## 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.
## Pretty cool (Score:2, Insightful)

All that computing power to verify what Einstein figured out with his head and a chalkboard.

## Re:Pretty cool (Score:5, Insightful)

## Re: (Score:2, Insightful)

It is remarkable in the fact that all of the previous attempts to mix Quantum-"anything" with Relativity have pretty much spectacularly failed.

I'm quite impressed.

## Re:Pretty cool (Score:5, Informative)

## Re: (Score:2)

Yep. Electron spin is a purely relativistic phenomenon. It can't be derived from "classical" QM.

## Re: (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: (Score:2)

## Re: (Score:2)

You mean, like Dirack did at the 20's? (Or was it at the 30's? I don't remeber.) Or like all kinds of nuclear, x-ray, and particle physics? None of those failed.

If we couldn't mix quantum-anything with relativity, one of those theories (maybe both) would have be disproved a long time ago. If there is something that makes people crazy is exaclty that those theories are consistent in all kinds of experiments that we are able to do, but not ont theory.

## Re: (Score:2)

Wrong.

The first relativistic extension of Schroedinger equation (http://en.wikipedia.org/wiki/Klein-Gordon_equation) has been derived in 1926.

We can't reconcile General Relativity and quantum field theories, but special relativity in quantum mechanics has been used quite successfully for quite a long time.

## 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: (Score:2)

It is remarkable in the fact that all of the previous attempts to mix Quantum-"anything" with Relativity have pretty much spectacularly failed.

Sorry, but this is complete and utter nonsense. The mixture of RT and QM is successfull since the 20s. That there is antimatter for instance could only be predicted by mixing RT and QM (Dirac equation). Quantum Electro Dynamics made some of the most accurate predictions in the whole field of science. The so called Standard Model, which is beeing tested at the different particle acceleraters (e.g. CERN) is based on RT *and* QM.

What amazes me, is that this comment was rated "insightful"...

## Re:Pretty cool (Score:5, Informative)

## Re: (Score:2)

Exactly. Well said. When we manage to solve the difference between the theories we now have, we should end up with the theory of everything. Perhaps then we'll all get our flying cars, and so everyone will know how to skydive.

I wonder how much more compute power we'll need to get some facts behind the eventual theory of everything, and will it's name be '42'?

## Re: (Score:2)

If a flying car is so unsafe that you are required to know how to skydive, I don't think I want to drive one!

## Re:Pretty cool (Score:4, Informative)

## Re: (Score:2)

Actually, the summary, and presumably the article it quotes, mangle to point into unrecognizability. The New Scientist article is much better.

The interesting point, though well recognized, is that most of the mass of hadrons comes from virtual particles -- most of it from virtual gluons. This research added in virtual quarks and got a result closer to the real mass - 2% off instead of 10% without the virtual quarks.

E=mc^2 is derived from special relativity, which is a critical component of quantum mechani

## Re:Pretty cool (Score:4, Insightful)

## Re: (Score:3, Insightful)

Einstein may have demonstrated that the math had to be right, but this sort of result was needed to demonstrate that the math correctly described the universe.

## Re: (Score:3, Interesting)

## Re: (Score:3, Funny)

Well they tried, but unfortunately the people were killed by an atomic bomb.

## Re:Pretty cool (Score:4, Insightful)

So you contest then, that atomic bombs would not work if it were E=mc**3?

## Re: (Score:3, Interesting)

Einstein may have demonstrated that the math had to be right, but this sort of result was needed to demonstrate that the math correctly described the universe.

By proving it hypothetically with another mathematical construct, aka a computer simulation? To my untrained mind, this sounds like proving 1+1=2 by typing it into Python and getting the expected result. Since these researchers obviously know more about this than I do, I'll assume the problem is with my lack of understanding. So, why is this simulation a valid demonstration?

## Re: (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: (Score:2)

Although the point of the exercise wasn't actually to verify E=mc^2, it was to develop a computer simulation capable of calculating the masses of baryons using quantum chromodynamics. You could write down a formula for them, but nobody had been able to solve it.

