(Phys.org)—An electron, as well as other subatomic particles with an electric charge, is actually a little magnet—it spins like a top, giving it its own magnetic moment.

It's the subtle change in this magnetic moment caused by emission and reabsorption of photons, a quantum phenomenon called the anomalous magnetic moment, that Toichiro "Tom" Kinoshita, the Goldwin Smith Professor of Physics Emeritus, has studied over his long career. Kinoshita became emeritus in 1995.

In two *Physical Review Letters* papers accepted for publication, Kinoshita and colleagues have calculated the value of the anomalous magnetic moment of the electron and muon to the most precise degree known to physics.

The papers, co-authored by Kinoshita's last Ph.D. student Makiko Nio of RIKEN institute of Japan, along with M. Hayakawa and T. Aoyama of Nagoya University of Japan, explain how the researchers have evaluated the anomalous magnetic moments of the electron and muon up to the fifth power of the fine structure constant. This is the fundamental fixed value of an electromagnetic interaction.

It's an unprecedented accurate calculation that involved more than 12,000 complex Feynman diagrams, which describe pictorially how electrons and photons interact. The researchers were able to achieve this calculation over 10 years of work on supercomputers at RIKEN. The calculations enabled the researchers to determine the anomalous magnetic moment value to a level of precision of one part in 1.5 billion.

Elementary particles and forces are described very well by the Standard Model of Physics, Kinoshita says, but there are some indications that new physics remains to be discovered—a driving principle of his work.

"If you push theory and experiment hard enough, you might get to the point where the theory and experiment definitely disagree," he said. "And that means there is some new physics just visible beyond the distant horizon."

**Explore further:**
Spin-polarized electrons on demand

## gwrede

In other words, every time we measure something with enough precision, we will find that it subtly deviates from or existing model. And then it's time to create a new, more precise model. It may well be that we'll never see the day when (for example the electron magnetic moment) is calculated with arbitrary precision.

## VendicarD

New epicycles to discover..

The other option of course is that the existing physics they used to perform the calculation is fundamentally wrong.

## Argiod

All precision is arbitrary; only as accurate as is practical to accomplish the task at hand. Example; we only need two decimal places to keep track of money, even though we could contrive to create a smaller unit than a penny, it would be impractical. Or, I could get totally anal and insist that my home be built to nano-tolerances. But, again, it wouldn't be practical or economically feasible. Our models must be scaled to the needs of the task being modeled. Otherwise, we might as well try to measure the distance between NYC and SF with a centimeter rule...

## VendicarD

## johanfprins

## antialias_physorg

For those who understand Feynman diagrams it's fun. You just have to put in that bit of effort. Science is like that: it requires that you do some work.

That really depends on what you call 'fundamentally wrong'. Is Newtonian gravity fundamentally wrong? It's a very good approximation for cases significantly slower than the speed of light. There's no 'right and wrong' if something works to some degree - just 'useful' and 'not so useful'. If you say that something is wrong because it wil not give you the exact value to the last digit then all scientific theories are wrong (mostly because Uncertainty tells us there is no last digit, while algorithms give you a last digit)

## johanfprins

## antialias_physorg

Mathematics is an abstract tool. Physics is what works. If renormalization works (and it seems to, since the predictions arrived at through renormalization have held true for a wide variety of experiments) then it really doesn't matter whether the idea or renormalization is to your liking (or meshes with what you deem to 'make sense') or not.

Reality is the arbiter of what is true. Not you.

## johanfprins

Reality is the arbiter of what is true. Not you.

## daywalk3r

Well, the truth is, that all calculations ever used in physics will allways be just an "approximation of reality", unless you decide to work within a framework which sets absolute discrete limits (like Planck units).

But does that render all those calculations nonsense?

If absolute precision is what you seek, then Yes..

Though then, one also has to ask how much sense there is, in seeking nonsensee? :-D

Can't really agree, as that particular "Uncertainty" you speak of, has about as much to do with it, as it has with the inability to calculate the last digit of Pi.

It does a good job however, in holding certain "discrete theories" afloat, against the viscious tides of scrutiny of reality :-)

## johanfprins

If they are based on concepts which are physically impossible, they are nonsense. Feynman diagrams are based on the path-integral method according to which coherent wave fronts can follow any path even if it requires the wave-fronts to be non-parallel. Coherent wave-fronts can never be non-parallel.

