Superheavy Elements

There are currently 118 known chemical elements. The most recent, 118 Oganesson (chemical symbol Og), was first synthesized in 2002 . Its only known isotope, $\mathbf{\frac{294}{118}\textrm{\textbf{Og}}}$ (118 protons + 176 neutrons = 294 nucleons), has a half-life of just 0.0007 seconds, and to date only five oganesson atoms have been produced.

It is possible, given our current knowledge of nuclear physics, that there is at least one island of nuclear stability where stable or quasi-stable isotopes of superheavy elements exist. One such island might exist around Z = 164, that is an element having 164 protons and something like 246 neutrons.

Are any superheavy elements stable enough to be found in nature? Is there any astrophysical process that could produce them? If superheavy elements exist, we would expect such matter to have a mass density in excess of the densest-known stable element, osmium (element 76), 22.59 g/cm3. Superheavy elements around Z = 164 are expected to have a mass density between 36.0 and 68.4 g/cm3.

Researchers at the University of Arizona in Tucson explain that superheavy elements might exist in nature, either in the exotic form of extremely dense alpha matter — nuclear matter composed of alpha particles in a Bose-Einstein condensate-like configuration — or as standard matter. Though a long shot, they suggest looking at asteroids (and other objects) possibly having anomalously high densities, which they call Compact Ultradense Objects (CUDOs).

In order to calculate the density of an asteroid, you need to measure its volume and its mass. The volume can be calculated if you know the size and shape of the asteroid, and the mass can best be calculated if the asteroid has a satellite (either natural or artificial), or from a spacecraft flyby. A less certain mass can be calculated by measuring how an asteroid gravitationally perturbs a neighboring asteroid as they both orbit around the Sun. We must keep in mind that any asteroids that presently appear to have an unusually high density may later be found to have a more normal density upon better estimates of the size and shape of the asteroid, and especially its mass.

The most recent available table of asteroid bulk densities can be found on the SiMDA (Size, Mass, and Density of Asteroids) web site. In that table, a bulk density accuracy rank of A (most accurate) to E (least accurate), and X (unrealistic) for each object is given. Among the A-rank densities, we find that 16 Psyche is listed as having the highest bulk density of 3.90 ± 0.29 g/cm3. NASA’s Psyche robotic spacecraft was launched on October 13, 2023 and is expected to begin orbiting 16 Psyche in August 2029.

Among the B-rank densities, two asteroids have nominal bulk densities higher than 16 Psyche’s: 135 Hertha at 4.45 ± 0.63 g/cm3 and 192 Nausikaa at 4.10 ± 0.70 g/cm3.

Among the C-rank densities, 21 asteroids have nominal bulk densities higher than 16 Psyche’s:

Rank "C" Asteroid Densities (> 16 Psyche)

 206 Hersilia 6.08 ± 2.55 181 Eucharis 5.46 ± 2.43 410 Chloris 4.96 ± 2.41 679 Pax 4.95 ± 1.45 110 Lydia 4.88 ± 1.75 97 Klotho 4.80 ± 1.01 124 Alkeste 4.74 ± 2.22 275 Sapientia 4.69 ± 1.12 92 Undina 4.64 ± 1.75 34 Circe 4.63 ± 1.21 56 Melete 4.57 ± 1.07 102 Miriam 4.46 ± 1.88 680 Genoveva 4.37 ± 2.06 129 Antigone 4.35 ± 2.14 69 Hesperia 4.33 ± 1.11 709 Fringilla 4.12 ± 1.98 89 Julia 4.01 ± 1.61 675 Ludmilla 3.99 ± 1.94 201 Penelope 3.99 ± 1.97 455 Bruchsalia 3.93 ± 1.29 354 Eleonora 3.93 ± 1.84

Among the D-rank densities, 16 asteroids have nominal bulk densities higher than 16 Psyche’s:

Rank "D" Asteroid Densities (> 16 Psyche)

 250 Bettina 7.84 ± 5.42 138 Tolosa 7.69 ± 4.39 360 Carlova 6.62 ± 4.51 388 Charybdis 5.80 ± 3.66 43 Ariadne 5.54 ± 2.84 536 Merapi 5.39 ± 4.77 172 Baucis 5.34 ± 3.31 420 Bertholda 4.94 ± 4.44 103 Hera 4.78 ± 2.87 491 Carina 4.58 ± 3.11 683 Lanzia 4.49 ± 2.69 849 Ara 4.29 ± 2.18 506 Marion 4.16 ± 2.29 363 Padua 4.10 ± 2.25 705 Erminia 4.02 ± 2.39 786 Bredichina 3.91 ± 2.28

