Time Travel – a deterministic, mathematical universe perspective

Is time travel possible?

As a garden-variety ape with a wifi password and no physics, mathematics, nor philosophy degree, here is my disproportionately long opinion.

1. You’ve been a time traveller your whole life

The first, and fairly trite point to make is that traversing through time is not only possible, but seemingly mandatory—though only in what we discern as the forward direction. You’re doing it all the time, at a rate of 1 subjective-second to 1 Earth-second. If you’re sufficiently keen and wish to travel faster through time, you can gear up with some special relativity lore (passed down from father Albert), build yourself a suitably fast and comfy spaceship, then travel in a big loop at a significant fraction of the speed of light for a year—invoking the effects of time dilation. Or, if you’re wanting to save some money and effort, you could just cryogenicize yourself in hibernation mode and set a 100 year thaw alarm (warning: we might never learn how to successfully unfreeze you). Both tactics will drastically decrease the ratio of your subjective-second to Earth-second (your clock will tick much slower than Earth’s), and upon your eventual return to Earth time, you’ll find all those you love to be dead, and potentially a totalitarian AI regime that’s eager to rearrange your atoms into paper clips. Score.

I know, I know, I can hear your thoughts, as they, too, echo impatiently in my mind: “That’s not what I mean by time travel, you flappy-doodle!”

Word, let’s get to it.

2. Temporal paradoxes

Clearly, the primary interest in time travel is the ability to venture backwards through time. So what would that even mean?

First, let’s have some fun with the idea of travelling back in time, and then we can explore the real reason I’m sitting here writing all this nonsense; I think the question is rooted in a misunderstanding of reality.

Putting aside all physics skepticism, how might time travel logically work? Theoretical physicist and mathematician, Brian Greene, imagines jumping into a time machine and zooming off 5 years into the future to see if any breakthroughs have been made in his primary field of study: string theory. What he finds is mind blowing. Not only has a unified theory of everything been discovered, but when he asks who developed the theory, he finds out it was his mother—a person who knows nothing about physics in the time he just came from. Bewildered, he decides that he needs to go back to his timeline immediately to start teaching his mother everything he knows about physics, in order for this beautiful future to unfold; but then he has another idea. Why not just read the paper she wrote, then go back to his original timeline and tell her what to write? This seems much easier than to embark on an extensive, 5 year lecture series. So he does just that, and exactly as he witnessed during his jump into the future, his mother submits the theory and changes the world forever. But where did the physics insight come from? Who actually deserves credit for this paper? It’s definitely not Brian’s mom, since she just wrote what he told her to write, but it’s also not Brian, since he simply plagiarized his mother’s paper from the future. This is an informational paradox, and there are many other similar paradoxes, such as going back in time and killing your grandparents before they meet each other. How were you able to kill them, when your existence requires them not to have been killed?

One possible resolve to these time travelling paradoxes is that instead of travelling back in time, you’re actually travelling to a different parallel universe that’s nearly identical to your own. If that’s the case, then going back in time (to another parallel universe) and changing history as to deny the possibility of your birth just means you won’t be born in that universe, while your universe remains completely unaffected. When you eventually return from your sci-fi adventure to your original universe and time, nothing in your reality will have changed.

Seeing as we’re now 2 levels deep into speculation, I’m going to pull back the reins and course correct to what I see as a far more interesting direction.

It’s time to get to the juicy stuff.

3. Our Mathematical Universe

The way I see it, there’s a fundamental problem with the question—one which demonstrates a misconception of the nature of time. Max Tegmark’s paper, titled The Mathematical Universe, and his subsequent book, Our Mathematical Universe, instilled an insight in me that has profoundly influenced the way I think of the Universe. His core thesis is that the “unreasonable effectiveness of mathematics in the natural sciences”, as Nobel Laureate Eugene Wigner reflected upon, is not just a wacky coincidence. The reason mathematics has proven to be such an invaluable tool in understanding the properties and laws of the Universe, is because the Universe is in fact a mathematical structure. Yes, we live in a world with particles and forces, but every particle and every force is actually just an object of pure mathematics. Jesus, what a claim; let’s unpack that.

