Early 19th-century physicists dealt with many strange phenomena, resulting in some remarkably advanced theories and experiments that advanced physics and our understanding of the universe.
Two of the most prominent theories we have of all time are the Quantum Field theory and the String Field Theory. Both of which, describe our reality. Quantum field theory explains all the forces in our nature and builds the basis of the standard model of particle physics. Earlier, it was very difficult for people to realize that light behaved both as a wave and ray (particles). This dual behavior of light led physicists to create theories on this basis. Several new phenomena such as the photoelectric effect and interference of light was explained by great scientists.
But there was one area that quantum mechanics was unable to explain: gravity. Particle physics couldn't explain gravity which was proven to be an attractive force by Newton. To explain this, another theory, the string field theory came into existence. This theory was initially used to explain very small particles, like protons and neutrons, called hadrons. Imagine a universe made up of strings that differed from each other only through their vibrations. It was a crazy idea to think of since it said strings vibrated at different positions and in different dimensions. There were more than 3 dimensions required for this theory to work. We only know four dimensions at present, the (x,y,z) and time (which was proved to be the fourth dimension). But according to the string theory, there are 6 other hidden spatial dimensions that we haven't yet discovered even through our best of experiments.
Then what help has this been to us? The string field theory can explain the phenomena of gravity which particle theory couldn't. The introduction of particles like graviton did not work out well in explaining the force of gravitation. Gravitons are considered as a hypothetical quantum of gravitational energy, stored as a particle, which were responsible for all the gravitational interactions in the nature. Can you even imagine particles can cause such force? But now you know it, it is just another mind-boggling quantum theory, hypothetical.
Both, the string field theory (which is often considered hypothetical) and the well established quantum field theory describe our reality in many aspects. That might hint you to ask, what reality are we talking about? Reality, in simple words, is everything we see around us, what constitutes the universe, us and our sole existence, whether or not we are real, or do not exist. The physical laws must be obeyed by such theories. So, both these theories model our universe in a mathematical framework, but their approach to the fundamental principles has different perspectives.
STRING THEORY
String theory says that, the most fundamental building blocks of the universe, are not those tiny particles (atoms), but 1-D "strings" which vibrate at different frequencies and in different dimensions. The different types of "combinations" of vibrations and dimensions describe all the matter, forces and energy in our universe. So, it's like describing the entire universe as a bundle of strings dancing around. Check out more on string theory here: The String Field Theory
QUANTUM FIELD THEORY
The quantum field theory is all about the excitations in fields, that is, the atoms or those tiny particles, are nothing but disturbances in the field of the universe. What do we mean by the word "field" here? Field in general refers to a region of space that is created due to the presence of any physical quantity which has the ability to create a field, for example, electric charges create an electric field, or simply, massive objects like the sun which has a massive gravitational field. So coming back to our quantum field theory, quantum refers to a very small and discrete form of energy which can be either absorbed or emitted. The term quantum was coined by a great physicist Max Planck in this theory. If you wanna know what quantum mechanics really is, we have a dedicated article written just on that subject here: What even is Quantum Mechanics?
We now know that both string field theory and quantum field theory are based upon special relativity and quantum mechanics precisely, both of which are mathematical frameworks to our reality. What's even interesting to know, is that the string theory isn't just one physics theory, there's actually a set of multiple string theories which are together a part of what's called the "M-Theory", which unifies all 5 consistent versions of the string theory and suggests that there's one "master" theory operating in 11 dimensions. And for the curious ones, the M in the M-Theory stands for a lot of things such as "Membrane", "Mother of all theories", and even "Mysterious" since it is one of the most mysterious theories in physics. Returning to Quantum Field vs. String Field, both theories can mathematically describe all the fundamental forces in the universe. But the thing is, QFT (Quantum field theory) is the most accurate mathematical theory we've ever had using which we can accurately predict and govern the motion of the fundamental and elementary particles, which according to Heisenberg's principle, is almost impractical.
The Why?
But then, why do we bother with other wacky ideas, such as string theory or M-theory, to describe our reality when we already have a well-established and successful quantum theory? The answer to this question is quite peculiar yet obvious: gravity. You see, the standard model of particle physics does not really explain the existence of the most fundamental force in nature, that is, gravitational force. Here is where string theory comes into play. According to it, there's a certain vibration which models a particle called a graviton, which is theorized to be the missing boson in the standard model of particle physics, that would carry the gravitational force, similar to the way photons carry EM waves, W and Z bosons carry the weak force, and gluons carry the strong force. But the thing is, the concept of gravitons is purely theoretical and has never been detected in real life. They are just the predictions of string theory.
Physicists thought that, through string theory, we could integrate gravity into quantum field theory using a mathematical framework based on the existence of gravitons, which would then be called the "Quantization of gravity"!
If we talk about the origins of string theory, it was originally theorized in the late 1960's to explain the strong nuclear forces that glue protons and neutrons together in the nucleus of an atom. But a more popular and accurate theory, called Quantum Chromodynamics (QCD), performed far better than this and achieved greater precision and accuracy. So does that mean the string theory was wasted? Well, not really, as you see; it provided other areas of interest, such as gravitons, which helped physicists theorize and complete the standard model of particle physics.
