Time as a Dimension

To explore this, we are really exploring the model that incorporates time as a dimension. We have no doubt heard of space-time, which we might imagine as some kind of four-dimensional fabric that permeates the universe, or as something that sets the stage upon which the universe exists. We might think of Albert Einstein as the father of space-time, and though several physicists took starring roles in developing this theory, Einstein no doubt brought the theory together.

All events in the universe take place in space-time. Space-time is actually a mathematical model. It fuses three spatial dimensions with one time dimension into a geometric whole. How can we conceptualize this? There is a common trap in physics, which is to confuse the theory or mathematical model with the actual thing, something physical that can be observed and measured. A wealth of experimental evidence, listed in the 4-minute video below, supports the theory of special relativity, which describes the space-time model:



This is good evidence that the space-time model used in special relativity accurately accounts for real observable and testable phenomena.

What is a Dimension?

Mathematically speaking, a dimension is the smallest number of coordinates you need to specify the location of a point. A line, for example, has a dimension of 1 because you only need one coordinate to specify a point on it. A surface or plane has a dimension of two and the inside of a sphere has three dimensions. To describe the location of a point inside a sphere, for example, you need three coordinates - we usually call them x, y and z coordinates. Building on this we can say that a point within a sphere (or any three-dimensional space) can potentially move in any combination of three possible directions - in the x, y and/or z direction. Borrowing from statistics, we can say that point possesses three degrees of freedom.

It's easy to visualize the three dimensions of space we live in. We've got up/down, latitude and longitude. An everyday example of a location in three-dimensional space might be "on the third floor in the northwest corner of the Black Building." We can pinpoint exactly where to go if we are given these directions. In our everyday world, time, however, feels different. Locations in space can be fixed but we experience time as fluid. It flows as events constantly recede into our past and reach into our future. Now when we revisit our directions, we notice that we need a "when." What if these are instructions for a dentist appointment, for example? The dentist wants me at a specific location at a specific time, such as in his chair at 2 pm on Wednesday. I've got all four coordinates you need. At 1 pm or 3 pm, someone else will be occupying that chair, those identical spatial coordinates. But only I will be in that chair at this specific time coordinate of 2 pm Wednesday. Therefore, we can see that to describe any event we'll need both spatial coordinates and a time coordinate.

But how is time related to space? I can explore this by describing my walking path to the dentist's chair. I will need to describe both space and time. I enter the east door of Black Building at 1:45, approach the elevators at 1:50, wait there for one for a minute for the door to open and then travel up to the third floor during the next minute before I walk down a corridor to the dentist office at 1:55. I plunk myself down in the dentist chair at 2 pm and remain there for 50 minutes. I am describing a series of events that flow through space AND time.

During these events spanning between 1:45 and 2:50 pm, I am moving through space and time, in other words, I am moving through four changing coordinates, or dimensions. However, I notice that I may be moving through one or two spatial dimensions simultaneously but in every case as I move through space I must also move through time. Time seems to have some rules that space doesn't. I can never "stop" in a time dimension. I can never move into a negative time dimension. Time, then, appears to have fewer degrees of freedom than any spatial coordinate. I, or anyone, can only move in one direction along this timeline and at a rate I can't control. Is time a dimension? If it is, it does not appear to be a fourth dimension in the same way as the other three spatial dimensions.

We can map out my progress between 1:45 and 2:50 pm on Wednesday using a framework that describes changes in all four coordinates of time (1) and space (3). Yet, as we just noticed we encounter some problems when we think about time as a fourth dimension equivalent to a spatial dimension. We can describe this impasse mathematically. As we will get into later, it was Hermann Minkowski, not Einstein, who formulated the dimensions of space-time, and these four dimensions are NOT equivalent to four-dimensional (Euclidean) space. Space-time is not, for example, this albeit mesmerizing four-dimensional rotating cube:

JasonHise;Wikipedia

This cube above is described by Euclidean space. There is no time dimension to it. Space-time does have geometry but it is different in important ways. The non-Euclidean mathematics used to describe space-time describes how time works with space. To make this connection conceptually, we can trace how the concept of space-time came about.

Time Was Once an External Stage

Isaac Newton: We probably all started our exploration of physics with this great man, a key figure in the scientific revolution in mid-seventeenth century Europe. In his time, a four-dimensional framework for any physical event would seem unnecessary and probably ridiculous. To describe his laws of motion, he needed only three spatial dimensions, the ones we experience every day, and he assumed it all happened while an absolute time progressed at a specific rate independent of everything else going on. Even physical space was likewise treated as outside all events. Every object either had an absolute state of motion or an absolute state of rest relative to the absolute space it found itself in. Time and space were treated much like an external stage on which all phenomena in the universe take place. The assumption made sense and it worked for a long time. It is how we experience space and time every day.

The idea was basically unquestioned until the mid-nineteenth century, shortly after James Clerk Maxwell and others, started to tinker with electricity, magnetism and light. Maxwell discovered that all three were a) related to each other and b) traveled as disturbances through (Newtonian three-dimensional) space.

Maxwell worked out that "light and magnetism are affectations of the same substance and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws." The "field" in this statement is the epicentre of what would become one of the most hotly contested debates in the history of science. What exactly was this field? His work would ultimately lead to the connection between space and time. To start with, he and others knew only two well-established facts: 1) light seemed to have a constant velocity through air and 2) light slowed down when it traveled through other transparent media such as water.

Aether Was the Medium of Space

Scientists at this time knew that electromagnetic disturbances act like waves so they figured they must travel through some kind of medium, which they called aether. Experimental results on aether, however, were confounding. For example, the speed of light through air was constant in any direction. Wind or air density had no effect. Even more confusing, the speed of an electromagnetic disturbance seemed to be independent from speed of the source of that disturbance. In other words, light seemed to disregard Newtonian physics. How? What about this aether substance could accommodate such findings? It proved frustratingly impossible to define electromagnetic waves mechanically. They did not act like other mechanical waves such as sound waves or water waves.

Like many other scientists at the time, Einstein, pondered how aether worked. Like physicists Paul Dirac, Louis de Broglie, Maxwell and others, he thought that aether was some kind of medium with physical properties filling empty space. There must be something there that carries the electromagnetic disturbance, and perhaps the results could be explained by some kind of elastic force through which the waves are propelled, analogous to water waves or sound waves. Even in 1920, after he developed special relativity, he stated that there must be something that allows for the "existence of standards of space and time (measuring-rods and clocks)" to allow for space-time intervals in the physical sense.

Aether Theories Run Into Trouble

Various aether experiments designed to find out how it worked mechanically, and there were many, yielded either contradictory or nonsensical results. An interesting and well-known example of this problem was the Fizeau experiment, conducted in 1851. At that time, a number of scientists were comparing the speed of light (an electromagnetic disturbance) in air versus water. They could observe that a beam of light slowed down in water. They wondered what process slowed the light-bearing aether down in the denser medium.

If you are wondering how light slows down when it has one invariant velocity, you ask a fantastic, often overlooked, question. A good concise answer can found here.

This phenomenon, called refraction, has been observed since ancient times and was described mathematically in the 1600's by Snell's Law. A number of researchers revisited refraction as possible evidence that aether could be partially dragged by moving matter such as water. The idea being tested was that aether moving against the direction of water flow might be slowed down. Vice versa, aether dragged along with the water flow might boost the flow rate of the aether and therefore the speed of light. Fizeau designed an experiment that compared the speed of light through water moving in the same direction as the light beam with the light's speed moving against the direction of the water flow. If their theory was correct, light would move faster along the same direction of water flow and slower when it's against the flow. They didn't know how or if aether interacted with matter but this experiment was designed as a first step to the answers. They made the assumption that because light could penetrate all transparent media, such as water, those media were permeable to the aether. If the medium is moving, does it carry the aether along with it? Is the aether partially dragged or is not affected at all?

