From bucket to branes: A quest to understand the meaning of space

In the early unilluminated times, space has never been a true matter of concern in our daily lives. Though it might have had some insights by philosophy and religion, in science, it had been neglected.  This has changed when Newton showed up his deep insights into the reality of space itself. Although he was pious by mindset he had never tolerated the misbehaviour with laws of nature. He was the one who first shed light on such a less-interesting topic, 'Space'. In contrary to this, many other mathematicians and physicists like Descartes or Leibniz, either never introduced about space or anything like this or rejected the notion of space as telling, "It has no independent existence". In result of this argument, he finally devised an analogy. Let's go through it!

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 spinning motion of bucket." Here's one video to summarize the whole thing upon:

Now, here's the thing that gets more weird, what if one would ask that this bucket is spinning relative to what? As you know, any object in motion or rest is because of a specific frame of reference or specific perspective. A person sitting at rest on a chair is at rest with another person sitting at rest too but to a person in motion would see the person with chair moving away from him! Same as if I would say, How can you differentiate the rest bucket and spinning bucket? The exact answer would be due to the curvature in the shape of the water level. Now, what if we go deeper to the concept and ask, "In relative to what, the shape of water level would change?" If we took the floor of the laboratory as a reference, vanish it! No any terrestrial example, let's do this in the oblivity of empty space only illuminated by distant stars! 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 to! He added that Absolute Space was the fundamental reference frame for anybody either at rest or in motion or while 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 any motion or rest exists then it is directly or indirectly relative to absolute space itself.

Later till mid-19th century, the idea of absolute was untouched by any argument, Newton's laws have become pathfinder to reality until another philosopher/physicist Ernst Mach put his ideas regarding this analogy. He introduced the 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 which were acting as a reference and perform this analogy just in the void, nothing exists even to vast distant of space, then was it possible to distinguish whether the bucket is spinning or not?

In clear terms, we tend to know about any motion with taking something as reference. If we eliminate even the possible speck of matter (Seems sort of like the possible fate of the universe, Big Rip, right? Well, it's not a matter of concern) then, would it be 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. Presence of something is necessary for the distinction between rest or 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 than previous analogy, as given by Mach? We would be able to make out these stars a frame of reference, that means the distinction between rest and motion would now become evident. What does it all mean to space?

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

In this way, Mach de-highlighted the topic of concern (as we did) of 'Space' and he was the last one who inherited the question of Leibniz 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 bucket analogy because it was an excellent insight.

Decades passed, the topic of concern also passed up to 'Absurdities of Classical mechanics and Electromagnetism'. The matter was, It was thought to be 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, so-called was 'Aether' was not found to exist. This was so clashing and absurd result (as Ultraviolet Catastrophe that led to the birth of Quantum Mechanics) found that beliefs and common sense started to shatter. Is it so that something was wrong in the pillars of Classical Mechanics?

Maybe yes. And there comes, ALBERT EINSTEIN! He thought what if both theories were right by their arguments, but there is something to do with fundamental thinking of space and time only. We know he had got his five miraculously amazing papers in the year 1905. Two of them was upon Special Relativity. He envisioned two postulates for his theory, that were:

• 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 stopped fog of photons!
• The laws of physics stay the same in all frames of reference.

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

With Special Relativity perspective, the bucket analogy which was question by Mach was now solved. Einstein actually showed the same thing as that of Newton's but there was a huge 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. With the results of Special Relativity, it was found, length and time are somewhat relative to different observers, that doesn't mean it indicated that everything is relative but even worse that, Space-time is absolute in itself. The holes in Newton's argument led 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 argument, there is much more to it. As Mach envisaged that in a completely empty universe, there wouldn't be any realization of spinning of the bucket and he also reasoned why is it so that we distinguish something between rest and motion? Actually, he said that matter in our universe is responsible for any motion is 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 constant motion of an observer, but in accelerating frame of reference, the consequence leads up to gravity. As one feels much gravity while in acceleration. In fact, gravity and acceleration are indistinguishable. This led Einstein to hang upon developing the framework gravity. After 10 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 as like rubber sheet ( a very foolish analogy, but useful). It says, Matter or Energy can bend space-time and it creates a curvature which we recall as the familiar force of gravity. In the last edition, I have included a statement of John Wheeler, here's it:

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

With the perspective of GTR, Einstein showed the that Mach's ideas were mature enough to shake Newton's theory but not that of Einstein's. Thus, we got to a conclusion: 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 General Theory of Relativity provides the elegant framework for the working of the cosmos, it has been tested to the most 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 realizing about space-time, there was another spark glowed at the 1900s, the birth of Quantum Mechanics. Einstein contributed it by revealing some profound results of light quanta aka., the photon. By that moment, a series of young physicists took up a task on reaching the fundamental of understanding. The thing 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! The triumph of understanding the 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 particle at a dual state. We took some years to get to know that a wave function we get of a particle, is just a probability wave!
• The particle has no mean and sense in the smallest picture of reality. For example, if we know of an electron then it is not that like hard mass with a specific charge but it is field permeating all through space and the thing is that it gets collapsed when we make out an observation. (A topic of coming series, for sure.)
• If we ever tried to get to know about particle's position and we would never ever 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 the position in space, the less we will get uncertain about the span of energy, it lasted!

With the development of such principles and concepts, it led to further even more exotic and unbelievable results. When Schrodinger developed his elegant equation for wave function of quantum particles, it led Pauli to introduce Pauli exclusion principle, in which he described that any 2 fermions (particles with half-integer spin) can't occupy same state or position at a moment but we have some cross results to this that, electron in the atomic orbitals tend to have same energy level and they might have the same state too. Pauli exclaimed, No if they have same energy orbitals then that doesn't mean they would have same position or state too, he introduced a kind of freedom from his strict principle that if it is so then electrons would have the difference in the intrinsic angular moment, what we call as spin. (Why are we talking about 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 a 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), in fact, 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 by just Mathematics. He what imagined about antiparticles was:

Particles tend to remain to settle at the lowest energy i.e zero, and what he envisioned that all of 'space' is filled with particles settled at zero from negative energy state and when a particle is in existence, that means it has positive energy. He envisioned that each particle would have its own 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 particle and when it happens, particle and antiparticle come in contact and annihilate releasing photons.

What all he thought was not correct but this came out to be one of the greatest realizations of empty space. The negative energy in the 'Dirac' Sea has nothing to do with negative mass or energy. When we apply Energy-time Uncertainty Principle (derived out of Heisenberg Uncertainty Principle) to a perfectly empty space as we see in the Einstein's vision of space-time fabric, we get to know that any region of space could have some non-zero value for some uncertain amount of time and vice versa. Thus, we came to a conclusion to space itself that, Empty space isn't that much empty. So what actually happens?

At the most quantum levels, space would be enormously teeming with particles and antiparticles from empty space, annihilating each other into nothing. This kind of nature of space is that much absurd that most of the physicists of that time have never expected such absurdity.

Skipping into a 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 you think, there could be even more fundamental analysis to space itself? Oh, yes. But to move further, I will say this is all in theory not yet observed that's not mean something not to be concerned.

The one thing we did not take seriously earlier is 'the presence of dimensions'. After all, 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 both were connected, say, for example, you see an arrow shot by an archer would now take a parabolic shape in 3 space dimensions (or spatial dimensions) but what about time? If we take this event in several instant moments of time placed one-by-one then only it will constitute an event. By that time, Einstein entwined the fabric of cosmos. But no one has ever asked, what if we would add some extra space dimensions to our picture of reality? (Originally questioned by Theodore Kaluza) With his insight, he wondered what if we would extend one another dimension of space as same as Einstein did with time. When his paper regarding the possibility of extra dimension to existing mathematically stable then it sent shockwaves to physics, but physicist even Einstein didn't have to get habitual of extra dimension to exist. Although he made his paper published there are a lot of flaws and question now just came out of this possibility, one of them, if they exist then where do they?