Among the E-rank densities, 7 asteroids have nominal bulk densities higher than 16 Psyche’s:

Rank "E" Asteroid Densities (> 16 Psyche)

 2004 PB108 6.74 ± 7.23 1013 Tombecka 6.39 ± 53.43 306 Unitas 6.23 ± 6.77 132 Aethra 5.09 ± 7.72 445 Edna 4.60 ± 4.91 147 Protogeneia 4.18 ± 5.03 769 Tatjana 4.09 ± 4.38

Among the X-rank densities, 14 asteroids have nominal bulk densities higher than 16 Psyche’s:

Rank "X" Asteroid Densities (> 16 Psyche)

 1686 De Sitter 430.61 ± 213.19 33 Polyhymnia 75.32 ± 9.72 1428 Mombasa 43.03 ± 14.78 152 Atala 42.29 ± 10.80 949 Hel 12.31 ± 5.14 582 Olympia 9.98 ± 27.31 61 Danae 9.74 ± 9.45 665 Sabine 9.05 ± 5.19 217 Eudora 8.94 ± 0.64 204 Kallisto 8.89 ± 26.79 234 Barbara 8.89 ± 29.30 202 Chryseis 8.66 ± 1.63 126 Velleda 8.64 ± 106.21 67 Asia 8.59 ± 1.23

Obviously, most—if not all—of the asteroids listed above will eventually be found to have bulk densities less than that of 16 Psyche as more accurate masses and volumes are determined. Presently, only the following asteroids have minimum bulk densities greater than that of 16 Psyche, assuming the mean error listed is correct:

Asteroid Densities > 16 Psyche (within error)

 1686 De Sitter 430.61 ± 213.19 33 Polyhymnia 75.32 ± 9.72 1428 Mombasa 43.03 ± 14.78 152 Atala 42.29 ± 10.80 949 Hel 12.31 ± 5.14 217 Eudora 8.94 ± 0.64 202 Chryseis 8.66 ± 1.63 67 Asia 8.59 ± 1.23

LaForge, Price, and Rafelski choose 33 Polyhymnia as the current best candidate to search for superheavy elements. Even a small amount of superheavy elements (especially in the alpha matter state) could significantly raise the bulk density of the asteroid as a whole. Kretlow lists the mass of 33 Polyhymnia as (6.20 ± 0.74) × 1018 kg and its volume-equivalent diameter as 54.0 ± 0.9 km, giving a bulk density around 75 g/cm3.

This finding is not without controversy, however. See the following discussion:

https://groups.io/g/mpml/topic/33_polyhymnia/101917502

References
Kretlow, M. Size, Mass and Density of Asteroids (SiMDA) – A Web Based Archive and Data Service” (2020). https://astro.kretlow.de/?SiMDA

LaForge, E., Price, W. & Rafelski, J. Superheavy elements and ultradense matter. Eur. Phys. J. Plus 138, 812 (2023). https://arxiv.org/abs/2306.11989
https://doi.org/10.1140/epjp/s13360-023-04454-8

Light Blue Blob in a Daytime Sky

See the light blue blob in the photograph above? Even though it is partly cloudy, the light blue blob is decidedly different in color from the nearby patches of blue sky. Is this some unusual atmospheric phenomenon, or was there a daytime on orbit rocket burn (such as an apogee kick motor)? If the latter, I have not been able to find any evidence online of a rocket firing around 1804 UT on 13 Apr 2023.

Joan Oesper took this photo from the campus of Sul Ross State University in Alpine, TX at 1:04 p.m. CDT (1804 UT) on Thursday, April 13, 2023. The exact coordinates where the photograph was taken are 30° 21′ 54″ N, 103° 39′ 00″ W. She was facing an azimuth of approximately 161° (SSE) and the altitude of the blue blob was approximately 15° above the horizon.

Joan writes, “The people I saw it with said they’d been watching it and that it had moved eastward during the 5-10 minutes they were watching. It seemed to be behind the clouds.”

Has anyone seen something like this in the past? Was there an on-orbit daytime rocket firing at this time?