Hippolyte Fizaeu got puzzling, but not entirely unexpected, results from his experiment. He showed that the speed of light in same-flow water was boosted but it was less than the sum of the speed of light in air plus the speed of the water flow, as Newton's laws would have predicted. The aether appeared to be dragged along, but only partially. It turned out that Augustin-Jean Fresnel had already established a dragging coefficient in the late 1700's, based on several earlier aether experiments that appeared to support the idea of partial aether dragging. All of these experimental results seemed to suggest that the aether might be denser inside mediums such as water than it was in air or in a vacuum and that light traveled more slowly through denser media. Fresnel's dragging coefficient was proportional to the refractive index of the medium.

Scientists at the time knew that the reduction in the speed of a beam of light depends on the index of refraction, which in turn depends on the light's wavelength. The refractive index decreases with increasing wavelength, so, for example, blue light bends more than red light when a light beam passes from air into water. This is why white light disperses into a rainbow when it passes through a prism. This presented a snag. The experimental data pointed to a seemingly complex scenario where aether is partially dragged by matter and the aether must flow (simultaneously!) at different rates for different colours of light, as a white light beam, containing all the colours, was used in their experiments. Were there a seemingly infinite number of aethers, one for each wavelength of light? The use of polarized light in this experiment presented the same problem. Light polarized in opposite directions both exhibited the same partial aether drag, suggesting that the aether was carrying two opposite directions of motion at the same time. These partial-dragging results were confirmed by numerous other experiments as well. Aether theory was offering complication rather than simplification.

Electromagnetism Re-imagined

It wasn't until around 1892 that Hendrik Lorentz approached these baffling experimental results from a new angle and a solution began to take shape. He assumed, first of all, that the aether was completely stationary.  He was then able to derive Fresnel's coefficient by using Maxwell's equations and an undragged aether. He looked at the problem as one of light speed transitioning between two reference frames, one where the system is at rest in the aether and the other where the system is in motion in the aether. By rest, he meant absolute rest in the absolute space of Newton. By doing this he introduced a clear distinction between matter (this time in the form of electrons) and aether. This meant a departure from any mechanical theory of aether.

Referring the work of Maxwell and others, he described the aether as "states" in an electromagnetic field. By doing so, he introduced an abstract aether replacing the previous and problematic mechanistic model. He also planted the seed for special relativity: A moving observer with respect to the aether will observe the same electromagnetic phenomena as an observer at rest in the stationary aether.

Lorentz's interpretation was that partial dragging was something that happened to the electromagnetic wave itself and not something that happened to the aether, which was stationary. This proved to be a critical first step in the evolution toward our modern theory of space-time. It was, however, a first step. It transformed mechanical aether into an abstract electromagnetic aether, but it still held onto the presence of some kind of aether and it held onto Newton's concept of absolute space.

The idea that space must contain something to support the propagation of electromagnetism (and gravity as well) was extremely difficult to let go. By 1901, as Lorentz was developing the theory underlying his famous Lorentz transformation, which would provide a bedrock for Einstein's theory of special relativity, Henri Poincaré wrote (in a state of philosophical angst?) that there must be no absolute space nor absolute time. Even so, Poincaré would not let go of aether: "If light takes several years to reach us from a a distant star, it is no longer on the star, nor is it on the Earth. It must be somewhere, and supported, so to speak, by some material agency."

Aether Evolves into Space-time and Fields

Quoting from Einstein once again in 1920, after he published his theory of relativity, "To deny the aether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view." Again, one can detect the angst.

Today, we can argue that Poincaré and Einstein were correct about space, but only in a sense. We can argue that the field itself has replaced the aether. Electromagnetic radiation, such as visible light, which was the focus of Fizeau's and other aether experiments, is carried as waves through an electromagnetic field. These waves operate by quantum rules rather than mechanical rules. We now have a concept of a physical universe that is described by the mathematics of space-time geometry, and within that geometry we describe various fields carried by force-carrying particles called bosons. Photons are the force-carrying particles of the electromagnetic field. Starting with the development of the theory of electromagnetism in the late 1800's and continuing through the development of quantum mechanics later in the early 1900's, physicists gradually abandoned the idea of a background medium altogether. Aether isn't required to explain how special relativity works.

How "real" is a field? Is it physical or strictly a mathematical construct? The concept of the field arose as a fundamental physical quantity that independently exists. For example, physicists envisioned the electromagnetic field extending indefinitely throughout space in all directions as a physical field interacting with matter. Maxwell's electromagnetic field equations were developed using classical field theory which obeyed Newton's laws. Later on they were refined further by incorporating special relativity and quantum mechanics. We now know that an electromagnetic field is carried by force-carrying photons. Subatomic particles, such as photons, are treated as excited states in the quantum field that obey the laws of quantum mechanics.

As treated in quantum field theory, a field is strictly mathematical and doesn't physically exist. The field still extends all over space and we can make an observation of the field by taking a measurement of it at a particular moment and location. In this sense, the field interacts with matter and we can argue that the field is physically real. We experience evidence of it all the time, such as when we see a burst of visible light photons when we turn on a light. We feel a static charge or watch iron filings arrange themselves according to the lines of force exerted by a magnet. In the case of magnetism, for example, we indirectly detect the virtual photons that carry the magnetic force. We understand these photons as mathematical wave functions.

The Speed Of Light Forces a Shift In Thinking

Einstein, wondering about space and time and perplexed by the nature of aether, turned his focus to the experimental findings. He knew that Lorentz was beginning to approach the aether problem in terms of changing frames of reference. He focused on one blaring observation. The speed of light appeared is a universally unchanging value. In itself this was a truly mind-blowing observation in a then largely Newtonian universe.

Imagine the headlight of a train approaching at the speed of light. The photons in that light beam would also be travelling at the speed of light, and never exceeding it. Why don't these two velocities add together, as they would if a man threw a ball forward from a train travelling forward at everyday speed? If photons followed the same rules of Newtonian dynamics as balls do, the two speeds would add up. What is it that slows the light down and keeps it in check? What is that process if it is not the work of some kind of elastic aether? Einstein knew that something in the description of this thought-experiment must give. One thing he could conclude with some certainty was that he did not yet have the entire picture of space as the medium through which light travels. By following a tactic similar to Lorentz by allowing the question of medium to take a back seat, he could reframe the problem. If the speed of light never changes, then time or space, or both, must. Put mathematically, space and/or time must transform.

Time Can Vary

The concept of transformation itself isn't new in physics. Galilean transformations operate in Newtonian physics. They tell us that any event that takes place in one frame of reference will operate under the same physical laws if it takes place in a different frame of reference. For example, barring all other sight cues, a car traveling at 50 km/h passing a car traveling at 30 km/h in the same direction will appear to the passengers of the 30 km/h car to be traveling at 20 km/h. It's the basic addition/subtraction of velocity vectors, operating under the same rules as the ball being thrown from a train example above. These kinds of transformations presume that the passage of time is the same for observers in different frames of reference. They presume that time is absolute in other words. These Newtonian rules are still useful and that's why we learn them. They work perfectly until we are dealing with velocities approaching light speed (or near gravitational fields). Lorentz and others tried to understand how the speed of light breaks these well-established common-sense rules. In any reference frame the speed of light is always the same. It does not obey the Newtonian laws that underlie a Galilean transformation.

A Galilean transformation holds up for events that happen at everyday velocities, but as an object approaches the speed of light in one reference frame compared to a stationary reference frame (we can call this frame a stationary observer), both space and time, for that observer, transform. Space and time depend on the reference frame. Any object approaching the speed of light experiences time dilation (time stretching or slowing down) and length contraction as observed relative to a stationary observer. To that observer, the object contracts in the direction it is traveling* and a clock attached to that object slows down.

