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E=mc^2 Verified In Quantum Chromodynamic Calculation
chirishnique and other readers sent in a story in AFP about a heroic supercomputer computation that has verified Einstein's most famous equation at the level of subatomic particles for the first time. "A brainpower consortium led by Laurent Lellouch of France's Centre for Theoretical Physics, using some of the world's mightiest supercomputers, have set down the calculations for estimating the mass of protons and neutrons, the particles at the nucleus of atoms. ... [T]he mass of gluons is zero and the mass of quarks is only five per cent. Where, therefore, is the missing 95 per cent? The answer, according to the study published in the US journal Science on Thursday, comes from the energy from the movements and interactions of quarks and gluons. ... [E]nergy and mass are equivalent, as Einstein proposed in his Special Theory of Relativity in 1905." Update: 11/21 15:50 GMT by
KD : New Scientist has a slightly more technical look at the accomplishment.
To me, it sounds more like verifying that Quantum Chromodynamics isn't inconsistent...
Not really the same thing. Einstein derived it for non-quantum objects (ie large ones, or ones for which we can otherwise ignore quantum effects). This team verified it for quantum objects. This is interesting because the two theories don't mesh well -- one works at small scales and the other at large scales. It's not a theory of everything, because it doesn't touch gravity, but it's important to know where precisely the region the two are in conflict is. This calculation helps map that border.
It's not quite that simple. QCD is a quantum field theory, so E=mc^2 is "built in". Really, the point is that experimental results (i.e. proton and neutron mass) are confirmed and a clear explanation for this "mass discrepancy" given. I wouldn't say it's proven, since lattice QCD is a (very very good) approximation to an exact theory.
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Also on Yahoo, but with a horrible headline. Anyway both just reproduce the AFP text.
The original article seems to be this:
"Hannibal's plans never work right. They just work." Amy/A-Team
"You fools! You've altered the outcome by observing it!" - Professor Hubert Farnsworth
Since E=mc^2 is a result of special relativity, and special relativity has been a feature of quantum mechanics since the Dirac equation, no, special relativity+QM has been spectacularly successful. GR and QM is slightly more problematic, but irrelevant to the issue.
I wouldn't say that. Not in this case. Just because the equation is "works" in one scale (non-quantum), doesn't mean it works at ALL scales.
Newtonian Mechanics at Relativistic speeds comes is a good example of that.
the correct statement is: E^2=m^2c^4 + p^2c^2
Science can't tell you whether some theoretical construct is "really" there. That's a matter of philosophical definition. All science can tell you is whether the predictions of theories agree with what is observed in the world.
The article at theage.com gives a completely bogus interpretation, which is repeated in the slashdot article. The New Scientist article is much better.
This is just total scientific illiteracy. E=mc2 has been verified over and over again. We see it, for example, in processes like alpha decay, where the sum of the masses of the product nuclei doesn't equal the mass of the original nucleus. Mass is converted into energy in that process, and that's been experimentally established since probably the 1920's. Likewise energy can be converted into mass, as when cosmic rays hit the atmosphere and create electron-antielectron pairs. The theoretical foundations of E=mc2 are also extremely firm; it's deeply linked to the basic logical structure of relativity, and relativity has been abundantly experimentally verified.
Saying that this calculation verified E=mc2 is just stupid. The calculation assumes (1) special relativity, (2) quantum mechanics, (3) some technical stuff about how to make special relativity and quantum mechanics work together (generic ideas about quantum field theory), and (4) a bunch of very specific technical approximations needed in order to get an answer out of this particular flavor of quantum field theory (lattice QCD). The calculation has a bunch of adjustable parameters (quark masses, coupling constants). You play with the adjustable parameters and get a bunch of numbers out (neutron and proton masses, etc). If the number of adjustable parameters that goes in is m, and the number of experimentally testable numbers that pop out is n, then n-m is the number of degrees of freedom that verify whether the calculation is right. (For n=m, it would just be a complicated exercise in fitting the data, like putting two points on a graph and saying "look, it's a line!") I assume they calculated more than just the mass of the proton and neutron, because otherwise n=2 would be less than m. I assume the n-m degrees of freedom checked out fairly well, because they're calling it a success.
To see why this calculation can't really be interpreted as a test of E=mc2, you have to imagine what would have happened if it had turned out wrong. If it had disagreed with experiment, then we would conclude that some of the assumptions built into it were wrong. Let's look back at the assumptions 1-4 above. Well, 1 (special relativity) has been verified a zillion different ways since 1905 (or even as far back as the 19th century, the Michelson-Morley experiment, with hindsight). 2 (quantum mechanics) has likewise been verified a zillion different ways since the 1920's. 3, the general framework of quantum field theory, has some ugly spots, but it's been used to verify things like the magnetic moment of the electron to a dozen decimal places, so it's still on fairly firm ground. 4 is extremely shaky; it's only very recently that anyone has claimed to be able to calculate anything at all useful and realistic with QCD. So if it had failed, no physicist in the world would have interpreted it as evidence that assumption 1 (relativity) was wrong. They would have interpreted it as evidence that assumption 4 was wrong: the lattice QCD approximations weren't good enough, probably for very boring, technical reasons that would only be of interest to a specialist in lattice QCD.
