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I have built a machine that I have connected to an ordinary desktop computer, which is in turn connected to the internet.

When turned on, the machine isolates a pair of quantum-entangled particles; one of the pair is manipulated in such a way that time severely dilates - the particle "ages" only one second for every hour that passes for everything else (including the particle's entangled partner). After operating like this for, let's say, 24 hours, the machine is set to its data transfer mode. This mode change stops the time dilation, so now one particle is effectively offset in time by just shy of 24 hours from its entangled partner. In this mode, a quantum state of one of the particles can be flipped in accordance with an input signal, and the corresponding quantum state of its entangled partner can be read to recover the original input signal. By this means a message can be sent back in time according to the offset created between the entangled particles.

A lottery holds weekly draws; tickets are sold up to an hour before each draw. After each draw, the winning number is published on a website.

My computer checks the website after each draw; it creates a message consisting of the current date and time and the winning lottery number and feeds that message into the machine. The computer listens to the machine for any messages and displays them on the screen.

Some 60 hours before the current week's lottery draw, I turn the machine on. 24 hours later (some 36 hours before the draw), I set the machine to its data transfer mode. A few hours before the draw (while there is still time to buy a ticket for it), I return to the computer to look for a message bearing a time stamp representing the upcoming draw and the winning number. Seeing the number, I go out and buy a ticket bearing that number.

I am pretty sure quantum entanglement does not/cannot work as I have depicted, but if it did (if this was the only conceit), is my scenario plausible? Are there any paradoxes, causality violations, or other time travel "gotchas"?

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    $\begingroup$ "Quantum entanglement" is becoming the catch-all phrase for "magic happens here." No, it doesn't work the way you've described. But does that matter? Is this a reality-check question, in that you've set up rules in your world and does the presented scenario work within those rules? It might be better to remove all those questions (technically, you only get one question mark) and ask if your method is logically sound (remove all the "quantum" references, too, they're nonsense anyway and will only distract us). $\endgroup$
    – JBH
    Apr 30, 2019 at 0:52
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    $\begingroup$ This is essentially : "If I had a crystal ball seeing into the future could I cheat the lottery people ?" Yes, you could. All the rest of the quantum-nonsense is just fluff. It's your magic, if you want it to do that, it will. It won't make sense to a physicist. Big hint : read "The Technicolor Time Machine" before you go any further and see a master (Harry Harrison) at time travel writing at work (and laugh a lot). No wasted techno-babble for Harry. $\endgroup$
    – StephenG - Help Ukraine
    Apr 30, 2019 at 1:46
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    $\begingroup$ If I may recommend, watch the movie Primer. It takes this concept to the extreme, though it can be a little confusing. $\endgroup$
    – Cort Ammon
    Apr 30, 2019 at 4:43
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    $\begingroup$ @CortAmmon I loved that movie! The kids who made that show really burned the midnight oil to create a conceptually practical time travel solution with a serious twist (what happens when you enter the machine? Oh, dang!) It's a good example of innovative time travel - which most authors don't achieve. $\endgroup$
    – JBH
    Apr 30, 2019 at 14:15
  • $\begingroup$ @CortAmmon I've seen Primer, got lost in the convoluted plot, recall that the device supposedly circumvents causality paradoxes but never fully understood why - I got lost in the convolutions. $\endgroup$
    – Anthony X
    May 1, 2019 at 2:21

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So, in the comments I mentioned Primer. It's a work of fiction using quantum mechanics for time travel. It's a great movie on the topic!

As an answer, I would like to offer the Delayed Choice Quantum Eraser, which is almost precisely the device you designed, only it was actually built, tested, and the results have been analyzed and agreed upon by the scientific community.

In the experiment, photons get split by beamsplitters twice after going through the double slit and then a Glan-Thompson prism to generate entangled pairs. The result is rather fascinating. You get one side of the output of the Glan-Thompson prism that goes towards a detecting grid, where one can either see interference patterns or not. The other one goes to the beamsplitters where a "decision" is made. The photon either goes to detectors that can determine which path the photon went through initially, or to a different detector that cannot (something called "path erasure" in the QM community).

Now here's what's really weird about this experiment. The path to the beamspltiter that makes the "decision" whether to observe path information or not is longer than the path to the detector screen on the other side. That means that photon has already hit the screen before the "decision" to observe path information is made. Somehow, if path information is observed, the screen shows no interference patterns (as expected if path information was not observed). If the path information is erased, those runs indeed show an interference pattern. It is as if the information about whether the path should be observed or not is sent back in time, so that the screen records the correct results!

