A brief History of Space

From Bucket to Branes: A quest to find a meaning of space

        

In the early days, space was not a significant issue in our daily lives. While it had some philosophical and religious implications, it was neglected in science until Newton presented his deep understanding of space itself. Despite his pious nature, he was strict with the laws of nature. He was the first to shed light on the previously less-interesting topic of space. On the other hand, mathematicians and physicists such as Descartes and Leibniz either did not address the concept of space or rejected it, stating "It has no independent existence". To resolve this argument, Newton devised an analogy

The Tale of Bucket

"Imagine if a bucket filled with water is tied to a rope and suspended like a pendulum and let the rope wind and later unwind itself. Due to this, we would see perturbations in water level due to the spinning motion of the 

bucket." Here's one video to summarize the whole thing: https://www.youtube.com/watch?v=DQsplQW7

Now, the interesting question arises: the bucket is spinning relative to what? Any object in motion or at rest has a specific frame of reference or perspective. A person sitting at rest on a chair is at rest with another person sitting at rest, but a person in motion would see the person with the chair moving away from them. The same applies to differentiating between a spinning and a stationary bucket. The exact answer would be due to the curvature in the shape of the water level. Now, what if we go a step further and ask, "In relative to what, the shape of the water level would change? To Newton, he used the term, 'Absolute Space', by which any motion can be pointed out. Absolute Space was the thing by which the concave shape of water was relative! He added that Absolute Space was the fundamental reference frame for anybody either at rest or in motion or while in acceleration. Newton was the one who showed the applications of absolute space but he never tried to define 'space', 'time', or 'motion'. What we get to know about space is that if any motion or rest exists then it is directly or indirectly relative to absolute space itself.

Later till the mid-19th century, the idea of absolute was untouched by any argument. Newton's laws have become pathfinders to reality until another philosopher/physicist, Ernst Mach, put his views regarding this analogy. He introduced a new bunch of questions and answers regarding this analogy. He asked:

What if we again return to that analogy and vanish even those distant stars acting as a reference and perform this analogy just in the void, nothing exists even to a vast distance of space, then was it possible to distinguish whether the bucket is spinning or not?

In clear terms, we know about any motion by taking something as a reference. Suppose we eliminate even the possible speck of matter (It seems sort

Like the possible fate of the universe, Big Rip, right? Well, it's not a matter of concern today!). Is it possible to benchmark any event as rest or motion? And the answers he came out with were:

No, It won't be possible to distinguish where the water level has been flat or curved. The presence of something is necessary for the distinction between rest and motion. But how?

To answer this question, let's get back to our empty-universe-bucket-analogy, now add some bunch of stars in the background as distant stars. Say, what would differ from the previous analogy, as given by Mach? We would be able to make out these stars as a frame of reference, which means the distinction between rest and motion would now become evident. What does it all mean to space?

Mach further argued that any motion is an outcome of the combined influence (or forces) of matter in the universe. He reasoned that the cothatshape of water is due to the resultant forces of even those distant stars on the cosmic horizon.

In this manner, Mach de-highlighted the topic of concern (as we did) of 'Space', and he was the last one who inherited the question of Leibni,z, and he was the one who pointed out that space has no mere existence without matter. Many physicists would have to be shut up to this realization of the bucket analogy because it was an excellent insight.

Decades passed, and the topic of concern also passed up to 'Absurdities of Classical mechanics and Electromagnetism'. The matter was thought that speed is relative by classical relativity, but in the dogma of Electromagnetism, the speed of light was seen as constant. Physicists expected that this speed should also be relative to something else (as you move through space is determined by an observer), so they did a cross-observation (what so known as Michelson Morley Experiment) and found something extraordinary. That was, whether you change your frame of reference to any velocity, you are always going to see light's velocity always be constant. And what we expected to be the medium of light through which it is mediated, the so-called was 'Aether', was not found to exist. This was a clashing and absurd result (as the Ultraviolet Catastrophe that led to the birth of Quantum Mechanics) found that beliefs and shared sense started to shatter. Is it so that something was wrong with the pillars of Classical Mechanics?

