More ado about (something out of) nothing!
The phenomenon of something emerging from nothing has already been considered when ruminating upon the origins of the universe in the context of the big Bang. Remember that in the quantum world there is no such thing as ‘empty’ space and no such thing as ‘nothing’, for when viewed at atomic scales, so-called empty space is still seething with activity, particles, and their quantum fluctuations, in other words - energy. So empty space does not consist of nothing and it is certainly not empty.
We also noted that contemplating a void without energy violates Heisenberg’s Uncertainty Principle (HUP), but did not go into that at any length. HUP postulates that it is not possible to measure with precision both the position and momentum of a particle: the more you know about the one, the less you know about the other, and the same principles may be applied to the related concepts of energy and time. If we were to examine a small amount of empty space in an isolated area, a void or box, from which everything else (matter, fields) has been removed leaving an apparent vacuum, in principle we can know how much energy is in the box very precisely, but if we slow things down and examine only a very small area over a tiny interval of time that has been stretched out, HUP tells us that the principle of energy conservation[1] can be ‘violated’ because one cannot determine energy precisely at a given time.
Particles can radiate energy (say photons) in apparent violation of energy conservation, so long as that energy is reabsorbed by other particles within a short space of time, and the more the energy account is overdrawn, the sooner it must be repaid [2], and in the quantum picture of the electromagnetic field, virtual photons (quantum bundles or ‘particles’ of light) flit across space-time and transmit the forces between remote objects [3].
Another way of expressing HUP in this context is that the uncertainty in the measured energy in a system is inversely proportional to the length of time over which we are observing it [4], the consequence being that in truly tiny amounts of time and space, something can come from nothing [5]. According to Einstein, energy is the equivalent to mass in the sense that a huge amount of energy can derive from a small amount of mass when the latter is multiplied by the speed of light squared: E=mc².
And conversely, mass can be produced from energy: m = E c²
As we saw when discussing the implications of E=mc², in 1927 Paul Dirac, pictured above, modified Einstein’s equation to include a particle’s spin and momentum along with its mass as relevant factors to be taken into account in determining a particle’s energy. Without these additions, it has been said that Einstein’s equation amounted to saying that energy is only approximately equal to mass. Dirac’s equations also successfully predicted the existence of antimatter in the form of a positively charged electron now called a positron. An electron and its anti-matter twin, the positron, have the same mc² and equal and opposite signs of electric charge. So if the energy exceeds 2 mc² it is possible for an electron and a positron to emerge [6].
Whenever a particle pops out of empty space, so simultaneously does its anti-particle, each mutually annihilating the other a moment later. The vacuum is literally alive with these quantum fluctuations, where little packets of energy appear - and disappear - very quickly. “Within nothingness there is a kind of fizzing, a dynamic dance as pairs of particles and anti-particles borrow energy from the vacuum for brief moments, before annihilating and paying it back again”.[7]
However, these energy fluctuations in the vacuum are constrained by Heisenberg’s uncertainty principle (HUP) [8] to last only a brief moment less than h/2 mc²,[9] a mere
10-21 seconds, a time so small that light would have been able to travel only across about one thousandth the span of a hydrogen atom. Such 'virtual particles' cannot be seen as any more than the deviation from energy conservations that these fluctuations amount to[10].
But if these virtual particles can pop into existence, where do they go, and why don’t we see them appearing all around us? The answer again takes us back to Paul Dirac who gave mathematical precision to these phenomena, thereby providing the answer to the riddle of so-called “empty space” and unifying Einstein’s theory of special relativity and quantum mechanics, in the process.[10.1]
Right: A simplified version of Dirac’s relativistic wave equation, as it appears on the floor of Westminster Abbey near Charles Darwin’s remains and Newton’s death mask (at right) is iγ · δψ = mψ, where i = √-1, γ represents four 4-by-4 square arrays of numbers, δ symbolizes rate-of-change calculations with respect to the 3 dimensions of space and one of time, ψ is a four-component wave equation for the electron, and m is the rest mass of the electron. So to the very casual observer, very complex indeed! [10.2]
We also noted that contemplating a void without energy violates Heisenberg’s Uncertainty Principle (HUP), but did not go into that at any length. HUP postulates that it is not possible to measure with precision both the position and momentum of a particle: the more you know about the one, the less you know about the other, and the same principles may be applied to the related concepts of energy and time. If we were to examine a small amount of empty space in an isolated area, a void or box, from which everything else (matter, fields) has been removed leaving an apparent vacuum, in principle we can know how much energy is in the box very precisely, but if we slow things down and examine only a very small area over a tiny interval of time that has been stretched out, HUP tells us that the principle of energy conservation[1] can be ‘violated’ because one cannot determine energy precisely at a given time.
