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One Hundred Years of E=MC2
Eric Ward writes "To mark the one hundredth anniversary of Einstein's
famous equation, E=mc2, NOVA has gone live this month with a Web site that features exclusive content and podcasts from ten of the worlds top physicists. This once-in-a-lifetime gathering of top scientists such as S. James Gates, Jr., Brian Greene, Neil deGrasse Tyson and Nobel Laureate Sheldon Glashow simplify what the equation means to our world today and the effect it has had on their careers. NOVA online also details how Einstein grappled with the implications of his revolutionary theory of relativity and came to a startling conclusion: that mass and energy are one,
related by the formula E=mc2.
Viewers will also find lesson plans through the
award-winning NOVA Teacher's Guide and a special
library resource kit."
All this business of E = mc^2 "giving us the nuclear bomb" is another example of newspaper pap-science. There's far more to a nuke than computing the mass defect.
The whole idea is a staple of Relativistic kinematics which has been verified in collider experiments, etc., etc.
You can define relativistic stuff in less than four dimensions (e.g., one of space and one of time). Take an electron-positron annihilation into two photons. A proper treatment requires quantum field theory, where mass can be understood (in one way) as a parameter constraining the dynamically allowed momentum-energy configurations of the physical ("on-shell") fields. It's [probably] not right to think of electrons as little dots of mass.
Again, you need to consider quantum field theory to [begin to] answer these questions.
Please. Einstein was awarded the Nobel Prize for his work on the photoelectric effect. He did publish a fantastic work on Brownian motion as well. If you had RYFSM (read your f**king source material) you would also know that, since it says so in the first paragraph.
/. and I should be happy with that.
I guess its just
Ummm, no. Einstein's NP was for his paper on the photoelectric effect. Read your source again.
"Lawyers are for sucks."
- Doug McKenzie
Energy is a derived unit.
it is in m^2kgs^-2
Speed is also a derived unit.
it is in ms^-1
So when you pick a definition for time and distance, everything matches up.
Tonights forecast: Dark. Continued dark throughout most of the evening, with some widely-scattered light towards morning
I think you are making the mistake that, for example, a 4-slice pizza is smaller than an 8-slice pizza, because, as everyone knows, 4 is less than 8. However, the pizzas are exactly the same size, it is just that the slices are larger in a 4-slice pizza.
Is there some science behind the selection of the units involved that allows this equation to be so simple, or are we to believe that some serendipitous magic just allows this to be an exact equation and the units somehow just happen to match up?Yes, there is a very challenging derivation of this simple relationship. It is just math, and it is not magic. I won't do the derivation, but I will show that the units do, indeed, make sense:
Energy is a force acting through a distance: F x d
Force is a mass undergoing an acceleration: F = m x a
Acceleration is a change in velocity over a change in time: A = deltaV/deltaT, whose units are length/time x 1/time. Let's use metric. That would be m/s x 1/s.
Substituting the units back into the general energy equation, we get:
E = F x d = m x A x d = kg x (m/s x 1/s) x m. If we pair the 1/s with the meter from "Force acting over a distance" The units are:
E = kg x (m/s) x (m/s), which are the same units as Einstein's famous relation. So, yes, the units do make sense, it is not serendipitous that this works out, and the reason it is so famous is because it is so simple.
Ok, here's a serious answer:
E = mc^2 holds true no matter what units c is expressed in - as long as the units for energy, mass, and c are consistent.
If you say c is expressed in meters/second, and m in kilograms, then energy must have the units of [kg*m^2/s^2] which we also call Newton-meters or Joules.
Just to confuse you further: sometimes we choose our units such that c=1! In this case, E = mc^2 becomes just E = m. Energy is mass.
Numbers in physics are just convenient ways to express a measurement; they are not of numerological significance (well, maybe the fine structure constant...).
Check out http://en.wikipedia.org/wiki/Physical_unit if you have more questions on the units.
To begin: Wolfgang Pauli postulated the neutrino, not Einstein.
Next: Whatever one concludes about the validity of Eddington's solar eclipse experiment, the predictions of General Relativity have been tested and proved out in hundreds, if not thousands, of repeatable and rigorous experiments since then.
And Next:
This quote falls somewhere between the irrelevant and a non-sequitur. Thanks for sharing man--but what does it mean? No physicist takes cold fusion seriously, and autodynamics is a competing theory to General Relativity, for which Richard Moody, Jr. is clearly a shill.
