The Relativistic Universe
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Let us begin this essay by backtracking almost to the beginning. As part of the logical path leading from the conservation laws to the postulates of Relativity we deduced theorems to the effect that space has the symmetry of a sphere, that it has finite extent, and that it expands at a finite speed that has the dynamic character of an infinite speed. Now contemplate the primary implication of those theorems. At any given instant in the past space had less extent than it has now: the further in the past we put that instant, the smaller the extent that space had. There was, thus, an instant, far in the past, when space had zero extent, when all of space comprised a single point.
And before that instant? Before that instant there was no before that instant. Just as space cannot exist outside the Universe (there being no outside in which it could conceivably exist), so time cannot exist prior to the Universe (there being no prior in which time could conceivably elapse). We could say that the Universe came out of Absolute Nothingness if the phrase Acame out of@ actually referred to anything meaningful. The verb Acome@ requires the existence of time and the prepositional phrase Aout of@ requires space as an underlying implicit referent, so the phrase Acame out of@ has properly no application in describing the relationship between the Universe and Absolute Nothingness and thus we must understand it as purely metaphoric. (But contemplate that relationship a little longer and you will understand why modern theologians, in their more esoteric flights of fancy, describe God as Nothing, meaning the hyper-fecund No-Thing whence all that exists emanates.)
So we have Nothing nonexistent and, somehow, a single point-instant existent. That single point exploded into an infinite proliferation of points as the initial instant elapsed into successive instants; thus, space expands and time flies. We have implied that much in what we have deduced so far. But the Universe comprises more than space and time, a fact that I have used throughout this presentation. Now we must ask Whence came matter? We believe that matter cannot emerge from empty vacuum, but in stating such a belief we have implicitly assumed that empty vacuum is indeed empty. As it turns out, that=s not a good assumption.
In the late 1940's, when he was helping to develop the quantum theory of electromagnetic interactions, Richard Feynman conceived a set of weird little hieroglyphs, simple-looking arrays of lines, loops, and squiggles that physicists have since come to call Feynman diagrams. Professor Feynman conceived his diagrams as bookkeeping devices that would help him to construct the equations by which he would calculate descriptions of various interactions among electrically charged particles. Each diagram is a rough sketch of some of the processes that make up the overall interaction and thus it serves as a kind of checklist for the various mathematical factors that must go into the description of the interaction. It thus provides a means of ensuring that only the right number of formulae of the right kind are included in the calculations. The necessity for such devices became clear when Feynman discovered that the most straightforward (and, therefore, the simplest) calculations gave descriptions that did not match the descriptions inferred from measurements made of experiments involving those interactions. The calculated descriptions were not so much wrong as they were of the Aclose but no Kewpie doll@ variety. But by adding more diagrams to the preparation of his calculations, Feynman made those calculations progressively more accurate. In theory he would need an infinite number of diagrams for perfect accuracy, but in practice he needed only a few diagrams to make the theoretical calculations as accurate as those made from experiments. That stands true to Reality because, as Feynman discovered, the more complex the diagram, the less it contributes to the result.
Evidently the simple act of two electrons repelling each other is not so simple. The basic diagram represents the electrons as a pair of lines with a squiggle going from one to the other, the squiggle representing the electromagnetic field. But Feynman had to supplement that basic diagram with other diagrams, some of which have more squiggles and some of which have loops. Feynman interpreted the loops as representing particles that go round and round in time; that is, each loop represents a particle that goes from one instant to another and then goes backward in time to the first instant to start the process over again. Because Feynman also interpreted a particle traveling backward in time as an antimatter particle, we can also conceive each loop as representing the creation of a particle and its antimatter counterpart followed a brief time later by the mutual annihilation of those particles. Physicists made of those interpretations a description of what they call the quantum vacuum, space that not only provides the places in which interactions can occur but participates in those interactions as well.