If you were to start zooming into any region of space (your hand, a raindrop, Jupiter’s rings, or “empty” space), you would eventually end up finding very peculiar particles in your field of view zipping about in an exceptionally disorientating manner. If you zoom in far enough with your imaginary microscope, say 10-18 meters by 10-18 meters (one millionth of a trillionth of a meter), and freeze the frame at just the right moment, you will have before your eyes, an electron. Of course, the interaction of light required for you to see the electron will affect its position, and the amount of photons required to bounce off of the electron are too numerous for it to remain even remotely still. However, for sake of argument, imagine you have an image of a hazy dot in front of you: a single electron. But what is it? As far as we currently know, there are no subcomponents of an electron. It’s one of 17 to 54 fundamental particles in the Universe (depending on how you count… Feel free to dive down that rabbit hole) that don’t have any characteristics aside from their mathematical properties. Okay, but what does that mean? It means that the only way you can describe a fundamental particle of nature is through numbers. They all have a certain mass, spin, charge, and so on, that can only be described by mathematics. There is no other way to perfectly catalog these particles.

Now, if “A” is perfectly described by “B”, then “B” just is “A”. A truly perfect, all encompassing description of anything, is simply synonymous with whatever you’re describing. Take a flower, for example. No amount of linguistic elegance and hand waving is going to allow you to perfectly describe a flower. If you want to perfectly describe a certain flower to someone, you’ll simply have to make that exact flower and give it to them. The flower describes itself exactly. Therefore, if an electron and all other fundamental particles that make up the entire Universe are perfectly described by mathematics (which they are), then they are mathematics; they are a mathematical structure. By extension, since the Universe only consists of particles and forces (which are all purely mathematical structures), then the entire Universe must therefore be an unimaginably complex, colossal mathematical structure. Tegmark’s paper and book both provide a far more comprehensive narration of logic, but this is a heavily condensed version of the line of reasoning that made me start seriously considering the idea.

Now that we have a foundational understanding of the Universe as a mathematical structure, we can introduce time into the picture. In fact, it might be helpful to see how time affects the Universe if we first understand what it would be like without time. Whatever state a timeless universe is in, it will be like that forever. It doesn’t make any sense to think about how it got to be in its current state, because it’s always been like that. Therefore, we can think of any possible arrangement of particles frozen in time as a timeless universe. An example of such an arrangement is the precise position of every particle in our Universe riiiiight…. now: frozen forever. However you’re standing or sitting, whatever thought just crossed your mind, and whichever complex configuration all other particles are in throughout this grand cosmos are now as static as a rock. There is no process.

By adding time, you introduce change into a universe. Now there can be translation and rotation of particles. However, change is just a transition from one frozen, timeless state to another. Here’s a diagram to help visualize what I mean.

EarthMoonOrbit
Figure 1. To simplify matters, this graph only has 2 dimensions of space, x (left-right) and y (forward-back), and 1 dimension of time (up-down).

On the right in figure 1, we can see 5 specific snapshots of the moon orbiting the Earth at different moments in time: infinitesimally thin slices, or cross-sections, from the full picture on the left. On the left is the entire mathematical structure without specifically selecting any particular moment in time. The left image represents all of time and space as one static, mathematical structure. The word static is key here, as you can imagine that if you were trapped within the bounds of time (as you are), you would only ever be able to see individual snapshots of the Universe (the moment you were born, your first heartbreak, your 42nd time eating asparagus, etc.). However, from a perspective that’s outside of the Universe (the way in which you look at the left image on your screen), you can see the whole picture as it really is: a static, unchanging, mathematical structure. You could think of this as a ground vs aerial perspective.

If you were to zoom into the blue cylinder that is Earth in figure 1, you would see a densely packed web of particle positions through time—representing every particle on Earth throughout all time, much like the streaks of light you see in long-exposure photographs. Within that dense, noodly network, there exists an interweaving structure of particles that is your body, as seen in the middle and right images in figure 2. The rightmost image also includes your death, which we can visualize as a process of particles diverging away from their previously interconnected structure—which is just a nice way of describing your decomposing corpse.

