“The idea of 10 dimensions may sound exciting, but they would cause real problems if you forget where you parked your car.”
Overview
Quantum theory and general relativity describe the phenomena that we observe in the universe on the scale of the very small and the very large, respectively. We discuss in this article how the predictions that they make about nature sometimes contradict one another; such contradictions necessitate the formulation of a quantum theory of gravity. But we also discuss how both theories, even though they disagree with one another starkly on how the world ought to behave on the scale of the very small, do find some common ground for agreement on both the macroscopic scales and on extremely vast cosmological scales. We discuss perhaps the most famous example of this “common ground” - namely, the prediction that this is not the only universe that we live in and that we in fact live in one of many in a much grander multiverse. We’re fairly certain that the general theory of relativity, even though we know it must be wrong on microscopic scales, is accurate on macroscopic and cosmological scales; thus, when Kip Thorn worked out that one of the predictions of the Einstein Field Equations was that different adjacent universes were connected to one another via wormholes that can be traversed at speeds lower than that of light, the scientific community was forced to take seriously that traveling to other universes might actually be possible!
With that said, even though general relativity clearly says that it would in principle be possible to travel to another universe, the caveat to this story is that to actually determine whether or not anyone or anything could survive the voyage through a wormhole to another universe, we must understand the effects of gravity on microscopic and submicroscopic. Essentially, we require a quantum theory of gravity. Now, this admittedly is something that we don’t yet have, though we have some pretty good candidates. The most promising candidate is string theory which we discuss in this article. String theory predicts that there are additional dimensions of space besides the familiar up-down, left-right, and forward-back dimensions; according to this theory, different universes are not necessarily separated from one another by distances across the familiar three dimensions of space. For example, the best direction to “look” for other universes is not up or down, or left or right, or forward or back, but some other direction through another spatial dimension which you cannot even point towards. What does string theory have to say about how gravity behave on super small scales? The answer is that we don’t yet entirely know and as we discussed in the article, Leaving the Solar System, it is our ignorance of the full range of predictions made by string theory which is why we are, to this day, still unable to know for sure whether or not someone could survive a trip through a worm hole. But, rest assured, string theorists are working on it!
Near the beginning of time, space, and matter all of the immense amount of space (billions of lightyears) that we see around us and all of the matter (trillions of galaxies worth) that we see around us was all concentrated into a size smaller than an atom. Indeed, according to the laws of quantum mechanics, it is impossible to measure a length that is tinier than the Planck length which is roughly equal to \(1.6\text{ x }10^{-35}m\) or about \(10^{-20}\) times the size of a proton. General relativity predicts that If you run the clocks backwards, you would see all of the galaxies—and even space itself—collapsing inward into a point smaller than even the Planck length. It is a profound idea that all of the planets, stars, and galaxies—and, indeed, everything in existence including all space, time, matter, energy, and so on—that we see around us sprung into existence from such a tiny point. This prediction made by general relativity does, however, contradict quantum mechanics and, in particular, the Heisenberg uncertainty principle. The Heisenberg uncertainty principle states that it is physically impossible to simultaneously measure and, hence, know the exact position of a particle; we are essentially certain that this principle is correct since it has been experimentally confirmed to an extraordinary degree of accuracy. Some of the counterintuitive predictions of this principle is that the singularity of a black hole cannot be infinitely small and that the universe was once infinitely small because, if they were, then we could determine their positions with arbitrarily high accuracy. This is one example of the disagreement between general relativity and quantum theory—the theory of the very large and the very small, respectively.
Real Vs Abstract
If you take trillions of galaxies and our entire universe and crunch them all together then, according to general relativity, you end up with a blackhole where all of the mass and energy comprising the black hole is crammed into a region of space that is infinitesimally small—that is, a size infinitely smaller than any real number. Most scientists—and especially mathematicians—have no problem with infinities appearing within the abstract realm of mathematics because, mathematics, after all, isn't real. It is just something that we made up. But when Einstein first used his general theory of relativity to predict the existence of black holes (and, according to his theory, the entire universe itself was once a black hole), this was something that deeply troubled Einstein because, in his view, infinities shouldn't appear in nature. The fact that they do blurs the line between reality and the abstract. Indeed, the cosmologist Max Tegmark famously posited that the universe is math, not something which is merely described by it. In other words, he proposes that there is no boundary between the abstract and the so-called real.