In the Platonic sense the quantum vacuum is full of ghosts. Physicists call those ghosts virtual particles, aetherial things that consist of nothing more than the patterns of electrons, protons, photons, and all of the other subatomic particles. Without energy (and the mass that it confers) virtual particles effectively don=t exist. What brings that spooky void into contact with Reality is Werner Heisenberg=s indeterminacy principle. According to that principle, the Universe cannot take account of any action less than Planck=s constant. Usually physicists interpret that statement to mean that no one can ever know the linear momentum and the position of a particle both to arbitrary accuracy; that is, that the product of the inherent uncertainties in the measured linear momentum and position must come out equal to or greater than Planck=s constant (which is equal to 6.6262 x 10-34 joule-second or 4.1357 x 10-15 electron-volt-second). But we can also interpret it as cover for some subatomic shenanigans: a virtual particle and its antimatter counterpart can gain the mass to come real by borrowing the energy to do so, but only if they repay the debt, by ceasing to exist, within the interval calculated by dividing Planck=s constant by that energy. For example, a virtual electron-positron pair, which requires a little over one million electron-volts of energy, can play this cosmic peek-a-boo, but only if they exist as real particles for less than four billionths of a trillionth of one second. It is just such ephemeral pairs that the loops in Professor Feynman=s diagrams represent.
What do you suppose would happen if some phenomenon were to intervene and pull the two particles away from each other before they could repay their energy debt and vanish? Unable to annihilate each other, as matter and antimatter do when they meet, the particles would continue to exist after their allotted time had elapsed. Of course, such a process would violate the law pertaining to the conservation of energy, so we don=t expect to see it operating in our part of the Universe. But might something like such a process operate near the boundary of space, where space is grossly deformed? Certainly linear and angular momenta must be conserved even in that region of the Universe, but there is no necessity that energy be conserved there as well. We want to contemplate, then, what physicists call the Sakharov process, named for Andrei Sakharov, the Russian physicist who first described it.
The Sakharov process went something like this: In the first instants following the instant of Creation space had a small enough extent that particles popping out of the quantum vacuum would have come into being in regions of space that were moving apart at high speed and, thus, those particles would have been carried away from each other much as the galaxies that they came eventually to comprise are still being carried away from each other by the expansion of space. The Universe filled itself to unimaginable density with a roiling mist of matter and antimatter, which then underwent the overt annihilation that releases radiation rather than the covert annihilation that it would normally carry out under the cover of Heisenberg=s principle. That radiation heated the leftovers to temperatures so high that even atomic nuclei could not exist. That there were leftovers, coming from a small excess of matter over antimatter, is still something of a mystery, though current studies of the decay modes of K-mesons may shed enough light upon the subject to dispel the mystery. The Sakharov process continued to create matter in that way until space had expanded enough that particles popping into existence were no longer carried too far apart to annihilate each other covertly. The result was an expanding space filled with a plasma so thick and hot that by comparison the material at the center of our sun would seem a downright frigid near vacuum.
That combination of heat and expansion as properties of the early Universe led theorists to compare the Creation to an explosion, an obvious analogy given the fact that astronomers and physicists devised the first theoretical descriptions of the Universe as expanding shortly after World War I. That description led Fred Hoyle, an astronomer who favors a steady-state theory of an infinite nonexpanding Universe, to ridicule it as involving Aa very big bang@ , thereby providing the unfortunate name that adheres to the theory today. But we could also make an analogy between the Creation and a blossoming. Imagine the incandescent-white bud of an infinite-petaled rose opening and fading to yellow, to orange, to red, and then to black lightly dusted with faint luminous smudges. That image gives us a description of the Universe and its history as valid as Georges Lemaitre=s description of galaxies as the fading embers of some primordial fireworks display.
Because we can conceive electromagnetic radiation as a collection of particles (i.e. photons), especially when it has short wavelengths, we can regard the radiation that filled the Universe immediately after the Creation as one component of a mixture of gases. As any gas does, the photon-electron-proton gas that came out of the Creation lost pressure and temperature precipitously as it expanded. Physicists call that process adiabatic expansion, the expansion of a gas without allowing heat to enter or leave it. Such an expansion cools the gas in the reverse of the process that creates Southern California=s Santa Ana winds by compressing and thereby heating air flowing downhill from the continental interior. So long as the electrons and protons remained separate from each other within the primordial gas, so long as the photons could interact strongly with them by way of their electric charges, we could rightly describe the Universe as cooling. But when the temperature reached about 3000 Kelvin (3000 Celcius degrees above absolute zero, about half the temperature of our sun=s photosphere) enough electrons and protons had come together to form electrically neutral hydrogen (and thus reduce the electrical conductivity of the gas) that the gas became transparent. The photons, which had been trapped within the gas, effectively confined to small volumes by their strong interactions with the electrically charged particles, suddenly sprang free of the gas to travel the full width of the Universe. At that time the photon gas stopped cooling, though the hydrogen and helium (which fusion within the plasma had created) could continue cooling by adiabatic expansion for some additional time.
