If you follow my blog you have probably noticed that I spend a good amount of time thinking about and simulating interactions and geometry in higher dimensional spaces. I enjoy looking for ways to describe mundane behavior we experience through higher dimensional mechanics. While this often describes the simple and obvious through convoluted means, I like to think that discovery is not always in solving a new problem but also in solving an old problem in a different way; I also hold out hope that I may find something that might surface evidence of actual higher spacial dimensions in nature.
One morning I was considering how we might experience a particle rotating through time with respect to us moving linearly through time. That is to say, holding relativity aside, consider time as a spacial dimension and ourselves as traveling through it, experiencing each 3 dimensional hyperplane along the way. Meanwhile a particle is not traveling along like us in time but is instead bouncing back and forth between a point in our future and in our past. What would we see?
Let’s setup this example a little more specifically. Let’s imagine the particle as a red ball rolling on the floor in an otherwise small empty room. Let’s get it started by rolling and bouncing it off the left wall of the room so that it rolls over to the right wall of the room and then bounces back yet again towards the left; imagine the ball rolling and bouncing back and forth frictionlessly for eternity like this. Let’s also get is started rolling through time and setup two “time walls”, one in the past at 12:00am and one in the future at 12:01am. We time this just right so that the ball hits the 12:01am time wall and reflects rolling backwards in time just as it is halfway rolling from the left wall to the right wall and then it hits the 12:00am time wall in the past and reflects rolling forwards in time again just as it is halfway on its way back rolling from the right wall to the left wall. While it is true that it is rolling back and forth in a straight line between the left wall and the right wall, its motion is actually circular when you consider how it is also traveling backward and forward in time out of phase with it bouncing off the walls of the room.
This diagram easily illustrates this:
So now using that diagram it becomes relatively easy to imagine what you would see as an observer in this room; your observation is defined by a horizontal line at the time of the observation. Read the annotations on the right from the bottom up to experience it chronologically.
Another point I want to underscore that is useful later is that just as the walls provides an equal and opposite force to reflect the ball, the “time walls” must too impart a force to bring the advance of the ball through time to a halt and then accelerate it back to the incoming speed in the opposite direction.
Now this scenario is not particularly profound, but what I recognized which I think is, and this is that this appears to fit the observation of how antimatter behaves.
Matter and antimatter are always created together and in equal proportions; Energy is applied and two particles (matter and antimatter) come into existence, they later meet and are annihilated releasing energy. I posit that the matter and antimatter are in fact the very same particle and their coexistence is due to their bidirectional travel through time and their apparent creation and destruction is simply our perception due to our different path through time.
By putting in energy we are setting up a reflection at the point of the apparent creation of the particles and the second bounding reflection is created by the apparent annihilation energy released when they come back together. Recognize that the apparent energy we see released upon the annihilation can be reinterpreted not as a release but rather another investment of energy when viewed from the perspective of the particle traveling backwards in time; it is putting in the equal and opposite force to reflect the particle back in time.
One experiment I considered to disprove this hypothesis would be to create and isolate a matter/anti-matter pair and force the annihilation of the anti-matter with matter that is not its matter pair. This would appear to violate the hypothesis that the pair are a reflection and so must annihilate with one another. After some consideration my defense is that reflections occur multiple times such that a particle need not annihilate with what appears to us to be its immediate antiparticle. In this case, the annihilated matter particle was another reflection of the same matter closing the loop after more than one pair of reflections through time. Here is an example of a double reflection:
Extending this resolution further it suggests that in fact there could be just one particle in all of existence; A single particle reflecting back and forth endlessly winding and threading its way through time such that we perceive it as the near infinite number of particles in the universe.
Thoughts and unanswered questions
Speed of Time:
- I realized that by considering time as a spacial dimension we could look to calculate the speed with which matter travels through time. I am not certain what this really means because “speed” is a distance traveled over time and we are defining time here as a spatial dimension but the answer is very interesting. If we know the energy it takes to reflect the particle in time as well as it’s mass we can calculate its speed (V = Sqrt(2E/M)*2). Fortunately we all know the formula for the energy to create matter/anitmatter, it is the famous E=MC^2! Plugging that in it suggestively resolves to indicate that matter travels through time at the Speed of Light!
Static 4-Space:
- This hypothesis rests on the premise that space-time is a static 4 space where time is simply the illusion of us traveling at the speed of light through each successive 3 dimensional hyperplane orthogonal to time. The word traveling is misleading here because it would denote that we are moving and so no longer exist where we came from and now exist uniquely where we now are, this is not the case. Again, as static 4-space we simultaneously exist at every point we will ever be but we have an instantaneous velocity in each 3-space hyperplane. In a more metaphysical sense, you might argue that from the perspective of consciousness, the experience we are having at any given moment resides frozen in a hyperplane and that all hyperplanes are happening simultaneously. This is not to suggest there isn’t any connection between the hyperplanes, causality is arguably still preserved, but it is fun to think about how and why you are aware of this one consciousness right at this moment and not the one you had last week or next year but it doesn’t make them any less real.
Geometry of Reflection:
- There is a convenient self-fulfilling causal aspect to this concept where the particles conveniently exist and interact with each other in utter perfect balance; Arguably it must or the 4d block of reality could not otherwise exist. What I mean by this becomes more obvious when you try to calculate the motion of a particle traveling forward in time interacting let’s say with the gravitational force of the its anti-particle travelling backwards. Each particle must effect each other in a way that perfectly alters it’s momentum, position, rotation, etc such that after it reflects in time it finds itself to be precisely in the state the particle it was previously interacting with so that it can bring itself to be what it is. It is essentially the classic time-travelling paradox where the act of going back in time to prevent something is what caused that something to be.