Maybe yes. And there comes ALBERT EINSTEIN! He thought, what if both theories were correct in their arguments, but there is something to do with fundamental thinking of space and time only? We know he got his five miraculously outstanding papers in the year 1905.

Two of them were upon Special Relativity. He envisioned two postulates for his theory:

• The speed of light is the same and constant in all the frames of reference; No matter how fast you propel your rocket fuel, you could never get light's view as a stopped fog of photons! 

• The laws of physics stay the same in all frames of reference. 

The very idea about space given by Einstein was that space and time were not as separated as Newton suggested. These two entities were fabricated into one. If an object is to move, so when we put a significant amount of force over it, it will get into motion and, in fact, move through time, as we all do. The groundbreaking phenomenon about space-time is that it is an absolute thing present all through the universe, and in any motion, the measurement of time and space gets local.

With the Special Relativity perspective, the bucket analogy, which was Mach's question, was now solved. Einstein showed the same thing as Newton, but there was a massive difference in entities. That was, Newton pursued the 'Absolutist' ideology and explained about separate absolute space and absolute time. But to Einstein, it was a thing of concern. The results of Special Relativity found that length and time are somewhat relative to different observers; that doesn't mean it indicates that everything is relative, but even worse, Space-time is absolute in itself.

The holes in Newton's argument led to his conception of 'Absolute space' shattered into pieces and followed even a far journey to 'Absolute Space-time'. But it was still not an end to Mach's argument; there is much more to it. As Mach envisaged that in an empty universe, there wouldn't be any realization of the spinning of a bucket, he also reasoned why it is so that we distinguish between rest and motion. He said that matter in our universe is responsible for any motion to get identified from rest. He attributed 'matter' as the convict of the whole heck but never reached up to gravitational influence as a reason. But this was the thing still nagging in the mind of Albert Einstein. His special relativity showed the world a revolution in the understanding of space and time in the constant motion of an observer. Still, in an accelerating frame of reference, the consequence leads to gravity as one feels much gravity while in acceleration. Gravity and acceleration are indistinguishable. This led Einstein to hang upon developing the framework of gravity. After ten years of publication of Special relativity, Einstein propounded humanity's most profound framework, The General Theory of Relativity. In GTR, he extended the idea of spacetime as they can curve, bend, and stretch like rubber sheets ( a very foolish analogy, but useful). It says that Matter or Energy can bend space-time and creates a curvature that we recall as the familiar force of gravity. In the last edition, I have included a statement from John Wheeler. Here's it:

https://youtu.be/a7uTKwbsFtg

"Matter/Energy tells spacetime how to bend, and Space-time tells Mass/Energy how to move.

With the perspective of GTR, Einstein showed that Mach's ideas were mature enough to shake Newton's theory but not that of Einstein's. Thus, we concluded that  No matter in which universe, you imagine yourself or your analogy to happen but the concave shape would take place due to spinning motion relative to space-time.

Skipping to Non-Classical Perspectives of Space

Although the General Theory of Relativity provides an elegant framework for the working of the cosmos, it has been tested to the extremes of the cosmic backyards but it is still a classical theory, it doesn't provide a quantum mechanical framework to quantize gravity. Meanwhile, Einstein amazed the whole world by realizing space-time. There was another spark that glowed in the 1900s, the birth of Quantum Mechanics. Einstein contributed to it by revealing some profound results of light quanta aka. photons. By that moment, a series of young physicists took up the task of reaching the fundamentals of understanding. Things would have been so easy if we applied classical mechanics, but when we observed the deep beneath the nature of reality of the smallest, we were blown away! The triumph of understanding reality was now demolished, Quantum particles were showing us some different kinds of things. Those were

• In the quantum picture of reality, any particle, we know of it, is both a wave and a particle in a dual state. We took some years to get to know that a wave function we get of a particle, is just probability waves! 