*An object travelling near light speed will actually appear rotated even though its measured length will be contracted. The object is moving so fast that light from the along the object reaches the observer at slightly different times. A receding object will appear contracted and an approaching object will appear elongated, while a passing object will appear skewed or twisted. This optical effect is called Terrell rotation).

This means that observers moving at different speeds relative to one another can observe different distances, different elapsed times and even, as a result of these transformations, experience different orderings of events. These transformations are not illusions. At the expense of getting ahead of myself, consider an example of a proton (a particle of matter) in the Large hadron Collider. It is accelerated to almost light speed and as it does so it experiences a Lorentz factor of about 10,000. The Lorentz factor is the factor by which time and length change for an object that is moving. To put this in perspective, if you could shrink down and ride on top of this proton from Earth to Alpha Centauri, your trip would you take only a couple of days. Alpha Centauri is four light-years away, which means it takes (traveling at light speed!) four years for its photons to make that same length of trip. An observer on Earth would record that your trip to Alpha Centauri took a little over four years.

Putting his thought-experiment observations into a formal framework, Albert Einstein published his game-changing theory of special relativity in 1905. It incorporated Lorentz transformations in space and time. A few years later, Hermann Minkowski formulated a geometric interpretation of the Lorentz transformations, and this is now the mathematical structure, called Minkowski space-time, on which the theory of special relativity rests.

Minkowski space-time mathematically combines three-dimensional Euclidean space with time to create a four-dimensional structure called a manifold. A manifold is a strictly mathematical concept that is nicely explained here.

The Space-time Interval

If we take the simple concept of distance, we can get a feel for how Minkoswki space-time works. In Newtonian physics, the distance between two points is invariant. It will be the same regardless of reference frame. In special relativity, however, that distance will depend on whether the observer is moving or not (length contraction). In four-dimensional space-time, a new invariant "yardstick" called the space-time interval replaces distance. Whereas in Newtonian physics, time and space (distance) are invariant, in Minkowski space-time, time dilates as distance contracts. These measurements are dependent on the frame of reference. The space-time interval of an event, which combines space and time, is the same in any frame of reference. A space-time interval extends from one place and time to another place and time. We can even build space-time by taking successive snapshots of space over time and adding them all together. Measurements of space and time can vary between observers but the space-time interval, obtained by measuring the distance and time between two events, will always be the same in every frame of reference. It doesn't matter how fast or in what direction an object is traveling with respect to the observer. The space-time interval displays Lorentz invariance.

To visualize how time and distance relate to one another geometrically in a space-time interval, as well as how the speed of light is constant in every frame of reference, try this 7-minute video:



How To Get From Length to a Space-time Interval

How did we get to this new invariant idea of "length" in space-time? When Minkowski developed the space-time manifold, he imagined that the space-time interval could be related to Pythagoras' theorem, but in four dimensions rather than the two we are all probably familiar with when we draw a right triangle on a sheet of paper, shown below right.

The Pythagorean theorem states that the length of the hypotenuse, z, is given by the square root of x² + y² where x is the horizontal measurement and y is the vertical measurement in a two-dimensional coordinate system such as a sheet of graph paper. If we want to describe z's length in three dimensions, we just add a measurement along an additional horizontal axis, w, which we can imagine as a line coming out of the page. Then we get z² = w² + x² + y². We can now describe line z's length and position in 3-dimensional space. To measure z's coordinates in time as well as in space, Minkowski introduced a time dimension, (ct) to the equation. Here, c is a conversion constant, which is the speed of light in a vacuum (metres per second), and t is the time interval (seconds) spanned by the space-time interval. We can think of it as the distance light travels in t seconds. This is a way to incorporate a new "length" along a new axis, and as we do this we are switching to a four-dimensional coordinate system. By doing so we are bringing time, as a unique dimension, into our geometry. The speed of light conversion constant makes this dimension uniquely different from the other three spatial dimensions. It also tells us that the speed of light can be used as an invariant measurement of time called proper time.

With a little mathematical finesse, we end up with three dimensions of space and one dimension of time:  s² = w² + x² + y² + (ict)². We've changed our variable z to s, to show that we are now measuring distance as a space-time interval. We've also added a new variable, i, to our time axis. The term i is an imaginary unit, also known as √ (-1). The old-fashioned picturesque descriptor "imaginary" doesn't mean an imaginary number is made up. It just helps us find solutions to mathematical problems. In our case, imaginary time is real time that undergoes a mathematical transformation called a Wick rotation. A Wick rotation is a way to convert a problem in Euclidean four-dimensional space into a problem in Minkowskian four-dimensional space-time. It trades one spatial dimension for a time dimension and allows the dimension to undergo a Lorentz transformation, which mathematically is a rotation of coordinates.

Since the ict term is squared we can multiply (ct) by -1. We end up with s² = w² + x² + y² - (ct)². Again, we can think of this (ct)² variable as "distance" along the time axis.

The introduction of an imaginary unit hints to us that even though we've put our equation into the form of a Pythagorean equation, the time dimension in it doesn't "act" like the other spatial dimensions. It does not have a simple Euclidean geometrical relationship with space.

Physicists now describe space-time in terms of a newer mathematical construct called a metric tensor. General relativity also describes space-time, but in that case, the space-time needs to curve under gravity. We can think of the metric tensor is a device that makes corrections to Pythagoras' theorem to enable the right triangle we used as our starting point to map onto curved space-time. It also does away with the imaginary unit (i) we discussed earlier by describing events in real time instead. The negative sign, however, is preserved in the metric tensor but it now describes how distance changes with time when space-time curves. The original Minkowski equation describes an incorrect but simplified flat space-time.

By creating a space-time interval, we can understand both the invariance of the speed of light as well as time dilation and length contraction.

Speed of Light Invariance

Imagine a photon traveling at the speed of light, c. All observers will observe that same velocity no matter what their velocity might be relative to it. The distance traveled by the photon (let's say it's traveling in the x direction so we'll call it distance x) for t seconds can be written as:

x = vt  where x is the distance traveled, v is velocity and t is time

Let's begin to transform this simple equation for distance into one for a space-time interval. First we'll incorporate it into the Pythagorean theorem in three dimensions, like we did earlier. I'll start using s for the distance even though I'm not quite correct yet because we haven't incorporated time.

s² = x² + y² + w²

There is no motion in any direction except the x direction so the w and y axes are zero. We need to describe this relationship in terms of space-time so we add the time dimension [-(ct)²]. We can now properly describe the distance (x) in terms of a space-time interval (s):

s² = x² + 0² + 0² - (ct)²

We can swap out x by incorporating our earlier equation x = vt.

s² = (vt)² - (ct)². Our object is traveling at the speed of light so we know v = c.

 s² = (ct)² - (ct)². We get s² = 0 so s = 0.

This means that the space-time interval for any object traveling at light speed is zero. It is invariant. It doesn't matter what reference point you measure the object from. You could be accelerating in the w or y direction as you measure its velocity. It will always be light speed and its space-time interval will always be zero. Put another way, only an object traveling at light speed will have a zero space-time interval. All observers will observe the same (zero) space-time interval for that object, which means they all observe it to have a velocity of c.

How does a photon experience the universe? We can get a feel for this surprisingly complex situation by comparing the world lines of three objects, all traveling at different constant velocities in the same direction, shown below in a simple space-time graph.

Jheise;Wikipedia

We have to be careful because we are not representing velocity or position versus time. Each line, called a world line, is built from a sequence of space-time events for each object. Each point on each line is a four-dimensional space-time event. An event in space-time is a specific location in three-dimensional space at a specific time. The t in the graph depicts proper time.

In this graph, t is time and x is distance along one space coordinate. We could draw a more complex space-time graph by incorporating all three space coordinates with one time coordinate, representing Minkowski space-time.