- After a good deal of thinking on this, I considered an empty universe in which there is just a single particle reflecting in time and subject to an attractive force with its anti-particle that is an inverse-squared force like charge or gravity. The geometry that arises which satisfies the requirements in both directions in time and delivers the particle to reflection points in the state required is described by the same mechanics we see with a ball bouncing on a mirror. Surprisingly (to me) the particle interacting with itself in perfect harmony describes the common path we recognize of a particle imparted with some trajectory into a gravitational field and watching it return.
Cosmological Implications:
- From a cosmological standpoint this can be extended to apply an interpretation on the big bang and the open question of where all the anti-matter is if matter and anti-matter are always created in pairs and we observe an overwhelming preference towards matter in our universe. It is possible that the big bang is a major cluster or singular, potentially enveloping, point of reflection in the past and that there is another big bang in the future that bookends the totality of time and space. It might suggest that there would be an anti-matter version of our visible matter universe travelling backwards in time from our perspective. Depending on the mirroring paradigms I describe later, it could be a reflection of our matter universe, or a post-reflection future or past of it. It would be particle for particle equivalent to our visible universe and when it becomes visible and we see ourselves approaching it we are reaching the cataclysmic event in which the universe will approach an energy barrier that will reflect us back in time. This will again appear that we have a big bang in our past and we will be escaping from our anti-matter counterpart again. If in perfect balance are these two points actually just one?
Compatibility with Relativity:
- I cannot begin to give this the attention this deserves. What I have illustrated and considered to date has been planted within a Newtonian paradigm and it is unclear to me how to evaluate the impact of introducing relativistic concepts with independent reference frames to this. I do recall starting to think down a related relativistic concept and contemplating that the speed of light may not be a speed limit but rather a constant speed through Space-Time such that as a particle moves faster in 3d space it must as a result slow down through time and vice versa; that it is just about the direction of the 4d vector, not it’s magnitude. This is likely a diversion but I come back around to this thought repeatedly so I thought I would mention.
Order of Events:
- If we considering that a particle ages, then a paradoxical situation arises.
- So what happens first? Imagine you are a particle traveling through time, much as you and I are right now, until we are reflected backwards in time. We would now be traveling backwards in time, do we see our earlier self walking beside us appearing to grow younger? Did we see the same before on our way forward through time? Once we we reach the point at which we started and are reflected again, are we the same age as when we started or do we keep aging? Where did this loop begin? Which way is forward in time and which is backwards? Perhaps these questions are flawed because we are trying to make time imply an order of events as we commonly think it does.
- Say you traveled through time with a radioactive element in hand, would the element in one direction emit radiation and in the other direction absorb it such that at the points of reflection it is identical? Could the experience be relativistic where you would continue to see the element in your hand wither away but an observer traveling from before your creation until after your annihilation may not agree on what they see? Would your reflection then present your future holding a smaller amount of radioactive isotope or your past showing you when you held a larger one?
- Ultimately I think this boils down to 5 possibilities. I will write these in a short hand that can be described as a circle made with an arrow going clock-wise. This represents that path of a particle in time. At the bottom is the past and at the top is future and on the left is A for Alice the particle traveling from Past -> Future and on the right is B for Bob the particle traveling from Future -> Past. We will denote what A and B experience of themselves and each other and what their cross-over state is at the Past and Future. We will describe state as starting at 1 and progressing towards 0 and describe this anecdotally as observing your anti-self in a mirror while holding a bucket that is leaking water.
1) The Mirror:
…Looking into a mirror that shows your bucket emptying while yours is emptying. Once empty your bucket starts filling again while your reflection’s bucket also starts filling…
- A(P->F) @P=1 @F=0 *B=1->0
- B(F->P) @P=1 @F=0 *A=0->1
- Asymptotic = False
- Symmetric = False
2) Mirror Repeating:
…Looking into a mirror that shows your bucket emptying while yours is emptying. When they are done your bucket is full again and you see your reflection emptying again…
- A(P->F) @P=1 @F=0 *B=1->0
- B(F->P) @P=0 @F=1 *A=1->0
- Asymptotic = True
- Symmetric = True
3) Trading Places:
…Looking into a mirror that shows your bucket filling while yours is emptying. When they are done doing so, you become your reflection holding a full bucket and watching your reflection’s empty bucket filling again…
- A(P->F) @P=1 @F=0 *B=0->1
- B(F->P) @P=0 @F=1 *A=0->1
- Asymptotic = True
- Symmetric = True
4) History Repeating:
…Looking into a mirror that shows your bucket being filled from a spigot in the past while yours is emptying. When they are done your bucket is full again and you see you are your reflection being filled from a spigot again…
- A(P->F) @P=1 @F=0 *B=1->2
- B(F->P) @P=0 @F=1 *A=1->2
- Asymptotic = True
- Symmetric = True
5) History Repeating in Reverse:
…Looking into a mirror that shows your bucket being emptied back into a spigot in the past while yours is emptying. When they are done your bucket is full again and you see you are your reflection being emptied back into a spigot again…
- A(P->F) @P=1 @F=0 *B=2->1
- B(F->P) @P=0 @F=1 *A=2->1
- Asymptotic = True
- Symmetric = True
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