Particles can radiate energy (say photons) in apparent violation of energy conservation, so long as that energy is reabsorbed by other particles within a short space of time, and the more the energy account is overdrawn, the sooner it must be repaid [2], and in the quantum picture of the electromagnetic field, virtual photons (quantum bundles or ‘particles’ of light) flit across space-time and transmit the forces between remote objects [3].
Another way of expressing HUP in this context is that the uncertainty in the measured energy in a system is inversely proportional to the length of time over which we are observing it [4], the consequence being that in truly tiny amounts of time and space, something can come from nothing [5]. According to Einstein, energy is the equivalent to mass in the sense that a huge amount of energy can derive from a small amount of mass when the latter is multiplied by the speed of light squared: E=mc².
And conversely, mass can be produced from energy: m = E c²
As we saw when discussing the implications of E=mc², in 1927 Paul Dirac, pictured above, modified Einstein’s equation to include a particle’s spin and momentum along with its mass as relevant factors to be taken into account in determining a particle’s energy. Without these additions, it has been said that Einstein’s equation amounted to saying that energy is only approximately equal to mass. Dirac’s equations also successfully predicted the existence of antimatter in the form of a positively charged electron now called a positron. An electron and its anti-matter twin, the positron, have the same mc² and equal and opposite signs of electric charge. So if the energy exceeds 2 mc² it is possible for an electron and a positron to emerge [6].
Whenever a particle pops out of empty space, so simultaneously does its anti-particle, each mutually annihilating the other a moment later. The vacuum is literally alive with these quantum fluctuations, where little packets of energy appear - and disappear - very quickly. “Within nothingness there is a kind of fizzing, a dynamic dance as pairs of particles and anti-particles borrow energy from the vacuum for brief moments, before annihilating and paying it back again”.[7]
However, these energy fluctuations in the vacuum are constrained by Heisenberg’s uncertainty principle (HUP) [8] to last only a brief moment less than h/2 mc²,[9] a mere
10-21 seconds, a time so small that light would have been able to travel only across about one thousandth the span of a hydrogen atom. Such 'virtual particles' cannot be seen as any more than the deviation from energy conservations that these fluctuations amount to[10].
But if these virtual particles can pop into existence, where do they go, and why don’t we see them appearing all around us? The answer again takes us back to Paul Dirac who gave mathematical precision to these phenomena, thereby providing the answer to the riddle of so-called “empty space” and unifying Einstein’s theory of special relativity and quantum mechanics, in the process.[10.1]
Right: A simplified version of Dirac’s relativistic wave equation, as it appears on the floor of Westminster Abbey near Charles Darwin’s remains and Newton’s death mask (at right) is iγ · δψ = mψ, where i = √-1, γ represents four 4-by-4 square arrays of numbers, δ symbolizes rate-of-change calculations with respect to the 3 dimensions of space and one of time, ψ is a four-component wave equation for the electron, and m is the rest mass of the electron. So to the very casual observer, very complex indeed! [10.2]
However, Al-Khalili reminds us that we should not be deceived by the apparent 'simplicity' of this equation. Think of it, he says, as the tip of a giant mathematical iceberg, encompassing entire branches of mathematics and the relationship between them.
There are in fact four equations represented by γ (gamma) compressing their meaning to a brief area on the page[. As revealed in footnote [11], of the 4x4 arrays, two have positive energy and two negative energy. Of the two positive energy states, one actually represents an electron with spin up, and the other an electron with spin down. So spin arises naturally in Dirac’s theory, even demands it![11.1] The negative energy states also arise naturally, and successfully predicted the existence of the anti-electron or positron.These equations also unexpectedly revealed the vacuum proceeding from nothing to a place absolutely teeming with matter and antimatter, which came to be known as virtual particles. Nothingness is thus revealed as a mass of virtual particles appearing and disappearing trillions of times in a blink of an eye[12].
In 1947 the American physicist Willis Lamb (1913-2008)’s experiments confirmed this by revealing an ever so slight wobble in the different orbits of the electrons in a hydrogen atom, disclosing small differences in their energy levels thereby revealing the presence of virtual particles in the vacuum – something like a plane hitting turbulence forcing it up to a higher altitude. The peak showed that the vacuum is filled with energy.
