In Search of a Wormhole

by Paul Gilster | Oct 29, 2019 | Breakthrough Propulsion | 17 comments

A star called S2 is intriguingly placed, orbiting around the supermassive black hole thought to be at Sgr A*, the bright, compact radio source at the center of the Milky Way. S2 has an orbital period of a little over 16 years and a semi-major axis in the neighborhood of 970 AU. Its elliptical orbit takes it no closer than 120 AU, but the star is close enough to Sgr A* that continued observations may tell us whether or not a black hole is really there. A new paper in Physical Review D now takes us one step further: Is it possible that the center of our galaxy contains a wormhole?

By now the idea of a wormhole that connects different spacetimes has passed into common parlance, thanks to science fiction stories and films like Interstellar. We have no evidence that a wormhole exists at galactic center at all, much less one that might be traversable, though the idea that it might be possible to pass between spacetimes using one of these is too tempting to ignore, at least on a theoretical level. At the University at Buffalo, Dejan Stojkovic, working with De-Chang Dai (Yangzhou University, China and Case Western Reserve University), thinks the star S2’s behavior may offer a way to look for wormholes.

Image: An artist’s concept illustrates a supermassive black hole. A new theoretical study outlines a method that could be used to search for wormholes (a speculative phenomenon) in the background of supermassive black holes. Credit: NASA/JPL-Caltech.

Note that the authors are not saying they find such an object in the existing datasets on S2 (the object has only been monitored since 1995 at UCLA and at the Max Planck Institute for Extraterrestrial Physics). Rather, they’re arguing for using the behavior of objects near black holes, where extreme astrophysical conditions exist, to see whether they exhibit unusual behavior that could be the result of a wormhole associated with the black hole. So this is a methodological approach that advances a proposed course of observation.

You may remember that a 1995 paper from John Cramer, Robert Forward, Gregory Benford and other authors including Geoff Landis (see below) went to work on this question, though not using a star near the Milky Way’s center (see How to Find a Wormhole, a Centauri Dreams article from the same year). Cramer et al. argued for looking for an astrophysical signal of negative mass, which would be needed to keep a wormhole mouth open. Let me quote from something Geoff Landis told me about the paper:

“If the wormhole is exactly between you and another star, it would defocus the light, so it’s dim and splays out in all directions. But when the wormhole moves and it’s nearer but not in front of the star, then you would see a spike of light. So if the wormhole moves between you and another star and then moves away, you would see two spikes of light with a dip in the middle.”

That’s an astrophysical signature interesting enough to be noted. And from the paper itself:

“…the negative gravitational lensing presented here, if observed, would provide distinctive and unambiguous evidence for the existence of a foreground object of negative mass.”

Back to Stojkovic, whose new paper notes a property we would expect to exist in wormholes. Let me quote his paper on this:

The purpose of this work…is to establish a clear link between wormholes and astrophysical observations. By definition, a wormhole smoothly connects two different spacetimes. If the wormhole is traversable, then the flux (scalar, electromagnetic, or gravitational) can be conserved only in the totality of these two spaces, not individually in each separate space.

Interesting point. An example: A physical electric charge on one side of the wormhole would manifest itself on the other side. There, where there is no electric charge, an observer would notice the electric flux coming from the wormhole and assume that the wormhole is charged. There is, in fact, no real charge at the wormhole, but the flux is strictly conserved only if the entirety of both spaces connected by the wormhole is considered. And as the paper goes on to state, a gravitational source like a star orbiting the mouth of the wormhole should be observed as gravitational perturbations on the other side.

The message is clear. Again, from the Stojkovic paper:

As a direct consequence, trajectories of objects propagating in [the] vicinity of a wormhole must be affected by the distribution of masses/charges in the space on the other side of the wormhole. Since wormholes in nature are expected to exist only in extreme conditions, e.g. around black holes, the most promising systems to look for them are either large black holes in the centers of galaxies, or binary black hole systems.

By now it should be clear why S2 is an interesting star for this purpose. Its proper motion orbiting what is believed to be a supermassive black hole at Sgr A* could theoretically tell us whether the black hole harbors a wormhole. The extreme gravitational conditions make this the best place to look for a wormhole, and minute deviations in the expected orbit of S2 could indicate one’s presence. That means we need to assemble a lot more data about S2.

