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Coffeeshop Physics
by Jim Pivarski
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Letters to the Editor

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Entangled particles and relativistic speeds....

Apr 23, 2012

by Erik Wecks

Lee Gibson recommended that I contact you with this question. I am writing a bit of science fiction about people trapped on a ship traveling at .995C, in other words at a speed which give approximately a 10x time dilation factor. In my scifi universe they use entangled particles for communication. Here is my question: if I spin particle A, which is at rest on the home planet, what happens to particle B traveling at .995C?

I speculate that it would spin at 10x speed of particle A. Am I correct? The reverse would also be true.

The true motive behind my question is that I would like a communications blackout while they travel. This might provide a convenient answer.

Any thoughts?

Erik Wecks
GeekDad contributor, Author

Response from the editor

    Your general question is easier than your specific one, so I'll answer it first.

    It is in-principle possible to communicate with a spaceship traveling at any speed, even with low-tech methods. UHF transmitters on Earth, broadcasting at 1 GHz, could be picked up by VHF receivers on the spaceship at 100 MHz (assuming that the spaceship is flying directly away from the Earth). The listeners would need to wait 10 minutes for a 1 minute transmission, so while the message is coming in, the listeners might play it again and again, until they hear the speaker say "over" and know it's their turn to talk. ("Roger. Over and out.") Because redshifts work both ways, the spaceship would have to transmit in 1 GHz UHF to be picked up on Earth as 100 MHz VHF. With the exception of the great distances involved (in a week, this spaceship would cover the same distance as Voyager 1's 35 year trek), the underlying technology is from the early 20th century.

    So if the travelers can't communicate, it's because their technology is too fancy and breaks. The reason could even be a silly one: perhaps all of their communication is digital. If the framerate of digital packets is just slightly off, they can quickly lose synchronization and the wifi would be constantly breaking off and trying to reconnect in an endless, maddening cycle. If the rate were off by a factor of 10, it wouldn't work at all. An electronics geek could overcome the problem with a lot of work--- soldering a new circuit to accumulate packets and feed them into the physical layer of a network stack, re-programming the higher levels of the stack to lengthen the hard-coded timeouts--- but that would take a while (several days at least for an expert) and requires parts that may not be available (probably a breadboard with volatile memory chips implementing a circular buffer). (If the options on board the ship are really limited, maybe they could build a delay line memory system...)

    The relativistic travel would have to be unanticipated or the ship's radio would have to be unexpectedly broken, because these are all solvable problems, given enough time. Maybe that fits into the idea that they've been trapped.

    Now back to your specific question. Entangled particles don't provide an alternative to conventional modes of communication--- they only add features like security. In all schemes that I've heard of, conventional communication by radio, laser, etc. is one of the steps in the process. For instance, "quantum teleportation," the most famous method of communicating by entangled particles, involves a classical channel as the third of four steps (see http://en.wikipedia.org/wiki/Quantum_teleportation). The value added from the entangled particles is that an interloper cannot construct the whole message without access to both the classical channel and the quantum system, in a more fundamental way than the complexity-based encryption that we use today.

    Also, particle spin doesn't have a speed ("I speculate that particle B would spin at 10x speed of particle A"). Spin is a quantum mechanical effect, so it comes in discrete units of angular momentum. (Angular momentum could be converted to rotation speed by dividing by the inertia tensor, but fundamental particles don't have anything like an inertia tensor.) Whether a particle is viewed at rest or at relativistic speeds, it still has the same spin states, but the probabilities of finding the particle in each state change.

    As a slight modification to this, suppose they send messages by polarized particle beams instead of electromagnetic waves (radio, lasers, gamma rays). I don't know why they would do that, since particle beams would be more attenuated by dust and defocused by magnetic fields, but suppose they do. The signal is encoded in the positive and negative helicity states of the particles: positive helicity is when the spin is aligned with the direction of the particle's motion, negative is when it's anti-aligned. Traveling at relativistic speeds would change the probabilities of positive and negative helicity in a random way. Information would be lost. But I still can't think of a good reason to send signals this way--- neutrinos might be better than electromagnetic waves, but 0.995c isn't nearly fast enough to change the helicity of neutrinos that have enough energy to be detectable. Maybe the particle beam is also the thrust for the ship, and being economical, the engineers designed all communications media into the engine? That sounds a bit like sending messages through the city electric grid (which people do).

    How are they going to accelerate to 0.995c? At 1g, it would take more than 2 years (see http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html). If the acceleration is much greater than 1g, they might have to be in some kind of bio-jelly to protect their organs (see http://archive.org/details/nasa_techdoc_19980223621).

