by AnonYMous
Flat.
Think of Charlie who is limited in the dimension of depth. He exists on his one flat sheet of paper, yet beyond that paper is a greater universe that holds an infinite amount of such sheets. Similarly, you can only perceive one world, though you are surrounded by many worlds. You can visualize the multiverse as a massive tree. From each moment sprout many branches of variation. These variations lead to more and more branches, creating a vast network of interesting universes. Like a fractal, each branch also functions as the trunk, the starting point of many new branches and variations.
Why can we only experience one of these branches?
The many worlds branch out through time, like a garden of forking paths. You are walking down a path, at each moment there is a fork in the road. Since there is only one of you, you can only take one path at a time. You are oblivious to what happens on the other paths. You can imagine them, but you are not physically there. This is the structural explanation of quantum mechanical unpredictability. Each moment has different possibilities. You can know the possibilities scientifically and mathematically. The Schrödinger equation, which is not limited by a single consciousness, will give you a bird's eye view of the different paths that the next moment will take. However, since you can only walk down one path, only one path will be observed by you. The Schrödinger equation is like a map that shows the many forks, but you can only physically experience one of these paths.
The paths are alternate dimensions.
No, they are all part of one dimension of the multiverse, the dimension of universe variations. I know this still sounds like fantasy to you, but from a logical standpoint, do you see that the idea of many worlds can unravel the confusion that you feel about time?
You are referring to the fact that I do not feel that time is already predetermined and unchangeable. That I would want to change my destiny if I could see the future?
Yes. I spent a lot of time trying to explain the nature of the time dimension to you, and I hope you understand that the future does actually exist. Therefore, if you knew of a future event, in a single variation universe, with only one end result, you could not change anything. But, in a multiverse of many possibilities, once you change your actions to avoid a future consequence, for instance getting hit by a bus, you are now simply observing a different branch of the multiverse. You don't actually change anything. The universe you were observing, the one where you did get hit by a bus, it still exists, but you are observing a different branch now.
So what happened to the me that decided to still cross the road and was hit by a bus?
That you still exists in another branch of the multiverse. After all you saw an actual future not an imaginary one. Thus, that you doesn’t cease to exist because you now made a different choice. That you is the you who didn't receive the information about the incoming bus, or the you who unfortunately chose to ignore the information, since it was just a spooky feeling.
But what you are saying is that at every moment, there are near identical me's branching out into many universes. I have a hard time imagining that there are an infinite number of almost identical me's scattered about in the universe.
It's a natural progression. Through the passage of time, humans have discovered, unceasingly, that they are a part of an ever larger and more complex world. In fact, that is a way of gauging a species' advancement. More primitive humans believed their world was not much large than their hunting ground. Later not only did humans realize they lived on a round planet much larger than what they could see or explore at the time, it was tiny compared to other celestial objects like the Sun. Then the Sun was just one of a vast ocean of suns in their galaxy. Now they know that galaxy is just a spec in an ever-expanding universe of galaxies.
I understand our universe is huge, but what you are talking about is unimaginable. That at every instant there are billions and billions of more universes; billions of variations of myself. It seems impossible.
I think that this was one of the reasons that the many worlds interpretation of quantum mechanics only gained popularity in the scientific community after the other interpretations were found to be unsatisfying. In the early part of the 1900's your scientists were still struggling with the disappointment that their single universe was not just one big clock. Both Einstein and Schrödinger were working hard to find out the hidden variables that would return the universe back to its more simple predictable form. The additional idea that this unpredictable universe was also just one of a potentially infinite number of universes was not seriously considered.
Was it just beyond the imagination of the scientists of that time?
Maybe beyond the imagination of some, but humans have wrestled with these concepts for thousands of years. More so, I think it went against what scientists were hoping for: a simple, easily provable answer. Nevertheless, these true scientific geniuses understood their own limitations. As Max Planck said, "A scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it." And in a sense that is what has happened; the old generation is gone, the new generation, now familiar with many worlds, in both fiction and science, takes it much more seriously. These days, the Copenhagen interpretation is basically dead or heavily reinterpreted. And while the masses only think of parallel worlds as science fiction, your scientists now think seriously about many worlds and it is considered a viable theory. Many of the scientists currently working towards the development of quantum computers believe in some form of the many worlds interpretation.
I still cannot comprehend a universe where every possibility that could ever exist, actually does.
Why? Is it less appealing than a universe where just one possibility exists, and all of the others do not?
It just seems too big.
The other you's in the universe would be quite upset to find out that the universe is too small for them, and only big enough for you.
Infinity
--There was a knock at the door at this time. I opened it to see the old Chinese man who lived at the other end of the hall. It was dark in the hallway behind him. My apartment was illuminated by the flashlight and he probably assumed I had either power or candles. The old man didn't speak English and when he started trying to speak to me in Chinese, all I could really do was stand there and listen. After a few seconds, my guest stood up and took another round light out of his jacket pocket. It turned on and he gave it to the old man. The old man thanked us and left. My guest returned to his seat, and grabbed another bottle of juice from the case. He sipped it slowly this time, and continued.
