Back-of-the-Envelope Gravitational Which-Way

There’s a new Science Express paper on interfering clocks today, which is written up in Physics World, with comments from yours truly. The quote is from a much longer message I sent– with no expectation that it would end up as anything other than a pull quote, I might add, but I thought the background would be helpful. Since I ended up doing a back-of-the-envelope estimate for that, though, I thought I would reproduce some of the reasoning here.

The basic proposal idea here is to do an atom interferometer inside a Ramsey interferometer for making an atomic clock. That is, before sending the atoms into the beamsplitter, you prepare them in a superposition state, like the first step in making an atomic clock. This gets you a superposition state with a phase that oscillates at the frequency associated with the atomic transition, which is what you use to make the clock.

In this case, though, the claim is that a different rate of “ticking” of the clocks along the different paths of the interferometer– say because one is at a higher altitude than the other, and thus subject to a gravitational time dilation from general relativity– could serve as a “which-way” measurement that would destroy the quantum interference effect. That is, the fact that the upper clock ticks more rapidly than the lower would let you distinguish which of the two paths the atom “really” followed on its way through, by making a clock measurement after you recombined the two paths. This would destroy the interference, which would reduce the contrast of the interference pattern. As a demonstration, they applied an artificial shift to the “clock” on one arm of their (horizontal) interferometer, and showed that when they make the resulting phase shift an odd multiple of π, the interference pattern gets wiped out.

As I said to Physics World, you would need to talk to a real atom interferometrist to clarify the difference between what they’re doing with the clock superposition state and a Ramsey-Bordé interferometer, and also to make sure there’s a sharp distinction between the gravitational shift they’re talking about and the phase shift people doing gravitational measurements with interferometers already measure. Assuming they’re right, though, you can try to estimate whether this would really be measurable.

The gravitational time dilation they’re talking about as making the “which-way” distinction is, near the surface of the Earth, approximately:

$latex T \approx T_0 (1+\frac{gR}{c^2} )$

where T is the time between ticks for the clock a distance R from the center of the Earth (something not too different from the radius of Earth), T0 the time for a clock far away from anything massive, and g the strength of gravity near the surface of the Earth. If you plug numbers in for two clocks at different elevations, this is a shift of about one part in 1016 per meter of difference.

(As a sanity check, that’s about what they see in the aluminum-ion clock experiment at NIST: they raised one clock above the other by about 33cm, and see a shift of a bit under 5 parts in 1017. So I’m not completely off base, here…)

The largest separation between paths I’m aware of in an atom interferometer is the 10-meter tower interferometer in the group of my old boss, Mark Kasevich. That’s from 2013, with a separation of a centimeter and a half. I have heard, but not seen solid documentation of, that they’ve expanded this to half a meter or so.

To get the interference-destroying effect, they applied a phase shift of π to one arm, which would correspond to half a “tick” of the clock– that is, half the oscillation period. To see this gravitationally, you would need to have that part-in-1016 shift amount of a difference of one oscillation period over the time in the interferometer (a couple of seconds for the 10-m tower). For a microwave clock transition like you have in the rubidium used in the Kasevich group, you’re a factor of a million away– the frequency is about 7,000,000,000Hz, so the shift would be on the short side of a microhertz. That’s not going to do much.

You might, however, get somewhere with one of the optical clock atoms, like strontium. the “clock” transition in Sr is in the visible region, at around 400,000,000,000,000Hz, so a part-in-1016 shift is close to 1Hz. Over a couple of seconds, that’s probably enough phase shift to significantly degrade the contrast, based on the graph in the new paper.

How plausible is that? Well, it’s not ridiculous. The 10-m tower experiments use a BEC of rubidium, and strontium has also been Bose condensed. So if you adapted the giant tower to use Sr rather than Rb (a challenge, but probably not impossible), you might be able to see something. Assuming you could distinguish this effect from the many, many other things that can degrade the contrast of an atom interferometer signal. (For that, I think you’d want to see a revival of the contrast, which means getting to a phase shift of 2π, and you could map the effect out by gradually increasing the separation through changing the momentum imparted by the laser beamsplitters in the interferometer.)

