Relativity

Physics Blogging Round-Up: Gravity, Pigeonholes, Groundhogs, and Weirdness

drorzel — Fri, 05 Feb 2016 07:05:25 +0000

Physics Blogging Round-Up: Gravity, Pigeonholes, Groundhogs, and Weirdness

A long-ish stretch of time, but I was basically offline for a bunch of that because I needed to finish a chapter I was asked to contribute to an academic book. So there are only four physics posts from Forbes to promote this time:

-- 'The Expanse' Is A Rare Sci-Fi Show That Gets Simulated Gravity Right: Another post on the SyFy adaptation of "James S. A. Corey"'s books, talking about a nifty bit of visual effects that nods at the Coriolis force you'd see on a rotating space station.

-- What Is The Quantum Pigeonhole Principle And Why Is It Weird?: A paper published in the Proceedings of the National Academy of Sciences got some press with claims that you can put three quantum particles in two boxes without having any two particles together. Digging into it more, it's both less and more weird than that description.

-- Groundhog Day Physics: Four Stories You Hear Over And Over Again: In honor of our dippiest public holiday and a great Bill Murray movie, some physics stories that repeat regularly enough that you might be forgiven for thinking you were stuck in a time loop.

-- How Do You Deal With Quantum Weirdness?: An attempt to explain the two major groupings of interpretations of quantum physics.

I've got a bunch of travel coming up (about which more soonish), so blogging will remain a little sporadic, but hopefully not as comprehensively silent as I was for the last week or two of January.

drorzel Fri, 02/05/2016 - 02:05

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Atoms and Molecules

Blogs

Books

Forbes Recap

Great article about simulated gravity and coriolis, but when it comes to pedantic explanations, no one does it better than these crazy Canadians:

https://www.youtube.com/watch?v=aRDOqiqBUQY

Me in the Media: Two New Interviews

drorzel — Fri, 30 Oct 2015 07:23:30 +0000

Me in the Media: Two New Interviews

I've been slacking in my obligation to use this blog for self-promotion, but every now and then I remember, so here are two recent things where I was interviewed by other people:

-- I spoke on the phone to a reporter from Popular Mechanics who was writing a story about "radionics" and "wishing boxes," a particular variety of pseudoscience sometimes justified with references to quantum mechanics. The resulting story is now up, and quotes me:

It is hard to investigate the ethereal thinking around radionics, but physics is something that can be parsed. So I got in touch with Chad Orzel, a physics professor at Union College in New York and the author of several popular science books, including How To Teach Quantum Physics to Your Dog. This sounded about my speed, and I ran a few ideas about physics and radionics past him, particularly "quantum entanglement," which several people offered as evidence that radionics is possible.

"Entanglement is a very strange phenomenon," says Orzel. "But it's a very real thing."

[...]

"People try to invoke this as a way of justifying ESP sorts of things: 'Well, maybe electrons in your brain are entangled with electrons somewhere else.' There's a couple of problems with it," Orzel says.

You'll have to click through to see what the couple of problems are, though...

-- A little earlier, Irene Helenowski interviewed me by email. This went live last week, when I was in California, which is my excuse for not posting it until now.

Professor, how is Emmy doing these days?

She's doing well. She's getting on in years for a dog-- she's 13-- so she's slowed down a bit. But she's still pretty spry, and can about pull me off my feet when she really wants to get to something on one of our walks.

You discuss simulating a black hole at CERN. What is the current status on the scientists' progress with that project?

It's not so much simulating, as trying to _create_ a black hole. The idea is that if you can pack enough energy into two colliding protons, you can create a situation where they get close enough together, and have enough total energy that they form a tiny black hole.

This is very much a long-shot possibility at the energy of the actually existing LHC-- if nothing exotic is going on, there's no way the LHC energy is enough to make a black hole. There are some exotic theories where gravity gets dramatically stronger at short distances, though, and if one of these turned out to be true, there's a chance you could get a black hole. This would evaporate through Hawking radiation almost immediately, spraying out a burst of particles that could identify it as a black hole rather than a more typical collision.

There have been some searches for this in data from the first LHC run, and no sign of black holes has been seen. They just recently re-started at a higher energy (by a factor of two, not enough to make mini-black-holes likely), and I'm sure there will be more such searches. Nobody really expects this to pan out, but it would be tremendously exciting if it did.

Again, click through to read the rest.

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And while you're clicking on things, please consider taking a few minutes to respond to Paige Jarreau's survey of blog readers. It's for SCIENCE!, specifically her postdoctoral research on communicating science online.

drorzel Fri, 10/30/2015 - 03:23

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Physics Blogging Round-Up: Two Weeks' Worth

drorzel — Fri, 14 Aug 2015 08:08:36 +0000

Physics Blogging Round-Up: Two Weeks' Worth

I forgot to do this last week, because I was busy preparing for SteelyPalooza on Saturday, but here are links to my recent physics posts over at Forbes:

-- What 'Ant-Man' Gets Wrong About The Real Quantum Realm: On the way home from the Schrödinger Sessions, I had some time to kill so I stopped to watch a summer blockbuster. The movie was enjoyable enough, thanks to charming performances from the key players, but the premise is dippy even for a comic-book movie. It does, however, provide a hook to talk about quantum physics, so...

-- Great Books For Non-Physicists Who Want To Understand Quantum Physics: I did a bit of name-and-title-dropping at the Schrödinger Sessions, and a few of the writers asked if I had a list of books I would recommend (other than, you know, How to Teach [Quantum] Physics to your Dog). I didn't have one already put together, so I made a new post listing a dozen good books to read.

-- How Quantum Randomness Saves Relativity: Inspired in part by the many discussions of entanglement at the Schrödinger Sessions, a discussion of why you can't actually use entangled particles to send messages faster than light. "Spooky action at a distance" is impossible because of "God playing dice," a cute bit of historical irony.

-- What Has Quantum Mechanics Ever Done For Us? I know you get more and angrier comments on political posts, but for sheer "WTF?" weirdness in the comment section, nothing beats quantum physics. This is a short explanation of the quantum underpinnings of major modern technologies, in response to a crank who left a bunch of angry comments on a G+ link to the quantum randomness article.

Not a huge number of posts for two weeks of blogging, but I'm very happy with them. And the quantum randomness one in particular is a nice counter to some myths about science communication-- over 20,000 people have clicked through to read an article that builds up to a citation of the no-cloning theorem. I'm pretty proud of that.

drorzel Fri, 08/14/2015 - 04:08

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come correct my rant on reddit if you're so inclined. Cheers!

https://www.reddit.com/r/Physics/comments/3h2sh5/reddit_what_is_your_be…

First thank you for your on-going contributions to understanding the new physics such as the "How Quantum Randomness Saves Relativity".
Talking of which, in the video at around 1'12'' you talk of repeating the same experiment and getting the same result IF not interrupted by another experiment. I am writing a book which includes a section on time and that comment of yours is extremely profound. Do you know the name/authority for that observation?
It seems, at the quantum levels at least, as if that repetition is taken as one unit of time until interrupted.
.

