The timemachine, take 1
Everything that cannot exist, does not exist
Congratulations! You have been issued a Mach One Predictor timemachine; hereafter we call it a MOP. You may have read about Ted Chiang’s take on a very similar device in Nature. To avoid any discussion regarding how it is made, we will assume that somebody from the future used a more powerful timemachine to give it to you. For your safety, we will also assume that some third-party researcher is conducting safety tests for you in some other universe.
The MOP is limited in its abilities:
It only sends information back in time, not matter.
It only sends information back in time by exactly 1 second.
It always works; never a “miscommunication”.
It sends back one bit of information at a time.
That information is “frame-locked”; when you push a button, the timemachine will wait until the next tenth-of-a-second “tick” to send information back in time. (We leave the analysis of how frame-locking could be implemented to the reader for now; it is useful to avoid the potential for timing-attack systems of sending information.)
A button and LED light are conveniently hooked up to the device. Push the button, and the light turns on one second ago.
Our first test is done with precautions to ensure that agency-causality concerns do not effect the test. We turn on a camera to log the results and put on a blindfold. We proceed to push the button, several times. As a control, we push several other buttons which are not attached to timemachines.
There are several possible outcomes of this test. As the author is inconveniently without access to a MOP, we must analyze all of them hypothetically.
The first possible outcome is that everything behaves as described on the box. The MOP causes a light to light up before the button is pushed, the other buttons turn on separate lights in the normal fashion (or do whatever else they were wired to do). The experimenter does not notice any strange compulsions, nor any indication that the buttons work differently when ta presses them.
A second possible outcome is that the MOP simply does not work. Aware of the attempt to scientifically analyze it, it spontaneously self-destructs. It is hardly fair to call that a timemachine at all. We haven’t even tried anything difficult yet.
A third possible outcome is that the MOP exerts a force (or a pseudo-force) across space and time that impacts the experimenter. Ta is aware of the immense temporal weight their interactions with one specific button possess. Ta is compelled towards specific timings to push the one specific button. The timemachine works exactly as described; it is the researcher who appears abnormal. And this occurs even when all precautions have been taken to avoid causality loops.
For our second test, our experimenter configures a computer to push the button. The computer and button-pushing actuator are fast enough to do any of the actions within a tenth-of-a-second frame. It is configured to push the button at two specific times (tests I and II), and then once randomly in a ten-second window (test III). Afterwards, it enables a camera, waits up to 30 seconds for the light to go on, and pushes the button one second later (test IV). It then attempts to wait for 5 seconds without the light going on, and then pushes the button (test V).
And we can quickly establish that the above protocol is impossible. Either the protocol will not occur as written, or the timemachine will not function as was written on the label. As one can easily demonstrate at home, the protocol is fine without a timemachine, the impossibility is clearly caused in some way by the timemachine. The most obvious problem is the temporal NOT gate loop established; the actuator pushes the button in test V only if the light demonstrates the button was not pushed. There is a different question regarding test IV; it is consistent for the light to go on at any point in the 30 second window.
There are certainly solutions that can prevent impossibility. The timemachine can simply malfunction; a timemachine that breaks as soon as you try to do anything interesting with it is not very interesting. It can (like Zeus) call down cosmic rays to change the computer’s programming. The pseudo-force mentioned earlier can convince the researcher not to conduct the experiment in the first place. We can also try to explain this with parallel universes; unfortunately this leaves us with two universes where the timemachine appears to malfunction, the explanation being that the timemachine sends information between them.
We leave it as an exercise to the reader to come up with a rigorous scenario where you promise to break the space-time continuum only if you do not win the lottery. The explanation that (once again) a mysterious force prevents you from trying the experiment is not satisfying, and neither is the suggestion you might win the lottery as a result.
We are left to conclude that our MOP must stay in the realm of fiction. Or at least that it must fail to do what is promised on the box. One MOP is problematic enough for consistency. Once you suppose there might be a million (or even two) of these devices, the entire scenario will collapse.
We will have to try again next time, with a better timemachine. One that does not make promises it cannot keep.
There are several issues with the MOP that, at this point, may be obvious. First is the insistence that it “always” works. I have said before that there are no perfect oracles, and this only serves to demonstrate that. As a second note, being able to use the MOP ten times per second may actually be a very high rate of usage, especially if you pre-establish an encoding to do something more useful with the data than turn on a light.
Most critically, the MOP does not attempt to resolve the hard problem of the arrow of causality and the arrow of spacetime pointing in different directions. Before we can introduce a solution to that, we will need to discuss the new riddle of induction.
Before we leave for today, a note regarding the malaise supposedly induced by exposure to the MOP in Ted Chiang’s story. I have heard that one can experience something similar, without resorting to a timemachine. The experimenter has a button which causes a light to flash between 50-500ms after it is pushed (I forget the exact timing). After some number of repetitions, the experimenter perceives the light as simultaneous with the button push. At some random time after this has occurred, the light instead flashes instantly. Ta sees the light flash before they perceive themselves to push the button. There is no paradox here; it is simply related to how the brain compensates for delays in sensory perception. Sensory data travels far, far slower than the speed of light; slower even than the speed of thought.