Even though it is hard work, it is quite satisfying to drill holes in concrete. Apparently, my degree covers everything from construction to theoretical quantum physics. Good to know that I’m getting a well-rounded education.
I’m sitting in a coffee shop in Takoma Park, enjoying some espresso. I have to say that to the north of me, the neighborhood is, well, colorful and diverse. Driving down with my car, I accidentally was in an exit-only lane, and I couldn’t merge, due to the traffic. So I took surface streets to my place. First, went through downtown Bethesda—very expensive. Then, through downtown Silver Spring—a rather nice area. Finally, through the diverse neighborhood near me, which is…not so nice. As I drove east, the area became progressively worse. At least I’m not in College Park. It seems like I get a crime report from the University every day.
I will definitely miss Michigan. Lots of good friends. Lots of good memories. It was a somber drive south. I’m glad to have spent some time with old friends at Michigan. It was nice to see you again. For my friends who I didn’t get to see, I’m sorry we weren’t able to meet up. Hopefully I’ll be around soon. To my new friends in Ann Arbor/Detroit, I’m sorry to have left you so soon. My last Saturday in Michigan was fun—drinks at the Rathskeller with my friend M__ (whose ex is dating my ex), and then to Downtown Detroit with S__ (who cuts my hair) for a rave.
There has been a small splash in the past couple days about a couple Germans who have purportedly violated special relativity (see here, and here). So what’s going on here? Is this another superluminal propagation of light in a region with strong anomalous dispersion? For starters, here’s another article with a bit more detail, as well as a comment from Aephraim Steinberg (a quantum opticist at University of Toronto). Additionally, here’s the paper on the ArXiv: arXiv:0708.0681v1.
Well, what they’ve done is worked with Frustrated Total Internal Reflection (FTIR). First of all, total internal reflection is when all the light is reflected at the interface. This only happens when moving from a denser optical material to a more rarefied material. Past a certain angle, all the light is reflected. You’ve seen this if you look up while underwater. Typically, you can see the sky above you, only in a small disc. Outside that, all you see is the water. This is the same principle by which fiber optics works—the light is confined in a small glass rod.
Now, here’s a slightly weird part. Even though all the light is reflected, there is a small portion of it that hangs out at the interface, and extends into the rarer material. This portion is called the evanescent wave. Now, it turns out if another dense material is placed close enough to this evanescent wave, the light can actually be transmitted to the second material. This is very similar to Quantum Tunneling, where a particle can be transmitted through a potential barrier. This process is called frustrated total internal reflection.
Back to the paper and experiment. They conducted a FTIR experiment with microwaves, and measured the arrival times of both the reflected and transmitted signals. They claim that the signals arrived at the same time. This means that since the transmitted signal travels a longer distance, it must be moving faster than the speed of light. The paper is slightly dubious, as there is no data present in the paper.
The crux of the matter is the tunneling time. Now, the notion of time is slightly problematic in quantum mechanics—there is no ‘time’ operator to give us the arrival time of particles. In fact there has been much research on this. If I had decided I wanted to be a theorist, I probably would have been working with Herbert Winful on the theory of this.
The two questions are: Is there superluminal propagation in tunneling? How do we interpret what is going on?
Now we’re getting somewhere interesting. In their paper, they have an interesting take on this. They identify the evanescent wave with virtual photons:
All three properties - the violation of the Einstein energy
relation, the zero time spreading, and the non observability of
evanescent modes - can be explained by identifying evanescent
modes with virtual photons as predicted by several authors, see
for instance references 6, 7, 8, 9, 10. The corresponding Feynman
diagram is sketched in Fig. 2. Tunneling and evanescent modes
are properly described by quantum mechanics.
That is, a photon that doesn’t really exist, but can have an effect on the system. Virtual particles are abound in particle physics, where we typically detect the decay products of a virtual particle. Does this interpretation hold water? Perhaps. The theorist in me wishes for there to be a thorough, rigorous QED calculation showing this.
Steinberg offers a different interpretation:
Steinberg explains Nimtz and Stahlhofen’s observations by way of analogy with a 20-car bullet train departing Chicago for New York. The stopwatch starts when the centre of the train leaves the station, but the train leaves cars behind at each stop. So when the train arrives in New York, now comprising only two cars, its centre has moved ahead, although the train itself hasn’t exceeded its reported speed.
That is, given a pulse of light, the back end of it is eaten up, giving the impression that the center of the pulse has moved faster. I’m not sure if this holds water in this particular case. Perhaps when dealing with superluminal propagation in an region of anomalous dispersion, sure. But for evanescent waves, I don’t know.
Winful has another explanation of this effect (a long paper on this is available in the New Journal of Physics). From PRL 90, 023901 (2003), the final paragraph is:
In conclusion, we have shown that the apparent superluminal
tunneling of pulses is a quasistatic phenomenon
in which the output envelope adiabatically follows the
input. The incident peak does not actually propagate to
the exit which means that the notion of a transit time is
meaningless. The input field merely modulates the amplitude
of a standing wave created through the interference
between forward and backward waves. When properly
interpreted in this context, no superluminal transport is
seen
So what does this mean? It’s sort of like saying that the input merely increases and decreases the level of an existing wave inside the barrier. The pulse that comes out is not the pulse that goes in.
Suffice to say, I don’t think that this issue will be resolved any time in the near future.
First of all, I no longer have internet at home again…
So, last week I was at the Gordon Conference on Atomic Physics. Aside from lots of interesting talks and posters, there was drinking. Lots of it. And it was quite fun, staying up to 3am drinking margaritas, playing foosball, and talking. One of the highlights was America vs. Britain in Beirut/Beer Pong—where I made the winning shot. Downside: I spent my birthday travelling and hungover. But the hour we spent in Boston before our flight was fun.
Last week was also my Thesis Proposal. Here, I stood in front of my committee, and gave a small presentation of what I’ve done and what I will be doing for the next several years. Some tough questions, but it went quite well. For some reason I was far more nervous giving my talk to my group than my committee. Perhaps it is because they know what’s going on, and can call me out if I have anything wrong.
And now, I’m working in the lab as long as possible. There’s so much to do, and not much time left to do it. I have to go down to Maryland next week to look for a place to live in a month. Work work work. Fun times. At least the next project I’ll be working on will be totally awesome.
You find out about bands in the weirdest ways. I am preparing for my (doctoral) prelim/thesis proposal, and was looking up Turing Machines, and noticed a line at the beginning: For the instrumental rock band named after the devices described by Alan Turing, see Turing Machine (band).
Since I’ve been quite into the whole instrumental/post-rock/post-metal thing lately, I decided to check them out on last.fm. So far, I like what I’ve heard. So that was a nice distraction from learning the CS part of quantum computing.
As for the thesis proposal, I don’t know how long it should be. Physics students seem to only have to write about five pages. But for Electrical Engineering? I’ve seen on the EECS website a couple thesis proposals that are fifty pages long! I’m definitely not going to write that much.
Anyways, back to writing. Or maybe I’ll spend time figuring out why I have the world’s worst Rabi Flopping.