Thanks Chad for taking the time to share your experience with this difficult arena of physics. One question please re what you said at about 1'12" of the video (How Quantum Randomness Saves Relativity). You say the experiment produces the same outcome until interrupted by another experiment.When reverting to the original experiment the outcome is again statistical in the first instance of the experiment.
This seems very profound in the understanding of time for the book I am writing. Can you please indicate the name or reference to that please?
It does seem by your example that time is a creation to keep events apart (when they are identical).

I am a regular reader but have not commented before. This post reminded me of a recent apod (http://apod.nasa.gov/apod/ap150615.html) about lunar corona. Where I got stuck was that they wrote "Lunar Coronae are one of the few quantum mechanical color effects that can be easily seen with the unaided eye." If this is standard diffraction of light around individual, similarly-sized water droplets in an intervening but mostly-transparent cloud (as they explain) why are they singling it out as a "quantum effect"?

Back-of-the-Envelope Gravitational Which-Way

drorzel — Fri, 07 Aug 2015 07:49:47 +0000

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.

drorzel Fri, 08/07/2015 - 03:49

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Precision Measurement

Not too long ago I tweeted you a link to a thing I wrote, on the off-chance that it might catch your eye. To no-one's surprise it didn't, but the topic is relevant to this post.

Here's the backstory. Earlier in the year I decided to see, just for fun, if I could guess a formula for gravitational time dilation near the surface of the earth. My tools were a crude notion of what general relativity entails, some high school Newtonian physics, and Ockham's Razor. I did not expect my result to be correct, not even approximately so, and was therefore astonished later to find that it checked out against results I found online.

Until now, that is. Applying my formula to the same sanity check you used, I get a shift of 3.6 parts in 10^17. That's the right order of magnitude, but 3.6 isn't quite "a bit under 5", so perhaps my formula is not all that accurate after all.

As I was saying, however, I decided to write up an explanation of how I acquired my result, and to present it as a faux popular science article aimed at an audience as scientifically literate as myself (i.e. not all that). I did this for three reasons:

(1) You learn by doing, and I figured the exercise would benefit me.
(2) An experienced science communicator might be persuaded to have a look and point out all the things I got wrong, and then I'd learn even more.
(3) If I was actually onto something, then said science communicator might be inspired to write a blog post of their own, covering the same ground only better.

My article (which is 1000 words long) is here: https://outerhoard.files.wordpress.com/2015/06/relativity.pdf

Chad, if there's an idea in there that you can use for a blog post, you are welcome to it. My only request is to be notified if you do.

3.6 sounds about right, actually. My "a bit less than 5" is based on remembering that the version of the figure in my book has tick marks every 5e17, and the shift is not a full tick mark.

Einstein and Revolution

drorzel — Tue, 28 Apr 2015 11:04:38 +0000

Einstein and Revolution

As mentioned over the weekend, I gave a talk last week for UCALL, part of a series on "The Radical Early 20th Century." I talked about how relativity is often perceived as revolutionary, but isn't really, while Einstein's really revolutionary 1905 paper is often overlooked. And, having put the time into thinking about the subject, I turned the basic theme into a new blog post over at Forbes:

Albert Einstein is easily one of the most recognizable people in history, and everybody thinks they know why. He’s the guy who, in 1905, completely revolutionized physics, overthrowing the prior order with a stroke of a pen and ushering in the modern era.

Only, he’s not. At least, not in the way you think. Einstein’s best known for the Theory of Relativity, the first part of which was published in 1905, but this was not, in fact, all that revolutionary. His actual revolutionary contribution to physics in that year was his paper on the photoelectric effect. This is somewhat overlooked, though it’s the one thing specifically mentioned in his Nobel Prize citation, and it played an essential role in launching quantum mechanics.

The actual lecture last week included a good deal more science, specifically a more detailed discussion of relativity with spacetime diagrams leading up to an explanation of why FTL travel is impossible, and a more detailed explanation of how Planck's quantum hypothesis fixes the blackbody radiation problem. But I'm keeping things non-technical at Forbes; maybe I'll upload the slides to SlideShare and post them here tomorrow. First, though, I need to grade a giant pile of exams...

drorzel Tue, 04/28/2015 - 07:04

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The Nobel prize was granted to Einstein in 1921 as a compromise. He had been nominated several times, for relativity theory, but the theory was viewed as being "jewish" and antisemitism was widespread. Granting the prize for the photoelectric effect seemed, at the time, to be less controversial. If anything, that goes against the idea that relativity was not Einstein's most revolutionary idea.

All knowledge contributes to revolution, it changes us and our environment for ever. We are revolutionary creatures, come what may of it and we are packing a bigger and bigger punch.
Fate has a habit of punching back and I dare say we have a serious contest on our hands. Originally the Catholic Church did its best to stem progress now other loud voices are trying to take control and at least guide our actions. Einstein had a great mind, great minds like great guns can be dangerous.

A Quantum of Sunshine

drorzel — Wed, 22 Apr 2015 11:03:00 +0000

A Quantum of Sunshine

It was nice and sunny this morning when I sat down at Starbucks to do some blogging, so I wrote a new Forbes post about the quantum physics that makes sunshine possible. This also brings in xkcd's take on the fundamental forces, and even a little bit of SteelyKid.

Sadly, it's now grey and dreary, but that's spring in New England for you. But if you'd like a small amount of quantum-mechanical sunshine, head on over to Forbes and check it out.

drorzel Wed, 04/22/2015 - 07:03

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I think you'd like this paper, in which a "weakless universe" is constructed (by adjusting other Standard Model parameters) that still has sunshine and pretty much everything else: http://arxiv.org/abs/hep-ph/0604027

Science Story: Impossible Conditions

drorzel — Thu, 05 Feb 2015 08:54:09 +0000

Science Story: Impossible Conditions

(When I launched the Advent Calendar of Science Stories series back in December, I had a few things in mind, but wasn’t sure I’d get through 24 days. In the end, I had more than enough material, and in fact didn’t end up using a few of my original ideas. So I’ll do a few additional posts, on an occasional basis, to use up a bit more of the leftover bits from Eureka: Discovering Your Inner Scientist…)

While we mostly think of science being done in comfortable institutes if not gleaming laboratories, one of the most impressive and inspiring things about science is that people can and do carry on scientific research in an amazing range of conditions. I've previously mentioned the story of Sin-Itiro Tomonaga mailing his version of QED to Oppenheimer in 1948. One of the amazing things about that story is that Tomonaga was working in Tokyo, which had been utterly devastated by WWII-- I spent a few months living in Japan in 1998, and visited the Edo-Tokyo Museum, and it's really difficult to convey the scale of the damage inflicted on the city by American bombing in 1945. It's difficult to imagine how Tomonaga and his group managed to make dramatic advances in physics in the disastrous conditions of postwar Japan.

But Tomonaga isn't the most impressive example of advancing physics in impossible conditions. A century ago this November, Albert Einstein completed work on his theory of General Relativity, and published a paper laying out the essentials of the theory and showing that it correctly predicted the precession of the orbit of Mercury, a problem that had been vexing astronomers for decades. The mathematics of General Relativity are fearsomely complicated, though-- Einstein had to laboriously learn a huge amount of math to make it work, which accounts for much of the ten-year delay between Special Relativity in 1905 and General Relativity in 1915. His calculation of the orbit of Mercury uses a bunch of simplifying approximations, as he thought it was too difficult to work out a general solution.