As we have seen when considering the big bang, all this has important ramifications for how the universe itself came into existence. Today our best theories tell us that the universe sprang from the vacuum, and that the rules of the quantum world appear to have contributed to the large scale of the entire cosmos: when our universe first came into existence it was many times smaller than an atom, and its subsequent development since then has been governed by quantum world rules. Our universe is just the quantum world inflated many, many times. Nothing has really shaped everything. We can see this using the Cosmic Background Explorer (COBE) satellite, revealing the picture of the first light after the big bang, something like seeing an embryo after 12 hours after human conception, as the American astrophysicist, cosmologist and Nobel laureate George Smoot has described the phenomenon[13].
The rest of the story is by now familiar. Tiny variations in temperature were revealed, representing the scars left on our quantum universe. Matter did not spread out completely evenly; quantum fluctuations became the seeds, eventually forming vast clumps making up our galaxies, all of which started life as a mere quantum fluctuation of the vacuum.
“Our best theories today tell us that the Universe sprang from the vacuum creating the matter and anti-matter predicted by Paul Dirac. But the universe we see today is made up of matter. Nearly all the anti-matter has vanished. According to current theory the big bang produced equal amounts of matter and anti-matter but as the universe cooled down matter and anti-matter annihilated almost perfectly, but not quite! For every billion particles of antimatter and matter, one particle of matter was left behind. These annihilations produced the heat of the big bang we see today as the microwave background radiation. The one in a billion parts of matter left behind made galaxies and people. We are the leftovers of an unimaginable explosion”[14]. As one observer has been moved to comment: for Dirac “to describe in so precise a form the motion and very existence of all fundamental particles of nature, the same stuff of which we are made, is an act of uncommon genius[15]”.
[1] The First Law of Thermodynamics dictates that the total amount of energy in an isolated system remains constant: energy can neither be created nor destroyed.
[2] Frank Close, Nothing, A Very Short Introduction, OUP, 2009, 95.
[3] Ibid.
[4] Lawrence M. Krauss, A universe from nothing, - Why there is something rather than nothing, Free Press, New York, 2012, 71.
[5] Jim Al-Khalili, Everything and Nothing, 2 Part series, 2nd part - “Nothing”, BBC documentary, 2011, repeated SBS23 Feb 2014. Partial transcript at
http://hassers.blogspot.com.au/2011/03/how-everything-was-formed-from-nothing.html
[6] Close, op cit, 106-107.
[7] Ibid.
[8] Which, be it remembered, sets a lower limit, based on Planck’s constant, on the accuracy with which certain pairs of physical quantities of a particle, such as its position and momentum, can be measured together: Richard Gauthier, Ph D, The Dirac Equation and the Superluminal Electron Model, http://www.superluminalquantum.org/diracequation.pdf.2
[9] h = Planck’s Constant, which describes the proportional relationship between energy oscillations and the frequency of the radiating waves.
[10] Close, op cit, 106-107.
[10.1] See also Black holes and information theory: the link between quantum physics and general relativity?
[10.2] Actually, Gavin Hesketh says this simplified form of the equation is indeed quite simple: the mass of the particle mψ (right hand side) affects how it moves iγ · δ (left hand side): The Particle Zoo - The search for the fundamental nature of reality, Quercus, Hachette, London 2016, 16, 131. The latter reference adds an additional symbol (A) to the right hand side to apply symmetry.
[11] In Dirac representation, the four contravariant gamma matrices (tables of numbers) which threw up the existence of the anti-electron (positron) appear as:
There are in fact four equations represented by γ (gamma) compressing their meaning to a brief area on the page[. As revealed in footnote [11], of the 4x4 arrays, two have positive energy and two negative energy. Of the two positive energy states, one actually represents an electron with spin up, and the other an electron with spin down. So spin arises naturally in Dirac’s theory, even demands it![11.1] The negative energy states also arise naturally, and successfully predicted the existence of the anti-electron or positron.These equations also unexpectedly revealed the vacuum proceeding from nothing to a place absolutely teeming with matter and antimatter, which came to be known as virtual particles. Nothingness is thus revealed as a mass of virtual particles appearing and disappearing trillions of times in a blink of an eye[12].
In 1947 the American physicist Willis Lamb (1913-2008)’s experiments confirmed this by revealing an ever so slight wobble in the different orbits of the electrons in a hydrogen atom, disclosing small differences in their energy levels thereby revealing the presence of virtual particles in the vacuum – something like a plane hitting turbulence forcing it up to a higher altitude. The peak showed that the vacuum is filled with energy.
