“People like us, who believe in physics, know that the distinction between the past, present and future is only a stubbornly persistent illusion.” —Albert Einstein
If you believe, despite this famous quote of Einstein’s, that there are real, even profound distinctions between the past, the present and the future, then you are one of the stubbornly persistent—those who refuse to relinquish our human reality to the laws of physics.
To be clear, we are not doubting the truth or validity of physics. We firmly believe in the active pursuit and continuing progress of science, of physics and even of Einstein’s theory of relativity. But we also believe in our human world, a world of the present moment, an existence where our actions and decisions affect the future—a universe with a flowing river of time, and free will.
Einstein is referring to the fact that the equations of physics show no preference for some mysterious moment now; rather, all moments in time exist equally. Emphasizing this fact, these equations work equally well in one direction of time—from the past to the future—as they do in the opposite direction—from the future to the past. The present moment, from this perspective, has no unique or special importance—it is merely an arbitrary dividing line between the past and the future.
More specifically, Einstein’s own theory of relativity demands the equal existence of the past, the present and the future. As he elaborated elsewhere, in more technical language: “The four-dimensional continuum is now no longer resolvable objectively into sections, all of which contain simultaneous events; “now” loses for the spatially extended world its objective meaning. It is because of this that space and time must be regarded as a four-dimensional continuum that is objectively unresolvable.” He adds, “It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence.”
Three-dimensional space is not evolving, through time (fourth-dimensionally); rather all of space and time equally exist as a continuum, a physical structure that is fixed and complete. Reality is a fourth-dimensional spacetime continuum, and within this reality there is no true distinction between the past, the present and the future.
And yet, our lives are based upon the differences between the past, the present and the future. We live in the present; it is the moment of our awareness, the time of decisions and spontaneous reactions, the time of being alive. The past, on the other hand, is over, complete, unchanging, fixed for all eternity. And the future is unformed, malleable, dependent upon our choices and plans—in other words, our free will.
Free will is built into the distinctions between the past, the present and the future. And free will is an integral part of our identities, of who we are.
We seek, then, to restore our identities, our very sense of self, our free will, while observing and honoring our laws of physics.
PEOPLE LIKE US
How to proceed? We will not, as one might first suppose, attack or even question the validity of Einstein’s theory of relativity. We believe this would be futile, even silly. The equations and predictions of relativity have been confirmed to an astonishing degree of precision, and continue to be confirmed every scientific day. In fact, the equations are being used by us every ordinary day, such as when we glance at the GPS location on our cellphones.
No, we will be going in the opposite direction, a direction, perhaps, no one else has tried before. We are not merely going to accept Einstein’s theory of relativity as an accurate description of reality, we are going to take this reality so seriously that we are going to end up taking it to its next logical step—to perhaps end up on an entirely new level of reality.
We are, in other words, going to take relativity more seriously than anyone has ever done before—even Einstein, himself.
This last claim may seem dubious, even audacious, considering the fact that Einstein 1) was a genius, and 2) spent the entire later part of his life, after completing his general theory of relativity, searching for a larger, more comprehensive theory. Certainly, if there were any higher truths to be discovered within relativity, Einstein would have been the one to find it.
But let us delve into a little history, to see if this is necessarily true.
Very soon after Einstein completed his special theory of relativity, in 1905, he almost immediately began searching for an even bigger, better theory, one which would include gravity. The result was his general theory of relativity, which he completed in 1915. (When we refer to “Einstein’s theory of relativity,” we are in fact referring to both theories, since the special theory is a special case of the general theory, but is still separate and important enough to retain an individual identity.)
But then, almost immediately after this accomplishment, Einstein—being Einstein—began searching for an even bigger, better theory, one which would include electromagnetism, as well. This search slowly broadened into a search for a general, all-inclusive theory that would explain all phenomena, one which might even do away with quantum mechanics, as it was currently formulated. He really disliked the prevailing interpretation of quantum reality, which was basically no “reality” at all.
This search, unfortunately, never bore fruit, but the point is that Einstein, we are suggesting, may have been a little too eager to move on to greener pastures. As Einstein himself said, “I have thought a hundred times as much about the quantum problems as I have about general relativity theory.”
On the one hand, Einstein of course accepted his theory of relativity—how could he not? But on the other hand, he was willing to abandon this theory if he could devise a larger, more inclusive theory—how could he not?
We would like to suggest, perhaps blasphemously, that Einstein was never 100% committed to his own theory. Consider this: When Einstein first formulated his special theory of relativity, it was without any concept of the fourth-dimensional spacetime continuum in mind. It took Hermann Minkowski to come along and reformulate the special theory of relativity into a geometrical vision of spacetime, and Einstein at first totally rejected this interpretation, calling it “superfluous learnedness,” even joking that, once mathematicians had got a hold of his theory, he could no longer understand it.