An object at rest would be a vertical line originating at the same origin point as the coloured lines and where x = 0. Its world line is space-like. A space-like world line could likewise describe the length of a physical object such as a ruler, as the distance between two space-like events. Each of the three coloured lines represents the world line of an object traveling at a specific constant velocity (hence all the straight lines). Their world lines, and the world lines of any objects traveling less than the speed of light, are time-like curves in space-time. Even though only straight lines are drawn here, any world line is considered to be a special type of curve in space-time.

This graph represents all times (future and past) and all possible distances along x in space-time. It is a simple representation because all three objects are traveling along in the same direction, along the x-axis. They all originate at the origin of time and distance on the graph. At that origin point, they share the same space-time interval. A physical example might be a single particle decaying into three particles, each having a different velocity.

A stationary object moves in time but not in distance. A slow object moves further in time than it does in distance. A faster object moves further in distance than it does in time. A very fast object moves in distance but very little in time. A photon has the fastest possible velocity. It moves in distance but not in time. It follows a light-like curve, which would be represented as a horizontal line moving along the x-coordinate, where t = 0. A light-like curve is a straight line in this simple graph where two spatial dimensions are not shown. Often the convention is to draw this horizontal line at a fixed 45-degree angle. By doing this we can draw the light-like curve in three spatial dimensions as an easier-to-visualize three-dimensional cone, directed upward into the future and downward into the past, shown below.

MissMJ;Wikipedia

Put more sophisticatedly, we can say the photon approaches the limit of proper time. A photon might be emitted from a distant star and travel through space for 4 billion years before it is absorbed. We can measure that journey as taking 4 billion years (a great "distance" in time), but for the photon there is no distance along the time axis. It is emitted and absorbed instantaneously. Remember Henri Poincaré's troubling question? He asked where the light beam is in the space between stars. He wondered what medium was carrying it. Can we say that the photon even has a journey? We observe photons of starlight traveling across great distances over light-years of time. But in the photon's frame of reference the universe does not seem to consist of the space-time we experience.

Time Dilation

Imagine setting up an array of synchronized clocks over a very large table in space, a table on the scale of thousands of kilometres across with no gravitational field are nearby. From one edge of the vast table you take a photo of all the clocks. You find that the clock closest to you is running a little faster than those furthest away. After a little thinking, you realize you need to take into account the transition time for the light from each clock to reach you. The speed of light is constant so this is a fairly straightforward synchronization calculation. You go back and adjust all of your clocks. Now they all read the same time when you take your photo of them. A friend flies past your clock arrangement at 0.95% light speed and takes his own photo of the array at exactly the same time you take your next photo. Comparing photos, you notice that his clocks are all a bit behind yours. Your frame of reference is at rest compared to your clock table so you don't experience time dilation. However, you and your clock table are in motion compared to his frame of reference. He records time dilation. His present moment was not the same as your present moment. The two events you experienced were desynchronized.

If an additional initially synchronized clock were glued to the outside hull of your friend's ship beforehand and you repeated the experiment, you might guess that you will see it as running faster than your clocks. Instead, you read it as running slower as he flies past you. For you, he is the moving frame of reference. For him, once again you are the moving frame of reference. You once again see in your photos that his clocks are slower. And yet, for him, your clocks were slower. This counter-intuitive effect is known as the twin paradox.

What is different in the two frames of reference has nothing to do with the mechanisms of the clocks. A moving mechanism doesn't get heavier or something such as that. The key difference is that the moving clock is traversing a longer distance between events (ticks). The events do not have to be hands moving on a clock face. The clocks could be mechanical, quartz digital, atomic or even hourglasses.

To get a feel for this it might be easier to imagine that our clocks are made of pulses of light bouncing between two mirrors. One trip from mirror to mirror is equivalent to one tick of our earlier clock. The speed of light is invariant, so the ticking mechanism of this clock will be perfectly constant. The clock moving with respect to the stationary clock will tick slower. The moving clock will, in its frame of reference, experience the stationary clock as the one moving and it will tick slower than the former one. This brings home the fact embedded in special relativity that there is no absolute motion and there is no absolute rest. The only absolute is the speed of light. We can visualize time dilation (and the twin paradox) in the set-up in the gif below.

Cleoris;Wikipedia

Each blue dot represents a pulse of light. Each pair of dots (red pairs and green pairs) are mirrors bouncing light pulses back and forth. Each pair is a clock. If we measure the time it takes for one light pulse to reach from one mirror to the other mirror we will always get the same result as long as we are in the same frame of reference. This is called proper time. It is the fastest possible time because it is the shortest distance traveled by the light pulses. For each group of clocks the other group ticks more slowly because the light pulse has a longer distance to travel when it is moving. Time dilation works not just for light. It works for any series of events. The physics of any event or process is constrained by relativity. In other words, special relativity forces all other laws in physics to obey. For example, a man in motion with respect to a stationary man ages more slowly.

Length Contraction

We can do another thought experiment to explore how length contraction occurs. Imagine two light clocks like the ones described above in which light bounces between two mirrors. We can put them close together or far apart and we can orient them in any way we want with respect to each other. If they are both at rest with respect to us, as observers, they will run at the same rate. Any direction or location in space (barring any and all gravitational influences) is physically the same and physical laws work the same anywhere in the universe. If we set them perpendicular to one another and then set them both in motion at 99 % light speed in the direction of one of the clocks, we get some interesting results.

We, as observers, remain at rest with respect to the clocks. This means that as the clocks fly by us, the light is bouncing parallel to the motion in one clock and the light is bouncing perpendicular to the motion in the other clock. We will find that they will both run slower, as we expect, but we also find that they are still both running at the same rate. This observation is not what we expected.

The clock that is perpendicular to the motion should slow down, as we figured out above. We can imagine that those light pulses must travel a longer distance because they are making a stretched out zigzag path of motion between the mirrors. The stretching is where the extra distance comes from. But what happens to the clock that is parallel to the motion? Aren't those light pulses going to take a much longer time to reach the front-facing mirror that's going just 1 % slower than them?

We can put together a more concrete example to show what's going on here. Let's say the mirrors in the clocks are 300,000 km apart, the distance light travels in one second. At rest with respect to us, the light will take one second to travel from one mirror to the other. Now we set them in motion like we did above, with one set of mirrors oriented perpendicular to the motion and one parallel to it. If the clocks are now moving at 99 % light speed and the light is moving perpendicular to the direction of motion in one of them, we can calculate that the light will now take about 10 times longer, or 10 s, to make one trip between mirrors. The clock is now going 10 times slower relative to us.

What about the parallel clock? At rest, the light takes one second to go from one mirror to the other. If the light pulses in the clock are moving in the same direction, at 99 % light speed, the light has to chase a rapidly receding mirror in one direction. We can figure out that it will take about 100 s to reach the front mirror when it's moving away at 99 % light speed. It will take just a tiny fraction of a second to make its return trip to the other mirror because the back mirror is approaching at almost light speed. We discover that the light takes ten times longer to bounce mirror to mirror in the parallel clock (100s rather than 10 s). Yet we measured them and they are both running at the same rate - 10 times slower than they did at rest with us. How is the parallel clock still keeping the same time as the perpendicular one? The only way it can is to physically shrink in the direction of the motion, shortening the bounce distance. In fact, it will shrink to 1/10th of its rest length at 99 % light speed. Length contraction and time dilation have a perfectly inverse relationship. Length and time compensate one another to preserve the invariance of the space-time interval we explored earlier.

If one of the clocks could travel at light speed (and it cannot because it has mass) the light pulses in it would not move at all. There would be no ticking forward in time. If we could somehow ride along with a photon of light, we would discover that it does not experience time. If we consider the effect of length contraction as well, we come to a startling conclusion. There is no distance at all between the two mirrors in the parallel clock. In that clock the mirrors themselves would have no depth. Time slows down and length contracts for objects travelling very fast. A photon's path of travel is shortened to zero. Proper distance, like proper time, does not exist for a photon. Realizing this gives new weight to the concept that light has a space-time interval of zero.