## 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: (Score:2, Insightful)

## Good news, everyone! (Score:5, Funny)

## Mathmatically verifiable (Score:3, Interesting)

As I understand it there were several geocentric models of the universe that were mathematically validated.

Am I mistaken or, doesn't that just mean that our theory matches all the known data and the data matches the theory. It Really doesn't have anything to do with whether or not the theory expresses reality.

## Re: (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: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.

## 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.

## Re: (Score:2, Insightful)

In other words, all scientific theories will eventually be proven wrong when better data is available.

As a man of science, coming to grips with this fact is central to not getting cought up in the "religion" of science (this theory says that, it is science, thus it is the 'truth'). As 'Weird' Al wrote, "Everything you know is wrong."

## Re: (Score:2)

Yes, you can constructed a mathematically consistant model of the universe with the earth as its unmoving center. That's part of the theory of relativity: you can construct a mathematically consistent model of the universe around *any* frame of reference. Since the earth is not an inertial frame of reference, it makes the math needlessly complicated, but you can do it.

## Re: (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 coordin

## Re: (Score:2)

There is no such thing as "proof" in science; only disproof. Also, there's nothing to say that our conception of maths isn't completely distorted by some aspect of the human mind which makes us convinced we're thinking correctly and getting the right answer when we're actually way off. In essence, any/all of us could be in a white padded cell right now, imagining all of this. In the end, it all comes down to faith.

## Re: (Score:2)

hmm... so would you claim that you must have faith in order to be rational?

Or rather that someone who denies the need for faith is not living in reality?

Seems like that means the arguments about faith have more to do with what one places faith in then.

Really kind of blows away the 19th century rationalist.

Not saying I necessarily disagree, just thought it was an interesting way of putting it.

## Re: (Score:2)

## Re: (Score:2)

>>. But it means the planets will be moving in extremely strange trajectories, doubling back on themselves

What you are saying is the math would be really complex and counter intuitive, much like the math involved in modern quantum theory.

Remember trying to create a truly heliocentric model would not have been much better or simpler and it wasn't for much of the scientific community working on those math problems those were the only two known options.

>>Whether or not the theory reflects 'reality'

## Re: (Score:2)

What you are saying is the math would be really complex and counter intuitive, much like the math involved in modern quantum theory.

Actually, the

mathinvolved in quantum theory is usually very straightforward, and much less complicated than in even classical dynamics: linear algebra, group theory, some path integrals, that's about it. To me, it's the message the math gives us about the real world which is counter-intuitive.## Re: (Score:2)

Don't get me wrong. I really am asking because honestly, the little bit of quantum theory I've tried to read the real mathmatical equations for wasn't all that easy do understand.

How exactly can you say the math is easy when it takes a super computer to verify your solution?

I mean this:

http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation [wikipedia.org]

doesn't look horribly complex, but nothing really is once you understand it.

Like you say, it is the strange conclusions it presupposes that make it difficult.

Not unlike ge

## Re: (Score:2)

oh, that makes sense. Do you suppose that will open any doors towards yet another mathematically verifiable super unified theory. Or helping to an experiment way to falsify some of them?

## Re: (Score:2)

This is mostly an advance in computational methods. You would apply it to a unified field theory for the same reason it was applied to QCD: the theory is so complicated that you need a supercomputer to even tell what it predicts. Once you know what it predicts, then you can test the theory against experiments.

## Re: (Score:2)

People had already applied E=mc^2, that's what led them to conclude that some energy was "missing" and how much of it. The advance is that they were actually able to calculate from theory how much energy ought to be "missing", and found that it agreed with the missing amount previously inferred from E=mc^2.

## Oh dear (Score:3, Funny)

New Scientist has a slightly more technical look at the accomplishment.

When I read a sentence like that, I begin to wonder if maybe I'm getting my science news from the wrong source.

## Dark matter (Score:2, Interesting)

Since the missing mass is from the movement, does this mean anything in the search for dark matter?