Of course, he did come to understand it, and went on to use this interpretation while formulating his general theory of relativity. And, from the quote we began with, he obviously came to accept the consequences of living within a fourth-dimensional spacetime continuum—that is, a physical reality that has no true distinctions between the past, present and future.
But, perhaps, this explains why he did not pursue the concept of the fourth-dimensional spacetime continuum conceptually, exactly as it was, to see if it held more gems about the reality we do live in, here and now.
He did, obviously, extensively explore the scientific consequences of his theory—realizing, for example, soon after completing his general theory of relativity, that it could be applied to the entire universe. But as far as analyzing spacetime for truths about our normal, human, everyday lives—that there might, in other words, be personal truths and meanings hidden within this physical universe described by relativity—Einstein simply did not think that way.
This, however, is the path we will explore.
CONCEPTS OF SPACE AND TIME
To be clear, we are not trying to downplay Einstein’s genius, in any way. In fact, we are going to use Einstein as our guide, and attempt following in his footsteps, as it were. Now, we know we are no Einstein (we have no such delusion), but we can use him as our role model, and attempt to emulate him. Specifically, we can follow the steps he took when formulating his special theory of relativity.
Einstein formulated this theory after grappling with two seemingly contradictory ideas: One, that the speed of light should remain the same for all inertial observers (that is, for all observers who are not accelerating), even if these observers were moving relative to one another, and, two, that the laws of physics should remain the same for all inertial observers. These two postulates appeared to contradict each other; if one was true, the other should be false. But Einstein mentally struggled with these two beliefs until he finally saw a way to reconcile them into a single, holistic reality.
To do this, however, he had to alter and rearrange the rest of reality, the very concepts of space and time.
Today, we accept that rearrangement as reality.
We will now attempt repeating this process, with Einstein as our inspiration and role model. We are going to hold on to two contradictory beliefs: One, that Einstein’s relativity is an accurate description of reality, and, two, that our human perception of a flowing time, with true distinctions between the past, the present and the future, is an accurate description of reality. We are going to grapple with these two beliefs until we emerge with a single, holistic reality.
And, if we end up rearranging reality, the very concepts of space and time, well…
LIVING IN SPACETIME
To begin, we will contemplate what it means for us humans to exist within a fourth-dimensional spacetime continuum: what it means for us personally. This is a topic sorely lacking in almost all popular science books on relativity and the spacetime continuum, even though it is a subject practically screaming to be heard and dealt with. We live here, for heaven’s sake.
Within the fourth-dimensional spacetime continuum, there is no real, objective distinction between the past, the present and the future. All moments in time have an equal existence. All of the past, the present and the future form a single, complete, physical structure. Reality exists as a continuum, a physical, fourth-dimensional spacetime continuum.
Within three-dimensional space, there exist three-dimensional objects: apples, people, planets. But all three-dimensional objects have a fourth dimension, meaning they extend in time as well as in space. All three-dimensional objects are really fourth-dimensional objects. We only see three dimensions of these objects, because our senses evolved to detect a three-dimensional world. But we have come to mentally comprehend the existence of time, which we now know is a fourth dimension of physical reality.
Conceptually, since the dawn of human consciousness (we will assume), we have known about movement, and change, which we have associated with this mysterious thing called time. We intuitively grasp the passage of time, even if, for thousands of years, we struggled to clearly define or understand its nature. But with the advent of relativity, we can now mentally equate what we came to describe as time as the fourth dimension of physical reality. We cannot sense this dimension with our bodily senses, but science has expanded our senses, so that we are now able to “perceive” more of reality.
Let us analyze this last thought a little more thoroughly.
Our five bodily senses slowly evolved over millions of years, steadily strengthening and enhancing our awareness of the world around us. We now see our surroundings in vivid color; we hear things happening as we see them happening, providing a deeper level of experience, but we also hear things happening that are out of view, around corners and behind us; with our noses we detect an entirely different world, such as the chemical makeup of flowers in bloom, burning forests and fresh cheeseburgers; with our mouths we can enjoy the taste of those cheeseburgers, or sweet fruit, and spit out the bitterness of poisons; and we feel our environment of clothes, tools, temperatures and other people in a practically infinite number of various levels and combinations. Our five senses of sight, hearing, taste, smell and touch provide us with a full and vibrant experience of the world we live in.
In a very real sense, we would like to suggest, we can view science as our “sixth” sense, a newly acquired ability of humans to perceive more of reality. The steady accumulation of scientific discoveries and inventions has expanded our awareness of our universe far beyond our five bodily senses. With microscopes, for example, we see organisms far too small to be seen with our normal vision. With telescopes we analyze stars and galaxies too distant to appear within our terrestrial skies. Telescopes also give us the amazing ability to actually see into the past, so that we are able to observe celestial events that occurred millions and even billions of years ago. Is this not a mind-blowing, newly evolved ability of our species?
Microscopes and telescopes expand our vision, our sense of sight, but science does more than simply improve the senses we already have. We now “sense” the invisible worlds of microwaves and radio waves, even using these as new “tools” to manipulate for our own purposes (we now have radios and microwave ovens, for example). The sciences of geology, archaeology and anthropology give us a “sense” of enormous time periods, far removed from our everyday perception of the passage of time.
