I mentioned in the post on time that we would be ignoring General Relativity (I meant Time Dilation as present in Special Relativity) for the purposes of that post because it makes the entire concept of time in a simulation far more complex. That doesn't mean I didn't have a possible way to implement special relativity inside of a simulation, it simply means that explaining it there in that post would have quickly derailed the basic concept.
This post will address the aspect of time dilation in that objects moving at different speeds have time actually pass at different speeds. This can be encompassed by the science fiction tales where a person travels at high speed some place in space for what they perceived as only a year and comes back to Earth to find that twenty years have passed.
This has been confirmed to occur with numerous devices, as well as studying the aging of cells moving at different speeds.
If time is being simulated as I described in that earlier post how could we account for this aspect of time dilation?
Special Relativity, Time, and the Simulation Hypothesis
The method to accomplish this is not actually that difficult once you understand the basic technique. The swirling rabbit holes of thought this may send you through can be mind melting. I myself am still lost in that mental maelstrom and have not yet found calm waters.
Revisiting the basics:
In order for time to be simulated I indicated that we needed to identify the fastest (smallest) unit of time that the simulation needed to track. We would call this a TICK. In this post I will now refer to this as T.
TICK = T
I explained the phenomena that as far as outside the simulation matters the simulation could be running at a much higher speed in terms of time. I gave the example of the simulation running so 1 second in the Creator/God's realm might be represented as the passage of 1 hour in the simulation. The Creator/God/Player could then observe/interact with the simulation and 24 seconds would cover the span of a 24 hour day in the simulation. This allows the Creator/God/Player to observe/interact with the simulation in terms of much larger amounts of time passing without it actually taking that much time to them. The things inside of the simulation operating on the concept of their TICK would see time passing the same speed. This would be true if for some reason you slowed it way down and were simulating 1 hour in God time being 1 minute in simulation. The things inside would not perceive a difference. Only the observer of the simulation would be aware of the simulation.
Restating that is important in order for how Special Relativity could be accomplished inside of a simulation.
Since time passes at different speeds for all known processes relative to speed we need to virtualize time. I am going to call that a VIRTUAL TICK. From this point on I will refer to it as V.
VIRTUAL TICK = V
In the simulation T would be the absolute fastest (smallest) unit of time it could track. It turns out due to relativity this likely is going to be present on the slowest moving thing that the perception of time must be tracked. Yes, that is kind of mind twisting. The slowest thing has the fastest time.
The simulation can adjust V accordingly to account for all the necessary times that need to be displayed. V will always be a multiple of T. In this case V can never be a fraction. In order to account for fractions instead the V would need to be expanded in size in terms of number of T that actually pass until the fractional nature is resolved. As far as the things perceiving time they would be unaware of this due to the earlier property explained. If your fraction is a fraction that does not end you would eventually need to drop some unresolved decimal points. This would create one of those possible boundaries I indicated we could be on the look out for to prove we are in a simulation. If you can find such a boundary that would be further evidence.
I am going to work with some hypothetical numbers here to explain this process.
Let's say we have three objects. One that time is 3 times slower than the slowest moving object perceives it. One that is 5 times slower than the slowest moving object perceives it.
SLOWEST = A
3 TIMES = B
5 TIMES = C
For every 1 V that B perceives 3 T will have needed to pass for A. For every 1 V that C perceives 5 T will have needed to pass for A.
Yet the relation between B and C would also need to be apparent in the simulation so you would need to represent this in a form that can be broken down between all of them.
If we were using the V of A as 1 T (i.e. 1 TICK) then you end up with some fractions that need their decimal dropped at some point when you consider the relationship between B and C.
B does not divide into C evenly. It comes out as 1.666666 (repeating) B is relation to C. You could try to solve for finding a value to set A, B, and C that will divide without fractions and base it around that.
Or you could set the V of A to 100 T (100 ticks) and adjust the V of B and C accordingly and DROP the fractional remainder.
Va = 100
Vb = 300
Vc = 500
Since the perception of time would be the same to those inside the simulation regardless of their V these numbers could get big. This does introduce some ramifications for the observer though. Observing this could get ugly. I am not going to resolve that conundrum (I mentioned mental maelstrom) I am just providing a mechanism whereby Special Relativity could indeed be simulated.
If you are resolving the fractions and can find something that works for all conditions it could be clean an undetectable. It is also highly unlikely. Thus if you are having to drop fractional portions at some point you will be creating time related boundaries that one might be able to detect. If they can be detected then that would be evidence of a simulation.
If we suddenly needed to track something moving called D that was moving 1.05 times faster in terms of time than A we could use the above and set it's V as.
Vd = 105
To provide an example of the boundary. Imagine then another object called E is chasing D but moving slower so time is actually moving at 1.055 the time of A?
Ve = 105
Due to setting the slowest speed to 100 the accuracy of that speed difference was lost due to fractional dropping and is an example of the boundary.
If the simulation can adjust all Vs relative to the slowest then this would be harder to detect but still possible.
To resolve the above problem all the simulation would need to do is adjust Va and then all the others accordingly.
Va = 1000
Vb = 3000
Vc = 5000
Vd = 1050
Ve = 1055
Note remember that V is the amount of actual simulation Ticks T that pass to simulate 1 virtual tick in the time for that simulated object. So in this top one ever 1000 ticks of the simulation only 1 tick is applied to A. To A they would not perceive anything differently.
Yet this is a way you could simulate Special Relativity.
The Mental Maelstrom
In the process of doing thought experiments and coming up with that I realized I have only an introductory level grasp of Special Relativity. I find myself grappling with mental problems that I am certain Physicists and Scientists have long ago dealt with and resolved. Likely Einstein himself resolved it in his publication. I haven't read it, but I am thinking maybe I should. I've had Special Relativity taught to me in several Physics classes but that doesn't mean we ever dealt with the things I found myself grappling with today.
It was namely thinking about some things that seem a little paradoxical about the nature of Special Relativity. What I am discussing now is outside of the simulation hypothesis. I just wanted to share the problems that are beating on my mind with you as I assume some of you understand Special Relativity better than I do and likely know a solution.
If I travel somewhere in space at a high velocity and we have a number for that velocity, yet when I return to my starting point a much larger amount of time has passed doesn't that introduce some paradoxes?
If I say I am moving 100 Miles Per Hour and I travel 100 miles, then I turn around and come back conventional understanding would state that 2 hours will have passed.
Yet by Special Relativity if we imaging those speeds were much faster and the equally further it is stated that when I return to the starting point a lot more than 2 hours will have passed.
If that is the case what do the people at the starting point observe? It doesn't seem like I'd be appearing to move at 100 miles per hour to them if it actually takes far longer than that to get there and back. In those cases it wouldn't seem like I was moving 100 miles per hour at all.
Now I can jump back into the simulation hypothesis and account for what the traveler observed simply by the tick system I presented above as their perception would be less significant in terms of what needed to be perceived from that of the things needing to perceive time faster. (oddly enough the slower moving things)
Yet that doesn't account for why the journey would take longer than it should if a person was traveling that fast.
It is a puzzle. One I haven't yet solved in my own mind. I've almost come up with a solution a couple of times only to think of somewhere that solution fails.
I'm going to stop this post here. I look forward to your replies. Hopefully someone reading this can help me find mental calm waters.