Some Parting Thoughts

To accept the well-established fact that we live inside time as part of four-dimensional space-time is a bit like accepting that we experience only a tiny sliver of visible colour within a far vaster array of electromagnetic radiation. We know that it exists but we don't directly experience it in our everyday lives. We intuitively understand the universe in three-dimensional space but it is almost impossible to conceptualize four-dimensional space-time.

The movie Interstellar plays with the fact that time is a dimension. In that movie, a future "us" has figured out how to manipulate time to make it act like a tangible physical dimension. We currently can't do that and I don't know if that ever could be possible, but the mathematical formulation of space-time, in particular the Wick and Lorentz rotations, appear to treat time and space as two facets of the same thing. We got to our understanding of time as a dimension of space-time by way of the speed of light. At the speed of light, both time and space reach their limits. Does space-time exist at the speed of light? Do space and time fully unfold to our perception only when we experience the universe at rest?

Our Universe Part 1: Water

NOTE: I HAVE EXPANDED, UPDATED AND IMPROVED THE ENTIRE "OUR UNIVERSE" SERIES OF ARTICLES AS OF NOVEMBER 2012

Using water as a model, we can learn a lot about how atoms and subatomic particles behave under everyday conditions on Earth and under some extreme conditions elsewhere in universe.

If you have ever wondered about the world we live in - all the different objects we encounter every day and how they interact with each other and the changes that they undergo, then you have asked a fundamental question that scientists are still asking. Experts are still wondering what matter is ultimately made up of and we don't know the whole story of how matter and energy interact. We are living in a curious age filled with strange phenomena like black holes and magnetars. At the same time, ordinary things right under our nose, the atoms inside a water molecule, for example, defy our common sense and even appear to defy the laws of physics themselves!

Let's first get a feel for matter and energy and then we can explore their origins with the birth of the universe itself.

Water

Water: Why start here? It's so mundane! Hold up a glass of pure water and you will see that it is nothing more than a transparent liquid, a collection of simple molecules lollygagging about amongst each other.

But even this very simple molecule has some bizarre secrets to share.

A water molecule is an oxygen atom covalently bonded to two hydrogen atoms.

Check out A Gentle Introduction to Water to see how a molecule of water is put together. This website also has a great introduction to water's various physical and chemical properties.

What is a covalent bond? Well first, every single interaction in our universe can be described as one of four fundamental forces, to which I will often be referring in these articles. Every force in our universe can be broken down into one or a combination of:

Strong interaction

Weak interaction

Gravitation

Electromagnetism

The covalent bonds that hold the atoms of water together to form a molecule are an example of the force of electromagnetism. In fact, every single chemical reaction relies on this fundamental force.

This force is based on the movement of electrically charged particles called electrons. Electrons, along with protons and neutrons, are part of the atoms that make up every molecule, including water. 

What is the stuff of these protons, neutrons and electrons and why do they interact with each other? This simple question gets to the heart of contemporary theoretical physics, and this is where water begins to get interesting.

The Nuts and Bolts of Water

Let's take water's oxygen atom for example. After hydrogen and helium, oxygen is the third most abundant element in the universe. It consists of eight protons and eight neutrons grouped together in a nucleus surrounded by two orbitals of electrons.  Protons are positively charged and therefore they naturally repel each other. The electromagnetic force is at work here. The strong fundamental force acts against this much weaker repulsive force and squeezes them together in the nucleus. The strong force, in fact, is much stronger than all the other forces. It is billions of times stronger than the force of gravity but it only acts over an extremely short distance, just a little beyond the diameter of the nucleus itself. The neutrons and protons are themselves made up of even tinier particles called quarks and these quarks are bound together by mass-less particles called gluons. You can think of gluons like photons. Photons carry light, or more precisely, electromagnetic radiation, whereas gluons carry the strong force. All the fundamental forces are carried out by tiny fundamental particles, except gravity. Physicists don't know how gravity works and that is a huge open question in physics.

A simple molecule like water is a whirring complex of tiny mysterious particles of matter being acted upon by a variety of forces. Below is a basic outline of what physicists presently know about matter and energy. Don't worry about unfamiliar words, we will explore them all in due time:

(Headbomb;Wikipedia) 

Electrons, as far as physicists know at present, cannot be broken down into anything smaller. An electron has a specific charge, energy and mass. But it is not a solid little sphere; it does not have a size and it cannot be located in any precise location around the atom's nucleus. It can only be narrowed down to a region of probability where it is most likely to be found. This is because the electron has a puzzling dual wave-particle nature, and in fact, all elemental particles have this nature. Some physicists believe that rather than thinking of quarks and electrons as zero-dimensional "objects", they can be thought of a one-dimensional "strings," labelled "6" in the diagram below of a carbon atom (4) in diamond (1). The specific vibration of a string is what makes it a quark or electron (matter), or even a photon or gluon (energy). It is as if each tiny bit that makes up an atom or a quantum of fundamental force is a musical note and the atoms and complex forces we experience are symphonies composed of these notes.

(MissMJ;Wikipedia)

In the oxygen atom, the electrons and quarks, all of this, is packed into a sphere roughly 10^-11 m wide. The nucleus is only 10^-15 m wide within that. To put this in perspective, if the oxygen nucleus were the size of a golf ball, then the first shell of electrons would be 1 km away and the second electron shell would be 4 km away! The rest of the volume of the atom is absolutely nothing. It is a vacuum. Fundamental forces keep everything in place where it should be. But there are places in the universe where even these powerful forces can be overcome so that electrons get squeezed into the nucleus or they get sheared off. Ordinary matter starts to look and act very strange when that happens. 

Some Strange Characters

Let's get back to our glass of water. You know that you could freeze this water to form ice or boil it to form water vapour.  Water, in each of these three physical states or phases, can be found in any kitchen.

But this isn’t the whole story. Water can also exist as a supercritical fluid, a fourth state, in hydrothermal vents when it becomes hot enough (about 400^oC) and dense enough (about 250 times higher than standard air pressure). The liquid and gas phases converge into a fluid that is both liquid and gas at the same time and which has unique properties all of its own.

There is also theoretical evidence that even more exotic phases of water may exist under more extreme pressure and temperature conditions inside ice giants such as Neptune and Uranus. Superionic water does not act like a solid or a liquid. It may be thought of as a frozen three-dimensional scaffold of oxygen atoms with hydrogen atoms whizzing around within it at very high speeds. Models suggest that this ice would be an iron-hard fluid so hot that it would glow bright yellow. If it were placed in a petri dish in a lab here on Earth, it would instantly explode. This ice has electrical insulating properties whereas another theoretical phase of water, called metallic ice, is thought to be solid and electrically conductive, like most metals. Under extreme pressure and temperature, water atoms become so disordered that multiple electrons states are simultaneously partially occupied. Orbitals of electrons overlap each other and this accounts for its conductivity because electrons can move around freely. Scientists have often wondered how the ice giant planets create their large magnetospheres when they have little or no electrically conductive metallic core, which Earth has. They now believe that these planets have fluid inner mantels composed of electrically conductive water and ammonia, and it is these mantels that create the magnetic fields surrounding the planets. This is what scientists think is inside Uranus:

So much for that deceptively simple-looking liquid in your glass.

A Connection to the Stars

Now where did the water molecules in your water come from? Most people believe that all the water on Earth has been here since early in its creation and that each molecule is simply cycled through what is called the hydrologic cycle, shown below . . .

. . . where water evaporates, rains down, is absorbed into soil or rained into lakes and oceans and then evaporates again. This is mostly true. The general volume of water changes very little on Earth over time.  However, individual molecules regularly come and go. Combustion reactions as well as many of the biochemical reactions in your body create "new" water all the time.