Infinity

George F. R. Ellis weighs in on the concept of infinity in his excellent paper, Issues in the Philosophy of Cosmology, available on astro-ph at https://arxiv.org/abs/astro-ph/0602280. He writes:

9.3.2 Existence of Infinities

The nature of existence is significantly different if there is a finite amount of matter or objects in the universe, as opposed to there being an infinite quantity in existence. Some proposals claim there may be an infinite number of universes in a multiverse and many cosmological models have spatial sections that are infinite, implying an infinite number of particles, stars, and galaxies. However, infinity is quite different from a very large number! Following David Hilbert, one can suggest these unverifiable proposals cannot be true: the word “infinity” denotes a quantity or number that can never be attained, and so will never occur in physical reality.38 He states:

Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea . . . which transcends all experience and which completes the concrete as a totality . . .

This suggests “infinity” cannot be arrived at, or realized, in a concrete physical setting; on the contrary, the concept itself implies its inability to be realized!

Thesis I2: The often claimed physical existence of infinities is questionable. The claimed existence of physically realized infinities in cosmology or multiverses raises problematic issues. One can suggest they are unphysical; in any case such claims are certainly unverifiable.

This applies in principle to both small and large scales in any single universe:

The existence of a physically existing spacetime continuum represented by a real (number) manifold at the micro-level contrasts with quantum gravity claims of a discrete spacetime structure at the Planck scale, which one might suppose was a generic aspect of fully non-linear quantum gravity theories. In terms of physical reality, this promises to get rid of the uncountable infinities the real line continuum engenders in all physical variables and fields40. There is no experiment that can prove there is a physical continuum in time or space; all we can do is test space-time structure on smaller and smaller scales, but we cannot approach the Planck scale.

Infinitely large space-sections at the macro-level raise problems as indicated by Hilbert, and leads to the infinite duplication of life and all events. We may assume space extends forever in Euclidean geometry and in many cosmological models, but we can never prove that any realised 3-space in the real universe continues in this way—it is an untestable concept, and the real spatial geometry of the universe is almost certainly not Euclidean. Thus Euclidean space is an abstraction that is probably not physically real. The infinities supposed in chaotic inflationary models derive from the presumption of pre-existing infinite Euclidean space sections, and there is no reason why those should necessarily exist. In the physical universe spatial infinities can be avoided by compact spatial sections, resulting either from positive spatial curvature, or from a choice of compact topologies in universes that have zero or negative spatial curvature. Machian considerations to do with the boundary conditions for physics suggest this is highly preferable; and if one invokes string theory as a fundamental basis for physics, the “dimensional democracy” suggests the three large spatial dimensions should also be compact, since the small (“compactified”) dimensions are all taken to be so. The best current data from CBR and other observations indeed suggest k = +1, implying closed space sections for the best-fit FL model.

The existence of an eternal universe implies that an infinite time actually exists, which has its own problems: if an event happens at any time t0, one needs an explanation as to why it did not occur before that time (as there was an infinite previous time available for it to occur); and Poincaré eternal return will be possible if the universe is truly cyclic. In any case it is not possible to prove that the universe as a whole, or even the part of the universe in which we live, is past infinite; observations cannot do so, and the physics required to guarantee this would happen (if initial conditions were right) is untestable. Even attempting to prove it is future infinite is problematic (we cannot for example guarantee the properties of the vacuum into the infinite future—it might decay into a state corresponding to a negative effective cosmological constant).

It applies to the possible nature of a multiverse. Specifying the geometry of a generic universe requires an infinite amount of information because the quantities necessary to do so are fields on spacetime, in general requiring specification at each point (or equivalently, an infinite number of Fourier coefficients): they will almost always not be algorithmically compressible. All possible values of all these components in all possible combinations will have to occur in a multiverse in which “all that can happen, does happen”. There are also an infinite number of topological possibilities. This greatly aggravates all the problems regarding infinity and the ensemble. Only in highly symmetric cases, like the FL solutions, does this data reduce to a finite number of parameters, each of which would have to occur in all possible values (which themselves are usually taken to span an infinite set, namely the entire real line). Many universes in the ensemble may themselves have infinite spatial extent and contain an infinite amount of matter, with all the problems that entails. To conceive of physical creation of an infinite set of universes (most requiring an infinite amount of information for their prescription, and many of which will themselves be spatially infinite) is at least an order of magnitude more difficult than specifying an existent infinitude of finitely specifiable objects.

