I will try to explain how the Universe can be created out of ‘nothing’, only by use of known science. Our Universe most probably had been created out of vacuum or ‘nothing’, but how and why, will require understanding of quantum physics and modern cosmology. I will use only universally accepted theory of quantum physics and gravity, and supported by the almost universally accepted ‘standard model of cosmology’, and satellite data and observations of structure formation of galaxies. I explain and elaborate further ideas supported by the most successful cosmologists in the world, including Stephen Hawking, Alan Guth and many others. The origin of Universe can be determined by science from detection of cosmic background radiation, as observed by space satellites.
Religious explanation of creation
How do the most educated and serious religious people try to explain creation of universe?
Religious arguments are mostly based on claims that big-bang and creation of universe was a cataclysmic explosion of matter. Then religious wonder where did all the energy for creating universe and all that matter came from — how does an entire Universe full of energy simply appears out of nothing? And make the conclusion that a prime mover (it is the Aristotle’s prime actualizer/mover) had to actualize all that matter and had to start the Universe. The problem of ‘prime mover’ was first defined by Aristotle, who was for both religious and secular the primary authority in science until Galileo and Newton. That is the strongest argument religious have. The problem requires explaining.
I emphasize, the article is written not with intent to criticize religion, but to explain how the Universe can and most probably exists without the necessity of a prime mover, and all the science data indicates that evolution of the Universe, and its creation, is governed by rules of quantum physics.
First, to define things properly, big-bang was not explosion of matter but expansion of space[9] — matter was supposed to be created by decay of the inflaton field (the field that started acceleration of expansion of the Universe) into particles when the exponential expansion of space ended. By definition inflation[9][11] is an accelerated expansion of space — a theory that is also supported by data[1][2], as I will explain further. Gravity can cause curvature of space, and expansion or contraction of space — for inflation it is accelerated expansion of space. Although it is possible that matter existed at Planck energy — which is energy at which all started. But, it would not be the same matter we are made of — probably the particles would have a larger mass by many orders of magnitude. Since we can not perform experiments at that energy, it is impossible to know.
Aristotle ideas on motion were completely wrong, as he did not understand the concept of friction. So, he believed that objects need force to keep moving — a simple example shows otherwise: a spaceship in space will continue moving without force because there is little friction in vacuum of empty space. Aristotle made the wrong conclusion because he was observing ships, which did not move without constant force. Classical Greeks did not develop a proper scientific method, perform experiments and peer review they work. Neither did they have advanced technology to perform precise experiments. Galileo was the first who reputed Aristotle, and in 19th century Aristotle’s concepts of potential and actualization were properly replaced by principles of classical mechanics by mathematicians/physicists Lagrange, Hamilton, Euler, Poisson and others, which were eventually applied to every theory in physics. However, Aristotle ideas on motion and physics are still used by religious and certain philosophers, to detriment of evolution of philosophy.
Popular example used to pose necessity for a prime mover is infinite regression argument: a cone and a tree, which was first in origin? I would not use the same example, but the example is used to claim that Universe can not exist without a prime mover, it has to be reputed and understood properly.
A cone is required for tree to be actualized, for it to exist, as the cone can grow into a tree. But a tree is required to make or create cones. So a tree is actualized from a cone, which is from a tree, which is also from a cone…argument continues until infinity. Which is first created, the tree or the cone? The only explanation is that the prime mover who created everything, made the first tree or a cone. Religious believe that it is a valid science argument that requires existence of a prime mover — that actualizes the Universe. Science has already explained the origin of life and planet Earth, I will not bother, as experts in evolution can do a better job, I am a physicist. If you deny theory of evolution of life, my work is not for you. But, what is important to explain is that a Universe can exist without a prime mover. In short, the answer is quantum mechanics. But how exactly, requires explaining.
The religious claim based on tree/cone example that the Universe requires to be actualized from nothing by a prime mover. First, the concept of actualization is a problem and it is not possible to instantaneously actualize anything, such actualizing the universe. Every physical process can not occur instantaneously.
As a simple explanation of how the cone starts turning into a tree is a chemical reaction which can be represented by an electron in a quantum state as a wavefunction in a molecule or an atom — the wavefunction is spread through space, and has a small probability of transferring the electron to another molecule starting a chemical reaction that will eventually after many reactions cause the cone to grow into a tree. So creation of a tree is a random process based on quantum physics — as is anything else.
