oh quantum causality, we hardly knew ye…

April 27, 2012

schroedinger's cat

Here’s what sounds like a rather typical experiment with quantum mechanics. A pair of devices we’ll call Alice and Bob, or A and B in cryptographic parlance, measure entangled photons which we know can be entangled at least 10,000 times faster than the speed of light. A third device called Victor, or an intermediary in the very same cryptographic convention that we just used, will randomly choose to entangle or not to entangle another pair of photons. So of course when Victor entangles its pair of photons, Bob and Alice would find the photons to be entangled, right? Except there’s a catch. Victor entangles or doesn’t entangle its photons after Alice and Bob already made their measurements. Barring some sort of technical guffaw in the setup, Alice and Bob are basically predicting what Victor will do or somehow influencing Victor’s supposedly random choice of whether to entangle its photons or not. In other words, causality just took a lead pipe to the kneecap as past and future are crossing wires on a subatomic level. This shouldn’t happen because the two pairs of entangled photons are not related to each other and Victor is dealing with a photon from each pair, and yet, it’s happening.

One of the reasons why the names of the devices are in cryptographic convention is because cryptography is the best way to follow what’s actually happening. Imagine sending two secure e-mails containing two entirely separate passwords to two friends, then, after these e-mails have been received, forwarding copies of those passwords to a system administrator who might just randomly reset them. And when those passwords are reset, somehow, your two friends get the new passwords instead of the ones you just sent them even though the system administrator hasn’t even received the original ones to reset yet. This prompts the question of why and how in the hell this could possibly happen. According to the researchers, we could view the measures of the photons’ states not as a discrete result but a sort of probability list of their possible states, i.e. they’re both entangled and not entangled depending on what will happen through the rest of the system. Then, when their fate is decided, the waveform collapses into the particular result like the famous Schrödinger’s cat taken one notch higher up the causality ladder, and which will only be truly dead or alive when the observer writes down the result of his or her observations into the official logbook after another observer confirms them.

Hold on though, what about the entanglement being nearly instantaneous? Maybe it’s more simple than all of this mumbo jumbo about collapsing waveforms and we don’t need to awaken the zombie of the Copenhagen interpretation of quantum mechanics? Victor could have entangled the photons and the spooky action moving much, much faster than the speed of light reached the detectors before the first measurements. We broke the rules of special relativity which dictate that information can’t travel faster than light, but surely this is a far more elegant solution, right? Unfortunately, we can’t prove that information travels faster than light as shown by the neutrino saga at the OPERA labs, and until we find a way to detect honest to goodness tachyons, we have to follow the special relativity framework, and in the experiment, the each half of the photon pair was measured a few femtoseconds prior to reaching Victor. Granted, since a glitch in OPERA’s fiendishly delicate arrangement turned into a 60 nanosecond error, surely a femtosecond or two discrepancy could be caused by a bad angle or a tiny manufacturing defect inside of the fiber optic wire as well. This is why the researchers suggest more experiments using much longer wires to make sure that the delay is even longer to see if their results will be further supported. However, the experimental setup here has been well calibrated and seems rather unlikely to be subject to a systematic error, so you probably shouldn’t bet the farm on their results being wrong.

Provided that future research validates their experiment, what does this mean for practical applications? Well, we may not have to cool a quantum computer to near absolute zero to measure its output if we can simply collapse the waveform with an algorithm that uses it as an input. Furthermore, we could implement quantum computer-like features in photonic computing for speeding up ordinarily time consuming processes we can’t readily parallelize across several CPUs with an algorithm that tries to collapse the waveforms on all possible relationships between objects, or all objects with a certain value. So obviously this is an exciting result and it’s interesting to think about all the things we could do with this quantum phenomenon in the realm of computing and ultimately, communications technology. And one also wonders whether objects much bigger than run of the mill photons can be induced to laugh in causality’s face by being cooled to near absolute zero since in the recent past, experiments have shown that objects much larger than we’d think can adopt the odd behaviors of subatomic particles and what we can ultimately do with these super-cooled pseudo-quantum things. But first and foremost, as with any groundbreaking and bizarre experiment, it may be a good idea to replicate it to rule out any interference or technical anomalies to avoid another OPERA-esque drama…

See: Ma, X., et al. (2012). Experimental delayed-choice entanglement swapping NatPhys DOI: 10.1038/nph…

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  • Tom

    Interesting, I wait whether they can reassure the results.

