I realize the following question is non-trivial, but I would greatly appreciate any all help.
I'm interested in creating a SciFi story that takes place in an alternate universe I'm calling Universe X. I potentially want to have notions of interstellar travel and other common SciFi situations. But, I want to work within the following constraints:
- No magic or hand waving. Everything in the world must follow precise rules.
- Any experiment or observation must net the exact same result in Universe X as it would in our universe.
- The physics of Universe X must be easy to understand. If a ship is able to travel FTL the reader should understand the physics of it. Perhaps at a level analogous to understanding the mechanism by which a microwave oven heats food.
With this in mind I have been working on a simplified physics for Universe X for a while now and in particular the mechanisms underpinning relativity / quantum mechanics / gravity, etc.
Things have been going pretty well and I personally have not found any experiments or observations that would net different results in our universe and Universe X. But, of course, I don't know of every experiment and certainly am not an expert in tensor calculus and Pseudo-Riemannian manifolds. So, as I mentioned before, any help would be greatly appreciated...
Does my fictional system of physics obey the three constraints I have listed above?
At a base level Universe X is made up of normal cartesian space and normal cartesian time. Placed in this cartesian space is a quantized aether made up of tiny cells, I'm calling aexels. The individual aexels form bonds with their direct neighbors that don't let them get too close or too far from one another. As a result this aether is a compressible liquid crystal lattice; it can flow; it can stretch, it can squish. Each individual aexel can have state; the states of these aexels can be communicated to their neighbors; it takes one 'tic' of time for a signal to move from an aexel to its neighbor. The fastest a signal can move across the aether is one aexel per tic. In Universe X one aexel per tic is referred to as the speed of light.
These state signals that jump from aexel to aexel can loop back to a previous state forming a stable state loop analogous to the 'particles' of Conway's Game of Life. These stable state loops form the basis of all matter in Universe X. Some of these loops have a property called 'mass'. Mass is a measure of the rate at which the loop destroys the aexels it is sitting upon. As these loops destroy aexels more aexels get pulled towards them due to the crystalline nature of the aether. As this occurs the 'mass' itself starts to clump up forming bigger and denser clumps of matter. As these clumps get more and more dense the rate at which aexels are flowing towards the clumps increases. Once the rate increases past one aexel per tic (the speed of light) the clump of matter becomes a black hole. In Universe X gravity is not a force, rather it simply the acceleration of the aether as it moves closer and closer to clumps of matter.
Just as in our universe the particles of Universe X are created through pair creation. During pair creation a particle and its antiparticle are created that are equal and opposite to one another. As a particle with mass is created, an antiparticle with antimass is also created; the mass destroys aexels and the antimass creates them. And while the particles tend to clump up into planets and stars and black holes, the antiparticles continually spread out as a dust between the particle clumps creating new aether at the same rate that the particles are destroying them. This creates new aether between galaxies and as such causes light traveling between those galaxies to become red shifted. Also the aexels being created between the galaxies cause a pushing on the outside of galaxies at the same time as the destruction of aexels in the inside of galaxies is causing a pulling. It may be difficult to differentiate between pulling from the inside and pushing from the outside.
All of the loops in Universe X can be divided between loops that move in a straight-line at the speed of light and loops that move back and forth in some alternating fashion at a net velocity of less than the speed of light. The directly moving loops are called edisons, the alternating loops are called teslons. The teslons can form complex composite structures. The motion of these structures are mediated by edisons. Due to the particular mechanism used in E&M only the roundtrip duration of the journey of these edisons between teslons matter. This round trip time will entirely be a function of the rate at which a composite system is translating across the aexels. If the system is not translating at all, the edisons will move maximally between the teslons and the composite system will animate quickest. As a system translates faster and faster across the aexels, the edisons will take longer and longer to travel back forth causing the rate of animation of the composite system to slow down. Translating systems will experience 'animation' dilation. Systems sitting still on a planet's surface will also experience animation dilation for the exact same reason, because the aexels are flowing into the planet and so even though the system doesn't appear to be moving, it is still translating across the aexel field (at the escape velocity).
Length contraction also exists in Universe X and is also entirely a function of the rate of translation of the composite system. Without length contraction differences in the roundtrip journey time between edisons moving perpendicular and parallel to the direction of translation would become apparent, but with length contraction, the difference is precisely masked and as a result the round trip time is equal in both directions.
In describing Universe X here I tried to be as concise as possible. However, I have created an iPhone / iPad / macOS app the goes into a little more detail and models difference aspects of Universe X: https://apps.apple.com/us/app/aexels/id935727868
At any rate, any flaws, discrepancies, oversights or potential problems what-so-ever that come to mind would be highly appreciated.
In order to clarify my motivation and better explain aspects of Universe X perhaps we can discuss a concrete example: the movie Interstellar within the context of Universe X.
The Wikipedia article currently has the following text:
... praised the film for its scientific accuracy and has said Interstellar "could set the gold standard for science fiction movies for years to come." Similarly ... a former NASA software engineer, said "Thorne's and Nolan's accounting of black holes and wormholes and the use of gravity is excellent."
Given the average person's lack of an intuitive understanding of black holes and Relativity they have no reason to doubt the above statements.
My hope is that armed with a 'microwave oven' understanding of Universe X an individual could easily identify numerous reasons big and small why the movie Interstellar's physics would be ridiculous in Universe X.
