Zero-energy universe

The zero-energy universe hypothesis proposes that every smallest amount of the universe's positive actual energy (this smallest amount is called the Planck quantum of action) is borrowed from the universe's gravitational field, making the latter's potential energy more negative by exactly the same amount. ^[1]

The erroneous concept of the zero-total-energy universe stems from its proponents' ignorance of the law of the diminishing marginal productivity of debt, which is a particular case of the law of diminishing returns (also known as the law of diminishing marginal productivity). As time goes by, the creation of the same amount of positive actual energy requires incurring an ever greater amount of debt in the form of negative gravitational potential energy, so that the total energy of the universe becomes increasingly negative.

According to Rudolf Clausius, the borrowed positive energy exerts a disgregating effect, ^[2] i.e. impedes matter's gravitational aggregation and thus plays the role of time as duration ("time is what prevents everything from happening all at once"). In the year 2025 AD, the marginal productivity of debt will decrease to zero, ^[3] and soon thereafter "time shall be no more"—by the end of the year 2026 AD (see Hyperbolic growth#Global macrodevelopment), the universe's matter will form a single hierarchic gravitational aggregate known as the eschaton, the world tree or the Christmas tree. After the ensuing millennium, the marginal productivity of debt will become negative, at which moment all the previously created Planck quanta of action will be instantaneously liquidated (the end of the world).

History

The idea that the universe's positive actual energy is borrowed from the universe's gravitational field was proposed in 1854 by William Thomson:

Thomson had adopted in 1854 the view that "the potential energy of gravitation may be in reality the ultimate created antecedent of all the motion, heat, and light at present in the universe". In other words, it was "the original form of all the energy in the universe". ^[4] Such a speculation conformed to his theology of nature in which God had created energy ex nihilo in the beginning by His absolute power and had sustained its quantity by His ordained power.

—Smith, Crosbie; Wise, M. Norton. Energy and Empire: A Biographical Study of Lord Kelvin CUP, 1989, p. 533

As a deeply religious man, Thomson merely restated the biblical concept that the material world has been borrowed from God, who is love, i.e. the universe's gravitational field. In the course of time, the sinful (i.e. unholy, devoid of holism) multiplicity of particles expiates itself by falling into the universe's gravitational field (i.e., by falling in love) and eventually regains holiness/holism by forming a universe-wide hierarchic singularity called the eschaton, the world tree or the Christmas tree, with the Man Christ Jesus standing on the hierarchy's top as the universe's provisional liquidator, preparing the insolvent world for its final liquidation known as the end of the world:

Sin is a debt, the world of sinners debtors, God the creditor, and the Man Christ Jesus the responsible surety.

—Kershaw, James. The Grand Extensive Plan of Human Redemption Sherdown and Son, 1797, p. 199

During World War II, Pascual Jordan suggested that because the positive energy of a star's mass and the negative energy of its gravitational field together may have zero total energy, conservation of energy would not prevent a star being created by a quantum transition of the vacuum. George Gamow recounted putting this idea to Albert Einstein: "Einstein stopped in his tracks and, since we were crossing a street, several cars had to stop to avoid running us down". ^[5] Elaboration of the concept was slow, with the first notable calculation being performed by Richard Feynman in 1962. ^[6] The first known publication on the topic was in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy. ^[7] In the subsequent decades, development of the concept was constantly plagued by the dependence of the calculated masses on the selection of the coordinate systems. In particular, a problem arises due to energy associated with coordinate systems co-rotating with the entire universe. ^[6] A first constraint was derived in 1987 when Alan Guth published a proof of gravitational energy being negative. ^[8] The question of the mechanism permitting generation of both positive and negative energy from null initial solution was not understood, and an ad hoc solution with cyclic time was proposed by Stephen Hawking in 1988. ^{[9] [10]}

In 1994, development of the theory resumed ^[11] following the publication of a work by Nathan Rosen, ^[12] in which Rosen described a special case of closed universe. In 1995, J.V. Johri demonstrated that the total energy of Rosen's universe is zero in any universe compliant with a Friedmann–Lemaître–Robertson–Walker metric, and proposed a mechanism of inflation-driven generation of matter in a young universe. ^[13] The zero energy solution for Minkowski space representing an observable universe, was provided in 2009. ^[6]

In his book Brief Answers to the Big Questions , Hawking explains:

The laws of physics demand the existence of something called 'negative energy'.