As we have seen when considering the big bang, all this has important ramifications for how the universe itself came into existence. Today our best theories tell us that the universe sprang from the vacuum, and that the rules of the quantum world appear to have contributed to the large scale of the entire cosmos: when our universe first came into existence it was many times smaller than an atom, and its subsequent development since then has been governed by quantum world rules. Our universe is just the quantum world inflated many, many times. Nothing has really shaped everything. We can see this using the Cosmic Background Explorer (COBE) satellite, revealing the picture of the first light after the big bang, something like seeing an embryo after 12 hours after human conception, as the American astrophysicist, cosmologist and Nobel laureate George Smoot has described the phenomenon[13].
The rest of the story is by now familiar. Tiny variations in temperature were revealed, representing the scars left on our quantum universe. Matter did not spread out completely evenly; quantum fluctuations became the seeds, eventually forming vast clumps making up our galaxies, all of which started life as a mere quantum fluctuation of the vacuum.
“Our best theories today tell us that the Universe sprang from the vacuum creating the matter and anti-matter predicted by Paul Dirac. But the universe we see today is made up of matter. Nearly all the anti-matter has vanished. According to current theory the big bang produced equal amounts of matter and anti-matter but as the universe cooled down matter and anti-matter annihilated almost perfectly, but not quite! For every billion particles of antimatter and matter, one particle of matter was left behind. These annihilations produced the heat of the big bang we see today as the microwave background radiation. The one in a billion parts of matter left behind made galaxies and people. We are the leftovers of an unimaginable explosion”[14]. As one observer has been moved to comment: for Dirac “to describe in so precise a form the motion and very existence of all fundamental particles of nature, the same stuff of which we are made, is an act of uncommon genius[15]”.
[1] The First Law of Thermodynamics dictates that the total amount of energy in an isolated system remains constant: energy can neither be created nor destroyed.
[2] Frank Close, Nothing, A Very Short Introduction, OUP, 2009, 95.
[3] Ibid.
[4] Lawrence M. Krauss, A universe from nothing, - Why there is something rather than nothing, Free Press, New York, 2012, 71.
[5] Jim Al-Khalili, Everything and Nothing, 2 Part series, 2nd part - “Nothing”, BBC documentary, 2011, repeated SBS23 Feb 2014. Partial transcript at
http://hassers.blogspot.com.au/2011/03/how-everything-was-formed-from-nothing.html
[6] Close, op cit, 106-107.
[7] Ibid.
[8] Which, be it remembered, sets a lower limit, based on Planck’s constant, on the accuracy with which certain pairs of physical quantities of a particle, such as its position and momentum, can be measured together: Richard Gauthier, Ph D, The Dirac Equation and the Superluminal Electron Model, http://www.superluminalquantum.org/diracequation.pdf.2
[9] h = Planck’s Constant, which describes the proportional relationship between energy oscillations and the frequency of the radiating waves.
[10] Close, op cit, 106-107.
[10.1] See also Black holes and information theory: the link between quantum physics and general relativity?
[10.2] Actually, Gavin Hesketh says this simplified form of the equation is indeed quite simple: the mass of the particle mψ (right hand side) affects how it moves iγ · δ (left hand side): The Particle Zoo - The search for the fundamental nature of reality, Quercus, Hachette, London 2016, 16, 131. The latter reference adds an additional symbol (A) to the right hand side to apply symmetry.
[11] In Dirac representation, the four contravariant gamma matrices (tables of numbers) which threw up the existence of the anti-electron (positron) appear as:
The anti-electron appears as the bottom two sets of numbers.
[11.1] Michael Box, "The Fundamental Nature of light", WEA course, 26 August 2019, 4.2.3.
[12] Al-Khalili, op cit.
[13] Ibid.
[14] Ibid.
[15] Rory Fenton, “Art versus science at Westminster Abbey”, http://rationalist.org.uk/articles/4208/art-versus-science-at-westminster-abbey
[11.1] Michael Box, "The Fundamental Nature of light", WEA course, 26 August 2019, 4.2.3.
[12] Al-Khalili, op cit.
[13] Ibid.
[14] Ibid.
[15] Rory Fenton, “Art versus science at Westminster Abbey”, http://rationalist.org.uk/articles/4208/art-versus-science-at-westminster-abbey