C = Speed of causality (otherwise known as speed of light)
What if the speed of light really is something different and we just experience it this way?
Consider the following world:
In a far distant universe things are different. Distances between objects are measured not spatially, but as space-time vectors which denote how far spatially and how far in time the events differ. This unit of measurement is more more useful since someone who stays still still moves at v=c in a completely vertical line parallell to ct.
Now if all that is clear, consider the following absurd difference. Rather than flat 4D Space you are working with round hyperspheres. What this really means is locally, you can travel in a straight line but in flat spacetime we percieve this as a circlular motion. Consider an orbiting object, it is moving in a circular path. To stay in orbit you need an attractive force towards the center of the object you orbit around F = mg as well as a velocity that escapes the ground quick enough let's set it to v = 10 000m/s.
In curved spacetime, this circular path is actually straight. Because the unit you measure a straight line with is circular, all circular paths are also straight paths. Now to blow your mind even further, what is F=ma really doing? A free falling object that circles the object itself travels at a straight path which means it is actually not experiencing any acceleration. This means the force F=ma is not needed if we assume the curvature is affected by the mass of the object. Gravity can manifest itself as something that bends spacetime in order for people to agree on what an inertial frame of reference really is.
Now to blow your mind with facts some facts.
In flat space and time, or even just flat spacetime observers do not agree about:
- Distance between things (spatial difference)
- Distance between events (time difference)
- Order of events (past, present future)
Proving the first two are very simple, consider if you travel at v = 0.99c and you consider a train going into a tunnel at the exact same size as the tunnel. A "considerably" inertial object at the surface of the earth or even in space will both observe the object exactly disappearing then reappearing on the other side, you however at v = 0.99c relative to the tunnel and train will never see the train completely hidden in the tunnel as you will see both ends stick out slightly. This is because the train moves relative to the tunnel and contracts the space of itself this way. The observers watching the train agree on the fact because the train's time is contracted as well and thus it appears larger to them, however you at v = 0.99c percieve larger time contraction than the train and will see it moving faster than it really is as well as being much longer than it really is.
The last one is quite difficult to prove with an experiment but in theory it could be done and has been resolved. It is possible for me to see an event that will appear in someone elses future and we will not agree on the order of the events. You can make this difference as large as you like having observer A saying "They were in order X Y Z" but observer B saying "Y Z X". However, in curved spacetime this is easily modeled by seeing that the distance between the events and the observer differ, but they agree on the spacetime difference between the events. This fact leads to the conclusion that space and time are harshly intertwined and can not be seen as separate things.
Back to programming, normally when making a render frame you consider the frame rate. You wanna update some physics? Fine let's pass in 1/60 s and hope the framerate is equal. What happens if the PC is too slow or the update is taking huge chunks of time? We get delayed, slowed down and when the PC runs fast enough the animations themselves speed up. This is not good. What's a solution then? Let's pass in variable rates,
that is the time it took to render the frame. If we are running 80fps, then we pass in 1/80s to the render method. This is fine in small quantities but easily gets out of hand when objects move close to the border then a large lag appears and suddenly the object moves through the wall with no collision.
This very model has a problem: Objects move in variable timesteps and thus there is no global maximum velocity or an agreeable constant of causality.
One solution is to agree on a maximum timestep, nothing can occur faster than 1/60 s and beyond that we can accept any timesteps. Anything beyond 1/60 s we experience we simply simulate at 1/60 s multiple times until we have a remainder greater than 1/60 s then we simulate the remainder. This solves the problem at first glance but runs into another problem. What if the simulation takes more than real time to run, and we run it at real time?
Well any small spike it experiences will make it try to catch up by doing more simulations. It will fail on those, and do more simulations and eventually it will die from falling behind too far and trying to do too much, and the simulation stops. The solution?
A constant of causality = c: the rate at which things happen
Always operate on this, and if you want to simulate say 3 seconds of physics you call the Simulation method with 3 as argument and asynchronously runs and responds in timesteps of c. The causality constant c determines the speed at which things can happen, per second.
This model closely looks just like our universe and can simulate gravity without force, circular paths without rotation and spherical expansion in straight paths.
