Filling the early universe with knots can explain why the world is three-dimensional

October 16, 2017 by David Salisbury
Filling the early universe with knots can explain why the world is three-dimensional
Credit: Keith Wood / Vanderbilt

The next time you come across a knotted jumble of rope or wire or yarn, ponder this: The natural tendency for things to tangle may help explain the three-dimensional nature of the universe and how it formed.

An international team of physicists has developed an out-of-the-box theory that shortly after it popped into existence 13.8 billion years ago the universe was filled with knots formed from flexible strands of energy called tubes that link elementary particles together. The idea provides a neat explanation for why we inhabit a three-dimensional world and is described in a paper titled "Knotty inflation and the dimensionality of space time" accepted for publication in the European Physical Journal C and available on the arXiv preprint server.

"Although the question of why our universe has exactly three (large) is one of the most profound puzzles in cosmology … it is actually only occasionally addressed in the [scientific] literature," the article begins.

For a new solution to this puzzle, the five co-authors – physics professors Arjun Berera at the University of Edinburgh, Roman Buniy at Chapman University, Heinrich Päs (author of "The Perfect Wave: With Neutrinos at the Boundary of Space and Time") at the University of Dortmund, João Rosa at the University of Aveiro and Thomas Kephart at Vanderbilt University – took a common element from the standard model of particle physics and mixed it with a little basic knot theory to produce a novel scenario that not only can explain the predominance of three dimensions but also provides a natural power source for the inflationary growth spurt that most cosmologists believe the universe went through microseconds after it burst into existence.

The common element that the physicists borrowed is the "flux tube" comprised of quarks, the that make up protons and neutrons, held together by another type of elementary particle called a gluon that "glues" quarks together. Gluons link positive quarks to matching negative antiquarks with flexible strands of energy called flux tubes. As the linked particles are pulled apart, the flux tube gets longer until it reaches a point where it breaks. When it does, it releases enough energy to form a second quark-antiquark pair that splits up and binds with the original particles, producing two pairs of bound particles. (The process is similar to cutting a bar magnet in half to get two smaller magnets, both with north and south poles.)

"We've taken the well-known phenomenon of the flux tube and kicked it up to a higher energy level," said Kephart, professor of physics at Vanderbilt.

The physicists have been working out the details of their new theory since 2012, when they attended a workshop that Kephart organized at the Isaac Newton Institute in Cambridge, England. Berera, Buniy and Päs all knew Kephart because they were employed as post-doctoral fellows at Vanderbilt before getting faculty appointments. In discussions at the workshop, the group became intrigued by the possibility that flux tubes could have played a key role in the initial formation of the universe.

According to current theories, when the universe was created it was initially filled with a superheated and electrically charged liquid called . This consisted of a mixture of quarks and gluons. (In 2015 the quark-gluon plasma was successfully recreated in a particle accelerator, the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, by an international group of physicists, including five from Vanderbilt: Stevenson Chair in Physics Victoria Greene, and Professors of Physics Will Johns, Charles Maguire, Paul Sheldon and Julia Velkovska.)

Kephart and his collaborators realized that a higher energy version of the quark-gluon plasma would have been an ideal environment for flux tube formation in the very early universe. The large numbers of pairs of quarks and antiquarks being spontaneously created and annihilated would create myriads of flux tubes.

Normally, the flux tube that links a quark and antiquark disappears when the two particles come into contact and self annihilate, but there are exceptions.

Computer graphic showing the kind of tight network of flux tubes that the physicists propose may have filled the early universe. Credit: Thomas Kephart / Vanderbilt

If a tube takes the form of a knot, for example, then it becomes stable and can outlive the particles that created it. If one of particles traces the path of an overhand knot, for instance, then its flux tube will form a trefoil knot. As a result, the knotted tube will continue to exist, even after the particles that it links annihilate each other. Stable flux tubes are also created when two or more flux tubes become interlinked. The simplest example is the Hopf link, which consists of two interlinked circles.

In this fashion, the entire universe could have filled up with a tight network of flux tubes, the authors envisioned. Then, when they calculated how much energy such a network might contain, they were pleasantly surprised to discover that it was enough to power an early period of cosmic inflation.

Since the idea of cosmic inflation was introduced in the early 1980s, cosmologists have generally accepted the proposition that the early universe went through a period when it expanded from the size of a proton to the size of a grapefruit in less than a trillionth of a second.

This period of hyper-expansion solves two important problems in cosmology. It can explain observations that space is both flatter and smoother than astrophysicists think it should be. Despite these advantages, acceptance of the theory has been hindered because an appropriate energy source has not been identified.

"Not only does our flux tube network provide the energy needed to drive inflation, it also explains why it stopped so abruptly," said Kephart. "As the universe began expanding, the flux-tube network began decaying and eventually broke apart, eliminating the energy source that was powering the expansion."