The wavefunction is usually a function called the Gaussian after mathematician Gauss, or some other similar eigenfunction. The importance of the Gaussian function will be elaborated and will eventually become clear that creation of Universe was a random process.
Big-bang and Initial conditions
At the beginning I emphasize that, EVEN if we are not completely certain how the Universe began, we have a plausible explanation that is in accordance with reason and laws of physics[9]. Which is certainly better then alternatives. Physics theory 10⁻¹² seconds after the big-bang is almost completely known, and had been tested by experiments, which composes the ‘standard model of particle physics’ (particle colliders and space satellites). Theory works almost certainly after 10⁻³³ seconds (which composes the ‘standard model of cosmology’), I will explain important content of theory in detail. Although what is exactly the field that caused inflation[9][11] is not precisely known — there is a list of most probable models based on recent data published in “Encyclopaedia Inflationaris”[3] (first candidate is non-minimal Higgs inflation). As the experiments become more precise, inflation model will be determined from strength of gravitational waves, or inflation theory will be falsified altogether.
Standard physics textbook explanation is that initial big-bang was a moment in time not in space — where the entire space of the Universe at beginning had the same infinite density. After which the Universe expanded and evolved.
Immediately there are problems, why did the Universe expand (and not contract) and how can density be infinite. Infinite density is infinite mass and infinite gravitational force, which is unphysical. The problem can be resolved by supposing the initial Universe had Planck energy density, which corresponds to average temperature of T=10³³ Kelvin. Did the density of the initial universe fluctuate, was it homogeneous? The fact is that the density of Universe now, is mos definitely homogeneous (the same at every location) and isotropic (the same in every direction). It was even more homogeneous at the beginning: which is known as the ‘flatness problem’. It is defined by a seeming coincidence that energy of expansion of the Universe is almost exactly equal to gravitational attraction of all the matter/energy in the Universe.
Every physical system has to be able to evolve from initial conditions. It is all the information the Universe has, the initial conditions[7] of the present. The most important problem is the initial conditions of the Universe, when it started — how did big-bang occurred?
To properly categorize and avoid misunderstanding what big-bang really is, I define types of ‘big-bang’:
- The ‘standard big-bang’ which describes the expansion of the Universe when the Universe and matter was already created — historically that is how concept of big-bang was introduced. Physicists a century ago did not have space satellite data, so they believed matter was already there, and Universe expanded from a plasma of matter. ‘Big-bang’ term was not supposed to be serious, as most physicists believed that Universe already existed in a steady state without the big-bang.
- The ‘original big-bang’ which deals with the real problem: how the Universe was created (from ‘nothing’) and how is it so flat, and how does it have the same temperature in every direction, and how did the expansion of space started.
Why Big Bang was not an explosion? It is sometimes described as: “Explosion of high density of pinpoints of matter” which does not make sense and is unphysical, there can not be an explosion if there are no chemical or nuclear reactions — and the result of an explosion would be a highly asymmetrical Universe. Universe is highly flat and has the same temperature in every direction.
The Universe example: Universe increases kinetic energy of expansion from potential energy of the inflaton field, which has negative pressure and that causes gravitational expansion of space. At the end of expansion of the Universe the slow down of expansion is caused when scalar field potential is not flat and reaches the end of slope, where friction is caused by interaction of the scalar field (which could be Higgs field) and all other fields including weak and electromagnetic field, causing loss of energy of expansion of the Universe and also energy of the scalar field. Energy is transferred to creation of energetic particles that become the regular matter in our Universe (electrons, protons, neutrons and photons). That is what is considered as the ‘standard big-bang’.
Example that can describe how can Universe expand from a microscopic size is a skier on top of a potential hill — the slope of the hill can describe potential of the inflaton field.
Total energy of the system is a sum of kinetic K and potential energy V:
E = K + V.
If the potential energy V decreases, the kinetic energy K increases.
In the ski example the field is classical and the kinetic energy is only related to potential of gravitational field and slope of the mountain. Initially potential is at maximum and the skier only requires a very small initial velocity, so the potential of gravitational field decreases, which is converted to more velocity, and skier moves down the mountain, increasing kinetic energy. Kinetic energy reaches maximum, and when it reaches the end of the potential slope, friction becomes important where kinetic and potential energy is converted to friction with particles — causing transfer of energy to heat, which causes the end of motion.