MathematicalYou
Figure 2. A couple more images of static, mathematical structures, the two on the right being a very simplified version of your particles throughout your life (in reality, there would be over 100 billion, billion, billion noodles, which is roughly how many elementary particles make up a human body at one time). The left image is some object that doesn’t rearrange much over time—perhaps a rock, or a toothbrush.

With this model in mind, change, and therefore time, is an illusion. Just because you’re experiencing this moment right now, doesn’t mean that the instant you ate asparagus for the 17th time doesn’t also exist on equal terms. What we call the past and future, are simply other temporal slices from the forever existing, static, mathematical structure that is our Universe. Additionally, the fact that you’re experiencing this exact instant, says nothing about the importance of this particular moment in time; it just means that in this infinitesimally brief (thin) snapshot (slice), there is a life form on Earth that calls itself *insert your name here* and through some yet-to-be-discovered process, it is manifesting conscious experience. The conscious creature that you remember being 10 seconds ago always has, and always will exist. Right now, you are simply the momentary consciousness that is locked in this infinitely thin, timeless slice of the static, mathematical structure that is our Universe.

Okay, that was fairly dense. To help further develop an intuition of what I’m talking about, here’s an analogy that I’ve found to be quite useful:

Consider a movie on a DVD (I know, so old school). All the information on a DVD is stored in a binary, static structure, engraved on the disc. Just like the DVD, the entire cosmos is the storage of a static, mathematical structure: unchanging and timeless. However, when you pop in the DVD and play the movie, all of a sudden this static structure (the disc) rolls out in a continuously evolving story with beginnings and endings. We know that this is an illusion, because we’re able to pause, rewind, fast-forward or skip through to different sections of the statically stored movie. We’ve all just agreed that movies are best experienced when the disc spins at a standard speed in a specific direction. In the same way, when a chunk of consciousness (you, for example) exists in the static, mathematical Universe structure, it feels like the cosmic story is also playing in a continuously evolving manner, with beginnings and endings. The reason that we don’t have an intuition of time being an illusion is that, unlike the popcorn munching movie watcher, we don’t have the ability to pause or rewind our experiences. This inability, however, doesn’t make our experiences any less static or forever existing.

To carry this analogy a bit further, let’s look at how a DVD is written and read. Though you can’t see it with your naked eye, one disc has roughly 29 billion “pits” etched into it, each separated by flat sections called “lands” (see figure 3). Together, these pits and lands make up a tightly bound, continuous spiral towards the center of the disc that if unwound would stretch to over 10 km. As the DVD spins in the disc player, a laser reads each pit and land (interpreted as a 0 and 1, respectively), resulting in the movie displaying on your screen. Each series of pits and lands are directly related to one particular moment in the movie, in just the same way that each infinitesimally thin slice of the mathematical Universe structure represents a moment of the cosmos. Your current brain state is analogous to a small section of pits and lands, forever etched into the structure of the unchanging Universe.

 

Microscope
Figure 3. Each slotted groove in this picture is a pit on a CD, imaged using an electron microscope.
pits_lands
Figure 4. Pits and lands as one would see if you cut a CD in half and looked at the cross-section. Protective layers sit on top, which is why you can’t feel any bumps on a CD.

Another way to think of the Universe, is as a flip book (see figure 5). As you flip each page, a similar, yet slightly different image is revealed, resulting in what feels like an evolving series of connected events. If you were to stop somewhere in the middle of the flip book, would you think that all previous pages no longer exist? Would you assume that there was something exceptionally special and unique about the page you stopped on? No, all the pages you passed are still there, and the page you’re currently on isn’t special at all. You had to stop at some page, and it just happened to be this one. This is the mathematical Universe diced neatly into frozen moments in time that always have and always will exist in their exact state.