To his great amazement, though, within about a month of the completion of the theory, he received a letter from Karl Schwarzschild (the fellow in the robes and magnificent mustache in the photo above) presenting an exact solution to the equations of general relativity. In the simplest geometry you can deal with, mind-- Schwarzschild assumed a uniform, stationary, spherical mass-- but still, an exact and general solution of the type Einstein had thought might be impossible.

Schwarzschild's solution is the first introduction of the modern idea of a black hole. It's relatively (heh) simple to show from his equations that if the radius of the massive sphere becomes smaller than some critical value, the curvature of spacetime becomes so extreme that anything inside that radius is cut off from the rest of the universe-- not even light can escape. This "Schwarzschild radius" is the location of the event horizon of a black hole, and investigating this phenomenon has driven a huge amount of fascinating physics (I highly recommend Kip Thorne's book on black holes, which presents a very detailed history of the ideas).

The most amazing thing about Schwarzschild's short letter, though, is the conclusion. He ended the letter with one of the most incredible sentences ever to appear in the scientific literature:

As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas.

Schwarzschild's letter was written in December of 1915, from his station with an artillery company of the German army on the Eastern Front of World War I. So, not only did he rapidly develop a solution that Einstein had doubted was possible, he did it in one of the worst environments imaginable. (And, in fact, within six months he was dead, of an autoimmune disease contracted on the front.)

So, the next time you're trying to do some science, and find yourself bothered by petty distractions-- people talking, bad music, crying babies-- give a thought to the example of Karl Scwarzschild, which puts everything else into a very different perspective.

("Too much fucking perspective," in the immortal words of David St. Hubbins...)

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(Awesome Schwarzschild photo from Potsdam University.)

drorzel Thu, 02/05/2015 - 03:54

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I recall reading something a long time ago about Einstein's calculation of the advance of the perihelion of Mercury and as I remember it seemed pretty loosey-goosey.

Speaking about the difficult conditions in postwar Japan I recall hearing that Iwasawa as a student at that time was trying to get ahold of Malcev's work on Lie Groups but couldn't obtain any copies. So he decided to work out Malcev's results on his own and wound up proving much stronger results.

A great example of a scientist operating under difficult conditions is Rita Levi-Montalcini, who received the Nobel Prize in medicine and Physiology in 1986. During WW2 she did experiments in a "lab" that she set up in her bedroom. As a jew in Italy during WW2, her opportunities were limited, but she made the best of a difficult situation. Considering that she was a both jewish and a female, her accomplishments are truly special

Basically the academics in Germany were so busy then that they went straight from the bath to the graduation ceremony. Hence the bathrobe.

What Does a Faster-Than-Light Object Look Like?

drorzel — Fri, 09 Jan 2015 09:12:49 +0000

What Does a Faster-Than-Light Object Look Like?

I exchanged a bunch of emails a week or two ago with a journalist who was working on a story involving the possibility of faster-than-light travel. He wanted me to check some statements about the relationship between FTL and causality. FTL creates problems for causality, because if you have an object moving faster than light, there will be pairs of observers who see events involving the FTL object happening in different orders, which means somebody will see an effect happen before its cause.

I talk about this is How to Teach Relativity to Your Dog using the example of a stationary dog, a moving cat, and an alien zipping by at four times the speed of light. Here's a figure showing how this appears to the dog:

A dog and cat interacting with an FTL alien, as seen by the dog.

In this "spacetime diagram," the left-right axis indicates the position along the direction of the cat's motion, while time marches upward into the future. Vertical lines are equally spaced position markers according to the dog, while horizontal lines are equally space instants of time according to the dog. The dashed red lines are rays of light sent out at the instant the cat and dog had the same position, and set the scale for everything.

The dog sees the cat moving left to right at half the speed of light. The alien comes in from the left, passes the dog first (event 1), and then the cat (event 2). Perfectly sensible, and the dog could, for example, hand the passing alien a water balloon which the alien could then use to soak that pesky cat.

This looks very different if you replace the dog's grid of position and time markers with the cat's, though. In that case, you get something that looks like this:

A dog and cat interacting with an FTL alien, as seen by the cat.

Both space and time look different to the cat, due to her high speed. Equally spaced position markers according to the cat have to tip to the right, parallel to the cat's trajectory, while the cat's time instants tip up. The regular squares of the dog's grid become rhombuses in this representation.

According to the cat, then, the alien passes the cat, and only later passes the dog. Which makes the whole water balloon thing kind of problematic-- the alien would appear to the cat to come in from the right empty-handed, soak the cat with a water balloon and then carry that balloon on to the left, and later on hand it to the dog.

This reversal of ordering obviously screws up causality, and is one of the best reasons why FTL travel is impossible. It's even possible to create paradoxes by using FTL communications, so sending information faster than the speed of light is ruled out.

My journalist friend had this basically correct, but we went back and forth a bit about a subtle issue of perception. This is always a tricky business in relativity, as it's very tempting to attribute weird effects to the finite travel time for light to get from one place to another, and say things like "The events according to the cat appear to be in the opposite order." That's not what's really going on, though-- relativity isn't about optical illusions. There is no measurement the cat can do that will tell her anything other than that the alien passed her first, and only later encountered the dog.

I think we got this cleared up-- I don't think the story has appeared yet, which is also why I'm being coy about the identity of the journalist, who is free to identify himself in comments. But it did raise the question in my mind of what this would actually look like from the point of view of the dog. That is, what would the dog see?

You see, the diagrams above are a sort of "God's eye" view of the scenario, not the kind of thing any of the participants could directly record. The dog could draw this diagram of events, but only after the fact, after either compiling the records of lots of individual observers at the different position markers, or by looking at the light she sees, and working backwards to correct for the travel time of the light emitted by different objects.

So, what would the "dog's eye" view of the scenario really look like? How would the dog perceive her interaction with the alien? Well, we can understand this by adding some extra events to the diagram:

A dog and cat interacting with an FTL alien, as seen by the dog, with extra events added.

Here, I've added events "a," "b," and "c," so there are two events on either side-- while the alien is approaching, and while the alien is heading away. To work out what the dog sees, we need to add lines corresponding to the light emitted by the alien as it passes each of these. Looking at the approaching side first, we see that things are a little weird:

A dog and cat interacting with an FTL alien, as seen by the dog, showing the light from the approaching alien.

The alien, moving at four times the speed of light, arrives well ahead of the light from earlier in its trajectory. Thus, the dog would have absolutely no warning of the alien's approach-- it would just suddenly be there. Then the light from nearby would arrive (event b), and then the light from farther away (event a). If we add in the receding side, we have:

A dog and cat interacting with an FTL alien, as seen by the dog, showing the light from the alien as it approaches and recedes.