Stojkovic doesn’t expect to find a lot of traffic coming through any wormhole we do find:

“Even if a wormhole is traversable, people and spaceships most likely aren’t going to be passing through. Realistically, you would need a source of negative energy to keep the wormhole open, and we don’t know how to do that. To create a huge wormhole that’s stable, you need some magic.”

In the absence of magic, we can still put observational astronomy to work. We may be a decade or two away from being able to track S2 this closely, and in any case will need a lot more data to make the call, but the scientist cautions that even deviations in its expected orbit won’t be iron-clad proof of a wormhole. They’ll simply make it a possibility, leading us to ask what other causes on our own side of the presumed wormhole could be creating the perturbations. And any wormhole we do come to believe is there would not necessarily be traversable, but if the effects of gravity from a different spacetime are in play, that’s certainly something we’ll want to study as we untangle the complicated situation at galactic center.

The paper is Dai and Stojkovic, “Observing a Wormhole,” Phys. Rev. D 100, 083513 (10 October 2019). Abstract / preprint). The Cramer et al. paper is “Natural Wormholes as Gravitational Lenses,” Physical Review D (March 15, 1995): pp. 3124-27 (abstract).

Artificial Singularity Power: A Basis for Developing and Detecting Advanced Spacefaring Civilizations

by Paul Gilster | Oct 17, 2019 | Breakthrough Propulsion | 40 comments

Could an advanced civilization create artificial black holes? If so, the possibilities for power generation and interstellar flight would be profound. Imagine cold worlds rendered habitable by tiny artificial ‘suns.’ Robert Zubrin, who has become a regular contributor to Centauri Dreams, considers the consequences of black hole engines in the essay below. Dr. Zubrin is an aerospace engineer and founder of the Mars Society, as well as being the president of Pioneer Astronautics. His latest book, The Case for Space: How the Revolution in Spaceflight Opens Up a Future of Limitless Possibility, was recently published by Prometheus Books. As Zubrin notes, generating energy through artificial singularities would leave a potential SETI signal whose detectability is analyzed here, a signature unlike any we’ve examined before.

by Robert Zubrin

Abstract

Artificial Singularity Power (ASP) engines generate energy through the evaporation of modest sized (10⁸-10¹¹ kg) black holes created through artificial means. This paper discusses the design and potential advantages of such systems for powering large space colonies, terraforming planets, and propelling starships. The possibility of detecting advanced extraterrestrial civilizations via the optical signature of ASP systems is examined. Speculation as to possible cosmological consequences of widespread employment of ASP engines is considered.

Introduction

According to a theory advanced by Stephen Hawking [1] in 1974, black holes evaporate at a rate given by:

t_ev = (5120π)t_P(m/m_P)³ (1)

where t_ev is the time it takes for the black hole to evaporate, t_P is the Planck time (5.39e-44 s), m is the mass of the black hole in kilograms, and m_P is the Planck mass (2.18e-8 kg) [2]

Hawking considered the case of black holes formed by the collapse of stars, which need to be at least ~3 solar masses to occur naturally. For such a black hole, equation 1 yields an evaporation time of 5e68 years, far longer than the expected life of the universe. In fact, evaporation would never happen, because the black hole would gain energy, and thus mass, by drawing in cosmic background radiation at a rate faster than its own insignificant rate of radiated power.

However it can be seen from examining equation (1) that the evaporation rate goes inversely with the cube of singularity, which means that the emitted power (=mc²/t_ev) goes inverse with the square of the mass. Thus if the singularity could be made small enough, very large amounts of power could theoretically be produced.