## antialias_physorg

There are other approaches which do not rely on approximative maths (e.g. look nito the history books and you will find something like Babylonian counting science where extrapolations/formulae were not part of how to describe nature - but which is also a method that can arguably describe nature to an arbitrarily exact degree)

The map is not the territory. We use the number zero all the time in math and physics. But zero is also an impossible state for anything to be in (if something has a zero value then it doesn't have that state at all). Does this mean that all maths that uses zeroes is therefore useless?

Metamaterials would disagree.

## johanfprins

You are writing claptrap here!

So? REALLY? How do you get to this "deep" wisdom? Maths which subtract infinity from infinity is obviously useless.

How?

## vega12

## antialias_physorg

The babylonians had a system of conuting math - in shich one could not transfer knowledge as we do when we say: "one silo contains x number of kernels of grain, so two silos will contain 2*x number of kernels of grain"

The babylonians would not have acepted that as accurate. They had to count out the number in each silo. While this is enormously less efficient it is, on the other hand, not prone to estimation error.

You can fashion a metamaterial that will take in an EM front. Move separate parts of that front in separate (non-parallel) directions and then reassemble the wavefront.

http://en.wikiped...loaking. If you add materials with different propagation speeds along the paths into the mix you can even cloak entire events

http://www.popsci...e-events

## johanfprins

Thank you! But this is not the issue: Obviously boundary conditions can GUIDE the wave-fronts to be non-parallel: But when the wave-fronts move in this manner the wave is NOT a coherent wave anymore. The latter demands parallel wave-fronts.

Thus, to assume that within free space (no boundary conditions) wave-fronts are able to move in a non-parallel fashion is wrong. Both a photon-wave and an electron-wave are coherent waves in free space, modelled by Maxwell's wave-equation, and must therefore propagate with parallel wave-fronts.

Feynman path-integrals assume that these wave-fronts can follow one another along any arbitrary path through space. This is physically impossible.

## VendicarD

Empty space is known to be full of virtual particles that manifest from the energy available in empty space itself.

This energy density has been computed, and measured. Small quantities of real energy have been extracted from the vacuum of empty space.

"Thus, to assume that within free space (no boundary conditions) wave-fronts are able to move in a non-parallel fashion is wrong." - iohanf

If there are particles, then there is scattering.

## VendicarD

I c is finite and charge differentials can be created and destroyed, it follows that there is a charge force carrier that moves through space that is also quantized.

Maxwel's view simply doesn't work.

"Both a photon-wave and an electron-wave are coherent waves in free space, modelled by Maxwell's wave-equation.."

Arguing Maxwell's view is pointless.

You might as well argue that the world is flat.

## VendicarD

"Maths which subtract infinity from infinity is obviously useless." - johanf

Clearly not.

## VendicarD

"If they are based on concepts which are physically impossible, they are nonsense" - johanf

But you are not familiar with the properties of things that are smaller than you can see or feel.

An electron approaches a double slit in a barrier and exits from the other side.

A detector on the other side detects the position of the electron and reports it to a computer that builds up a picture of where the electrons are falling.

The picture is equivalent to that of an extended wave of a specific frequency having passed through the slit.

Feel free to explain this to us using the "real" properties of everyday "real" objects.

## johanfprins

incorrectly yes. Each wave does have energy fluctuations but this do NOT mean that the vacuum has energy!. Extracted to be dissipated? When and where?

There are NO particles in free-space: Both light and matter consist op EM-wave energy: Therefore a free photon (or electron) moving through free space is a coherent-wave with parallel wave-fronts modelled by Maxwell's equations.

## johanfprins

Then why when I use E^2=(p^2*c^2) (m*c^2)^2 as a template (the same template as used by Klein-Gordon and Dirac) do I obtain Maxwell's equation for the potential of light for both a photon moving with speed c (when setting m=0) and an electron (moving with speed v lower than c) when setting m=m(e)? I need not fudge the mathematics to get this, like Dirac has done to get his equation.

I am not doing this: Neither am I arguing that the world is the centre of the universe as you seem to be doing.

## johanfprins

You have just proved my point: This equation is meaningless according to the rules of calculus. It is called mathematical fudging. No wonder qunatum-field theory is Voodoo!