One should note here particularly that problems arise in the multiverse context from the continuum of values assigned by classical theories to physical quantities. Suppose for example that we identify corresponding times in the models in an ensemble and then assume that all values of the density parameter and the cosmological constant occur at each spatial point at that time. Because these values lie in the real number continuum, this is a doubly uncountably infinite set of models. Assuming genuine physical existence of such an uncountable infinitude of universes is the antithesis of Occam’s razor. But on the other hand, if the set of realised models is either finite or countably infinite, then almost all possible models are not realised. And in any case this assumption is absurdly unprovable. We can’t observationally demonstrate a single other universe exists, let alone an infinitude. The concept of infinity is used with gay abandon in some multiverse discussions, without any concern either for the philosophical problems associated with this statement, or for its completely unverifiable character. It is an extravagant claim that should be treated with extreme caution.

38An intriguing further issue is the dual question: Does the quantity zero occur in physical reality? This is related to the idea of physical existence of nothingness, as contrasted with a vacuum. A vacuum is not nothing!

40To avoid infinities entirely would require that nothing whatever is a continuum in physical reality (since any continuum interval contains an infinite number of points). Doing without that, conceptually, would mean a complete rewrite of many things. Considering how to do so in a way compatible with observation is in my view a worthwhile project.

So, given this discussion of infinities, the answer to the doubly hypothetical question, “Can God make a rock so big he can’t pick it up?” is likely a “Yes”! – D.O.

Emergence

Physics is the fundamental science in that it describes the workings of the universe at all scales.  No other science is so comprehensive.

Will our knowledge of physics finally lead us to a “Theory of Everything”?  Perhaps, but the Theory of Everything alone will not be able to describe, predict, or explain its full expression upon/within the universe—no more so than our musical notation system can explain how a Brahms symphony was composed, nor its effect upon the listener.

Reductionism states that the whole is the sum of its parts, but emergence states that the whole is more than the sum of its parts.

There are many examples of emergent properties in the natural world, what one might call radical novelty.  Some examples:  crystal structure (e.g. a salt crystal or a snowflake), ripples in a sand dune, clouds, life itself.  Social organization (e.g. a school of fish or a city), consciousness.

John Archibald Wheeler (1911-2008) created a diagram that nicely illustrates an emergent property of the universe that is important to us.

Richard Wolfson writes,

At some level of complexity, emergent properties become so interesting that, although we understand that they come from particles that are held together by the laws of physics, we can’t understand or appreciate them through physics alone.

I like to think of emergence as an expression of creativity. Our universe is inherently creative, just as we humans express ourselves creatively through music, art, literature, architecture, and in so many other ways.

Creativity is the most natural process in the universe. It’s in our DNA.

But DNA alone can’t explain it.

References

Richard Wolfson, The Great Courses, Course No. 1280, “Physics and Our Universe: How It All Works”, Lecture 1: “The Fundamental Science”, 2011.

“And the end of all our exploring will be to arrive where we started and know the place for the first time.” – T. S. Eliot

Antistars

Do stars made of antimatter exist in the universe? Possibly.

One of the great mysteries of cosmology and astrophysics is that even though equal quantities of matter and antimatter appear to have been produced during the “Big Bang”, today there is only a negligible quantity of antimatter in the observable universe. We do not appear to live in a matter-antimatter symmetric universe.

If antimatter stars, “antistars”, do exist, how could we distinguish them from stars made of normal matter? The light emitted from an antistar would look identical to the light emitted by a normal-matter star.

But if normal matter were infalling upon an antistar, the contact between matter and antimatter would generate an annihilation spectrum of gamma ray photons that peaks around energy 70 MeV (half the mass of a neutral pion) up to a sharp cutoff around 938 MeV (mass of the proton).

A recent analysis of data collected by the Fermi Gamma-ray Space Telescope found fourteen possible antistars. These fourteen point sources produce a gamma-ray signature indicative of matter-antimatter annihilation.  These point sources do not exhibit the characteristics of other known gamma-ray sources.  For example, they are not, ostensibly, pulsars, active galactic nuclei, or black holes.

The positional error ellipses for these fourteen point sources range from 11×10 arcminutes up to 128×68 arcminutes (95% confidence). Here are optical images of these sources from the Palomar Digital Sky Survey, in order of right ascension (epoch 2000 coordinates).