This possibility was quickly grasped by science fiction writers, and such propulsion systems were included by Arthur C. Clarke in his 1976 novel Imperial Earth [3] and Charles Sheffield in his 1978 short story “Killing Vector.” [4]

Such systems did not receive serious technical analysis however, until 2009, when it was examined by Louis Crane and Shawn Westmoreland, both then of Kansas State University, in their seminal paper “Are Black Hole Starships Possible?” [5]

In their paper, Crane and Westmoreland focused on the idea of using small artificial black holes powerful enough to drive a starship to interstellar-class velocities yet long-lived enough to last the voyage. They identified a “sweet spot” for such “Black Hole Starships” (BHS) with masses on the order of 2×10⁹ kg, which they said would have lifetimes on order of 130 years, yet yield power of about 13,700 TW. They proposed to use some kind of parabolic reflector to reflect this radiation, resulting in a photon rocket. The ideal thrust T of a rocket with jet power P and exhaust velocity v is given by:

T = 2P/v (2)

So with T = 13,700 TW and v=c = 3e8 m/s, the thrust would be 8.6e7 N. Assuming that the payload spacecraft had a mass of 1e9 kg, this would accelerate the ship at a rate of a=8.6e7/3e9 = 2.8e-2 m/s². Accelerating at this rate, such a ship would reach about 30% the speed of light in 100 years.

There are a number of problems with this scheme. In the first place, the claimed acceleration is on the low side. Furthermore their math appears to be incorrect. A 2e9 kg singularity would only generate about 270 TW, or 1/50th as much as their estimate, reducing thrust by a factor of 50 (although it would last about 20,000 years). These problems could be readily remedied, however, by using a smaller singularity and a smaller ship. For example a singularity with a mass of 2e8 kg would produce a power of 26,900 TW. Assuming a ship with a mass of 1e8 kg, an acceleration of 0.6 m/s² could be achieved, allowing 60% the speed of light to be achieved in 10 years. The singularity would only have a lifetime of 21 years. However it could be maintained by being constantly fed mass at a rate of about 0.33 kg/s.

A bigger problem is that a 1e9 kg singularity would produce radiation with a characteristic temperature of 9 GeV, increasing in inverse proportion to the singularity mass. So for example a 1e8 kg singularity would produce gamma rays with energies of 90 GeV (i.e. for Temperature, T, in electron volts, T = 9e18/m.) There is no known way to reflect such high energy photons. So at this point the parabolic reflector required for the black hole starship photon engine is science fiction.

Yet another problem is the manufacture of the black hole. Crane and Westmoreland suggest that it could be done using converging gamma ray lasers. To make a 1e9 kg unit, they suggested a “high-efficiency square solar panel a few hundred km on each side, in a circular orbit about the sun at a distance of 1,000,000 km” to provide the necessary energy. A rough calculation indicates the implied power of this system from this specification is on the order of 10⁶ TW, or about 100,000 times the current rate used by human civilization. As an alternative construction technique, they also suggest accelerating large masses to relativistic velocities and then colliding them. The density of these masses would be multiplied both by relativistic mass increase and length contraction. However the energy required to do this would still equal the combined masses times the speed of light squared. While this technique would eliminate the need for giant gamma ray lasers, the same huge power requirement would still present itself.

In what follows, we will examine possible solutions for the above identified problems.

Advanced Singularity Engines

In MKS units, equation (1) can be rewritten as:

t_ev = 8.37e-15 m³ (3)

This implies that the power, P, in Watts, emitted by the singularity is given by:

P = 1.08e33/m² (4)

The results of these two equations are shown in Fig. 1.

Fig 1. Power and Lifetime of ASP Engines as a Function of Singularity Mass

No credible concept is available to enable a lightweight parabolic reflector of the sort needed to enable the Black Hole Starship. But we can propose a powerful and potentially very useful system by dropping the requirement for starship-relevant thrust to weight ratios. Instead let us consider the use of ASP engines to create an artificial sun.

Consider a 1e8 kg ASP engine. As shown in Fig 1, it would produce a power of 1.08e8 Gigawatts. Such an engine, if left along, would only have a lifetime of 2.65 years, but it could be maintained by a constant feed of about 3 kg/s of mass. We can’t reflect its radiation, but we can absorb it with a sufficiently thick material screen. So let’s surround it with a spherical shell of graphite with a radius of 40 km and a thickness of 1.5 m. At a distance of 40 km, the intensity of the radiation will be about 5 MW/m², which the graphite sphere can radiate into space with a black body temperature of 3000 K. This is about the same temperature as the surface of a type M red dwarf star. We estimate that graphite has an attenuation length for high energy gamma rays of about 15 cm, so that 1.5 m of graphite (equivalent shielding to 5 m of water or half the Earth’s atmosphere) will attenuate the gamma radiation by ten factors of e, or 20,000. The light will then radiate out further, dropping in intensity with the square of the distance, reaching typical Earth sunlight intensities of 1 kW/m² at a distance of about 3000 km from the center.