What is the difference between the ski example and inflation and beginning of the Universe? Instead of the gravitational field it is the inflaton scalar field that represents the slope — potential energy of the field that makes inflation as a function of the value of the field. That field can be the Higgs field[3] (data is not yet precise enough to determine if it is Higgs or other field).
What is the difference between the ski example and inflation and beginning of the Universe? Instead of the gravitational field it is the inflaton scalar field that represents the slope — potential energy of the field that makes inflation[9][11] as a function of the value of the field value. That field can be the Higgs field[3].
Initially Universe is at top of the potential hill. The Hubble rate which is related to kinetic energy of expansion of the Universe is the velocity in the example. The difference being is that for the ski example, energy of gravitational field is being converted into kinetic energy of motion of the classical object (the skier), but for the Universe, vacuum energy or the energy of the scalar field is the source of kinetic energy of expansion of space. How? Because negative pressure of the vacuum energy creates a repulsive effect on space — the space expands and the Hubble rate of expansion increases enormously.
Potential energy of the scalar field is converted into exponential expansion of space and the Universe moves down the potential hill. When it reaches the end, friction starts and enormous energy is converted to real particles that we know from our Universe (regular matter: first the heaviest particles Higgs, W and Z bosons, and then quarks, protons, neutrons, photons and electrons). Friction ends inflation and also creates regular matter — known as the ‘standard big-bang’. Which is not an explosion, but a phase transition.
Religious then also claim that extreme flatness of the Universe (also observed in cosmic background radiation) is fine tuned and highly improbable. That is also an important argument religious have, which requires explaining.
Cosmic background radiation is the first light of the Universe, as radiation released 300 thousand years after the big-bang, and it can be used to understand how Universe was created. As space expands photon wavelength expands also and initial average T=3000 K radiation became T=2.7K (space expanded by a factor of a thousand) — which is the average temperature of the Universe now. Which is cosmic radiation that comes from every direction. What is difficult to understand is that radiation and the entire Universe has the same value of temperature across the sky in every direction — which implies that Universe has the same density. Such mathematically perfect radiation can not be even created in a laboratory experiment. How can that be possible? Quantum physics.
Every quantum field has constant vacuum energy, which should be very large, and therefore would cause accelerated expansion of space, that would even out space and make it flat. The problem is not why Universe is so flat, but why is vacuum energy which is observed as cosmological constant [4][5][6] so small now, as measured from recent accelerated expansion of space. Flatness of the Universe can be explained by inflation — and in fact the Higgs field itself (in combination with gravity) can generate inflation (and is the most probable candidate) — so there is no need for hypothetical physics to explain the flatness of the Universe. Flatness of the Universe is quite generic and consequence of vacuum energy. Existence of vacuum energy has been confirmed experimentally from Casimir effect, Lamb effect and accelerated expansion of Universe.
Universe could have been created by a random process
To create a Universe from nothing you need at least one quantum field with opposite charge attraction (which can be the electromagnetic field where positive and negative charge cause attraction but same charge causes repulsion) and another field as a force with same charge attraction, which is gravity. Why?
Because, if a force has the property that particles with same charge attract — such as gravity where mass is always positive and produces attractive force — the potential energy of the field is negative. Why? Because bringing mass together can be used to produce work, which is positive. If work is obtained by bringing massive particles together, then the potential energy of the field has to be negative, because of conservation of energy — total energy: work and energy of the field has to be zero.
For electromagnetic field it is the opposite: same charge repels, and work is required to bring particles with same charge together — since work is negative, potential energy of electromagnetic field is positive.
Universe expands during matter era, and energy is small enough (T=3000K) for protons and electrons to combine into Hydrogen atoms, releasing the cosmic background radiation with the same temperature, and observed small Gaussian fluctuations that show how Universe was created from ‘nothing’. The Universe expands further by a factor of a thousand and temperature of cosmic radiation and the Universe is now T=2.73Kelvin. Strong force is the strongest and gravity the weakest.
If the gravitational field and other fields have the same strength, particles that are created with negative gravitational energy and positive electromagnetic energy, can have zero total energy and can expand and create their own Universe. As the space expands, whatever the original potential energy was at moment of creation, remains total energy for the entire Universe. It is an argument by Stephen Hawking and many other cosmologists and physicists.
