The promise of a Theory of Everything (v1.0)
In previous essays on science, I noted the
following. It might be a good idea to read them before reading this essay to
refresh.
1. There are four fundamental forces – gravity (or is this just
spacetime curvature?), electromagnetic force (includes electricity, magnetism),
strong nuclear force (forces that binds the atomic nucleus and its constituent
quarks together) and the weak nuclear force.
2. There are 4 fundamental particles that make up ordinary matter – electron neutrino, electron, up quark, and down
quark. The standard model of particle physics shows other particles that can
exists including a class of particles called antimatter which interacts with
its corresponding matter particle to annihilate each other into energy.
3. Energy and matter are convertible.
Energy converts from one form to another also.
4. There are four laws of conservation – energy, momentum, angular
momentum, and charge.
5. There are 4 states of ordinary matter - solid, liquid, gas and
plasma.
6. There are three fundamental theories – quantum mechanics, the
standard model of particle physics (which heavily uses quantum mechanics) and
special/general relativity. Higher level disciplines like chemistry, nuclear
physics, astrophysics, plasma physics, cosmology, thermodynamics,
electrodynamics, etc can be or already has been founded on these.
All I can accept is that some phenomenon whose nature is unknown, and cannot be answered by the scientific method, was the source of spacetime and matter and energy, and imparted into the universe, assembly instructions in terms of the well governed laws of physics, laws of chemistry, and the laws of biology and evolution. These shaped the primordial universe to what it is today – one with great order, connectedness, harmony, and beauty, yet complexity and richness, and a world teeming with intelligent humans on earth and likely intelligent beings on other planets too. Are these laws the guiding instructions put into the primordial universe by God that resulted in such order, connectedness, harmony, and beauty, yet complexity and richness? Doesn’t that signal the existence of an intelligence and possibly purpose? I leave that up to you to judge. Einstein said “God does not play dice” when first presented with quantum mechanics. That implies he believed in God and likely saw beautiful and elegant equations like E=MC **2 as the handiwork of this intelligence. This conception of God does not invoke causality, space, or time. It does not require faith. It makes no statement on shape or form. But does attribute intelligence, and observes the universe is intelligently put together. It should pass scrutiny by philosophers.
Einstein said “I want to know how god created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know his thoughts. The rest are details.” This blog is about his thoughts. It is about the BIG picture.
The particle physics standard model is the closest we have to a theory of everything today. We have three main groups of particles in matter and force - quarks, leptons and bosons. The quarks form a group of six particles called up, down, charm, strange, top, and bottom. Hadrons are composite particles that contains quarks and baryons are a subgroup that contain an odd number of quarks. Mesons consist of a quark, antiquark pair. As I explained previously, up, and down are the quarks that make up protons and neutrons in the nucleus. The next group is called leptons. They consist of six particles called electrons, electron neutrino, muon, muon neutrino, tau, and tau neutrino. In quantum mechanics, forces are represented by particles. In quantum mechanics, force is exerted by an exchange of a particle. It is like two boats facing each other. When a sack is thrown from one to the other, both boats will move away from each other!! This last group of 4 is called Guage bosons and represents force and are Z boson, photon, w boson, gluon. As explained previously, photons mediate electromagnetic interaction. Finally, we have the mysterious Higgs boson which is believed to confer mass to particles.
Quarks have a half integer spin. Up, charm and top quarks have charge of +2/3. The down, strange and bottom quarks have -1/3. Protons have 2 up quarks and 1 down. Neutrons have 1 up quark and two down. While other quark combination is possible, they decay rapidly. While up and down are stable, the others are not and live only a small fraction of a second. The up and down quarks have a mass of about 1/100th of a proton. The top quark is the heaviest. The bottom quark is next, and the charm quark is third and all three are heavier than a proton. The strange quark is a little less than the mass of a proton. Quarks feel the strong nuclear force/color. Quarks have a property called color – labeled red, green, and blue. Like Pauli’s exclusion principle, two identical quarks with the same color cannot be in a single composite particle. We have never been able to isolate a single quark alone so far. Scientists call this quark confinement. When we try to pull it apart from a composite particle, it stretches like a rubber band and breaks and the energy released results in a quark, antiquark pair. One of the new quarks is pulled back into the composite particle and the other new quark (an antiquark) along with the original quark being pulled forms a new meson particle with two quarks - a quark/antiquark pair. Quarks experience all three forces - strong, weak and electromagnetism.
Almost all the mass of an atom is the nucleus. Protons and neutrons are heavy. But if you add up the mass of the quarks inside them, they only contribute a small amount. It turns out the binding energy that binds the quarks when converted to mass is the biggest part of the mass.
The leptons are much lighter. They have a half integer spin. You can think of muon and tau as heavier versions of an electron. They all have a charge of -1. Electrons are stable, but tau and muons are not and live only a small fraction of a second. They experience the weak and electromagnetism force. The three neutrinos only experience the weak force. They pass through matter without interacting!! Over quadrillion neutrinos pass through you every second!! Mass of a neutrino is close to zero. They are ghost like.