•  The particle has no meaning and sense in the smallest picture of reality. For example, if we know of an electron then it is not that like a hard mass with a specific charge but it is a field permeating all through space and the thing is that it gets collapsed when we make an observation. (A topic of the coming series, for sure.)

• If we ever tried to get to know about a particle's position, we would never be able to get to know about the velocity of the particle simultaneously and vice versa. This relation would now tell something much more fundamental about Energy. If we ever get to know about energy at a position in space, the less we will get uncertain about the span of energy, it lasts
  

The development of such principles and concepts led to further exotic and unbelievable results. When Schrodinger developed his elegant

equation for the wave function of quantum particles, it led Pauli to introduce the Pauli exclusion principle, in which he described that any 2 fermions (particles with half-integer spin) can't occupy the same state or position at a moment. Though, we have some cross results to this that, an electron in the atomic orbitals tend to have the same energy level and they might have a same state too. Pauli exclaimed, No if they have the same energy orbitals then that doesn't mean they would have the same position or state too, he introduced a kind of freedom from his strict principle that if it is so then electrons would have a difference in the intrinsic angular moment, what we call as spin. (Why are we talking about a Quantum world? Isn't this out of topic? Wait and read further)

Things were going still smoothly until a young British physicist named Paul Dirac took up the task of unifying Special Relativity with Quantum Mechanics. In doing so, he finally wrote up his equation but now, the equation needed more freedom of state (the same thing added by Pauli to adjust his principle to work) he found plus 2 freedom of states of the same spins but different charges. This changed the whole and sole of Quantum mechanics. He, at once, predicted the existence of antimatter purely by Mathematics. He imagined antiparticles were:

Particles tend to remain to settle at the lowest energy i.e zero, and he envisioned that all of 'space' is filled with particles settled at zero from a negative energy state and when a particle is in existence, that means it has positive energy. He envisioned that each particle would have its existing field and the particles with negative energy are Antiparticles. He thought if a hole in that sea of the particle would be created then it would have to be filled by positive energy particles and when it happens, particles and antiparticles come in contact and annihilate releasing photons.

He thought it was not correct but it went on to be one of the greatest realizations of space. The negative energy in the 'Dirac' Sea has nothing to do with negative mass or energy. When we apply the Energy-time

Uncertainty Principle (derived from Heisenberg Uncertainty Principle) to a perfect space as we see in Einstein's vision of space-time fabric, we get to know that any region of space could have non-zero value for some uncertain amount of time and vice versa. Thus, we concluded that space itself, space isn't that empty. So what happens?

        

At the most quantum levels, space would be enormously teeming with particles and antiparticles from space, annihilating each other into nothing. This kind of nature of space was so absurd that most of the physicists didn’t expect it then.

Skipping into the much deeper picture of reality

Space has been a foundation for classical and relativistic mechanics whereas, in quantum mechanics, it has become a playground of all heck. Can there be an even more fundamental analysis to space itself? Oh, yes. But to move further, I must mention it’s all in theory and not yet observed.

One thing which we didn’t take seriously are dimensions. Newton's absolute space was of 3 dimensions and we were wholly satisfied by these dimensions until this familiar idea was not challenged by 25 years old patent clerk, Albert Einstein. What he envisioned about space and time was that both were connected, for example, when observed, an arrow shot by an archer would now take a parabolic shape in 3 space dimensions but what about time? If we take this event in several instant moments placed one by one then only it will constitute an event. By that moment, Einstein entwined the fabric of the cosmos. But no one has ever asked, what if we would add some extra dimensions to our picture of reality? This was asked by Theodore Kaluza. With his insight, he wondered if we could extend one another dimension of space in the same way Einstein did with time. When he published his paper regarding the possibility of extra dimensions, it sent shockwaves to physics world. Still there was a lot of holes in this theory.