If the strength of the gravitational force and other forces is the same, then
so total energy, as the sum of all potential energy of all fields of the Universe can be exactly zero
It has been determined mathematically through quantum field renormalization equations that all fields/forces including gravity and electromagnetic force have the same strength at Planck energy — which is the energy scale when the big-bang occurred.
Then as Lawrence Krauss independently provides an explanation: Heisenberg uncertainty principle creates short time particles. Add gravity and the particles have negative gravitational energy — then total energy of the system can be zero, and particles can exist. Empty space is unstable to spontaneous creation of particles. I add that the effect can be neglected for energies less then Planck energy — so probability that a Universe spontaneously forms now is extremely negligibly small (gravitational force between virtual positron/electron pair formed in vacuum at energy now, in the current Universe, is negligibly small).
As I have shown in a separate article, Heisenberg uncertainty principle is a necessity and inevitable conclusion of the ‘infinite precision measurement’ problem. There has to be a limit to precision of a measurement to make sense of the Universe. So quantum mechanics is a inevitable feature of every Universe: quantum theory is built from uncertainty and law of probability — which itself is built from logic. So all that is required to start a Universe is a small amount of energy ΔE, that can come from Heisenberg uncertainty principle for energy and time:
Also a necessity is the Higgs field for acceleration of expansion of space and a symmetry breaking process.
Through spontaneous symmetry breaking and quantum phase transitions, quantum fields can combine or break apart. The most obvious example is combination of electromagnetism and weak force into a electro-weak force — which is caused by symmetry breaking of the Higgs field at temperature of around million times larger then nuclear explosion.
The big-bang was not a explosion but a series of phase transitions described by the standard model of cosmology. The most probable big-bang theory starts with a first phase transition of a super-heated field that forms a microscopic bubble universe that inflates to macroscopic size by a cosmological constant [4][5][6] type of accelerated expansion, caused by a constant potential energy of a scalar field. It is a period in evolution of the universe called inflation era that started at approximately 10⁻³⁴ seconds after the big-bang. Next the energy of the scalar field is transferred to standard model particles by friction, causing the standard hot big bang. Only 10⁻¹¹ seconds after the big-bang at temp of 100 thousand trillion Kelvin, the second order electroweak phase transition occurs separating the weak nuclear force from the electromagnetic force. The heaviest particles such as Higgs bosons decay to the lightest: electrons and quarks that form protons and neutrons. After which everything is known for the most part, formation of matter and galaxies. As the universe expanded and cooled down 300 thousand years after the big-bang, hydrogen atoms form emitting the first light that can be observed as cosmic background radiation. I will explain the inflation era, nucleation of a Universe requires understanding of Euclidean quantum gravity [14] (and work by Stephen Hawking and others), and is beyond the scope of this chapter.
The problem of the ‘original big-bang’ is the problem of initial big-bang singularity — and why the Universe did not just collapse gravitationally. Another attempt at describing initial big-bang singularity is the ‘no-boundary proposal’ by Hawking and Hartle, where geometry of the Universe is smoothed out with in imaginary time. Such attempts make all spacetime Euclidean. Difficult to describe without mathematics, but the important thing is that it can be done mathematically.
Stephen Hawking quote: “[At big-bang] classical histories of the universe are singular in the sense that their matter densities exceed the Planck density. But for [certain conditions they are not singular]. This is possible despite the [Penrose-Hawking] singularity theorems because of energy conditions and [of a] scalar field and the cosmological constant.” [15]
I.e. existence of big-bang singularity can be prevented by a scalar field (which can cause inflation) or cosmological[4][5][6] constant.
What does ‘nothing’ or vacuum look like?
Remove all the matter particles from space. All the electrons, all the atoms. Is the space empty? Not really, there are photons from thermal radiation and from the cosmic background radiation from the big-bang. Remove the photons, and there are neutrinos. Remove neutrinos, there are cosmic rays. Remove them and the space is still not empty. There are still quantum fields that represent particles which permeate the entire Universe.
The vacuum or empty space consists of these quantum fields in the lowest energy state — which is a state without real particles. As mentioned in the book, according to Heisenberg uncertainty principle that exists for energy and time, and as well as uncertainty that inherently exists in creation and annihilation of particles in vacuum, the empty state is a fluctuating vacuum state where virtual particles are being created and destroyed on short time-scales of 10⁻²¹seconds or less. These virtual particles have an effect on the real world in many ways.