Since there appears to be no known way to distinguish a star made of antimatter from one made of matter—except for the gamma-ray signature of matter infalling onto the antimatter star, a higher-resolution gamma-ray telescope or interferometer (10 – 1000 MeV) needs to be developed to localize these candidate sources to within a few arcseconds. Higher spectral resolution will help as well, allowing a more detailed characterization of the gamma-ray spectrum.

References

S. Dupourqué, L. Tibaldo and P. von Ballmoos. Constraints on the antistar fraction in the solar system neighborhood from the 10-year Fermi Large Area Telescope gamma-ray source catalog. Physical Review D. Published online April 20, 2021. doi: 10.1103/PhysRevD.103.083016.
https://arxiv.org/abs/2103.10073

M. Temming (2021, June 5). Antistars could lurk in Milky Way. Science News, 199(10), 8-9.
https://www.sciencenews.org/article/antimatter-stars-antistars-milky-way-galaxy-space-astronomy

Extreme Gamma Rays

The highest-energy gamma ray photon ever recorded was recently observed by the Large High Altitude Air Shower Observatory (LHAASO) on Haizi Mountain, Sichuan province, China, during its first year of operation.

1.42 ± 0.13 PeV

That is 1.4 petaelectronvolts = 1.4 × 1015 eV! The origin of this fantastically energetic photon hasn’t been localized, but possible candidates are the Cygnus OB2 young massive cluster (YMC), the pulsar PSR 2032+4127, or the supernova remnant candidate SNR G79.8+1.2.

How much energy is 1.4 PeV, actually?

We can calculate the frequency of this photon using

$\textup{E}=h\nu$

where
h = Planck’s constant = 4.135667696 × 10-15 eV·Hz-1
ν = the photon’s frequency
E = the photon’s energy

Solving for ν, we get

ν = 3.4 × 1029 Hz

Next, we’ll calculate the photon’s wavelength using

$c=\lambda \nu$

where
c = the speed of light = 299792458 m·s-1
λ = the photon’s wavelength

Solving for λ, we get

λ = 8.9 × 10-22 m

To give you an idea of just how tiny 8.9 × 10-22 meters is, the proton charge radius is 0.842 × 10-15 m, so 1.9 million wavelengths of this gamma ray photon would fit inside a single proton! An electron has an upper limit on its radius—if it can be said to have a radius at all—between 10-22 and 10-18 m. So between 1 and 2000 wavelengths of this gamma ray photon would fit inside a single electron.

Using Einstein’s famous equation E = mc2 we can find that each eV has a mass equivalent of 1.78266192 × 10-36 kg. 1.4 PeV then gives us a mass of 2.5 × 10-21 kg. That may not sound like a lot, but it is 1.5 million AMUs (Daltons), or a mass comparable to a giant molecule (a protein, for example) containing ~200,000 atoms.

This and other extremely high energy gamma ray photons are not directly detected from the Earth’s surface. The LHAASO detector array in China at 14,500 ft. elevation detects the air shower produced when a gamma ray (or cosmic ray particle) hits an air molecule in the upper atmosphere, causing a cascade of subatomic particles and lower-energy photons, some of which reach the surface of the Earth. It is the Cherenkov photons produced by the air shower secondary charged particles that LHAASO collects.

References
Conover, E. (2021, June 19). Record-breaking gamma rays hint at violent environments in space. Science News, 199(11), 5.
https://www.sciencenews.org/article/light-energy-record-gamma-ray

Z. Cao et al. Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sourcesNature. Published online May 17, 2021. doi: 10.1038/s41586-021-03498-z.

James Clerk Maxwell

Today we celebrate the 190th anniversary of the birth of Scottish mathematician and physicist James Clerk Maxwell (13 Jun 1831 – 5 Nov 1879). Between 1864 and 1873, Maxwell developed four important mathematical equations that describe the behavior of electric and magnetic fields and their interrelated nature. He showed that any oscillating electric charge produces an electromagnetic field, and that this electromagnetic field propagates outward from the oscillating charge at the speed of light. He then correctly deduced that light itself is an electromagnetic phenomenon, and proposed that since electric charges can oscillate at any frequency, there should be a whole spectrum of electromagnetic waves of which visible light is only a small part. We now know that the electromagnetic spectrum does include many other types of “light”, namely gamma rays, x-rays, ultraviolet, infrared, microwave, and radio waves. They are all exactly the same phenomenon, differing only in their properties of frequency, wavelength, and energy.