Does this sort of thing have anything to say about the interaction of gravity and quantum mechanics? Probably not, in my semi-informed opinion. It’s a much more clearly defined mechanism than you see in most theories invoking gravity as a reason for a loss of “quantum-ness” in macroscopic experiments (which tend to be of the form “We don’t understand the quantum-to-classical transition, and we don’t understand gravity, therefore they’re related”), so it’s at least something you could probe experimentally. It’s a really small effect, though, even in the most impressive interference experiments done to date, and seems to require a rather special set of experimental conditions (both a vertically oriented interferometer and a superposition of internal states), so I think the implications for quantum foundations are probably minimal.

It’s a clever idea, though, and it would be interesting to see somebody give it a try.

My Week in Waterloo

I spent the last few days in Ontario, attending the Convergence meeting at the Perimeter Institute. This brought a bunch of Perimeter alumni and other big names together for a series of talks and discussions about the current state and future course of physics.

My role at this was basically to impersonate a journalist, and I had a MEDIA credential to prove it. I did a series of posts at Forbes about different aspects of the meeting:

The Laser Cavity was Flooded: a revisiting of the idea of True Lab Stories, which was a loose series of funny disaster tales from the early days of ScienceBlogs.

Converging on the Structure of Physics: Talks from the first day fitting a loose theme of looking for underlying structure.

All Known Physics in One Meeting: The second day of talk covered an impressive range, from subatomic particles to cosmological distances.

Making Lampposts to Look for New Physics: Tying the closing panel discussion to an earlier metaphor about searching “where the light is” for exotic phenomena.

As I said, I’ll have some more follow-up next week, picking up and running with a few asides or themes that came up at the meeting. For the moment, though, I’m pretty wiped out, having put in almost 780 miles of driving over the last four days, and staying up late hanging out with science writers and theoretical physicists. So this summary post will have to hold you…

Tiny Forces, Artificial Materials, and Wobbling Stars: Physics Post Round-Up

I’ve been really busy with year-end wrap-up stuff, but have also posted a bunch of stuff at Forbes. which I’ve fallen down on my obligation to promote here… So, somewhat belatedly, here’s a collection of physics-y stuff that I’ve written recently:

Using Atoms To Measure Tiny Forces: A post reporting on some very cool atom interferometry experiments, one working to measure the very tiny (but known to exist) force of gravity, the other searching for a possible “fifth force” sort of thing.

Making And Shaking New Materials With Ultracold Atoms: A post reporting on a couple more DAMOP talks, on Cheng Chin’s group using physical shaking to simulate unusual band structures, and Cindy Regal’s group using single atoms trapped in optical tweezers to study few-body physics.

What Are The Limits Of Physics?: Having gone to a bunch of precision-measurement talks at DAMOP, I talk about three rough categories of effects that limit our ability to use experimental physics to understand the universe.

Using Ultrafast Lasers To Look For Earth-Like Worlds: A post about the ongoing “astro-comb” project using femtosecond lasers as reference sources to improve radial-velocity measurements for extrasolar planet hunting.

The first two were banged out at breakfast while I was at DAMOP, so they’re a little rough. I’m very happy with the other two, though. I also had a post about fictional magic and one about the real purpose of conference talks.

As always, the traffic stats for these are sort of bizarre. Half-assed philosophy of science got about five times the hits of solid physics reports, but the academic conference thing drew so few views that I thought the analytics package might’ve crashed. Go figure.

Anyway, that’s what I’ve been up to. This weekend, I’m off to another meeting, the Convergence workshop at Perimeter Institute. I’m function mostly as a journalist at this, which ought to be interesting.

Amazing Blackbody Radiation and LHC Basics

I was proctoring an exam yesterday in two different sections of the same class, so I had a lot of quite time. Which means I wrote not one but two new posts for Forbes…

The first continues a loose series of posts about the exotic physics behind everyday objects (something I’m toying with as a possible theme for a new book…), looking at the surprisingly complicated physics of an incandescent light bulb. A light bulb filament emits (to a reasonable approximation) black-body radiation, which is historically important as the starting point for quantum physics. But when you think about it, it’s kind of amazing that you get a black-body spectrum from a large collection of atoms that absorb and emit at discrete frequencies…

(As I type this, I have a crude Monte Carlo simulation running in VPython, so there will be more on this subject later…)

The second post was prompted by the news that the LHC is now colliding protons at 13TeV, and offers answers to some really basic questions about the LHC.