Our scientific universe reveals a reality that exists far above and beyond the one we evolved to perceive with our bodily senses.
This brings us to Einstein’s theory of relativity, which perhaps marks the epoch of this expansion. Relativity exponentially enlarges our vision of reality, describing the universe we live in as a fourth-dimensional spacetime continuum. This reality is so far removed from our everyday world that it remains mostly unknown and unrecognized by the average person.
In 1908, Hermann Minkowski, referring to relativity, made the famous prediction: “Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” Strangely, despite the extraordinary success of relativity within the scientific domain, this prediction remains unfulfilled—over a hundred years later. Within our normal, human world, space is still space, time is still time, and little speculation is even spent on what their union might mean to our ordinary human lives. And yet this world potentially contains the answers to the age-old questions of who we are, where we are, when we are, and, perhaps, even why we are.
Relativity unifies space with time into a single physical structure. Within this universe, the existence of time is as real as the existence of space, and both are essential for an accurate description of reality.
Within the fourth-dimensional spacetime continuum, there exist fourth-dimensional objects. Apples, people and planets extend in time as well as in space. The equations of special relativity describe how fourth-dimensional objects change their appearance within three-dimensional space, as they move.
Superficially, the same phenomena occur within three-dimensional space when an object moves, as we see the object from a new angle. A coin, for example, looks like a round circle when we view it straight-on, but the circle flattens as we turn the coin until, edge-on, it appears as a straight line. We know the coin has not actually changed, only our perception of it. The equations of special relativity describe the same phenomena, but in four dimensions. As fourth-dimensional objects move, relative to one another, the three-dimensional “picture” we have of them changes appearance. The faster an object moves through space, the more it “tilts” fourth-dimensionally, from our perspective, and the more we see it from a different angle. Its length, its mass, even its passage through time all change according to the equations of special relativity, simply because we are seeing this fourth-dimensional object from a new angle.
The equations of special relativity are describing fourth-dimensional objects, objects that exist within fourth-dimensional spacetime.
Apples, people and planets are fourth-dimensional objects, but we do not normally refer to people as objects. We refer to them as people, as living beings.
People are fourth-dimensional beings. They extend in time as well as in space.
FOURTH-DIMENSIONAL BEINGS
For us, personally, this means that our past moments still exist, within the fourth-dimensional spacetime continuum. Our growth within our mother’s womb, our birth, our childhood, our continuing development and maturation, still exist within the fabric of spacetime.
Our future, also, “already” exists, within the spacetime continuum. Our aging, our future experiences, our eventual death, all exist out there, within spacetime.
But these moments do not simply exist as separate entities, having no relationship to one another. Relativity describes spacetime as a continuum. We exist continuously through time, as a single, complete, holistic fourth-dimensional organism.
We are fourth-dimensional beings.
In three-dimensional space we might define our physical bodies as existing between, say, the bottom of our feet to the top of our heads. In fourth-dimensional spacetime we likewise define the physical existence of our fourth-dimensional beings as existing between, say, two distinct “events.” The first event we might define as the moment we were first conceived, as a single cell; the last event we define as the moment we die, and our awareness ceases. We exist between these two events as a physical, continuous fourth-dimensional body—as a fourth-dimensional being.
We have now slightly passed beyond the point in which the ordinary human, both layman and scientist, stops thinking about these things.
Why? Why is this concept never elaborated upon in popular science books?
Is this concept simply too far beyond our everyday experience? Does it mark the boundary beyond which the mind struggles too hard to comprehend?
Perhaps, but consider paradigm shifts from the past, ones we have already successfully conquered. We learned the earth is not the center of the universe, that humans and apes evolved from the same ancestors, that winds and earthquakes have natural explanations, and are not the whimsy of the gods. Our concept of reality has steadily evolved and matured over the years, improving and clarifying our picture of the world we live in.
We believe it is premature to suggest the human mind has reached a limit of comprehension, a level beyond which we simply cannot pass.
Another possibility, then, is perhaps we simply need more time to digest this new reality. We need more than the hundred years that has already passed; perhaps we need several hundred years.
Although possible, we stubbornly persistent refuse to wait that long. So, we will focus on a third possibility, instead.
Perhaps there is simply a psychological barrier preventing us from seriously contemplating our existence as fourth-dimensional beings. After all, if our past, present and future exist, then free will must be an illusion. We cannot be making decisions in the present that will decide our future, because that future already exists. We are not really reacting spontaneously to situations, making meaningful plans or goals, weighing outcomes, making choices. All future moments exist, and we only think we are making decisions, choices and plans.
We are forced to the conclusion that our fourth-dimensional beings are frozen, static and unchanging, along with the rest of the spacetime continuum. Our beings resemble fossils stuck in amber—the amber of spacetime. We cannot move, which within the fourth-dimensional spacetime continuum means we cannot change our destinies. We are trapped, unable to live freely.