To help you get your head around this weird but crucial concept, let me draw on a simple analogy. Imagine a man wants to build a hill on a flat piece of land. The hill will represent the universe. To make this hill he digs a hole in the ground and uses that soil to dig his hill. But of course he's not just making a hill—he's also making a hole, in effect a negative version of the hill. The stuff that was in the hole has now become the hill, so it all perfectly balances out. This is the principle behind what happened at the beginning of the universe. When the Big Bang produced a massive amount of positive energy, it simultaneously produced the same amount of negative energy. In this way, the positive and the negative add up to zero, always. It's another law of nature. So where is all this negative energy today? It's in the third ingredient in our cosmic cookbook: it's in space. This may sound odd, but according to the laws of nature concerning gravity and motion—laws that are among the oldest in science—space itself is a vast store of negative energy. Enough to ensure that everything adds up to zero. ^[14]

Experimental refutation

In the course of time, the negative energy (suction) of our black-hole universe's central singularity grows in importance, so that the funnel-shaped gravity well, representing the universe's gravitational field, becomes increasingly stretched towards the central singularity. This stretching of space is often misinterpreted as the expansion of the universe.

The universal funnel-shaped flow of space, flowing at ever greater speeds towards the future central singularity, is engendered by a flaring beam of negative energy (suction), travelling into the past from the future central singularity. Inside the singularity, the speed of the flow of space and of the matter entrained thereby becomes equal to the speed of light, so that the universe's matter, which hitherto existed as a puppet engendered and driven by the future singularity, itself becomes the singularity, becomes the puppeteer, becomes God:

"A beam of negative energy that travels into the past can be generated by the acceleration of the source to high speeds."

"... the central singularity is still at r = 0. The conclusion is that motion forward in time is motion towards smaller r. An object entering the horizon is carried down to r = 0 just as surely as you and I are carried into next week."

The inhabitants of this ever longer and thinner funnel are literally longing for the future— people with elongated, serpentine bodies are more future-oriented and godlike than people with spheroidal bodies:

"... be wise as serpents ..."

"And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, that whoever believes in him may have eternal life."

The zero-total-energy universe is called "flat" or "Euclidean". But the observed flatness of the universe at very large distances cannot be used as an experimental evidence in favour of the zero-total-energy universe because it is the flatness of the primordial universe (it takes light many billions of years to arrive from large distances to the terrestrial telescopes). The modern universe is hierarchic even at the largest distances, which implies that the total energy of the modern universe is negative.

Astronomical observations suggest that by falling into its own gravitational field, the universe becomes ever more dominated by the gravitational field and acquires an ever more negative total energy:

The only explanation, according to Chaboyer and Krauss, for an accelerating universe is that the energy content of a vacuum is non-zero with a negative pressure, in other words, dark energy. This negative pressure of the vacuum grows in importance as the universe expands and causes the expansion to accelerate.

—‘Dark energy’ Dominates the Universe SpaceRef, 2003 01 02

The peculiar properties of the false vacuum stem from its pressure, which is large and negative (see box on the right). Mechanically such a negative pressure corresponds to a suction, which does not sound like something that would drive the Universe into a period of rapid expansion.

—Guth, Alan H. Was Cosmic Inflation the ‘Bang’ of the Big Bang? Beam Line, fall 1997, p. 20

The negative energy force that moves water is called suction.

—Sachs, Paul D. Dynamics of a Natural Soil System Edaphic Press, 1999, p. 56

The drain hole sucking water toward it is equivalent to the singularity at the center of a black hole sucking space toward it.