    Otherwise while i read the Lorentz transformations, i still cant understand the arguments, why would FTL signaling could lead to time travel…

    If an FTL signal can arrive before it was sent, than a radio signal arrives instantly or what??
    Yes an imaginary tachion could OBSERVE LOCALLY time flowing backward, as it catches up the previously started photons… but it is like rewinding a video tape no way it could change the past.

  • Paul451

    “i still cant understand the arguments, why would FTL signaling could lead to time travel…”

    I don’t understand the general FTL case, but I do understand it specifically for wormholes. (“Understand” at a pop-sci level, anyway. Likewise I’ll assume you’re familiar with the idea of relativity and time-dilation, at least at the pop-sci level…)

    Imagine you have a tame wormhole, the two mouths are held open by a pair of special devices. Send a signal through, and it arrives instantly. Take one device into space, and it carries its end of the wormhole with it, the other end stays with the second device still in your lab. The wormhole means you have instant two-way comms regardless of distance.

    But now accelerate the ship at relativistic velocities for a decade. Time dilation, caused by relativity, means the ship and it’s contents age more slowly than the wormhole device still on Earth. But apparently general relativity says the two ends of the wormhole share the same frame of reference. Ie, there’s no SF-show effect like one side of the wormhole sees the other… talking… very… slowly. Sharing the same frame of reference means they must age at the same rate.

    So the ship must be experiencing relativist time dilation, and ageing more slowly than Earth… But because of the wormhole connection, the ship must also be ageing at the same rate as Earth.

    How to reconcile the two? This is the part where it gets head-spinny. According to general relativity, each end of the wormhole stays linked to the other end when it was the same age.

    How to visualise this: Draw a 2d graph. Y-axis is time (T) on Earth. X-axis is distance between the two wormhole devices. At T=0yrs, the two devices are side-by-side, linked directly to each other. Ie, the wormhole is a horizontal line between them.

    As the ship accelerates away, it experiences time dilation relative to Earth, so it ages more slowly, and its wormhole device remains connected to the Earth-device at the same age. So at T=10 years, the two devices are lightyears apart, the Earth end has aged 10 years, the ship end has aged, say, 5 years.

    The ship end is now connected to the Earth-device at T=5 years. The Earth-device at T=10 years is connected to the ship whenever the ship-device has aged 10 years. The womhole line is now diagonal, not horizontal.

    Bring the ship back home, and the two devices are side by side again at T=20 years. The Earth-device is 20 years old, but the ship-device has aged just 10 years. So, because the wormholes are (must be!) connected to the other end of the same age, they are no longer connected directly to each other, even though they are sitting back in the same lab! The ship-device is connected to Earth-device 10 years in the past. The Earth-device is connected to the ship-device 10 years in its future.

    So send a signal through the Earth-device at T=20 years, and won’t emerge from the ship-device until T=30 years. Send it through again, and it arrives in T=40, 50, 60, as far in the future as the wormhole exists… (On your graph, it’s a saw tooth pattern.) Send a signal back through the ship-device from T=30, and it arrives back at T=20. Send it again, and it emerges from the Earth-device at T=10 years – before the ship-device had even returned!

    While you might argue, “Well just don’t accelerate it relativistically (or at least, don’t bring it back) and there’s no paradox!” but it doesn’t make any difference. The fact that you can do this is all that matters.

    I’ve used years of time dilation to make it obvious, even a few nanoseconds time difference is enough to create a bench-top temporal paradox.