The mass of the artificial star will be about 10¹⁴ kg (that’s the mass of the graphite shell, compared to which the singularity is insignificant.). As large as this is, however, it is still tiny compared to that of a planet, or even the Earth’s Moon (which is 7.35e22 kg). So, no planet would orbit such a little star. Instead, if we wanted to terraform a cold world, we would put the mini-star in orbit around it.

The preferable orbital altitude of the ASP mini-star of 3000 km altitude in the above cited example was dictated by the power level of the singularity. Such a unit would be sufficient to provide all the light and heat necessary to terraform an otherwise sunless planet the size of Mars. Lower power units incorporating larger singularities but much smaller graphite shells are also feasible. (Shell mass is proportional to system power.) These are illustrated in Table 1.

The high-powered units listed in Table 1 with singularity masses in the 1e8 to 1e9 kg range are suitable to serve as mini-suns orbiting planets, moons or asteroids, with the characteristic radius of such terraforming candidates being about the same as the indicated orbital altitude. The larger units, with lower power and singularity masses above 1e10 kg are more appropriate for space colonies.

Consider an ASP mini-sun with a singularity mass of 3.16e10 kg positioned in the center of a cylinder with a radius of 10 km and a length of 20 km. The cylinder is rotating at a rate of 0.0316 radians per second, which provides it with 1 g or artificial gravity. Let’s say the cylinder is made of material with an areal density of 1000 kg per square meter. In this case it will experience an outward pressure of 10⁴ pascals, or about 1.47 psi, due to outward acceleration. If the cylinder were made of solid Kevlar (density = 1000 kg/m³) it would be about 1 m thick. So the hoop stress on it would be 1.47*(10,000)/1 = 14,700 psi, which is less than a tenth the yield stress of Kevlar. Or put another way, 10 cm of Kevlar would do the job of carrying the hoop stress, and the rest of mass load could be anything, including habitations. If the whole interior of the cylinder were covered with photovoltaic panels with an efficiency of 10 percent, 100 GWe of power would be available for use of the inhabitants of the space colony, which would have an area of 1,256 square kilometers. The mini-sun powering it would have a lifetime of 84 million years, without refueling. Much larger space colonies (i.e, with radii over ~100 km) would not be possible however, unless stronger materials become available, as the hoop stress would become too great.

Both of these approaches seem potentially viable in principle. However we note that the space colony approach cited requires a singularity some 300 times more massive than the approach of putting a 1e8 kg mini-sun in orbit around a planet, which yields 4π(3000)² = 100 million square kilometers of habitable area, or about 80,000 times as much land. Furthermore, the planet comes with vast supplies of matter of every type, whereas the space colony needs to import everything.

Building Singularities

Reducing the size of the required singularity by a factor of 10 from 1e9 to 1e8 kg improves feasibility of the ASP concept somewhat, but we need to do much better. Fortunately there is a way to do so.

If we examine equation (3), we can see that the expected lifetime of a 1000 kg singularity would be about 8.37 x 10^-6 s. In this amount of time, light can travel about 250 m. and an object traveling at half the speed of light 125 m. If a sphere with a radius of 125 m were filled with steel it would contain about 8 x 10¹⁰ kg, or about 100 times what we need for our 1e8 kg ASP singularity. In fact, it turns out that if the initial singularity is as small as about 200 kg, and fired into a mass of steel, it will gain mass much faster than it losses it, and eventually grow into a singularity as massive as the steel provided.

By using this technique we can reduce the amount of energy required to form the required singularity by about 7 orders of magnitude compared to Crane and Westmoreland’s estimate. So instead of needing a 10⁶ TW system, a 100 GW gamma ray laser array might do the trick. Alternatively, accelerating two 200 kg masses to near light speed would require 3.6e7 TJ, or 10,000 TW-hours of energy. This is about the energy humanity currently uses in 20 days. We still don’t know how to do it, but reducing the scale of the required operation by a factor of 10 million certainly helps.