At the end of the day, it doesn't matter whom it was that provided the first, or the first accurate, derivation of e=mc^2. It could have been Einstein, Poincare', or William goddamn Shakespeare, for all I care. What matters is that both Special and General Relativity have withstood an awful lot of testing over the last century, and stood up well under that onslaught.
The autodynamics camp also seems to believe that Special Relativity is used in radioactive decay calculations, and I could have sworn that Quantum/Statistical Mechanics holds sway there....
Einstein was not awarded the Nobel for special relativity because much of it was in fact unveiled by the great mathematician Henri Poincaré. Poincaré found the key point, i.e., everything stems from defining time as being obtained by synchronizing clocks with electromagnetic signals.
Not really. Poincare did do a lot of the interesting math, following on from Lotentz, that provides a lot of the mathematical foundations for relativity, but what he didn't do was redefine time. Poincare still viewed the different time in the calculations as a sort of "local time" which was in a sense merely a mathematical fiction required to make the calculation go through. Poincare still believed in the ether, and thus an absolute referene frame and an absolute time. It was Einstein who, with his observations about the very nature of time being relative, did away with a ficntional "local time" and an absolute reference frame. In Einstein's view there was no true reference frame and all time was "local time" - local to the observer. The effects on time were thus not a mathematical fiction, but a physical reality. It was this observation and new conception of time that Einstein is highly regarded.
That does not, of course, in any way diminish Poincare's work - and he did a great deal of work besides just that relating to relativity (he is the father of algebraic topology for instance). Certainly Poincare deserves a little more recognition for his great achievments than he gets outside of the mathematics community. Misrepresenting Einstein's achievements is not the way to give Poincare his due credit however.
(As a side note, more recognition should probably also be given to David Hilbert, who did a lot of the pure maths required to lay the foundations of General Relativity).
Jedidiah.
Craft Beer Programming T-shirts
Bzzrt. Wrong answer. Motion is relative, acceleration is not. Rocket Twin accelerates and decellerates to leave and come back. He will always be younger at the end.
Why?
If we are getting pedantic...
[PEDANTIC]
For things like photons that have zero rest mass
E = m0*c^2 / sqrt (1-(v/c)^2)
Doesn't work so well... By using the following:
(E^2) = (m0^2)*(c^4) + (p^2)*(c^2)
Now photons (which by definition are moving and have momentum) can have kinetic energy associated with them without having to divide zero by zero (since photons travel the speed of light v/c = 1 and the denominator is zero in your equation).
[/PEDANTIC]
I realize it's gauche to reply twice to the same comment, but there were a couple things I didn't answer:
What did E=MC2 give us the past 100 years?
It's a fact (approximately) about the nature of the universe. It doesn't need to give us anything. What did the discovery of the planet Neptune do for us? Nothing practical, but I think knowledge is worth seeking for its own sake.
What I think is more useful from E=MC2 is the idea of relativity. It is true, not just for science, but for almost every field of study.
If by "the idea of relativity" you mean, roughly, "there are no privileged inertial frames of reference", then I have a hard time imagining what bearing that idea has on, say, art history, or comparative religion. If you just mean that "everything is relative", then I'd say that your idea of relativity has very little to do with Einstein, and is probably too vague to be much use in any other field, either.
Nope. Grandparent is completely correct (even though he says he's not in a later post). Burning is exactly analogous to nuclear reactions. Bonds are broken and energy is released. In both cases, matter is converted into energy. It does not matter whether the bonds are electromagnetic (chemical) or strong (nuclear).
.04 milligrams.
In chemical reactions, the amount of mass converted to energy is very small and nearly impossible to measure, but that's not the point.
Example: To heat your house, you use on order of 1000kWh per month, obtained by burning natural gas. 1000 kWh = 3.6 * 10^9 Joules. E=mc^2, solving for m: 3.6 * 10^9 J / (3 * 10^8 m/s)^2 = 4 * 10^-8 kg =
My credentials: I'm a graduate student in physics at the University of Minnesota.
Velocity causes the time and distance dilation yes, but the accelleration is what breaks the symmetry between the two.
While twin two is heading away from twin one, you can't say who's older - From Twin One's perspective Twin Two is aging slowly, and From Twin Two's perspective Twin One is aging slowly. It's just as legitimate to say that Twin Two is stationary and everything else is moving around him. It's the fact that he _turns around and comes back_ that breaks the symmetry between the two frames of reference and allows you to say that he is in fact the younger one.
You've covered the part about how the second twin is able to see himself covering the distance in that time, but ignored the fact that while he is not accelerating, the frames of reference are relative and that you can just as easily say the _other_ twin is aging slowly. In short, you ignored the principle of relativity. :)
Why?