Again, the alien outraces its own light, so it's gone just as suddenly as it appears. The light from its departure lags well behind the actual events, with nearby events appearing only after some delay (event c) and more distant events much later (event 2, the soaking of the cat).

So, the answer to the question "What does the dog see?" is "Some weird stuff." Adding markers for the arrival of the light from each of the events gives you the idea:

A dog and cat interacting with an FTL alien, as seen by the dog, showing the order of events as seen by the dog.

From the dog's point of view, the alien appears without warning (event 1), then seems to move away in both directions simultaneously-- like two identical aliens headed in opposite directions. Light from a given distance on the approaching side will arrive a bit ahead of light from the receding side (event b is seen before event c, though they're the same distance away), so it will look sort of like the alien zipping off to the left is heading away a bit faster than the one heading off to the right. The "dog's eye" sequence of events is not the "a-b-1-c-2" sequence of the "God's eye" view, but "1-b-c-a-2." It's only after the fact, when she's had time to say "What the hell was that?" and do a bit of math that the dog can construct the global picture shown in the diagrams.

So, there's the answer. You could extend this to the cat's scenario by a similar process of event-adding and line-drawing, but I'm not going to. We'll call that homework-- draw and label your diagrams neatly, and send them to Rhett for grading.

And don't even think about moving faster than the speed of light. Seriously, it'll mess with your head.

drorzel Fri, 01/09/2015 - 04:12

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I'll come out as the journalist you refer to. I don't think my issue was thinking of relativity as an illusion, but how to explain it without giving this impression. And your post is a great example of how to do so.

Thus, the dog would have absolutely no warning of the alien’s approach– it would just suddenly be there.

This resembles the lies-to-children explanation for why shock waves develop in fluids containing objects moving supersonically: the presence of a moving object in the fluid would normally be transmitted to other locations by sound waves, and of course that can't happen if the object is outrunning its sound waves. Weird things do happen at shocks, like discontinuous changes in density and flow speed (and magnetic field, if the fluid in question is a magnetized plasma). Of course, in fluid mechanics there are other ways to transmit information, so a Mach number greater than one is not a sufficient condition to create a shock. For example, current thinking is that the interface between the Sun's magnetic field and the interstellar medium does not produce a bow shock. That's why this explanation is a lie-to-children in fluid mechanics. But in this scenario, any alternate way of transmitting information would not be any faster than photons, so this explanation might actually be correct, or would be if the scenario were allowed.

I remember doing something similar after learning about Lorentz transforms. Being a total nerd I had a Tardis instantaneously jump to a departing USS Enterprise at 0.9c. Then jump back instantaneously using the Enterprise frame of reference and finding I had traveled back before I left. Just showed up there's no such thing as "at the same time" when FLT is involved.

I wrote an article about faster-than-light travel for a Swedish popular science magazine last year. Unfortunately, it only appeared online in Swedish. (I think I sent an English version to George at some point.) I didn't go into these details though as my point was mainly to say there are different ways to allow faster than light travel. (Hit me over the head. We're all slightly nuts in quantum gravity, I know.) Your post would have made the perfect primer :)

If we observed an object actually crossing close to our path faster than the local speed of light, we would presumably look very closely at whatever happened to space-time close to the object for whatever new physics we might see. Fortunately the dog [and the cat] would see it appear before it passed the cat [the dog], so both get a (fleeting) chance to start the camera to record any weird physical effects. Something moving as you have it doesn't preclude /local/ Lorentz invariance (hopefully in 3+1 dimensions the alien's path doesn't actually intersect with the paths of either dog or cat; I certainly wouldn't want to be too close but please may I have a towel).

i think that is paradox existing only on the einstain TR ground (i mean that on the newton theory ground nothing happen or not??)maybe that vanishing when we found ultimate theory ? but back to story if dog give alien water ballon that he easy found right sequence events no matter how he be tangled that be always way to found right sequence alien come-i give him water ballon-alien gone

The problem getting the causality issues across may be just with saying things like "someone will *see* effects happening before their causes."

To my mind, that's not really the problem at all; the big problem is, as you briefly mentioned, backward-in-time communication: the way that, if Lorentz invariance holds, you must be able to string a couple of these things together to have effects happen inside the cause's own past light cone. That's what induces all the associated causal paradoxes (unless some hackish out intervenes, as some have proposed).

Hi Chad,

Something similar to your explanation of what the dog sees---an alien appearing out of nowhere, and then basically two copies of the alien flying off in opposite directions---is similar to a picture Feynman invoked when discussing various implications of relativity for quantum mechanics. The combination of relativity and quantum mechanics famously leads to the prediction of antiparticles. I won't go into all the details here, but you can think of the spontaneous creation of a particle/antiparticle pair as essentially what is going on with the alien from your dog's perspective. Let's suppose that instead of flying away, the "two" aliens were to then come back and converge on the dog and then disappear (as spontaneously as they appeared) once they have fully re-converged, you'd basically have the annihilation event. If you draw the spacetime diagram, what you'll see is that the alien worldline is a circle in spacetime! This is the picture Feynman proposed for thinking about particle/antiparticle creation and annihilation.

Naturally, one has to think very carefully about how to make such a picture fully consistent and their are many subtleties.

So, what does it look like from the perspective of the alien?

So the alien is like particle that spontaneously appears and then decays into a pair of particle/antiparticle?

There are some superficial similarities between the appearance of a faster-than-light object as seen in the light arriving from it at the position of a particular observer. It's important to remember the distinction between what you see and what's really happening, though.

That is, in the case of the FTL alien, the dog sees two aliens pop into existence from nowhere and zoom off, one of them moving backwards, but that's an optical illusion. After the fact, she can work backwards and show that it was really a single alien moving at FTL speed.

The cat would see something similar when looking at the light from the alien, but again, would be able to reconstruct the trajectory of a single alien rather than a mysterious pair. she would disagree with the dog about the direction of the alien's motion, though. Neither cat nor dog, however, will ever be able to do a reconstruction showing that there were two aliens present at the same instant at different locations in space.

In the case of a particle-antiparticle pair, though, there's no reconstruction you can do that will show anything other than two particle tracks converging at a single point. Now, for reasons of mathematical convenience, you can choose to view this as a single particle reversing the direction of its motion through time, but there's no ambiguity about the existence of a single vertex, and the fact that both particles are observed at different locations in space at the same time. The dog and the cat will disagree about what constitutes a single instant of time at two different positions, but both will see a particle and its antiparticle existing in different places.

From the perspective of the alien, this isn't that exciting. Both the dog and the cat move from right to left at superluminal speeds, the cat somewhat slower than the dog. The big difference in terms of appearance would be that the alien would be utterly incapable of seeing anything behind it, because the light from events in the wake of its passage could never catch up.

I agree that there is a major difference between the underlying physical reality of the alien speeding by versus the particle/antiparticle pair that spontaneously appears and then annihilates.

I actually think that you're shortchanging the alien-eye-view of the situation. Let me focus on the dog...

If you draw light rays emanating from the time axis (the dog's worldline), you'll notice that for each moment in time, there is pair of light rays being sent out by the dog (or bouncing off of her). Actually, if you want to think about it in 3D space, you should think of it as a spherical shell of light emanating out from the dog at every instant.