So, you know, if you’d like some physics-y stuff to read as you wait for the official start of the weekend, well, there you go…

Breaking Boards

One of the highlights of teaching introductory mechanics is always the “karate board” lab, which I start off by punching through a wooden board. That gets the class’s attention, and then we have them hang weights on boards and measure the deflection in response to a known force. This confirms that the board behaves like a spring, and you can analyze the breaking in terms of energy, estimating the energy stored in the board, and the speed a fist must have to punch through the board. As a sort of empirical test, we can drop a half-kilogram mass from the appropriate height to match the calculated speed, and see if it goes through.

As mentioned earlier this week, I have a camera that shoots high-speed video now, so of course I decided to get a shot of the breaking boards:

It’s interesting to see how quickly the break happens– this is shot at 1000 fps, and between one frame and the next, the board goes from solid-but-bent to broken more than halfway through. It’s also interesting that in the second break shown in the video, the break occurs at a point a good deal away from the spot where the mass hits.

And, of course, there’s the obligatory gag reel at the end, from one of the several shots where the board didn’t break, and the mass bounced up to knock over the big demo caliper set that I propped up to provide a reference scale behind the board. Good times, good times…

On Toys in Science

The big social media blow-up of the weekend was, at least on the science-y side of things, the whole “boys with toys” thing, stemming from this NPR interview, which prompted the #GirlsWithToys hashtag in response. I’m not sorry to have missed most of the original arguments while doing stuff with the kids, but the hashtag has some good stuff.

The really unfortunate thing about this is that the point the guy was trying to make in the interview was a good one: there’s an essentially playful component to science, even at the professional level. I took a stab at making this same point over at Forbes, only without the needlessly gendered language to make people angry.

(Which, of course, will cut into its readership, but I’m not so far gone that I’ll resort to deliberately offensive clickbait…)

Toy Roller Coasters and the Energy Principle

One of the points I make repeatedly in teaching introductory mechanics (as I’m doing this term) is that absolutely every problem students encounter can, in principle, be solved using just Newton’s Laws or, in the terminology used by Matter and Interactions, the Momentum Principle. You don’t strictly need any of the other stuff we talk about, like energy or angular momentum.

Of course, just because you can solve any problem using the Momentum Principle doesn’t mean that you want to solve those problems that way. As an example of a problem that’s really annoying to solve with just the Momentum Principle, I generally break out a toy looping roller coaster that we have in the department’s collection of demo gear. And, sinc eI have a slow-motion camera now, I shot some video of it:

That’s three clips spliced together, partly because the camera’s format doesn’t play nice with Tracker Video (sigh…), but mostly because it makes a useful point, namely that if you don’t start the car high enough up the track, the car won’t make it all the way around the loop.

It’s easy enough to calculate the speed the car needs to have at the top to make it around using just the Momentum Principle, but finding the position on the hill where it will reach the necessary speed at the top of the loop is a harder matter. You can get a good estimate of the start position very quickly if you think about the problem using energy methods, though– at the top of the loop, the cart has to have a minimum speed, and it’s above the ground by some amount, so you can work out the total kinetic plus potential energy it has as it makes the loop. all of that had to come from the gravitational potential it has at the top of the hill, which lets you get the start height. And, indeed, that’s how I figured out where to have my student hold the cart for the second and third clips in the video…

Since I have this, of course, I can crank the clip into Tracker Video Analysis (once the idiot format problem is fixed, sigh…) and measure the position of the car as a function of time. Which gets me a reconstruction of the track that looks like this:

Reconstruction of the roller coaster track from positions measured in Tracker Video.
Reconstruction of the roller coaster track from positions measured in Tracker Video.

(Yeah, it’s a little oblong, but I was selecting these positions using a trackpoint on a laptop, so I wouldn’t read too much into that…) Those positions let you work out the velocity of the car as it goes, which can be combined to find the speed:

Speed of the car going around the loop, as a function of time. Smoothed by taking a running average of five points.
Speed of the car going around the loop, as a function of time. Smoothed by taking a running average of five points.

This shows basically what you expect: the speed increases to a maximum at the bottom of the hill, drops as the cart climbs the loop, reaching a minimum at the top, then goes back up on the way down. The reconstruction of the loop shows a radius of about 15cm, which implies a minimum speed to complete the loop of around 1.2 m/s. The minimum seen in the speed graph is a bit over 2 m/s, a nice safety margin.