On the other hand, water molecules can be split apart through the process of electrolysis into hydrogen and oxygen. This happens naturally in our bodies and even during lightning storms to a small extent.

Now that we know that water is continually assembled and disassembled all the time, what about its constituent elements, oxygen and hydrogen? Where in the world do they come from? It turns out they don't come from this world at all.

Hydrogen and oxygen and in fact all elements are created during a process called nucleogenesis, and extreme energies are involved (I explore this process in my article How Atoms Are Made).

Hydrogen is the simplest of the elements and it accounts for over three quarters of the entire mass of the universe. Almost all of the universe's hydrogen was created after the universe exploded into existence in what is called the Big Bang. After the Big Bang, a pre-particle soup of quarks and gluons settled into protons and neutrons and a little later into electrons, all within about a second. It took about another 400,000 years for electrons and nuclei to combine into atoms, mostly hydrogen.

The process of fusion shut down soon after nuclei the size of lithium were made as much of the initial energy of the Big Bang was lost to expansion and cooling, about 20 minutes post-bang. Oxygen is too large an atom to have been created this way. It first showed up on the universal stage millions of years later when the first stars expanded into red giants toward the ends of their lifespan, blowing their outer layers rich in elements, including oxygen, away to be dispersed into space and carried on stellar winds. Below is an image of the evolution of our universe, starting with an unimaginably powerful explosion - the Big Bang, the bright white spot at the left, and ending up today almost 14 billion years later:

So the hydrogen in water can be traced back to the birth of our universe. Oxygen, fused in the bellies of stars, is still being formed as stars die.

On Earth, we and in fact all life exist because this planet resides just the right distance from the Sun to support liquid water in our oceans and water vapour in our atmosphere. The water on Earth is thought to have come from the release of gases from its interior rocky material as it was forming as a planet.  Later, impacts with icy comets contributed some water as well.

Water, one of the most abundant molecules in our universe, has been detected on the moon, on Mars and several other planets in the solar system as well as in the form of vapour on various planets outside our solar system. It has even been detected in massive high-energy jets streaming from black holes in the centers of very distant and very old galaxies. It is the molecular signature astronomers look for as they search for life in the universe.

How and why did water, and in fact all matter and energy, begin? For our answer we must look back to the beginning of the universe itself, the Big Bang, coming up next.

Our Universe Part 2: The Big Bang

We begin with an utterly unfathomable newborn universe and probe the nature of the singularity it is. How does physics itself begin?

Planck-Time

In 1929, Edwin Hubble noticed that distant stars are moving away from us in all directions and that the further away they are, the faster they are moving. He looked at the light spectra from various distant galaxies and compared them with the Sun's spectrum. He found that black lines, called absorption lines, shifted toward the red end of the spectrum in all of the distant galaxy spectra he looked at, as shown below.

(Georg Wiora; Wikipedia)

This red shift is a Doppler effect. It means that the galaxies are all moving away from us. He then compared the galaxies' brightness, an indication of its distance away, to how much its spectrum was redshifted and he discovered that the further away the galaxy was, the faster away it was moving.

This observation was the seed that brought the Big Bang theory to life. Later, using the theory of general relativity as a theoretical framework, scientists were able to extrapolate the expansion of the universe backwards to a point of infinite temperature and density about 14 billion years ago. This theory has been tested using a variety of data from both cosmology and particle physics and it has gained a great deal of scientific support. There is one catch though - the infinite values for temperature and density at the very beginning of the Big Bang. Singularities, as these are called in theoretical physics, are usually taken to be a sign that the there is something wrong with the calculations, and this point still bothers physicists. Either the theory is wrong or the laws of physics themselves break down at the exact point the universe began.  Most physicists today are willing to put their money on the latter being true, and this willingness to explore the unfathomable is bearing some very strange fruit.

The graphical timeline of the Big Bang below, part of the Wikipedia page of the same name, provides a theoretical timeline of the universe that will be very handy as we begin our exploration of its birth (the website has a clearer image).

The very beginning of the universe from zero to 10^-43 seconds is called the Planck epoch. Scientists can't make any predictions about events that occurred in an interval shorter than Planck time (10^-43 seconds). Planck time is the time it takes light to travel 1.6 x 10^-35 meters (this length is called Planck length).

Check out this website Planck Scale to put this strange value into perspective and to find out how it is obtained. There are values for Planck energy, time, length, mass and temperature. These values are all derived from combinations of fundamental constants in physics and some of them represent the smallest (length and time) or largest (temperature) possible theoretical measurement.

Why is this Planck value so significant? When scientists explore intervals smaller than this, our current theories about gravity and space-time cease to be valid. No smaller division of length or time has any meaning according to our current theories and this is why:  Electrons and, in fact, all subatomic particles break down at this point into wave functions. A wave function is a function of a subatomic particle's spin and momentum, two characteristics that distinguish one subatomic particle from another. It is nothing more than a probability amplitude - all measurable certainty goes out the window. You can think of an electron's orbital inside an atom as an example. You cannot know its exact location; you can only know where it might be. Below is a diagram of an electron orbital in a hydrogen atom. The electron could be in any one of the three doughnut shapes. It is even accurate to say the electron is a wave function "smeared" over all three regions:

This is not an easy concept to grasp let alone accept. It feels so counter-intuitive. All quantum mechanical systems like this one break down into wave functions when we approach the Planck scale universe. That means all particles of mass and energy. It makes pinning down an exact point where the universe began impossible, and it leaves us stuck at the Planck-scale border of time and length, where the entire universe, as best as physicists can describe it, is a wave function.

You could think of Planck-scale as the ultimate limit of resolution, as in a photograph. Beyond a specific point (Planck time or length) our understanding of reality breaks down into nonsense (the picture is just a fuzzy grain).

So, we have established that we can only make sense of the universe at the baby age of 10^-43 seconds and older. At zero seconds we just can't know or understand the universe. Extrapolating backward gives physicists infinite temperature and density values squished within an implied infinitely small volume: zero volume.

There is another example of a singularity in our universe - black holes. I explore them in Stellar Objects Part 5. Within a black hole, all matter and energy collapse into an infinitely dense and small space. And according to current theories, not just matter and energy disappear but information itself is obliterated. Some physicists speculate that the birth of the universe may have been a black hole operating in reverse, and they call it a white hole. This theory suggests that a big bang occurs at the core of a black hole, creating a new universe independent of its parent universe. Our universe is thought to contain countless black holes, each one potentially spawning a new universe on the other side, with its own physical laws that may be different from ours, an hypothesis called the fecund universes hypothesis.

Mother Force?

Back to our universe, what is happening at 10^-43 seconds? Most physicists believe that all four of the fundamental forces are jumbled into one unified force in this ultra-energetic environment. This enormous energy, expressed as particle energy, is measured in gigaelectron volts (GeV). Researchers believe the maximum energy of the universe right after the Big Bang was about 10¹⁹ GeV. This is another example of a Planck value, a theoretical energy maximum. At this energy, all four fundamental forces are believed to unify into one "mother force."

Three researchers, Abdus Salam, Sheldon Glashow and Steven Weinberg, helped provide direct evidence that two fundamental forces, the weak force and electromagnetism, combine into one force, called the electroweak force, at energies higher than around 100 GeV, earning them a Nobel prize in 1979. The particle energy of our current universe is very low, in comparison, about 10^-4 eV, or 3K above absolute zero.

The weak force, strong force, and the electromagnetic force can be theoretically unified in terms of the particles that mediate them. They are each mediated through the exchange of closely related virtual particles called gauge bosons. Quantum particles of matter, called fermions, attract or repel each other by exchanging bosons. Bosons carry energy and momentum between the fermions, changing their speed and direction. Examples of these gauge bosons are photons and gluons (remember them from the previous article?) However, no boson has yet been discovered for the fourth fundamental force, gravity, and no one has been able to fit gravity into the same theoretical framework as the other three fundamental forces.

