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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.
All that computing power to verify what Einstein figured out with his head and a chalkboard.
Trolling is a art,
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
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.
âoeTolerance applies only to persons, but never to truth. Intolerance applies only to truth, but never to persons.
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.
Since the missing mass is from the movement, does this mean anything in the search for dark matter?
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.
I'm picturing a tiny kitten peering intently at his cute little paw, with a macro over his head reading "My quark has a flavor?"
Welcome to the Panopticon. Used to be a prison, now it's your home.
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.
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.
From what I've been reading, it appears that there are two kinds of mass - intrinsic and relativistic. In the case of photons, they have zero intrinsic mass in the same way that the quarks have only 5% intrinsic mass of the proton. However, their relativistic mass is derived from their energy (E/c^2), analogous to the remainder of the mass that makes up the proton as described in the article. I'm no expert, but that's what it sounds like.
I have left slashdot and am now on Soylent News. FUCK YOU DICE.
the correct statement is: E^2=m^2c^4 + p^2c^2
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....
Use Heim Mass Calculator 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. 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?
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.
E^2 = (mc^2)^2 + (pc)^2
Political Correctness has found it's way into Physics now, I guess.
Tiller's Rule: Never use a word in written form that you've only heard and never read. You will end up looking foolish.
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.
and how do you see relativistic speeds as scale restricted? Indeed that is what is being tested here...
Because you can - or because you should?
> 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 believe that the science is bad on both sides.
It's deliberately designed to appeal to people who don't know the difference between climate and weather. It should be pretty clear that I can predict that it'll be colder in January than August (in the northern hemisphere) without being able to tell you it will rain tomorrow.
There is science on one side, and a deliberately anti-scientific campaign on the other. Science has uncertainty, quantified and part of the theory. The other side exploits that people don't understand how scientists deal with uncertainty to achieve a political, not scientific, goal.
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.
Slashdot's rate-of-post filter: Preventing you from posting too many great ideas at once.
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.
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.
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.
Shameless linking, I know. But someone had to say it.
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. :-)
Snarkiness is inversely proportional to wisdom because it emphasizes feeling right rather than being right.
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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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.
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.
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
Yes, it's wikipedia, but this one's well-written and sourced.
Let's be clear about what these results actually mean, because both the summary and the article are extremely misleading.
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...