Look, if you think back to Charlie Brown, after you explain to him that his simple 2D universe is lacking an entire dimension, he would say exactly what you are saying to me right now. "My universe is vast, huge, infinite in fact. I could walk forever and never see the end. I could climb forever and never see the end. Now you are adding an entire new dimension to the universe that would create infinitely more space for me to deal with."
You are right, to Charlie, the universe didn't just double or triple in size, it became infinitely bigger. You could fit an infinite amount of his 2D universes into our 3D one. He would insist such a massive universe, comprising of an infinite amount of his flat universes, is impossible.
Of course this notion is laughable. To us, adding a dimension of depth to his flat world, no matter how massive or even infinite, seems completely natural, not mind blowing at all.
Could Charlie ever accept such a possibility?
Yes, it is not so difficult. Just like you, Charlie would need to overcome one very significant mental obstacle; this obstacle is a misunderstanding of infinity. You can try to imagine infinity in your mind, however what you imagine is not infinity, it is just something really, really big. This is because in your world, you are surrounded by the finite. All things around you are limited; even your known universe.
I th
ought you said our universe is an infinite universe.
Actually, it is impossible to know whether your universe is truly infinite. You can only know for certain if it is finite. You can only know what you can observe, and your observable universe, the one you can see and measure with your telescopes, is definitely finite, but expanding.
So what we can see is finite, but the actual universe beyond that may or may nor be infinite?
Yes. Your knowledge is limited by a lack of information. Nothing travels faster than the speed of light, and light is information about space. Thus information about the universe travels at the speed of light. When you look at a star that is five light-years away, you are actually looking at what the star was like five years ago. The star could have exploded yesterday, but you won't know it until five years from now when its light, its information, reaches you. Hence you we look at the observable universe, you can only see as far as it has taken light to travel since the big bang. The big bang happened around 14 billion years ago.
So the farthest we can see is 14 billion light-years.
Actually it is more than that because the universe has been expanding. You can really see about 50 billion light-years in any direction. You cannot see what is beyond 50 billion light-years, because light has not reached earth from any further yet.
But what is beyond the 50 billion light-years?
Well light is you source of information. What is beyond it you do not know. Literally, to you, it does not exist. You get no information from beyond your 50 billion light-years in all directions. You can think of it as a flashlight illuminating one round spot in the darkness. Some of your scientists have compared it to a patchwork quilt, where your observable universe is one patch in an infinitely large blanket.
All right, our scientists don't know if the universe is infinitely large. But do you know if the universe is infinitely large?
If you truly understood infinity, you would realize that I could not know that for certain. I could only be sure if the universe was finite, and to my knowledge it is not.
Why can't you know if it is infinite?
Once you understand the nature of infinity, you will answer your own question. Understanding infinity is one of the keys to understanding many worlds. Once you have a clear conception of infinity, you will have a much deeper understanding of the world around you.
--He must have seen a lack of confidence in my expression, because he stopped to take a sip of juice and reassured me.
Actually, of the things we have already discussed, this is one of the easier concepts for humans to grasp, at least initially. Infinities can take many forms. Humans are generally familiar with three of these forms: mathematical infinities, imagined infinities and actual physical infinities. Obviously, you can't observe physical infinity, and your ability to imagine infinity is what we are trying to improve. So we are left with mathematical infinity, which for followers of science, is the easiest to comprehend and leads to insights in the understanding of the other types. In math, the set of whole numbers, 1, 2, 3, etcetera is actually an infinite set. No matter how high you count, you can simply add one to create an even larger number. There is no number that serves as the end of the set.
So if numbers are in fact infinite, we deal with pretty small ones.
Indeed you do. Have you heard of a googol?
You mean the search engine?
No, I am referring to the mathematical number.
Yes it is a one with one hundred zero's behind it. And a googolplex is 10 to the googol.
Yes, the googolplex. It is such a massive number; it is bigger than all the elementary particles your scientists know of in the entire universe. A short and simple mathematical representation, for instance a googolplex of atoms, represents more stuff than there is in the entire observable universe. Now, this is a lot of stuff, but is this the largest number you can imagine?
I don't think I can really imagine how much that is, but I can write it.
Actually if you tried to write a googolplex in the traditional way, 1 and then 0's after it, you could spend a billion years doing it, and you would not have even come close to actually writing the number. In fact, there would not be enough room in your observable universe to write this number.
I could forget writing zero's and just write operators, like a googolplex times a million, or a googolplex to the googolplex to the googolplex.
Yes, that is a good way to do it. You could write googolplex to the googolplex to the million times googolplex. And how many of your universes would that number represent?
