Notes on Quantum Field Theory
Quantum physics is likely the underlying mechanism for universal consciousness.
Plants use quantum processes to efficiently convert light into energy.
All the electronics in the world is all based on ‘simple’ quantum mechanics.
Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons.
At the scale of atoms and electrons, many of the equations of classical mechanics, which describe how things move at everyday sizes and speeds, cease to be useful. In classical mechanics, objects exist in a specific place at a specific time. However, in quantum mechanics, objects instead exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B and so on.
In quantum physics, a particle does not exist in the way classical physics observes it, with a definite physical location. Instead, it exists as a cloud of probabilities. If it comes into contact with its environment, as when a measuring apparatus observes it, then the particle loses its “superposition” of multiple states. It collapses into a definite, measurable state, the state in which it was observed.
“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”
~ Tesla
Quantum Field Theory
String Theory
Multiverse
Special Relativity
General Relativity
Quantum Mechanics
Quantum mechanics emerged in the first two decades of the 20th century as the result of a key breakthrough by Max Planck in 1900. Planck discovered that a long-standing anomaly in classical physics – an example where theory and experiment clashed – could be resolved if we assumed that the whole of reality was “quantised” rather than continuous. You might say that the nature of reality is more like a CD than a vinyl record – at the smallest level, everything was divided into discrete little packets.
It took until 1926/27 for the complete mathematical theory to emerge, discovered independently by Werner Heisenberg and Erwin Schrodinger. But there was a problem. Quantum theory didn't make absolute predictions about the location and momentum of quantum entities. It only made probabilistic predictions. This sets up a clash with our direct experience of the world, since we do not experience a smeared out set of probabilities – we experience a material world filled with entities which have absolute positions and momentums, or near enough. How was this clash to be resolved or explained? This question caused a great deal of serious debate, but somebody had to come up with an answer everybody could rally around. That someone was Neils Bohr, and the compromise he came up with was called “The Copenhagen Interpretation”:
“At the quantum scale” everything behaves like a wave. Entities such as electrons and photons don't have fixed positions – they are in every possible place at once, obeying Schrodinger's wave function. Until, that is, they are “measured”. When you measure them then their probability-wave collapses and they turn into normal objects, with a specific position and momentum. The problem is that nobody knew what “measurement” actually means, and nobody could explain why reality behaved so differently at different scales, or where the cut-off point (“the Heisenberg Cut”) came, or why. Schrodinger believed this interpretation to be absurd, so came up with his famous thought experiment about a cat in a box – the unobserved/unmeasured cat ends up simultaneously dead and alive, provided whatever is “measuring” it is isolated from the system inside the box. Schrodinger didn't believe in dead-and-alive cats – he believed there was a fundamental problem with the Copenhagen Interpretation. Schrodinger later made clear that his own metaphysical views were in line with those which were mathematically justified 5 years later by the greatest mathematical genius of the 20th century – John Von Neumann. Arguments from authority suck, but it is worth taking a look at just how exceptional Von Neumann really was.
In 1932 Von Neumann published a book which is still regarded as the mathematical foundation of quantum mechanics (which was its name). In this book, Von Neumann claimed that the Heisenberg Cut was an entirely arbitrary invention which could not be mathematically or scientifically justified. The problem was that absolutely anything could qualify as a “measuring device” - from a geiger counter to a human eye. In other words the Heisenberg Cut could be anywhere, from the alleged measuring device to the conscious awareness of the human observer. Von Neumann mathematically proved that the entire universe could be considered as a giant quantum system, and the wave-function being collapsed by interaction with a conscious observer outside of the whole system. He didn't go for this solution because he was a mystic – he was considerably less mystical than most of his contemporaries. He went for this solution because it was clean and consistent, didn't involve any arbitrary assumptions, and didn't split physical reality into two radically different realms at different scales with no explanation of how or why. His theory was simply that the laws of quantum mechanics apply at all scales.
This is not the end of the story, but it is the most important part of it, at least as far as this essay is concerned. Although there is one other theory that is important, and that is the Many Worlds Interpretation. MWI (which comes in various versions) is the belief that the wave function doesn't collapse at all. Instead, all quantum outcomes happen simultaneously in an unimaginably huge array of different timelines. This theory, like Von Neumann's, gets rid of the notorious Heisenberg Cut and arbitrary “measuring devices”, but it implies that humans too, including their minds, also continually split. It has therefore also been dubbed the “Many Minds Interpretation”. MWI is what you get if you take the physics seriously, get rid of the measurement problem, but totally ignore the hard problem of consciousness.
There are no other metaphysical interpretations of QM that are less strange than these. Probably the most important is David Bohm's pilot wave theory, which creates a new class of physical object - quantum waves which exist alongside the particles and guide where the particles go. It is mathematically consistent with quantum theory, but these "pilot waves" are unlike any other entity proposed by physics, involving faster-than-light connections. This takes us down another rabbit hole called "non-locality" and leads us to Bell's Theorem, which proved reality is non-local, but this is more than enough for one post apart from to say that if you are interested in Von Neumann's interpretation the best book to read is Mindful Universe by Henry Stapp.
