The Electron is Still Round

My experiment’s paper just got published today in Nature: Improved limit on the electric dipole moment of the electron.

An accompanying blog post:

Basically, even with our 12-fold increase in precision, we still found that the electron’s electric dipole moment is zero, casting doubts on the viability of many versions of supersymmetry (which is required for more fancy theories such as string theory) as well as mechanisms for how there came to be more matter than antimatter! Particle physics still doesn’t know why the universe exists.

This result is also very significant because it is effectively probing for particles at the 3-30 TeV level. This means that as we didn’t find anything deviating from the Standard Model of particle physics, it’s likely that people at the Large Hadron Collider also will not find anything unexpected in the next few years. We’re basically all kind of stumped at this point.

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Very nice. I imagine it was inspired by discussion on this form . I seems to recall on of your early conversations with us was precisely on this topic.

In all seriousness, this is really exciting for you, and us because we know you. Be proud:

https://www.nature.com/articles/s41586-018-0599-8

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Congratulation and nice work. I am glad the electric field of the electron is still round. I am sure that if it wasn’t, a flat electron society would emerge.

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@dga471 Congratulation you made Science Daily!

https://www.sciencedaily.com/releases/2018/10/181017140928.htm

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Congrats on the paper, Daniel!

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Yes - congrats from UK, too. Supersymmetry isn’t having a good time at present.

Electrons are round - the universe is flat. Whatever next?

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@dga471 you’re being covered at UD:

We should invite them to talk to you here.

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That’s interesting. I guess they just cover random science results? I didn’t see any sort of spin for ID in that article.

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Congratulations!

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They do, somewhat as Patrick does here. However, if there’s a sub-text, it’s on the departure from empirical evidence in physics in favour of explanations allowing self-creation, and notably string-theory (hence multiverse, etc). Peter Woit is fairly often quoted at UD.

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I see. Well, the interesting thing is that despite the frequent invocation of multiverses, string theory, and other speculative concepts in philosophical debates about origins, most experimental physicists who actually test these theories seem to be neutral or skeptical about most of these ideas. While nobody is skeptical of the modern practice of science as some ID proponents are, the prevalent view seems to be “shut up and measure”.

As a physicist who’s also a Christian, I marvel at the fact that we’ve been able to formulate and empirically verify a theory as complex and sophisticated as the Standard Model, flawed and incomplete as it is. It’s as if God has allowed us a little glimpse into the inner workings of His creation. But it could be that there are limits to what He allows - that even though we continue to try our best, we will never be able to empirically verify a theory that unifies all the four forces (or even three of them), because we would need to conduct experiments with unfathomably high energies. It could be that one day, the astounding success of particle physics in the last century will come to an end. I really hope this isn’t the case, though!

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@dga471, how smooth is an electron? Quoting from your paper, you say the

\left| d \right| < 1.1 \times 10 ^ {-29} 1e cm

With confidence 90%, and 1e cm equal to 1.6 \times 10^{−21} Cm, and e is the electron charge. So what is the typical “width of an electron”?

Consistent with this limit, if we scaled an electron up to the size of the earth, how high could the deepest valley and highest mountain be? What would be the highest average deviation from sphere we could see?

What if we scaled that electron up to the size of the sun?

How smooth is an electron, really?

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@dga471, here is one naive calculation, which I am curious if it is correct.

The dipole moment, which you measured, is equal to distance apart times charge. The charge of an electron is 1e. So, then, we should be able to compute the max distance as…1.1 \times 10 ^{-31} m.

So…what is the “radius” of electron. Well, I’m not sure that is so well defined…hmm. How about we do this relative to a proton? Which as a radius of 0.87 \times 10^{−15} m. The ratio of these is Now, the earth is 3,959 miles wide. Multiplying this radius times the ratio of the max dipole and the proton radius, we get:

5.00563218 × 10^{-13} miles

Which is about 0.8 nm, just a little less than a buckyball (which is about 1 nm). If we use the sun instead, this is about 100 times more radius, which gives us 80 nm, not much bigger. What if we make the proton as big as the Milky Way galaxy? That is a 52 850.0417 light years large proton. Now we are getting somewhere. In this case, with a milky way size proton, the electron dipole distance would be at most 39.28 miles.

Which all goes to say that the electron is very (x31) round.

Now, I’m ready for @PdotdQ and @dga471 to clean up my math here. What did I get off? Where did I miss a factor or miscalculate?

In the Standard Model, electrons are fundamental particles, so they are point particles without a literal size or “width”. So when we say it is “round” we are referring to the electric field it produces. There’s not a clear, completely accurate way to convert the units of e\cdot cm into something tangible. The units of the electron electric dipole moment (EDM) reflect the fact that the energy of a dipole in an electric field is
H = \vec{d}_e \cdot \vec{E}
and the electric field \vec{E} is in units of V/cm. Thus multiplying with units of e cm give you units of eV, which is an energy unit. This is why an EDM is measured in units of e cm.

That being said, for illustrative purposes, we often assume the “size” of electron to be the classical radius of an electron, which is equal to 3 \times 10^{-15} cm. We don’t use this classical radius in particle physics calculations incorporating quantum mechanics, but it does establish some sort of rough upper bound of what length scales are relevant to an electron. My professors usually use this for illustrating how precise our experiment is. The precision of our experiment is (quoted from our paper)

\sigma_{d_e} = 4 \times 10^{-30}~e\cdot cm

(Note that the 1.1 \times 10^{-29}~e \cdot cm figure is a converted upper limit for a non-zero electron EDM, not the actual precision of the experiment, so the above number is more faithful to the original experiment.)

Thus we are measuring 1 part in 10^{15} deviations in the size of the (classical) electron. If we blow up the classical electron to the size of the Earth (~10^8 cm) then we are looking with a precision of 10^{-7} cm = 1 nanometer. Note that this is about 1/100,000th of a human hair!

You can now choose your own scaling here: just multiply by 10^{-15}. If we blew up the electron to the size of the sun, we would be measuring deviations of 100 nm, or 1/1000th of a human hair. My favorite: if we blew up the electron to the size of the solar system (4.5 billion km), we would still be measuring deviations of millimeters. This is how amazingly precise the experiment is.

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I see that your calculation here basically gives similar results to mine (1 nm deviation for electron the size of the Earth), so we’re roughly in agreement.

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I’m mainly puzzled why your electron is about the same size as my proton. What gives there? How is that possible?

(now, if we are lucky, the @physicists will instruct the ignorant biologists in some physics)

All the calculations are based on the symmetry of the fields around the electron. The electron is still zero in size. r=0 You got to accept this as provisionally true. No faith nor beliefs required. Just acceptance of the model and the experimental results until a better model is experimentally verified. I know it is hard to accept a zero sized electron, but look at the wonderful things you can do by manipulating electrons.

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