People have problems understanding how quantum fields work and how ‘nothing’ — the vacuum (or empty space) looks like. Because it is so abstract they can not compare it with anything real (or what is considered to be real). But I will show that consequences of quantum physics and quantum fields, and creation from nothing can be observed in reality. In fact according to latest theory and data, the entire Universe is nothing more then an overlap of quantum fluctuations of virtual particles that existed in the moment of creation of the Universe. So quantum fields and the ‘nothing’ can be observed just by looking at the map of the Universe.
It is always possible to create and annihilate particles corresponding to a specific field, usually as an example an electron quantum field cₚ and the photon electromagnetic field aₚ is used.
Mathematically annihilating the vacuum, which already contains no real particles, produces no result so has to be equal to zero (not even a quantum state with no particles but literally zero).
It is the vacuum state of empty space. I have restored the constant (the result is dependent on mass and frequency of the particle and Planck constant, which can be summarized into a standard wavelength of the particle λ).
For a virtual electron λ ≈ 10⁻²¹m. I did not include time dependence, but the time component is an oscillating function of energy and time. The solution basically describes creation and annihilation of virtual particles in space as Gaussian fluctuations.
The same function that describes creation of an electron in free space also describes the form of virtual particles that are being spontaneously created in the vacuum. Gaussian is also called the normal distribution — which defines a result of measurements in a random ensemble, which is properly defined through central limit theorem.
So, what does nothing or vacuum state looks like? Believe it or not, the ‘nothing’, the vacuum can be measured, but how? One way the effects can be observed is through Casimir effect. But also, it can be measured because the Universe was most probably created from nothing — at least that is what the latest data implies.
The first light emitted by the Universe occurred when the plasma of mostly protons and electrons in the early Universe combined to form Hydrogen atoms and releasing photons to spread throughout space — which occurred 300 thousand years after the big-bang. Before, the temperature was large, and photons were constantly interacting with particles, being absorbed and emitted.
Hydrogen atoms can only form at certain temperature that allows electrons to combine with protons into stable Hydrogen atoms.
Definition: cosmological horizon is a sphere with planet Earth at the center representing the Universe that we can observe — parts of the Universe that we can observe by observing light or photons in general.
That first light has formed the cosmic background radiation across the entire skymap of the Universe in every direction.
The image of the Universe when it was only 300 thousand years after the big-bang had been observed by many experiments including space satellites COBE, WMAP[1] and lastly the Planck[2] satellite. Then the Universe had an average T=3000 Kelvin temperature across the entire sky, with only small variations in temperature ΔT, approximately 10000 times less then actual temperature (or even less for smaller fluctuations). These variations have a specific form — the form of the fluctuations in space is exactly Gaussian.
The entire Universe is a superposition: an overlap of many Gaussians, that have after Universe formed had collapsed in the center of the function to galaxies as seeds of structure formation. Our galaxy (and our galaxy group) had formed from gravitational collapse of the centers of one of these Gaussian fluctuations. The virtual fluctuations in the quantum fields in the exact moment of creation of our Universe had become the seed of structure formation of galaxies (that resulted with formation of planet Earth) and also formation of life.
In fact these variations are so precisely Gaussian and have the exact thermal properties in every direction across the sky for the entire Universe, that it is technologically impossible to achieve the same thermal state in a laboratory experiment. That is known as a the Horizon problem — because how can the Universe have the same temperature in every direction, if it has not been in causal contact. Information travels with speed of light c and the cosmological horizon can only be 300 thousand light years at the moment of emission of cosmic radiation — since only 300 thousand years had past after the big-bang. But the Universe was much larger then the 300 thousand light years (it was approximately 50 million light years in size) — which is only approximately comparable to an angle of 1 degree across the skymap — yet it has perfect exact temperature and the same Gaussian fluctuations in every direction. How is that possible? The answer is quantum mechanics and inflation.
I claim that beginning of the Universe and big-bang was not an explosion — which is asymmetric and caused by chemical reactions (it is a state where there is a temporary increase in temperature and positive pressure which causes expansion of volume of gas — made from real classical particles). Positive pressure causes mechanical expansion of gas, not expansion of spacetime which remains static.