Gravity: A Big Problem When Describing the Planck Universe

The fly in the ointment when trying to understand the Planck epoch universe is gravity. Gravity is so incredibly feeble compared to the other three forces that it is simply ignored when working on particle physics problems. Physicists don't yet have a quantum mechanical theory for gravity, as they do for the other three fundamental forces. This, at first thought, might not seem to be a huge problem, because gravity is so weak it can be ignored when describing physics at the scale of particles. Gravity is described very well, however, at the macroscopic level and especially at the cosmic scale, where its effects are significant, by using the framework of general relativity. But what about black holes and the Big Bang, where gravitational effects are enormous and take place in the super-squeezed down subatomic quantum realm? Here, both general relativity and quantum mechanics must be used to describe what is going on, and at least for now, the two theories cannot be made to work together.

What Scientists Know About Gravity

We know that gravity has some peculiar qualities:

It is the only force that acts on all particles having mass (and it has an infinite range of influence over them).

It cannot be absorbed or shielded against.

It always attracts and never repels (nothing "cancels" gravity).

Gravity was first scientifically described by Galileo Galilei and later refined by Isaac Newton. Newton's laws of gravitation work well for objects on Earth but Albert Einstein's general theory of relativity, on the other hand, is the gravitational theory we rely on today for all objects, both here on Earth and heavenly bodies. It describes gravity in terms of the geometry of space-time and it works perfectly for all macroscopic objects. Try Spacetime 101 for a very good tutorial on general relativity.

We know how gravity works on large objects but we don't know how it works at the quantum level. How do you pin down the gravitational field of a subatomic particle which is a wave function? 

Gravitons?

Unlike the gauge boson, no mediator particle has been discovered for gravity, although physicists are currently in hot pursuit of a hypothetical massless spin-2 particle called a graviton that they believe might carry out this force.  Physicists want to come up with a unified theory that resolves quantum gravity, special relativity and general relativity to explain the bizarre behavior of this very early universe, as well as black holes. The theoretical graviton could bridge the gap between quantum mechanics and general relativity. Many of the unified theories in vogue right now such as string theory, superstring theory and M-theory all depend to some extent on this theoretical graviton.

Even though there is no evidence yet for it, many physicists hold to the idea that one primordial force operated in the Planck-time universe. It is possible, according to other theorists that gravity is different from the other three fundamental forces. Einstein describes gravity as the curvature of spacetime in his theory of general relativity. It is possible that gravity, therefore, has no particle associated with it.

The recent well-publicized discovery of the Higgs boson may play a role in understanding quantum gravity. Physicists do not know why some particles have mass and others do not and they believe this massive zero-spin boson may "give" mass to those particles. If so, there could be a connection between this particle and the graviton, if it exists.

There are more questions than answers when we explore the very mysterious Planck-epoch universe. The first entity to explode from absolute nothingness is believed to be some kind of primordial force from which the four fundamental forces will evolve. This primal unified force doesn't seem likely to ever be experimentally observed because scientists would need to recreate the unimaginable energy in which it existed in order to observe it. At this point, physicists cannot even put the Planck universe into a complete theoretical framework, with gravity being the problem. Without the four fundamental forces in place yet, it is reasonable to assume that the laws of physics themselves do not exist between zero and 10^-43 second. No one knows if spacetime exists right from the very beginning, or if it appears with the appearance of gravity as it breaks away from the other three (still unified) fundamental forces. This is where we are in bullet-point form:

• There is a fuzzy primal unimaginably enormous energy from which everything in our universe has yet to evolve.
• There is no mass and there are no objects, not even a subatomic particle, with the possible exception of some very exotic particle that has burst into existence at this point to mediate the primal unified energy, or "mother force," from which the four fundamental forces will evolve.
• Time begins, and it has jumped mysteriously from zero to 10^-43 seconds for us observers because we cannot know any smaller time unit.
• There is as yet no framework in which energy operates.  It is about to explode into being now. Is it space-time as we know it or something stranger yet . . . ?

Stay tuned. Next: The Planck Epoch.

Our Universe Part 3: Planck Epoch

The Planck epoch universe is a point of unimaginably immense energy confined in an incredibly tiny space. What space-time is made of, and how does a unified force "break" into the four fundamental forces of the universe today?

At 10^-43 seconds, the universe is about 10^-33 centimeters across with a temperature of 10³² K. It's an unimaginably tiny bubble of indescribably immense energy. This particular size is is Planck length, the smallest theoretical size possible, and in string theory, it is the size of one "string," about 10^-33 centimeters long. It is 10^-20 times smaller than a proton inside an atom. 

How hot is HOT?

The temperature, 10³² K, is also a theoretical limit, called Planck temperature. Above this temperature, calculations break down because particle energies become so large that gravitational forces between them become as strong as the other three fundamental forces. The forces essentially melt into one unified force and predictions about everything we know about the universe, including spacetime, break down into nonsense. A recent discovery may help put this bizarre temperature into scale. Physicists recently created the highest ever measured temperature, inside the Relativistic Heavy Ion Collider, about 4 trillion degrees Celsius (about 7 x 10¹² K). At this temperature, they observed atoms "melting" into a gluon-quark plasma soup, all within a temporary bubble. In this bubble, there was evidence that some laws of physics began to break down - the electromagnetic force and the weak force began to combine into a unified electroweak force. At 10³² K, theoretically at least, quarks and gluons, and in fact all matter and energy simply melt together. You will find out what quarks and gluons are in a future article - these particles will make their first appearance in the Quark Epoch Universe. For now you can think of them as the building blocks of atomic nuclei.

Spacetime

What's really weird about this Planck universe is that there is absolutely nothing beyond it! There is not even a vacuum because even an absolute vacuum exists within the framework, or manifold as it is called, of spacetime. There is no space or time outside the tiny newborn universe, unless . . .

We start here with a Planck-time universe in which time is now beginning and the laws of physics are just shifting into place. There is a theory that the laws of physics may not be absolutely fixed. There could be many universes, each with its own physical laws, matter and force particles. Below, a ten minute interview with physicist Michio Kaku puts this multiverse concept into perspective, and he gives us an introduction to another strange concept, extra dimensions, as well:

Let's begin with what we think might be the birth of space-time, that is, the three dimensions of space and one dimension of time that exist throughout the universe today.

First we need to know what space and time are. Time seems simple until we examine it closely. We perceive time differently from spatial dimensions. Einstein's theories of relativity treat space and time as components of a four-dimensional manifold called spacetime. The quantum mechanical model treats time a little bit differently: the perception of time flowing forward in one direction is an artifact of the laws of thermodynamics. In the quantum realm there is no rule against a backward time arrow but in the macroscopic realm we live in, time reversal is forbidden. A spilled glass of milk cannot refill itself like a film being played backward. For a photon on the other hand, or any object traveling at light speed, time stops altogether. This is a consequence of relativity. It gives time a stretchiness that becomes apparent only near the speed of light or under extreme gravity. Time is not nearly as simple as it first seems and I explore the puzzle of time in the article, Time. This being said, we may be able to set aside any questions about multiple dimensions of time. There is no evidence for multiple time dimensions and adding time dimensions does not simplify the quantum mechanical equations or help marry them to general relativity.  Yet there is an interesting article by physicist Itzhak Bars that explores the possibility of two time dimensions.