And yet we are conscious; we are alive.
Who would want to live in such a world? How could you live in such a world? What would be the basis of living, of thinking, of doing? How can we not make decisions, have spontaneous reactions, have plans for next week, next year, or tonight?
The mind rebels. Let us stop thinking about such matters; let us turn our mind to other things.
This is the mental barrier causing most people (we will assume) to turn away, to look elsewhere. But we believe it is time we moved passed this barrier, to grab the bull by the horns and face our scientific world on its own terms, and ours.
We live here, for heaven’s sake.
THE PHYSICS OF TIME
In order to move passed this barrier, we need to have a clear objective. We will word this objective as a series of questions, like this:
How do we free our fourth-dimensional beings? How can we free them from the amber of spacetime?
How can our fourth-dimensional beings live within a flowing river of time, with true distinctions between the past, the present and the future?
How can our fourth-dimensional beings have free will?
Clearly defining the problem this way begins to suggest a way forward, to possible solutions.
We offer one such possible solution to these questions in our book, The Stubbornly Persistent: Melting the Frozen River of Spacetime. Before discussing our solution, however, we want to explore another possibility, offered within a book we only stumbled upon after completing our own book. (This other book was published before our book—shame on us for not knowing about it—but, hey, we were busy preparing our own book at the time.) This other book offers a completely different solution than the one we propose, and we find this theory not only exciting (and revolutionary) in its own right, but in a strange way it strengthens our own theory.
It is found in the book, Now: The Physics of Time, by Richard A. Muller.
The solution Muller offers is elegant in its simplicity, even astonishingly so. Upon hearing it the question that immediately springs to mind is, how could no one have thought of this before?
In his book, Muller does not mention fourth-dimensional beings. (We understand; no one else does, either.) In fact, even though he discusses the fourth-dimensional spacetime continuum, he never actually uses this phrase; the closest he comes is when he refers to “four-dimensional space-time” in passing, a few times. This is not a criticism; it simply shows how he thinks about the problem, which is a clue to the solution he comes up with.
Muller is primarily concerned with “the moment now,” and searches for a way to restore the meaning of this moment within the physical universe we live in—that is, within the laws of physics. This replicates our dilemma, the one we have outlined above. Although he does not elaborate on this issue, if you solve the problem of now, so that the present moment has the meaning we humans have always given it (spontaneity, free will, etc.), then you automatically restore meaning back to the concepts of the past and the future.
We have known for many years that the universe is expanding. Muller proposes that not only is space expanding, but that time is, as well. There is not only more space, with the expansion of the universe, there is also more time. What we call now is the leading edge of this expansion. The future does not yet exist. We are free in this present moment to decide our fates, to make our decisions and plans.
He calls this universe “the 4-D Big Bang,” to emphasize the fact that both space and time are still being created, right up to the moment now.
If nothing else, with the publication of his book, Richard Muller demonstrates that he is stubbornly persistent—he believes, despite the equations of physics, and of Einstein’s relativity, that our human perception of a flowing time is an accurate description of reality. Free will exists. But he is also a dedicated scientist who honors and respects the laws of physics. (In our book, we collectively refer to all such adventurers, scattered throughout spacetime, as The League of the Stubbornly Persistent.)
The genius of this simple idea is that it respects the spirit and equations of relativity. The basis of the special theory of relativity is the concept of simultaneous events—that the simultaneous events in my frame of reference will not be simultaneous events in your frame of reference. But in Muller’s theory, no matter whose frame of reference it is, their now is at the edge of the expansion of time.
All of us only see into the past, anyway. Light takes a moment of time to reach our eyes, and the farther away an object is, the more we are seeing the object “in the past.” Our other senses take even longer to record the world around us. Everything we sense is in some degree in the past. We can define our “present” by subtracting (intellectually, mathematically) how long it took light to reach our eyes, and extrapolate from there, but we can never actually sense this “present” moment in the present.
This is a somewhat removed way of describing the special theory of relativity. Everyone will define the present moment somewhat differently from everyone else, because of their unique location within the spacetime continuum.
In Muller’s theory, everyone’s now is at the leading moment of the creation of time, and our free will is flowing forward with the present moment.
Translating Muller’s theory into our own terminology, our fourth-dimensional beings are not yet “complete.” They are still coming into existence; they exist up to the moment now. Our future selves have not yet formed. Our beings only exist completely when we die, and then they become that fossil stuck in the amber of spacetime.
However, the closest Muller comes to discussing our existence as fourth-dimensional beings is in these few lines, when he asks the question,
“Why do you feel you exist in the present? Actually, you exist in the past too; you know that quite well. You exist backward in time right up to the moment you were born (or conceived, depending on your definition of life). Your focus on the present comes largely from the fact that, unlike the past, it is subject to your free will.”
Then, a few pages later, he says,
“We live in the past just as we live in the present, but we can’t change the past.”