Now let us look at the force particles (gauge bosons). They have an integer spin. The photon mediates the electromagnetic force. It has no mass. When two electrons bounce off each other, one electron shoots a photon at the other. The gluon mediates the strong force. Gluons like quarks experience confinement but have zero mass. The W and Z bosons mediate the weak force and are massive.
There is a hypothetical particle called graviton that would mediate gravity, but it has not been discovered, and the standard model currently does not include gravity. The best theory of gravity we have today is general relativity where spacetime is like a trampoline that is warped by a mass or energy blob on it. This creates a depression, and the motion of other particles near it can be explained by this depression.
That leaves the Higgs boson. This was proposed in 1960, but only very recently discovered in 2012. It has a spin of 0. Mass isn't an easy concept. We tend to equate it with weight, but that is really a measure of gravitational attraction, even though the terms weight and mass are often used interchangeably. A proper definition of mass relates to inertia, in the sense of how much an object resists acceleration when a given force is applied to it. A bicycle has a certain inertial mass; a 50-car freight train, much more so. Named after theorist Peter Higgs, one of the people who predicted its existence, the Higgs field is what gives particles inertial mass. Neither force nor matter, the Higgs field is unique among quantum fields in having a finite intensity at all points in space, even in a vacuum when there isn't enough energy for its particle manifestation, the Higgs boson, to be present. The matter particles, as well as the W and Z bosons of the weak interaction, are effectively bogged down by the Higgs field to varying degrees, thereby acquiring inertial mass. Otherwise, they would be massless and move, like photons and gluons, at the speed of light.
There is a vast number of interactions happening and the full complement of the standard model particles must be used to explain them fully. Also please note that all force carrying particles and the Higgs boson are bosons and have integer spin while all quarks and leptons (what we think of as normal matter) are half integer spin called fermions. This points to some underlying symmetry.
There is a whole lot more to the standard model, but that is beyond the scope of this blog. The standard model reduces everything to 6 quarks, 6 leptons, and the 4 force particles and the Higgs Boson. Add to those the corresponding anti particles. The force particles (except gravity) are unified to a partial extent because in the 70's it was discovered that all of them arise from a gauge principle and spontaneous symmetry breaking (beyond the scope of this blog to explain). The symmetry breaking results in them having different properties. A Higgs boson is required to mediate the Higgs field that it happens in.
While the standard model explains the subatomic very well, there are at least 19 parameters that we cannot derive from first principles that must be entered by hand. Also, it does not explain dark matter and dark energy deduced by cosmologists that constitutes 95% of the universe. So, it is incomplete beyond just the fact it is missing gravity. But it is considerable progress and the closest we have to a theory of everything!! But there is still a long way to go. So let us truck on with our journey!!
Two major steps towards unification in more recent decades deserve special mention to show how we got to where we are today. These are quantum electrodynamics and electroweak unification.
The first successful attempt to blend quantum mechanics with relativity occurred with quantum electrodynamics which is a modern theory of how particles interact with electric or magnetic force and replaces the older electric/magnetic field theory. In 1927, Dirac laid the foundation with the Dirac equation which successfully blended quantum mechanics with special relativity and incorporated the spin of the particle involved. A profound outcome is it predicted the existence of antimatter. For example, it showed that both electron and positron (antimatter of electron) existed. Positron was discovered in 1932. We now know that all forms of matter have antimatter. Matter and antimatter are essentially identical except for charge which is reversed. Matter and antimatter annihilate each other with a huge burst of energy (given by E = mc**2). Quantum electrodynamics describes the interaction between electrically charged particles and the mathematics is based on the Dirac equation. For interaction, they are constantly emitting and absorbing (exchanging) a bath of photons with different probabilities. The average of that all approaches the smooth classical picture of the electric and magnetic field. Richard Feynman was the key contributor and was one of the Nobel recipients in 1965 for this. Quantum chromodynamics used this as a model and was another major success and describes the interaction of quarks mediated by gluons.
An example of weak force is beta radiation in radioactivity. A major success was the unification of the weak force with the electromagnetic force. It was shown in 1968 that the Higgs field combined with 3 particles (which were later detected as W-, W+ and Z boson. Higgs boson that mediates the Higgs field was detected in 2012 which put in place the final piece) resulted in the forces of electromagnetism and the weak force. This is called the electroweak theory that showed both had a common origin. When this was finally verified, the two forces were unified as aspects of the same force.
What is dark matter? Astronomy
showed that estimation of mass of galaxy’s observed was substantially less than
the motion observed implied. The difference is called dark matter. Dark matter
is estimated to have 5 times more mass than observed ordinary matter in the
universe. Observation of a gravitational lensing effect in one instance showed
the dark matter was centered at the centers of two colliding galaxies. There is
a lot of speculation, but nothing proven. Could it be a new form of never seen
matter? It is critical to solve this for a theory of everything and an army of
scientists are working on this.
