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Originally Posted by guthmund
Surprisingly, not for a paper, just some general....curiousity.
I've been reading a lot on physics lately. Brian Greene's two books, some stuff by Michio Kaku, Richard Feynman and the latest by Bodanis (I think that's who wrote it..) about E=mc^2, not to mention dozens of sites on the internet, including this one, mind you.
I understand bits and pieces, but I still have a few questions and I thought the gurus here might have the answers.
Okay...first. I understand that c is squared, what I don't understand is why. Bodanis remarks that s'Gravesande found that when he dropped his metal spheres into soft clay he noticed that if he propelled the second ball twice as fast it fell into the clay four times as far, three times as fast, it fell nine times as far into the clay. Kaku termed it "force multiplier" and further explained that in similar instances it worked the same. He wrote that a car increasing speed from 20 mph to 80 mph had increased in speed some four times and logically, the car moving at 80 mph should have four times as much 'energy' as the car moving at 20 mph, but in reality, the car moving at 80 mph has sixteen times as much 'energy' as the car moving at 20 mph.
Every book, I've read (unless I managed to miss it somewhere or misunderstand  ) fails to explain "why." They just say it is or that's the nature of energy. So...why? Is just taken for granted that the force multiplier effect is there or is there a reason why?
One more...
Kaku and Greene explain that if I could watch a car travelling at about the speed of light (since you can't really travel at the speed of light, which, again, I sort of understand ) the car would look compressed toward the direction of motion. That the height of the car (or whatever) would stay the same, but lengthwise it would compress like an accordion. As I understand it, inside the car everything would be 'normal,' it's only from the outside looking in that it gets crunched. As the car slowed down and eventually stopped, everything would be back to 'normal' from everyone's point of view. Kaku asks who was really compressed, you? or the car? He further states that "According to relativity, you cannot tell, since the concept of length has no absolute meaning."
So, the question is...why compressed? I get that nobody really knows why it happens, but do they know why 'compressed?' I mean, if length has no absolute meaning, why can't the car look elongated? Why doesn't it stretch?
That's all for now, but I've got some questions on general relativity as well if anyone's interested. |
Wow, it's been a while since a
Relativity thread happened in this forum. We've probably been through all this before but this thread is so slow these days that I welcome another opportunity to show the simplicity and straightforwardness of an all too often convoluted subject. You do seem genuinely confused and I blame the sources you've chosen to learn off of. I personally find that the best source to learn Relativity (and other branches of Physics) is from a genuine text book. They can be purchased at relatively (ha ha) reasonable prices from used book stores, especially if they are not for any class of any academic program. My favourite is
Young, although
Giancoli is also quite good. The big secret that all your various sources probably neglected to tell you is that a firm understanding of Special Relativity requires nothing more than highschool mathematics, which is probably why a math flunky was able to formulate this theory.
Another thing you should know is that science doesn't explain
why things happen, it merely describes
how things happen. While many things can be explained in terms of other things, ultimately, things just behave the way they do and all we can do is make a note of it.
Now, I'm afraid to go into great length over details you already understand so I'm going to go really fast and you can come back with everything you know and what you don't understand, okay?
There are really only two things you need to know about Special Relativity. They are the two assumptions, or
postulates of Special Relativity. Two simply facts that the entire theory is based on. They are:
1) The laws of Physics are the same regardless of your inertial reference frame.
2) Light travels at the same speed regardless of your inertial reference frame.
The first postulate is obvious. No one point of view is any more valid than another and, literally, the laws of Physics don't change simply because you're going somwhere else.
The second postulate is a little less obvious and tricks a lot of people up. We're used to the idea that Relativity dictates that if a car travelling at 20 kph is passed by another car travelling at 30 kph, the first car will see them pass at 10 kph. While this appears to be true for most objects, light doesn't behave that way. While it travels along the road at the
speed of light, it will actually pass the 20 kph car at, also, the speed of light. Strange but true!
Now that we understand these fundamental observations of reality, lets try to answer your questions, starting with the second one. Length contracts (shrinks) because time dilates (shortens). The longer you travel, the farther you go. So, if time dilates, length contracts. Get it?
Of course, time dilates because light must travel a greater distance for the moving object so, as per our earlier understanding, it must have taken a longer time to do so. But, because of the first postulate, that longer time for us translates into a slower time for the moving object.
Your first question is a little more subtle. First of all, your concern for why
c is squared is misguided. The simply fact is that the units would not be right if it weren't. Energy is force
×distance, or mass
×distance<sup>2</sup>/time<sup>2</sup>. If you didn't square
c, which is speed (distance/time), then the formula would come out mass
×distance/time, which is momentum, a very different quality!
The derivation of the formula E
=mc<sup>2</sup> comes from the integration of force over distance, the very defition of energy! If you accept that you can put an arbitrary amount of energy into moving an object yet that object's speed must remain finite, it follows that the speed of the object becomes asymptotic to some speed while its energy is unbounded. Integrating this asymptotic formula shows that as the speed approaches zero, the energy becomes a finite, non-zero value and that value is mc<sup>2</sup>.
So, there you have it. The Relativity speed course with all the actual diagrams and formulas cut out. This is really an opportunity for you to specify exactly which part you didn't understand in your travels through the theory of Relativity. I can expand on any part to any amount of detail so that you
will understand! I hope you have a desire to do so...