Topic Sections
Quantum Entanglement
Unified Field Theory
Dark Matter
Dark Energy
Quintessence
Negative Mass/Matter
Antimatter
The Standard Model
Quarks
Leptons
Bosons
Hadrons
Baryons
Mesons
Nucleons
The Higgs Field
Bose-Einstein Condensate
Gauge Theory
Hopf Fibration
Quantum Group
Dirac Equation
Dirac Spinors
Fermi's Golden Rule
Lorentz Transformation
String Theory
Consciousness
Interesting Articles
New Quantum Paradox Clarifies Where Our Views of Reality Go Wrong
The Farce of Modern Physics
Quantum Fields: The Real Building Blocks of the Universe
Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons.
At the scale of atoms and electrons, many of the equations of classical mechanics, which describe how things move at everyday sizes and speeds, cease to be useful. In classical mechanics, objects exist in a specific place at a specific time. However, in quantum mechanics, objects instead exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B and so on.
All the electronics in the world is all based on ‘simple’ quantum mechanics.
“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”
~ Tesla
In a nutshell, QFT is formulated in terms of oscillations at 0-dimensional points while string theory is formulated in terms of vibrational excitations of 1-dimensional strings.
If you look from a distance, the wobbling string looks like the field oscillation of QFT. if you look from a bigger distance, localized packages of field oscillations look like particles.
Quantum Field Theory
Since both quantum physics and relativity are incomplete theories, they may point at a deeper theory, a quantum field theory that represents an undivided wholeness in the universe.
Quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics, by treating a particle as an excited state of an underlying physical field.
A field essentially is an object that assigns a value for each point in space and time.
So if you have a set of properties that you are interested in, then the field would tell you what their exact values are for all of time and space.
A field something that fills space that takes on a value everywhere. For example, the temperature of the air in a room is a field at every point in space there is a temperature value.
The universe is full of fields, and what we think of as particles are just excitations of those fields, like waves in an ocean. An electron, for example, is just an excitation of an electron field.
Forces are made of fields. Particles are made of fields. Everything is made of fields. Vibrations and oscillations in these fields make everything.
Everything touches everything else and ‘communicates’ to its nearest neighbors not to the whole rest of the universe.
Fields are what reality is made of.
There is a field for every fundamental particle.
All the fields are coupled to each other.
These vibrating quantum fields interact with each other creating a quantum foam, churned up, in constant motion.
One vibrating field can affect another one, transferring its energy into different fields.
Fields vibrating in different ways, transferring their energy from one to another.
If we think in terms of fields, the sudden appearance and disappearance of new kinds of particles and how one particle can change into another one starts to make more sense. (i.e. neutron decays into a proton, electron and neutrino for example.
What we observe can be very different from what actually exists.
Often what we observe comes in discrete amounts, called quantums.
Reality is a combination of all the observable possibilities, combined into a single wave function.
The wave function is what exists but we can’t observe it directly without collapsing it into individual particles of energy.
Particles are merely bubbles of froth, kicked up by underlying fields.
These particles are vibrations in the associated quantum field.
Each particle is simply a quantum oscillation.
Particles are what we see, individual quanta of energy, like a photon.
The energy and excitation of one field transfers to others as they vibrate against each other, making it seem like new types of particles are appearing.
The mass of a particle is just the energy required to push the mass around, the energy to get a field vibrating is the mass of the article.
What’s really happening in LHC collisions is that especially excited excitations of a field—the energetic protons—are vibrating together and transferring their energy to adjacent fields, forming new excitations that we see as new particles—such as Higgs bosons.
The Higgs field interacts with other fields, giving them—and, by extension, their particles—mass.
Mass is just an oscillation in the Higgs field.
Elementary particles like electrons and quarks gain mass from the surrounding Higgs field. (Not protons as they are not elementary)
The Higgs boson (which decay in one zepto-second)itself is what makes life itself possible.
Quantum Field Theory explains:
Quantum Tunneling
Superposition
Entanglement
String Theory
The 11 multiple dimensions may appear to us as new quantum fields
Multiverse
Many world interpretation of quantum mechanics is that every quantum event splits the universe into multiple branches which never interact with each other.
Inflationary multiverse (string theory predicts this), there are regions so far away from us where light does not travel with different numbers of dimensions and where different laws of physics apply
Special Relativity
Required to understand QM as it provides the relationship between energy and momentum
The laws of physics are the same for all non-accelerating observers.
The speed of light within a vacuum is the same no matter the speed at which an observer travels.
Space and time were interwoven into a single continuum known as space-time.