When the alien is to the left of the dog's worldline, it will intercept the light rays that are moving out to the left and will see the dog getting older. However, when the alien crosses the dog's worldline something really interesting happens: it starts to catch up to the light rays that were going to the right. So after meeting the dog, the alien should start to see the dog aging in reverse---getting younger.

So the alien does indeed see some weird stuff!

Going with the thought experiment's idea that the metric is constant, there is a frame in which the alien travels at infinite speed from one side of the universe to the other. There isn't a Lorentz invariant property for the alien of moving from left to right or from right to left. In 3+1 dimensions the quotient group O(4)/SO(4) has four discrete components, with time-like forward/backward being invariant under the connected subgroup SO(4), but with no such invariant property for space-like 4-vectors.

But in a space-time in which the metric is locally Lorentzian, in GR it is usually /assumed/ that the manifold is both spatially orientable and temporally orientable (http://en.wikipedia.org/wiki/Orientability#Lorentzian_geometry: "a space-time is time-orientable if and only if any two observers can agree which of the two meetings preceded the other", Mark J. Hadley.The Orientability of Spacetime. Class Quantum Grav.19(2002)4565-4571 arXiv:gr-qc/0202031v4).

From the perspective of the alien, this isn’t that exciting.

Why not? Let's take the cat out of the scenario for the time being. The situation with just the dog and the alien should be symmetric: in the alien's frame of reference, the dog is moving superluminally. So the alien should see the dog appear and move in two different directions, just as the dog would see the alien appear and move in two different directions. In the alien's frame, the cat would just be a second superluminal object. The alien, if he were recording the scenario, could work out after the fact what happened, and deduce that the dog and cat are moving at different speeds. (What the cat's speed would be, I am not sure, because I'm not sure how to do a double Lorentz boost when one of the boosts is superluminal.)

Also, the alien should be able to see backwards. The speed of light in the alien's frame is the same as the speed of light in the dog's frame. The alien's backward direction may not be backward in the dog's frame, but it would be in his frame.

The only way the scenario with just the dog and the alien could not be symmetric is if there were something to tell us that the dog's frame is preferred. This is exactly what relativity says we can't have, as long as neither dog nor alien is accelerating.

Dumb Layperson Questions dep't:

I'm always skeptical of arguements that go "it can't be, therefore it isn't." In the present case, the well-known arguement that superluminal communication & travel are impossible "because" they would produce logical paradoxes with causality. Therefore:

1) Are there empirical data demonstrating that FTL travel/comms are never observed to occur and for which some alternative hypohesis is not tenable?

2) Are there solid maths that also demonstrate that FTL travel/comms are impossible? In which case how does this math interact with the stuff from kinetics wherein equations work regardless of whether the value for time is set as positive or negative?

3) What ever happened to tachyons, that are supposed to move backward across time?

4) What about the idea that any sort of causal paradox that might be produced, is instead isolated in a manner similar to that of a local universe: each element in the paradox becomes separated from the other so they both occur but cannot interact locally? (You can visualize this as each element of the paradoxical events getting trapped in vacuoles;-) (Or have I just come up with an inelegant way of describing the same situation you've already described but I failed to understand?)

In the superluminal dark, no cats are grey because the gamma rays from those receding are red-shifted into the blue , and the photons from those approching would torpedo any retina made by God or man

@comment #16: I imagine that different people will approach your questions differently. Here are some of my takes:

(1) We have *never* observed any signal or physical phenomenon that can travel faster than light. That doesn't mean that we won't ever do so, just that it's never happened. Furthermore, the aether hypothesis suggested that we should be able to observe light moving at different speeds and was soundly put to rest by the famous Michelson-Morley. experiments.

There are alternative hypotheses---Lorentz and Poincare derived the transformations at the heart of relativity by trying to save the aether theory. They proposed that physical bodies moving in the aether deform and their clocks run slow precisely so as to make it *look* like light has a universal speed. However, I would say that Einstein's more parsimonious approach is the more attractive one.

(2) Special relativity begins with the assumption that light moves at a speed that all inertial observers (observers who don't have any external forces applied to them) agree on. Remarkably, from that one can show that (a) if an object has a real mass (you know, the kind that we all have), then it is impossible for it to ever reach the speed of light. As you accelerate the object, more of the energy is effectively diverted into an increasing mass rather than an increasing speed. This means you need more force to maintain the same amount of acceleration. To get to the speed of light, you will need to expend an infinite amount of energy.

And yes, the maths here is quite solid!

(3) Tachyons in the context of special relativity are objects that move faster than light (incidentally, whether you take them to go backwards or forwards in time is a matter of perspective. The alien in Chad's example would be a tachyon). The problem with the naive view of tachyons is that they would require imaginary masses which is typically taken as a sign that they aren't physical.

On a more sophisticated level, there are situations that can fruitfully be described as tachyonic. The existence of a tachyon in your model typically means that your model is unstable or that you are approximating around an unstable equilibrium. The tachyon isn't really an object in this situation, it's more a sign that tells you that some sort of decay or change is going to occur that takes you to a different "sector" of your theory. I won't elaborate on this here.

(4) I'm not sure I follow here. There'd need to be a clear physical mechanism for this and I don't know of any plausible ones.

David @ 17:

Thanks! (And another question at the end of this.)

1) Agreed, parsimony wins over the aetheric equivalent of epicycles;-) If it was necessary to add a bunch of needless bits to save the idea of a variable speed of light, that doesn't work. (Though, I assume that the observation that photons slow slightly in water is accounted for without going back into the proverbial aether.)

2) Aha! You just supplied me with a big missing piece. (Here I should mention that I'm not a dumb-dumb but I'm dyslexic so I can get this stuff conceptually but I've never been able to get the maths.)

I've known that in the current body of theory, acceleration of objects toward c produces an increase in mass that theoretically becomes infinite (for which reason, when I speculate about interstellar migration, I assume the best we'll be able to do is a small single-digit percentage of c and I use .01c as an example). But I've always taken it "on faith" and never had an idea of the mechanism before (blush).

What you said was "more of the energy is effectively diverted into an increasing mass rather than an increasing speed." Keyword "diverted." Bingo!, that would seem to be the mechanism. Presumably Einstein's equations govern that diversion. That's the piece I was missing: the mechanism for the increasing mass approaching c.

Question: Would it be correct to consider that a form of "energy conversion," in a manner that's very roughly analogous to other types of energy conversion (e.g. sunlight reaches planet's surface and is converted to heat, or electrons in an LED are converted to light, etc.)? If not, then what?

3) Tachyons: from what you said, they appear to be a creation of theory in order to deal with mathematical errors or instabilities that shouldn't exist. Something like this: "if you get tachyons here, you made a mistake somewhere." Alternately, "a different sector of your theory," which suggests a different reference frame (yes I'd like to know what you meant by that but you said you weren't going into it further here, so I'll park that question for the moment and look for some other opportunity to ask someone;-)

4) Apologies for not marking that item off with "the following isn't science, it's a wild speculation." What I was looking for were ways the "paradox" might be "solved." Something like Everett's many-worlds theory: "the universe splits here" so each branch of the paradox exists in a separate universe.