The Four Fundamental Forces
There are four fundamental forces of nature—namely gravity, the electromagnetic force, and the weak and strong nuclear forces. (As an aside, researchers recently discovered a fifth possible fundamental force; but we shall save discussion of this for another time.) Around the time of the begining of the universe, all four of these forces were united into a single unified force. This means that gravity, electromagnetism, and the strong and weak interactions were all different aspects (or components, to be more precise) of just one force. There was so much mass and energy bunched together so compactly that gravitational interactions—the warping of spacetime—must have been so substantial that general relativity would be required to describe the gravitational effects. But the matter was compacted into a space so small that quantum physics would also be necessary to describe the effects taking place. Thus, when the universe was very young and tiny, general relativity and quantum theory must have been united into a single theory. Both relativity theory and quantum theory were describing different aspects of just one more general theory. Admittedly, we are not entirely sure what this single more general theory is, but some of the greatest scientists and physicists of our time including Edward Witten and Leonard Susskind think that this theory is something called string theory. Like all of the other grand theories and unifications in the history of physics, string theory also makes an enormous range of profound predictions which, before string theory, no one could have even imagined. Below, we shall discuss some of these predictions.
More than 3 Spatial Dimensions?
“String Theory predicts the existence of more than the 3 space dimensions and 1 time dimension we are all familiar with. According to string theory, there are additional dimensions that we are unfamiliar with because they are curled up into tiny complicated shapes that can only be seen on tiny scales. If we could shrink to this tiny, Planck-sized scale we could see that at every 3D point in space, we can also explore 6 additional dimensions. This animation shows an array of Calabi-Yau spaces which are projections of these higher dimensions into the more familiar dimensions we are aware of.”\(^{[1]}\)
The image above shows how various different small objects compare to each other in terms of size.
Image retrieved from: http://www.particlecentral.com/strings_page.html
All of the theories and law of physics which come before string theory could be derived assuming that the universe has three spatial dimensions (up-down, left-right, and forward-backward) and one dimension of time. That sounds perfectly reasonable. What is peculiar, though, is that general relativitry (one of the most successful theories in all of science) predicts that there must be additional dimensions of space. For example, general relativity predicts that the Sun curves all three of the dimensions of space around it. But this raises the following question: those three dimensions of space curve into what? It is easy to imagine what a two-dimensional space (i.e. a sheet of paper) curves into. The answer is it curves into a third dimension of space. This is easy to imagine because a third spatial dimension is something that we can visualize and something which we have everyday experience with. To answer the question I posited earlier about what three-dimensional space curves into, the answer is that it curves into a fourth dimension of space. But there could be additional dimensions of space that our three-dimensional space curves into. I mention that because I want to make it clear that general relativity does not preclude the existance of more than four spatial dimensions.
Many Worlds
Our universe may be one of many, physicists say.
Credit: Shutterstock/Victor Habbick
Another prediction of general relativity is that this isn't the only universe that we live in, but rather that there are many universes in a much grander multiverse. According to a paper written by the physicist Kip Thorne, one of the leading experts in the field of general relativity, rotating black holes are connected to other universes via worm holes and, according to his calculations, some of those wormholes can be traversed by matter traveling at speeds less than that of light. This raises some very profound questions such as, Can K2 civilizations migrate to other universes?, Are K4 and K5 civilizations possible?.,Would those K4 and K5 civilizations be able to send signals and cargo from one universe to another?
One of the great mysteries in quantum mechanics and of our time is, What is the correct interpretation of a quantity called the wavefunction? And, in particular, what happens to that wave function when you measure something (the thing which you measure is the eigenvalue of an observable. In Greg School's section on quantum mechanics, the interpretation of this quantity which we took is called the Copenhagen interpretation of quantum mechanics. According to this interpretation, whenever we measure an eigenvalue of a quantum system, this causes the associated wavefunction of that quantum system to "collapse." Before the measurement is made, the state of the quantum system exists in a superposition of all possible states. For example, suppose that we have an electron in a small, isolated box. Before measuring the position (an eigenvalue) of that electron, that electron could, quite literally, be located anywhere in the universe.
