RECENT ARTICLES

Microbead 'motor' exploits natural fluctuations for power.

New photon experiment gives new meta-framework, 'constructor theory,' a boost.

Experiments seek to use quantum observations as fuel to power mini motors.

Sally Shrapnel, a quantum physicist and medical practitioner, on her experiments into cause-and-effect that could help us understand time’s arrow—and build better healthcare algorithms.

'Artificial atoms' allow physicists to manipulate individual electrons—and could help to reduce energy wastage in electronic devices.

FQXI ARTICLE

October 17, 2021

Spot the Difference to Reveal Exotic Particles

Questioning the symmetrization postulate of quantum mechanics and the notion that electrons are indistinguishable could reveal whether hypothetical new particles exist.

FQXi Awardees: Philip Goyal

October 29, 2014

Philip Goyal

University at Albany (SUNY)

It may seem like a frivolous question, but the answer has profound consequences for the foundations of quantum theory. When carrying out quantum calculations, physicists must assume that electrons are identical and indistinguishable, and they formalize this using a rule called the

To understand why physicists developed the view that electrons are indistinguishable, picture the helium atom, which is made up of a nucleus and two orbiting electrons. (To get the simplest model of what’s going on, it pays to ignore any interaction between the electrons and their internal magnetic properties, known as their "spins.") The normal way to work out how the atom changes and evolves over time is to write down mathematical expressions for the energy of each electron and plug these into an equation, developed by one of the founding fathers of quantum theory Erwin Schrödinger.

In classical physics, we would treat identical electrons as distinguishable; that is, we could imagine labeling one as "electron A" and the other as "electron B" and then tracking their separate journeys over time. If you make that same assumption in quantum theory, however, you encounter a roadblock. The answer you get shows that both electrons can simultaneously exist in the lowest energy "ground state" of the helium atom. The trouble is that this directly contradicts another fundamental rule of quantum mechanics, the

Early pioneers of quantum theory in the 1920s, including Paul Dirac, realized that the situation could be rescued by enforcing a cunning mathematical rule called the symmetrization postulate. This requires treating two electrons as indistinguishable. If that’s the case, the math needs adjusting. The upshot is that the probability of two spinless, non-interacting electrons occupying the ground state also goes to zero—it’s impossible. Very conveniently the problem is solved. "It preserves the Pauli Exclusion Principle," says Goyal. But does that mean that it is necessarily correct? "What I want to know is whether the symmetrization postulate is just a rule of thumb that happens to work, or whether it is something more fundamental," Goyal adds.

Shaky Ground

Goyal’s mission to unlock the puzzle of the symmetrization postulate began when he was a student. "When I first encountered it as undergraduate I just didn’t believe any of the textbook arguments for it," he says. "Later I discovered that it had been on shaky ground from the very beginning of quantum theory. I find it fascinating that no-one knows where it comes from." Goyal plans to use a $93,127 FQXi grant to get the bottom of the mystery.

Experiments have already been carried out to test whether electrons really are identical and indistinguishable. They involve two electrons fired from electrons guns, one positioned on the left and the other on the right. The fired electrons enter a collision area in the middle and either scatter up or down. So there are two possible scenarios: either the left electron goes up and the right goes down, or the left goes down and the right goes up.

It turns out that you can calculate the probability of observing each outcome based on the idea that electrons are distinguishable—that they have some individuality of their own. The experimental results do not fit with this calculation, however. The measured probabilities do fit with calculations carried out assuming that the electrons are truly indistinguishable. These experiments suggest that this feature is fundamental, rather than something that arises through an experimental limitation.

Electron Identity

In 2013, the orbital structure of a hydrogen atom, with a single electron was imaged using

photoionization microscopy (

Dirac did present a logical argument for such a derivation in his original 1926 work on the subject; however, a flaw in his work was pointed out to him soon afterwards. Many others have since tried to bridge the gap between the abstract idea of indistinguishability and the symmetrization postulate. One of Goyal’s goals is to analyze and carefully critique those arguments. He also hopes to reconcile them as they lead to very different conclusions about the quantum nature of identical particles.

The lack of a rigorous grounding of the symmetrization postulate in fundamental physics opens the door to a tantalizing possibility. This hinges on the different rules needed for combining particles of different types. Electrons are part of a larger family of particles called "fermions." According to the postulate, to combine the wavefunctions of two fermions in order to carry out further quantum calculations, you first swap the two electrons over and subtract the resulting wavefunction from the original one. This is called "anti-symmetrizing" the wavefunction. By contrast, if you add the swapped wavefunctions, then you are "symmetrizing" the wavefunction, which is the process required when describing the family of particles called "bosons" (which includes photons and the famous Higgs particle).

What this means is that without proof that either option isn’t just a cute mathematical trick, you can’t rule out other types of as-yet-undiscovered particle that violate the symmetrization postulate.