Events that occur at the same time for one observer could occur at different times for another, time dilation.
Energy is equivalent to mass.
E=MC2
Michelson-Morley (testing of the aether was a master reference frame) interferometer experiment proved the speed of light is identical from all measured reference points
General Relativity
Factors gravity into the relativistic view of the universe.
The key concept is the equivalence principle, which states that gravity pulling in one direction is equivalent to acceleration in another.
This is why an accelerating elevator provides a feeling of increased gravity while rising and decreased gravity while descending.
If gravity is equivalent to acceleration, then it means gravity (like motion) affects measurements of time and space.
This would mean that a sufficiently massive object like a star warps time and space through its gravity.
Einstein's theory altered the definition of gravity itself from a force to a warping of space-time.
Quantum Mechanics
Quantum mechanics (QM – also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.
Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales.
Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter.
Quantum mechanics is the non-relativistic limit of Quantum Field Theory (QFT), a theory that was developed later that combined Quantum Mechanics with Relativity.
The math works perfectly, the experiments coincide exactly with the theory but makes no sense, the theory fits the data beautifully it is obviously right but it doesn’t make a great deal of intuitive sense to us.
Starting with de Broglie’s matter waves, The Austrian physicist, Erwin Schrödinger, formulated an equation that describes how matter waves change under the influence of external forces.
Is Schrödinger’s wave equation, the thing that ‘waves’ is the nonmaterial matter wave amplitude, a mathematical entity called a wave function.
The Wave Function
In standard quantum mechanics, a quantum system such as a subatomic particle is represented by a mathematical abstraction called the wave function.
Physicists calculate how the particle’s wave function evolves with time.
Equation represent the possibilities that can occur in a system.
Mathematical expression that defines all possible observable states of a quantum system, such as the various possible locations of a particle.
It's important to realize that in Bohr and Heisenberg's interpretation of quantum mechanics (Copenhagen), the wavefunction is something that represents epistemic knowledge about a system, it was never intended to represent the objective "state" of a system.
Von Neumann also emphasized that when the "collapse" occurs is arbitrary, and doesn't refer to any physical process.
The particles’ locations, are mere matters of chance, defined by a spread-out probability wave, until the moment of measurement, when the wave mysteriously collapses to a point, the particle “hops to”, and a single reality sets in.
Up until a measurement is made and the wave function collapses (whatever that means), there is no reason to attribute any greater a degree of reality to any of the possible states than to any other.
In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate.
It is the essence of measurement in quantum mechanics and connects the wave function with classical observables like position and momentum.
All points of reference are arbitrary; they are conveniences, they are non-existent in fundamental reality.
When we denote a point in space, it is actually the collapsing a fluctuating field of vibration into solid form.
The squared amplitude of the wave function of an energy field gives the intensity of the wave at that point, a measure of the concentration of the substance which is waving in the wave, in the quantum sense, this means the probability density of finding a particle (photon, electron) at a certain point.
As for matter waves, we don't know what is actually waving.
The wave itself is matter, so we can't speak of matter waving in a matter wave.
That is why we've got a mathematical entity called wave-function which does the same function as amplitude of the wave.
The probability density is the square of the wave function
Squaring this we get the intensity i.e. probability of finding the material particle per unit volume at that point.
This probability/vol is nothing but probability density.
It’s not that the quantum system is actually in one or other of these states but we don’t know which; we can confidently say that it is not in any one of these states, but is properly described by the wave function itself, which in some sense “permits” them all as observational outcomes.
Wave function collapse seems to be demanded in order to connect quantum theory to reality.
Where, then, do they all go, bar one, when the wave function collapses?
If you’re not confused, you’re not paying attention.
In the 1920s, Bohr persuaded most of his contemporaries to embrace the weirdness of a probabilistic universe, the inherent fuzziness of nature, and the puzzling wave-particle duality of all things.
But some physicists objected, Albert Einstein and de Broglie among them. Einstein doubted that God “plays dice.”
It is the wave nature of matter that keeps atoms apart and gives bulk to matter in the world around us. Otherwise, everything would collapse and there would be no matter as we know it.
There are a wealth of interpretations of quantum mechanics, and almost all of them have to do with what happens to the wave function upon measurement. Take a particle’s position. Before measurement, we can only talk in terms of the probabilities of, say, finding the particle somewhere. Upon measurement, the particle assumes a definite location. In the Copenhagen interpretation, measurement causes the wave function to collapse, and we cannot talk of properties, such as a particle’s position, before collapse. Some physicists view the Copenhagen interpretation as an argument that properties are not real until measured.
Quantum Entanglement
Einstein referred to quantum entanglement as “spooky action at a distance,” and it is one of the strangest phenomenon’s in quantum mechanics.
Put simply, when two particles are allowed to interact in close proximity, they influence each other’s basic properties, such as their spin, polarization, momentum, etc. When these particles are separated, a change to one particle results in a corresponding change to the other at the exact same time. No matter the distance, the particles are intimately connected in a way that has to be fully explained.