For example (using the nonviolent version of the Grandfather Paradox), you call your grandfather on the tele-time-phone and ask him to use condoms for a month. You don't ever find out if he actually does so. But if he does, then something similar to your local universe splits, whereby your existence continues in the universe where he does not use condoms (or a condom fails), and another timeline occurs into a different universe where the condoms work and you don't exist: but you never get to observe the second universe.

To my mind that's approximately as counterintuitive as the idea that the universe splits at every wavefunction collapse.

And while we're on that subject, another question that's been bugging me for years:

Where does Everett get the energy needed to create multiple universes at every wavefunction collapse?, or, are the splits in his theory confined to the immediate locality of each particle? (I'm highly skeptical of "the whole universe splits" but I'm agnostic about "the immediate locality of the particle splits," and in any case I don't see where the energy would come from to duplicate a universe either generally or locally.)

Hi G,

1) Light does propagate more slowly in a medium other than vacuum. This is essentially due to the fact that light---thought of as an electromagnetic wave---interacts with the atoms or molecules making up the material. This interaction is often characterized as the photons of the light being absorbed and re-emitted by the electrons in the medium, but that isn't quite right. The actual story is more complicated. But the gist of it is as I said, an interaction between the light and the medium.

(and no aether is needed! We have a real medium in this case.)

2) I'm glad that this explanation helps. Let me try to be a bit more precise instead of speaking about "effective" increases in mass. Einstein derived a formula for the total energy of a freely moving object. This formula combines the rest energy and the kinetic energy of the object as the two contributions. However, the kinetic energy is different in form from the non-relativistic one that we learn in school. In particular, it is strongly modified at very high speeds so that it goes to infinity as the speed approaches that of light.

The kinetic energy and rest energy (the energy inherent in the mass you'd measure when the object is at rest) combine in a rather natural way to give you the following for the total energy:

m c^2 / sqrt(1-v^2/c^2)

where m is the mass as measured at rest. Some people take this total energy and divide by c^2 to get a quantity that is called "relativistic mass". You can think of this as a generalization of the rest mass which includes the effects of it being in motion. If you look at the formula above you'll notice that the total energy, and thus, the relativistic mass increases to infinity as the speed v approaches the speed of light c.

Some people prefer not to describe things in terms of relativistic mass since this type of mass is completely equivalent to the total energy of the object. Instead, you can say that since energy and mass are interconvertible, energy itself also resists being accelerated. So if the energy stored by an object (say its kinetic energy) goes up, then it becomes harder to accelerate, so you have to push it harder.

So the answer to your follow up question is that this is not exactly the same thing as transferring energy from one store of energy to another, such as solar to chemical. Rather, the kinetic energy has an in-built resistance to acceleration that is basically the same as the resistance that the Newtonian concept of mass captures. As the kinetic energy goes up, the overall inertia of the object goes up.

That said, the energy stored up in the rest mass of an object can indeed be unlocked. In fact, turning this story around, we find that the majority of the mass in our bodies is actually in the form of the binding energy! The nuclei of the atoms in our bodies are made of protons and neutrons. These protons and neutrons are themselves bound states of subatomic particles called quarks and gluons. The quarks themselves have tiny masses, but it is the *energy* that binds them together that is responsible for most of the mass in a proton or a neutron.

3) I'd put this a bit differently. There is nothing in special relativity that mathematically forbids one from asking what the properties of an object would be if it travels faster than light. However, when you do this, you discover the bizzaro result that the mass would have to be described by an imaginary number. So at first blush you might say, well the theory is saying GIGO---garbage in, garbage out. The assumption that this thing can be going faster than light is garbage, so I'm getting garbage results.

However, it turns out that there is a utility to the notion of imaginary mass or energy. This will likely be cryptic and will probably set off more questions than answers since I don't have time to get into all the details, but here goes!

Consider the following mathematical functions:

e^(-gt)

e^(i E t)

where g and E are some constants chosen in units of inverse time (let's say in Hertz). The first function is just an exponentially decaying function. As time gets big, the function approaches zero exponentially fast.

The second function is an oscillatory function. Yes, it is imaginary, but you can take its real part and you get a cosine that oscillates with a frequency determined by the constant E.

In quantum theory, a free particle is described by a wavefunction that looks like this sort of persistent oscillatory function. The constant E really is related to the free particle's energy in this case.

A particle that decays isn't actually free, but its wavefunction will look like a damped oscillatory function, that is, it will look like a product of the two functions above. The constant E will again be related to the energy, and the constant g will set the time scale over which this particle decays. So you end up with a wavefunction that is sort of like this:

e^{i E t} e^{-gt}

but this can be rewritten as

e^{iEt - gt}

Now let me introduce a new notation. Let the complex number

q = E + ig

be the "complexified energy" of this particle. Notice that the real part is just the ordinary energy, while the imaginary part is related to the decay constant. We can rewrite the "wavefunction" as

e^{i q t}

this is the same information as before, but its a nice notation. Intriguingly, you can see that giving the energy an imaginary part yields a description of something unstable---something that decays away. This is a hint that tachyons are somehow connected to instabilities.

The analogy can be pushed further. Again, you won't find that tachyons can be observed as real, physical particles. Rather, they represent fields that are unstable.

I'll end with what may be an enigmatic note: the version of string theory that is used to introduce the subject---the so-called bosonic string theory---has a tachyon as its lowest energy field. This is taken to imply that bosonic string theory is unstable and requires completion by embedding into some other type of theory where the theory may evolve into a stable regime (getting rid of the tachyon). This is still an area of active research in string theory.

4) Ah, I think I see---the idea here is that paradox is avoided by thinking of the universe as branching off so that if you go back in time and do something, your time line ends up going to a different branch, not intersecting itself in a potentially contradictory manner.

That's certainly a valid way of trying to solve time-travel paradoxes, but there aren't really physical mechanisms that suggest that such a thing actually can happen. I suppose that if you are a many worldser (someone who subscribes to the many worlds interpretation of quantum theory) then you might concoct some explanation of this as interference between different branches of the universal wavefunction...but color-me-skeptical! (I'm actually rather skeptical of the whole many worlds approach in general. It's actually a much less straightforward interpretation than meets the eye. Much of its messiness is ignored or obfuscated in popular discussions).

I've got to run, but I'll try to answer your last question when I have some time.

Alright G, let's see if we can tackle that last question.

You asked about where all that energy comes from in Everett's many worlds interpretation for the creation of new universes or at least the "unzipping" of a universe at certain events in time.

Well, first one needs a more precise model of what many worlds is and what these universes are. The simplest approach is to start with the assumption that the state of the entire universe is described by a wavefunction that I'll call Psi. Let me point out from the get-go that this is actually a major assumption---something that often is glossed over in discussions about many worlds. It is not at all clear that our universe and its evolution can indeed be described by the assumption that its dynamical state is captured by a wavefunction evolving via the Schrodinger equation. What if the universe is fundamentally an "open" quantum system? In that case, the dynamics can be much harder to grasp...