## johanfprins

Correction: A coherent electron-wave with parallel wave-fronts approaches the double slit which the wave encounters as new boundary conditions. As all waves do, and have always done, the electron-wave morphs to adapt to the new boundary conditions, so that its parallel wave fronts each move simultaneously through both sllits. The wave-fronts emanating on the other side intefere. (argument to be continued in next post)

## johanfprins

In order to detect the electron, it has to be stopped in its tracks: The detctor represents new boundary conditions which do just that. When an electron becomes a stationary-wave its dimensions becomes smaller than when it is a coherently-moving wave with parallel wave-fronts. Therefore it has to collapse and is thus observed as a spot. A stupid experimenter then concludes that the electron has been a "particle" while it moved through the slits: "Zere iss a condratiction here". How stupid can one be?

This is so since this is exactly what has happenned for each electron-wave!(to be continued in next positing)

## johanfprins

As already explained above, each electron is a coherent wave with parallel wave-fronts which forms a diffracted intensity distribution on the other side. In order to detect the electron, it has to resonate with the detector on the other side. This IS how everyday "real" waves are detected in a "real" manner. Think about radio-waves.

When a diffracted electron-wave reaches the detector it has a better probability to resonate at a position where its intensity is the highest: Thus, after many identically diffracted electron-waves resonated and collapsed into the detector, the identical intensity distribution for each diffrcated electron-wave is generated by the spots within the detector.

Thus, the electron-waves act like "real" waves are supposed to act: NO Voodoo needed! Feel free to explain why you rather believe in Black Magic!

## VendicarD

"The wave-fronts emanating on the other side intefere." - Johanfprins

We now immediately have a problem because your space and my space are not the same depending on our relative motion.

But lets ignore that for a moment because there is a bigger problem.

The wave is an extended object that can set to be as wide as we like by moving the detector farther away from the slit.

But when the electron is absorbed by an atom it is absorbed as a whole electron, not some fragment of a wave. And when it is absorbed no portion of the wave front remains to be absorbed by any other atoms.

The conversion from extended object to localized electron must be instantaneous for if it is not it would be possible for 2 or more atoms to interact with the same electron wave front within the time window for the conversion.

So by what physical mechanism does a extended physical object vanish through all of space at the same time. Cont.

## VendicarD

And of course there is another problem with synchronization, and that is that depending on my speed relative to yours, two events that are instantaneous in your reference frame will not necessarily be in mine.

Instantaneous for you is not instantaneous for me.

On the other hand you might think that the electron is slowly absorbed into the atom piece meal. If that is the case, then it isn't fundamental since you can have a fraction of an electron hanging around at times.

Another problem with this view is that using mirrors and absorbing materials you can shape the electron's wave function into an arbitrary shape.

How does the atom know where it all is?

How does the electron manage to keep itself intact when it's wave function can be arbitrarily shaped?

## VendicarD

I can scoop out a fraction of a "real wave" and keep it in a jar.

If I can do the same thing with an electron wave, then how is an electron fundamental and integral?

On the other hand if the electron then zips off to cosmic mongolia after I capture part of it, then when it is captured by an atom there, does my fraction of the electron in the box vanish?

Through what mechanism does it do so?

## johanfprins

Again correct.

Correct! It MUST be instantaneous: This is where "quantum jumps" come from.

This requires a very long post involving concepts like entanglement and timeless space, as found within a Black Hole, and also within the mass-intensity of a stationary electron-wave.

I am trying to publish a manuscript on this but cannot get it past the Orwellian swine in control on physics.

## VendicarD

If it didn't then all of calculus would be wrong.

"This equation is meaningless according to the rules of calculus." - Johanfprins

Is that your claim as well?

## VendicarD

Timeless space? What happened to your requirement that explanations be real?

Feel free to post an overview of your thoughts on the means by which an extended wave front is instantaneously converted to an electron - whatever that is.

## johanfprins

You are asking relevant questions which require long answers backed by mathematics. I am impreesed. I will have to be selective.

I do not: This is not possible.

You obviously can since an electron can be an extended wave that fills a block of metal.

The electron-wave is self-entangled and is thus in instantaneous contact with itself throughout its whole volume. Time does not exist within the volume of the electron wave. This is why, when stationary, it has a complex wave-amplitude.

## johanfprins

You cannot do this with an electron-wave just as you cannot "scoop" a part of a photon-wave. The latter is the lowest energy that a coherent light-wave can have.