## Re: (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 th

## 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: (Score:2)

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.

Who said anything about proving something? Nowhere in the summary or either of the links does it use the word "prove". Proving and verifying/confirming are very different things.

As noted in other posts, what is exciting about this isn't necessarily that E=mc^2 is confirmed (that's been done plenty of times before), but that it was done in a quantum world (which historically has been at odds with relativity).

Besides, if you want to get really pedantic, we cant prove anything with absolute certainty. Its po

## Re: (Score:2)

As noted in other posts, what is exciting about this isn't necessarily that E=mc^2 is confirmed (that's been done plenty of times before), but that it was done in a quantum world (which historically has been at odds with relativity).

What's exciting is, technically, that people were able to calculate the energy of the quark-gluon fields inside a baryon. Everyone knew what it had to be (the difference between the baryon mass and the masses of the quarks inside), but nobody had been able to calculate it directly from theory.

E=mc^2 has never been at odds with quantum field theory. It's only relativistic

gravitywhich is at odds with quantum mechanics.## Poor correction (Score:2)

## Higgs Boson? (Score:3, Interesting)

I could be totally wrong, but I was under the impression that all the 'missing mass' of subatomic particle was believed to be generated by the Higgs Boson/Field.

## Re: (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: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: (Score:2)

Siiigh, no matter how much you check one or two always slip through... It's not just fermions that have non-zero rest masses. Some bosons ( W and Z ) also have nonzero rest mass, which is quite important because it limits the range of the weak nuclear force. Heisenberg's uncertainty relation only allows virtual particles to exist for a time corresponding to their energies, so if the particles have nonzero rest mass it limits this time, and thus the distance they can travel. In contrast the electromagnetic f

## Re: (Score:2)

## Re: (Score:2)

I could be totally wrong, but I was under the impression that all the 'missing mass' of subatomic particle was believed to be generated by the Higgs Boson/Field.

It's subtly different. If you believe E=mc^2 (and there's no reason not to--it's been verified too many times to count, despite the misleading headline), then the energy in a field (electromagnetic field, gluon field, etc.) is equivalent to mass. In a proton, there is a non-zero gluon field that caries energy and hence mass.

The question then becomes, how can an elementary particle (like an electron) have mass? A free electron is not interacting with any fields, so how can it act like it has mass? Thi

## Maybe, maybe not (Score:2)

In a theory of everything that tries to explain things 100% in terms of fields, there is no mass and everything is accounted for in the energy of fields generated sub-atomic particles.

In the case of this experiment, the "color" lattice fields of QCD make up most of the field energy and account for most of what would normally be attributed to mass. Earlier compuatations of quark field energy were able to account for all but about 10% of the "mass-effects" in field energy, but didn't take into consideration

## Its NOT E=mc^2 (Score:5, Insightful)

## Re:Its NOT E=mc^2 (Score:5, Informative)

## 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: (Score:2)

There is such a thing as relativistic mass, but most people just call it "energy" (or "mass-energy" when they're being pedantic), since as you say, you can't just blindly plug it into all the relativistic formulas where mass appears.

## 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.## Wasn't he... (Score:2)

...led by Laurent Lellouch...Wasn't he the pitcher in "Bull Durham" [imdb.com] that hooked up with Susan Sarandon?

Oh wait, that was Ebby Calvin 'Nuke' LaLoosh; nevermind!

## Funny. This Java script doesn't need supercomputer (Score:3, Interesting)

Use Heim Mass Calculator [daimi.au.dk] to easily compute masses of proton, neutron, electron and a lot of other particles as well, with a great precision (relative errors less then 0.00001) when comparing with most precise laboratory measurements available. The only hardware you need is Java in your browser.

This algorithm is based on 50-year old equations of Burkhard Heim thanks to his beautiful theory [wikipedia.org]. Notice that it include computation of neutrino mass which was found in recent years. When Heim was working on his theory almost all scientist were sure that neutrino is massless. The only input which this algorithm needs is a bunch of well known constants: h (Planck's Constant), G (Gravitational constant), vacuum permittivity and vacuum permeability.

