## The Handwavy Physics of Interdimensional Exchange

I’m currently in the process of writing a series of stories, some of which i’ve decided to set in a fictional parallel universe i call the Caroline timeline.  Details of it can be found here:

http://althistory.wikia.com/wiki/Caroline_Era

In the story “Buttonless”, an underachieving menial worker at a university in our version of reality finds himself transported into the Caroline timeline.  This entry is to explain the imaginary science behind the story.

First, some real physics:

1) The light cone:  An event cannot influence other events faster than the speed of light.  Therefore, whatever happens on Alpha Centauri can only influence what happens here about four years later.  Until then, it’s irrelevant.  This also works in the other direction:  what happens here cannot influence anything on Alpha Centauri for more than four years.  This is because Alpha Centauri is about four light years away.

Thinking about this in three dimensions, it means that every event can be thought of as starting a spherical ripple of cause and effect which expands out from the point where it occurs at the speed of light.  If time is thought of as a dimension like those of space, this means that every event is at the end of a cone stretching back into the past and at the beginning of another cone stretching forwards into the future, like an hourglass whose waist is the present place and time, except that these cones are four-dimensional:  a “horizontal” section through such a cone would be spherical rather than circular.  This is referred to as a light cone.

Any events linked by cause and effect to here and now must be within that cone, because the velocity of light is the ultimate speed limit and for a chain of cause and effect to pass from the outside to the inside of the cone, something would have to travel faster than light.

2) Time travel paradoxes:  If travel backwards in time is possible, it appears to create a problem because of the “grandfather paradox”, whose classic version is that if one prevented one’s own conception, one wouldn’t exist to perform the act which prevented one’s existence in the first place, and so on without resolution.

Now some more speculative stuff:

Two possible solutions to the grandfather paradox:

1) Travel backwards in time must be accompanied by displacement outside the light cone.  Whereas “back travel” is possible, it must also involve something similar to moving faster than light in space.  That is, if one travels one year back in time, one must also be at least a light year away from one’s departure point.  This would prevent paradoxes because it would be impossible to influence anything within the past light cone of the departure point.  It also has a symmetry to it because ordinary travel in space also involves travel forwards in time, again within the light cone, but stretching into the future from one’s point of departure.

2) Travel backwards in time must involve moving into a different timeline, i.e. a parallel universe, in which the paradox caused happened anyway.  There is however a problem with this because in such a parallel universe, the event may not have been caused by the time travel itself.

I suggest that these two solutions are compatible and linked, as follows:

When an event occurs which could go either way, it can be seen as causing a “fork” in a time stream.  If someone tosses a coin to decide whether to take one course of action or another, the point of divergence (POD) between those two time streams appears to be the coin landing as heads or tails.  In fact, the POD is earlier because a coin landing a particular way up is in a chain of cause and effect connected to how high it is tossed, air currents, the initial height of the coin above the surface it lands on and so forth.  Therefore, the real POD is conceivably much earlier, perhaps even the beginning of time.  However, that then involves another problem.  It means that an entire universe has to be posited simply to account for a toss of a coin, which offends the sensibilities.  It would also mean that we don’t know which of a very large number of different universes we inhabit because we will never observe which of almost all PODs is actually the case.

There is a solution to this.  Rather than seeing the forking of timelines as a metaphor, they can be seen as literally arrayed along a dimension representing probability.  Since at any moment there are a very large number of possible forks, their density then becomes effectively a continuum of points and time can be seen as a plane rather than a series of forking paths.  Measuring the distance of a possible event then becomes a measurement of its probability and probability is then effectively an extra dimension.  If we never find out about the truth, that simply means we are ourselves extended in this dimension rather than just confined to the actual universe of time and space.  We have breadth across a series of possible worlds.

There is another problem with this view.  It cannot account for more than three separate events of exactly equal probability.  If two coins are tossed, the two heads possibility could be seen as to the left of the two tails possibility and the “direct” future could be seen as containing a possibility of a heads and a tails outcome.  However, there are two heads and tails outcomes, so this cannot work if they are equally probable.  One solution would be to suppose that no two events are of exactly equal probability, but this feels like a kludge.  There is, however, another solution:  two probability dimensions.  That would allow for a circle to be drawn of equally probable events, in other words an infinite number, thereby solving the problem.

Although two probability dimensions seems to be the minimum feasible number, nothing specifically rules out more.  To keep it simple though, i want to assume there are only two.

So, returning to the time travel paradox problem, if this is an accurate description of the state of affairs of the Multiverse, travel backwards in time which avoids paradoxes by shifting into a different timeline then simply becomes a diagonal shift similar to that involved in a straightforward spatial solution to the paradox problem where there is displacement outside the light curve with travel backwards in time.