(Though, admittedly, if the potential function of that box is very high, the odds of finding the electron outside of the box would be vanishingly small.) The wavefunction would be\(\psi_i=\sum_{I=1}^nα_i|\psi_i>\) where \(α_i\) (the probability amplitude) can be used to calculate the probability (given by \(|α_i|^2\)) of finding that electron at any position. Before the measurement is done, there is some probability \(|α_i|^2\) of finding that particle at any position in space. But according to the Copenhagen interpretation, when we measure the position all of the terms in the sum \(sum_{I=1}^nα_i|\psi_i>\) collapse into a single term (say \(α_7|\psi_7>\)), where \(|α_i|^2=1\). The wavefunction "collapses" into a single "reality," so to speak. There is some probability that before the measurement you could've measured the electron at any position; but after the measurement is made, there is a 100% probability that the electron's position must be what you measured. That's essentially the Copenhagen interpretation of quantum mechanics in a nutshell.
But there is another interpretation of what happens to the wavefunction when you measure the eigenvalue associated with a quantum system. This interpretation is called the Many Worlds Interpretation of Quantum Mechanics. According to this interpretation, the wavefunction never actually "collapses." This interpretation predicts that we live in one of many universes and that, in the aforementioned example, every possible measurable position of the electron is measured in different parallel universes. In other words, in this universe when you measure the position of the electron to be say \(x=1\), in another universe totally identical to your universe an identical copy of you measures a different position of say \(x=2\), in a third identical universe an identical copy of you measures a different position of say \(x=3\), and so on. If our entire universe was just a big vacuum of space with just one electron, the the total number of universe in the multiverse would be the total number of all possible measurable values (the eigenvalues) associated with that system and these possible measurable values include the position, momentum, energy, and so on. The multiverse would represent all possible versions of reality. In a The Theory of the Universal Wave Function paper written by the physicist Hugh Everett, he considered the total number of possible states of every particle in the universe to estimate the total number of universes in the multiverse. According to his calculations, this number is \(~10^{500}\). Each of those universes are separated by additional dimensions of space that we cannot see. In this scheme, universes are continually born and die in a perpetual, never ending cycle.
To summarize some of the things that we have discussed thus far:
General Relativity predicts the existence of extra spatial dimensions.
Both General Relativity and Quantum theory predicts that we live in a multiverse.
Quantum theory and relativity theory are two special cases of a deeper, more general theory which we think is string theory.
Different universes are connected vie worm holes which are traversable by objects traveling at speeds slower than the speed of light or at the speed of light.
Why String Theory?
The reason why we are confident that string theory is the correct theory is because it matches the data perfectly and, as Leonard Susskind once remarked, resolves many of the extant theoretical problems in physics, the most obvious one being the difficulty in combining relativity theory with quantum theory. While the derivation of all other theories in physics before string theory could be done assuming that the universe has three dimensions of space and one dimension of time, in order to derive string theory we must assume that there are more spatial dimensions than the three which we are already familiar with. In particular, we must assume that the universe consists of 9 spatial dimensions and 1 temporal dimension (that is, one dimension of time). What is interesting is that this is an assumption we have to make to get string theory; and, once that assumption is granted, we are able to unify quantum theory and relativity theory into a single deeper and more general theory.
Portals to other Universes
Quantum theory and relativity theory describe all physical phenomena involving the interactions of matter and energy. This is true for all the matter and energy in the universe. But it turns out that at a specific energy called the Planck energy, quantum theory and relativity theory must be describing different aspects of just one theory which we'll assume to be string theory. The Planck energy is given by 10^{19} billion electron volts. At this energy level, all known laws of physics break down and we must use string theory to describe space-time, matter, and energy. Because the early universe and the center of blackholes exhibit the Planck energy, it follows that we must use string theory in order to understand them.
The image above shows a section of the LHC (Large Hadron Collider).
What if there was an artificial way to produce one Planck energy in a tiny region of space? If we somehow did that, we would be creating conditions (including energy levels) similar to those of the Big Bang some 13.8 billion years ago. Indeed, according to calculations done by the cosmologist Allen Guth, this would create a blackhole that would lead to another universe. A halo of dark energy would need to surround that blackhole in order to keep it open and to prevent it from collapsing. This raises the possibility of a highly advanced civilization creating a wormhole to another universe or to other regions of this universe. The latter implies the possibility of faster-than-light speed travel. Using the Large Hadron Collider (the most powerful device in the world), we could produce one quadrillionth of a unit of Planck energy. This, of course, is insufficient to creating a portal through hyperspace which leads to other universes.
