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| 19 Sep 2014 06:28 PM |
Believe it or not, but E=mc² was not devised through experimentation, but simply through a thought experiment of Albert Einstein's.
Imagine a box on a race track. The left end of the box is as 0 meters just touching the starting line. And the right side of the box is at L meters, so the width of the entire box is L. Let's also call the center of mass of the box "x".
Let's also imagine that the box isn't touching the race track, and there's no air or anything to interact with the box, that it's an isolated system.
Now imagine something weird. Imagine if a photon was emitted inside the box on the left end, and traveled towards the right end.
Momentum of a photon is defined as the energy of that photon over the speed of light, or ρ=E/c.
So, if the photon is emitted and begins to move, then, based on the law of conservation of momentum, the box should also move. Stand on a scale and jump on it. You will notice that just before you jump, you gain a lot of weight. This is because of conservation of momentum. The momentum that pushed you in the air pushes the opposite way against the scale so it reads a greater weight.
Within the time it takes for the photon to move from the left side of the box to the right, the box would have moved a certain amount to the left. Let's call that change in distance ∆d.
This means that the left side of the box has now moved from 0 on the race track to -∆d and that right side is now on L-∆d. The center of mass of the box is still x. Also, the time that has taken place is ∆t.
We know that velocity is distance over time by definition just by its definition. This also means that ∆t=∆d/v just by rearranging the formula. We also already know the velocity, it's the speed of light, which is "c". So ∆t=∆d/c.
But there's one more thing we also know, the distance. The distance it covered isn't just the length of the box. Even though the photon moved from the left side of the box to the right, it didn't cover a distance of L because the box reacted and moved against the photon by a distance of ∆d. So that means that the distance the photon covered is actually L-∆d. We can substitute this and say ∆t=(L-∆d/c).
So now, let's go back to the equation v=∆d/∆t as the definition of velocity. We can plug things into this equation now to get the velocity of the box.
v=∆d/(L-∆d/c)
Do a little rearranging and you get v=(c∆d)/(L-∆d).
Now, let's thing of the center of mass. The center of mass cannot change unless an external force acts on the system. This is simply a law in physics.
So, now we have a problem. The box moved, but its center of mass remained the same. That doesn't seem to make sense, now does it?
Let's think for a second that maybe the photon carried mass from one side of the box to the other, therefore shifting its center of mass. Now let's say that the mass of the box is its mass minus the photon's mass, or M-m. Based on the equation ρ=mv, we can say that ρ=v(M-m). The momentum is equal to the wave of light's momentum because of the conservation of momentum, so we can also say that v(M-m)=E/c.
Now, let's substitute v for that equation we made a little while ago.
(M-m)[(c∆d)/(L-∆d)]=E/c
Also...
(M-m)∆d=m(L-∆d)
Why? Because the center of mass has to be the same. So the mass displacement of the box must be equal to the mass displacement of the photon. That's just conservation of mass.
You can rearrange that to get
[(M-m)∆d/(L-∆d)]=m
If you notice in the previous equation (M-m)[(c∆d)/(L-∆d)]=E/c, the term [(M-m)∆d/(L-∆d)] exists, and we defined it here as equal to m. So we can substitute all that with simply "m" and get mc=Ec.
So, just rearrange that a bit, and we get E=mc².
thanks for you time. c:
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vladut04
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| Joined: 02 Oct 2011 |
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| 19 Sep 2014 06:29 PM |
e=mc2 = emo confirmd
u wot m8 ill bash ye | hail our master doge | I LOVE FNAF |
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| 19 Sep 2014 06:33 PM |
this is the kind of education i want to see
thank you |
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Manchenzo
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NotAshley
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roniray
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| Joined: 05 Jun 2012 |
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| 19 Sep 2014 07:52 PM |
E=mc² = Energy= Momentum Cliche at the power of two
he was watching pron or a spanish novel |
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| 19 Sep 2014 07:53 PM |
| thank you for this fair exchange of information my fellow enlightened individual *tips fedora* |
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