Since Rhett is already done for the semester (I have two more weeks of class, grumble mutter grump), I guess it falls on me to assign you some physics homework, so:

— The graphs above are for the first of the video clips. Do your own video analysis of the second and third clips, and find the minimum height for the release.

— Use the difference between the peaks in the speed graph to estimate the force of friction and air resistance acting on the car as it rolls along the track.

— Use the reconstruction of the roller coaster loop to write a VPython simulation of the car moving on the track using only the Momentum Principle.

Send your homework to Rhett for grading, since he has lots of free time these days.

Colliders, Observatories, and Precision Measurements, Oh My!

The editor at Forbes suggested I should write something about the re-start of the Large Hadron Collider, so I did. But being me, I couldn’t just do an “LHC, yay!” post, but talk about it in a larger context, as one of three major approaches to filling the gaps in the Standard Model:

The big physics story over the weekend was the re-start of the Large Hadron Collider at CERN, the world’s largest and highest-energy particle accelerator. It was initially started in 2008, but some key circuits failed shortly after it was switched on. A relatively quick patch job allowed it to operate at half its designed energy for a few years, long enough to discover the Higgs boson and secure a Nobel Prize for two of the half-dozen theorists with a claim to have invented it, then it shut down for two years of more comprehensive repairs. It’s back now, and better than ever, hopefully able to begin colliding protons at its original specs within the next several months.

But you might be asking “Why is this a big deal, anyway?” Well, it’s a big deal because our very best theory of fundamental physics is wrong, and everybody knows it. We just don’t know how it’s wrong.

So, you know, if that sounds appealing, go over there and check it out…

How Fast Is SteelyKid’s Nerf Gun?

SteelyKid is spending a couple of days this week at “Nerf Camp” at the school where she does taekwondo. This basically consists of a bunch of hyped-up kids in a big room doing martial activities– taekwondo class, board breaking, and “Nerf war” where they build an obstacle course and then shoot each other with dart guns. Which, of course, required the purchase of upgraded Nerf weaponry, as seen in the “featured image” above.

This thing fires darts at a fearsome speed– they hit the ceiling with really loud “thwack” that was a huge hit with both kids. Of course, you know what’s coming next, given that she has a new toy gun, and I have a camera with a high-speed video mode:

There are two short clips here of SteelyKid firing the gun in front of a wooden ruler for scale: one at 480 frames per second, the other at 1000 frames per second. Of course, the obvious thing to do with these is to crank them into Tracker Video and measure the speed of the darts. This turned out to be needlessly complicated because digital video formats are stupid and evil– in fact, the main reason I pasted those clips together in the YouTube video above is that the raw video from the camera didn’t behave properly in Tracker. After an inordinate amount of work, though, I got the following graph of the dart position as a function of time:

Dart position vs. time for SteelyKid's Nerf gun, from video clips with two different frame rates.
Dart position vs. time for SteelyKid’s Nerf gun, from video clips with two different frame rates.

As you can see, each of these produces a very nice straight line (after a frame or two delay at the start of the analysis, to set the zero position). The field of view for the 1000fps setting is smaller than for the 480 fps setting, so that track stops sooner. But both sets of points agree very, very nicely with each other, which is great.

I can fit straight lines to both of these, and get the speed of the dart, which comes out to 22.1+/-0.3 m/s from the 480 fps data, and 20.9+/-0.2 m/s for the 1000 fps data. Those don’t quite agree within the statistical error bars, but given that both images are pretty blurry, I would say they agree within the uncertainty imposed by my scaling. That’s a speed of about 47mph, if you favor American units of measure, or “pretty damn fast for a toy dart gun” in any system of units. Fortunately, the darts are really light, so don’t hurt all that much even if you put your hand six inches in front of the barrel and let SteelyKid fire a pair of darts into it. It doesn’t feel good, mind, but it’s not that bad…

One more quick item from this: the box proudly proclaims “Shoots up to 75 feet!” a claim that positively demands further investigation, because it doesn’t specify some critical information. Specifically, it doesn’t say anything about the angle of launch, or the direction of measurement, and the actual range of a projectile will depend critically on both of those.