So why is big-bang different from an explosion? Inflation and formation of the Universe is different — it is a state where vacuum energy density remains almost constant, and has constant negative pressure which causes gravitational repulsion — which is the source of accelerated expansion of space. Here, the space itself expands (not real particles or matter), as during expansion of space vacuum energy, as property of ‘empty’ space is constant. It can be also caused by a scalar field that has constant potential energy for a certain region[3][9] — like the Higgs field. Constant vacuum energy has negative pressure, and everything that has energy gravitates: positive pressure causes gravitational attraction and contraction of space as does anything else hat has mass, but negative pressure causes gravitational repulsion and accelerated expansion of space.
Cosmological constant and vacuum energy pressure-density relation is
p=-ρ, and pressure p is negative and equal in magnitude to density.
The Universe like that can increase to enormous size by a factor of trillion trillion or more, in just approximately 10⁻³³s— that can be achieved by vacuum energy comparable to Planck energy (which corresponds to temperature of about a billion trillion trillion Kelvin). That is how microscopic vacuum wave-like fluctuations formed by virtual particles in vacuum that have a Gaussian form, became macroscopic in size, so that they can be observed in cosmic background radiation map of the Universe. As the Universe expanded exponentially, the Gaussians created during inflation have all possible sizes across the sky — from very small that are now size of a galaxy, to very large, that are almost the size of the Universe. After the inflation ended, the Universe expanded linearly for another trillion trillion times, and microscopic vacuum fluctuations that were originally approximately 10⁻²³m in size became comparable to the size of the Universe now: 10²³m or billions of light years.
One of few parameters of the universally accepted ‘standard model of cosmology’[9][2] is the spectral tilt nₛ. Fluctuations in the cosmic radiation caused by the virtual particles in the vacuum at the beginning and during inflationary expansion of the Universe have an amplitude — which can be dependent on the Gaussian standard length as a wave-like fluctuation, represented by a wavelength λ. The spectral tilt quantifies the amount of tilt in the amplitude or power of the Gaussian fluctuations depending on the size of the fluctuation on the skymap of the Universe.
Gaussians with different size (for example if now the size of fluctuation is the size of a galaxy group or even bigger the size of a galaxy cluster) can have different amplitudes, so there can be a different amount or density of matter contained for a specific Gaussian. If the tilt is exactly one (nₛ=1) there is no difference between large and small fluctuations.
The tilt and difference in fluctuations reveals how Universe was created. If the tilt is slightly less then one (nₛ≤ 1) that implies that an accelerated expansion caused by a field that works as a cosmological constant ensued, after which the Universe expansion slowed down and ‘regular big-bang’ proceeded where physics is mostly known.
All the data from all the satellites show that spectral tilt is slightly less then one (Planck satellite[2] data nₛ=0.967) in accordance with inflation and in contradiction with many other theoretical models of Universe.
Which implies that the largest fluctuating Gaussians have more power (have a larger amplitude).
In summary the ‘nothing’ or empty space looks just like the Universe (the image of the Universe when it was 300 thousand years after the big-bang) with a slight tilt in amplitude of Gaussian fluctuations of different size, which is not noticeable in the image. It is just a superposition of many Gaussians all across the sky (which can be represented by quantum virtual particle fluctuations of all size), amplified to macroscopic size by inflation.
At the moment of ‘original big-bang’, in the moment of creation of the Universe from ‘nothing’, the empty space or the vacuum as it is always is, is filled with vacuum fluctuations that constantly oscillate, as created and annihilated virtual particles (such as gravitons) come in and out of existence. Then the scalar field such as the Higgs field (or vacuum energy) with a large effective cosmological constant starts with inflation as accelerated expansion of space.
During inflation virtual particles as vacuum fluctuations will generate Gaussian random fluctuations in the spacetime of all sizes, since the inflation occurs faster then speed of light and expands space, fluctuations with different size will be generated as space expands. But as inflation expands the space faster then speed of light, the generated Gaussian vacuum fluctuations will not be able to continue with oscillations and will freeze as they will no longer be in causal contact. Inflation expands space with such velocity that Gaussians are all out of cosmological horizon, and become static. Expansion of space is defined through scale factor a(t) and increases as the space expands. The scale factor is defined to be approximately a=10⁻⁵⁰ at beginning of inflation and is defined to be exactly a=1 now, which implies that the Universe had expanded by a factor of trillion trillion trillion trillion at least since it was created.
