Fourth dimension, general theory of relativity and time — an easy explanation for everyone.

Let me tell you, Many people confuse the biological passage of time with the physical concept of time.

To disorient your sense of biological time, all I have to do is deliver a calculated blow to your brain’s temporal lobe. That could cause retrograde amnesia and your sense of time would be lost as you juggle between disappearing memories. Your sense of space and time fades away.

In the brain, biologically, the passage of time is maintained in a region called Hippocampus in the medial temporal lobe. The hippocampus is part of the limbic system, the survival system of the species, which is encompassed within the Paleo-mammalian brain. It plays important roles in the consolidation of information; from short-term memory to long-term memory, and in spatial memory that enables navigation. It is essentially the Inertial Measurement Unit of our body. Both our moments through space and time are recorded in the Hippocampus.

Like I explained before, to disorient your sense of biological time, all I have to do is deliver a calculated blow to your brain’s temporal lobe. Your time-index fades away. Your anchor drifts off and you start tripping in between biological sense of space and time. There is a very possibility that you will slip in between different biological timelines, and you won’t be able to draw a distinction between the past and the present. The other portions of your brain will try to coordinate with the Hippocampus but will fail.

If I could elucidate more, I would say Clocks doesn’t measure time.

Clocks don’t measure time. Clocks measure intervals between events. How fast does the second hand of a clock tick? A second per second? Absurd. Clocks only measure events and index them with a number. That number is associated with a mental state of you, the perceiver at that time. That is how information in the brain is timestamped. Roughly speaking, it can be expressed as a set of {time, event} (again, oversimplified: this is the result of the firing of billions of neurons, creating a complicated chaotic circuit).

That’s all. It serves a biological and socio-cultural purpose. Without that index, we won’t be able to store anything in our memory. Just like the index in our books, or a computer database, biological time is a concept used by us to efficiently store and then retrieve memories whenever they are needed. For us, it is always yesterday, last year, next year, or today. That is the index we make. That is our anchor in time that lets human beings plan, store and commit things to memory and to run the civilization better by coming up with a common clock, that measures these intervals between events.

By matching up our measure of intervals of time with everyone else’s, we invented the world’s most powerful collaboration and planning tool ever — time- which governs all our activities, and even the activities of billions of intricate machines that we make every year.

Now that the clear separation has been made between the biological and physical concepts of time, let’s delve into the physical one.

For now, imagine time as a higher dimensional concept. You are not able to perceive it visually because you haven’t yet developed sense organs to do so.

You can see the world because light reflects from all the objects around you, and it hits your retina, the retina converts it to a series of electromagnetic signals and send to your Visual Cortex in the Occipital lobe. This portion of brain then creates an approximation of what you might be seeing. What you see, hear and sense are not really as it seems to you. They are electromagnetic approximations your brains create mathematically. This is how you see the world. Your eyes can pick up only visible light in the wavelength between 370 to 740 nanometers. The rest of the electromagnetic spectrum is out of your perception. We don’t see the colors in any other EM spectrum because we are not evolved for that. For instance, bees see into the 300 to 650 wavelength. That lies the UV spectrum. Why can’t we?

“Their ability to see ultraviolet light gives them an advantage when seeking nectar. Many patterns on flowers are invisible to humans. These nectar “bulls-eyes” are visible only to animals, such as bees, that have the ability to see ultra-violet light. This “bee vision” makes finding nectar much easier. In fact, some flowers such as sunflowers, primroses and pansies have nectar guides that can only be seen in ultra-violet light.

Bees also have the ability to see color much faster than humans. Their color vision is the fastest in the animal world-five times faster than humans. So while we may have trouble distinguishing one flower in a group from another, bees don’t. They see each individual flower. Some flower petals appear to change color, depending upon the angle. This is known as iridescence. It’s often in the UV spectrum, so we can’t see it. But, bees can. They see these shiny petals and associate them with sugar. Thus, the flower becomes more attractive to the bee and gets pollinated.

So the bee, and the plant that hosts the flowers, all evolved in a way that maximizes their survival.” - — beeculture.com

So, you can safely assume that you are not evolved to sense or handle anything higher-dimensional. There was no need to. You were evolving while surviving a tiger jumping at you from beyond the bushes; not a higher dimensional beast lashing out at you from the next dimension.

So it would be a favor you do to yourself to make use of an analogy to understand that concept. Imagine that you are two-dimensional ants living on a two-dimensional universe made of flat paper. You can move all you want in X and Y spatial dimensions. You can traverse the length and the breadth of your Euclidean universe, — but alas, not the depth or height.