When the network broke down, it filled the universe with a gas of subatomic and radiation, allowing the evolution of the universe to continue along the lines that have previously been determined.

The most distinctive characteristic of their theory is that it provides a natural explanation for a three-dimensional world. There are a number of higher dimensional theories, such as string theory, that visualize the universe as having nine or ten spatial dimensions. Generally, their proponents explain that these higher dimensions are hidden from view in one fashion or another.

The flux-tube theory's explanation comes from basic knot theory. "It was Heinrich Päs who knew that knots only form in three dimensions and wanted to use this fact to explain why we live in three dimensions," said Kephart.

A two-dimensional example helps explain. Say you put a dot in the center of a circle on a sheet of paper. There is no way to free the circle from the dot while staying on the sheet. But if you add a third dimension, you can lift the circle above the dot and move it to one side until the dot is no longer inside the circle before lowering it back down. Something similar happens to three-dimensional knots if you add a fourth dimension – mathematicians have shown that they unravel. "For this reason knotted or linked tubes can't form in higher-dimension spaces," said Kephart.

The net result is that inflation would have been limited to three dimensions. Additional dimensions, if they exist, would remain infinitesimal in size, far too small for us to perceive.

The next step for the physicists is to develop their theory until it makes some predictions about the nature of the that can be tested.

Explore further: 'Littlest' quark-gluon plasma revealed by physicists using Large Hadron Collider

More information: Knotty inflation and the dimensionality of spacetime. arXiv. arxiv.org/abs/1508.01458

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26 comments

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sevensixtwo
3 / 5 (6) Oct 16, 2017
>This period of hyper-expansion solves two important problems in cosmology.

Not really. It moves the implications of the problems to a region of the universe that is further detached from the part we can observe
Chris_Reeve
1.4 / 5 (9) Oct 16, 2017
Fred Hoyle, Home is where the wind blows, p.225

"... almost the entire body of astronomers can go wrong in a way that, in later years, seems absurd. To hear scientists talk today, you would think the first moment in human history in which nonsensical views are not widely held is now. Yet, when I contemplate the strong belief of many, that every thing of real importance in the big-bang Universe happened in the first 10^-43 seconds of its existence, I am compelled to wonder."
eric96
not rated yet Oct 16, 2017
The whole is greater than the sum of its parts. It means there is insufficient evidence in the universe to reconstruct its first moments of existence. In that light, saying that everything happened in the first 10^-43 seconds of its existence is simply acknowledging that many secrets of the universe will never be unraveled. Cosmologists will always have a job (there is no ultimate formula that can be proven) unless we dismiss their profession. Still, the universe has many exciting [single perspective (not 3D) ] secrets ready be be unraveled and less exciting 3d ones. The epi-leaps of scientific marvel lie in how we view, acquire and manipulate information and in this sense we are still quite young as is our mathematics, but we'll get there or extinct. There refers to an era of indisputable scientific and mathematics excellence from a grain of sand (today) to a beach.
Spaced out Engineer
1 / 5 (2) Oct 16, 2017
Yet tubes can catch similar to strings in 4D, preserving some information content of the configuration space of braiding. The spooky thing is that this also aligns with LQG. Spacetime to space provides an evolution of operators that matches lattice field theory.
Even stranger is that a new inflationary field maybe kicking off right now!
Personally I like the fate of the false vacuum as entanglement, tunneling. It matches theories that do not have determinable decoupling, and it permits incompleteness of points and spheres. It may match flat space flung from the singular, and permits a kind of faith in the born rule, projective spaces, and the orthogonal. It may exact a means of skipping upon the naked singular here, now, withstanding dark energy. No FLRW model left behind.
Interoperability, to have it physics would no longer be existential, to be denied it, we remain at a loss, unless we can adopt another's perspective in the dialect.
Hyperfuzzy
1 / 5 (6) Oct 16, 2017
Nonsense
rogerdallas
5 / 5 (3) Oct 16, 2017
This is an interesting theory and I hope it can be developed to the extent of predicting some observable consequence that can be tested. Otherwise, it is just an interesting theory.
Da Schneib
5 / 5 (7) Oct 16, 2017
The ability to predict a 3+1 dimensional universe is actually quite an important characteristic. I'll be interested to see what emerges from this.
znamenski
not rated yet Oct 17, 2017
How to understand all of this?
PoppaJ
not rated yet Oct 17, 2017
Any one else get a chuckle at the fact the images do not reflect "knots"
tallenglish
1 / 5 (4) Oct 18, 2017
Alternate explanation is the universe (or rather the energy within it) is folding, so it starts 1D, then 2D, then 4D, etc the folds being at 0 and infinity. We also need to stop using red shift to explain everything in the universe as we are biased towards red shift due to our close proximity to a yellow sun (the light makes spacetime expand) - if we were around a neutron star or black hole the universe would be blue shifting in all directions (which should be obvious as they absorbe phtons not emit them).
nikola_milovic_378
Oct 23, 2017
This comment has been removed by a moderator.
nikola_milovic_378
Oct 23, 2017
This comment has been removed by a moderator.
antialias_physorg
not rated yet Oct 23, 2017
Any one else get a chuckle at the fact the images do not reflect "knots"

