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One Hundred Years of E=MC2
Posted by
CmdrTaco
on Thu Aug 18, 2005 03:05 PM
from the i-still-don't-get-it dept.
from the i-still-don't-get-it dept.
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."
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Time for a physics limerick (Score:5, Funny)
whose movement exceedingly brisk
so quick was his action
the Fitzgerald Contraction [wikipedia.org]
reduced his rapier to a disc
Re:Time for a physics limerick (Score:5, Funny)
A1: To actualize its potential
A2: Unknown; the fact is, most of the poultry in the universe seem to be missing
A3: It didn't. It simply moved its legs standing still, while the road passed underneath.
A4: It didn't cross the road - it simply returned to where it started, but was momentarily moving backward in time.
A5: There exist numerous parallel universes in which the same chicken is in differing stages of crossing the road. Only when one of the chickens has concluded crossing the road do their wave functions coalesce.
A6: Chickens at rest tend to stay tend to stay at rest, and chickens in motion tend to cross the road. Given an equal and opposite reaction, clearly, it was pushed onto the road by another chicken who consequently moved away from the road.
A7: The chicken never actually crossed the road (a task impossible for a chicken of it's energy level). Instead, through uncertainties in its position, it found itself tightly clustered in with other chickens inside a coop just beyond the road, and unable to escape and return to its starting side.
Parent
Re:Time for a physics limerick (Score:3, Funny)
A9: Scrodinger's Chicken is <blink>not</blink> dead.
Re:Time for a physics limerick (Score:5, Funny)
A: to get to the other...uh...
Parent
Happy 100th (Score:5, Funny)
"I explode like a bomb. No-one is spared. My power is my mass times the speed of light squared."
Re:Happy 100th (Score:5, Funny)
Twinkle, Twinkle little star
Power = I squared R
Parent
What if E = mc^2.0000000001? (Score:3, Interesting)
Newton's 3 laws survived 239 years, I wonder how long Einstein's will last?
Re:What if E = mc^2.0000000001? (Score:5, Insightful)
Einstein's _theories_ will last until evidence no longer supports them (just like all science).
Newton's _laws_ were and still are wrongly named.
And another pedantic relativity thing. The E=MC^2 was part of the _Special_ Theory of Relativity which says that measurements of time and distance vary as anything moves relative to anything else. This is where the twins where one goes in a rocket near the speed of light and the rocket twin comes back still young and the stationary twin is old (I really hope I didn't embarrass myself by reversing this, but I think this is right).
The other theory of Relativity that Einstein came up with was the _General_ Theory of Relativity that came out in 1915. This is the space-time continuum being bent by gravity.
Einstein was a little upset that he was able to join the two theories into one, but then again that is the goal of many physicists today.
Einstein was a very interesting and good person from everything I have heard and read. RIP.
Parent
Re:What if E = mc^2.0000000001? (Score:3, Insightful)
-everphilski-
Re:What if E = mc^2.0000000001? (Score:4, Informative)
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.
Parent
Re:What if E = mc^2.0000000001? (Score:5, Informative)
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. :)
Parent
What if cows could fly? (Score:3, Interesting)
That's the beauty of science... Science is INQUIRY... it is not static.
Until someone does prove it was an approximation, we'll use it. Once that occurs, we will use the new figure until someone else is able to make it more accurate.
Re:What if E = mc^2.0000000001? (Score:4, Insightful)
Which is like Newton's equations. They had known for quite a while that the orbit of Mercury couldn't be accuratly described by his theories, but they were the best avalible.
Einstein's are the best avalible now, for non-quantum events. Someday someone will come up with something that handles both. Then they'll be the genious hailed as the greatest.
Parent
Albert Einstein's performance review, 1905 (Score:5, Funny)
Don't miss the rest of his site [norvig.com] while you're there.
