# E=MC2

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 202615.  Tue Aug 21, 2007 1:19 pm The quotation is correctly remembered, but not the person quoted; it was in fact Niels Bohr. http://www.biology.ualberta.ca/bsc/news25_2/quipsandquotes.htm No harshness required.

202756.  Tue Aug 21, 2007 10:55 pm

 Curious Danny wrote: "If you aren't confused by quantum physics, you haven't understood it"

That's the one.

202767.  Wed Aug 22, 2007 3:17 am

According to Richard Dawkins in his TV show on Monday, Richard Feynman said something similar:

 Quote: Anyone who says they understand Quantum Mechanics doesn't understand Quantum Mechanics

 212102.  Fri Sep 21, 2007 9:07 am Could someone explain the twins paradox... i dont get it, excuse me if im not remembering this right but in a brief history of time, hawking says about the measurement of time at the top and bottom of a water tower be different in that the top clock runs faster than the bottom clock...but then it says later about travelling at the speed of light away from the earth and the time running slower hence the lack of aging... have i confused the first point ie the clock at the top of the water tower runs slower thatn the one at the bottom..or am ijust not getting it???

 212138.  Fri Sep 21, 2007 10:07 am The two are completely separate phenomena. The twins paradox is about time travelling more slowly if you're travelling very fast, as explained in Special Relativity. The water tower thing is about time travelling more slowly in the presence of gravity, as explained in General Relativity. But you're right, the watch at the bottom of the tower will run more slowly because it's in a (marginally) stronger gravitational field.

 214999.  Sun Sep 30, 2007 6:34 am I would go with the motion that the equation depends on the medium the mass is in. Oh crap, what if the medium the mass is travelling in is an opaque medium. Light can't get though and is reflected. The equation breaks down here I think.

 215267.  Mon Oct 01, 2007 4:21 am Light in a medium is not "pure" light. It's a bit of a semantic nightmare, but in fact it consists of both electromagnetic oscillations coupled with mechanical oscillations of the charged particles that make up the medium. Light, as in "the speed of light", is a pure electromagnetic wave. Also, the equation does not "break down" because the "c" in E=mc^2 refers to "the speed of light in a vacuum".

 215304.  Mon Oct 01, 2007 5:43 am The one thing that annoys me about the whole SOL travel is impossible because you need infinite energy to move an object at SOL is that it seems to be untrue. Photons have a miniscule mass, do they not? They move at the speed of light. Or, is this untrue and they move, like electrons down the powerlines? c",) Tas

 215457.  Mon Oct 01, 2007 9:16 am The Lorentz transformations show that the energy associated with any mass as it travels at velocity "v" is given by: E = mc^2 / (1 - v^2/c^2) When the velocity reaches the speed of light, v^2/c^2 = 1. Therefore the bottom half of that fraction becomes 1 - 1 = 0. This gives you a positive number divided by zero, which is either undefined or infinite depending on which mathematician you ask. However, "m" in this equation is the rest mass of the object that's moving. Photons have a rest mass of zero. Thus, this gives you an equation of zero divided by zero. This is not infinite, though I'm not sure it's precisely defined either. In conclusion, objects with a non-zero rest mass cannot achieve the speed of light. Objects with zero rest mass, such as photons, can.

 215493.  Mon Oct 01, 2007 10:22 am Clear as mud, that. But I think I got through it okay. Still does not make the greatest of sense, but then a lack of caffeine and sleep (three and a half hours last night) don't help. :-) Tas

215742.  Tue Oct 02, 2007 4:09 am

 dr.bob wrote: E = mc^2 / (1 - v^2/c^2) -snip- In conclusion, objects with a non-zero rest mass cannot achieve the speed of light. Objects with zero rest mass, such as photons, can.

If one assumes v<c, then it is clear that a zero-mass particle also has zero energy (doesn't exist); if v>c then (1 - v^2/c^2) is negative, which leads to all sotrs of problems. So, although the energy is undefined when v=c, it is also the only situation in which such a particle can have a positive energy. It would therefore seem that a zero-mass particle must travel at the speed of light.

 215781.  Tue Oct 02, 2007 4:43 am Ali, That appears to be a logical analysis and hence 'must' appears to be correct. I await Dr bob's comments with interest.

215790.  Tue Oct 02, 2007 4:58 am

As I mentioned in post 213310

 Quote: Any object without rest mass can be shown mathematically to be required to travel at light speed and no slower.

I'm deeply hurt that you haven't all memorised my every word, but ali is completely correct.

 215801.  Tue Oct 02, 2007 5:27 am Memorising your every word would a very Victorian method of education. Understanding the meaning behind your words should be the objective. Leading students to make their own well thought out arguments is more important than route learning. In this you have achieved some measure of success.

 215829.  Tue Oct 02, 2007 7:37 am Bolox! It's woolly, liberal thinking like this that has resulted in all of our teenagers becoming practically feral. The streets are awash with happy slapping hoodies with ASBOs and ringtones (to coin a phrase). Let's get back to Victorian values! Start memorising now. There'll be a test in the morning.

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