—Sen, Paul. Einstein's Fridge: How the Difference Between Hot and Cold Explains the Universe Simon and Schuster, 2022, p. 228

The basic idea, outlined in a nontechnical manner in ref. [7 ^[21] ], is that as inhomogeneities grow one must consider not only their backreaction on average cosmic evolution, but also the variance in the geometry as it affects the calibration of clocks and rulers of ideal observers. Dark energy is then effectively realised as a misidentification of gravitational energy gradients.

—Wiltshire, David L. Gravitational energy as dark energy: cosmic structure and apparent acceleration arXiv, 2011 02 10, p. 2

To us, falling towards the central singularity, our gravity-dominated ^[22] and because of that shrinking ^[23] black-hole universe seems to be expanding:

Now let us consider an astronaut explorer who goes to visit a black hole and falls in. According to her own proper time, the explorer can soon arrive in the vicinity of the horizon. Any light emitted at r_s in the outward radial direction as she falls in stays at the horizon, according to outer observers, but travels at c relative to the astronaut. Therefore, in the astronaut's rest frame the horizon moves outwards at c.

—Steane, Andrew M. Relativity Made Relatively Easy OUP, 2012, p. 368

Negative-energy universe

The universe is a vortex of space, engendered by the suction exerted by the universe's central singularity. At the wide entry mouth of the vortex, the rotational frequency is close to zero, and the angular momentum is potential, zero-rotational-frequencied. At the narrow exit mouth of the vortex, the rotational frequency is maximal, and the angular momentum is actual, nonzero-rotational-frequencied. As space swirls towards the central singularity, each consecutive segment of the spiral path incurs an ever greater amount of negative-energy debt (which is the suction exerted by the central singularity), but borrows into actuality an ever smaller amount of positive energy (which is nonzero-rotational-frequencied angular momentum ). It is because the vortex becomes narrower, and its moment of inertia decreases together with its radius measured perpendicularly to the axis of rotation. Thus, the marginal productivity of debt diminishes, so that the total energy of the vortex universe becomes ever more negative.

As the figure skater stepwisely decreases her radius by retracting her arms and legs, her moment of inertia (which is potential or zero-rotational-frequencied angular momentum) decreases, but her rotational frequency f increases, so that angular momentum becomes borrowed from zero-frequency potentiality into nonzero-frequency actuality. Consequently, her positive energy (E = hf) becomes greater. However, because her moment of inertia decreases together with her radius, each consecutive step of the decrease in her radius borrows into actuality a smaller amount of angular momentum.

If the total energy of the universe were zero, the negative gravitational potential energy of the universe would be cancelled out to zero by the positive actual energy of the universe, so that the universe's matter would be infinitely rarefied and thus nonexistent. The very fact that the universe exists proves that its total energy is negative, not zero.

The universe's positive energy (E = hf) consists of Planck quanta of action (h), which are quanta of angular momentum, ^[24] borrowed from the universe's gravitational field at the cost of deepening and narrowing the funnel-shaped gravity well ^[15] representing the field (to its inhabitants, the deepening and narrowing gravity well seems to be expanding ^[25] ):

The universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing was inflation. The universe expanded and borrowed at an ever increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe.

—Hawking, Stephen. The Beginning of Time A lecture written in 1996

During inflation, while the energy of matter increases by a factor of 10⁷⁵ or more, the energy of the gravitational field becomes more and more negative to compensate. The total energy—matter plus gravitational—remains constant and very small, and could even be exactly zero. Conservation of energy places no limit on how much the Universe can inflate, as there is no limit to the amount of negative energy that can be stored in the gravitational field.

This borrowing of energy from the gravitational field gives the inflationary paradigm an entirely different perspective from the classical Big Bang theory, in which all the particles in the Universe (or at least their precursors) were assumed to be in place from the start. Inflation provides a mechanism by which the entire Universe can develop from just a few ounces of primordial matter.

Inflation is radically at odds with the old dictum of Democritus and Lucretius, "Nothing can be created from nothing." If inflation is right, everything can be created from nothing, or at least from very little. If inflation is right, the Universe can properly be called the ultimate free lunch.