Timing (Score:3, Insightful)
If Einstein Was So Smart... (Score:5, Funny)
One Hundred Years of E=MC2 (Score:4, Funny)
Re:One Hundred Years of E=MC2 (Score:5, Funny)
e = 2.71828 18284 59045 23536 02874 7135... [wikipedia.org]
Or are we being case-sensitive?
- shazow
Parent
E = mc^2 is Not Einstein's Discovery (Score:3, Informative)
Robert A. Herrmann
1. Introduction
It appears that some scientists have not received the proper credit for significant discoveries for which they have priority. However, without specific and irrefutable information, it is not possible to give convincing reasons why these individuals have been denied recognition and why others have been given credit for their scientific discoveries. In 1996, I was asked whether certain aspects of General Relativity were originally formulated by Einstein or Hilbert. (Hilbert presented the gravitational equation(s) prior to Einstein.) The questioner said that he knew very little about Einstein's achievements except for such things as "E= mc^2." I answered his question relative to the Hilbert verses Einstein controversy but I neglected to discuss the more easily explained E = mc^2. What follows in this short article shows exactly who developed the idea that "radiation" can be characterized as having an apparent mass and that it was not Einstein in his 1905 paper. Except for the last remarks on Olinto De Pretto, this article is concerned mostly with "radiation" and its relation to E = mc^2.
read more... [serve.com]
Michael. [michael-forman.com]
serious question (Score:4, Insightful)
But I have a few nagging question about this famous equation. People just tend to explain c^2 by saying something like "a little matter represents a lot of energy, and c is a big number and so c squared is even bigger". Well, that certainly is true if c is measured in meters per second or any other common unit. But it's all about the units. If c is expressed in light-seconds/second rather than meters per second, or worse yet light-years/second then the "logic" of that argument is exposed as just hype. So the real issue comes down not to the equation e=mc^2 itself, but the selection of the units that e, m and c are expressed in. Use a different unit and, as I try to show above, the whole thing breaks down.
Al himself made a pretty famous point of saying that c was a constant. So c^2 is also a constant. So the equation boils down to expressing an important relation between e and m. But it all depends on the units of measure. So here's the question:
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? After all, I certainly don't know of any reason why a meter is any more of a valid unit to do this calculation with than a furlong, or a foot, or a parsec. And I am under the impression that the units of both mass and energy were determined before the equation, not as a result of it. So should I believe that this equation is just a serendipitous chance match up of units, that Einstein made some sort of deal with God, or that the equation just might be a bit over simplified?
If a meter were and inch shorter or an inch larger, there would still be an equation that could show the relation between e and m, but a conversion number would have to be added to the equation to make up for the slight difference in the size of the meter. How is it that this equation works out with the current rather arbitrary length of a meter to such whole numbers?
Re:serious question (Score:3, Informative)
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.
Re:serious question (Score:5, Informative)
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.
Parent
Re:serious question (Score:5, Informative)
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 [wikipedia.org] if you have more questions on the units.
Parent
Einstein was so wrong (Score:5, Funny)
Quantum debugging (Score:3, Funny)
Obligatory lame physics joke: (Score:4, Funny)
Re:Obligatory lame physics joke: (Score:3, Funny)
Plagiarism is at least better than bullshit (Score:4, Informative)
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....
It is E=mc^2 (Score:5, Insightful)
But m = \gamma m_0, where \gamma = 1/sqrt(1 - \beta^2), and, of course \beta = v/c.
I.e., E = mc^2 = m_0 c^2 / sqrt(1 - (v^2/c^2))
Oh, m_0 is rest mass, in case you didn't know that, and m is the relativistic mass.
Parent
Re:It is E=mc^2 (Score:5, Funny)
I.e., E = mc^2 = m_0 c^2 / sqrt(1 - (v^2/c^2))
Oh, m_0 is rest mass, in case you didn't know that, and m is the relativistic mass.
Do you get laid much? I can just imagine the bar talk.