Why No New Einstein?

In the June 2005 issue of Physics Today there is an article by Lee Smolin with the provocative (or evocative) title, Why No ‘New Einstein’? That year marked the 100th anniversary of Albert Einstein‘s annus mirabilis (year of wonders), in which the 26-year-old Swiss patent examiner submitted and had published revolutionary papers on the photoelectric effect, Brownian motion, special relativity, and matter-energy equivalence in a prominent German physics journal, Annalen der Physik. These papers were so important that they completely changed the course of physics and led to great opportunities for Einstein to further develop his career as a physicist.

Here are some excerpts from Smolin’s article.

“Many of Einstein’s contemporaries testified that he was not unusually talented mathematically. Instead, what enabled him to make such tremendous advances was a driving need to understand the logic of nature, tied to a breathtaking creativity and a fierce intellectual independence.”

“Perhaps a lesson might be learned from the fact that this one person, who was initially unable to find an academic job, did more to advance physics than most of the rest of us [physicists] put together have since.”

“It follows that new Einsteins are unlikely to be easily characterized in terms of research programs that have been well explored for decades. Instead, a new Einstein will be developing his or her own research program that, by definition, will be one that no senior person works on.”

“Are our universities, institutes, and foundations doing all they can to identify and promote individuals who have the creativity and intellectual independence that characterize those who contribute most to physics? I say that they are not.”

“People with the uncanny ability to ask new questions or recognize unexamined assumptions, or who are able to take ideas from one field and apply them to another, are often at a disadvantage when the goal is to hire the best person in a given well-established area.”

“It is easy to write many papers when you continue to apply well-understood techniques. People who develop their own ideas have to work harder for each result, because they are simultaneously developing new ideas and the techniques to explore them. Hence they often publish fewer papers, and their papers are cited less frequently than those that contribute to something hundreds of people are doing.”

Marfa Lights

Yes, I’ve seen the Marfa lights. Bernie Zelazny and I were coming back from doing a star party for a culinary group at El Cosmico in Marfa on April 7, 2011 when we decided to stop at the Marfa lights viewing station just off of US 67/90. For the first couple of minutes (Thursday evening around 11:00 p.m. or so) we saw nothing, but then, sure enough, a slowly moving white light appeared near a small tower with red lights, providing a good point of reference for the motion. The light gradually changed brightness, sometimes brighter, sometimes dimmer, moving left to right, then disappeared. Soon, another would appear: sometimes higher, sometimes lower, usually moving to the right, but sometimes to left. My first thought: distant headlights. Sometimes, more that one could be seen at the same time.

Quickly, I ran back to my car to get the 15 x 70 binoculars and binocular mount (an Orion Paragon Plus) and set them up to view the Marfa lights, which by now were happening frequently. When viewing each Marfa light through these powerful binoculars, the first thing I noticed is that I was not able to focus! No matter how I changed the focus of the binoculars, I could do no better than to see a round amorphous blob of light.

Next, I decided to see if any of the fixed distant lights would focus. First the red tower lights. Nope, red blobs. Then a distant ranch light to the left of the light dome of Ojinaga/Presidio. Nope, a while blob. Then, another distant ranch light. Another white blob. Then some distant headlights on US 67/90 near Marfa heading toward Alpine. The headlights were too far away to resolve, and in the binoculars they, too, were an unresolvable white blob. Next I moved the binoculars up a few degrees to look at some stars. Perfect focus! Back down to the ground lights and Marfa lights: out of focus blobs!

So, it appears to me that some atmospheric phenomenon is defocusing and distorting terrestrial lights in the distance. Perhaps some sort of superior mirage. I think the most likely explanation for the Marfa lights is distant vehicle headlights.

Next steps in the investigation of this curious phenomenon: Use a micrometer eyepiece in a low-power rich-field telescope to measure the angular sizes of the Marfa light blobs, as well as the angular sizes of the blobs from identifiable terrestrial lights. Determine the distance to the terrestrial light sources in the daytime (if possible) using triangulation. Better yet, determine the great circle distance to each terrestrial light source by obtaining GPS coordinates of each of those light sources, and the Marfa lights viewing station. Even better would be to shine a mobile light source at the Marfa lights viewing station from various GPS-determined locations at different distances on an evening when the Marfa lights are visible. Determine if the size of each known light blob is a function of distance. Using this information, estimate the distance to the Marfa light sources.