Our current "mainstream" (hate this word) theory known as Standard Model is full of inconsistencies which are forcing scientists to constantly mumble about "dark mass" and "dark energy" stuff.

It remembers me about Enrico Fermi's comment "Beautiful theory, wrong universe". Does it apply here?

## Did you read the page on that theory? (Score:2)

Might want to read your own Wikipedia link about particle masses. See that table with the mass of the electron and such? See the errors listed? Being off by 102.5 standard deviations on the mass of the electron is NOT close. The proton, his BEST calculation, is "only" 94.5 standard deviations off.

There might be some interesting ideas in there, but it doesn't appear to be cutting edge. He wasn't the first to posit neutrinos with mass, either.

## needs to be repeated (Score:2)

What if these guys actually discovered a glitch in the theory, a mode where the amount of energy out exceeded the amount going in, tantamount to a free energy source - and then falsified the result in order to use the glitch for profit? "Nothing here, everything's consistent, now go away."

Conspiracy theory rules. ;-)

## 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.

## Misread (Score:2)

Did anyone else read the headline as "Emacs Verified In Quantum Chromodynamic Calculation" at first?

## Re: (Score:2)

M-x QCD, but only if you have qcd.el and sr.el installed.

## Science. It works, Bitches. (Score:3, Insightful)

## Using mass to test Quantum Chromodynamics (Score:3, Interesting)

Okay, so here's my take on all of this.

First, here's a different spin on what E=mc^2 actually means. What it says is that if you want to measure the total internal energy of some object (i.e., the part that is independent of its kinetic energy), then all you have to do is measure its mass. This is actually a very remarkable fact because it says that you don't have to know anything about it's internal structure; instead, you only have to know one of two things: A) its weight in a gravitational field of known strength, or B) its acceleration in response to a known force. (The "equivalence principle" asserts that these two very different experiments actually measure the same quantity.) So in other words, you can take this "black box" and do an experiment on it that tells you its full internal energy.

Because of this, since we have done experiments of type (B) to measure the mass of the B_c meson (the particle of the article), we in principle already know its internal energy. However, in addition to knowing its mass, we also have a theory -- Quantum Chromodynamics -- that claims to tell us exactly what its internal structure is. One way to test this theory is be seeing whether the total energy it gives us of the particle is equal to what we measured via. its mass.

To see this in a different light, suppose that we were trying to figure out how much energy is in an oscillating spring, and the only measurement tool we had was the ability to weigh the spring very, very precisely. Then if we thought we had a theory for how much energy the oscillation contributes to the spring, one way could verify it would be by measuring the weight of the spring before and after we start it oscillating and checking whether the difference matches our independent calculation of what the energy should be based on our theory of how the oscillations work.

This is the spirit of what this calculation does. We know that the meson consists of two quarks, but like a spring there are all sorts of crazy oscillations going on that we are also trying to understand precisely. So given that we know the mass of the quarks, we can check to see if our theory of how much energy the "oscillations" contributed by the gluon field agrees with the mass of the meson (which is very roughly speaking, quarks + oscillations); of course, this alone doesn't tell us that Quantum Chromodynamics is the correct theory of nature, but if we didn't see agreement between the two calculations then we would have to re-think our theory.

The thing is, actually sitting down and calculating exactly what these oscillations contribute to the energy is very hard, which is why it has taken people so long to actually succeed in doing it. Now they have an answer: our theory does indeed predict the same quantity we see in nature, so in this respect it is not obviously wrong. :-)

## 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.

## 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....

## Re: (Score:2, Funny)

Girls = Time * Money

Time = Money

Thus:

Girls = Money * Money = Money^2

Money = sqrt(Evil)

Therefore: Girls = (sqrt(Evil))^2

Simplified: Girls = Evil (Shamelessly stolen from an old 'funny internet' picture)

## Re: (Score:3, Funny)

BEHOLD, Sarah Palin also does mathematics.## Re: (Score:2)

You can thank the Idle section for that.