Indeed, one of the most influential approaches that attempts to derive the symmetrization postulate from scratch, proposed in 1977 by Leinaas & Myrheim (

Quasiparticles

There have been hints of anyonic behaviour seen in the experimental phenomenon known as the "fractional quantum Hall effect." In these experiments, an electron gas, confined to two dimensions, is subjected to a magnetic field. Under these conditions, the gas appears to behave as though it is made up of a new kind of "quasiparticle" that conducts in such a way that it appears to have a fractional charge. The 1998 Nobel prize in physics was awarded to the physicists who discovered and described this effect.

If we didn’t have the symmetrization

postulate, we wouldn’t understand

basic chemistry or star formation.

postulate, we wouldn’t understand

basic chemistry or star formation.

- Yasser Omar

In September 2013, Goyal published a paper in which he describes a way to derive the symmetrization postulate using an information-theoretic approach that does not involve labeling the electrons ( arXiv:1309.0478). Crucially, his derivation implies that identical particles do not generically exhibit anyonic behaviour in two dimensions. Goyal plans to use his FQXi grant to understand how to square this with the conclusion of Leinaas & Myrheim’s 1977 argument.

Yasser Omar at the Instituto de Telecomunicações in Lisbon, Portugal finds Goyal’s work to be "very intuitive and elegant." "I give him great credit for tackling a problem that a lot of people assume is solved when it isn’t," he says. "If we didn’t have the symmetrization postulate, we wouldn’t understand basic chemistry or star formation, so it is great to see a new take on the problem of where it comes from." However, Omar believes that it important to investigate how Goyal’s new work fits with the fractional quantum Hall effect experiments.

"I’m glad this fundamental research is being funded. It really touches the heart of quantum physics," says Guglielmo Tino, a quantum physicist from the University of Florence, Italy. "There have been many attempts to find a good justification and formal treatment" of the symmetrization postulate, "but there is still a lot of room for new ideas."

Comment on this Article

Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!

function ValidatePostText_main () {
form = document.addPostForm_main;
var recaptcha = $("#g-recaptcha-response").val();
if (recaptcha === "") {
event.preventDefault();
alert("The reCaptcha Box below must be checked before you submit the form");
}
else if (form.postText_main.value == '') {
alert ("The post contains no text");
return false;
}
else {
return true;
}
}

**Your name:**
(optional)

Recent Comments

read all article comments

Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!

Please enter the text of your post, then click the "Submit New Post" button below. You may also optionally add file attachments below before submitting your edits.

HTML tags are not permitted in posts, and will automatically be stripped out. Links to other web sites are permitted. For instructions on how to add links, please read the link help page.

You may use superscript (10

^{100}) and subscript (A_{2}) using [sup]...[/sup] and [sub]...[/sub] tags.You may use bold (

**important**) and italics (*emphasize*) using [b]...[/b] and [i]...[/i] tags.You may also include LateX equations into your post.

Insert LaTeX Equation
[hide]

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation

clear equation

insert equation into post at cursor

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation

clear equation

insert equation into post at cursor

Attachments
[hide]

You may optionally attach up to two documents to your post. To add an attachment, use the following feature to browse your computer and select the file to attach. The maximum file size for attachments is 1MB.

Once you're done adding file attachments, click the "Submit New Post" button to add your post.

You may optionally attach up to two documents to your post. To add an attachment, use the following feature to browse your computer and select the file to attach. The maximum file size for attachments is 1MB.

Once you're done adding file attachments, click the "Submit New Post" button to add your post.

AMRIT wrote on February 22, 2019

God Particle has died.

https://www.amazon.com/dp/1797718037

God Particle has died.

https://www.amazon.com/dp/1797718037

RESMI GIRL MALIK wrote on March 5, 2018

I really enjoy simply reading all of your weblogs. Simply wanted to inform you that you have people.like me who appreciate your work. I regard all that you have incorporated the degree that anyone is the concerned base.

Call girls in Delhi

I really enjoy simply reading all of your weblogs. Simply wanted to inform you that you have people.like me who appreciate your work. I regard all that you have incorporated the degree that anyone is the concerned base.

Call girls in Delhi

QUANTUM ANTIGRAVITY wrote on April 17, 2017

EXPERIMENTAL quantum Anti-gravity — https://quantumantigravity.wordpress.com

I have made a theoretical as well as an empirical scientific discovery

of quantum gravity and quantum antigravity.

Present day quantum gravity theories suffer from

too many mathematical space dimensions, and from

too few conclusive experimental results.

My hypothesis is simple, clear,

and subject to easy empirical verification :...

EXPERIMENTAL quantum Anti-gravity — https://quantumantigravity.wordpress.com

I have made a theoretical as well as an empirical scientific discovery

of quantum gravity and quantum antigravity.

Present day quantum gravity theories suffer from

too many mathematical space dimensions, and from

too few conclusive experimental results.

My hypothesis is simple, clear,

and subject to easy empirical verification :...

read all article comments