Googols of them. I suppose if each googolplex is larger than the known universe, it would be a universe of universes.
Now imagine you wanted to create a number much greater than that; the greatest number ever created by humans. How large a number could you create?
Well I supposed as large as I could think of, or say or write.
Imagine you spent the rest of your life saying googolplex to the googolplex to the googolplex like a yogi reciting a mantra. Or you sat down and wrote googolplex to the googolplex all day and night. Let's go further, you could just imagine numbers running through your head, googolplex after googolplex after googolplex, every moment, for the rest of your life.
That would be a massive number.
Yes, after doing this for many, many years, you would certainly believe that you hold the world record for the largest number ever imagined in the history of mankind. Surely just before your death I would visit you, and you would proudly say to me "There, I have spent my entire life thinking of a giant number, I have achieved the largest number ever thought of by man. After eighty years of tireless googolplexing, I have achieved it, and I have called it the SuperGoogol." And I will reply, "Supergoogol times two."
--I laughed a little here. He took a brief pause to let me think about it, and then continued.
I have encompassed your entire life of counting in one second, and I have named my new number Supergoogolplex Extreme. Now, to give you a taste of infinity. Do you know how my Supergoogolplex Extreme; the number that would encompass googols and googols of your universes, would compare to infinity?
What do you mean?
I mean like a ratio, one third of infinity, or one fourth or one tenth of infinity.
Since infinity is infinitely bigger, I am not sure.
If we have 25% of something, it is the same as saying one fourth, mathematically written 1 over 4. If we want to know what part of infinity my number is, we need to put it over infinity. So my number, as it relates to infinity would be written mathematically as Supergoogolplex Extreme over infinity. And in math we know that any real number, any actual number, no matter how large over infinity has a limit of zero, which mathematicians typically treat simply as zero. The Supergoogolplex Extreme, as large as it is, would be, in the vastness of an infinity of numbers, nothing.
But how can it equal nothing, it is a real number, it is a part, even if a small part, of infinity.
You make a good point. To be completely accurate, this number is actually called an infinitesimal. An infinitesimal is smaller than any actual number, just as infinity is bigger than any actual number. So compared to infinity, my Supergoogolplex Extreme is too small to be measured, too small to have any actual value. Thus your known universe, in the scope of the infinite multiverse is also too small to be measured, it is basically, nothing. I will show you another way of looking at the situation. Let's try to mathematically remove the Supergoogleplex Extreme from infinity. Do you know what number you get? You will still get infinity. In mathematics, infinity minus any finite number is still infinity. Thus if you remove your known universe, or even a massive Supergoogolplex universe from the infinite multiverse, what you will be left with is still an infinite multiverse. If you tear one patch out of an infinite quilt, you still have an infinite quilt. If you tear out a million patches, you will still have an infinite quilt.
This is confusing.
Yes because you still think that infin
ity is a really large thing. Infinity doesn't act like a giant number. Unlike a googol, if I take infinity, times two, I do not get twice as much of infinity, I still have, infinity. If I add infinity to infinity, I still have infinity, not something twice as big as infinity. If I take any countable amount of stuff, no matter how large, out of infinity, I still get infinity.
Perhaps Infinity is unfathomable to finite creatures.
Not really, great mathematicians like George Cantor and Kurt Gödel made major insights into its nature. They transcended the traditional ways of thinking to gleam real insights into infinity, and these days mathematicians rely heavily on the use of infinity and infinitesimals in their equations to solve real world engineering problems. The main thing I want you to understand is that when dealing with an infinite universe, simply adding another dimension to it does not make it too big, or even bigger at all, it is still infinite. This is why we laugh at Charlie Brown when he protests that our infinite 3D universe is too big, while his infinite 2D universe is just big enough. Though his infinite 2D universe is bigger than we can possibly imagine, adding another dimension does not confuse us. So now, if I tell you that in an infinite universe there are also infinite variations, can you comprehend it?
I am not sure. Logically I understand it, psychologically not so much.
It will take time, but you believe in logic and mathematics, and as you accept your logical understanding, it will become more natural to you. It will become something that you can feel is true, and this leads us back to whether I can know if the multiverse is infinite. Here is the concept that is really important to understand when dealing with infinities. You cannot imagine or comprehend infinity in the same way you comprehend finite concepts; by putting parts together or breaking them apart. No matter how much finite stuff you have, you will never reach infinite stuff. No matter how much finite knowledge you have, you cannot reach infinite knowledge. So when dealing with an infinite concept, like an infinite universe, or an infinite God, you cannot fully understand it by combining finite parts. Nor can you prove or disprove such a thing by breaking it down into smaller parts, as its parts themselves, are infinite. I can tell you that the universe behaves as if it is infinite, in that there is nothing in its nature that would point to any limit. But do you understand that unless I had infinite knowledge, I could not truly know if the universe was infinite?