For example, when electron A interacts with electron B, one will take on an up-spin state, while the other takes on a down-spin state. Any change in the spin of one instantaneously affects the spin of the other, regardless of distance. In fact, researchers have demonstrated this between entangled particles separated by over 1,200 kilometers.
Unified Field Theory
Quantum Field Theory plus Gravity
Waves and Ripples and Vacuum Fluctuations within Quantum Foam with particles and anti-particles appearing and disappearing
Cosmologists believe about 70 percent of the universe consists of dark energy, 25 percent is dark matter, and only four percent normal matter (the stuff that stars, planets and people are made of).
Dark Matter
Dark Matter 25%
A particle(s) we haven’t yet discovered
The rest - everything on Earth, all normal matter, everything ever observed with all of our instruments anywhere - adds up to less than 5% of the universe.
Come to think of it, maybe it shouldn't be called "normal" matter at all, since it is such a small fraction of the universe.
As far as we know, regular matter, regular mass, nothing special happening in the gravity department, but doesn't participate in the EM force, just like neutrinos don't, (so we've seen this property before) except we're quite sure they're not neutrinos. Could just be a hitherto unknown conventional particle, could be something more interesting. We don't know.
Dark Energy
Dark Energy 70%
We don’t know but it Does not dilute away as energy expands so it is not a particle, the amount of dark energy stays the same as space expands, empty space itself has energy, which is enough to make the energy accelerate
The name for the fact that as the energy/mass in our universe fuels the further expansion of said universe, "creating new space" between any and all points in space (I know some people don't love this analogy) as it goes, that "new space" comes into existence with a fixed, constant amount of new energy. Without dark energy the expansion of space would be like spreading the same amount of butter over an ever-growing piece of toast, with dark energy, new butter is being brought in with each growth. Thus the expansion, which is related to the amount of butter per area, is accelerating.
Could be the same as the cosmological constant according to Penrose and others
Quintessence
Though dark energy constitutes about 75 percent of the universe, scientists don't know exactly what it is.
They've developed several different ideas, including the theory of "quintessence," which proposes a sort of anti-gravitating agent that repels rather than attracts.
The mysterious dark energy that's driving the universe's accelerated expansion may have its roots in the background "vacuum energy" that pervades all of the cosmos.
In physics, quintessence is a hypothetical form of dark energy, more precisely a scalar field, postulated as an explanation of the observation of an accelerating rate of expansion of the universe.
Gravity
The fundamental axiom of science is that the Universe is describable using discoverable patterns that are subject to human analysis. Quantum mechanics is far and away the most successful theory of the Universe ever devised. However, it completely omits the effects of gravity, which are generally either grafted or spliced in where that is possible (e.g. Hawking radiation). Understanding the interaction between systems well described by quantum theory and gravitational systems requires a self-consistent pattern/theory that encompasses them both.
Classical mechanics had a similar problem 110 years ago: Maxwell's Equations very clearly and obviously described electromagnetic phenomena, and were highly precise and accurate. Newton's Laws of Motion very clearly and obviously described mechanical phenomena, and were also highly precise and accurate. But the two descriptions of nature are incompatible, because Newton's Laws remain unchanged under Galilean transformations, while Maxwell's Equations remain unchanged under Lorentz transformations. This means that the predictions of fundamental physics would be different (as in inconsistent, as in wrong) when compared between a setup in a stationary laboratory and similar setup in a moving laboratory. It took Einsteinian relativity to break that logjam and render mechanics and electrodynamics mutually consistent.
A similar kind of revolution is now needed to make gravity and quantum mechanics mutually consistent, because their predictions can be made to align in certain cases but then they disagree in others or yield no answer in still others.
Negative Mass/Matter
A physics bending concept that comes from saying "you know, if this value in this equation COULD be negative, this math would predict some very interesting things happen".
We have no reason to suspect it CAN be negative, we have never observed it, we have never thought it might exist, we have just commented that if it DID exist, it would do some very interesting things.
Antimatter
Opposite CHARGE (and a couple other numbers parameterizing a state), same mass as regular matter, (as far as we know, the quantities we produce are quite small so it's hard to "weigh"), nothing special happening in the gravity department. Not particularly exotic, we make it and work with it all the time.
https://www.youtube.com/watch?v=gEKSpZPByD0#action=share
The Standard Model
The standard model is a theory that describes two fundamental classes of particles fermions and bosons.
· Fermions (quarks and leptons) are the basic building blocks of all matter.