If we try to take an intuitive sense of dimension then it is an extension for an object to move in. Space is not a dimension but also can't be defined without dimensions, if we draw a line on a blackboard then it seems a 2d distance but what if we extend one dimension, it would look as if we have got another way to look things and to analyze things much better in 3 dimensions. The question was remain blinded by some staggering results of Quantum Mechanics until 1926 when Oskar Klein it by stating, There could be extra dimensions but we won't be able to observe them, it as if a man is to walk on a rope then for him, it's a one-dimensional string but to an, it's a whole extra dimension in the curls of rope. He showed that the 5th dimension of space could be wrapped and curved up to the smallest scales possible, to the Planck scales. What he imagined and took Kaluza's idea to that level of functionale is that one can get to the point that until you don't have observations, you can't prove it wrong.

What if our familiar three dimensions: length, width, and altitude, are to be used to locate a particle or any individual exactly? It would seem like an easy task by taking xyz axes as dimensions to carve out

particles' position in space but there is no means of it until the time is added. We usually ask, At what time? This is what time has meaning and sense itself, hence, it's a dimension as Einstein exactly contemplated. As Klein theorized, he said that the same rope dimensions would be curved at small scales, so it would be only one dimension far off the location. Same as with reality, our fifth dimension aka. the fourth spatial dimension would be curved up to Planck scales like circular dimensions. If we now locate a particle then the coordinates would be x1, x2, x3, x4 (the rolled-up dimension with smallest scales), t. Then, why don't we add just that dimension, x4? Well, the reason is that its numbers would be of no sense because their presence is too mere.

Although Kaluza Klein's theory was soon forgotten as it floated in hypotheses and didn't catch that much concern until the age began to take a different flow!

The Heck with Quantum Vacuum

The discrepancies we meet between the operations of the quantum world and the physical world are wholly out of sense. We do not see the stars as being at many places simultaneously, we don't use probability to predict future events. The very familiar discrepancy is The quantization of gravity. The union of the Quantum Uncertainty Principle with the General Theory of Relativity was producing absurd results about every fundamental aspect of space.

            

In GTR, we acknowledged that space-time can bend, wrap, curve, wave, or a ripple-like wave in presence of mass/energy, we know any mass exerts gravity or mass creates curvature or what we can say gravity. If we apply the uncertainty principle to GTR, so as we know, fields of different energies undulate at the smallest moments, our smooth representation of space macroscopically wouldn't be the same at the finest scales. As we know matter and antimatter pairs come in and out at the smallest scales and these are ripples of those energy fields causing space-time to boil up and forth like never before.

There was such a clashing moment that remained up until we tried to explain the universe's by far, the most truly defined framework, The standard model of particle physics. Gravity was once expelled by the picture of reality in this model because of its least interaction and observational pieces of evidence at quantum scales. Time went on, revealing a whole new set of theories to emerge- The Birth of String Theory and M-Theory.

The Tale of Strings and Branes

The discontent among the physicists towards the most observational model, The Standard Model was due to the exculsion of gravity. It led to formulation of a new theory, The String Theory. What they introduced was:

Even the fundamental elementary particles are not fundamental; they are the different notes of a single string vibrating in extra dimensions. (This is wholly weird by far!) Strings are fundamental to everything and what we knew about space has now become the actor of the picture of reality!

        

Physicists like John Schwarz and Joel Sherk took a new journey to introduce a new particle or boson named Graviton. While devising the mathematics they predicted this particle would be the quanta of gravity. It paved a whole new way to understand the fabric of the cosmos. String theory was devised to predict a massless boson with a spin of two, as Schwarz and Sherk calculated but string theory even leaped for explaining the sets of laws in its meaning. With the evolution of String Theory in the 1980s, it began producing research beyond observant with pure mathematics.

