Quote:
|
Originally Posted by stingc
The point of E=mc^2 is that energy and mass are equivalent. Originally, the point of it was to say that a body's inertia (mass) depended on its energy content.
Now, saying energy and mass are equivalent in words doesn't quite work if you sit down to calculate anything. The two quantities have different units. Energy is expressed in joules, foot-pounds, ergs, etc. Mass is in kilograms or slugs. Equating these things directly is meaningless. If mass and energy are indeed equivalent, you need a conversion factor. This should be a constant of nature, and it needs to have units of velocity squared (you can easily check this by using the fact that 1 joule is by definition 1 kilogram-meter^2/second^2). c^2 is the natural choice.
|
Believe it or not, that made sense. A much better explanation than 'just because."
Quote:
|
If you want to know why that is, I could refer you to some better (but harder) books than the ones you're reading.
|
Yes, please do. Although I enjoy the simpler works because often they take the time to explain with analogies (easier to wrap my head around than straight mathematics), I sometimes feel as if I'm missing the bigger picture because the books have been 'dumbed' down.
Quote:
|
The statement about spheres in clay is to help you understand why energy has the units it does. If you simply accept this, the example is irrelevant. In reality, energy was given its present definition (not that the basics are really new, or were even new 100 years ago) due to many complicated and interwoven discoveries. The concept of energy also encompasses so much more than just motion that I think the example is basically useless. I hope that your books contain a much more substantial explanation of what energy is than that.
|
Well, yeah. I think the example of s'Gravensande was really more an attempt to explain why the velocity term was squared rather than explain the concept of energy. I'm interested though, if you've got a more substantial explanation then I would like to hear it, if you don't mind.
[quote]This is actually quite simple to define. If lengths are always different to people moving at different speeds, just define the absolute length to the be the one measured by someone moving at the same speed as the object itself. You might think that this is cheating, but you can set things up such that anyone will measure exactly the same length without actually changing speed to do so. [quote]
Ha! I never thought of it like that, but, yeah, that makes all sorts of sense.
Quote:
|
As for the why things don't expand, this can be shown intuitively through a couple of diagrams, but that would require too much background for me to describe here. If you're interested, I'd highly recommend that you get a relativity book which uses spacetime diagrams to explain things. The viewpoints given in most popular books - while correct - were basically abandoned by most physicists after 1908 or so. The geometric formulation of relativity is far easier to understand, and makes all the length contraction business really simple. It also removes most of the 'wackiness' and apparent paradoxes of 'traditional' relativity.
|
It has to do with Lorentz' doesn't it? At least, Lorentz Transformations are used to measure the amount of the contraction, right? Okay, spacetime diagrams...got it.
Quote:
|
I hope that helps. I can answer your general relativity questions also, if you're still interested.
|
It helped immensely, stingc. I will certainly have some general relativity questions in the near future and I would certainly appreciate the help.
/off to read KnifeMissile's post..