—Guth, Alan. The Inflationary Universe Beam Line, fall 1997, p. 19

The concept of the zero-total-energy universe is based on the wrong assumption that making the universe's negative potential energy (which is the debt) more negative by one unit always makes the universe's positive actual energy more positive by the same one unit.

In other words, the concept of the zero-total-energy universe ignores the law of the diminishing marginal productivity of debt, which is a particular case of the law of diminishing returns (also known as the law of diminishing marginal productivity).

The angular momentum (L) of the universe's funnel-shaped gravity well is the product of its moment of inertia and its angular velocity:

${\displaystyle L=I\omega ,}$

where

• ${\displaystyle I}$ is the moment of inertia, equal to the product of the mass and the square of its radius measured perpendicularly from the axis of rotation;
• ${\displaystyle \omega \ }$ is the angular velocity.

In the course of time, the universe's funnel-shaped gravity well deepens and narrows, ^[15] so that its moment of inertia (which is potential or zero-rotational-frequencied angular momentum, i.e. the reservoir from which angular momentum becomes borrowed into actuality by increasing its rotational frequency) decreases. Consequently, the marginal productivity of debt diminishes, so that the total energy of the universe becomes ever more negative.

The universe's moment of inertia is the universe's rest mass, space or volume, or gravitational potential energy:

The student is advised to regard moment of inertia as being equivalent to ‘angular mass’; equations in rotational mechanics are generally analogous to those in translational mechanics. Wherever an equation occurs in translational mechanics involving mass m, there is an equivalent equation in rotational mechanics involving moment of inertia J. The units of moment of inertia are kilogram metres² (abbreviation kg m²).

—Atkinson, P. Feedback Control Theory for Engineers Heinemann Educational Books, 2012, p. 50

The quantity factor of potential energy is space or volume which however is equivalent to mass.

—Mathews, Albert P. The Nature of Matter, Gravitation, and Light W. Wood and Company, 1927, p. 106

Therefore, the self-accelerating decrease in the universe's moment of inertia implies that the volume of the universe is shrinking. To human observers, the shrinking universe seems to be expanding because the atoms of which the observers consist are shrinking progressively faster than the entire universe:

All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom". <...>

Let us then take the whole universe as our standard of constancy, and adopt the view of a cosmic being whose body is composed of intergalactic spaces and swells as they swell. Or rather we must now say it keeps the same size, for he will not admit that it is he who has changed. Watching us for a few thousand million years, he sees us shrinking; atoms, animals, planets, even the galaxies, all shrink alike; only the intergalactic spaces remain the same. The earth spirals round the sun in an ever‑decreasing orbit. It would be absurd to treat its changing revolution as a constant unit of time. The cosmic being will naturally relate his units of length and time so that the velocity of light remains constant. Our years will then decrease in geometrical progression in the cosmic scale of time. On that scale man's life is becoming briefer; his threescore years and ten are an ever‑decreasing allowance. Owing to the property of geometrical progressions an infinite number of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being.

We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing.

—Eddington, Arthur. The Expanding Universe CUP, 1933, pp. 90–92

At the end of the year 2026 AD, the 13.7-billion-year-long process of matter's gravitational hierarchization will finish, and the matter of the entire universe will become organized into a gravitational hierarchy, supportive of psychokinesis and known as the world tree or the Christmas tree:

"More fundamentally, the results suggest that gravity may, in fact, emerge from entanglement. What's more, the geometry, or bending, of the universe as described by classical gravity, may be a consequence of entanglement, such as that between pairs of particles strung together by tunneling wormholes."

"In any case, the peculiarities of the quantum mechanics of highly entangled particle pairs seem much less mysterious in this picture, once one swallows the very large pill of the odd metric, essentially a one-dimensional universal wormhole."

After the ensuing millennium, the universal wormhole will instantaneously swallow all Planck quanta of action:

"The latest theory on how the universe will end involves everything being swallowed by a giant wormhole—a scenario dubbed the ‘Big Trip’."

