A Second Bite Of The Gamma-Ray-Burst Apple

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Let’s lighten up a little on the otherwise-unmitigated pessimism and gloom involved in considering the consequences of gamma-ray bursts (GRBs) for galaxies that experience them. The Universe is a big, big place, big enough that, even with GRBs irradiating galaxies, we might realistically anticipate that there would remain at least a few galaxies where GRBs did not occur, at least within the lifetime of an intelligent, technological species within such a galaxy. (I define “technological” as possessing means of communication capable of sending messages to other species in other star systems. By that criterion, the Earth is host to an intelligent, technological species of life.) So I propose we run the numbers and see what they look like.

We may consider the Universe as a sphere with a radius of, in round numbers, 14 billion light-years (ly). The formula for the volume of a sphere, which we all learned in junior-high school is:

Vsphere = 4/3 x pi x r3

where r is the radius of the sphere. If we plug in the relevant numbers, we calculate that, for the entire Universe, the volume is

VUniverse = 4/3 x pi x (1.4 x 1010)3 = 4/3 x pi x 2.74 x 1030 cubic ly = 1.15 x 1031 cubic ly

As I said, the Universe is a big, big place:  that is how big in quantitative terms.

Now, let’s suppose that there are, say, 100 intelligent, technological civilizations in the entire Universe. (Why 100? It is a round number, therefore easy to work with. In any case, the subsequent calculations are easy to modify if you like a different number. If so, feel free!)

This means that that volume of 1.15 x 1031 may be carved up into 100 sub-spheres, one for each of our intelligent, technological species. So each species is allotted a volume of

Vspecies = 1.15 x 1031 / 100 cubic ly =1.15 x 1029 cubic ly

What would be the radius of each such “species bubble”? Quite easy. Now that we know the volume of each “species bubble,” we simply plug that volume into the above formula for calculating the volume of a sphere and solve for r, i.e. for the radius of the “species bubble”. So we derive

Rspecies=(3/4 x 1/pi x 1.15x1029)1/3 = (0.275 x 1029)1/3 = (27.5 x 1027)1/3 = (27.5)1/3 x 109 ly = 3.02 x 10**9 ly

(Note that, to derive the radius of the “species sphere,” we have to take the cube root, because we are starting with a spherical volume, i.e. a three-dimensional quantity.

Note also that I am skating over issues pertaining to inflationary cosmology. If Prof. Alan Guth of MIT is right, as he almost certainly is, about inflation, then the above geometry is almost certainly too simplistic: if inflation is still occurring at remote places in the Universe, then this complicates the simplicity of the "species spheres" paradigm.

I am also skating over the issue of dark energy / the "cosmological constant". If the entire Universe is expanding, the "species spheres" as envisioned above are almost certainly too small: everything everywhere is getting bigger and drawing away from everything else. My "species spheres" scenario is, at best, a snapshot of this moment in time. Intelligent technological species will become progressively more remote from each other as the ages roll on, thanks to dark energy. But let's keep matters relatively simple for now, shall we?)

But now note that that approximately 3 billion ly number only gets us as far as the outer surface of one “species sphere”. To get to the center of the nearest “species sphere” from there -- i.e., to the location of the intelligent, technological species inhabiting it that occupies the center of that neighbor "species sphere" -- we have to travel an additional 3 billion ly, i.e., the radius of the nearest “species sphere”. So the total distance to be traversed from one “species sphere” to its nearest neighbor is approximately 6 billion light-years.

So a signal, traveling at the speed of light in a vacuum, would require 6 billion years to get from the sending to the receiving intelligent species. Six billion years is about half again as long as the entire Earth has been in existence (about 4 billion years). Actually, even that is an optimistic estimate, because it tacitly assumes that each “species sphere” is immediately adjacent to its neighbor. In actuality, each “species sphere” would most likely be separated from its neighbors by who-knows-how-many billions of light years of empty space. It is almost certainly not the case that the “species spheres” would be packed, belly-to-butt and cheek-to-jowl, like morning commuters in a subway at rush hour or like eggs in a cardboard supermarket case.

So what is the bottom-line conclusion? There are 2, one optimistic, the other pessimistic. Let’s consider the good news first.

  • The good news is that, for reasons of blind chance if nothing else, it is unlikely that GRBs have eradicated literally all life, intelligent and otherwise, in the entire Universe
  • However, the bad news is that it may well be the case that GRBs have “thinned the herd” to the point that the surviving intelligent, technological species are so widely separated that the speed of light renders communication between them impossible, both practically and in principle.

(It might be a fun exercise to re-calculate the above numbers under the assumption that there are, say, 1000 intelligent, technological species in the Universe; then, say, a million. I have done this, and the news is only marginally better, certainly not good enough to be realistically encouraging. In fact, here is a simple formula for calculating the radius of the "species spheres" for hypothetical numbers of intelligent, technological species:

Rspecies  = (3/4 x 1/pi x 1.15 x (1031 / Nspecies))1/3

where Nspecies is the number of intelligent technological species in the Universe you want to hypothesize, e.g., 1000, a million, etc., i.e., the number of “species spheres”. Rspecies will be the radius of each hypothetical species’ “species sphere”. But remember that whatever this radius turns out to be, you have to double it to get the true distance from one intelligent, technological species to its nearest neighbor. So, in the case of a million intelligent technological species in the Universe, the radius of the million-species "species spheres" will be a bit over 140 million light years. So the distance from one intelligent technological species to its nearest neighbors will still be 2 x 140 million ly = 280 million ly. Anyway, have fun!

Bottom line:  there probably is no Star Trek or Star Wars galaxy teeming with intelligent life like students on mid-term college break in Fort Lauderdale.

Dr. Enrico Fermi

Now, to be sure, all the above assumes that all the intelligent species, and therefore all the “species spheres” are evenly distributed across the entire Universe, as I said previously, like commuters at rush hour or like eggs in a supermarket carton. In reality, such an even distribution would most likely not be the case. For reasons of blind chance, if nothing else, there would most likely be some “clumping”:  intelligent, technological species comparatively close to one another. But, if that is the case, then Fermi’s Paradox assumes an even sharper edge:  if there are indeed “clumps” of intelligent species sprinkled through the Cosmos, then the various “clump members” would surely at some point detect one another’s electromagnetic emissions – and it would be reasonable to conclude that we on Earth would detect at least a bare remnant of this “spillover,” rather like a dog picking up random scraps that fall from a banquet table. But, at least so far, that has not been the case. We hear nothing. From anyone. Ever. “Oh,” you say, “but perhaps the ‘clump’ is too far away!” Then we are back to the original even-distribution conclusion. You cannot have it both ways.

For all practical purposes, Enrico Fermi’s famous question of “Where is everyone?” may have been answered by GRBs – plus, to be sure, more mundane catastrophes like cometary collisions, environmental catastrophe, and species-wide war.  My conclusion:   we are probably alone in the Universe, in the sense that whoever else may be out there is separated from us by such a stupendous distance that communication is impossible. So even if someday we were to invent a workable warp drive, no passing Vulcan starship will help us celebrate.

Hence the Great Silence.

"The silence of these infinite spaces terrifies me." -- Blaise Pascal, Pensees

James R. Cowles

Image credits

Supernova / GRB … European Space Observatory … Public domain
Enrico Fermi … NARA … Public domain
"Star Wars" aliens … Pixabay … Public domain
Galactic cluster … Wikipedia … No attribution given
Spiral galaxy … Wikipedia … No attribution given
Radiotelescope … CSIRO (Commonwealth Scientific and Industrial Research Organization) … Public domain
Veil nebula … JSchulmann555 … CC by 3.0