E=mc^2 Verified In Quantum Chromodynamic Calculation 268
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.
Re:Pretty cool (Score:5, Informative)
Also on Yahoo, (Score:5, Informative)
Also on Yahoo, but with a horrible headline [yahoo.com]. Anyway both just reproduce the AFP text.
The original article seems to be this [sciencemag.org]:
Re:Mathmatically verifiable (Score:3, Informative)
It Really doesn't have anything to do with whether or not the theory expresses reality.
If you're using Popper's way of doing Science, you'll never know for sure if a theory expresses reality. The theory will be more plausible as it provides data about the reality and when it shows correct predictions about observable facts.
Re:Pretty cool (Score:5, Informative)
Re:Pretty cool (Score:4, Informative)
Re:I've only got one thing to say... (Score:5, Informative)
Newtonian Mechanics at Relativistic speeds comes is a good example of that.
Poor headline (Score:3, Informative)
This does not prove anything about E=mc2. You can't "prove" fundamental equations by twiddling bits.
They ASSUME that E=mc2, then use that equation to calculate the details of nuclear energies.
Re:Photons (Score:3, Informative)
Re:Silly question... (Score:5, Informative)
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.
Re:Its NOT E=mc^2 (Score:5, Informative)
Re:Dark matter (Score:3, Informative)
No. They're just verifying that gluons contribute to the binding energy of baryons. A gravitational analogy: we know that the total energy of a binary star system is different from the energy of two random stars millions of light years away from each other. That's because the energy of the system is not just the mass of the stars, but the star masses plus the gravitational energy in the system. For protons, the quarks are like individual stars. We knew that the mass of the proton equals the mass of the quarks plus their binding energy (from the strong force), but until now, we weren't able to calculate that energy.
This doesn't have relevance to dark matter because dark matter can't be due to nuclear binding energy between distant particles: the nuclear force is short ranged.
Re:Higgs Boson? (Score:3, Informative)
The mass of fundamental particles, like quarks and electrons, yes. Hadrons are not fundamental, they're made up of quarks and gluons, some of which are real and some of which are virtual. Most of the mass of the composite particle actually comes from the virtual components, NOT the real ones.
Re:Ah, so THERE'S the dark matter everyone looks f (Score:5, Informative)
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.
Re:I've only got one thing to say... (Score:5, Informative)
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.
Re:Pretty cool (Score:2, Informative)
That's not true, actually. But it's a very commonly held misconception.
Spin is not a relativistic phenomenon in itself, although it does arise naturally from the Dirac equation. It is not even a QM property in itself; It can be viewed physically as a circulating energy flow in the wave field of the electron. This was shown by Belinfante in 1939.
If you're interested, see, e.g. "What is Spin?" Ohanian, Am J Phys, 54(6), 500-505
Re:Higgs Boson? (Score:5, Informative)
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.
Re:I've only got one thing to say... (Score:5, Informative)
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.
Only General, not special (Score:4, Informative)
It is remarkable in the fact that all of the previous attempts to mix Quantum-"anything" with Relativity have pretty much spectacularly failed.
Well, except for the attempt in 1931 by Dirac that was spectacularly successful and united Special Relativity with Quantum mechanics giving rise to the field of particle physics. You can even quantized GR but you have to put an energy cut-off in to make it renormalizable. Since there is no justification for such a cut-off such models are regarded as seriously flawd so we have a problem with GR+quantum but not SR+quantum.
Re:Mathmatically verifiable (Score:2, Informative)
As I understand it there were several geocentric models of the universe that were mathematically validated.
As well they should be. In physics you can pick your coordinate system to be anything you like. If you pick your coordinates to have the earth at the center then you get a geocentric model: it looks like everything is spinning around us. It's perfectly sound, and even describes reality in that coordinate system. Yeah, it's a real pain to do any calculations with these coordinates because the model gets horrendously complex, but that doesn't make it false.
Heliocentrism is nothing more than choosing a coordinate system that is better suited to computations.
Re:Pretty cool (Score:3, Informative)
The problem was that the math gave a formula for the mass of the proton, but the formula was so complicated nobody could actually solve it, in order to see if its prediction agrees with the proton's true mass. The advance here is to use a supercomputer to solve the formula.
Re:Its NOT E=mc^2 (Score:4, Informative)
That's true: E=mc^2 is valid for moving particles if m is interpreted as the relativistic mass.
The grumbling comes about because physicists themselves almost never talk about relativistic mass in this sense anymore. Nowadays we usually say that a particle has an invariant mass m (its rest mass) which determines the relationship between its energy and momentum; E^2 = (mc^2)^2 + (pc)^2. That way a particle's mass has a single, well-defined value regardless of how fast it's moving. What you might call the "relativistic mass" I just call E/(c^2).
The two formalisms are completely equivalent, of course, but modern notation has swung toward defining "mass" as the rest mass only.
Re:I've only got one thing to say... (Score:5, Informative)
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.
this press release is horribly misleading! (Score:4, Informative)
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.
Re:Incomplete Equation (Score:3, Informative)
No, it wouldn't.
E^2 = (mc^2)^2 + (p+c)^2 would, but not when multiplied.
In fact, here's the support of the equation I typed above: http://en.wikipedia.org/wiki/Mass_in_special_relativity [wikipedia.org]
Yes, it's wikipedia, but this one's well-written and sourced.
Re:I've only got one thing to say... (Score:3, Informative)
All quantum field theories presume that the laws of special relativity hold, and couldn't even be written down if the assumptions of special relativity were not correct (to the relevant approximation, at least). They are formulated over 4 dimensional space-time with the usual Minkowsi metric (ds^2 = dt^2 - dx^2 - dy^2 - dz^2), and really couldn't be formulated any other way, that's how tied they are to relativistic physics. E = mc^2 is a special case of the equation for 4-momentum, and is just a definition of we mean when we use the word "mass." There's nothing even remotely interesting or questionable about it, let alone something that needs to be verified.
However, in QCD, the equations that actually determine the effective energies in real matter are so damn complicated that nobody knows how to solve them except by approximating them. So while no scientist in his right mind had any doubt that E = mc^2 was "correct" in the context of QCD (it's assumed to be true in the construction of the theory, dammit!), it was never proven that whole system of quarks and gluons in QCD could account for the full observed proton and neutron masses. So much of the observed mass is assumed to arise from quantum field fluctuations that it was never clear that the theory could give us the numbers that we actually measure in the lab. In this respect, it was not relativity that was being "verified," it was QCD itself.
So all this really tells us is that QCD may be consistent with the world that we actually see. Which shouldn't surprise any of us, as it's pretty widely considered to be the only viable theory of the strong force at the energy scales we're working with. But of course a science reporter could never get something that boring published, so they try to sex it up by pretending it has something to do with Einstein and the one physical equation that the public actually recognizes...