising that, for example, it doesn't apply to photons. (Or trying to apply equations of SR to situations where GR is required. Or ...) In other words, one needs to have an understanding of the meaning of the equations you are using. So we know that the chemistry equation cited earlier doesn't mean that energy is created from nothing (as a dimensional analysis might suggest) but that irrelevant details have been omitted. Maybe what this means is that it may be more important to check that a dimensional analysis says what you expect, rather than being perfectly consistent (if you have decided to omit some things). Edited March 9, 2018 by Strange 1
studiot Posted March 9, 2018 Author Posted March 9, 2018 19 minutes ago, Strange said: Maybe what this means is that it may be more important to check that a dimensional analysis says what you expect, rather than being perfectly consistent (if you have decided to omit some things). I don't think anyone is denying that dimensional analysis is an incredibly useful tool. But that is not reason not to reconsider it from time to time ( as was indeed done in the case of the move from cgs to MKS units ) A more fundamental move was of course the change from charge as a fundamental dimension to current or current density. The point is that the set L M t T I n Iv is not the only set we could use. Each possibility has its own pros and cons (apart from the clash of first letters). One of the obvious difficulties with M, L and t is that they are not immutable (They change in relativity for example one man's metre is not the same as another man's metre). Further there are so many types of mass - Proper mass, rest mass, effective mass, active mass, passive mass, inertial mass, gravitational mass.... the list goes on.
Eise Posted March 9, 2018 Posted March 9, 2018 1 hour ago, studiot said: One of the obvious difficulties with M, L and t is that they are not immutable (They change in relativity for example one man's metre is not the same as another man's metre). Is that really a problem? You just must be sure that the definition you use for your unity (kilogram, meter, second, whatever) is defined in such a way that it can be measured in the same inertial frame. 1 hour ago, studiot said: A more fundamental move was of course the change from charge as a fundamental dimension to current or current density. Why would this be 'more fundamental'? On one side, we know the relationships between many physical parameters (Newton's law, Ohm's law, etc). So we can 'span' all possible dimensions based on different 'basic vectors'. But when e.g. it is easier to make an experiment for exactly determining what 1 Ampère is than what 1 Coulomb is, then of course one would take Ampère as basic unity.
Strange Posted March 9, 2018 Posted March 9, 2018 1 hour ago, studiot said: One of the obvious difficulties with M, L and t is that they are not immutable (They change in relativity for example one man's metre is not the same as another man's metre). That is not really any different from switching from feet to metres. The dimensions are unchanged. Quote Further there are so many types of mass - Proper mass, rest mass, effective mass, active mass, passive mass, inertial mass, gravitational mass.... the list goes on. Again, doesn't change the dimensional analysis.
Bender Posted March 10, 2018 Posted March 10, 2018 13 hours ago, Strange said: The point being that forums get a lot of people trying to support their "personal" theory by using e=mc2 but not realising that, for example, it doesn't apply to photons. (Or trying to apply equations of SR to situations where GR is required. Or ...) If I'm not mistaken, E=mc2 can be used to calculate the relativistic mass of photons, which in turn determines the amount that the photon deforms spacetime. 13 hours ago, studiot said: I really don't understand this. What is y? A variable that can have any value in both your equations. You still haven't illustrated that the meaning of = is different when it is used in different kinds of mathematical expressions. What meaning does = have in this expression : x+y=5+y It is true for all y, but only for one x
studiot Posted March 10, 2018 Author Posted March 10, 2018 11 hours ago, Eise said: Is that really a problem? You just must be sure that the definition you use for your unity (kilogram, meter, second, whatever) is defined in such a way that it can be measured in the same inertial frame. Why would this be 'more fundamental'? On one side, we know the relationships between many physical parameters (Newton's law, Ohm's law, etc). So we can 'span' all possible dimensions based on different 'basic vectors'. But when e.g. it is easier to make an experiment for exactly determining what 1 Ampère is than what 1 Coulomb is, then of course one would take Ampère as basic unity. Well that assumes inertial mass is the same as gravitational mass, and I know of no law of Physics that says this must be so. That is particularly poignant when you consider how many quantities include M in their dimension lineup. Yes convenience has dictated the amp over the coulomb, but you can have (theoretically) charge without current, but not the other way round. The dimension system we have today is very good and have seen development and improvement since Buckingham's day. But are you claiming it is perfect? For it is any imperfections this thread seeks to discuss. 10 minutes ago, Bender said: If I'm not mistaken, E=mc2 can be used to calculate the relativistic mass of photons, which in turn determines the amount that the photon deforms spacetime. A variable that can have any value in both your equations. You still haven't illustrated that the meaning of = is different when it is used in different kinds of mathematical expressions. What meaning does = have in this expression : x+y=5+y It is true for all y, but only for one x y does not appear in any of my equations so how can it have a value there?
Bender Posted March 10, 2018 Posted March 10, 2018 9 minutes ago, studiot said: Well that assumes inertial mass is the same as gravitational mass, and I know of no law of Physics that says this must be so. That is particularly poignant when you consider how many quantities include M in their dimension lineup. Yes convenience has dictated the amp over the coulomb, but you can have (theoretically) charge without current, but not the other way round. The dimension system we have today is very good and have seen development and improvement since Buckingham's day. But are you claiming it is perfect? For it is any imperfections this thread seeks to discuss. y does not appear in any of my equations so how can it have a value there? That's quite easy: just assign one. Its value could eg be 5. Or 42. 10 minutes ago, studiot said: Well that assumes inertial mass is the same as gravitational mass, and I know of no law of Physics that says this must be so. What about general relativity? Its basic premise is that they are equal.
studiot Posted March 10, 2018 Author Posted March 10, 2018 16 minutes ago, Bender said: That's quite easy: just assign one. Its value could eg be 5. Or 42. What about general relativity? Its basic premise is that they are equal. I prefer my equations as I wrote them (unless, being human, I made one of those silly errors that John Cuthber so likes to point out) thank you. Perhaps you would be so good as to shown how this occurs?
Bender Posted March 10, 2018 Posted March 10, 2018 Why don't you start by simply answer the question "what is different in the meaning of = in both expressions?" Both expressions allow me to add a y on either side.
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