· 12 elementary particles (plus all have associated anti-particles)
Quarks
o 6 quarks
§ Up
§ Down
§ Charm
§ Strange
§ Top
§ Bottom
Leptons
o 6 leptons
§ electron
§ electron neutrino
§ muon
§ muon neutrino
§ tau
§ tau neutrino
The neutrinos change flavors between them (electron/tau/muon), they oscillate into each other back and forth
Bosons
o Bosons are force carrying particles that mediate the interactions between fermions (quarks and leptons)
o 6 force carrier particles
§ photon
· electromagnetism
§ W boson
· weak interaction
§ Z boson
· weak interaction
§ gluon
· strong interaction
§ Higgs boson (a vibration in the Higgs Field)
· mass
§ graviton (hypothetical)
· gravitation
Our universe are these 18 fields interacting with each other, oscillating rippling and interacting with each other, interlocking, swaying together.
Hadrons
Hadrons refer to any particle made of quarks.
Baryons
Baryons are formed by 3 quarks.
Mesons
Mesons are formed by quarks and anti-quarks.
Nucleons
Nucleons are a sub-class of Hadrons, protons and neutrons.
All normal matter (atoms) is made of only three types of fermions.
1) up quarks (two up/one down is a proton)
2) down quarks (two down/one up are a neutron)
3) electrons (type of lepton)
All atoms made of nucleons (subclass of hadron) and electrons.
All elements made of atoms (hadrons (protons, neutrons) and electrons).
All molecules made of elements.
All compounds made of molecules.
Under the Standard Model, elementary particles (only 4% of the known universe)— that is, those that cannot be split up into smaller parts — are the building blocks of the universe.
· All the known matter particles are composites of quarks and leptons, and they interact by exchanging force carrier particles, bosons.
· Quarks and leptons are the basic building blocks of the building blocks of matter.
· Quarks and leptons make up a category of sub atomic particles called fermions.
· Fermions are the building blocks of matter.
· By contrast, bosons are the other major category in the Standard Model and are messenger particles for the four forces of nature in addition to the Higgs boson, which causes mass.
· Each of the four forces results from the exchange of force-carrier particles.
· The strong force is carried by the gluon
o Gluons are the bosons that hold all the quarks in place so that protons and neutrons can co-exist in the nuclei of atoms.
· The electromagnetic force is carried by the photon.
o Photons are the messenger bosons for the electro-magnetic force.
· Graviton is theoretically the force-carrying particle of gravity, but it has not been found yet.
· The weak force is carried by the W and Z bosons.
· Fermions are elementary particles whose spin, a quantum property related to rotation, is expressed in odd multiples of the fraction 1/2, and they include both quarks and leptons.
o Among the leptons are electrons, muons, tauons, and their associated neutrinos (as well as their antiparticles).
o Protons and neutrons, common non-elementary particles, are also fermions.
· Bosons, in turn, are particles with integer spin values.
o They include the particles responsible for forces (photons, carriers of the electromagnetic force; gluons, carrying the strong nuclear force; W and Z bosons, carrying the weak nuclear force), as well as the Higgs boson.
There are exactly 17 elementary particles in the current standard model.
They are the six quarks, six leptons, four (force carrier) vector bosons, and one scalar (Higgs) boson.
For each kind of matter particle there is a corresponding antimatter particle.
So we have 29 including 6 quarks, 6 leptons, 6 antiquarks, 6 antileptons, and the 5 force carriers, which matches the chart…..gravitons would make 30.
The quarks make up another 100 or so mesons (two color bound quarks) and baryons (three color bound quarks).
Many of these have been observed, while some are predicted but have not yet been observed.
Scientists haven't seen any indication that there is anything smaller than a quark, but they're still looking.
There are six types, or "flavors," of quarks: up, down, strange, charm, bottom and top (in ascending order by mass).
In different combinations, they form many varied species of the subatomic particle zoo.
For example, protons and neutrons, the "big" particles of an atom's nucleus, each consist of bundles of three quarks.
Two ups and a down make a proton; an up and two downs make a neutron.
Changing the flavor of a quark can change a proton into a neutron, thus changing the element into a different one.
Another type of elementary particle is the boson.
These are force-carrier particles that are made up of bundles of energy.
Photons are one type of boson
Gluons are another.
These particles were predicted by Nobel laureates Steven Weinberg, Sheldon Salam and Abdus Glashow in the 1960s, and discovered in 1983 at CERN.
W bosons are electrically charged and are designated by their symbols: W+ (positively charged) and W− (negatively charged).
The W boson changes the makeup of particles.
By emitting an electrically charged W boson, the weak force changes the flavor of a quark, which causes a proton to change into a neutron, or vice versa.
This is what triggers nuclear fusion and causes stars to burn.
The burning creates heavier elements, which are eventually thrown into space in supernova explosions to become the building blocks for planets, along with plants, people and everything else on Earth.
The Higgs Field
· The Higgs field is a field of energy that is thought to exist in every region of the universe.