That is because you still haven’t grown sense organs or intelligence yet to perceive the 3rd dimension.

Now Imagine that your paper is crumpled, which produces 3-dimensional distortions in your flat X-Y Cartesian plane, creating mysterious hills and valleys in the third dimension that you won’t be able to see.

But, while walking up the slope of the hill, which you can only perceive as a flat land, you will find a mysterious, unseen force that prevents you from moving in a straight line, tugging you left or right. Thus, you will understand that, force is a consequence of a higher-dimensional geometry. It is a manifestation of a geometry — in this case a wrinkle that exists in the 3rd dimension- which only the god like extra-dimensional beings like humans would be able to see - but not you, petty 2D ants.

Would it make you wonder that a group of few smart, imaginative ants then started thinking about this extra-dimensional wrinkle and started writing down the mathematical equations that predicts the shape of the curve and the force created by that particular wrinkle even if they can’t see it? Yes.

Then they tested it. Depending upon the force experienced by the ants at at different places, they determined the shape of the wrinkle, and depending upon the shape of the wrinkle, they could calculate the force experienced by anybody moving along that curvature. It worked out experimentally.

They couldn’t see the higher dimension, but as elegant as mathematics is — they could use it to derive equations that changed the understanding of their world, shattering the very core of their existence, as well as their perception of reality.

They thought, Maybe one day they could use those equations to navigate out of their dimension to the next one.

One day, they could meet the gods that their holy books called “humans” — gods powerful enough to create ripples of wrinkles in their feeble ant world, destroying or creating worlds as they pleased.

This is an over-simplification of the analogy of the brilliant Bernhard Riemann who was among the first ones to formulate the mathematical apparatus of gravitation which Einstein used decades later to write down the most elegant, equations of our entire history — field equations for gravity.

Riemann concluded that electricity, magnetism, and gravity are caused by the crumbling of our 3-dimensional universe in the unseen fourth dimension. Therein, you have the presence of a 4th dimensional manifold.

This time around, you are the ants, living in a 3D world with 4D wrinkles.

By this one intuition alone, Bernhard Riemann, in 1800s, broke the 3-dimensional Euclidean dogma in physics , which limited us from looking outside our perception for thousands of years.

Now, just like the ant’s 2nd dimension is curled up in an unseen 3rd dimension, our 3rd dimension is curled up inside a 4th dimension that we won’t be able to see, but we would be able to sense it by the way it interacts with us and make equations that govern that higher dimension. That is what Einstein did. As all our intuitions were stuck inside the world we could only perceive, both Riemann and Einstein perceived a mathematical world we couldn’t. They derived the laws governing that dimension. All the equations check out- in every experiments we have ever conducted. The beauty of it is that it’s almost metaphysical, yet mathematical, goes in the same lines as with spirituality — but still grounded in reality by the most beautiful set of equations the world has ever seen.

The implications of this discovery changed our world forever.

On the surface of Earth, you can move anywhere along the north-south, east-west combinations. You require just two pieces of information to encode that spatial information — latitude, and longitude. If you are going underground or flying on a plane, you may require a third piece of data — altitude. Without that data, even if two persons are standing on the same lat-long, you won’t be able to see each other. In the absence of altitude, you are at separate locations. Three independent pieces of information are required to describe your spatial location.

This is the same with time.

In 1905, Einstein’s special relativity taught us that the speed of light is a universal speed limit, and as you approach it, “mysterious” things start to happen. Time slows down, and your length will contract.

This is the only equation I am going to lash at you with; regarding time dilation, because going into the complete sets of equation of the theory of relativity is out of the scope of this article.

As you can see from the equation for time dilation, as the numerator, velocity inside the root component approaches the speed of light, time dilation increases, and when it reaches the speed of light, as in V =C, you can see that time becomes zero.

But perhaps the biggest breakthrough came in 1907 when Minkowski, who was Einstein’s teacher, realized that Einstein’s relativity had an extraordinary implication: mathematically, time behaves exactly the same as space does (except with a factor of c, the speed of light in vacuum, and a factor of i, the imaginary number √(-1).

Einstein saw, however, that the fourth dimension can serve a higher purpose. This was a zillion dollar intuition. To unify the principles of nature.

He had just shown that in a four-dimensional space, time and space can be rotated against each other, and so it can be treated as a single entity, called space-time (just like length, breadth and depth can be rotated and interchanged in a 3d world through a 3d rotation).

It means, whatever equations we had, we could replace time with space and vice versa, and the results remained the same.