Horizon and observable Universe during inflation decreases and when inflation ends, Universe expands slower then speed of light, the cosmological horizon increases again.
When inflation ends as the Universe expands with smaller speed the speed of light, the first Gaussians that enter the cosmological horizon and become visible in the cosmic background are the smallest fluctuations that were generated at the end of inflation (when acceleration slowed down) — and then because of it, they will have a smaller amplitude (which is exactly what spectral tilt of nₛ ≤1 describes). Then as the Universe expands with speed less then speed of light, larger and larger Gaussian fluctuations enter the observable cosmological horizon (have a larger amplitude) and cause structure formation of galaxies and clusters of galaxies. The largest Gaussians lastly become part of the observable Universe and become observed on the largest scale of the Universe. The scale factor increases exponentially during inflation, when inflation ends, radiation and matter are primary constituents of mass/energy on the Universe and expansion slows down to linear expansion.
The Higgs field breaks into lowest energy state, and electromagnetic and weak nuclear force separate into different forces at t=10⁻¹² seconds after the big-bang. Then nucleus of Helium atoms form as 25% of regular matter at approximately 1 second after big-bang. And then Hydrogen atoms form and release cosmic background radiation of photons at T=3000K (and 300 thousand years after). Until accelerated expansion of the Universe starts again, approximately 5 billion years ago and largest Gaussian fluctuations are again being removed from the observed cosmological horizon — because parts of Universe at the horizon are accelerating and moving faster then speed of light.
That is what is observed in cosmic background radiation of the Universe: frozen Gaussian vacuum fluctuations of all size, frozen in the moment of creation of the Universe as a snap image of what it looked at the moment Universe was created. If there were no Gaussian fluctuations as seeds of gravitational collapse, there would be no structure formation and no galaxies and no planets. They are of quantum origin, random and product of statistics and chance.
How can we know if the Higgs field caused inflation? Or if not, then another field? From the value of spectral tilt and strength of gravitational waves[2][3]. Which will either be observed, or if not, inflation theory will be reputed, which makes it a scientific theory, as it can be falsified.
Logical argument religious have is: change exists in the world, all change is actualization of potential for change. No potential can be actualized unless something already actual exists — which requires infinite regress or a prime mover that actualizes — as a prime cause. So either a prime mover or infinite regress is necessary to describe actualization of the Universe.
There is another option — a universe governed by quantum physics that actualizes things by random virtual fluctuations in vacuum, in form of Gaussians — which is exactly what is observed in the cosmic background radiation.
What exactly happened at Planck energy, which is called the Planck era is not known as it is inaccessible by experiments. But that will change, precision of gravitational wave detectors will reach accuracy necessary to detect directly gravitational waves from inflation and big-bang itself in this century. Then we will observe how was the Universe created, was it prime mover/actualizer or quantum physics?
In fact the largest wavelength fluctuations in cosmic background radiation are observed to be anomalous[10] — for some reason they are not random — which may indicate unknown physics of creation of the Universe. Some of the Gaussian fluctuations comparable to size of the observable Universe seem to be aligned — these Gaussians were frozen and created first. All the fluctuations should be random, but as observed, the largest fluctuations are not completely random. Statistically the result is at 3 sigma (or probability that alignment of Gaussians is not a statistical fluke is 99.7%).
Complete description of anomalies in cosmic background radiation are documented in reference[10].
What remains to be shown is how exactly the Universe had been nucleated out of nothing: there are many theories, which can be through spontaneous nucleation by uncertainty principle, nucleation of a bubble of true vacuum out of false vacuum, or no boundary proposal by Stephen Hawking. The ideas require understanding of (Euclidean) quantum gravity. I reiterate, these are difficult topics that can not be explained simply in an article.
Creation is random as is Quantum physics
Standard length sigma σ measures how spread out the distribution is:
- 68% of values are within
1 standard length σ of the mean - 99.7% of values are within
3 standard length σ of the mean - 99.9999% of values are within
5 standard length σ of the mean
5 sigma (σ) is used extensively in science as the standard of scientific achievement, a necessary probability to claim the result of an experiment was success — which implies that probability that result is wrong is only 0.0001%. It is the norm for scientific discovery, a required successful claim that result is truly right and not just a statistical fluke.