    First the non-paradox version: You’ve seen those bench-top laser experiments. Prisms and mirrors and so on. In this one, we have a laser that sends a beam that bounces off a mirror back onto a photodiode swtich. When the beam hits the photodiode, it turns off the laser. What happens? The laser beam switches on and off at a rate determined the distance between the laser/mirror/photodiode. A few metres gap and it switches on/off at around 50MHz.

    Instead of a mirror, run the laser down a few kilometres of fibre-optic cable, then back onto the photodiode, and the signal takes about 1/100th of a second. So, ignoring any delays in the switch, the laser pulses at around 50 kHz. (Bounce the beam off the moon and it takes nearly three seconds to make the trip, giving a six second on-off cycle.)

    Now we take our two (table-top) wormhole devices. One gets flown around in a plane for awhile, or sits at the top of a mountain. Enough to build up a few nanoseconds of time dilation, thus a few nanoseconds time difference between the ends. (The one that ages slowest, I’ll call “the young end”.) We put the young end in front of the laser, and the old end in front of the photodiode.

    Turn on the laser, it sends a beam through the wormhole, back in time a few nanoseconds, then out the other side onto the photodiode. Same set up as before, but with a tiny bit of time-travel in between.

    Now look at it again from your point of view. You reach over and switch on the laser, a few nanoseconds before it turns on, a beam emerges from the old-end of the wormhole and hits the photodiode, turning the laser off before it had even turned on.

    Since your laser never got a chance to turn on, it didn’t send a beam into the wormhole. But if it didn’t, then there wouldn’t have been a beam turning it off, so it would have turned on, then there would have been a signal and it wouldn’t have turned on… etc etc etc. So if your laser didn’t turn on, where did the beam that turned it on come from? It changed its own past, prevented itself from coming into existence. This is the grandfather paradox stripped to its bones.

    As I said, I don’t know how to take this idea and turn it into a general case for all FTL/tachyons/etc, but apparently the same principle holds. You can turn any FTL system into a temporal paradox.

    The possible “out” is the Many Worlds hypothesis. That there are an infinity of alternative time-lines forking off each other. So the beam that turned off your laser experiment came from another time-line, another universe. Boo.

    tl;dr – commenters who write longer posts than the main article need to get a life/go to bed now.

  • Tom

    Interesting thoughts. :)

    IMHO, all time and space is local, on a mountain top, all electromagnetic based interaction is slower, and our known, observed space and time stretches according to that, as rulers shrink and expand, clocks ticking faster or slower.

    http://en.wikipedia.org/wiki/Time_dilation

    But its not a paradox, that we cant find mammoths there, its not a separated time zone, we could go up and hunt them down for example.

    Wormhole is an extreme thing… but i think it is similar to connecting between different time zones, one could see, the others time slowed down, while the other can see, the one’s time speeded up, as previously synchronized clocks now tick with a different rate.

    I think, gravity can be like an absolute frame, in normal means you can progress faster than c compared to local gravity field. Well that comes even without theory of relativity, because rockets also based on electromagnetic interactions, that has a max speed.

  • Paul451

    “IMHO, all time and space is local, on a mountain top, all electromagnetic based interaction is slower,”

    Faster. They are slightly further out of the gravity well, so they experience less time-dilation

    “Wormhole is an extreme thing… but i think it is similar to connecting between different time zones, one could see, the others time slowed down, while the other can see, the one’s time speeded up, as previously synchronized clocks now tick with a different rate.”

    No. That’s the problem. The two ends of a wormhole are actually the same point in space-time. There’s really only one end, the wormhole “tunnel” itself is just our way of visualising it because we can’t picture do four dimensional warping. Because the wormhole connects the two locations directly, in space-time, then the lab and the ship must age at the same rate. But since they don’t, because of other aspects of relativity, one end of the wormhole must… lag behind in time.

    (And I have to trust theoretical physicists’ interpretation of General Relativity for me, I can’t do the maths myself.)