A Thank-you for the Great Articles

Mar 27, 2012

by Seyithan Teymur

As a mathematics undergraduate, I find your articles very easy to understand -for a mathematics student who hasn't studied physics in detail- and much more fun to read than any other's. I check your website's feed twice, just to make sure I haven't missed any of your articles, every time I check my RSS reader.

I just want to thank you very much for these great articles and tell you that at least I, with several of my friends here, always look forward to read more from you. I would really like to read an article or two from you about General and Special Relativity.

Best regards,
Seyithan Teymur

Ask Faraday:

Mar 6, 2012

Dear Mr. Faraday,

what is the scientific explanation for this experiment?
http://www.youtube.com/watch?v=VYuSt9FSccE

Sincerely, Ahmed Tarek

Dear Ahmed Tarek,

In return for the honor you do me by inquiring on the matter of this video, I propose to give you my account of it. We see a man, poised between his reservations over the possible loss of a favorite ceramic cup and the revelation he intends to bring about by way of a dramatic experiment.

He drops the cup from a height and onto a surface that would smash the cup to bits--- and yet, the cup is not smashed to bits. Tied to the cup is an arm's length of string and at the end of it, a cork, to serve as a meager counterweight. The cup is dropped alongside a metal bar in such a manner as to force the cork to wind the string around the bar as it falls.

This winding is the action that saves the cup. Though the demonstrator draws your attention to the imperiled mug, watch the cork. The cork falls not straight down, but in an arc like a child on a swing. The swinging cork acquires angular momentum, a conserved quantity of motion. Only the application of a torque--- an angular force--- can change a body's angular momentum. Gravity constrained by the string provides the torque to increase the cork's angular momentum, and nothing removes it until it ends its motion by hitting the metal bar.

As the cork swings, the falling cup shortens the cork's rope. This action is not a torque; this is because of its direction: it shrinks the radius of the cork's swing, but does not apply any perpendicular force, as gravity does. Thus the cork must conserve its angular momentum with an ever-shortening rope. Now, angular momentum is a special thing--- it is proportional to the cork's mass, as we might expect, but it is also proportional to the square of the string's length. Our eyes are unaccustomed to squared relationships in motion, so the sight of a lightweight cork impeding a heavy cup's fall looks like a bit of trickery.

As the cork's rope shortens by half, it must swing four times faster to maintain the same angular momentum. By the time its rope is a mere stub, it is swinging so fast, wrapping somewhat around the bar, that its momentum is sufficient to slow the cup and preserve it from disaster. To complete this narrative, note that a change in momentum is force, so the stopping of the cork supplies an upward force to the cup, just in time.

If you would like to learn more about angular momentum, I heartily recommend the lectures of Professor Lewin:
http://videolectures.net/mit801f99_lewin_lec20/

Sincerely, Mike

A little more about FTL neutrinos

Feb 28, 2012

by Jim Pivarski

In the past week, I've heard a little more about OPERA's neutrino speed updates. It's a bit more complicated than just finding a faulty connection that explains everything: the faulty connection could explain *as much as* the whole effect, but the exact size of the correction is not known. Also, it was not the only error: a master clock in the circuit was running fast, but correcting this error will make the neutrino speed faster, not slower. The two corrections go in opposite directions and their magnitudes are not known. This means that the problem has not been solved, but that the original experiment was inconclusive and needs to be repeated.

The reporting on this issue was better than I had expected. It wasn't as high-profile as the original story, but it did appear on the top of most newspapers' science sections.

The article linked below is excellent; I recommend it if you're interested.

References

Neutrinos do not travel faster than light

Feb 22, 2012

by Jim Pivarski

Since I wrote about this last year, I should provide an update: an error was found in the faster-than-light neutrinos result. See the link below for the full story; it was a faulty connection in a fiber optics cable.

Now I'm curious to find out if the news media will follow up on this one. It's often the case that they'll announce hints of a discovery with a lot of fanfare, but barely mention real gains in knowledge.

References

I know what you mean

Sep 21, 2011

by James Bellinger

I get those party conversations too. The worst was one I didn't get to hear: my mother-in-law to be described my occupation to a friend who replied: "That's terrible! He seemed like a nice young man; why does he have to make bombs?"

It feels like the dividing line that makes physics seem impossibly esoteric might be quantum mechanics. People can follow the ideas of rocket science, even if they don't care to try the calculations, but wave/particle and Heisenberg uncertainty are too far from everyday experience. (You'll notice the double caveat above--I haven't actually tried to psychoanalyze anybody to learn why they balked at physics. It seems a little rude.)