Negative potential energy consists of a negative number of Planck quanta of action. That is why the catastrophically self-accelerating increase in the negative energy of the universe's gravitational potential field cancels the multiplicity (i.e. locality, resistance to psychokinesis) of the universe's Planck quanta of action (protons, electrons, etc.) by organizing them into a universe-wide hierarchic singularity, supportive of psychokinesis and known as the eschaton, the world tree, or the Christmas tree:

It is thus obvious that according to the ordinary conception we can assert no more than that the potential energy belongs to the system, that this conception therefore involves no localization of the energy in the system, and consequently no erroneous localization.

—The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science Vol. XXXVI, Taylor & Francis, 1893, p. 24

We must conclude that the potential energy belongs not to one body, but to the whole system of interacting bodies involved! This is evident in the fact that the potential energy gained is available to any one or to all of these interacting bodies.

—Cassidy, David C.; Holton, Gerald; Rutherford, F. James. Understanding Physics Springer, 2002, p. 239

After a millennium of the eschaton's existence, all Planck quanta of action cease to exist (the end of the world).

So, the universe is most alive just before it dies. The very fact that the extreme negentropy of terrestrial life exists indicates that the total energy of the universe has already become extremely negative and has organized all Planck quanta of action into a single hierarchy ^[29] with the planet Earth at its top:

The negative energy of the gravitational field is what allows negative entropy, equivalent to information, to grow, making the Universe a more complicated and interesting place.

—Gribbin, John. In Search of the Multiverse Penguin, 2009, p. 131

Hydrogen is a light, odourless gas, which, given enough time, turns into people.

—Chaisson, Eric J. Cosmic Evolution: The Rise of Complexity in Nature HUP, 2002, p. 2

The 13.7-billion-year-long catastrophically self-accelerating hierarchization and shrinkage of the universe's protons is expected to finish by the end of the year 2026 AD—see Hyperbolic growth#Global macrodevelopment.

However, the universe's protons will not disappear at the end of the year 2026 AD. Any self-gravitating proton, converting its rest mass into radiant energy, radiates away only a half of that radiant energy but retains the other half. ^{[30] [31]}

Therefore, upon converting all of its rest mass into radiant energy, a proton will retain a half of that radiant energy circulating within itself and serving as a quasi rest mass. Those end-time protons will formally have rest masses but essentially will be massless "radiant spirits".

Thus, at the end of the year 2026 AD, the universe will become entirely made of light and will enter the last millennium of its existence called the eschaton, during which the universe will consist of ephemeralized to the point of being amenable to psychokinesis, ghostlike atoms, frantically performing their danse macabre on the verge of instantaneous disappearance:

"Well, then, if you picture what I'm describing, it's a funnel of some sort, which begins with an extremely wide mouth, but which has now narrowed to an extremely small and fast-moving kind of situation. And this is why history is a self-limiting process. It isn't that we have broken away from the slow-moving processes of ordinary nature. It's that we represent nature at a different time frame. And I think this is why history is ending. Because it's going so much faster than it used to go that it's going to finish very soon. There may be as much experience ahead of us as there is behind us, but we're moving through it so much faster than we used to that we're literally approaching the end of time at a faster and faster speed."
       —McKenna, Terence. Reality is Complexifying 1992

"It's this idea that we represent some kind of singularity, or that we announce the nearby presence of a singularity. That the evolution of life and cultural form and all that is clearly funneling toward something fairly unimaginable."
       —McKenna, Terence. A Weekend with Terence McKenna August 1993

"‘It all just seemed unbelievably boring to me,’ Penrose says. Then he found something interesting within it: at the very end of the universe, the only remaining particles will be massless. That means everything that exists will travel at the speed of light, making the flow of time meaningless."
       —Brooks, Michael. Roger Penrose: Non-stop cosmos, non-stop career New Scientist, 2010 03 10

"In other words, we end the whole thing. We collapse the state vector and everything goes into a state of novelty. What happens then I think is the universe becomes entirely made of light."
       —McKenna, Terence. Appreciating Imagination 1997