With v I don't mean spatial velocity, I mean spacetime velocity. The spatial velocity is 0 for every object from the object's own frame of reference, and from any objects reference another object's velocity is v = ct + v(s) where v(s) = spatial velocity
I'm not claiming spacetime is entirely hyperbolic, I'm claiming objects with mass induce local curvature relative to their total energy. I do however encourage you to do some hyperbolic maths since it does make the idea simpler to understand. The only basic equations you need to realize this is v = ct + v(s) (Spacetime velocity) and Spacetirme distance ds = (dx)^2 - (c dt)^2 where dx = spatial distance and c dt = time distance. Play with a 2D graph of the y axis being ct and the x axis being spatial location (normally in 3D space). From this you can easily model gravity using straight vertical lines as relative stationary objects and curved paths being heavy mass objects. The reason again, that the objects with large masses have curves in a 2D straight plane is that spacetime really is curved around the object, not straight which is hard to model as a 4D graph.
That is, if you are very far from heavy mass objects and experience little of what we normally call "gravitational force" then your spacetime looks locally straight with very small curvature, and thus little "gravitational force"
Mass is something we experience as a result of higgs field interaction. In order to exist, some particles (for example the electron) must obtain a weak hyper-charge to be in left-handedness or lose it to flip its spin. The higgs field bombards particles with charges like this and interacting with the field itself is what gives the particle mass. Relative mass that increases as you increase velocity according to Einstein's famous equation v = mc^2 comes from the fact that when you consider someone's spacetime momentum it really doesn't exist. Spacetime isn't something you travel through. Your entire future, past and present exist as one long line along 4 dimensional spacetime. This essentially doesn't mean your don't have free will, only that what you will decide already exists in spacetime. All those points and events has a value for energy density, some have extreme energy density because they have extreme mass. Others travel very quickly (close to v(s) = c) and on the graph this simply means they line is longer and they experience more of reality. If you consider your existing reality when traveling through wind at a constant speed say v(s) = 2m/s you experience some force trying to slow you down when you bump into particles. Moving very quickly along spacetime also means you move further in spacetime bumping into more higgs field and experiencing more mass. I hope I explained that well, since it's a topic I only recently started to consider and experiment with.
With this in consideration, think about what E = mc^2 means in this context. If we consider c = causality constant, and ct is simply one of the axes on our graph then that means that your total energy over the causality constant squared is your mass. What is the total energy in this context? It can take many forms, charge, mass, spatial velocity, spacetime velocity .. yes you can travel quicker through time since it's just a line you move along at... there's no rate at which
you move but it can also be considered the total amount of causality you occur.
Think about this for a moment.. why is energy conserved? It could be that, if energy wasn't conserved then spacetime couldn't exist as one complete state since any actions to the energy could change your path. I have no verification of this but before I run into the X and Y problem, I will give you another quite obvious but hard to come by statement. Energy isn't consumed but our screens glare at us with energetic particles, how? High school teachers like to mention "Energy quality" isn't conserved but I'd like to rephrase it into something else. Energy quality usually refers to that the electrons which were gathered with low entropy move to the positive charges and you lose energy quality. I'd like to call this the value of 'information'. In the end I actually don't think the basic foundation of the universe is energy, I think it is information. Why is it that we are not allowed to transport particles with mass faster than or equal to v(s) = c? In spacetime graph, an angle that grows closer to the space axis than v(s) = c would imply that it moves through more than one spatial point per 'tick', which our causality constant prevents. In order to send information from one place to another, a particle with or without mass must carry it where we can model massless particles are pure waves which travel at most at v(s) = c because it needs to be measurable at each 'tick' according to the causality constant in order to preserve the rules. One good reason to model the reality like this is how physicists traditionally explain that light experiences gravity... they say the particles experience relative mass.. which we should be able to measure and we probably will just like the explanation above goes for anything with abs(v(s)) > 0.
Back to information, what happens with the electrons? They travel from a collective negative charge to a big mix. What did we really lose other than "energy quality"? Well, previously because we knew there was a collection of positive and negative charges we could connect the wires and see the effect. Without this information we wouldn't know and most of the time the energy spent connecting cables (moving physical objects and thus curving or bending their world lines) would've been wasted. It requires the knowledge that the particles are sorted. We spend this information in order to mix them up and receive new information.
A quick detour back to E = mc^2 reveals to us that there may be some preserved information laying around and possibly it may be information that causes the universe to change state and it may or may not be convertible to energy itself. Information should be able to travel instantenously but as you require an energetic particle, field or otherwise causality bounded thing to exchange this you will never achieve anything with it.And to wrap up what you see in your screen surely are energetic particles you absorb and reemit. However, what you did was you converted information in the form of sorted particles to a set of ordered light that makes up the screen you read this post on. That information in itself may or may not be preserved, but it does go into your brain and serve some purpose to change the future.
>What if the speed of light really is something different and we just experience it this way?
but there is no what if, the properties of light, the speed of light, has been measured and understood.