But, taking the plunge, assume that Psi describes the universe and that there is a quantum law (a Hamiltonian) that gives us the evolution of Psi via the Schrodinger equation. According to many worlds, that's all there is.

So, where are the many branches of the universe (or multiverse)? They come from how you can decompose Psi into different terms. This is similar to how you can decompose a position vector into x, y, or z components. The idea is that at any given time, there is a decomposition of Psi into (probably infinitely) many components. If all goes well with the interpretation, our universe is described by one such component or branch, while other universes correspond to the different branches. As time evolves, macroscopic interactions with microscopic objects leads to decoherence, a process whereby initially "quantum" looking things tend toward looking more classical. It's thought that this describes how universes split into new branches.

So what about energy? Well, the simplest answer to write down is that the universe may not have a well-defined total energy. The components of Psi that describe the different universe-branches also don't have to have a well-defined energy. So there's no sense in which "splitting" would have a well defined energy either.

But suppose that it just so happened that the branches that describe macroscopically familiar universes do have precise energies associated with them (technically we'd say that these branches are "eigenstates" of the universe's Hamiltonian---it's energy operator). If that's the case, then each branch has a total energy of its own that won't change as it evolves, so within a universe-branch, there will be conservation of the total energy.

Actually, I'm not sure how to make the second picture consistent with the idea of branching. It seems to me that in such a scenario (where the energies are well defined for each branch) then the universal wavefunction would have to come with a predefined branching structure that is already in place. That's rather unlikely.

So the first answer is probably a better one: total energy is probably not a well defined property of the various branches that make up the universal wavefunction. That precludes any problems with the "creation" of new energy when a split occurs.

As a parting note, I'll point out that the total energy of the universe is actually not a generally well defined concept in general relativity either. For example, our universe probably does not have a well-defined total energy. This occurs because space itself is able to evolve in non-trivial ways in general relativity, and the dynamics of space ends up potentially messing up any general definition of total energy you might try to dream up.

General Relativity With Toddler Toys

drorzel — Mon, 10 Nov 2014 08:14:57 +0000

General Relativity With Toddler Toys

A couple of times last week, I mentioned on Twitter that I was going to demonstrate relativity with toddler toys and string. This was an inspiration that hit late on Thursday, when I was trying to think of a better way to explain embedding diagrams (the technical term for those stretched-rubber-sheet pictures that everybody uses to illustrate general relativity).

Specifically, I was hearing a lot from students who didn't understand the point of what was supposed to be weird about those. So I was trying to think of how to do a demo, when I realized we could measure the change in geometry that comes with a curved surface using the plastic stacking hemispheres that SteelyKid and The Pip have now outgrown.

The idea is to show how distance measurements on a curved surface change basic facts about geometry. So I had the students experimentally determine the "value of π" for different points on the hemispheres. The ones we have have lots of little ridges, that serve as convenient places to wrap string around, so I gave a half-dozen groups of students each a hemisphere, a length of string, and a plastic ruler. I asked them to measure the circumference at three different points, by wrapping the string around one of the ridges and measuring the length of string needed to go around. Then I asked them to measure the "diameter" along the surface of the sphere, by stretching the string across the top, from one side to the other.

I did the same thing after class, with the addition of a pair of calipers borrowed from the teaching labs, which I used to measure the actual diameter of the ridge in question. The results make this graph:

The value of "pi" measured by taking the ratio of the circumference to the radius for various points on the stacking hemisphere.

As you can see, for points near the top of the sphere, where the string over the top doesn't experience much curvature, the value is fairly close to the expected value of π. As you go farther out, though, the ratio drops significantly, getting down toward 2 (which you can easily convince yourself is the correct answer for a perfect hemisphere). The measurements using calipers are all a bit high for π (probably because the pinch-the-string-at-the-right-length measurement isn't all that precise), but basically constant as you go out.

The point here is that the curvature of the surface changes the apparent value of π because the distance you measure over the curved surface is longer than the "real" distance between the opposite sides of the circle. This is the point of the stretched-rubber-sheet stuff in General Relativity-- the way you measure distance changes as you get near a massive object, compared to the standards of a distant observer in flat space, and as a result you see longer distances than you expect.

This, of course, was a nice lead-in for a quick mention of the Viking Relativity Experiment, which did exactly this sort of thing by tracking radio signals between Earth and the Viking probes on Mars. They saw a significant delay compared to what you would expect from the orbital parameters when the signals needed to pass close to the Sun, which is a result of the bending of spacetime in exactly this sort of manner.

I'm not sure how much difference this will really make in terms of students understanding and appreciating spacetime curvature, but it went surprisingly smoothly in terms of getting the measurements done, and showing the desired pattern of variation. So, yay for last-minute inspiration, toddler toys, and string...

drorzel Mon, 11/10/2014 - 03:14

Tags

I suspect that they will learn a lot from this, although I'm not sure how to assess their understanding of curved space and curved space-time. Did you mention that the earth is curved, hence the relevance of "great circle" routes as the shortest distance between two points, or the fact that parallel lines will eventually meet?

I suspect that New York was surveyed in a haphazard fashion because it was settled along rivers and around lakes and mountains long before there was any organized system, but you can find some clear indications of the earth's curvature in the mapping of states that were surveyed into townships and sections when they first became territories.

In the latter case, you ought to be able to find topographic maps or even county maps that show the correction line required so that sections remain approximately a mile square. N-S roads have an unexplainable jog every six or twelve miles. The effect is clearest if the area you are looking at is far enough north and some distance from the meridian used as the east-west centerline.

Quick Interstellar Thoughts

drorzel — Sun, 09 Nov 2014 06:30:57 +0000

Quick Interstellar Thoughts

I'm teaching a Gen Ed course on relativity this term, which means I'm spending the last few weeks of the term discussing black holes. Which, in turn, means there was no way I couldn't use that story about Kip Thorne calculating the appearance of a black hole for the movie. Especially since I have the students reading Thorne's book.

And that, in turn, meant I needed to see the movie. So we got a sitter for the kids Saturday night, and went to the local theater to check it out. And, you know, it's pretty much what it's advertised as: A very pretty giant SF movie, with all that implies, both good and bad.

On the good side, they really did take some pains to get actual science content in there. There's the black hole from the promo stuff, a wormhole, and even some old-school orbital mechanics. More relevant to my current obsessions is the fact that scientists and engineers are unambiguously the heroes of the piece, and the day is saved by people who stop and think things through in a systematic way.

On the bad side... well, the failure mode of grand cosmic SF is and always has been mystical twaddle, a narrative force whose attraction is more inescapable than gravity. And Interstellar doesn't even come close to avoiding that problem. There's a whole bunch of "fifth dimension" hooey, and that's even before you get to the Power of Loooove transcending time and space.

And those flaws are somewhat magnified by the fact that a lot of the science is badly bent for narrative purposes. They fit gravitational time dilation in there, but the degree of time dilation they see is ridiculous, and real gravity isn't like Angry Birds Space, with effects that cut off a fixed distance from the center of the black hole. And the characters are kind of stupid for not realizing that there was a problem with the water-planet probe, and the Blight doesn't make any sense, and blah, blah, blah. Many of these questionable elements are also delivered in speeches that strain to rise to the heights of clunky dialogue. If you're inclined to poke holes in the science and story, there are no end of holes you can poke.