"The conventions of relativity say that time slows down as one approaches the speed of light, but if one tries to imagine the point of view of a thing made of light, one must realize that what is never mentioned is that if one moves at the speed of light, there is no time whatsoever. There is an experience of time zero. <...> One has transited into the eternal mode. One is then apart from the moving image; one exists in the completion of eternity. I believe that this is what technology pushes toward."
       —McKenna, Terence. New Maps of Hyperspace 1984

"What exactly is immortality? It's the negation of time. How do we negate time? By getting close to, and perhaps matching, the speed of light. If you ARE light, everything is instant."
       —Time fUSION Anomaly, 1999 10 11

"And the angel that I saw standing upon the sea and upon the land lifted his hand up to heaven, and swore by him who lives forevermore, who created heaven and the things that are in it, and the sea and the things that are in it, that time shall be no more, but in the days of the voice of the seventh angel, when he begins to blow, even the mystery of God shall be finished, as he preached by his servants the prophets."
       —Revelation 10:5-7 New Matthew Bible

See also

• A Universe from Nothing
• False vacuum
• Heat death of the universe
• List of cosmology paradoxes  – List of statements that appear to contradict themselves
• Ultimate fate of the universe

References

1. "A Universe From Nothing lecture by Lawrence Krauss at AAI". YouTube . 2009. Archived from the original on 2021-12-15. Retrieved 17 October 2011.
2. Clausius, 1867 "By help of this conception the effect of heat can be simply expressed by saying that heat tends to increase the disgregation of bodies."
3. Misra, Siddharth. Plummeting ‘Energy Return on Investment’ of Oil and the Impact on Global Energy Landscape Journal of Petroleum Technology, 2023 03 20. "The global energy landscape is facing a crucial turning point. Various studies show that oil liquid production is expected to peak in 2035 at a magnitude of 500 petajoule per day (PJ/d), but when the energy required for the extraction and production of these liquids is taken into account, the net-energy peak is expected to occur in 2025 at a level of 400 PJ/d (Delannoy et al. 2021)."
4. MPP. 2, 40; William Thomson and P.G. Tate, 'Energy', Good Words, 3 (1862), 601–7, on p. 606
5. Beyond Einstein: The Cosmic Quest for the Theory of the Universe - Michio Kaku, Jennifer Trainer Thompson - Oxford University Press, 1997 - p189
6. Berman, Marcelo Samuel (2009). "On the Zero-Energy Universe". International Journal of Theoretical Physics. 48 (11): 3278–3286. arXiv: gr-qc/0605063 . Bibcode:2009IJTP...48.3278B. doi:10.1007/s10773-009-0125-8. S2CID   119482227.
7. Edward P. Tryon, "Is the Universe a Vacuum Fluctuation?", Nature , vol. 246, p. 396–397, 1973.
8. Alan Guth, in his book The Inflationary Universe, ( ISBN   0-224-04448-6) Appendix A.
9. Stephen Hawking, A Brief History of Time , p. 129.
10. "We might decide that there wasn't any singularity. The point is that the raw material doesn't really have to come from anywhere. When you have strong gravitational fields, they can create matter. It may be that there aren't really any quantities which are constant in time in the universe. The quantity of matter is not constant, because matter can be created or destroyed. But we might say that the energy of the universe would be constant, because when you create matter, you need to use energy. And in a sense the energy of the universe is constant; it is a constant whose value is zero. The positive energy of the matter is exactly balanced by the negative energy of the gravitational field. So the universe can start off with zero energy and still create matter. Obviously, the universe starts off at a certain time. Now you can ask: what sets the universe off. There doesn't really have to be any beginning to the universe. It might be that space and time together are like the surface of the Earth, but with two more dimensions, with degrees of latitude playing the role of time." – Stephen Hawking, "If There's an Edge to the Universe, There Must Be a God" (interview), in Renée Weber, Dialogues With Scientists and Sages: The Search for Unity, 1986. (Also partially reprinted in "God as the Edge of the Universe", in The Scientist , Vol. 1, No. 7, February 23, 1987, p. 15.)