In his book, Muller does not elaborate any further on these ideas. On these ideas, however, we wish to elaborate much further.
TAKING SPACETIME SERIOUSLY
In our theory, which is based upon the popular theory of spacetime, our fourth-dimensional beings exist as complete organisms, within a fourth-dimensional spacetime that is also complete.
Our beings are conscious; they are alive and aware. They are aware now, and they remember being aware in the past. Those past moments are frozen, unchanging, meaning our awareness is frozen, as well. It continues to exist within the fabric of spacetime; it eternally exists within the fabric of spacetime, as a part of its structure.
Within this reality, we are eternally aware of existence—the existence of physical reality, and the existence of our selves. What we call “death” is really only a boundary of our physical beings, like the top of our heads is a boundary of our physical three-dimensional bodies.
This is one of those mind-blowing consequences of taking relativity seriously that is inexplicably missing in all popular science books on the subject. We exist eternally within the fabric of spacetime. We will always be aware; we will always be alive.
We may not be alive in the future, of course, after our death, but this is no different than not being alive in the past, before we were born. We are alive where we are alive, in time and in space, and that life, and our awareness of life, and existence, is eternal.
We will always exist.
How can you not be absolutely astounded by this conclusion, a conclusion derived simply by taking relativity seriously? Relativity, we remind you, is of one of the most accurately confirmed scientific theories in existence.
Of course, looking beyond this amazing conclusion, we still have the problem of free will. So how do we solve this problem?
Of necessity, the solution we offer is more elaborate than the one Muller proposes, although, we admit, before we encountered Muller’s theory, our worry was that our theory was too simplistic. By this we mean we brushed aside, the same as Muller, such topics as string theory, eleven-dimensional spacetimes, supersymmetric particles and all those other esoteric mathematical nightmares. We stuck completely to the single premise that Einstein’s theory of relativity is all we needed to solve all of our problems.
Our theory, we repeat, is more elaborate than Muller’s, but, on the other hand, we end up solving a host of other problems, as well. But let us start at the beginning, with the basic concepts of spacetime, and see if we can start anew, with fresh and naive eyes.
We wish to reexamine the fundamental concepts of space and time.
STARTING OVER
To begin, imagine a single moment in time.
At this moment in time, all of three-dimensional space exists, frozen, unmoving. We will further imagine that this one moment of time is all that exists. The entire universe consists of this one single moment, filled with three-dimensional space.
Within this three-dimensional space there exists three-dimensional objects, such as apples, people and planets. These three-dimensional objects are frozen along with the rest of the universe, unmoving, static, eternal, at this one moment in time.
We wish to give the three-dimensional people within this reality the gift of life—to allow them to move, to change, to grow. How would we do this? We will assume we know nothing of time, or of spacetime. (Our concepts are without preconceived notions of space or time.)
It would not work to try and give these three-dimensional people the ability to move, if the rest of the universe remained frozen. That simply would not make any sense. Our only choice, here, then, is to somehow give movement to all of three-dimensional space. Then our three-dimensional people will be moving with the rest of the universe, as a single physical existence.
One way to do this (the only way we know) is to create or imagine a fourth dimension, a dimension that exists at a right angle to three-dimensional space. This fourth dimension will give three-dimensional space the freedom of movement—it will give three-dimensional space the space to move to—it will give it somewhere to go.
Worded this way, the fourth dimension we are imagining has four dimensions. It has the three dimensions of space, plus another dimension, which allows for the movement of space. This fourth dimension is a higher dimension than three-dimensional space, because it has one dimension more than three-dimensional space. Because it is a higher dimension, the fourth dimension “has room for” an infinite number of three-dimensional spaces.
The fourth dimension, in other words, is a natural enlargement of the third dimension.
From our normal perspective, it is easy to recognize this fourth dimension as time. Time is what gives three-dimensional space the ability to move, to change and evolve.
This may seem like a simplistic way of wording the situation, but, surprisingly, perhaps perplexingly, no one ever words it this way.
Why? We have no idea.
Instead, the wording you will find in all popular books on the subject goes something like this: Relativity unites the three-dimensions of space with the one dimension of time, which results in the fourth-dimensional spacetime continuum. Even though space and time are united in spacetime, time is still different than space.
With this wording, you have three dimensions of space and one dimension of time. Time is different than space; in fact, time is mysteriously different than space. It is a different kind of dimension. No one really knows what time is; it is simply accepted as a given, in the same manner the three dimensions of space are accepted as a given.
Time is one-dimensional, while space is three-dimensional. Uniting these two together produces a fourth-dimensional spacetime, but these four dimensions retain their unique identities (up to a point).
This wording opens up all sorts of questions and confusions. Some popular questions encountered in science books are, why does time only move forward? Why not backwards? (Why, in other words, is there an arrow to time?) Why do we always move forward through time, whether we want to or not? In three-dimensional space, by contrast, we can stand still, or move in any direction we please.
Why, in other words, is time so different from space?