  • Tom

    But a mountain-top rotates faster, and Earth’s rotation doesnt drag the gravity field that much, i dont know what effect is the stronger.

    A spaceship and a lab on Earth cannot share the same place, i think, no matter how small is the distance, it is like connecting different time zones.

  • Paul451

    “But a mountain-top rotates faster, and Earth’s rotation doesnt drag the gravity field that much, i dont know what effect is the stronger.”

    It’s got nothing to do with rotation. Just acceleration. Being slightly higher in the gravity well means the mountaintop experiences slightly less time dilation (relative to sea level). Likewise satellites, in spite of their velocity. This has actually been measured with atomic clocks.

    (I believe relativistic frame dragging is a vastly smaller effect, and hasn’t been measured directly yet.)

    “A spaceship and a lab on Earth cannot share the same place, i think, no matter how small is the distance, it is like connecting different time zones.”

    Relativistic effects are caused by differences in acceleration (General) and velocity (Special). If the lab and the ship are connected via a wormhole, then they are a precise and unchanging distance apart, as measured through the wormhole. They aren’t moving apart, nor accelerating relative to each other, as measured through the wormhole. Therefore there can be no relativistic differences between them, as measured through the wormhole. So no time dilation.

    However, when measured through real space, they are moving relative to each other, hence experience relativistic differences in measurements (of time & distance).

    Apparently, the only way to reconcile the two, is if the wormhole connections themselves moves in space-time at a different rate than the ship/lab. So they are no longer directly connected (at the same point in time) when the ship returns. Mind boggling, I know. But that’s what the equations of General Relativity produce when you plug in the properties of a wormhole (apparently).

    I get this, at a basic laymans level, but I don’t see how to generalise it to all FTL. However, if you can’t get your head around the wormhole version (which I think is easier), you have no chance of understanding the general case.

    My advice, leave it. Let it sit in the back of your head for a few weeks. Let your brain rewire itself to adapt. Then come back and read it again. Because there are two aspects, understanding the effect, and understanding my attempt to explain the effect.

  • TheMechanicalAdv

    In experiments like the one in this article, there is only one issue that matters. How long did it take for the results to be collected into a report of macroscopic size? If it took long enough to be reached from all the devices at the speed of light or slower, then causality was not violated. A state of more than one particle is, in known math, a function of more than one position. But there is no evidence of the extra dimensions that would be required for the state to be arrayed that way. We can only assume the state is embedded, in some unknown way, in the spacetime we know to exist. And we can only assume that that embedding propagates at the speed of light or slower.

    This means that none of the events in the experiment actually occurs. All that really happens is that the various possibilities diffuse at the speed of light, and when they meet they do a gambler’s ruin fluctuation until they reach a possible result state.

    This is the collapse locality loophole, and it follows from relativity. A traditional interpretation like the one you gave postulates a faster-than-light process and then tries to return to relativity by rearranging events so it reads like that process didn’t happen. And after such a dishonest manipulation, you wonder why causality seems to be violated!?!

    This is a simple concept, and it’s been explained many times by people far smarter than me. Just google “local state” and “local causality”. I don’t get why so-called popular science articles like this insist on using the illogical interpretation instead. Isn’t the purpose of science education to de-mystify?

  • TheMechanicalAdv

    GR, in its bare form (which is the only experimentally verified form so far), does not provide a predicate for two spacetime points being equal. The familiar concept of equal points in geometry comes from compatibility with a topologically flat coordinate system. It’s what’s left of the statement that each coordinate is pairwise equal after the coordinates have been removed. However, part of what makes structures like wormholes exotic is that they are not topologically flat. The only way to express them physically relevantly is as an overlapping union of coordinate patches. And the only way two world-lines can be made to merge is if there’s one patch that can cover the process flatly, in which case you’re just saying the ship crashed into the lab.

    So going through a wormhole would bring you to another patch. I think this would have to be a newly created empty space. Otherwise if there were anything in it like the lab, it would be a copy, which would violate conservation laws.