By adding higher dimensions, Einstein could unite physical concepts that, in a 3d world, have no connection, such as matter and energy, hence his famous equation of E = MC² or mass-energy equivalence. It is an equation that derived it’s relationship from a higher dimension.

For this purpose, you can have an analogy which I am shamelessly copying over form Michio Kaku’s Hyperspace. Whenever battles happened in Rome, those parties who had access to mountains or hills had an advantage over their enemies. They could see the enemy army formation from a higher plane. In that case, a higher plane, or dimension- altitude served as a platform that could simplify their observations and enabled them to obtain them insights and patterns that existed beyond their line of sight.

This is the classic example of how laws of nature are simplified in a higher dimension. Being prisoners to the 3 dimensions, what we can do is extend this same thinking to 4th dimension.

Likewise, another set of baffling equations were the 8 equations(4 coupled equations) of Maxwell’s electromagnetic field, which were baffling even to the masters of physics at a time being.

Those partial differential equations, in one master stroke, were reduced to one beautiful symmetric equation when time was incorporated as the 4th dimension. All the information present in the original 8 equations are still present in the final 4-dimensional equation, which possessed a higher symmetry. In that equation, space and time could be interchanged with no consequence — the equation doesn’t give different results.

Thus, time, incorporated as a 4th dimension, simplifies the laws of nature.

As we go up in dimensions, a simple, intuitive, but trivial equation could eventually be constructed. One which could unite the field equations for gravity, electromagnetism, and nuclear forces, in one single equation.

It could explain all the phenomenon in the universe — called the “theory of everything” — or the “final theory” — the holy grail of physics .

It is as close as we can get to god, and the mechanics of the entire universe; all present in one eloquent equation that can be verified experimentally.

But as wise men would say, spirituality and imagination, even if lacking empirical proof, can give rise to a kind of thinking that can act as extensions in places where scientific principles lacks a leap of faith. Just like we imagined the 4th dimension.

The general theory of relativity painted a new picture of the Universe, with the following implications.

1. Even if you remain completely stationary, you move through time.

2. The faster you move through space, the slower you move through time.

3. If you move at the speed of light, or if you were completely mass-less, you would traverse the space-time instantaneously. That means, no time will pass for you. So as far as a photon is considered, it doesn’t “experience” passage of time. For a photon, the Big bang, and the heat death of the Universe are instantaneous — occurring at the same time.

If you take the third point, an unstable particle like a muon, which belongs to an elementary class of particles called leptons, can be used to observe time-dilation. Being unstable, it’s lifetime is 2.2 µs. With that short lifetime before it disintegrates, the distance it can travel at the speed of light is given by the basic high-school equation, distance = velocity * time. That gives it a mere 660 meters before it decomposes. But we have observed Muons formed in the upper atmosphere, traversing the entire distance to reach the surface of Earth.

That means it has experienced only a lesser time than we have.

The implications of these are, according to General relativity, space and time can be rotated against each other, and both of them are nothing but the same. Hence, the term space-time.

Einstein had the proof and the intuition for his field equations for gravity, but he didn’t have the apparatus required to express his derivations. Decades before Einstein, Riemann had the mathematical apparatus but didn’t have the physical intuition that Einstein would have in the future.

Riemann, who considered himself a man of faith, who believed that mathematics was his way to serve the god, died of extreme poverty and Tuberculosis in 1866 , seeing his higher dimensional equations not being accepted by the scientific community.

Half a century later, Albert Einstein came across Riemann's tensor quite coincidentally while searching in a “mad rage” to mathematically express his gravitational field equations. He saw that his field equations could perfectly be expressed by Riemann’s tensor. Thus, Riemann’s tensor found its rightful home in the most celebrated equation of all time- half a century after his agonizing death.

Consider space-time like a 4 dimensional manifold, which can be impacted by the presence of Mass. Einstein postulated the stress-energy tensor to describe this field. This tensor gives us the exact “curvature” of the space-time in the presence of mass and energy (Which are equivalent to mass-energy equivalence or E =mc²), and this curvature, which can be called a Geodesic- a curve in a higher dimension for which we can write down equations for precisely- whose rule will be obeyed by bodies traveling through that space-time.

Let me tell you that the above image over-simplifies it. The space-time lattices, or the coordinates you see in the image essentially shrinks in the presence of mass, giving rise to geodesics.

This gives rise to the force called gravity. This is why gravity pulls you. Gravity is the consequence of distortions in the space-time blanket in the 4th dimension. Just like the hills and valleys in the flatland of Ants, which they couldn’t see, but could feel.

There are still decades of derivations and explanations left, for instance, a thermodynamic explanation of time that gives us the “arrow of time”, but that is for another blog.