But the thing is, QFT isn't empty-handed when it comes to explaining gravity. It describes gravitons as excitations of the theoretical graviton field. QFT uses the help of what's called renormalization, where we deal with phenomena at an infinitesimally small scale as the name quantum suggests. Unlike QFT, string theory solves this issue of quantizing gravity but with the cost of extending our known dimensions to 11. This is a problem as these dimensions have never been detected. You might say then go find them, no? Well there's no lack of trying, its just that scientists have tried, tested and failed in doing so multiple times. So does that mean we should throw the string theory out and replace it with another wacky theory to explain our reality, our physics laws, our true nature?
Where Are The New Dimensions?
Well no, the inability to discover new dimensions, does not prove the string theory to be entirely incorrect. In fact, our physicists have come up with theories explaining where these missing dimensions could really be! One such theory is "Compactification". This means, as explains from its literal word meaning, is the shrinking down of new dimensions which are far beyond our capability to even notice. For example, take a sheet of paper, for an ordinary healthy eye, it looks like a flat 2D surface, but if we zoom in and look through its edges more carefully through some magnifying lens or microscope, we'll realise it also has a third dimension, right? Well this is what compactification is. What if there are multiple such hidden dimensions so small for us to even realise or notice, even at the sub-atomic level.
Another possible solution to this problem could be the existence of super dimensions or (mem)branes. The universe may have more dimensions, than we may have access to in reality. These might be isolated from our well known dimensions. We would have to look outside our local branes to actually see these extra dimensions. The thing is, determining the presence of such dimensions at such a small scale requires a lot of energy levels and technology which we are not yet capable of. Humanity is currently at a scale of 0.75 in the Kardashev scale of civilizations, far lower than what an actual futuristic world looks like. To know what exactly is this Kardashev scale, check out here: Alien Civilizations: The Kardashev Scale. So yes, not being able to detect small dimensions does not really make the math invalid.
The Baby and The Mother God
Let me give you another beautiful analogy. We humans think that we have discovered everything in this world, and nothing is hidden from us etc. Some even argue that gods do not exist, there is no life other than on Earth and many more vague arguments. Well lets take a simple analogy which will answer all your vague questions. Consider a developing baby in the mother's womb. For him, his mother's body is his universe. The food he eats, the water he drinks, the oxygen he breathes, all comes from his mother. But has he seen his mother yet? No. For him, there's some god who is giving him everything to survive in the womb even though he hasn't seen her yet. The god is his mother which he will meet only if he gets out of his so called "universe" i.e his mother's womb. Exactly how it is, we humans live on a small speck of dust called Earth and there is someone who's giving us everything, our Mother, our God. We've never seen her, but we know she exists. Using the same analogy, we can say that there are so many new things which the baby gets to know only after he comes out in this world, the same way there are so many things hidden from us, so many new dimensions hidden from us, just that we haven't seen them yet.
Maybe we could still work with the string theory, and keep on trying to detect these extra new dimensions! If we are able to do that, it would prove that the String theory is the ultimate superior model of our reality, our universe and that the QFT is just an approximation. This is exactly how Einstein proved that general relativity is a superior model of Newton's gravity, where general relativity is the more accurate and precise framework whereas the Newtonian model is a good approximation.
So what's the difference between QFT and string theory? In simple words, in QFT, particles are actually excitations in the quantum field which keep on oscillating. These particles are dimensionless and they vibrate in what's called the space time. Whereas in string theory, there's a 1 dimension string vibrating in at least 10 other dimensions! It can be an open or closed string just like a rubber band. It's scale is around the Planck scale, that is 10^-33 cm. Analogous to the strings of a guitar, just like how the frequency of the strings determine what sound and pitch it produces, the frequency of vibration of the strings in the string theory determine what type of particle it is. So each string can vibrate uniquely like different particles. One similarity in both the theories is, the amplitude of oscillation on both theories tell us about the number of particles.
The Problem
String theory can actually unify the standard model of particle physics with the general relativity which explains gravity. But general relativity is not a quantum theory and breaks down at the quantum levels. Nature could not be quantum for everything, but we want gravity to be quantum in order to make a unified theory of everything. The mathematics of string theory require 6 other dimensions because it wont work in just the 4 we currently have. In fact QFT can also theorize extra dimensions, but we don't need them because its mathematics works just fine in the 4 we have, as long as we ignore gravity. Quantizing gravity could potentially be one the hardest problems in physics which we are trying to solve. We can't just throw out a crazy sounding theory just based upon impracticality. The string theory has a good mathematical exercise, but a limited physical significance.
CONCLUSION
So all this boils down to the fact that our reality needs one unified theory to explain all the basic principles, including gravity, to understand what the true nature of our reality is. We exist as humans, is what we think, but we still don't know about our reality, what are we made up of, what exactly governs everything, how things work, how did we originate etc. These theories that we see are just a better and better mathematical approach to our existence and reality. We must keep exploring this until we hit the jackpot! Quantum mechanics is something nobody can understand.
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