· The Higgs is actually a field that permeates all of space and drags on every particle that moves through it. Some particles trudge more slowly through the field, and this corresponds to their larger mass
· In physics, when particles interact with fields, the interaction must be mediated by a particle. Interactions with the electromagnetic (EM) field, for example, are mediated by photons, or particles of light. When a negatively charged electron is pulled by the EM field toward a positively charged proton, the electron experiences the EM field by absorbing and emitting a constant stream of "virtual photons" — photons that momentarily pop in and out of existence just for the purpose of mediating the particle-field interaction. Furthermore, when the EM field is "excited," meaning its energy is flared up in a certain spot, that flare-up is, itself, a photon — a real one in that case.
· Along the same lines, the Higgs particle mediates interactions with the Higgs field, and is itself an excitation of the Higgs field. Particles are thought to trudge through the Higgs field (thereby acquiring mass) by exchanging virtual Higgs particles with it. And, the thinking goes, a real Higgs particle surfaces when the field becomes excited, flaring up with energy in a certain spot. Detecting such a flare-up (i.e. the particle) is how physicists can be sure the field itself exists.
· The field is accompanied by a fundamental particle known as the Higgs boson (aka The God Particle), which is used by the field to continuously interact with other particles, such as the electron.
· Particles that interact with the field are "given" mass and, in a similar fashion to an object passing through a treacle (or molasses), will become slower as they pass through it.
· The result of a particle "gaining" mass from the field is the prevention of its ability to travel at the speed of light.
· Mass itself is not generated by the Higgs field; the act of creating matter or energy from nothing would violate the laws of conservation.
· Mass is, however, "given" to particles via the Higgs field's use of Higgs boson particles.
· Higgs bosons contain the relative mass in the form of energy and once the field has endowed a formally massless particle, the particle in question will slow down as it has now become "heavy".
· If the Higgs field did not exist:
o particles would not have the mass required to attract one another and would float around freely at light speed
o gravity would not exist because mass would not be there to attract other mass
· Giving mass to an object is referred to as the Higgs effect.
· This effect will transfer mass or energy to any particle that passes through it.
· Light that passes through it gains energy, not mass, because its wave form doesn't have mass, while its particle form constantly travels at light speed.
Higgs Field vs the Aether
· The aether was considered to be at rest in a specific frame of reference, also called the preferred frame of reference.
· Measurements of the earth's speed against the assumed aether (in particular the famous Michelson-Morley experiment) giving a null result was the main reason for the development of Special Relativity.
o The Higgs field, on the other hand, is a Lorentz scalar field, and as such does not lead to a preferred frame of reference.
· The aether was considered to be the medium in which electromagnetic waves propagate, that is, the electromagnetic field was considered to be a property of the aether.
· The Higgs field, on the other hand, is a completely separate field which does not even interact with the electromagnetic field such as the aether which was the medium for EM waves, (if it would, the photon would have mass).
Symmetries play a huge role in physics because they are related to principles of conservation.
The principle of the conservation of energy involves symmetry with respect to shifts in time.
The principle of the conservation of momentum relates to symmetry of spatial displacement.
The principle of the conservation of angular momentum relates to rotational symmetry.
-
Bose-Einstein Condensate
· Of the five states matter can be in, the Bose-Einstein condensate is perhaps the most mysterious. Gases, liquids, solids and plasmas were all well studied for decades, if not centuries; Bose-Einstein condensates weren't created in the laboratory until the 1990s.
· A Bose-Einstein condensate is a group of atoms cooled to within a hair of absolute zero. When they reach that temperature the atoms are hardly moving relative to each other; they have almost no free energy to do so. At that point, the atoms begin to clump together, and enter the same energy states. They become identical, from a physical point of view, and the whole group starts behaving as though it were a single atom.
· Bose-Einstein condensates were first predicted theoretically by Satyendra Nath Bose (1894-1974), an Indian physicist who also discovered the subatomic particle named for him, the boson. Bose was working on statistical problems in quantum mechanics, and sent his ideas to Albert Einstein. Einstein thought them important enough to get them published. As importantly, Einstein saw that Bose's mathematics — later known as Bose-Einstein statistics — could be applied to atoms as well as light.
· What the two found was that ordinarily, atoms have to have certain energies — in fact one of the fundamentals of quantum mechanics is that the energy of an atom or other subatomic particle can't be arbitrary. This is why electrons, for example, have discrete "orbitals" that they have to occupy, and why they give off photons of specific wavelengths when they drop from one orbital, or energy level, to another. But cool the atoms to within billionths of a degree of absolute zero and some atoms begin to fall into the same energy level, becoming indistinguishable.
· That's why the atoms in a Bose-Einstein condensate behave like "super atoms." When one tries to measure where they are, instead of seeing discrete atoms one sees more of a fuzzy ball.
· Other states of matter all follow the Pauli Exclusion Principle, named for physicist Wolfgang Pauli. Pauli (1900-1958) was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics.