This was the somehow unintuitive question until we don't know what are the dimensions? If you will take an intuitive sense of dimension then it is an extension for an object to move in. Space is not a dimension but in actuality, space can't be defined without dimensions, if we draw a line on the blackboard then it seems a 2d distance but what if we extend one dimension, it would look like as  we have got another way to look things and to analyse things much better in 3 dimensions. The question was remain blinded by some staggering results of Quantum Mechanics until 1926 when another physicist, Oskar Klein answered the question by saying, There could have 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 functionality that one can get to 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 mean of it until the time is added. We usually ask, At what time? This is what time has meaning and sense itself, so, it's a dimension as Einstein exactly contemplated. As Klein theorised, he told that same as 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. 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 as because their presence is too mere.

Although Kaluza Klein theory was soon forgotten as this was just floating in hypotheses and this doesn'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 Quantum Uncertainty Principle with General Theory of Relativity was producing very absurd results about very fundamentals of space.

In GTR, we were acknowledged that space-time can bend, wrap, curve, wave, 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 uncertainty principle to GTR, so as we know, fields of different energies undulate at the smallest moments of time, our smooth representation of empty space macroscopically wouldn't be same at the finest scales. As we know matter and antimatter pair comes in and out at smallest scales and these are ripples of those energy fields which causing the space-time to boil up and forth like never before.

There was such clashing moment which 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 standard model because of its least interaction and observational 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 within the physicists towards the most observational model, The Standard Model, because of the expulsion of gravity into the laws led a rebellion to introduce a new (not that new, but reformed!) theory emerged, String Theory. The matter was to predict a particle for to quantize gravity as same like photons, and observations showed no friendliness towards it. After all, taking the concepts of Kaluza Klein Theory, physicists introduced a whole set of laws independent upon itself by the base of Mathematics, they introduced String Theory. What they introduced was:

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

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Physicists like John Schwarz and Joel Sherk took a new journey to introduce a new particle or boson named as Graviton. What they told about by the mathematics of string theory that this particle would be the quanta of gravity. But, they had never thought that they had paved a whole new way to understand the fabric of the cosmos. The string theory was devised to predict a massless boson with the spin of two, as Schwarz and Sherk calculated but string theory even leapt for explaining the sets of laws in its own meaning. With the evolution of String Theory in the 1980s, it began producing several types of research beyond the observation but pure mathematics.

Actually, the number of dimensions checks upon strings' vibrational pattern 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 has come to be known as 'Calabi-Yau Space'. In each Calabi-Yau space, there would be a string vibrating back and forth to be recognised as a particle!

One of another research by String Theory was 'Supersymmetry' (A topic for another time). As this grew up, the string theory itself divides up into 5 parts, each has its own 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 the higher dimension. But, when time went on, one theory says 26 dimensions while other says 10. When the problem with the dimensions grew up, it was last found that string theory settles down at 10 dimensions i.e, 9 spatial dimension plus time as a dimension. Still, it was lacking some type of need of a such an elegant framework which can talk with 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, they found something translational, something elegant picture of reality. What finally was considered about a number of dimensions was 10, including time too. Till to that extent, nobody even dared to increase the number of dimensions, and what they did by introducing M-Theory was just so. 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 can 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 just a theory of strings, there is much more to it! Starting out 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 a one-dimensional string vibrating, 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, refers to the number of dimensions. Branes of different dimensions would act as a stage of the dance of one-dimensional string 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 a 2 dimensional then the 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 as 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 energies. 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 had the universe started, expansion of 3 dimensions, with energies of Planck scales. Could this be the reason why is our universe 3 dimensional, headed by time? We actually don't know how actually the Big Bang occurred, but the idea fits well that our universe could also be a brane and all the particle, we ever interacted and loved, is just confined to our 3 braneworlds only! What we know about time, is the least. But it can be visualised that our 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 smaller branes and are stacked upon higher and higher branes.

So, what's space?

This has been a long journey when we have ever passively interacted to space and then at present, made them the guardian of everything. Space is not just defined by its dimensions because this includes even our strings giving rise to particles confided to that universe or you may say, to that brane only. The very idea of space is that much elementary that string theory even made this passive until we get a wonderful framework, M-Theory. But, the very nightmare that dreads a string theorists is all about experiments. So far, however, we have another gate to physics but it won't be that much real until we prove 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 does the way it leads to but we need it!

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Article derived from the E-magazine, Cosmic-Window! Author is same in both cases.