If someone has this sort of thought in their head there are likely serious fundamental misunderstandings. They probably won’t be solved simply by trying to explain dimensional analysis.
I think it was on This American Life that I heard the guy’s story. They even contacted a physicist to look at his “theory”, who tried to explain to him that the units didn’t work out. The guy’s response was “OK, but besides that …”
He really seemed to think that this was just a minor nitpick that scientists were using as an excuse to dismiss him.
Why isn’t it a minor nitpick? I mean, we use dimensioned constants in other areas; why, in principle, couldn’t the equation be E=mc (1 m/s)? If that was the only objection, and the theory made better predictions (which, obviously, it didn’t, but bear with me), then I don’t see any reason not to adopt it. Given that, I’m not sure why it should be a significant* objection.
Edited to add: Although I suppose that would privilege the meter and second (actually, the ratio between them) in a universal law, which would be very surprising. Just saying that there are trivial ways you can make the units check out, without tossing out the theory. Likewise, of course, the fact that the units do check out shouldn’t be taken too strongly in a theory’s favor. Not that anyone here hadn’t seen the XKCD, but I still need to link it, lest I lose my nerd license.
The whole point of dimensional analysis as a method of error checking is that fudging the units doesn’t work. If you have to use an arbitrary constant with no justification besides “making the units check out”, then that is a very bad sign.
If I say “you can measure speed by dividing force by area”, and you point out that that gives you a unit of pressure rather than speed, then I can’t just accuse you of nitpicking and say “well obviously you have to multiply by a constant of 1 m²s/kg”. You wouldn’t have to tell me why that operation isn’t allowed. I would have to explain why it’s justified.
That guy needed to be taught basic dimensional analysis, apparently. E=mc has units of kg-m/s, which is the unit of momentum, not energy.
If someone has this sort of thought in their head there are likely serious fundamental misunderstandings. They probably won’t be solved simply by trying to explain dimensional analysis.
Upvoted for insightful prediction confirmed by evidence!
I think it was on This American Life that I heard the guy’s story. They even contacted a physicist to look at his “theory”, who tried to explain to him that the units didn’t work out. The guy’s response was “OK, but besides that …”
He really seemed to think that this was just a minor nitpick that scientists were using as an excuse to dismiss him.
Why isn’t it a minor nitpick? I mean, we use dimensioned constants in other areas; why, in principle, couldn’t the equation be E=mc (1 m/s)? If that was the only objection, and the theory made better predictions (which, obviously, it didn’t, but bear with me), then I don’t see any reason not to adopt it. Given that, I’m not sure why it should be a significant* objection.
Edited to add: Although I suppose that would privilege the meter and second (actually, the ratio between them) in a universal law, which would be very surprising. Just saying that there are trivial ways you can make the units check out, without tossing out the theory. Likewise, of course, the fact that the units do check out shouldn’t be taken too strongly in a theory’s favor. Not that anyone here hadn’t seen the XKCD, but I still need to link it, lest I lose my nerd license.
The whole point of dimensional analysis as a method of error checking is that fudging the units doesn’t work. If you have to use an arbitrary constant with no justification besides “making the units check out”, then that is a very bad sign.
If I say “you can measure speed by dividing force by area”, and you point out that that gives you a unit of pressure rather than speed, then I can’t just accuse you of nitpicking and say “well obviously you have to multiply by a constant of 1 m²s/kg”. You wouldn’t have to tell me why that operation isn’t allowed. I would have to explain why it’s justified.