ASP Starships

We now return to the subject of ASP starships. In the absence of a gamma ray reflector, we are left with using solid material to absorb the gamma rays and other energetic particles and re-radiate their energy as heat. (Using magnetic fields to try to contain and reflect GeV-class charged particles that form a portion of the Hawking radiation won’t work because the required fields would be too strong and too extensive, and the magnets to generate them would be exposed to massive heating by gamma radiation.)

Fortunately, we don’t need to absorb all the radiation in the absorber/reflector, we only need to absorb enough to get it hot. So let’s say that we position a graphite hemispherical screen to one side of a 1e8 kg ASP singularity, but instead of making it 1.5 m thick, we make it 0.75 mm thick. At that thickness it will only absorb about 5 percent of the radiation that hits it, the rest will pass right through. So we have 5e6 GW of useful energy, which we want to reduce to 5 MW/m² in order for the graphite to be kept at ~3000 K where it can survive. The radius will be about 9 km, and the mass of the graphite hemisphere will be about 6e8 kg. A thin solar sail like parabolic reflector with an area 50 times as great and the carbon hemisphere but a thickness 1/500th (i.e. 1.5 microns) as great would be positioned in front of the hemisphere, adding another 0.6 e8 kg to the system, which then plus the singularity and the 1e8 kg ship might be 7.6e8 kg in all. Thrust will be 0.67e8 N, so the ship would accelerate at a speed of 0.67/7.6 = 0.09 m/s², allowing it to reach 10 percent the speed of light in about 11 years.

Going much faster would become increasingly difficult, because using only 5% of the energy of the singularity mass would give the system an effective exhaust velocity of about 0.22 c. Higher efficiencies might be possible if a significant fraction of the Hawking radiation came off as charged particles, allowing a thin thermal screen to capture a larger fraction of the total available energy. In this case, effective exhaust velocity would go as c times the square root of the achieved energy efficiency. But sticking with our 5% efficiency, if we wanted to reach 0.22 c we could, but we would require a mass ratio of 2.7, meaning we would need about 1.5e9 kg of propellant to feed into the ASP engine, whose mass would decrease our average acceleration by about a factor of two over the burn, meaning we would take about 40 years to reach 20 percent the speed of light.

Detecting ET

The above analysis suggests that if ASP technology is possible, using it to terraform cold planets with orbital mini-suns will be the preferred approach. Orbiting (possibly isolated) cold worlds at distances of thousands of kilometers, and possessing 3000 K type M red dwarf star spectra, potentially with gamma radiation in excess of normal stellar expectations, it is possible that such objects could be detectable.

Indeed, one of the primary reasons to speculate on the design of ASP engines right now is to try to identify their likely signature. We are far away from being able to build such things. But the human race is only a few hundred thousand years old, and human civilization is just a few thousand years. In 1905 the revolutionary HMS Dreadnought was launched, displacing 18,000 tons. Today ships 5 times that size are common. So it is hardly unthinkable that in a century or two we will have spacecraft in the million ton (10⁹ kg) class. Advanced extraterrestrial civilizations may have reached our current technological level millions or even billions of years ago. So they have had plenty of time to develop every conceivable technology. If we can think it, they can build it, and if doing so would offer them major advantages, they probably have. Thus, looking for large energetic artifacts such as Dyson Spheres [6], starships [7,8], or terraformed planets [9] is potentially a promising way to carry out the SETI search, as unlike radio SETI, it requires no mutual understanding of communication conventions. Given the capabilities the ASP technology would offer any species seeking to expand it prospects by illuminating and terraforming numerous new worlds, such systems may actually be quite common.