· It says that fermions — the kinds of particles that make up matter — can't be in identical quantum states. This is why when two electrons are in the same orbital, their spins have to be opposite so they add up to zero. That in turn is one reason why chemistry works the way it does and one reason atoms can't occupy the same space at the same time. Bose-Einstein condensates break that rule.
· Because particles in a Bose-Einstein condensate don’t obey the Pauli exclusion principle, they can be observed to all share the same wavefunction, leading to observable macroscopic phenomena such as an extremely high index of refraction.
· Because it’s functionally created from an extremely cooled down gas, if it were created in any appreciable amount and kept from reverting back to a standard state of matter— we might expect to see something similar to a mirage on a road as far as light and indices of refraction are involved, but using entirely different principles from the interaction between hot and cold air (that is, the principle of Bose-Einstein statistics for a large number of particles sharing the same quantum state).
· A Bose–Einstein condensate is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero.
· Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference, become apparent.
· A BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal air, to ultra-low temperatures.
Gauge Theory
· Gauge theories are important as the successful field theories explaining the dynamics of elementary particles.
· Gauge theory, class of quantum field theory, a mathematical theory involving both quantum mechanics and Einstein’s special theory of relativity that is commonly used to describe subatomic particles and their associated wave fields.
· In a gauge theory there is a group of transformations of the field variables (gauge transformations) that leaves the basic physics of the quantum field unchanged.
· This condition, called gauge invariance, gives the theory a certain symmetry, which governs its equations.
· In short, the structure of the group of gauge transformations in a particular gauge theory entails general restrictions on the way in which the field described by that theory can interact with other fields and elementary particles.
· The classical theory of the electromagnetic field, proposed by the British physicist James Clerk Maxwell in 1864, is the prototype of gauge theories, though the concept of gauge transformation was not fully developed until the early 20th century by the German mathematician Hermann Weyl.
· In Maxwell’s theory the basic field variables are the strengths of the electric and magnetic fields, which may be described in terms of auxiliary variables (e.g., the scalar and vector potentials).
· The gauge transformations in this theory consist of certain alterations in the values of those potentials that do not result in a change of the electric and magnetic fields.
· This gauge invariance is preserved in the modern theory of electromagnetism called quantum electrodynamics or QED.
· Modern work on gauge theories began with the attempt of the American physicists Chen Ning Yang and Robert L. Mills (1954) to formulate a gauge theory of the strong interaction.
· The group of gauge transformations in this theory dealt with the isospin (q.v.) of strongly interacting particles.
· In the late 1960s Steven Weinberg, Sheldon Glashow, and Abdus Salam developed a gauge theory that treats electromagnetic and weak interactions in a unified manner.
· This theory, now commonly called the electroweak theory, has had notable success and is widely accepted.
· During the mid-1970s much work was done toward developing quantum chromodynamics (QCD), a gauge theory of the interactions between quarks.
· For various theoretical reasons, the concept of gauge invariance seems fundamental, and many physicists believe that the final unification of the fundamental interactions (i.e., gravitational, electromagnetic, strong, and weak) will be achieved by a gauge theory.
Hopf Fibration
· Hopf math is required to explain symmetry in gauge theory
· We generalize gauge theory on a graph so that the gauge group becomes a finite-dimensional ribbon Hopf algebra, the graph becomes a ribbon graph, and gauge-theoretic concepts such as connections, gauge transformations and observables are replaced by linearized analogues.
· The Hopf fibration occurs in Quantum groups, an algebraic structure that appears among the operators of certain quantum field theories and statistical physics models.
· Their representation theory enables the computation of the spectrum of the energy operator, which is also the evolution operator, enabling the complete solution of these models.
· The Hopf fibration shows how the three-sphere can be built by a collection of circles arranged like points on a two-sphere.
· In the mathematical field of differential topology, the Hopf fibration describes a 3-sphere in terms of circles and an ordinary sphere.
· Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle.
· While no two fiber circles intersect, they are nevertheless linked like two metal rings in a chain.
· Each fiber circle passes through every other fiber circle exactly once.
· It is this linking that distinguishes the Hopf fibration.
Reference https://www.physicsforums.com/threads/hopf-fibration-stereoprojected-fibers-look-close-can-be.960769/
In this animation we see specific points on the two-sphere synchronized with the circles (fibers) over them.
https://www.youtube.com/watch?time_continue=1&v=AKotMPGFJYk
https://www.youtube.com/watch?v=xTKVIVaPZL8
Each fiber is linked with each other fiber exactly once.
This is the property that first attracted attention to the Hopf fibration, and a pair of circles in this configuration is called a Hopf link.
The collection of fibers over a circle is a torus (doughnut shape), and each such pair of tori are linked exactly once.
The collection of fibers over an arc form an annulus whose boundary circles are linked. This is known as a Hopf band; it is a Seifert surface for the Hopf link.
Quantum Group
· An algebraic structure that appears among the operators of certain quantum field theories and statistical physics models.
