Inspired by this question regarding reality as simulation and this question about a continuous time line, it made me wonder: if our time were indeed like a high frame-rate simulation, how could we detect it, if at all?
So, assumptions are, of course - yes, time is discrete. And the "frame-rate" is high enough to not contradict what we already know in physics/science. What evidence could we find that time is discrete?
Actually, the world as described by the standard model of particle physics cannot account for time intervals lower than the Planck time, which is approximately $5.4\times 10^{-44}s$. But the current smallest time interval uncertainty in direct measurements is approximatevely $1\times 10^{-20}s$. Litteraly any experiment (such as those described in other answers) would need to be more precise by more than $20$ orders of magnitude in time measurement than the most precise currently known experiment.
I have no idea what a world where physical constants are different from ours by more than $20$ orders of magnitude would realistically look like.
Collision penetration by velocity.
As a starting note, we cannot talk about a graphics fps, and only a physics fps. Graphics fps only exists to the outside observer, we can only experience our universe through physics.
This is a classic problem in video-games. If physics is checked by frames and if objects are overlapping, then if something travels fast enough it can be before an object one frame, and past the object next frame. Collision never triggers and it goes flying by. Too bad they knew so we got that pesky speed of light to deal with. Instead we just need to make our objects small enough.
Cool part is that physics almost supports this. There is only a probability that two objects will collide. Now by using the width of objects and how often they collide we can calculate the frame rate of the universe. At least the physics loop frame-rate.
High spin rates would prevent certain orientations. For example, an object spinning at 100th the universal frame rate would never achieve an orientation in between 3.6degree steps. Spinning at half, it would always be at two ends of a line.
This would invoke the collision detection problem mentioned here. The resulting interactions such as audio or electromagnetic field could be Fourier analysed and the spectrum would show the universal framerate.https://math.stackexchange.com/questions/1002/fourier-transform-for-dummies
The object could be a rod a thousand kilometers long rotating in space at one millionth the frequency of the frame rate. Noise artifacts in the interaction with a magnetic field would still be observed.
an object spinning at 100th the universal frame rate would never achieve an orientation in between 3.6degree steps Who says the framerate is fixed? Secondly, as long as the "lightframe" (= distance that light travels between two frames) is smaller than your smallest measurable unit, the frames are still undetectable.
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Yes, possibly.
Relativistic time dilation effect may help us to detect time quantization. If the universe is a simulation running at a uniform speed, then time dilation effects must be simulated ones.
In the world of video production, there is a longstanding problem of converting the frame rate when a video is converted from one media to another. In classic film, frame rate is 24 fps. In PAL video, it's 25 fps. In NTSC, it's 30 fps. Individual frames are too short for humans to take notice, but when we have to convert frame by frame, the resulting artifacts are becoming visible to an untrained eye.
Similarly, if we have two very precise clocks moving with respect to each other, or one in a strong field of gravity, and one away from it, the time will be running at different speeds for them. If time is continuous, the "slow" clock will measure time exactly as Einstein's theory had predicted. But if time is discrete, and the "slow" clock has to actually run in a "fast" timescale world, we would be able to see some weird effects, like some seconds will be shorter, and some longer than others.
The "slow" clock and its attendants would not be able to notice that without referring to the "fast" clock, and vice versa.
I do simulations by trade, so forgive me if this is more technical than you intended. I will have to massage some of the details to get closer to what actually happens in simulations to cause artifacts like the ones you seek.
First off, we have to start with an assumption: the universe is supposed to be modeled as a set of Ordinary Differential Equations (ODE). The current models of the universe are all based on ODEs. We have to assume that velocity is a measure of the rate of change in position. So we're detecting differences between what the universe actually is and what could be represented as ODEs. If the universe is supposed to be something other than ODEs, then the actual answer of what we detect is completely dependent on what the laws of the universe actually are. If my universe consists of "Use the known laws of physics until Jan 1, 2020, then break all the laws and summon a dragon into the middle of Washington DC," then that's probably the artifact we'd notice!