Mathematical_Universe
Figure 5. Imagine each page is a slice of time out of an evolving universe. No page is special, as all of them always exist, irregardless of which page you’re looking at. Thinking that because you’re conscious of this and only this moment right now in your life, and therefore only the present moment exists, is analogous to you looking at a certain page in the flip book and concluding that all the other pages you passed no long exist, and any future pages you might turn to won’t exist until you look at them—which is clearly ridiculous.
4. Actually answering the question

Now that we have this new tool of temporal understanding, let’s return to the original question: is time travel possible?

Answers: (1) You’re confused; (2) no; (3) but also yes.

  1. You’re confused, because all moments (cross-sectional slices) in the static, mathematical Universe always have, and always will exist. So if you’re wondering if it’s possible to replay a previous chunk of time (rewinding the clock), then you’re just showing that you don’t understand the fact that they are always “playing”—in just the same way that this moment is “playing”.
  2. No, since I imagine what people really want is to transport their body and all of their current memories with them to the past (the past being a lower slice, where time is the z-axis from figures 1 and 2). If that version of them wasn’t always in those previous time slices, then that’s that. Since they weren’t always there, they will therefore never be there at that time (hence the term static). This is the equivalent of looking at the ground 1 meter in front of you and asking, “am I standing there right now?” No. You are not where you are not, just as you were not when you were not.
  3. Yes, although prepare yourself for disappointment. I see no laws of physics being broken by a fully functioning person being “born” into the world through the miraculously unlikely event of particles randomly colliding into each other to more or less instantly form the same creature (atom for atom) that was born and died at some time still far off in the future (see figure 6). The odds are exceptionally not in your favour, but it’s not impossible as far as I can tell. The downside here, is that given the static, deterministic nature of the Universe, you don’t get to randomly choose to jump in a time machine and change history forever. In fact, a time machine is not even part of the picture. You’re simply living a normal life and then dying, while in the past, a conscious being that is atomically and mentally identical to you right before you died, appeared out of random particle collision chance. They would have all your memories, including your most recent ones of being on your deathbed or failing to avoid driving into that poll at 100 km/hr. You could think of this as reverse reincarnation. 
RealTraveller
Figure 6. Given this new view of the Universe as a static, unchanging, mathematical structure, the right image is what it would look like to be a time traveller. The “Fully grown human” is the exact same person as the human right before “Death 1”. The left image is of a normal life, provided for comparison.

There are many topics that naturally demand answers from this world view that I’ve been describing, such as determinism, free will, the self, multiverse theory, Boltzmann brains, teleportation, matter-mind dualism, and so on. However, I have to stop somewhere eventually, or else my laundry will never get done. Since the view of the mathematical Universe hinges quite heavily upon some form of determinism, I’ll briefly address this as a bonus topic before bringing this post to a close.

5. Determinism

Determinism is the idea that every event in the Universe has been predetermined due to the initial conditions of the big bang: cause and effect. No one thinking clearly will dispute the fact that the world is at least mostly deterministic, if not fully. Determinism is the reason science and all life on Earth has been so successful; if you understand how the world has previously worked, and you know some initial conditions, you can accurately predict what will happen in the future.

The one thing that seems to stand in the way of a fully deterministic universe is randomness. Some may think that free will is also a legitimate competing ideology, though free will is almost surely an illusion—one which plays the role of a damaging, cultural meme that many of us can’t seem to kick. I recommend watching this video if you’re confused on the matter, and with that, I’ll safely sidestep that topic.

Coming back to randomness, discoveries into the nature of quantum mechanics have sparked a whole host of confusion, which is why I tried hard to avoid the “Q” word, but ultimately felt it was necessary to touch upon. The bottom line (and a massively simplified explanation) is that we seem to live in a world where some predictions must break down to probability—even when we know all the initial conditions and physical laws at work. That is, for some experiments we can only be certain that 60% the time it will result in “A”, and 40% we will observe “B”—and this has nothing to do with how our observation of the experiment influences the experiment.

Thus, it seems like randomness has foiled the view of full determinism, since the Universe doesn’t know exactly what it’s going to do until the moment it does it. And the further forward in time you venture from your known initial conditions, the more reality will deviate from predictability, due to compounding quantum uncertainties. There is, however, a way to navigate around this deterministic blockage, but it requires taking a stance on understanding quantum mechanics conceptually—as opposed to mathematically—which is admittedly a dangerous and ill-advised road. With reservation and skepticism held closely, let’s briefly merge into the lane of the Many Worlds Interpretation (MWI) of quantum mechanics as a means of revealing a fully deterministic universe.