Of course, that isn't quite what's happening. If you run the QM mathematics, no time travel really occurs. You just get an expected outcome of the equations we've developed for QM. The key to this is that the pattern is not visible until afterwards, in post processing. At that time, you have all the information, and what you find is nothing more interesting than "the data collected is consistent with the information we gathered." But if you don't run the math, it sure as heck looks like the decision to observe the path or not traveled back in time!

When you really run the numbers, what ends up happening in entanglement situations like this is that you send "back in time" an observable state which will be consistent with the entangled particles you'll use later to send the lotto ticket numbers. However, due to the rules of QM, you won't actually be able to determine the correct way to interpret the message until after the message has been sent. Until then, the message appears random... though it will happen to be consistent when you finally send it. Any technique to try to sneak any more information through than that will end up disentangling the particles (there's lots of clever ways to try to send the information, and every one of them has one subtle quirk which prevents it from working!)

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  • $\begingroup$ Quantum mechanics: If it looks utterly impossible, do the maths. It’s probably quite simple. $\endgroup$
    – Joe Bloggs
    Apr 30, 2019 at 5:24
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    $\begingroup$ I can’t count the number of times in Quantum Computation lectures that I got annoyed at the fact all you had to do to solve the problems was the equivalent of adding 0 and then multiplying by 1. $\endgroup$
    – Joe Bloggs
    Apr 30, 2019 at 5:27
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Quantum entanglement doesn't work that way. An entangled pair is a pair of particles with correlated quantum states (eg. if you generate a pair of entangled photons, one might be horizontally polarized while the other is vertically polarized).

The reason why entangled pairs are so interesting is that you can prove that the pair haven't decided which particle is in which state until you measure them, and you can prove that once you measure one, the other takes on the corresponding state in a faster-than-light manner. But it's useless for sending information: anything you do to the entangled pair, including trying to see if the entanglement has been broken, breaks the entanglement.

Your proposal breaks down at this step:

In this mode, a quantum state of one of the particles can be flipped in accordance with an input signal

When you flip one of the particles, the entanglement breaks and the other particle of the pair takes on a random state.

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    $\begingroup$ Entanglement : the universe has a laugh - you try and use it and it breaks the entanglement. :-) $\endgroup$
    – StephenG - Help Ukraine
    Apr 30, 2019 at 1:48
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    $\begingroup$ My suspicion is that whatever you do to cause such severe time dilation in one of the particles will break the entanglement, but I'll freely admit that's beyond me. $\endgroup$
    – Cadence
    Apr 30, 2019 at 1:51
  • $\begingroup$ @cadence: It’s got nothing to do with severity. Pretty much anything you do will cause the entangled pair to start behaving classically instead of quantum-ly (up to and including daring to have a gravitational field). It’s definitely the case that ‘quantum’ gets overused as a sci-fi term. It’s like polarity. $\endgroup$
    – Joe Bloggs
    Apr 30, 2019 at 5:22
  • $\begingroup$ You can flip one of the particles, that is no trouble. The real trouble is making a measurement. You need to measure the particle before you impart your information. Also entangled pairs are correlated, they don't carry any information themselves. That is why qunatum mechanics does not allow for superluminal communication. $\endgroup$
    – Whitecold
    Apr 30, 2019 at 7:56
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"Are there any paradoxes, causality violations, or other time travel "gotchas"?"

There is no difference between physical time travel and informational time travel. If time can be changed, it can create paradoxes which means you need one of the possible solutions to the paradox issue.

1: Time cannot be changed. You can travel in time but the past, present and future are set in stone. Any attempt to change something will fail or actually cause the original event to happen.

2: Changing time creates a new branch. If you go back and kill your grandfather, you still exist because you're in a new branch of time. You can't actually return your original timestream, just new branches thus paradoxes can't be created.

3: You can't go back in time.

I would however recommend not sending lotto results. It's good once but winning a second time would have the government/police watching you. A third time could result in confiscation of winnings and jail. It's not something you can win day in and day out. Ditto for all betting and even the stock market.

There are far better sources of income to be made from time travel.

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  • $\begingroup$ Believe it or not, having won the lottery already is a greater indicator than any other of likelihood of winning the lottery in the future. $\endgroup$
    – Separatrix
    Apr 30, 2019 at 6:49
  • $\begingroup$ A really fun story to write would be the affects on "now" (the present) because the future keeps getting rewritten (different "branch") thanks to the info sent back to the past. Something like ST:VOY's episode "Year of Hell," but from the backwards point of view (because "now" never changes, right? RIGHT?) $\endgroup$
    – JBH
    Apr 30, 2019 at 14:20

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