In our wording, three-dimensional space is moving through the fourth dimension, which naturally defines that movement as forward, through time. (Of course, one may still ask, why is it moving this way, and not that way? In our book, we offer a natural, physical explanation for the forward movement of space, but that explanation would take us too far off our present topic.)
In our wording (and, we would like to emphasize, this is a rewording only; we are not attempting to alter spacetime, physically, in any fundamental way), the fourth dimension is different from the three space dimensions simply because it allows for the movement of three-dimensional space—it is a higher dimension, occupying a higher reality than three-dimensional space. But there is nothing mysterious about this higher reality; it is simply a natural, physical enlargement of three-dimensional space.
In the popular way of wording these things, many other questions also arise, such as: Why is space three-dimensional? Why doesn’t space have two dimensions, instead, or ten dimensions, or twenty-eight? And why is time one-dimensional?
These questions provoke answers, of course, and many have been offered. Maybe space does have ten dimensions. Then why can’t we sense these other dimensions? Maybe they are curled up so small they are invisible. And now we have opened the door to an ever-growing realm of speculation.
Our simple definition of dimensions avoids all of this confusion. Space is three-dimensional because space is defined to be three-dimensional, and higher and lower dimensions will have their own unique definitions. A two-dimensional plane, for example, is a two-dimensional plane—it is not space. If you imagine a third dimension existing at a right angle to the two-dimensional plane, then this third dimension will give the two-dimensional plane a freedom of movement, into this third dimension. The third dimension is a higher dimension than the second dimension, and can hold an infinite number of two-dimensional planes. The same concept applies to all dimensions, from the zero-dimensional point, all the way to infinity.
To elaborate:
We begin with the concept of a zero-dimensional point. We define this zero-dimensional point as the zeroth dimension. We then have this zero-dimensional point expand out (mentally, mathematically or physically), in opposite directions, into the next higher dimension, becoming a one-dimensional line. We define this one-dimensional line the first dimension. We then let this one-dimensional line expand out, in opposite directions, into the next higher dimension, becoming a two-dimensional plane. We define this two-dimensional plane the second dimension. We now let this two-dimensional plane expand out, at a right angle, in opposite directions, into the next higher dimension, becoming three-dimensional space. We define this three-dimensional space the third dimension. We now let this three-dimensional space expand out, at a right angle, into the next higher dimension, becoming the fourth-dimensional spacetime continuum. We define this fourth-dimensional spacetime continuum as the fourth dimension.
The reason we are equating the fourth dimension with the fourth-dimensional spacetime continuum is because, worded this way, the fourth dimension contains all of three-dimensional space, as space is moving fourth-dimensionally.
This reality, in other words, remains logically consistent as it becomes more complex. There is a natural hierarchy to the dimensions of physical reality.
Of course, nature could (as a theory) create existence with any number of dimensions existing at right angles to each other. In this reality, the question of why space has three dimensions remains mysterious. Or nature could (as another theory) create physical reality as a hierarchy, with one natural, logical extension at a time. In this latter theory, physical reality becomes more complex with each additional dimension, and these additional dimensions are higher dimensions, with one more dimension than the one below.
Reality is a hierarchy of physical dimensions.
Are we implying, then, that some of these lower dimensions might actually exist, within our physical reality?
Yes, in fact, we are implying this, as a strong possibility. Zero-dimensional points, for example, have an uncanny resemblance to the point particles of quantum mechanics. One-dimensional lines resemble electromagnetic waves (which are simultaneously vibrating within two of the higher dimensions). Two-dimensional planes resemble the boundaries that exist between two different states of a phase transition. Three-dimensional space resembles the simultaneous hyperplanes of special relativity. And fourth-dimensional spacetime—well, now we are getting a little ahead of ourselves.
In our way of wording the fourth-dimensional spacetime continuum, spacetime has four dimensions, meaning it is a higher dimension than three-dimensional space, with another dimension, and this other dimension allows for the movement of three-dimensional space. However, because it is a higher dimension, it has a different reality than three-dimensional space.
What does this mean?
From the perspective of three-dimensional space, it is moving fourth-dimensionally. Because it is moving, and changing, it now has a past, a present and a future. The people within this three-dimensional space are only ever aware of a single three-dimensional moment, because they are three-dimensional beings. They perceive this movement as a changing three-dimensional space.
From the perspective of the fourth-dimensional spacetime continuum, however, this reality appears different. Within spacetime, the past states of three-dimensional space still exist. Rather than moving through the fourth dimension, then, from a fourth-dimensional perspective it appears as if three-dimensional space is expanding out, fourth-dimensionally. Three-dimensional space is gaining an additional dimension, so that the three-dimensional objects within space are becoming fourth-dimensional objects. But the people within three-dimensional space still only perceive three dimensions, and perceive these three dimensions as moving fourth-dimensionally, through time.