In the sense of topology they do (though it's a very weird representations in that while columns are linked rows do not seem to be)
Merrit
not rated yet Oct 23, 2017
I wonder if this could be another theory for dark matter as well. Suppose for instance, that not all these knots have broken up yet. Maybe the knots still around today can account for dark matter
cantdrive85
1 / 5 (1) Oct 23, 2017
"We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture." Hannes Alfvén

And in the above the astrophysicists gift us with their imaginary conjecture. LOL!
Merrit
5 / 5 (1) Oct 23, 2017
@cantdrive that is the nature of conjectures. Science is about asking questions, conjectures, and finding answers, experiments. You need both advance scientific knowledge.

Also, the article states that they are still working on coming up with testable experiments. My conjecture was simply something worth looking into. Stars, for example, take billions of years to use their fuel and burn out. A massive jumble of knots that they proposed in this article could very well take a long to become undone as well.
Hyperfuzzy
1 / 5 (1) Oct 23, 2017
@cantdrive that is the nature of conjectures. Science is about asking questions, conjectures, and finding answers, experiments. You need both advance scientific knowledge.

Science begins with an assumed truth; hypothesize if [x] given [y] then [Z] is T/F; For every ...; first logically. Without logic no truth is defined. i.e. Define a universe of discourse; Define Logical Rules for {Sets}; Mathematics, experimentation, proof of causality, ... Modern Physics is not science, it's science fiction,
cantdrive85
1 / 5 (1) Oct 23, 2017
@ Merrit,
My comment was not directed at you necessarily, but the imaginary conjecture suggested above. Although I must say, your imaginary conjecture is just as valid as that of the plasma ignoramuses, not that that is saying much...
Hyperfuzzy
1 / 5 (2) Oct 23, 2017
@ Merrit,
My comment was not directed at you necessarily, but the imaginary conjecture suggested above. Although I must say, your imaginary conjecture is just as valid as that of the plasma ignoramuses, not that that is saying much...

To respond to and obvious false Theory that begins as conjecture based on someone playing with math, makes interesting science fiction. The disrespect of defining the work emotionally dose not meet the challenge of discovery. Ok, application(F), method, genius!
Hyperfuzzy
1 / 5 (2) Oct 23, 2017
First, there are no particles only charge, charge is the charges field from its center to infinity. It's field is apparently updated with respect to its center. Fields don't bother other fields. You can define the universe from these. One can define the geometry of the combined fields according to some of the actual measurements in spite of the nonsensical theories. We give NOBLEs and rightfully so; for it's the dedication, the added knowledge gained, attempting the impossible. I can visualize this structure of a group of fields. The4 implications when applying truth is always a new Discovery. Juz say'n
Merrit
not rated yet Oct 23, 2017
@cantdrive true enough. It will be interesting to see if any truth is found from this theory. I don't doubt that knots were formed since we can form them artificially, it just might not have been significant to the development of our universe.
Merrit
5 / 5 (2) Oct 23, 2017
@hyperfuzzy yes, our science is flawed. There are no base truths from which to work from. We have had to make our own theories and determine how likely they are. There is no perfect solution. Scientists do the best they can in the real world we live in. If we were to only use what is 100% truth without any assumptions we would have no science and still be living in caves.
Hyperfuzzy
1 / 5 (1) Oct 23, 2017
@hyperfuzzy yes, our science is flawed. There are no base truths from which to work from. We have had to make our own theories and determine how likely they are. There is no perfect solution. Scientists do the best they can in the real world we live in. If we were to only use what is 100% truth without any assumptions we would have no science and still be living in caves.

This is an error.
Whydening Gyre
not rated yet Oct 23, 2017
Any one else get a chuckle at the fact the images do not reflect "knots"

looks more like maille
Whydening Gyre
not rated yet Oct 23, 2017
@ Merrit,
My comment was not directed at you necessarily, but the imaginary conjecture suggested above. Although I must say, your imaginary conjecture is just as valid as that of the plasma ignoramuses, not that that is saying much...

Sorta like you see your own conjectures, CD...?
Hyperfuzzy
not rated yet Oct 23, 2017
My issue, it could be a magnetic field. Since fields do not affect fields, the crossover seems suspicious since each E field is a unique continuous field. However, if this reflects how these imaginary particles are manifested, i.e. the field events; then this is ground breaking. Seems this would be seemingly impossible. Tough to work out as charge center motion, more like a stability matrix; but with a difficult proof. But yes magnetically? Write the curl, then offer proof.

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