Instead of thinking about the experiment resulting in “A” 60% of the time, and “B” for the other 40%, the MWI proposes that both “A” and “B” happen. The theory is that whenever there is a probabilistic quantum phenomenon, the universe you are in diverges into two different parallel universes that before that moment, were identical. To use an example from Max Tegmark’s book, let’s look at the result of a man asking a woman out on a date from the standard view point many of us have (figure 7) and the view of the MWI (figure 8).

JustOne
Figure 7. This is what the two people experience. There is no indication of something else also happening.
BothPaths
Figure 8. According to the MWI, this is what actually happens: a splitting of parallel universes, allowing for all possible paths to be taken (for sake of clarity, only 2 paths are shown, but in theory there are infinitely many solutions to this scenario).

If the MWI is true, then our view of the static, mathematical Universe simply changes from 1 mathematical universe to an infinite number of separate, unchanging, mathematical structures that make up all the possible universes (governed by the same laws of physics). All of these parallel universes co-existing in the same higher dimensional space, called Hilbert space (see figure 9).

Multiverse
Figure 9. An infinite number of parallel universes residing in Hilbert space, covering all possible ways a universe with our laws of physics could evolve and die.

Therefore, instead of an event having a probabilistic result, what we’re actually measuring is whether we’re in universe “A” or universe “B”—where both of those parallel universes are static, deterministic, mathematical structures. Since both of the universes have always existed as unchanging mathematical structures, the problem that we’re facing with quantum uncertainty is not which of the two events occurred in the one and only Universe, but instead it’s determining which of the two universes we’re in. The fact that both universes have always existed in Hilbert space, means that they are fully deterministic, due to their unchanging, mathematical structure. Therefore, by understanding quantum mechanics through the lens of the MWI, we’re able to convert the randomness that previously foiled the possibility of a fully deterministic universe, into an infinite array of every single mathematically possible universe—all of which are static and deterministic.

6. Closing thoughts

I am fully aware that by walking through the door of determinism, I just opened a bunch of other strange and interesting doors, largely concerning the different possible levels of the multiverse and quantum mechanics. Again, my laundry will never get done if I attempt to explore all questions that branch off of this initial investigation.

In this post, I used the question of time travel as a vehicle to navigate through the view of the static, mathematical Universe, as I find it to be incredibly interesting and explanatory of the mysterious situation we find ourselves in. And though at times I’m sure I seemed to be swimming in confidence, I am by no means a fully committed subscriber to this theory. Even if I saw it as the most convincing explanation of our Universe, I must acknowledge how incredibly stupid I am, and the likelihood that I’m abundantly confused about almost everything one could be confused about.

On that note, I’m going to leave you with one of my favourite quotes from one of my favourite physicists:

“I have approximate answers and possible beliefs and different degrees of certainty about different things. But I’m not absolutely sure of anything, and there are many things I don’t know anything about, such as whether it means anything to ask why we’re here … I don’t feel frightened by not knowing things—by being lost in the mysterious Universe without having any purpose, which is the way it really is, as far as I can tell, possibly.”

– Richard Feynman

9 thoughts on “Time Travel – a deterministic, mathematical universe perspective

  1. People like Maxwell ,Einstein and Smolin (part natural philosopher, part theoretical physicist ) can’t help speculating on the fundamental meanings of space, time, reality or existence. Our physical existence might just be a part of some still unknown abstract logic(HUP?). So we are part of a mystery. But our souls shiver to call it a mystery.

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    1. Mystery indeed. Thankfully, one needn’t possess a mind with a creative and intuitive bandwidth such as those who’s shoulders we stand upon to contemplate the big and interesting questions of existence. Shivers for all.

      Liked by 1 person

  2. Lovely piece of writing, however, it is not static. Stuff is eternally in motion. And we can’t travel in time because what was once here is now way over there. And the only way to go backward would be to move everything back to where it was. That’s why everything only moves “forward” in time.