In your imagination choose a point, say one occupied by some of the matter that will eventually become our galaxy, at a time shortly before the gas becomes transparent. The gas at that point (and at all other points) is as perfectly uniform as it is possible for it to be. The photon component, the major component of the gas (one billion photons for every proton, according to modern estimates), exerts an internal pressure that prevents the matter component from developing clumps. After the gas becomes transparent, though, that constraint vanishes and the matter is free to condense. Some of the gas remains ionized, a situation that is notoriously (among physicists at least) unstable: the ionized gas can respond to any stray magnetic fields and the moving, electrically charged particles that comprise it generate magnetic fields, so the ionized component of the gas acts out a vicious cycle that breaks it up and pulls it into an array of kinky filaments (if you have ever seen pictures of the Crab Nebula, which is the remnant of a supernova that was visible in 1054 AD, you can gain an impression of what the condensing plasma looked like: the Crab originated in a uniform gas and has since developed a distinct filamentary structure). If enough plasma remains ionized after decoupling occurs, magnetic instability would gather matter into galactogenic filaments, like the structures that we see in the Crab Nebula. We don= t need full ionization for magnetic force to shape plasma: the gas in the sun=s photosphere is only mildly ionized and yet we see magnetically shaped features, such as sunspots. The gravitation of those proto-galactic filaments, weak though it was, pulled the remaining matter into them, thereby precipitating the evolution of galactic clusters and of the vast, achingly lonely voids that separate them from their neighbors.
As I said above, when the gas became transparent the radiation thus freed could no longer cool. Released at 3000 Kelvin (that is, having the spectrum of the radiation emitted by a perfectly black body whose temperature is 3000 Kelvin), it will remain forever at 3000 Kelvin. But the radiation coming from the sky today, discovered in 1965 by Arno A. Penzias and Robert W. Wilson at Bell Labs in Holmdel, New Jersey, has a temperature of 2.735 Kelvin, too cold to do so much as to bring liquid helium to a boil. How, then, can I claim that the radiation has not cooled since the day the Universe went transparent? You can gain a hint at the answer by contemplating the question Why do we see any cosmic background radiation at all? If the Universe went transparent when it was still small, then surely all of the radiation that was going to pass our location did so a long time ago. Find in that statement the hidden assumption that Relativity voids and you can anticipate what=s coming next.
Go back, in your imagination, to the instant when the gas around you went transparent. You occupy a point that appears to float at the center of a uniformly expanding Universe. The gas around you is still: you seem becalmed in some cosmic doldrum. Elsewhere, though, the gas moves away from you; the farther away it is, the faster it moves. That moving gas is subject to time dilation, which means that it didn=t go transparent at the same time that the gas at our location did. At progressively larger fractions of the distance to the boundary of space the primordial plasma went transparent at progressively later times. We can easily calculate, then, that the radiation falling from the sky today came free of the primordial plasma when the Universe was just about half its present age (at least in our inertial frame).
But time dilation does something else to solve our problem. By slowing down all physical processes it makes moving objects colder than they would be at rest. If the object in question moves away from us, the Doppler shift makes the radiation from it appear colder still. Thus, radiation that has a temperature of 3000 Kelvin in the frame occupied by the gas that released it comes to us with an apparent temperature of 2.735 Kelvin. And now we can calculate. We have the relativistic Doppler factor as (3000 divided by 2.735 as required by Wien=s displacement law) about 1097, which corresponds to a Lorentz factor of about 548.45 and a recession speed that= s 0.498339 kilometers per second (1114.46 miles per hour) shy of the speed of light (670,444,952.4 miles per hour). Thus the cold radiation coming to us at the speed of light was released from matter that is flying away from us at a speed close to the speed of light, so we calculate easily that the radiation was released in our frame when a time almost equal to half the present age of the Universe had elapsed since Creation, as we require.