Next, we have to point out that "frame-rate based" is only part of the problem. One of the nice things about ODEs is that you can solve them perfectly given one frame: the initial state. This means that our frame rate could be as low as 1/113 billion years ($10^{-19} Hz$) without generating any artifacts. That number, of course, is the current predicted lifespan of the universe, from big bang to heat death. If you want a different estimated lifespan number, you get a different minimum frame rate, but the numbers are equally broken. It's not just the frame rate that matters.
To see the artifacts we need to start taking shortcuts. The first shortcut we take is to say that we don't process everything. We observe convenient symmetries, and we take it. If I'm simulating a pingpong ball flying through the air, I typically don't model every atom and the inter-molecular forces that hold its plastic shell together. I model it as a "rigid body," with a position, velocity, and a rigid shape.
It's when we take these shortcuts that we run into frame-rate issues. If my rigid body assumption on the pingpong ball is not reasonable, then I generate a poor model. For example, during the impact between a pingpong ball and a paddle, the ball deforms quite a bit. I need to remember to model this period differently, with more expensive physics.
The most common frame-rate issues are the ones mentioned in others: interactions between two solid bodies that don't follow the laws of physics. This happens because the simulation starts at a frame where one of these simplifications is valid, but during the integrated path of the universe, those assumptions broke down. A pingpong ball can be modeled as a rigid body, until you have to model the eletrostatic interactions between it and the paddle which deform it during a hit. If you use these assumptions when you shouldn't, you get artifacts. You get fast moving objects that pass through eachother. You get solid objects that stick together. Stuff like that.
This issue doesn't happen in conservative simulations. Conservative simulations will do some sort of look-ahead process to see whether it can prove the simplifications will still be valid. If so, it does it the easy way. If it can't prove it, it does it the hard way, even if it turns out that those simplifications would have worked for the actual path (it's hard to find 100% whether the simplifications hold, but finding the 99% case and being conservative 1% of the time is easy). For example, your simulation might virtually "expand" every object in all directions by its velocity + max-acceleration * frame-period, and then look for collisions. If there's a collision in that expanded world, then its possible that one will happen in the real world. If there's no collision, then it's easy to prove that no collision would occur in the real world as well. This approach is very fast, computationally, and will let you avoid these frame-rate artifacts. We wouldn't observe anything as being wrong.
Now we typically don't solve these ODEs directly. We do what is called "numeric integration," which is an approximation tool. Some numeric integration approaches have artifacts that we can detect. For example, if you have a bias in your equations, you may develop what is called energy-drift. When this happens, your equations predict that energy will be conserved, but the approximations actually don't perfectly conserve it. This can accumulate over time and be detected.
Of course, we have solutions for that as well. This energy drift is easily accounted for using Hammiltonian mechanics, which admit a particular class of numeric integrators which are sympletic. These integrators do not have energy drift, because they only integrate along paths that conserve energy. If the universe used one of them, we'd never see it.
Now with all of this, we leave open the question: why? Why does the universe exist with a frame rate. If it exists because an intelligent species created a simulation, we have to ask whether they are designing their simulation to fool us within the simulation. If so, it's much harder to notice artifacts because someone is actively trying to prevent you from noticing. If I'm simulation a machine vision system for a robot, there's a whole host of artifacts that I don't actually care about because I know the algorithms the development team are putting together happen to not see those artifacts. If they add an algorithm that does see it, I'll have to change my simulation to model the physics more accurately.
For example, if there is some fixed number of frames per second, you'll see harmonics form in the small number of multiples of frames per second. You'll see things like aliasing if the algorithm is simple. However, modern simulations have something called adaptive frame rates available. If the situation gets complicated, you just decrease your frame period to improve the resolution of your answer. You can always do this unless the simulation has to run in real-time (in some true time sense). In that case, you'd look out for the out-of-simulation entities which don't seem to obey the laws of physics.
So in the end, there's lots of open questions, but the real answer is that you might be able to see the frame-rate in some trivial way, or it may be intentionally obscured from you so it can never be seen. The story is yours, design it as you see fit.
The Arrow of Time, or macro system temporal asymmetry, is the observable irreversibility of chemical and mechanical reactions, it forms the basis of entropy. It is also a demonstration of time's passage in that to reverse reactions effected by it one would have to turn back time.