But, to bring it back around to the good side, I don't think any of those holes are any harder to retcon away than any other SF movie. A lot of them probably should've been addressed with an extra line or two of dialogue here or there, but it's not hard to imagine off-screen conversations (and while it's a very long movie, there are conversations off screen...) that could plug a bunch of the holes.

And I greatly appreciate the movie for what it isn't, which is any of the things we saw in the trailers. Which, for our showing, were for the seventh Fast and Furious movie, the third Hunger Games movie, the second Avengers movie, and Ridley Scott remaking The Ten Commandments. (We also got trailers for a MLK biopic and a dreadful-looking Mark Wahlberg movie, but those aren't relevant here.) For all Interstellar's flaws, it's at least got ambition-- it's an original story, not a sequel or a remake or based on something that was successful in another medium. And those are depressingly rare these days. The flaws of Interstellar are, for the most part, present in pretty much every big-budget movie, but at least it's trying to do something ambitious and original.

So, I'm overall pretty happy with the movie. It also helps that Christopher Nolan's general directorial style works well for me, making me more inclined to forgive the plot holes and bending of science to serve dramatic purposes-- if you're allergic to the Inception horns, you'll probably feel less charitable. But it's a great-looking movie, with spectacular design work, and while it takes liberties with astrophysics, it presents a very positive view of science on the whole. I'm glad I saw it in the theater, and I hope it makes a giant pile of money, mostly so people in Hollywood will keep giving Nolan the resources to make movies that aim high.

drorzel Sun, 11/09/2014 - 01:30

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Great review- it definitely takes some liberties, but I think getting terms and concepts like the ones covered into the public consciousness is overall a net positive, even if they played fast and loose for dramatic effect.

The acting, cinematography and score were all top-notch, and overall, as a piece of dramatic science fiction, I feel it knocked it out of the park.

Considering Kip Thorne wrote a short article describing how the movie is extremely accurate, I'd say the source of "hooey" is your analysis.

I saw it with my 22yearold son, who is far too much into finding and complaining about scientific holes (of which he found many).

But, at least I saw exactly zero references to current monotheism, I thought that was pretty amazing. This was pretty much humans versus an impersonal universe (except for the mysterious benefactor that placed the wormhole and tesseract there, and the movie concluded that those were some from some far- future progeny of humans that did that).

Chad, an otherwise fine review spoiled by a truly embarrassing foot-in-mouth maneuver: "...the Power of Loooove..."

You can make fun of it all you like, but "love" and its siblings "compassion," "care," and, yes, "empathy," are so central to human existence, that by making fun of any of them, you only succeed in doing exactly what you set out not to do, which is to alienate the hell out of a large chunk of your potential audience. Way to go, dude (not!).

Understand this: The reason a large chunk of the public are alienated from science is that they see science and scientists as cold, heartless, and inhuman. You just reinforced that stereotype in spades. That is exactly what we do not need.

Read Ethan's columns on astrophysics. He's doing it the right way: by recognizing that emotions are the key to getting people interested in science. He even had a devout Catholic drop in to say that he (the devout Catholic) really appreciated being able to learn about science from someone who wasn't going to clobber him with the aggressive atheist proselytizing he'd run into in many other places online.

Reasonable people can agree or disagree about the existence or nonexistence of deities and other untestable hypotheticals, but for purposes of civic engagement, what matters is getting people onboard with science and scientific method. And ideally, getting people to start using scientific method as part of their basic "operating system" for understanding life / the universe / and everything. Once someone starts doing that, much else follows.

The way to encourage humans do those things is, first of all, by not mocking the humans for being human.

G@5: Please recalibrate your snark detector. Chad is a child of the 1980s (as am I), so it makes some sense for him to riff on the title of a hit song of that era (perpetrated by Huey Lewis and the News; IIRC it was in the soundtrack for one of the Back to the Future movies).

Hollywood is a strange machine…At its face value, it comes across as this glitzy glamourous hit-maker, looking towards skin and sex to sell it, but it inherently ends up strengthening our faith in a higher force or at least something supernatural out there.

In recent years, as more and more post-apocalyptic films grace the big screen, human endeavor seems to be the champion every time, sometimes pushed forward by a miracle or an ‘unexpected twist’ as a critic would call it.

Christopher Nolan, whose Interstellar is wowing audiences across the world, has had a blooming relationship with the space-time conundrum, since his early days in Hollywood. He also fiddles with the idea of the ‘manufactured memory’.

All of his films, have this disturbing and bizarre concept of forgetting, of time being a fourth and powerful dimension and the depth and magnitude of the human sub-conscious. Even his Batman series, deals with passage of time, the power of the human will and the element of mysticism that makes Nolan’s Batman the most brooding of them all.

His earlier film, Memento was the troubled story of a young man who has short term memory loss and takes Polaroid photographs to jog his lost memory…At the end of it, one is lost in these photographs wondering whether they are his, or have they been planted by other forces!

In his dream within a dream within a dream thriller, Inception, memories and dreams collide to create a mysterious world, where all of us dread to tread even when we are awake. The concept of the totem, the disturbing hijacking of dreams by one’s most powerful memory are a world, unknown to us, but possible.

Most battles of the heart and the mind are as such, fought at the sub-conscious level…It is said that had Freud met Hitler in his childhood, then the infamous dictator’s life-story would have been starkly different.

Coming back to Nolan, with Interstellar, he has taken his questions about existence, about the boundless universe and the existence of a higher benign force, to the next level.

As the film’s protagonist relives his life through a time-space warp, we are suddenly struck with that notion that are we really moving forward, backward or is it so that time is so powerful like the sun is; for our solar system. The fact that time is simply not moving and that old phrase ‘stuck in time’ is true for all of life and civilization. That everything else is moving, expanding, procreating, contracting, withering and rotating around a constant, static monolithic all-powerful time in complete mad abandon.

Is that possible! Is time a concept created by us or is it really 6:30 in the evening and the world should catch the best possible option to head home to watch their favourite 9PM TV re-run…

Mad! But then, who said being sane was Godly!

Why, for all the care with the physics and science, do they give the dimensions and distances in non-metric measures? Do physicists really use feet and inches when they calculate measurements? Also, would it have been too much to ask to have more of the extras be non-white? Why so many , many white men, one black guy, and nary an Asian in sight?

"Interstellar" could not approach the grand spectacle of "2001, A Space Odyssey". Lacking the classical music score of Waldteufel's "Skater's Waltz" they simply cranked up the volume of the sound track to a thunderous level of interference. I missed at least half the dialog because the music was too loud. In "2001" I did not expect a biblical theme to be promoted but in "Interstellar" they made it a point to denigrate and behead any biblical point of view by showing a volume of Darwin's Origin of the Species bound in thick leather with gilt edged pages. This was one of the books that was being pushed off the bedroom shelf to make the intellectual connection with McConaughey's daughter. I got the message clearly.