## Kyle E. Ballantine

St Andrews, Scotland, United Kingdom

**AAAS** profile:

• There are many ways to spin a photon: Half-quantization of a total optical angular momentum

• PDF: http://advances.sciencemag.org/content/2/4/e1501748/tab-pdf**Articles**: *Meissner-like Effect** , *Phys. Rev. A: Dicke Models**ArXiv****ResearchGate**: What are the different methods of separating a light beam into components, having different orbital angular momentum?

First email: 9 October 2018

Dear Dr. Kyle Ballantine:

Congratulations on your work to produce your AAAS *Science Advances* article: *There are many ways to spin a photon: **Half-quantization of a total optical angular momentum** *(April 2016). Outstanding work with John Donegan and Paul Eastham. And, of course, congratulations on that PhD.

I have started an article about your work in light of our on-going studies about the Planck base units. Most scholars are sure our work is specious thinking (and we have too many times over the years). Yet, doubling mechanisms are abundant throughout science and there are so many open questions and there must be root-root causes to everything, so we tarrying on.

Let me say, “Thank you for your work.” You will see that the article that I’ve started is replete with questions that I have directed to Prof. Paul Eastham.

Notwithstanding, I thought as a young, vibrant mind, you might have some comments (guidance) for us as well.

Thank you.

Most sincerely,

Bruce

PS. I keep a record of every email/tweet to all the scholars. It keeps my work focused (perhaps it just helps to control the redundancy). You’ll see my link to our working page of references to your work and to this email embedded within your picture on the article’s webpage.

**Endnotes**:

In 2011 in a high school geometry class we applied base-2 to the Planck base units to outline the universe in 202 doublings. The first 64 doublings are well below the threshold of instrumental measurements so we’ve been studying transformations between what we’ve called the CERN-scale at the 67th doubling (or notation) and any of the smaller notations.

We believe each of the 64-to-67 doublings are potential keys to understand the deeper dynamics of light.

Within your article’s **Abstract**, the following claims are made:

“In the usual three-dimensional setting, the angular momentum quantum numbers of the photon are integers, in units of the Planck constant *ħ*. We show that, in reduced dimensions, photons can have a half-integer total angular momentum. We identify a new form of total angular momentum, carried by beams of light, comprising an unequal mixture of spin and orbital contributions. We demonstrate the half-integer quantization of this total angular momentum using noise measurements. We conclude that for light, as is known for electrons, reduced dimensionality allows new forms of quantization.”

Within the **Introduction**, the following claims are made:

(*3*). Angular momentum effects are also emerging in the radio-frequency domain, for applications in astronomy and communications (*4*). Fundamental interest focuses on optical angular momentum in the quantum regime (*5*). The angular momentum of single photons has been measured (*6*), and entanglement (*7*) and Einstein, Podolsky and Rosen correlations (*8*) have been studied. This unique degree of freedom provides a basis for quantum information applications, with high-dimensional entanglement (*9*)…

**(14) F. Wilczek, Magnetic flux, angular momentum, and statistics.** Phys. Rev. Lett.48, 1146, 1982. CrossRefWeb of ScienceGoogle Scholar

- The orbital angular momentum of an electron orbiting in two dimensions around a magnetic flux need not be an integer, but can include an arbitrary fractional offset (
*14*). - Here we show, in analogy to the theory of fractional spin particles (
*14*), that an unexpected half-integer total angular momentum can arise for light. - For the electron, there is a fractional offset in the spectrum arising from the Aharonov-Bohm phase accumulated over a complete orbit around the flux line (
*14*).

**(15 & 16) F. Wilczek****, Quantum mechanics of fractional-spin particles**. Phys. Rev. Lett. 49, 957–959 (1982). CrossRefWeb of ScienceGoogle Scholar

The same mechanism introduces a phase factor in the exchange of particle-flux composites, implying that such particles have generalized or fractional statistics (*15*) as well as fractional spin.

**Paul R. Eastham** and Bernd Rosenow, “Disorder, synchronization and phase locking in non-equilibrium Bose-Einstein condensates” in “Universal Themes of Bose-Einstein Condensation”, eds. Proukakis, Snoke, Littlewood (CUP 2017)

**Focus, focus, focus**:

https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate

https://en.wikipedia.org/wiki/Quantum_state