Worm Hole at Saturn
In Universe X the speed of light limitation is due to the aexels only being able to signal their neighbors and that signal taking one tic of time to occur. However, in theory there are no limitations in the speed that the aexels, themselves, can move.
In theory in a flat cartesian universe such as Universe X, an aexel "river" could be created between two points in space where the aexels flowed considerably faster than the speed of light allowing a vessel to enter the river and move to another point in the universe without causing dilation effects.
However, there would need to be some mechanism that motivates these aexels to flow. The river would take up actual space all the way from point 'a' to point 'b'. The flow would be one way, unless there was a mechanism for reversing the flow or the river had two paths, one there and one back.
Also, currently the only known way to cause the flow of aexels in Universe X is by destroying them or creating them using mass or antimass, so its entirely unclear how such a river could come about.
In short, a worm hole in Universe X while being theoretically possible seems spectacularly unlikely for numerous reasons.
"Every hour we spend on that planet will be seven years back on Earth"
That equates to a $\gamma$ of 61,360 or the aexels flowing through the system at (and consequently an escape velocity of) $0.999999999867201 c$.
Worried about the time they will lose due to dilation at Miller's planet they decide to keep their main ship ('the endurance') mostly outside of the black hole's gravity well and land on the planet using their shuttle craft ('the ranger'). It is unclear why leaving the endurance outside of the gravity well is particularly helpful since they will be losing time in the ranger instead, but let's give them the benefit of the doubt that for some reason taking the ranger alone is quicker...
Once they are done visiting the planet they'll need to fly the ranger back to the endurance. This will require accelerating to a velocity greater than the escape velocity.
Their main ship just took two years to travel from Earth to Saturn, but now their shuttle craft is capable of accelerating to 9 9s c?! Why didn't they just do that on the way to Saturn in order to arrive in less than 2 hours?
Jumping into a Black Hole
In Universe X there is nothing particularly magical about a black hole. It is simply an accumulation of mass dense enough to draw the aexels into it at the speed of light.
For any spherical mass the escape velocity will be greatest at its surface and will drop off in both the outward and inward direction from the surface. This means in Universe X a black hole will necessarily have material all the way to its event horizon. It would not be possible for matter to sit still on aexels moving faster than the speed of light because the matter itself can not translate faster than the speed of light. (I.e., splat or the falling into a star equivelant)
Furthermore, in Universe X there is absolutely no theoretical basis, likely or unlikely, that allows for information or forces to affect events in the past what-so-ever. The entire premise is preposterous.
Realizing the non-trivial aspect of this question and the fact that I've had a lot more time to think about it than someone just coming to it now, I thought I'd perhaps give people a head start and discuss 3 potential issues.
I also hope to hint to people that this question is perhaps a bit less frivolous than it may seem.
My original thinking on the MMX was that with aexels, the flow of aether would be directly into the Earth and since the MMX was only looking for changes of the aethereal flow horizontal to the surface of the Earth the null result would make sense in Universe X, but that if somehow someone could repeat a vertical version of the experiment the flow could be seen.
However, I later realized that a vertical MMX would show a null result in Universe X just as it would in ours and it does so because of length contraction.
In Universe X, since gravity is not a force, it can not directly cause a system to translate over the aexels, only E&M can do that. As such, a tennis ball placed infinitely far from a static non-rotating planet will not translate across the aexels, but rather will just float down on top of them as they flow towards the planet like a leaf floating down a stream.
As such, the motion of the tennis ball will indicate the motion of the aexels themselves. Using Newton's law of Gravitation we can calculate the velocity of the tennis ball when it hits the planet, which is the escape velocity. That velocity will indicate the velocity of aexels flowing into the planet at the surface, therefore, we can then calculate the dilation at the surface of the planet by simply plugging the escape velocity into the Lorentz factor.
Perhaps shockingly, this calculation which uses only concepts of Universe X exactly foots with the time dilation at the surface of a non-rotating planet in our universe.
However, using this same analysis we can "calculate" the dilation of the tennis ball as it's falling towards the planet. The tennis ball is never translating across the aexels and therefore will never experience any dilation on its journey from infinity to the planet.
The same analysis in our universe using the Schwarzschild metric will instead net $\gamma(v_e)^2$ (where $\gamma$ is the Lorentz factor and $v_e$ is the escape velocity).
So, it seems we have found a discrepancy! The problem is that while there have been a handful of experiments that have verified the phenomena of 'time dilation', 'warping of spacetime', 'expansion of the universe', there have been none showing that the Schwarzschild metric is physical and actually there are indications that it is not.
One of the first steps in the derivation of General Relativity is to define a 4-vector with time and 3 spacial dimensions and define a value $ds^2=dt^2-dx^2$ and then assert that $ds^2$ is an invariant value in all inertial frames.
It is quite easy to devise a thought experiment in Universe X and see that $ds^2$ would not be invariant in all frames in Universe X.
So, once again it seems we've found a discrepancy! But, just as before there never has been any experimental verification of Minkowski's assertion that $ds^2$ is invariant in our Universe.
(And the fact that we see the ISS's clocks moving faster and they see our clocks moving slower seems to directly counter Minkowski's assertion.)
The result being that I still have not been able to find an experiment that would net different results in Universe X and our Universe.
And so I again ask, does anyone know of an experiment or observation in our universe that would net a different result in Universe X?