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Hi folks. I'm Will aka @lethain.If you're looking to reach out to me, here are ways I help. If you'd like to get a email from me, subscribe to my weekly newsletter.

I know that this is an exercise in electromagnetism in non-inertial frames, and so the domain of general relativity. Beyond that, I have not had time to look into it, and am asking out of curiosity if the problem has already been solved.

I’ve consistently noticed that emails generate far more discussion than other distribution methods, which really shouldn’t have surprised me: I’ve been sending company-internal updates for some time and they’ve frequently created important, spontaneous conversations.

Second, one of the important contributions of leadership is creating ambient connective tissue across teams and projects. By sharing what I’ve learned about a new project, I find that often there are other folks who benefit from knowing, and that they wouldn’t have learned about the project otherwise. Is reading a huge number of status emails the right way to learn everything? No, absolutely not, but it’s a good supplemental method.

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where $\omega$ is the optical frequency and $\mathbf{r}$ picks out some location in 3D space. $\mathbf{E}$ is the complex electric field vector.

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This illustration explains how the photons, which can only have spin +1 or -1 to their direction of momentum, build up a polarized beam

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As an interesting note, these emails do not need to be widely read to be useful. I often find myself ignoring them initially but then going back to find the latest update from someone to answer a specific question later. Further, a small amount of sporatic reading goes a long way: I’ve found there is herd-immunity for missing information. If just one or two folks in a given group know something important, it’ll end up where it needs to go.

As is often the case, we drove adoption by modeling the behaviors, without ever asking folks explicitly to send them. Most of the folks I work with directly have taken up the practice of sending out similar updates. Which have reduced status updates in one-on-ones, and been helpful to refresh both their and my memory when writing their performance reviews.

This makes perfect sense. The circularly polarised wave was described by an electric field vector of constant length but with orientation going in a circle over time. In the rotating frame we don't see this rotation and are left with a vector of constant length and direction.

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Finally, each half around performance review time, I use these emails to compile my brag documents for the preceeding six months. Inevitably I’ve forgotten most things I’ve worked on, and these emails remind me of what I’ve done in a concise format.

5-15 report

Difficult but fascinating idea. I try to partly answer the classical EM question (note definite photon z spin say +1 corresponds to right hand circular polarized light wave). Assume we have a square (!) cross sectioned cylindrical beam of finite width. To get an angular momentum is tricky and the outer surfaces are very important in the momentum integrals. Anyway the EM field is not like a spinning solid pencil. The outer field parts do not in any sense circulate around the central ray. True, each parallel ray independently has its local E and B field rotating. So it is like a lot of separate spinners over a transverse plane. The outer spinners just spin in place they don’t circulate around the central ray. Choosing a frame rotating about a central ray may give E B static along that ray but further out from the center ray the E B fields would not be static in direction but would be rotating more and more as we move away from axis. It would get quite tricky using rotating system in special relativistic flat spacetime, similar to GR.

Note that in the rotating frame the circular polarised wave does not become the same as a linearly polarised wave. A linearly polarised wave with $\mathbf{E} = [1, 0]$ gives rise to $\mathbf{ \epsilon }(t) = [\cos(\omega t), 0]$. This is not the same as $\mathbf{ \epsilon }(t) = [1, 0]$. The overall magnitude of the instantaneous electric field for a linearly polarised wave has zeros, the circular field does not. The move to a rotating frame does not change this. Similarly starting with a linearly polarised field a move to a rotating frame does not make it become a circularly polarised field (it still has zeros).

About a year ago I started my most recent approach to sending weekly updates to relevant public (within the company) mailing lists. This practice is sometimes called a 5-15 report, reflecting the goal of spending fifteen minutes a week writing a report that can be read in five minutes. Personally, I create a new Google Doc each week and record anything I complete there, spending ten minutes polishing the list into something readable each Friday.

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For a circularly polarized plane wave, the $\mathbf{E}$ and $\mathbf{B}$ vectors rotate in a particular direction. For concreteness, say the electric and magnetic fields are given by: \begin{align} \mathbf{E} & = \frac{E_0}{\sqrt{2}}\left(\hat{i} +i\,\hat{j}\right)e^{ikz - \omega t} \text{ and}\\ \mathbf{B} & = i \frac{\mathbf{E}}{c}. \end{align} Now, if I enter a frame rotating with angular frequency $\omega$ that, if $\mathbf{E}$ and $\mathbf{B}$ were rigid physical vectors, would render them stationary, what do I see?

The trendy thing to do on the internet is to start publishing a newsletter. Trendy enough that even I started sending out my blog posts each week in email format.

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The "stationary" would be linearly polarized light at the instantaneous framework. The "seeing" may be achieved by rotating a linear polarisation filter at that frequency,( although I do not know it is feasible in the lab). Anyway one does not need general relativity to have non inertial frames.

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But it is clear the E B fields cannot be fixed in such a rotating frame except right on the central ray you choose for axis of rotation.

Perhaps for a very thin beam it may be approximately possible. Experimentally we would probably need ultra low radio frequency to be able to rotate an observer/measuring device but then the wavelength would be long and diffraction would make difficult the narrow beam requirement. It is a very tricky question imo.

I do recommend rolling out this practice, but if you’re considering rolling them out, I’d propose two quick rules to ease your initial rollout: (1) create a new mailing list for folks to send them to, not cluttering up existing lists, (2) make them optional to read, as their volume can grow quickly.

First, it’s easy for folks to become detached from their leadership’s priorities, and having a weekly update, sometimes a pointed weekly update, is a good way to close that gap. For this purpose, it helps to be as honest and direct about focuses and concerns as you can be without rocking the boat too much. (You probably should be rocking the boat a small amount.)

First of all photons are not electromagnetic light. Classical electromagnetic waves emerge from the quantum mechanical superposition of the wavefunctions of a large number of photons.

Now, if I enter a frame rotating with angular frequency ω that, if E and B were rigid physical vectors, would render them stationary, what do I see?