Nce Again Consider a Spatially Flat Universe Containing Only Matter

Using the Hubble telescope, it took NASA scientists eight years to get a measurement of the expanding universe. This spiral galaxy -- NGC 4603 -- was the near afar milky way helpful to the study. Jeffrey Newman/NASA hide explanation

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Jeffrey Newman/NASA

Unfortunately for previous cosmological theories, the universe appears reasonably convincingly to be expanding at an accelerating rate. This, all physicists know, is no minor problem. It is and so severe that physicists now invoke "Dark Energy" to explain this accelerating expansion.

Hither is the cardinal trouble: Throw a ball into the air. If you do so at less than the escape velocity from the earth's gravitational field, information technology will fly upward, exchange kinetic and gravitational potential energy until the 2 are equal at the top of its trajectory, and then the ball will fall back to earth. If the initial velocity of the ball is but equal to the globe's gravitational field, the ball will "declension to infinity" always more slowly, reaching infinity at 0 velocity, in the absence of other matter in the universe to provide boosted gravitational fields. If the initial velocity of the ball is still higher, it will fly from the earth and coast to infinity at an ever decreasing, but finite velocity.

The Large Bang, well, Banged. To put the result over-only, vast energy arising from nothing became a quark gluon soup, became affair and fields containing energy, hence, by E=MC^two, matter, equally the universe expanded. The mutual gravitational attraction of all the mass and energy in the universe is supposed to forever slow the expansion of the universe. Given General Relativity, the universe should either expand then collapse in the Big Crunch, like the ball falling again to earth, it should expand forever to infinity reaching infinity at a nix charge per unit of expansion, a disquisitional state of affairs, or it should expand forever, but at an always slowing only finite rate.

The first and last cases represent past General Relativity to a positively curved spacetime, and a negatively curved space time. The critical case corresponds to a flat spacetime. Cosmologists thought the universe was critical.

What the universe should not be doing is expanding at an accelerating rate.

But it seems to exist.

Einstein made a "mistake."

He thought the universe was of abiding size, and his equations did not predict this. He "fudged" and added the simplest correction term to his equations, the "Cosmological Constant." Using it, Einstein could accomplish a universe of constant size. Hubble soon discovered that galaxies recede from 1 some other in proportion to their distance autonomously and concluded the universe was expanding. Einstein admitted it was the worst mistake of his scientific life.

But the Cosmological Constant has remerged as a start to account for Night Free energy. With it, one can achieve an accelerating expansion of the universe. The Cosmological Constant is as if at that place were a "repulsive force" in space, pushing any two regions of space further apart, and the more so equally their distance apart increases.

Einstein realized that his Cosmological Constant implied an increasing energy in the expanding universe, such that the vacuum energy per unit of measurement book remained constant. This flies in the face of the Big Bang conventionalities that all the energy of the universe came to exist in that Bang. Well, OK, then information technology does.

The problem is, at that place is, in a deep sense, no physics backside the Cosmological Abiding, information technology is just a constant added the only place Einstein could in his equations and go along the rest of the physics of General Relativity unmodified.

Thus, the deep question is: What conceivable physical process(es) could constitute the Cosmological constant.

I am going to propose a related prepare of concepts that might do the job:

1. Space is Not CONTINUOUS. Infinite, on the smallest length scale, the Planck length of 10³⁴ centimeters, comes in detached units. These units cannot interpenetrate, otherwise, once again, space would be continuous. An approach to quantum gravity, Loop Quantum Gravity, kindly taught to me by Lee Smolin, a founder of that field, proposes that on the Planck calibration, infinite is comprised of tetrahedra.
2. These units of space too cannot expand. But this implies that space itself cannot expand! The only style "infinite" can expand is if more units of infinite, the tetrahedra, come into existence. In Loop Quantum Gravity this is allowed: tetrahedra can build new tetrahedra on whatsoever of their four faces in what are chosen Pachner moves. So for space to "expand" it must build itself by "cloning" itself.
3. Tetrahedra or units of space accept a constant "rate" or probability per unit time, of cloning themselves. This postulate implies that space builds itself and expands E'er FASTER. Indeed, like a bacterial colony freshly plated, space expands exponentially. Nosotros are stepping towards Nighttime Energy and a Cosmological Constant which yields an exponentially expanding space. Before I go farther, it is articulate that the more space now exists, the more than tetrahedra in that location are, so any two regions of infinite are being "pushed apart" past the cloning of tetrahedra between them.
4. Every time a tetrahedron of space is created, new energy enters that tetrahedron from nowhere, so the vacuum energy is abiding as space expands at an accelerating rate. This accords with Einstein'south realization that the Cosmological Abiding could imply can constant free energy per unit space as infinite expanded: Dark Energy we now say. I note that information technology makes u.s. uncomfortable in imagine energy arising from "zippo", but we take this magic at the Big Bang It is no more than magical here. Some energy per unit of measurement space is needed for signal v) side by side. Likewise physicists say that once in that location is matter, energy, expansion, and gravitation, energy is not conserved.
5. Newborn tetrahedra are quantum objects. More than, by Pachner moves, quantum geometry tin can be in a superposition of more one "graph structure" connecting the nodes of the tetrahedra in a diverseness of means. Merely because they contain energy, they contain mass. At some calibration and book of cloning tetrahedra, considered as a "arrangement" in a still larger spatial volume considered as the "surround" of the "system", the mass in the infinite in the "organisation" is sufficient that some number of quantum tetrahedra DECOHERE into CLASSICAL Space.
6. Now two culling postulates: 6A, even classical space tin requite nativity to new tetrahedra. 6B, decoherence can be reversed occasionally, and newly quantum tetrahedra can clone themselves and give birth to new tetrahedra. The culling postulates matter of course, but I will not favor either.