## Re: (Score:3, Funny)

## Re:I've only got one thing to say... (Score:5, Informative)

Newtonian Mechanics at Relativistic speeds comes is a good example of that.

## 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:I've only got one thing to say... (Score:5, Insightful)

## 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.

## Re: (Score:3, Interesting)

There is no frame of reference in which Newtonian mechanics is correct. How objects are moving has nothing to do with what frame of reference you choose to use. You can choose a frame which is at rest with respect to one or more objects, but you don't have to, and your choice is irrelevant to the laws of physics.

Whether E=mc^2 is valid for a non-stationary argument depends on how 'm' is defined. That symbol has been used in more than one way in the literature, although your usage is now the most common.

## Re: (Score:3, Insightful)

## Re: (Score:3, Informative)

extremelymisleading.Allquantum 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 ho## 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.

## 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?

## Re: (Score:2)

Literally.

He just has tons of energy stored up for later use.

## Re: (Score:2)

## Re: (Score:2)

No, they're saying that 95% of the mass of the normal matter is in fact interaction energy between the subatomic particles.

So 5% or 5% is actually "stuff" :)

## Re: (Score:2)

Yes. This 95% is the mass everybody expected to see in plain old ordinary matter, but wasn't previously accounted for in the QCD theory. We already had the experimental observation; now, we just know that the the theory gives the same answer.

Essentially, it's not telling us anything we didn't already know, so we don't get any new theories out of it. It does increase the confidence in the existing theory, so people who are trying to figure out what the dark matter is can rely more strongly on the theories

## 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: (Score:3, Insightful)

> 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.

No, they don't. One side has a vast array of scientists who all draw the same conclusions from peer-reviewed research with near universal accord. They also have a good deal of data to back up their theories.

The other side has a bunch of deliberately designed, mutually contradictory, un-peer-reviewed theories for the sole purpose of making non-climate-scientists believ

## Re: (Score:3, Informative)

## Re: (Score:2)

You're right. The "intrinsic" mass is usually called "invariant" mass or sometimes "rest mass" (although the latter doesn't apply to photons). The "relativistic mass" is called "relativistic mass", or "total mass-energy".

## Re: (Score:2)

So in this scenario, are they then combining the two types of mass to account for 100%? The type of mass that accounts for 95% of the particle is the energy given off from gluons and quarks, which is a relativistic mass since movements and interactions don't have intrinsic mass? But the intrinsic mass of quarks makes up 5%?

Yeah, that's basically it.

Aren't they confusing various definitions of mass to explain the total mass which they think should be there?

The conserved quantity is relativistic mass. The relativistic mass of the quarks, plus the relativistic mass of the gluons, equals the relativistic mass of the proton.

This is somewhat confused by the fact that relativistic and intrinsic mass of a particle are the same at rest. So if the quarks aren't moving too much, you can basically equate their relativistic mass with their rest mass. I'm not sure which is the 5% they refer to. And then, if the proton is at rest, then the rel

## 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: (Score:2)

Fun fact: Robert Mills taught my freshman honors Physics class in Spring 1994. He got sick (heart problems I think) that quarter and couldn't finish it out, so the prof I had the previous two quarters finished for us. RM actually made the undergrad quantum mechanics vaguely understandable in class. I thought he was a really great teacher and I was sad not to finish the quarter with him.

But at the time I didn't know there was an equation named after him. :-)

## Re: (Score:2)

You perhaps could solve it by diagonalizing gigantic matrices, but that's not what they do. The main computational effort comes from computing gigantic multidimensional integrals over millions of variables, one for each point and link in the spacetime lattice. That's what Monte Carlo methods are for; they're the only tractable way to handle very high dimensional integrals.

## Re: (Score:3, Funny)

E^2 = (mc^2)^2 +

(pc)^2Political Correctness has found it's way into Physics now, I guess.

## Re: (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.