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We know that e^(pi*i)=-1
and i=Sqrt(-1)
So, to prove that e=mc^2,
we substitute for e, and you get
(mc^2)^(pi*sqrt(-1))=-1 or
(mc^2)^(sqrt(-pi^2)=-1
mc Hammer only had 15 minutes of fame, so squaring that is 225 minutes
If you had a pie, and you squared it off, and I took it from you, and made it round again, you'd have the square root of a negative pie squared.
But this is pi, not pie, so we need to divide by e, which we know is 2.71828...
So 225^(1/2.71828)=-1
I know this worked yesterday... one moment....
It's not solving the Dirac equation (which is for a free fermion), but the full Yang-Mills equations, including the strong nuclear force. And they're not really solving DEs by finite element methods. They're evaluating functional integrals via Monte Carlo (integrating configurations over field space). But the functional to be evaluated (the action) is defined on a spacetime lattice and involves field derivatives, which is where the finite differencing comes in.
Take 'global warmming' both sides have a lot of theory but very little in the way of good tests that can prove it one way or the other.
You can test it by observing that natural sources of warming don't agree with the magnitude, rate, or timing of the observed warming; and that human sources do. You can further observe, for instance, that an enhanced greenhouse effect will lead to stratospheric cooling as a result of heat being trapped lower in the troposphere, and we do observe that. There are further predictions which distinguish manmade warming from various types of natural warming, depending on the type of natural warming. For instance, warming from the atmosphere means the oceans warm from the top down, which is observed, and disagrees with theories that have the surface heat come from the oceans. The greenhouse effect also means that you get shifts in the diurnal and seasonal patterns of warming which disagree with the shifts predicted by solar-induced warming, because of the daily/seasonal patterns in sunlight shifts which do not occur for the greenhouse effect. And so on.
Newtonian Mechanics is wrong at any speed. Just the error becomes more noticeable near light speed.
F=MA, yet a 1kg mass accelerated by 10 neutons for 1 second from stationary, will NOT be traveling at 10 m/s
It will be traveling just, very slightly slower....
Anyhow, I thought the actual thought experiment that leads to the derivation of e=mc2, (the one with a photon and a box), assumes the existance of the 'photon' a quantum scale particle.
Not quite. The Higg's mechanism is a suggested explanation for why some particles have nonzero rest mass ( such as electrons ) while others do not ( such as photons ). The idea is that just like photon-particle interactions can make light travel slower than C when it passes through a medium, so can interactions between fermions and the Higgs field allow fermions to move at speeds lower than C , which implies they have mass. Massless particles travel at C in all inertial frames, while particles with rest mass can never be brought to this speed since their kinetic energy diverges to infinity as their speed tend to C.
As it happens this explanation works quite well and can predict the rest masses for some particles with great accuracy, with one minor catch. It also implies that there should exist a boson with some particular properties, called the Higg's boson, which nobody has yet managed to detect. This is the Higg's particle. If detected it would provide strong evidence for the Higg's mechanism, strongly suggesting that it is indeed interactions with the Higg's field that cause fermions to have nonzero rest mass. Furthermore, the predictions of a few theories in particle physics depend upon properties of the Higg's boson that we can't deduce from other theories. As a consequence if you can detect the Higg's boson and determine some of these properties, it would further our understanding of particle physics.
Nobody expected E=mc^2 to be violated. That's not why they ran the calculation. They ran the calculation because, until now, nobody has been able to calculate the mass of a proton from the masses of its constituent quarks. You could write down the formula, but it takes a supercomputer to solve it.
Yeah, all those stupid PhD physicists, wasting money on experimental rigorous verification of stuff that any random geek on /. already knows is true. Tell you what, why don't you send them an e-mail explaining how they're wasting time and money, and let us know how that turns out?
The correlation between ignorance of statistics and using "correlation is not causation" as an argument is close to 1.
The first law defines an inertial reference frame, which should now be thought of as a free-falling frame.
The second law is correct as long as you use the relativistic definition of momentum.
The third law is still true in its original form. It basically says momentum is conserved.
Newtonian Mechanics as it's taught in schools is wrong at any scale. Newtonian Mechanics as Newton stated it is still valid when relativity is taken into account. Newton didn't state "F = MA", he said that "force is proportional to the rate of change of momentum". A 1kg mass accelerated by 10 neutons for 1 second from stationary will not be traveling at 10 m/s, but it will no longer be a 1kg mass either. The momentum will still be 10 newton seconds, though, just as Newton said it would be.
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i'm one of the authors of the original paper (Christian Hoelbling) and unfortunately the AFP press release has seriously misquoted another press release and the end result is horribly misleading. we did *NOT* set out to proove E=mc^2 and we did not corroborate it any further than it already is.
what we did was calculating the mass of the proton and other elementary particles from the underlying theory with controlled systematic errors, no more, no less.