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E=mc^2 Verified In Quantum Chromodynamic Calculation
Posted by
kdawson
on Fri Nov 21, 2008 11:31 AM
from the tee-shirts-were-right-all-along dept.
from the tee-shirts-were-right-all-along dept.
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.
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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]:
Good news, everyone! (Score:5, Funny)
Its NOT E=mc^2 (Score:5, Insightful)
Re:Its NOT E=mc^2 (Score:5, Informative)
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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.
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completely bogus interpretation (Score:5, Interesting)
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.
Scientists are bankers (Score:4, Funny)
It seems odd that scientists now claim that something (matter) is creating from fluctuations in the nothing (vacuum).
Previously, the audacity was only had by bankers creating value from no-documentation mortgage-backed securities.
Re:Pretty cool (Score:5, Insightful)
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Re:Pretty cool (Score:5, Informative)
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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.
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Re:Pretty cool (Score:5, Informative)
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Re:Pretty cool (Score:4, Informative)
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Re:Pretty cool (Score:4, Insightful)
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Re:I've only got one thing to say... (Score:5, Informative)
Newtonian Mechanics at Relativistic speeds comes is a good example of that.
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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.
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Re:I've only got one thing to say... (Score:5, Insightful)
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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.
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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.
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Re:I've only got one thing to say... (Score:5, Funny)
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?
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Re:Mathmatically verifiable (Score:5, Insightful)
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.
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Re:Mathmatically verifiable (Score:4, Interesting)
Hadn't heard of him before. That is truly fascinating. It almost appears to have come full circle.
Prior to Galileo, scientists never made the assumption that their theory actually had correspondence to reality. They were mostly concerned with whether or not it corresponded to the data and considered a theory 'true' if it corresponded to the existing data and had predictive power. There was a phrase which was used to mean that but I can't remember it right now.
'conservation of aspects' 'preservation of aspects' something like that.
I once read a work by Hippocrates called which I believe was titled: 'advice to traveling physicians'
In it he begins by explaining that a traveling physician should take into account the environment of the town he is about to enter, because it will help him predict the type of diseases likely to exist in the population.
He then enumerates different environments and diseases.
For example he predicted , correctly , that people living in areas where there were 'strong seasonal winds' --- I assume monsoons, had a higher number of stomach related ailments. He noted this was most likely because they tended to drink brackish or salty water. He then explained that the reason for the stomach problems was because the salt made their heads soft and caused the phlegm to run into their stomach, which also explained why they tended to be much stupider then the rest of the world.
I think it makes that makes an interesting example how the 'testable' part of a theory can be completely correct and useful for predictiveness and the 'un-testable' part of the model can by wholly wrong.
That being said there are a lot of people trying to do silly things like , prove God does or doesn't exist using science or prove people do or don't have immortal souls or free will.
The problem comes in of coarse with testability and shows that science, while incredibly useful as a tool to the race, simply has it's limits which it is unlikely to easily transcend and are of coarse tied to our ability to gather, and interpret data.
Questions like whether or not God exists are simply outside the realm of science proper, because of the ability to gather sufficient and repeatable data with proper controls.
That includes, however, both the positive and negative answer. I have never quite understood the instance, some people seem to have, that you cannot prove God exists while insisting it is possible to prove he doesn't.
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My proof (Score:5, Funny)
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....
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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.
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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.
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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.
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