ASP starships are also feasible and might be detectable as well. However the durations of starship flights would be measured in decades or centuries, while terraformed worlds could be perpetual. Furthermore, once settled, trade between solar systems could much more readily be accomplished by the exchange of intellectual property via radio than by physical transport. As a result, the amount of flight traffic will be limited. In addition, there could be opportunities for employment of many ASP terraforming engines within a single solar system. For example, within our own solar system there are seven worlds of planetary size (Mars, Ceres, Ganymede, Calisto, Titan, Triton, and Pluto) whose terraforming could be enhanced or enabled by ASP systems, not to mention hundreds of smaller but still considerable moons and asteroids, and potentially thousands of artificial space colonies as well. Therefore the number of ASP terraforming engines in operation in the universe at any one time most likely far exceeds those being used for starship propulsion. It would therefore appear advantageous to focus the ASP SETI search effort on such systems.

Proxima Centauri is a type M red dwarf with a surface temperature of 3000 K. It therefore has a black body spectrum similar to that of the 3000 K graphite shell of our proposed ASP mini-sun discussed above. The difference however is that it has about 1 million times the power, so that an ASP engine placed 4.2 light years (Proxima Centauri’s distance) from Earth would have the visual brightness as a star like Proxima Centauri positioned 4,200 light years away. Put another way, Proxima Centauri has a visual magnitude of 11. It takes 5 magnitudes to equal a 100 fold drop in power, so our ASP engine would have a visual magnitude of 26 at 4.2 light years, and magnitude 31 at 42 light years. The limit of optical detection of the Hubble Space Telescope is magnitude 31. So HST would be able to see our proposed ASP engine out to a distance of about 50 light years, within which there are some 1,500 stellar systems.

Consequently ASP engines may already have been imaged by Hubble, appearing on photographs as unremarkable dim objects assumed to be far away. These should be subjected to study to see if any of them exhibit parallax. If they do, this would show that they are actually nearby objects of much lower power than stars. Further evidence of artificial origin could be provided if they were found to exhibit a periodic Doppler shift, as would occur if they were in orbit around a planetary body. An anomalous gamma ray signature could be present as well.

I suggest we have a look.

Cosmological Implications

One of the great mysteries of science is why the laws of the universe are so friendly to life. Indeed, it can be readily shown that if any one of most of the twenty or so apparently arbitrary fundamental constants of nature differed from their actual value by even a small amount, life would be impossible [9]. Some have attempted to answer this conundrum by claiming that there is nothing to be explained because there are an infinite number of universes; we just happen to live in the odd one where life is possible. This multiverse theory answer is absurd, as it could just as well be used to avoid explaining anything. For example take the questions, why did the Titanic sink/it snow heavily last winter/the sun rise this morning/the moon form/the chicken cross the road? These can all also be answered by saying “no reason, it other universes they didn’t.” The Anthropic Principle reply, to the effect of “clearly they had to, or you wouldn’t be asking the question” is equally useless.

Clearly a better explanation is required. One attempt at such an actual causal theory was put forth circa 1992 by physicist Lee Smolin [10], who says that daughter universes are formed by black holes created within mother universes. This has a ring of truth to it, because a universe, like a black hole, is something that you can’t leave. Well, says Smolin, in that case, since black holes are formed from collapsed stars, the universes that have the most stars will have the most progeny. So to have progeny a universe must have physical laws that allow for the creation of stars. This would narrow the permissible range of the fundamental constants by quite a bit. Furthermore, let’s say that daughter universes have physical laws that are close to, but slightly varied from that of their mother universes. In that case, a kind of statistical natural selection would occur, overwhelmingly favoring the prevalence of star-friendly physical laws as one generation of universes follows another.

But the laws of the universe don’t merely favor stars, they favor life, which certainly requires stars, but also planets, water, organic and redox chemistry, and a whole lot more. Smolin’s theory gets us physical laws friendly to stars. How do we get to life?

Reviewing an early draft of Smolin’s book in 1994, Crane offered the suggestion [11] that if advanced civilizations make black holes, they also make universes, and therefore universes that create advanced civilizations would have much more progeny than those that merely make stars. Thus the black hole origin theory would explain why the laws of the universe are not only friendly to life, but the development of intelligence and advanced technology as well. Universes creates life because life creates universes. This result is consistent with complexity theory, which holds that if A is necessary to B, then B has a role in causing A.