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    1. Thanks for the comment, Marvin!

      I see where you’re coming from, and I agree that “we” can’t travel through time (as expressed in section 4, answer #2). I believe that these are the two perspectives you’re discounting that may change your thinking: (1) the sense of being a continuous self is an illusion, as each moment in time “you” are a different arrangement of particles; and (2) in just the same way that the space in which you occupied ten minutes ago didn’t disappear when you vacated that area, the time in which we were all in does not vanish from existence simply because we are the later revisions of “us” that can recall it as a memory.

      Hope you have a lovely day!

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      1. I think “illusion” is often misused these days. The brain creates a “model” of our internal and external environment by processing sensory data through several levels of abstraction. Since the model is our only cognitive access to reality, we call it “real” when it is accurate enough to be useful, and we call it an “illusion” when when it is inaccurate, as when we walk into a glass wall, thinking it is an open space.

        With imagination, we can create all sorts of alternate realities. But we refer to these as “imaginary”, because if we took them too seriously we’d end up tripping over things in the real world.

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      2. We are not one unified entity, but rather a process of many different subsystems that are sometimes, but not always, in communication with each other.

        The feeling of “I” is an emergent quality of neurological interactions, just like everything else you experience. In the same way that one experiences the colour red, one also experiences this feeling of there being a center to experience (or a CEO, if you like) that’s looking down upon all other conscious experiences (from the outside) and travels more or less continuously through time. There is no logical or physiological place for the self to be hiding in the brain or mind, since the very fact that you experience this feeling of self, means that it must arise from neurological interactions, in just the same way you experience everything else. Therefore, this feeling of self is not looking down upon all conscious experience, but is itself just another object of conscious experience—just like red, hunger, pain, and the occasional pinch of spiritual oneness. It is within the sphere of conscious experience, not looking into the sphere as an outside observer (which is what we imply when we say we have a body, and that we have a brain).

        So, who is experiencing this illusion? Well this is obviously a false and paradoxically silly question, since the question presupposes a false answer to itself. There is no “who”; there is only experience. It’s as though you just asked, “In what way will I articulate the sensations of dying once I am dead?”.

        This is a super interesting topic, but I can’t say that I currently harbour the will or time to continue illustrating points about the human experience five levels deep in a comment thread. I highly recommend you look more into this for yourself. And although there are many ways of understanding the illusion of the self intellectually, methods of meditation and other techniques have widely been known to induce an experiential understanding of this illusion.

        Best of luck!

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      3. As the saying goes, “been there, done that”. And I’d recommend Michael Graziano’s “Consciousness and the Social Brain” for a reasonable theory of consciousness. He describes awareness as a data set that tracks attention. He suggests that the specific process of conscious awareness is likely located in the superior temporal sulcus and the temporo-parietal junction. He points out that injuries to these areas are associated with a “Hemispatial Neglect” syndrome, in which the patient loses conscious awareness of objects on one side of the visual field. The odd thing is that autonomic functions, like flinching, are still in play, but you cannot explain why you flinched. So, these areas seem to relate specifically to conscious awareness while sensory input is still intact.

        My point is that the philosophical position that “self” is an “illusion” is unfounded. While neuroscience can explain how “self” works, it cannot “explain it away”. All it can validly say is that there is a lot more to know about it than we previously thought. And then neuroscience can proceed to explain how it works.

        In our model of reality, we use “self” to refer to our body when we are negotiating our entry through a doorway. And we use it to refer to the “interpreter” function (Michael Gazzaniga’s “Who’s in Charge? Free Will and the Science of the Brain”) that explains our behavior to ourselves and others.

        I’m just saying that “illusion” is the incorrect concept to apply to self. It is a conceptual model that refers to a real world object (the body, the brain, the process running on the neurology, conscious awareness, etc.). And it is “true” and “real” to the extent that it serves to accurately model events in the real world. And it is only “illusion” when the model is inaccurate (as when a patient experiences an out-of-body experience during an operation, also described in Graziano).

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