If we try to dissect and examine space-time, it is impossible to know exactly what the components are made of, but when physicists attempt to consider the laws of quantum mechanics and general relativity together, spacetime can be divided up into chunks as small as Planck-length. When they get down to pieces this small, spacetime loses its smooth appearance; it "boils." It becomes what is called quantum foam. To explain quantum foam, let's begin with a larger piece of space-time. This piece of space-time fabric appears completely smooth at a scale of 10^-12 cm and larger; some roughness shows up at 10^-20 centimeters, and as we zoom in to 10^-33 centimeter range, the Heisenberg uncertainty principle tells us that spacetime has a certain minimum energy. This energy, called vacuum energy, means that virtual particles randomly and continuously pop into and out of existence, without violating conservation laws. With this activity, spacetime resembles a three-dimensional frothing sea.

Enter Strings

As I have mentioned in an earlier article, we have a conundrum of two well-established theories that physicists have so far been unable to mesh together into a single theory of everything. General relativity accurately describes planetary motion, the evolution of galaxies and stars and even recently observed black holes and gravitational lenses - it describes gravity perfectly on the big scale. On the other hand, quantum mechanics describes the behaviour of atoms and subatomic particles wonderfully, but it neglects gravity. For most experiments this isn't a problem because at this scale gravity is monumentally weak, but a chasm forms when physicists try to describe particle behaviour under the extreme conditions of the very early universe, where gravitational force needs to be taken into account.

String theory is a developing theory that might close this gap.  It suggests that particles arise as vibrations of tiny one-dimensional Planck-length strings which themselves arise from the quantum foam I mentioned earlier. The graviton, the theoretical mediator particle of gravity, would for example be a closed string with a vibration frequency that translates into two units of spin. Likewise, electrons and quarks are one-dimensional strings with their own specific oscillations, which give them their momentums and spins. I explore string theory in the article, String Theory.

Travel to the Fourth Dimension and Beyond!

M-theory is an extension of string theory and for its equations to work, a string has to vibrate in 10 dimensions of space. Don't worry, no one can visualize what this might look like. 10 dimensions implies six extra dimensions to our four, which have not yet been experimentally verified. Also, according to the theory, these strings exist along with sheets called branes. Strings can be confined on branes like waves on the surface of a sea. Some strings may be able to move through them. According to Einstein's general relativity, the gravitational force that arises from mass tells space-time how to curve and the solutions to his equations allow for many different curvature geometries ranging from a circle, to very complex shapes. Working with a number of dimensions, the geometry will try to minimize the energy it builds up as a result of its curvature. As a result of the elegance of string theory, many physicists embrace the idea that we have three spatial dimensions with several hidden dimensions that do not change over time. Think of energy as a ball rolling down in a spiral toward the bottom of an inverted energy cone. Energy-wise, we are sitting at the bottom of that cone. More accurately we are sitting at the bottom of a three-dimensional curve, which is just one slice through a complex multidimensional mountain range. In this sense, our particular universe may be just one of many points where that ball could rest. In other words, according to string theory, there may be many stable multidimensional possibilities for a universe to adopt as it pops into being - we just happen to have three observable spatial dimensions. These dimensions determine not only which particles can exist but also which and in what form fundamental forces exist.

How do we reconcile the predicted 10 dimensions with our three observable spatial dimensions? One idea is to consider that the extra dimensions are very small. A common analogy for this multidimensional space is a garden hose. From far away it appears to have only one dimension, length. Now imagine getting closer to the hose and finding out that it contains a second dimension, its circumference. An ant crawling in one direction down the outside of it would move in two dimensions and a fly stuck inside flying around inside it would move in three dimensions. This new third dimension is only visible within very close range of the hose. If you extend this rationale to the theory of particle-wave duality, you will discover that as you experiment with particles of smaller and smaller wavelengths and you approach the radii of some of these smaller dimensions you run the chance of coming face to face with direct evidence for the existence of even more dimensions (it is hoped). In quantum mechanics, this means blasting particles with very high energies, and that is one reason why people are putting so much money and effort into building better particle accelerators.

Extrapolating from this idea, we will surmise that the universe began with 10 dimensions. What caused some to contract and others to expand into our current space-time geometry?

String theory tells us that, when a dimension is curled up like a circle, a closed string can wrap around it and keep it from expanding. All dimensions in the very early universe may have been wrapped up by string loops. Each string-looped dimension couldn't expand beyond one Planck-length in any direction. However, strings may wrap around a dimension in one of two directions. When two strings wrapped in opposite directions come into contact they should annihilate each other. If this process happens rapidly enough some strings should annihilate each other, allowing only some dimensions to expand, but why exactly three spatial dimensions and not four or two? Some theories suggest that this is simply because three unfurling dimensions present the right number of trajectories that are least likely to interfere with one another during a very rapid expansion. Other theories suggest that we just happen to have three expanded dimensions by chance but we could have had more (or maybe less like the 2-D world in which the Simpsons live). So, we have three dimensions growing and six dimensions settling into tiny but stable curled up shapes called Calabi-Yau shapes.

This might explain why gravity is so weak. Gravity might function in more than three spatial dimensions. The graviton string might be able to move through and across dimensions. In a three-dimensional world, the strength of gravitational attraction is squared when the distance between two masses is halved. But in four dimensions strength varies as a cube rather than a square, and in five dimensions as the fourth power and so on. It's possible that gravity isn't weak at all - it just seems that way in three spatial dimensions. The extra dimensions don't need to be large for this argument to work.  This website explores how this might be so, and also how both the graviton and extra dimensions might someday be experimentally proven.

Let's go back and reconsider the beginning of spacetime fabric. We will operate on the assumption that gravitons exist and that a gravitational field is composed of an enormous number of gravitons much like an electromagnetic field is composed of an enormous number of photons, and each of these gravitons is a string executing the graviton vibration. A gravitational field is encoded in the bending of spacetime, so imagine the fabric of space-time being composed of an orderly fabric of strings all vibrating in tune. This is called a coherent state. We could ask ourselves if there is a precursor to this orderly string state, a precursor of spacetime itself. We can think of each graviton string as an indivisible unit of space-time much like an atom is an indivisible unit of an element. Now we have a problem because the whole notion of string theory presupposes strings operating within a spacetime framework. And if we take this argument further, we begin to wonder if space, time and the dimensions that arise from them are not fundamental aspects of the universe but artifacts that emerge from a much more primitive state. This is a thought to consider and I have no good answer for you.

Symmetry

Let's get back to our Planck-time universe - we'll again assume that gravity is analogous to the other three fundamental forces; that it is carried out by gravitons. Physicists don't know for sure if this is a true picture of gravity.  It could be just the geometry of stretchy spacetime instead, rather than a true force like the other three fundamental forces. For now, we'll treat gravity as a "normal" force, so the universe begins with one unified force, from which four different forces will arise. Think of this state as being analogous to four metals melted together to form a smooth amalgam. This amalgam is perfectly symmetrical, that is, it contains no lumps or inconsistencies. Now look at our universe today: it is full of lumps and inconsistencies - all different kinds of matter and energy clumped into gas clouds, neutron stars, galaxies and so on, separated by the vacuum of space. What happened to the symmetry?

Think of a glass of water freezing into ice. At 0^oC you notice something interesting - crystals of ice are forming in random patterns. The symmetry of the "smooth" water breaks as it undergoes a phase transition into ice. This process is true of larger systems and of the universe itself. The primordial unified force in this very young universe will very soon break into the fundamental forces as it begins to cool. The image below attempts to show how the universe underwent a series of phase changes that coincide with symmetry-breaking, and the separation of the four fundamental forces from one unified force:

Because we are considering that the fundamental forces are consequences of the interaction of strings and the multidimensional branes through which they move, we can assume that the symmetry-breaking of the unified force must coincide with the expansion of four dimensions into spacetime and the settling of six additional dimensions into very small Calabi-Yau shapes.

Keeping in mind that string theory is strictly theoretical and gravity might not be a particle-mediated force, we now have at least a theoretical framework in which the universe can "become." But wait. Things are about to get even weirder! Next: The Grand Unification Epoch.