For example discovery of the Higgs boson was confirmed by groups ATLAS and CMS at Large Hadron Collider in CERN, when thy both achieved a 5 sigma statistical likeliness (ATLAS 5.9 sigma [13]) for existence of Higgs boson in the data (for which Nobel prize was awarded).
As a particle physics example, the function of particle collider events with respect to energy for the Higgs boson is also a Gaussian, where sigma has another, physical property: it is related to decay lifetime of the particle (t=1/σ). The average location of the Gaussian is the mass/energy of the particle (which is for the Higgs m ≈ 125 GeV, according to latest data), and average decay lifetime of ≈ 10⁻²⁵ seconds.
The way the experiment at LHC proceeds is: protons are collided at a large energy. Then all possible particles that Higgs boson can decay into are observed in detector ATLAS. In example I am showing, decay of Higgs boson into pair of photons is observed. Number of events of detection of photon pairs with combined energy larger then 100 GeV is observed in intervals of 2 GeV (as in the plot). Then if there is an excess of events at some energy, and if the larger number of detection events resembles a Gaussian, the center of Gaussian and sigma is observed in data — from which mass and decay lifetime of the particle can be extracted. The same is observed for other particles — for example detection of W and Z bosons.
Also detection of gravitational waves by LIGO gravitational wave detector was statistically a 5.1 sigma discovery [12] (also a Nobel prize).
To further describe the tree and cone example it is clear that it is not an infinite regress, but an evolution, which is governed by quantum mechanical processes (chemical reactions) that can be traced back to creation of the Universe which was also a random process.
The randomness is inherent in creation, it is not just there by accident, or can be removed from laws of nature by a better experiment or a better theory (further explained by Heisenberg microscope experiment). Because of it, it can be observed in many natural phenomena.
When Universe creates, it creates randomly and uses Gaussians as a statistical method to provide and describe the properties of what was created. To use the same example that religious use, the volume of the tree is also a random Gaussian variable: value of volume of ensemble of trees will be a normal distribution. Success of the cone being cause of another tree is again dependent on the statistical distribution. Also, for example, production of a component (properties of the component) in a factory can be also describes by normal Gaussian distribution — examples are endless — because that is how Universe works.
The same way quantum physics is tested: an electron state (the position of particle) is measured many times, after which a statistical distribution is determined — which will be a Gaussian.
Results of examinations are statistical and approximately Gaussian — defined by average result of exams and standard width in results.
In comparison for a quantum particle with a Gaussian wavefunction there is an average position and standard width sigma related to uncertainty principle for position and momentum/velocity. Gaussian is a special function in quantum physics, for the Gaussian the uncertainty principle is exactly true
- no other function has that property. Examples of Gaussians in quantum theory are endless. The Gaussian itself is not a just a mathematical construction but a consequence of statistical and random nature of the Universe — as shown by the Central Limit Theorem of statistics.
AI and creation
The effects of quantum mechanics are prevalent in physics of the Universe. Randomness is inherent in the Universe, inherent in creation, seemingly without a need for prime mover. The tree when it creates, it creates a Gaussian.
Even the AI generator of images knows how to make a proper tree with a random Gaussian. I did not need to explain to the AI generator what exactly to produce, it produced a Gaussian from a first attempt, based on a simple prompt to make a tree with cones. Gaussian normal distribution can describe the probability of a cone becoming a tree. For example a cone far from tree will have more probability of success of becoming a tree.
If anything it shows that generation of trees (or any other process such as production of Higgs bosons, results of exams, components in factory, structure formation of galaxies from Gaussian fluctuations and so on) is governed by a similar random process to processes described by quantum mechanics. And even if prime mover somehow exists, it had started a Universe that creates random and needs quantum mechanics to function properly. Creation and motion in the Universe is governed by rules of quantum mechanics, and not by the prime mover.
Conclusion
So the answer to what was first, tree or a cone, is neither, it was the Gaussian and vacuum state that was first.
As it can be observed in cosmic background radiation, creation of the Universe was a random process as is creation of particles in the vacuum, which is a consequence of the Heisenberg uncertainty principle. Quantum mechanics and the Universe does not require a prime mover to exist — although it does not completely exclude existence of one. How do the original quantum fields form, and what process forms them (perhaps a Higgs mechanism for gravity exists), is unknown. Not because of failure of physics, but because we can not perform experiments at that energy, and have no data to support any theory. And there are many ideas and competing theories, which is a not a subject of present chapter, but of Theory of Everything.
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