So, ladies, did you know that if. wait. I need my blackboard. Would you mind pushing the pints down a little, I need more space to show you this. Screw it, lets just go back to my TA office. I sure hope professor Greennuts is not there. He steals all my women with his theory of relativity- they're not related to him. bada-boom-bang.
I admit it, I am crazy and my mind entertains me.
BTW, I am shocked you would put a link on slashdot to your picture. You will have to let us know if this has brought you any nerd on nerd love?
Parent
Re:It is E=mc^2 (Score:3, Informative)
People like it because many equations in mechanics are nonrelativistic, such as p=mv, F=ma, and ironically, E=mc2, and the concept of "relativistic mass" makes them work out again if you interpret the "m" as being a function of v: m="m0"/sqrt(1-v2/c2). In fact that is how the concept of "relativistic mass" historically became popular and stayed popular. People wanted to extend the Newtonian laws of mechanics that they were already familiar with, and since we still teach Newtonia
(E^2) = (m^2)*(c^4) + (p^2)*(c^2) (Score:4, Informative)
[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]
Parent
This story is a dupe (Score:5, Funny)
Parent
Re:Plagiarist? (Score:5, Interesting)
einstein was awarded the nobel prize for his brownian paper. relativity, published the same year, was all but ignored.
source:t ml [kyoto-u.ac.jp]
http://www.bun.kyoto-u.ac.jp/~suchii/einsteinBM.h
Parent
Re:Plagiarist? (Score:3, Informative)
I guess its just
Re:Plagiarist? (Score:5, Informative)
Ummm, no. Einstein's NP was for his paper on the photoelectric effect. Read your source again.
Parent
Re:Plagiarist? (Score:3, Funny)
Re:Plagiarist? (Score:5, Informative)
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.
Parent
Re:Plagiarist? (Score:5, Insightful)
Seems like a scientist's National Enquirer.
Parent
Re:Plagiarist? (Score:3, Funny)
This word "anonymous." I don't think it means what you think it means.
Re:Plagiarist? (Score:4, Funny)
"When you are a student, it's called plagiarism; when you are a professor, it's called scholarship."
But for all I know he ripped that quote off from someone else . . .
Parent
Re:Ok guys... educumacate me (Score:3, Interesting)
Re:Ok guys... educumacate me (Score:3, Interesting)
First thing to realise is that there are two theories of relativity - special and general. Special came first, is much easier to get your head around, and concerns motion, energy and that equation. The second, general theory came after, concerns gravity and is a complete pig to work with (Riemann curvature tensors [wikipedia.org] anyone?)
As to why do
Re:Ok guys... educumacate me (Score:3, Insightful)
Einstein noticed that there's a discrepancy between Newton's laws and Maxwell's laws of electricity and magnetism (E&M). To patch this, most physicists assumed special treatments for E&M like ether. Einstein went backwards and decided Newton must be wrong.
The most amazing conclusion he reached was that the speed of light is a constant in any reference frame. ANY reference frame.
Re:What did E=MC2 give us the past 100 years? (Score:5, Informative)
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.
Parent
Did it in 1932 (Score:3, Informative)
Here's the link you need to CD Anderson's 1932 experiment [physlink.com] using gamma rays
Re:What did E=MC2 give us the past 100 years? (Score:5, Insightful)
And Newton's first law of motion didn't ring true to Aristotle—clearly objects in motion tend to come to a stop if nothing is pushing them. Our intuition about how the universe works is based on our limited experience of medium-sized objects moving at low speeds on the earth's surface, with the result that all physics post-Aristotle is more or less counterintuitive. The fact that you can't imagine it doesn't mean it isn't so.
Parent
Re:What did E=MC2 give us the past 100 years? (Score:5, Informative)
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.
Parent
Re:Using ints? (Score:3, Funny)
God does not use rand() on the universe.
Re:If c is the speed of light... (Score:3, Insightful)