The number of dimensions checks upon strings' vibrational patterns to create particles of several properties. Same as Klein did with the fourth dimension of Kaluza, the need was to compress extra dimensions in one curved, curled space at the Planck scales. This came to be known as 'Calabi-Yau Space'. In each calabi-Yau space, there would be a string vibrating back and forth to be recognized as a particle!

Another idea originated from String Theory was 'Supersymmetry' (A topic for another time). As this grew up, string theory itself divided up into 5 parts, each having its conception of reality. The number of dimensions was now becoming more diverse even causing more disparity! What Kaluza thought and Klein did, was a unification at a higher dimension. But, as time went on, one of the theory made a claim about 26 dimensions while the other said ten. When the problem with the dimensions grew, it was lastly settled at 10 dimensions i.e, 9 spatial plus time. Still, it lacked an elegant framework that can unify these five separate theories. The theory came out to be, The M-theory.

The mathematical-genius physicist, Edward Witten along with his colleagues, when looking upon the argument of 5 different parts of string theory, found something translational, something elegant in the picture of reality. 

What they did by introducing M-Theory was that they added one extra dimension of space making 10 to 11, making the whole thing lucid and translational. Introducing M-Theory was a deed of taking theoretical physics to that elegance that no one could imagine. Mathematics carved out something more scary results into the theory, what it did was:

All the space we know of it is the foundation of the most elementary bits of energy, Strings. But, the most important thing about String Theory was that it was not a theory of strings, there is much more to it! Starting with its name, 'M', perhaps, stands for 'membranes' and what much was thought about string theory in M-Theory was to predict the existence of another ingredient of string theory, called 'membranes' or simply, 'branes'. In string theory, we learnt about a particle, say 'graviton' which is just a loop of the one-dimensional string vibratinjust g, with the factors of lowest-ever-possible frequencies, in what? Space. What M-theory imagined was there is another so-called ingredient called, 'p-branes'. Here, 'p' stands for a whole number less than 10, which refers to the number of dimensions. Branes of different dimensions would act like a stage of a dance of one-dimensional strings as we knew that they were bound to a Calabi-Yau space including extra dimensions, wrapped giving strings more diversity. Say, if a brane would be 2 dimensional then string would seem like frothing one-dimensional threads. If a more energetic string would exist then, its frequencies would be higher and it would be larger than that of a graviton. This reminds us that if a string could be enlarged then why not the branes? If a one-dimensional brane would be enlarged to infinity then it would seem like a wire of no width, but for that, it would require enough energy. Same with 3-dimensional branes, if it were to be enlarged to infinity then could we be able to differentiate our space with 3 dimensional brane?

The simple answer would be, 'No'. Think about how the universe started, the expansion of 3 dimensions, with energies of Planck scales. Could this be the reason why our universe is 3 dimensional, headed by time? We actually don't know how the Big Bang occurred, but the idea fits well that our universe could also be a brane, and all the particles we ever interacted with and loved, are just confined to our 3 brane worlds only! What we know about time, is the least. But it can be visualized that the 3-dimensional universe is dictated by time. Opening even great riddles of M-Theory reveals that our universe could be a 3-brane floating over small ones and stacked upon higher and higher branes.

So, what's the space?

This has been a long journey when we have passively interacted with space and then at present, made them the guardian of everything. Space is not just defined by its dimensions, it includes even strings giving rise to being confined to that universe or you may say, to that brane-world only. The very idea of space is so elementary that even string theory made this passive until the wonderful framework of M-Theory. But, the very nightmare that dreads a string theorist are all about experiments. So far, however, we have another gate to physics but it won't be that much real until we prove it with our observations. It still seems like a dictator ruling over the possibilities. Mathematics, by far, has reflected many of the unintuitive results of the universe. And when it comes to being applied over 'out-of-the-universe', it seems it fits quite well. Space, time, and Energy could be the elementary terms to be questioned, no matter where it leads but we need it!

Thanks for getting yourself here! Love your universe! It's quite important beyond all priorities!

        - Adityadhar (MS22)