Dirac Equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928.
In its free form, or including electromagnetic interactions, it describes all spin- massive particles such as electrons and quarks for which parity is a symmetry.
Dirac Spinors
In geometry and physics, spinors are elements of a vector space that can be associated with Euclidean space.
Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight rotation
Thee vector space of spinors ˜is the simplest set of objects that Euclidean rotations act nontrivially on. These objects are familiar from quantum mechanics as the spin-up and spin-down states of spin-1/2 fermions. It is interesting to observe that spin is a perfectly classical property arising from symmetry.
Spinor
In geometry and physics, spinors are elements of a vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight rotation.
Spinorials require 720 degrees to return to their starting points instead of 360 degrees
Paul Dirac has one of the three most important equations in physics
Fermi's Golden Rule
In quantum physics, Fermi's golden rule is a formula that describes the transition rate from one energy eigenstate of a quantum system into other energy eigenstates in a continuum, effected by a weak perturbation. This rate is effectively constant.
Lorentz Transformation
The Lorentz factor or Lorentz term is the factor by which time, length, and relativistic mass change for an object while that object is moving.
The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations.
The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.
Due to its ubiquity, it is generally denoted γ (the Greek lowercase letter gamma).
Sometimes (especially in discussion of superluminal motion) the factor is written as Γ (Greek uppercase-gamma) rather than γ.
In physics, the Lorentz transformations are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.
There are many ways to derive the Lorentz transformations utilizing a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory.
String Theory
String theory is a mathematical theory that tries to explain certain phenomena which is not currently explainable under the standard model of quantum physics.
The Basics of String Theory
At its core, string theory uses a model of one-dimensional strings in place of the particles of quantum physics. These strings, the size of the Planck length (i.e. 10-35 m) vibrate at specific resonant frequencies. (Note: Some recent versions of string theory have predicted that the strings could have a longer length, up to nearly a millimeter in size, which would mean they're in the realm that experiments could detect them.) The formulas that result from string theory predict more than four dimensions (10 or 11 in the most common variants, though on version requires 26 dimensions), but the extra dimensions are "curled up" within the Planck length.
In addition to the strings, string theory contains another type of fundamental object called a brane, which can have many more dimensions. In some "braneworld scenarios," our universe is actually "stuck" inside of a 3-dimensional brane (called a 3-brane).
String theory was initially developed in the 1970s in an attempt to explain some inconsistencies with the energy behavior of hadrons and other fundamental particles of physics.
As with much of quantum physics, the mathematics that applies to string theory cannot be uniquely solved. Physicists must apply perturbation theory to obtain a series of approximated solutions. Such solutions, of course, include assumptions which may or may not be true.
The driving hope behind this work is that it will result in a "theory of everything," including a solution to the problem of quantum gravity, to reconcile quantum physics with general relativity, thus reconciling the fundamental forces of physics.
String theory, often called the “theory of everything,” is a relatively young science that includes such unusual concepts as superstrings, branes, and extra dimensions. Scientists are hopeful that string theory will unlock one of the biggest mysteries of the universe, namely how gravity and quantum physics fit together.
String theory is a work in progress, so trying to pin down exactly what the science is, or what its fundamental elements are, can be kind of tricky. The key string theory features include:
All objects in our universe are composed of vibrating filaments (strings) and membranes (branes) of energy.
String theory attempts to reconcile general relativity (gravity) with quantum physics.
A new connection (called supersymmetry) exists between two fundamentally different types of particles, bosons and fermions.
Several extra (usually unobservable) dimensions to the universe must exist.
There are also other possible string theory features, depending on what theories prove to have merit in the future. Possibilities include:
A landscape of string theory solutions, allowing for possible parallel universes.
The holographic principle, which states how information in a space can relate to information on the surface of that space.
The anthropic principle, which states that scientists can use the fact that humanity exists as an explanation for certain physical properties of our universe.
Our universe could be “stuck” on a brane, allowing for new interpretations of string theory.
Other principles or features, waiting to be discovered.
Einstein Rosen Bridges
· AKA wormholes
· When black holes in different regions of the universe are entangled, an Einstein-Rosen bridge connects them via a wormhole.
Consciousness
Consciousness is fundamental like the speed of light or gravity
Consciousness is also a product of field interaction, vibrations and resonances.
The flux of consciousness
The Hippies Were Right: It's All about Vibrations, Man!
What is consciousness?
https://www.ted.com/talks/david_chalmers_how_do_you_explain_consciousness
Panpsychism
The flux of consciousness
Interesting Articles
New Quantum Paradox Clarifies Where Our Views of Reality Go Wrong
The Farce of Modern Physics
http://davidpratt.info/farce.htm#f2
Quantum Fields: The Real Building Blocks of the Universe
https://www.youtube.com/watch?v=zNVQfWC_evg