Of course there are the "I really liked physics and I try to keep up with what's happening even though I wasn't any good at it" conversations--which are a lot more fun.

References

Results from LHC et al

Sep 20, 2011

by James Bellinger

One little problem with collider physics applications was pointed out in a letter to Physics Today some 25 odd years ago: the energy scale isn't well suited for human use. We can use radio waves easily, light with no problem, UV without too much worry, X-rays only with care and caveats--but once you're in the MeV range you have no easy tools to control the particles. Electricity flows using low energy states in metal, and we can control it using differences of energy states in semiconductors, light we bend with lenses, but ordinary matter doesn't hold up so well trying to maneuver even moderately high energy particles. Maybe the inhabitants of a neutron star could make household appliances that relied on positrons. (The only SF I read set in such a locale didn't go into details of technology. Pity.)

References

Dimensions of color

Sep 1, 2011

by Jim Pivarski

Srikanth Bangalore writes that it's possible to think of dimensions--- arbitrarily many dimensions--- as variables in a computer program ("private members of a class in computer science"). He's right, and this is how mathematicians think about spaces with any number of dimensions. If a computer can store x, y, and z, which could represent the three coordinates of a position in space, why not store 100 variables and represent a point in a hundred-dimensional space?

He also touched on color, which happens to be a great example of non-spatial dimensions. It turns out that color has many more dimensions than it seems. We see three primary colors: red, green, and blue; the rest are perceived only as combinations of these three. When we see yellow, we see it as a mixture of red and green. We see orange as a similar mixture, but with more red. The world of color appears to be a three-dimensional world: red, green, and blue are the length, width, and height, while yellow and orange are diagonals with different slopes. However, this is just a human limitation: there are actually infinitely many primary colors.

If we want to talk about the color of light independently of human eyesight, we'd talk about the wavelength of the light wave. Long wavelengths are generally perceived as red, medium as green, and short wavelengths as blue. A light that we see as yellow could be a single wave with a wavelength of 570 nm or it could be two overlapping waves, one with 650 nm and another with 510 nm. These two situations are as different as a single B note played on a piano (69 cm) from an A note and a C played simultaneously (66 cm and 78 cm: a minor third). We can hear the difference between one note and two notes, but we can't see the difference between the one wave and two overlapping waves. If we used the same terminology for our ears as we do for our eyes, we would say that we hear with 15-20 thousand primary colors of sound, mixed into unspeakably many combinations.

When we see light in only three primary colors, we are projecting this high-dimensional space into a smaller, three-dimensional space, just as a shadow is a two-dimensional projection of a three-dimensional object. The projection loses information. Most mammals don't see as much as we do, either: cats can only distinguish two colors [1]. Our three-dimensional color sensitivity helps us to identify fruits, a useful skill for primates. The Mars rovers had eyes that could distinguish sixteen primary colors [2], to identify minerals in rock formations from a distance. All those pictures from Mars had to be flattened into a red-green-blue color space for the poor apes back home.

Fundamentally, each wavelength of light is an independent degree of freedom, an independent variable in the computer program of the universe. There are as many wavelengths as there are numbers with fractions: infinitely many. A computer can't store all of this information, though it can be represented mathematically as an infinite-dimensional Hilbert space. If only we could see that!

I have to strongly disagree, however, about time not being a dimension like space. Even leaving aside the abstract notion of dimensions as arbitrary variables, time is a dimension with units of length (a nanosecond is 12 inches long on an inch-tape) and it even mixes with the spatial dimensions. All motion mixes time with space, in the same sense that rotating a picture frame mixes length with height. I've been thinking about doing an article on Special Relativity, so perhaps I'll leave this for later.

References

  • [1] I had heard this as an anecdote among veterinarians, so I looked up the source. The first conclusive paper on color vision in cats appears to be M S Loop, C L Millican, and S R Thomas, _Photopic spectral sensitivity of the cat_ (1987) (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1183040/)
  • [2] A file describing how to interpret Mars rover images: see field number 25. The left eye sees eight primary colors, and the right eye sees another eight, different from the left. (http://marsrover.nasa.gov/gallery/edr_filename_key.html)

A Simple way to think in 13 dimensions

Sep 1, 2011

by Srikanth Bangalore

I wanted to share an idea I have been harboring for many years now regarding the "dimensions" of the world. I was reading some article regarding string theory (or the superstring theory, I cannot recall) and all that I remember of that article is that there were a lot of dimensions. For some strange reason, the authors were very worried whether there were an odd number of dimensions or an even number of dimensions. As if somehow having 14 dimensions was more satisfying than 13 or 15 dimensions. So, I started thinking about all these dimensions.