Taking the above non-mathematized schema of a physical a theory of Nighttime Energy equally the cloning of infinite by space, the first thing to exercise is approximate the rate of cloning of space needed to account for the observed accelerating expansion of the universe. This is a relatively straightforward job.

The Existent Line is a Existent Mess. Best if space is discrete on some small scale.

There is a split reason to consider space on some smallest scale to exist discrete: The real line is a real mess. Recall that the real line, a human being invention, is a continuous line, for example from 0.0 to 1.0 on some calibration like a meter stick. The real line has both an infinity of rational numbers, where rational numbers can be expressed as the ratio of two whole numbers such as 34/6501. Just every bit Pythagoras proved, there are numbers that cannot be expressed every bit such ratios. These are the irrational numbers and are expressed every bit INFINITELY LONG sequence of the integers, 0,one,2,three,4,5,six,7,8,9 afterwards the "decimal point". How many irrational numbers are there? Well, between whatever two rational numbers, no affair how shut, at that place are an space number of irrational numbers. The rational numbers are of the aforementioned lodge of infinity as the integers. The irrationals are of second order infinity.

Hither is the trouble. Mathematics is largely founded on prepare theory. But suppose I want to form 2 sets of irrational numbers, each with specific irrational numbers in it. How can I do so? Each irrational number is an space series of the first ten integers above. How can I pick a "specific" irrational number?

One reply would seem easy: take a computer algorithm to compute each such number, like Pi, or the square root of two, both of which are irrational, and then just class the sets.

Unfortunately, Alan Turing of the Turing Auto that is the basis of all digital classical and quantum computers today, proved that almost no irrational numbers were "effectively computable" using a Universal Turing Auto. So nosotros cannot employ this idea for our 2 sets.

The mathematicians, wishing to preserve ready theory, postulated an Axiom of Option asserting, well what the heck, that 1 can just go ahead and course the two sets.

Axioms are fine, just Turing tells u.s. there is no effectively computable fashion to attain the formation of these two sets for arbitrary choices of irrational numbers.

Why should we care? Because on the one manus, classical physics is based on the continuous line, rational and irrational numbers included. But then, classical physics works at length scales far to a higher place the Planck length scale of x to the - 34 centimeters.

We don't need a continuum at that scale for classical physics.

On the other hand, if we think that information technology is nosotros who invented the idea of the real line and have learned to love it, this does not mean that the existent line is the correct description of reality. And it is filled with issues. As I said, the real line is a mess.

Then if we surrender the real line, infinite must have a smallest length scale. The Planck length scale is the obvious scale. Then we become to Loop Quantum Gravity's tetrahedra, or another minimal discrete units of space, avoid the continuous line, and with the postulates that these minimal units of space cannot interpenetrate, cannot expand, and tin can clone themselves nosotros have the showtime of an exponentially expanding space. If we add energy per new unit of measurement of space and decoherence of quantum units of infinite, we get classical space and a constant vacuum free energy. And if on 6A or 6B space tetrahedra tin can go on to clone themselves at some rate per unit of measurement volume of infinite we have Nighttime Energy.

There is as yet no matter or other energy in this infinite, of class, to add its mutual gravitational attraction to that of vacuum energy, as described by General Relativity, but given CLASSICAL Infinite accomplished by the decoherence of breakthrough regions of space considered as "systems" into larger regions of breakthrough infinite considered as "environments, General Relativity seems safe.

This could conceivably institute a theory, or office of a theory, of breakthrough gravity. The ideas could just possibly unite General Relativity and Quantum Mechanics. It seems worth thinking virtually.

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Source: https://www.npr.org/sections/13.7/2010/05/28/127234796/discrete-space-dark-energy-and-the-real-line-toward-quantum-gravity

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