But if you built a particle accelerator with a radii equal to the distance between the Sun and the asteroid belt, you could produce one unit of Planck energy and create a blackhole which leads to another universe. In our previous discussions about Dyson swarms and star lifters in particular, we discussed how it would eventually become desirable for humanity to build an immense ring of current around the Sun to extract its matter. We could also build enormous particle accelerators around the Sun which extend out to the asteroid belt and use them to recreate conditions similar to the Big Bang in order to create a black hole and a wormhole. Provided that the wormhole is traversable and that we can keep it open long enough, this would allow beings to travel to other universes. This would also give us the conditions necessary to prove whether or not string theory is actually correct. Of course, such a megastructure could be scaled up enormously; you might be able to end up with a black hole and wormhole large enough for very large objects to travel through and this raises the possibility of a highly advanced civilization escaping the death of the universe.
In a section we covered earlier called, Intergalactic Colonization, in the article entitled Star Lifting: Colonizing the Stars and the Galaxies, we talked about how dark energy is causing all of the galaxies to rush away from one another. Assuming that a K3 civilization wants to maximize their long term survival, this fact would incentivize them to colonize and subsequently merge together galactic groups and clusters within their galactic supercluster; subsequently, it would also be desirable (for reasons we discussed in the aforementioned section, Intergalactic Colonization) to deconstruct these galaxies and use their materials to build Birch planets which are huddled very closely together. It would take much longer for dark energy to cause a system of Birch planets to recede away from one another than the galaxies in a galactic supercluster to recede away; this would be one of the main reasons why an advanced civilization would want to build these Birch planets in the first place. But after a long enough time, dark energy would cause these Birch planets to recede away from one another.
Indeed, after an unimaginably long period of time, dark energy will tear apart the atoms themselves. As we discussed in previous sections, even when the universe becomes totally uninhabitable, Einstein's theory of gravity gives us a potential loop hole. We could possibly build a traversable wormhole and migrate to another universe; one which is much younger and with similar laws of physics. Now, you might think that such beings, capable of hopping from universe to universe is immortal. That is, they could live infinitely long. This is, however, untrue. It turns out that, according to the laws of quantum mechanics, it is physically and mathematically impossible for any civilization and any universe to live forever. Allow me to explain. The strange world of quantum mechanics is governed wholly by chance. For every particle (including those which comprise a Birch planet or matryoshka brain running simulations of an artificial universe), the position of that particle is governed entirely by a probability distribution.
“A matrioshka brain is a hypothetical megastructure proposed by Robert Bradbury, based on the Dyson sphere, of immense computational capacity. It is an example of a Class B stellar engine, employing the entire energy output of a star to drive computer systems.”\(^{[2]}\)
Image from Steve Bowers
Take, for example, an electron. We are all familiar with the electron orbital structures from chemistry class; those shells represent the most likely spot in space you'll find the electron. After a certain distance, the probability of finding the electron becomes unimaginably small, but still finite. This means that, despite being unimaginably unlikely, there is some chance the electron in your hand could end up on the opposite side of the universe. The same is true for every atom in your body which are, themselves, objects governed by the laws of quantum mechanics. Indeed, it has been noted by Michio Kaku that it is routine for PhD students to calculate the odds of the atoms comprising your body, by chance, reassembling themselves on Mars. As strange as it might seem, the probability of that happening is actually finite, though it's so small that it would likely never happen for the remaining lifetime of the universe. But, what is so interesting, is that events which are unbelievably unlikely in the short term become more and more likely in the long term and, after a long enough time, become almost inevitable. If you were to hypothetically imagine letting the age of any structure composed of atoms to approach infinity, then the probability of that structure spontaneously falling apart due to quantum fluctuations would approach one. After a long enough time, the atoms comprising a structure appearing on opposite sides of a universe actually becomes a near inevitability (and I repeat this is only true over unbelievable long time periods). Ultimately, due to quantum mechanics, nothing made of atoms can live forever.
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References
1. “Higher Dimensions from String Theory.” Wolfram Alpha,
members.wolfram.com/jeffb/visualization/stringtheory.shtml.
2. Wikipedia contributors. (2019, March 10). Matrioshka brain. In Wikipedia, The Free
Encyclopedia. Retrieved 23:06, March 20, 2019, from
https://en.wikipedia.org/w/index.php?title=Matrioshka_brain&oldid=887040852