Also, note whether the angular size of each Marfa light is related to its altitude above the horizon.

More ideas: Take a series of 30-second digital camera exposures over the course of an evening to determine if the Marfa lights take preferred paths. The results might support or refute the vehicle headlights hypothesis. Determine if the Marfa lights paths change from night to night or during the course of one night.

Finally, I’d suggest using the same kind of wide-field spectroscopic equipment used to obtain meteor spectra to determine the spectral characteristics of the Marfa lights. This would tell us much about their chemical composition, temperature, and origin.

Space Travel Under Constant 1g Acceleration

The basic principle behind every high-thrust interplanetary space probe is to accelerate briefly and then coast, following an elliptical, parabolic, or mildly hyperbolic solar trajectory to your destination, using gravity assists whenever possible. But this is very slow.

Imagine, for a moment, that we have a spacecraft that is capable of a constant 1g (“one gee” = 9.8 m/s2) acceleration. Your spacecraft accelerates for the first half of the journey, and then decelerates for the second half of the journey to allow an extended visit at your destination. A constant 1g acceleration would afford human occupants the comfort of an earthlike gravitational environment where you would not be weightless except during very brief periods during the mission. Granted such a rocket ship would require a tremendous source of power, far beyond what today’s chemical rockets can deliver, but the day will come—perhaps even in our lifetimes—when probes and people will routinely travel the solar system in just a few days. Journeys to the stars, however, will be much more difficult.

The key to tomorrow’s space propulsion systems will be fusion and, later, matter-antimatter annihilation. The fusion of hydrogen into helium provides energy E = 0.008 mc2. This may not seem like much energy, but when today’s technological hurdles are overcome, fusion reactors will produce far more energy in a manner far safer than today’s fission reactors. Matter-antimatter annihilation, on the other hand, completely converts mass into energy in the amount given by Einstein’s famous equation E = mc2. You cannot get any more energy than this out of any conceivable on-board power or propulsion system. Of course, no system is perfect, so there will be some losses that will reduce the efficiency of even the best fusion or matter-antimatter propulsion system by a few percent.

How long would it take to travel from Earth to the Moon or any of the planets in our solar system under constant 1g acceleration for the first half of the journey and constant 1g deceleration during the second half of the journey? Using the equations below, you can calculate this easily.

Keep in mind that under a constant 1g acceleration, your velocity quickly becomes so great that you can assume a straight-line trajectory from point a to point b anywhere in our solar system.

Maximum velocity is reached at the halfway point (when you stop accelerating and begin decelerating) and is given by

The energy per unit mass needed for the trip (one way) is then given by

How much fuel will you need for the journey?

hydrogen fusion into helium gives: Efusion = 0.008 mfuel c2

matter-antimatter annihilation gives: Eanti = mfuel c2

This assumes 100% of the fuel goes into propelling the spacecraft, but of course there will be energy losses and operational energy requirements which will require a greater amount of fuel than this. Moreover, we are here calculating the amount of fuel you’ll need for each kg of payload. We would need to use calculus to determine how much additional energy will be needed to accelerate the ever changing amount of fuel as well. The journey may well be analogous to the traveler not being able to carry enough water to survive crossing the desert on foot.

Now, let’s use the equations above for a journey to the nearest stars. There are currently 58 known stars within 15 light years. The nearest is the triple star system Alpha Centauri A & B and Proxima Centauri (4.3 ly), and the farthest is LHS 292 (14.9 ly).

I predict that interstellar travel will remain impractical until we figure out a way to harness the vacuum energy of spacetime itself. If we could extract energy from the medium through which we travel, we wouldn’t need to carry fuel onboard the spacecraft.

We already do something analogous to this when we perform a gravity assist maneuver. As the illustration below shows, the spacecraft “borrows” energy by infinitesimally slowing down the much more massive Jupiter in its orbit around the Sun and transferring that energy to the tiny spacecraft so that it speeds up and changes direction. When the spacecraft leaves the gravitational sphere of influence of Jupiter, it is traveling just as fast as it did when it entered it, but now the spacecraft is farther from the Sun and moving faster than it would have otherwise.

Of course, our spacecraft will be “in the middle of nowhere” traveling through interstellar space, but what if space itself has energy we can borrow?