What is dark energy? We can measure the rate at which the universe is expanding by measuring the distance and speed of many galaxies. Distance can be measured by measuring the brightness of type A supernova in it. They have a known brightness. Speed can be measured by measuring the doppler shift of light from stars in that galaxy. In 1998, researchers observed that the expansion of the universe is accelerating. The gravity of the universe should have been slowing it down. Cosmological models showed that about 5 or 6 billion years ago, the expansion started speeding up. Ordinary matter and dark matter make up only 25 to 30% of the mass in the universe today. The rest is dark energy!! Dark energy is something unknown that pushes and accelerates the expansion. It is critical to solve this for a theory of everything.
Stephen Hawking discovered that black holes evaporate over time. As early as 1974 Hawking described how a black hole's mass and its temperature are inverse -- the smaller a black hole, the cooler it is, as Science Alert explains. This could only happen if a black hole emitted radiation, i.e., lost particles and mass. Such lost particles have come to be called Hawking radiation. But this is impossible, non-quantum physics would state, because a black hole's gravity is too strong. But it's not impossible if we take quantum mechanics into account, where a black hole loses particles non-locally, anywhere in the cosmos. This also concurs with the first law of thermodynamics -- energy can neither be created nor destroyed -- and brings us closer to a Theory of Everything.
Gravitational force is so incredibly weak compared to the electromagnetic force (the latter is 10 ** 36 stronger) that we will never be able to measure it in an atom with an experiment on its quantum nature. But it is necessary to explain what is happening at the center of a black hole, or when black holes merge when general relativity breaks down, or in the plank epoch in cosmology where general relativity breaks down. This explanation is necessary for a theory of everything. So, some new physics is needed – quantum gravity?. The development of this new physics is entirely a thought experiment. Cannot recrate the conditions inside a black hole or plank epoch in the lab.
There are four major theories that separately or together hold some promise towards a theory of everything and are being actively researched.
One theory is the MSSM (Minimal Supersymmetric Standard Model) which extends the standard model of particles and predicts new particles. But these predicted particles take incredible energy to produce in particle accelerators and have not yet been observed.
One theory predicts the
existence of a graviton to mediate gravity. This has not yet been observed. If it exists, it
is massless, electrically neutral, no color, with spin 2. It interacts with
mass and energy and other gravitons and has extremely low energy. This would
finally represent a particle for gravity that would further complete the
standard table.
One theory is superstrings.
This theorizes minute strings or hoops that vibrate in three space, one time
and 6 more dimensions. The extra 6 dimensions are small and constrained
(example a thick wire with a circumference, where one dimension is going around
the wire, or a point with a knot in a hoop). Each mode of vibration corresponds
to a particle in the standard model. This, if successful, would collapse all
the particles in the standard model to a common foundation and merge relativity
and quantum mechanics which further advances towards a theory of everything. I
have written a separate essay on superstring theory for more details.
Another theory is loop quantum gravity. Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. As a theory LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Plank Length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure. LQG is formally background independent. Meaning the equations of LQG are not embedded in, or dependent on, space and time (except for its invariant topology). Instead, they are expected to give rise to space and time at distances which are 10 times the Plank Length.
Superstring theory currently focuses on particles and forces in space-time (background dependent), while loop quantum gravity currently quantizes space-time itself. There is a third recent proposal that introduces stochasticity into space time instead of quantizing it. I wrote an essay on it.
We still have a way to go for a theory of everything and everything described by a single equation, but I am confident we will eventually get there. I am just as confident as a religious figure is confident there is God with the same amount of empirical evidence!! Another essay dwells into the opportunities and challenges of superstring theory.
Update sept 20, 2024: did a huge breakthrough in physics just occur with a single relativistic quantum mechanical equation to fully mathematically unify quantum mechanics and general relativity - in other words everything? Did all the constants in physics collapse into just two?? We need to wait for the mathematicians and physicists to fully vet the math first!! Wow!!
Here is the article: Magical equation unites quantum physics, Einstein’s general relativity in a first (msn.com)
Here is the math underlying the article: On the same origin of quantum physics and general relativity from Riemannian geometry and Planck scale formalism - ScienceDirect
Crisp mathematical formulation in physics is very important.
- After Newton's equations of motion there was a lot of advancement in Physics.
- After Einstein's equations of special relativity there was a lot of advancement in Physics.
- After Einstein's equations of general relativity there was a lot of advancement in Physics.
- After Schrodinger and other's equations of quantum mechanics there was a lot of advancement in Physics.
- After Dirac's equations fusing quantum mechanics and special relativity there was a lot of advancement in Physics.
- After these new equations fusing quantum mechanics and general relativity (once accepted) there will be a lot of advancement in Physics.
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