Putting this all together, i get this:

A technique is found which can cause an object to change its space-time coordinates.  Applying this technique causes an object to shift in space without time passing forwards.  At first, this appears to be an instantaneous teleportation technique, but it soon emerges that the shift also takes place in time.  The object is shifted backwards in time by a distance equivalent to how far it is shifted in space.  So, moving an object a distance of one light year also causes it to travel back in time one year, because otherwise it would involve a problem with special relativity.  This is not, however, the complete picture of what’s happening.  An anomalous feature of these shifts is that the objects sometimes seem to alter when they arrive.  This is in fact because they are not simply shifting in time and space but also into completely different timelines, and there is a corresponding event in the other timeline where a similar object shifts into this one.  Since the other timeline has a different history, this object is often different.  This has to happen because otherwise mass and energy would be lost from one timeline and gained in another, which violates the first law of thermodynamics - energy cannot be created or destroyed, and according to relativity, mass is energy, so mass cannot be created or destroyed either.  Therefore, the technique appears to combine teleportation, time travel and the ability to enter an alternate universe, but is in fact an exchange of objects between two timelines.  Also, in order for this to happen, the “teleportation” must take place simultaneously in both timelines.

Associated phenomena might therefore be that a laboratory mouse exchanged with another timeline would have a 50% chance of having the opposite sex of its counterpart, a stopwatch might be designed differently and so on.

I have also chosen to assume that although in the ordinary spatial dimensions along with time, only distance can be controlled rather than direction, in the probability dimensions the control of direction is also possible.  Therefore, the Caroline and Gordon timelines can swap items freely.

The objects swapped can be trivial and inconsequential.  For instance, an eighty kilogramme human being can be swapped with eighty kilogrammes of air molecules, so they would be replaced by a large volume of air which would lead to them being briefly surrounded by a vacuum in the timeline they entered and cause a sudden increase of pressure in the one they exited and the air entered.  Alternatively, they could be exchanged with soil, leading to a less dramatic event of a human-shaped pile of soil replacing them where they exited but them being buried alive where they entered.  It is therefore much easier simply to swap individuals.

How the exchange device works:  There are two grids of electrically charged singularities in the booth, one at the top, one at the bottom.  These are fired towards each other at close to the speed of light using a pulse of electromagnetic induction.  As they pass through the matter in the booth, they displace it into the other timeline, location and time at a very high rate, effectively in the form of countless cylindrical slices.  These are so close together that it does not damage the matter - the forces between the particles composing it are conserved and there is no time for it to lead to any kind of physical movement.  At the same time, particles are exchanged between the two timelines to conserve mass and energy.  Hence the objects are swapped.

I have assumed that the inventors of this device are initially unaware of what it actually does.  The only hint they have is that they need to provide it with what seems to be too many parameters for it to work.  However, they have assumed that some of the parameters are arbitrary when in fact they determine the timeline with which the contents of the booth is exchanged.

What are quaternions and octonions?
This bit is based on genuine mathematics.
Quaternions and octonions are hypercomplex numbers.  A complex number is a two-dimensional value on the “number plane”.  Just as there is a real “number line” stretching from minus infinity to plus infinity, on which real numbers lie, so there is a second imaginary number line forming a second axis like a graph.  Imaginary numbers are seen as valid entities because they provide a solution to the equation x*x=-1.  As it stands, no single real number can be multiplied by itself to give the answer -1:  -1*-1=1 and 1*1=1.  Therefore, it was posited that there is a second number line perpendicular to the first.  A number on the plane formed by these two coordinates is known as a complex number, and they appear as solutions to the equations in relativity as the values of the mass of particles travelling faster than light.

Hypercomplex numbers are a generalisation of this idea to more coordinates.  A quaternion is a “four-dimensional” number, and an octonion is an “eight-dimensional” number.

Here comes the vaguer, more hand-wavy bit:  I have assumed that the physicists studying the displacement booth were describing its behaviour using quaternions because it seems to be a complete description of where the booth appears to relocate objects:  a certain distance away from the starting point in the three dimensions of space and the fourth of time.  However, they found that the equations needed to describe this seemed to be more complicated than they needed to be because what they were in fact describing was a displacement in eight dimensions rather than four.  Tom’s insight is that the displacement is best described by octonions, eight-dimensional numbers, rather than quaternions because of this.  His dreams are hints that this is what’s going on, but the Caroline-to-Gordon Tom realises this before the Gordon-to-Caroline Tom.

There are also eight PODs between the Caroline and Gordon timelines.  These partly represent the eightfold coordinate position of the Caroline and Gordon timelines relative to each other, in other words the “direction” of the Caroline timeline.  The Gordon timelines are in fact a “cluster” of eight timelines, each of which is itself a cluster, so they are a region in the multiverse rather than a single timeline like the Caroline one.  The Caroline timeline is also “straighter” and the Gordon timelines more “divergent”, in the sense that the Caroline is an extrapolation of apparent trends taken forwards from the 1970s and has fewer improbable events in it than the Gordon timelines.  For example, the Gordon timelines depend on two major figures narrowly escaping assassination attempts and two other major figures being improbably assassinated, and two divorces occurring at a time when they were rare.  Therefore, it’s our timeline which is improbable and not the Caroline one, so we’re “off to one side” compared to it.