In Muller’s theory, this expansion has reached the moment now, and is continuing to expand out, into the fourth dimension. In our theory, however—which is the popular theory—space has completely expanded out into the fourth dimension, so that all of the fourth-dimensional spacetime continuum simply, eternally exists.
Within fourth-dimensional reality, defining three-dimensional space now becomes arbitrary, depending upon the location and movement of fourth-dimensional objects. Simultaneity, in other words, becomes relative to the observer. But this leads us to the contemplation of fourth-dimensional objects, which was the goal of our conversation.
Within fourth-dimensional spacetime, fourth-dimensional objects are not really moving. All of the fourth dimension exists, as a complete, physical structure. So why does it seem as if reality is moving, changing and evolving?
The popular answer is that this is all an illusion—a stubbornly persistent illusion. But we want to move passed this answer, into a human world of a flowing time, and free will.
So we will now take the bull by the horns, and come up with a completely different answer.
THE FIFTH DIMENSION
We are going to postulate the existence of a fifth dimension, a dimension that exists at a right angle to the fourth-dimensional spacetime continuum. This fifth dimension allows for the movement of spacetime; it gives spacetime somewhere to move to. It is a higher dimension than spacetime, having one additional dimension. It has the four dimensions of spacetime, plus a dimension at a right angle to spacetime. As a higher dimension, it “has room for” an infinite number of spacetime continuums.
In our definition, the fifth dimension is the next logical, higher dimension up from the fourth-dimensional spacetime continuum. This fifth dimension allows for the movement of the fourth-dimensional spacetime continuum; it can potentially contain an infinite number of spacetime continuums.
Within the present state of modern physics, however, there exists no such definition of the “fifth” dimension. Within physical science, the fifth dimension can essentially mean anything at all—it simply refers to the existence of another dimension, a dimension other the ones making up the fourth-dimensional spacetime continuum. The fourth-dimensional spacetime continuum has four dimensions, so if one wants to speculate on other dimensions, through default these other dimensions become a “fifth” dimension.
This definition (or lack of one) has resulted in a chaotic number of speculations, such as the existence of countless numbers of incredibly small, hidden spatial dimensions, calabai-yau manifolds, eleven-dimensional spacetimes, and multi-universes, to name but a few of the currently popular scientific theories.
We have nothing personally against eleven-dimensional spacetimes, or any of those other theories, except for the fact that they have lost all contact with our normal, human reality—which, come to think of it, is another way of saying they’re crazy.
When a person loses contact with our normal, human reality, they are usually locked up and sedated. Perhaps these other theories need to be locked up and sedated, for a while—for their own good, of course.
All we are searching for is a reality that makes sense to us ordinary human beings.
Some of those crazy theories are more interesting than others, however, from our point of view. One of them actually sets up a strong precedence for our theory, coming from such a distinguished figure as Stephen Hawking.
Stephen Hawking died in March of 2018, but we still think of him as existing out there, within the fabric of spacetime, alive, well and thinking away.
In his books, Stephen Hawking describes the existence of imaginary time, which exists at right angles to real time. (See the similarity?) He uses this concept in an attempt to unite Einstein’s general relativity with Richard Feynman’s formulation of quantum mechanics as a “sum-over-histories.” As Hawking describes it, the alternate histories of quantum mechanics actually exist, every single one of them, in imaginary time. They exist as “alternate universes.” Our universe is surrounded by an infinite number of alternate universes, and we also exist in many of those alternate universes (an infinite number of them), as alternate versions of ourselves.
Many other scientific theories also postulate the existence of alternate universes; they are actually quite popular in the scientific literature.
In these theories, all of these alternate universes—all of these fourth-dimensional spacetime continuums—eternally exist. They are as frozen and static as our own universe.
This, unfortunately, does not solve our problem of free will—in fact, it multiplies our problem by an infinite amount.
So, we give a slight tweak to Hawking’s imaginary time. We postulate that there is only one universe—our universe—and that this universe is moving through imaginary time. It is moving at a single, right angled extension through imaginary time. We call this right-angled extension the fifth-dimensional cosmic universe.
In this interpretation of reality, we have not completely done away with alternate universes—we simply make them more meaningful to our human existence. In our reality, alternate universes become the past fourth-dimensional states of our evolving spacetime continuum.
They are the past states of the universe, as it is evolving fifth-dimensionally.
The reason we describe this as fifth-dimensional, rather than as imaginary time, is to emphasize the fact that we are talking about the next higher, logical extension of the fourth-dimensional spacetime continuum. In Hawking’s description, imaginary time exists at right angles to real time, but in our proposal the fifth dimension exists at a single right-angled extension through imaginary time. (As we discussed above, the same concept applies to our definition of the fourth-dimensional spacetime continuum—it exists at a single, right-angled extension to three-dimensional space.)
This new reality has many interesting consequences, but here we need to stay focused on our present discussion. (Those other discussions are found in our book.) Here, then, is a summary of our new concept of a moving fourth-dimensional spacetime continuum, as it relates to a human flowing river of time:
Within this reality, the present moment is moving—it is changing and evolving, open and free—exactly as we experience the present moment.