11. Xulu, S. S. (2000). "Total Energy of the Bianchi Type I Universes". Int. J. Theor. Phys. 39 (4): 1153–1161. arXiv: gr-qc/9910015 . Bibcode:2000IJTP...39.1153X. doi:10.1023/A:1003670928681. S2CID   15413640.
12. Rosen, Nathan (March 1994). "The energy of the universe". General Relativity and Gravitation. 26 (3): 319–321. Bibcode:1994GReGr..26..319R. doi:10.1007/BF02108013. S2CID   121139141.
13. Johri, V. B.; Kalligas, D.; Singh, G. P.; Everitt, C. W. F. (March 1995). "Gravitational energy in the expanding universe". General Relativity and Gravitation. 27 (3): 313–318. Bibcode:1995GReGr..27..313J. doi:10.1007/BF02109127. S2CID   120110466.
14. Hawking, Stephen (2018). Brief Answers to the Big Questions. New York: Bantam Books. p. 32. ISBN   978-1-9848-1919-2.
15. Battersby, Stephen. Big Bang glow hints at funnel-shaped Universe New Scientist, 2004 04 15
16. Skinner, Ray. Relativity for Scientists and Engineers Courier Corporation, 2014, pp. 188–89
17. Steane, Andrew M. Relativity Made Relatively Easy OUP, 2012, pp. 387–88
18. Sheldon, William H. The Varieties of Temperament Harper & Brothers, 1942, p. 48. "In a very general sense, viscerotonia may be said to look back toward childhood, while somatotonia looks to the present, and the vision of cerebrotonia is fixed upon the distant future."
19. Matthew 10:16 ESV
20. John 3:14–15 ESV
21. D. L. Wiltshire, in Dark Matter in Astroparticle and Particle Physics: Proc. of the 6th International Heidelberg Conference, eds H. V. Klapdor–Kleingrothaus and G. F. Lewis, (World Scientific, Singapore, 2008) pp. 565-596 [arXiv:0712.3984].
22. Seeds, Michael A.; Backman, Dana. Foundations of Astronomy Cengage Learning, 2010, p. 75. "Gravity rules. The moon orbiting Earth, matter falling into black holes, and the overall structure of the universe are dominated by gravity."
23. The universe is shrinking because its central singularity sucks space out of it.
24. Biedenharn, L. C.; Louck, J. D. Angular Momentum in Quantum Physics Addison-Wesley Pub. Co., Advanced Book Program, 1981. "The Planck quantum of action, h, has precisely the dimensions of an angular momentum ..."
25. Steane, Andrew M. Relativity Made Relatively Easy OUP, 2012, p. 368. "Now let us consider an astronaut explorer who goes to visit a black hole and falls in. According to her own proper time, the explorer can soon arrive in the vicinity of the horizon. Any light emitted at r_s in the outward radial direction as she falls in stays at the horizon, according to outer observers, but travels at c relative to the astronaut. Therefore, in the astronaut's rest frame the horizon moves outwards at c."
26. You can't get entangled without a wormhole: Physicist finds entanglement instantly gives rise to a wormhole ScienceDaily, 5 December 2013
27. Coyne, D. G. A Scenario for Strong Gravity without Extra Dimensions arXiv, 2006, p. 31
28. Swarup, Amarendra. Phantom energy may fuel universe-eating wormhole New Scientist, 2005 11 11
29. The observed flatness of the universe at very large distances is the flatness of the primordial universe (it takes light many billions of years to arrive from large distances to the terrestrial telescopes). The modern universe is hierarchic even at the largest distances.
30. Böhm-Vitense, Erika. Introduction to Stellar Astrophysics CUP, 1992, p. 29. "After each infinitesimal step of collapse the star has to wait until it has radiated away half of the released gravitational energy before it can continue to contract."
31. Cameron, A. G. W. Technical Note D-1682: The Collapse Phase of Early Solar Evolution NASA, January 1963, p. 5. "As the protostar contracts, half of the gravitational potential energy released will be stored as internal heat, and the remaining half will be radiated away from the surface."