These are very interesting speculations. So let us ask, what would we see if our universe was created as a Smolin black hole, and how might we differentiate between a natural star collapse or ASP engine origin? From the above discussion, it should be clear that if someone created an ASP engine, it would be advantageous for them to initially create a small singularity, then grow it to its design size by adding mass at a faster rate than it evaporates, and then, once it reaches its design size, maintain it by continuing to add mass at a constant rate equal to the evaporation rate. In contrast, if it were formed via the natural collapse of a star it would start out with a given amount of mass that would remain fixed thereafter.

So let’s say our universe is, as Smolin says, a black hole. Available astronomical observations show that it is expanding, at a velocity that appears to be close to the speed of light. Certainly the observable universe is expanding at the speed of light.

Now a black hole has an escape velocity equal to the speed of light. So for such a universe

c²/2 = GM/R (5)

Where G is the universal gravitational constant, c is the speed of light in vacuum, M is the mass of the universe, and R is the radius of the universe.

If we assume that G and c are constant, R is expanding at the speed of light, and τ is the age of the universe, then:

R = cτ (6)

Combining (5) and (6), we have.

M/τ = (Rc²/2G)(c/R) = c³/2G (7)

This implies that the mass of such a universe would be growing at a constant rate. Contrary to the classic Hoyle continuous creation theory, however, which postulated that mass creation would lead to a steady state universe featuring constant density for all eternity, this universe would have a big bang event with density decreasing afterwards inversely with the square of time.

Now the Planck mass, m_p, is given by:

m_p = (hc/2πG)^½ (8)

And the Planck time, t_p, is given by:

t_p = (hG/2πc5)^½ (9)

If we divide equation (8) by equation (9) we find:

m_p/t_p = c³/G (10)

If we compare equation (10) to equation (7) we see that:

M/τ = ½(m_p/t_p) (11)

So the rate at which the mass of such a universe would increase equals exactly ½ Planck mass per Planck time.

Comparison with Observational Astronomy

In MKS units, G = 6.674e-11, c= 3e+8, so:

M/τ= c³/2G = 2.02277 e+35 kg/s. (12)

For comparison, the mass of the Sun is 1.989+30 kg. So this is saying that the mass of the universe would be increasing at a rate of about 100,000 Suns per second.

Our universe is believed to be about 13 billion years, or 4e+17 seconds old. The Milky Way galaxy has a mass of about 1 trillion Suns. So this is saying that the mass of the universe should be about 40 billion Milky Way galaxies. Astronomers estimate that there are 100 to 200 billion galaxies, but most are smaller than the Milky Way. So this number is in general agreement with what we see.

According to this estimate, the total mass of the universe M, is given by:

M = (2e+35)(4e+17) = 8e+52 kg. (13)

This number is well known. It is the critical mass required to make our universe “flat.” It should be clear, however, that when the universe was half as old, with half its current diameter, this number would have needed to be half as great. Therefore, if the criteria is that such a universe mass always be critical for flatness, and not just critical right now, then its mass must be increasing linearly with time.

These are very curious results. Black holes, the expanding universe, and the constancy of the speed of light are results of relativity theory. Planck masses and Planck times relate to quantum mechanics. Observational astronomy provides data from telescopes. It is striking that these three separate approaches to knowledge should provide convergent results.

This analysis does require that mass be continually added to the universe at a constant rate, exactly as would occur in the case of an ASP engine during steady-state operation. It differs however in that in an ASP engine, the total mass only increases during the singularity’s buildup period. During steady state operation mass addition would be balanced by mass evaporation. How these processes would appear to the inhabitants of an ASP universe is unclear. Also unclear is how the inhabitants of any Smolinian black hole universe could perceive it as rapidly expanding. Perhaps the distance, mass, time, and other metrics inside a black hole universe could be very different from those of its parent universe, allowing it to appear vast and expanding to its inhabitants while looking small and finite to outside observers. One possibility is that space inside a black hole is transformed, in a three dimensional manner analogous to a ω = 1/z transformation in the complex plane, so that the point at the center becomes a sphere at infinity. In this case mass coming into the singularity universe from its perimeter would appear to the singularity’s inhabitants as matter/energy radiating outward from its center.