We can say something about whether this is a reasonable claim, though, using the measured velocity and basic intro-physics kinematics (in the form of the trajectory calculators at HyperPhysics, because I’m lazy). If you do the lazy-physicist thing, and ignore air resistance, a projectile with an initial speed of 21 m/s launched at 45 degrees for maximum range would travel about 45 meters, or almost 150 feet. Of course, ignoring air resistance is a terrible approximation for lightweight Nerf darts, so that range would be much shorter. Is half as much reasonable? I don’t know, probably.

Interestingly, if you take that same launch speed, and direct it straight up, you find a predicted maximum height (ignoring air resistance) of about 22.5m, or just a hair under 75 feet. So, the real question here is, does the “Shoots up to 75 feet!” claim come from experimental tests to measure the maximum range of the real darts, or does it come from a lazy freshman-physics calculation for a vertical launch?

The only proper way to test this would be to go somewhere and make measurements of the true maximum range. As the outdoor temperature is currently in the negative Fahrenheit range, with a wind chill down low enough that you don’t need to specify units, though, I think that will have to wait for spring…

Particle-Wave Duality for Eight-Year-Olds

Over at Scientific American’s Frontiers for Young Minds blog, they have a great post on what happens when you ask scientists to explain key elements of a different research field. It’s pretty funny, and rings very true, as SteelyKid asks me tons of science questions, very few of which have anything to do with atomic, molecular, or optical physics. so I spend a lot of time faking my way through really basic explanations of other fields.

Of course, even pitching stuff from my own field at the right level for small kids is a challenge. Which reminds me, I never did explain my presentation for the young kids at the Renaissance Weekend, and I probably ought to say something about that.

When I signed up to do stuff there, I said I’d be happy to talk to kids about science, not entirely realizing what level I was getting myself in for. they put me down to do “What Every Dog should Know About Quantum Physics” for their “camp” program, which turns out to be ages 6-12. And I had half an hour, instead of the usual hour. Which presented what you might call a formidable challenge…

I decided to try for something at least somewhat active, rather than just PowerPointing at them. Since the goal was to get a little sense of the weird-and-cool part of quantum physics, I opted to try to explain particle-wave duality via the double-slit experiment.

The wave part is easy– I carry a green laser pointer in my laptop bag basically all the time, and I borrowed a couple of double-slit slides from the teaching labs, one to pass around, and one to shine the laser through. Laser pointers in general are endlessly fascinating to little kids, and seeing it go through slits and make lots of spots is way cool.

How to do the particle half, though? Well, I remembered a public talk I saw at the Perimeter Institute ages and ages ago where one of their outreach folks gave a talk on quantum, and talked about doing the double-slit with progressively smaller things. At one stage, he was imagining doing it with grains of sand, and passed a pinch of sand to people in the front row, “In case you need to remind yourself how big a grain of sand is…”

So, I latched onto that, and produced this:

Experimental set-up for the double-slit experiment with classical particles (salt crystals).
Experimental set-up for the double-slit experiment with classical particles (salt crystals).

That’s a double-slit experiment done with particles that are small, but undeniably classical particles. For this test at home, I used table salt; at the actual event, I used colored sugar. I cut a couple of slits in a piece of cardboard, propped it up on a stand (actually the box for my laser pointer), and poured particles through. You can see a big pile on the top, because only a fraction of the particles made it through the slits, and two distinct piles down below. Which is exactly what you expect for classical particles that have to go through either one slit or the other.

So, I had live demos for both particle and wave behaviors, and could then go to Hitachi’s awesome single-electron interference video to show the quantum version. Which I think works to make the key point: when you get down to really small things, the rules change, and you get the weird quantum case, that’s both particle-like and wave-like at the same time.

How did it work in practice? Kind of a mixed bag.

For one thing, I had somewhat overestimated the audience– the median age of the kids was probably eight. The handful of slightly older kids were duly impressed, but the younger ones mostly just wanted to eat the colored sugar. I also had had to remove most of the dog material, which was a mistake– if I ever need to do this again, I’ll lead into it with some additional cute-dog photos.

I’m not quite sure how I would end up needing to do this again, but I’d be willing to give it another shot, so if you’d like me to talk quantum physics to second-graders, drop me a line. But really, if I go to Charleston again and find myself speaking to the campers, I’ll probably stick with the classical physics of sports equipment

(Completely independent of this, I do have an idea for a way to introduce quantum physics to the picture-book set, which I’d be happy to talk about to anybody who might have the art skills to help make such a thing…)