Of course I couldn't think even in 4 dimensions. I always felt that it was cheating to use Time as the fourth dimension. After all you couldn't measure Time with an inch tape, could you?

Then, one day, I started thinking about vision. On how we perceive the "blue" color. Whether the "blueness" lies in the frequency or the wave length or the neurons that get triggered? If it lies in the neuron that gets triggered, then the purpose of the EM wave was just to excite it. If we somehow excited that same neuron, then we would still see "blue". (The biologists have definitely worked this out for Smell and Taste - look up Pubmed for John Carlson). So, perhaps the blueness lies within the neuron. But neuron is so big - it has a nucleus, many mitochondria, endoplasmic reticulum and what not! By following this line of thinking, I concluded that every ATOM must be capable of sensing blue. Like wise every ATOM must be capable of sensing the smell of rose. Or the hotness or coldness. Basically, every "feeling".

(By ATOM, I mean the fundamental indivisible particle - 'quarks' at this stage?)

[As an aside, I concluded that "Consciousness" we have is a result of the Circuit in our brain. While our legs could have the sense of taste too, it is just not accessible to our brain, because we are not wired that way. .... Anyway, how consciousness works is interesting in itself. It is just sufficient to note that all attempts to explain consciousness in terms of physics are bound to fail if we do not postulate that the ability to sense light, sound, temperature, smell, touch etc already exists in each ATOM to begin with (because we follow Reductionism, and you cannot reduce "Blue" to 3 dimensions).]

So, coming back to 13 dimensions ... If we accept that every ATOM is capable of multiple senses, then, we can associate with each ATOM, not only the space co-ordinates, but also, the various senses - at least 7, if not more - color, sound, texture(soft->hard), temperature, smell, taste and emotion. If we add charge, mass and spin , we have 13 dimensions.

Or 13 properties associated with each particle. Note that we have not even counted Time as a dimension. I still feel it is cheating to treat time as a dimension. After all, you know that a "moment" has elapsed when there has been a "change" in any of these 13 values. If there has been no change, then there is no way of determining passage of time.

Ultimately, I think of dimensions as "private members of a class" in computer science. We can have an arbitrary number of them. 14 is no better than 13 or 15.

Letters to the Editor

Aug 28, 2011

by Jim Pivarski

Hello and welcome everyone! I'm Jim Pivarski, the author of this website.

As I was creating it, I thought a lot about what seems to work and what doesn't in the magazines that I like to read. Often, the best part was the Letters to the Editor, since a lot of the people writing in had interesting counter-points, anecdotes, and corrections. It was a lot more fun to read a work followed by a critique than to read one perfect article. I'd like the same sort of thing to happen here, including the criticism, as long as it's not mean-spirited.

As magazines moved to the web, it became possible to make the letters automatic, instantaneous, and attached to the articles that inspired them. These technological improvements are great, but somewhere along the way, the good feedback started to get swallowed up by chatter. There are still good comments out there, but the distribution has skewed. As an example, Physics Today (mostly a print magazine) still has interesting letters [1], but PhysicsWorld comments often sound like a petty argument [2]. What I think has happened is that the communication became too easy: it doesn't feel like publishing, it feels like texting. The only problem with this is that most readers aren't interested.

That's why this website has a Letters section, rather than comment boxes. If the letter is directly related to one of the articles (like a comment), you can make the connection by clicking on the "post a letter" typewriter below the article. Letters made this way appear as links with subject, author, and date (there's an example on the Leprechauns article). I didn't want to put the full text of the letters below each article because then the pages could become too long.

When you post a letter, it is sent to me as an e-mail so that I can moderate it. If I'm not sure that you meant what you said, I might reply and ask you directly, otherwise, I'll publish it to the site. The turn-around time is usually not more than a day, and less than that if I'm at my computer when it arrives. (This is much faster than Physics Today!)

The letters now have an RSS feed, so you can read them in an RSS reader (full text). It's a separate feed from the main articles, so you can stream one, the other, or both [3 and 4]. If you're a Facebook user, you can alternatively get a stream of articles as wall updates [5], but not the letters. Letters are RSS-only.

While developing the website, I thought about including all of this explanation on the page itself. The length of the explanation fluctuated up and down; now I just have the brief "Guidelines" below the send-letter form. I didn't want the Comment Box Manifesto to always be there, since it will become obsolete once you, the readers, set the tone for the kinds of feedback you'd like to read.

Best,
-- Jim

References

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