Irrelevant nonsensical argument. Although an electron wave can move as two separate parts through the diffrcation slits, these parts are entangled and remains entangled. You cannot disentangle them as in the case where each part can become a separate single-electron wave.

## johanfprins

In calculus you NEED to take the limit to obtain a physically realistic answer: In your expression you do not need to take the limit. AS long as X is not equal to zero the difference will be zero: However, In the limit each term goes to infinity so that each term becomes undefined. To argue that by taking the limit so that you can substract infinity from infinity is absurd mathematical Voddo: Just like renormalisation is absurd in QED.

## johanfprins

Post your explanation why this is only possible when you interpret the wave-intensity as a probability distribution. Whatever the correct interpretation is, the experimental observations can only be explained by concluding that the wave's intensity MUST collapse instantaneously. When assuming that the wave has an energy-intensity that collapses (or inflates) instantaneously, less Voodoo is produced than assuming a probability distribution. It also supports Guth' s inflation.

## VendicarD

"The electron-wave is self-entangled and is thus in instantaneous contact with itself throughout its whole volume" - Johanfprins

The phrase "self-entangled" is just a place holder for what is really happening. And if an electron is just a wave as you say then there are no gears in place that allow it to collect itself into a nicely coordinated and synchronized whole as it is absorbed by an atom.

What is the internal mechanism by which this is done?

## VendicarD

"You cannot do this with an electron-wave just as you cannot "scoop" a part of a photon-wave. The latter is the lowest energy that a coherent light-wave can have." - Johanfprins

And if photons are just waves, then what is the internal mechanism that is preventing me from putting some in a reflective box, and taking it home?

Your answer should be that I can do this and I can keep it in the box until the photon proper is absorbed in which case the portion of it in my box just vanishes by decoherence.

But if I had something in the box, then how was it's energy instantly moved somewhere else at speeds > c?

If your claim is that I can't have a photon fragment in a box, then that disagrees with what we know about quantum states.

I can for example construct a photon wave puffer by trapping a photon in a reflective box that has a hole in it. There will be a periodic probability that the photon will escape through the hole and that CONT

## VendicarD

## VendicarD

I sympathize.

What you have replaced the concept with is a real wave that for some reason can't be subdivided, and which vanishes instantly over all of space without a mechanism for doing so.

I fail to see the improvement.

## VendicarD

It is possible that some portion of the electron is integrated into the atom and the remainder is manufactured, the bits of the electron that aren't integrated are left in the zero point froth that constitutes the vacuum.

"Whatever the correct interpretation is, the experimental observations can only be explained by concluding that the wave's intensity MUST collapse instantaneously." - Johanfprins

## VendicarD

"Post your explanation why this is only possible when you interpret the wave-intensity as a probability distribution." - Johanfprins

The only thing I can add is that the absorbing body is extended as well, and hence overlaps the particle being absorbed at least partially.

## johanfprins

I will proceed after you have answered this question.

## VendicarD

You are.

"Neither have you for the collapse of a "probability-wave." - Johanfprins

So the obligation is upon you to provide a reason why your brand of magical wave function collapse is any different than the standard one.

I have asked you several questions. So far, you haven't answered any of them other than claiming that your wave function collapses because it is self-entangled.

I sympathize with your view, but what is the physical mechanism behind this instantaneous - can vanish in an instant - no time is flowing - through the entire universe - absolutely fantabulous series of claims?

## VendicarD

The problem with this view however is that the remains of the initial electron are free to roam around the universe in a "virtual" state. How does the universe known that the remains are "virtual"?

Without some form of accounting there would be nothing preventing an electron from spontaneously appearing from nothing without a corresponding anti-electron.

I know of no evidence for spontaneous particle production like this.

"Do you agree that there must be a collapse of the wave for an electron or a photon to be absorbed. YES OR NO?" - Johanfprins

## cdt

## VendicarD

Those worthy of public execution will receive none.

"Let me just pipe in to say that it's nice to see a disagreement being hashed out respectfully in this forum" - cdt

## johanfprins

You have not yet answered my question: Whatever your interpretation of what an electron-wave is, do you agree that a free electron moving through space can diffract and that therefore it must have a wave-property that allows it to this? Do you agree that when observing the position of the electron with a detector this electron-wave MUST collapse! YES or NO?