So far, so good.
Within this reality, the future “already” exists—but that future is also changing and evolving, and is largely dependent upon what happens in the present. Influences from the present travel outwards, effecting the future.
So the future, also, now agrees with our human experience of time.
Within this reality, the past needs a little more explanation.
If the fourth-dimensional spacetime continuum is moving, changing and evolving—all of its past, present and future—then what we always thought of as our past is changing and evolving, as well (at least, this is how we always thought of the past, within spacetime, for the past hundred years).
In this sense, then, the past is only a stubbornly persistent illusion.
However, fifth-dimensionally, the fourth-dimensional spacetime continuum has a past. This fifth-dimensional past is done, complete, unchanging for all eternity. In fact, the entire fourth-dimensional spacetime continuum has a past, a present and a future, and this is the flowing river of time that we experience. We may have had the terminology wrong, but we were right about the actual reality.
Within this reality, the past, the present and the future equally exist—just like in Einstein’s spacetime. But rather than all three of these times being frozen, static and eternally unchanging, now all of these times are changing and evolving.
(Seriously, doesn’t that make just a little more sense? Just asking.)
Within spacetime, the past is changing and evolving. These influences reach our present, and help to shape our present. However, the past continues to change and evolve. But these further changes travel out through spacetime at the speed of light, at the most. But special relativity informs us (at least this is one way of describing relativity) that we in the present are traveling through spacetime at the speed of light. This means that any further changes in the past will never actually reach our “present,” because that present is traveling through time at least as fast as those changes in the past.
Some of you may have noticed that, throughout our entire post, we have barely even mentioned quantum physics. That may strike you as a strange omission in our theory of reality. However, our present discussion has been focused on Einstein’s relativity—our theory has a lot to say about quantum mechanics, as well. For that discussion, as well as several others not mentioned here, we refer you to the book.
For now, we will finish the current topic at hand:
Within the fifth dimension, fourth-dimensional spacetime has a past, a present and a future. Our fourth-dimensional beings, existing within the spacetime continuum, have a past, a present and a future, and this is the flowing river of time we humans know.
Our fourth-dimensional beings are reacting and responding to an evolving spacetime continuum. As they do, their conscious awareness is flowing down the length of their fourth-dimensional beings, from one end to another, so that their beings can react in a consistent and holistic manner to the changes occurring around them.
We three-dimensional beings define this mental journey, this flowing of consciousness from one end of this being to the other, as “our life.”
Within Einstein’s spacetime, our life is frozen for all eternity—frozen with all of its flaws and imperfections, all of its suffering and pain, eternally surrounded by all of the imperfections, misery and grief of the world (and, admittedly, also all of the happiness and joy, even if the former vastly outweighs the latter, for most humans). And our awareness is frozen within our fourth-dimensional beings, unable to change our world, our selves or our destinies.
And yet, at the deepest of levels, we identify with our conscious awareness—as who we are, as what we are, as why we are.
Within our vision of spacetime, we still have the same awareness, but it is an awareness of an evolving existence. In fact, it is that awareness that gives our fourth-dimensional beings the ability to react and respond in a consistent, holistic manner to an evolving spacetime. We are the awareness of our fourth-dimensional beings; we are how our beings react and respond to an evolving existence.
We are the conscious free will of our fourth-dimensional beings.
Instead of identifying with a single journey down the length of our fourth-dimensional beings, we may now (perhaps) begin identifying with an eternal awareness of an evolving existence. What we thought of as an awareness of a single life, is the awareness of a life eternal.
Our fourth-dimensional beings have the ability—the free will—to change their world and their destinies—one small life at a time.
Our next intellectual leap, then, is to identify with our fourth-dimensional beings. We are fourth-dimensional beings, after all.
This leap will be the leap of a lifetime—a quantum leap, one might say.
It may take some time to make this leap. But we have the time.
In fact, we have eternity.
References and Related Material
The Stubbornly Persistent: Melting the Frozen River of Spacetime, by Anderthal Kord.
Einstein: “The four-dimensional continuum is now no longer resolvable…” This is from Relativity: The Special and the General Theory, by Albert Einstein, 100th Anniversary Edition, 2015, pages 170-71.
Einstein: “I have thought a hundred times as much…” This is quoted from Subtle is the Lord, by Abraham Pais. A larger quote is more revelatory: “I came to understand how wrong I was in accepting a rather wide-spread belief that Einstein simply did not care anymore about the quantum theory. On the contrary, he wanted nothing more than to find a unified field theory which not only would join together gravitational and electromagnetic forces but also would provide the basis for a new interpretation of quantum phenomena. About relativity he spoke with detachment, about the quantum theory with passion. The quantum was his demon. I learned only much later that Einstein had once said to his friend Otto Stern, ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory.'”
Now: The Physics of Time, by Richard A. Muller
For more on Stephen Hawking, and his books, see his website.