Is there a model that can reconcile all the observations of modern astronomy with those that would be obtained by observers inside either a natural black hole or ASP universe? Speculation on this matter by scientists and science fiction writers with the required physics background would be welcome [13].

Conclusions

We find that ASP engines appear to be theoretically possible, and could offer great benefits to advanced spacefaring civilizations. Particularly interesting is their potential use as artificial suns to enable terraforming of unlimited numbers of cold worlds. ASP engines could also be used to enable interstellar colonization missions. However the number of ASP terraforming engines in operation in the universe at any one time most likely far exceeds those being used for starship propulsion. Such engines would have optical signatures similar to M-dwarfs, but would differ in that they would be much smaller in power than any natural M star, and hence have to be much closer to exhibit the same apparent luminosity. In addition they would move in orbit around a planetary body, thereby displaying a periodic Doppler shift, and could have an anomalous additional gamma ray component to their spectra. An ASP engine of the type discussed would be detectable by the Hubble Space Telescope at distances as much as 50 light years, within which there are approximately 1,500 stellar systems. Their images may therefore already be present in libraries of telescopic images as unremarkable dim objects, whose artificial nature would be indicated if they were found to display parallax. It is therefore recommended that such a study be implemented.

As for cosmological implications, the combination of the attractiveness of ASP engines with Smolinian natural selection theory does provide a potential causal mechanism that could explain the fine tuning of the universe for life. Whether our own universe could have been created in such a manner remains a subject for further investigation.

References

1. Hawking, S. W. (1974). “Black hole explosions?” Nature 248(5443): 30-31. https://ui.adsabs.harvard.edu/abs/1974Natur.248…30H/abstract

2. Hawking Radiation, Wikipedia https://en.wikipedia.org/wiki/Hawking_radiation accessed September 22, 2019.

3. Arthur C. Clarke, Imperial Earth, Harcourt Brace and Jovanovich, New York, 1976.

4. Charles Sheffield, “Killing Vector,” in Galaxy, March 1978.

5. Louis Crane and Shawn Westmoreland, “Are Black Hole Starships Possible?” 2009, 2019. https://arxiv.org/pdf/0908.1803.pdf accessed September 24.

6. Freeman Dyson, “The Search for Extraterrestrial Technology,” in Selected Papers of Freeman Dyson with Commentary, Providence, American Mathematical Society. Pp. 557-571, 1996.

7. Robert Zubrin, “Detection of Extraterrestrial Civilizations via the Spectral Signature of Advanced Interstellar Spacecraft,” in Progress in the Search for Extraterrestrial Life: Proceedings of the 1993 Bioastronomy Symposium, Santa Cruz, CA, August 16-20 1993.

8. Crane, “Searching for Extraterrestrial Civilizations Using Gamma Ray Telescopes,” available at https://arxiv.org/abs/1902.09985.

9. Robert Zubrin, The Case for Space: How the Revolution in Spaceflight Opens Up a Future of Limitless Possibility, Prometheus Books, Amherst, NY, 2019.

10. Paul Davies, The Accidental Universe, Cambridge University Press, Cambridge, 1982

11. Lee Smolin, The Life of the Cosmos, Oxford University Press, NY, 1997.

12. Louis Crane, “Possible Implications of the Quantum Theory of Gravity: An Introduction to the Meduso-Anthropic principle,” 1994. https://arxiv.org/PS_cache/hep-th/pdf/9402/9402104v1.pdf

13. I provided a light hearted explanation in my science fiction satire The Holy Land (Polaris Books, 2003) where the advanced extraterrestrial priestess (3rd Class) Aurora mocks the theory of the expanding universe held by the Earthling Hamilton. “Don’t be ridiculous. The universe isn’t expanding. That’s obviously physically impossible. It only appears to be expanding because everything in it is shrinking. What silly ideas you Earthlings have.” In a more serious vein, the late physicist Robert Forward worked out what life might be like on a neutron star in his extraordinary novel Dragon’s Egg (Ballantine Books, 1980.) A similar effort to describe life on the inside of a black hole universe could be well worthwhile. Any takers?

Robert Zubrin
Pioneer Astronautics
11111 W. 8th Ave, unit A
Lakewood, CO 80215
Zubrin@aol.com