If we establish that there is a minimum time frame over which such asymmetry can be observed to occur this would demonstrate a minimum duration for the definite forward movement of time, proof that time only moves in one direction and in discrete parcels as well. Actually getting experimental proofs concerning events that occur so quickly is however impossible, by definition, if time is discrete since we couldn't measure the time it takes for time to happen in increments smaller than itself.
In "frame-based" universe, there is fixed smaler amount of time, it is like looking on kino/tv one monent we see static reality, then we do not see anything (and everything is recomputed to new positition) then we see static reality ... and so on. As nothing can be done faster than the "reality-frame" allows, for normal people would suffice like 120fps to have illusion of smooth move. (the reality frame must be much faster, as people are terribly slow anyway).
But no camera in our universe could run as fast as reality frame-rate. So regardless how far we push, we would not be able "photo" either movement during visible reality-frame, nor dark during space between reality-frames. But it is not needed to detect those frames. If we can run camera "near" reality-rame speed (like 1000 times slower or so), and THEN rewind it much slower, if those two are not direct multiply of each other, we would find, that there is small noise between frames of our camera - if we film something really fast moving, we may found, that we constatntly get more (or less) better frames/worse frames/the item position varry slightly over the frame in regular pattern.
We see (say 50 fps) TV as smoothly moving, but if we film it on camera with different rate (say 60 fps), there are moving stripes in the film we could see even in bare eyes, as those are running at the difference speed (10 fps) which is simply visible as flickering. But if we would film a fast TV (say 5001 fps) with slow camera (say 50fps), we would see nothing, but one of 100 frames would be duplicate or missing or distorted. If we could get near the reality-fps, (even on many orders slower), we would not notice it by bare eyes, but statistically comparing changes in the frames, we would notise, that with regurarity one of many of them is distorted somehow, even if in avarage the movement would be smooth. and the systematic error on magnitude of 10, 100, 10.000.000 frames would signal us, that there is "frame-based" reality and we could compute its frame rate, even if it may be impossible for us to go near such speed.
The same way, as you can compute, how fast is your camera, if you film fast running car and at some moment the wheels seems to rotate slower, then stop, then rotate reverse, while car is still moving ahead.
That said it is still possible, that we live in "frame-based" reality with so insanely fast frame rate, that we could not make for this effect even with best possible equipement. Then we would not know.
And for computational speed of that simulation - we cannot say anything, as in "frame-based-reality" time is already stopped and there may be "millions years" between next sub-femptosecond frame is computed - for all what we know.
If the frame rate is constant (rather than variable), then for complex waves we might be able to detect intermodulation and aliasing of its harmonics (which in theory should go on to infinity).
High speed cameras would not only allow us to detect that reality is frame-based, but it would also allow us to record what the framerate is. Between each frame any number of things can happen(i.e., you can move 5ft or 1000ft), but the results of what happened in one frame is only visible on the next frame.
Answers to this Physics SE question suggest that there is no upper-limit to the maximum framerate of a camera, and some cameras available today are already capable of 200 million FPS. That's about one picture every 5ns!
So, if reality was frame-based then as high-speed cameras achieved higher and higher framerates, eventually we'd begin to see the discreteness of the universe as the pictures look more and more like a slowed-down stop-motion film. Eventually, we'd be unable to take unique pictures in between two very small moments of time, as there is nothing to view between one frame and the next.
If we are living in a high frame-rate simulation it means that whatever may be running this simulation is subject to limits. If it was not the case, why would it choose discrited time ?
So, if this thing is not perfect, there must be numerical limits inherent to the "language" it use to simulate us. As instance, C++ code max double value is 1.79769e+308. So let's just wait for one of the billions and billions of variable needed to run this incredible simulation to hit this limit. May it be the "univers volume" as it expends in every direction at the speed of light ? I don't know, but if these superior beings have opted for discreted time one may think that this simulation cannot fully handle the concept of infinite either.
Then, see what happen... A big crash ? Some totally unexpected bugs ? At least I guess we will see that something is wrong ; if we are not just totally erased...