Nobody knows the age of the Universe to any great accuracy. Various accounts give values that range between ten and twenty billion years, the variability reflecting the various astronomical methods of measuring the rate at which space expands. The historical trend in the values seems to be converging on 13.7 billion years, so that=s the value that I will use. Half that value is 6.85 billion years. Divide that by the Lorentz factor of 548.45, which is the amount by which time is dilated in the primordial plasma that released the cosmic background radiation that we see today, and now we know that the matter that comprises our galaxy first became transparent about 12.5 million years after the Creation. That figure gives us something to talk about because most cosmology texts give 300,000 - 400,000 years as the time that elapsed between Creation and transparency and no text gives a time greater than one million years. That fact might lead us to suspect that cosmologists have not payed proper attention to the basics of the physics involved in describing the Universe at the largest scale and that their theories are due for some revision. Those revisions should open up some interesting lines of research.
Given that time dilation operates upon the regions of the Universe that move away from us and has delayed their becoming transparent until long after our part of space cleared up, we now know that somewhere, out there, moving away from us at the speed of light, the instant of Creation stands frozen in time forever. The Creation Point has a temperature of absolute zero, because that point recedes from us at lightspeed. That temperature defines the minimum temperature that any thermodynamic system can reach, so we know that the Universe will not get colder than Creation. Nonetheless, the temperature of the radiation coming to us from the time-dilated era of decoupling decreases with time (2.735 K and decreasing), though ever more slowly the closer it gets to absolute zero. We also know that in regions close to the Creation matter is still being conjured into existence in slow, cold subatomic pas de deux. Somewhere beyond the veil of cold starfire, in the realm of cosmic glory, trapped in dilated time, matter is yet being torn from the quantum vacuum by Heisenberg=s indeterminacy, ghosts embodied by spatiotemporal riptides. Most of those particles comprise matter-antimatter pairs with only a small excess of matter, so the resulting gas is primarily radiation. In regions not so close to the Creation the first galaxies of those spaces are forming and their first stars beginning to shine. Every astronomy text tells us that when we look into deep space we also look into the deep past because of the time that the light has taken in coming to us. But now we know that the farthest reaches of the Universe don=t merely look younger than our part of it does: they are younger.
We also know that the Universe will continue to expand forever; that it will never collapse. Slowly the radiation from the sky will become colder and the spaces among the galaxies grow emptier and wider. As long as stars burn and smolder and as long as the sky=s temperature continues to drop, thermodynamic processes can proceed, even if the working fluid must be liquid helium passing between its superfluid and normal states. In time the last stars will fade out and the galaxies will grow dim and then dark and cold.
As the sky continues to cool toward absolute zero intelligent life may eke out an existence in the darkness. Such a bleak future reminds us of the scene in H.G. Wells= novel AThe Time Machine@, in which the Time Traveler has gone into a time when the sun has become a bloated red ember barely illuminating a cold Earth where sluggish life-forms play out Evolution=s final act. Such a depressing scenario seems unavoidable; one of the most fundamental laws of physics seems to decree it.
The second law of thermodynamics tells us that any system will so evolve that it will maximize its entropy. The hidden assumption is that the system will reach equilibrium, that the conditions in which the system exists do not change to keep the equilibrium condition changing.
The hidden assumption behind the heat death hypothesis is that the Universe is static and that it can thus reach an equilibrium state. But the Universe is not static: it=s expanding and it=s doing so in a way that brings relativistic thermodynamics into play. Nonetheless, the heat death scenario is still played out in current theories, albeit in more protracted form. Are we then to infer that we live in a Golden Age from which the cosmos can only decline into a lifeless abyss? Is our ultimate legacy to be, over the next trillions of years, a cosmic diaspora of frozen ghost cities? That=s what our current knowledge of physics implies. But now let me share a doubt with you.
If we have learned anything over the past two centuries, during which modern physics has achieved its current form and content, it is that we must not assume that we have found all of the knowledge that the Universe has to offer. Processes yet undiscovered, as radioactivity was prior to 1896, may give our descendants the ability over millions of years to reshape planets and stars. Ultimately that far-future Humanity will gain the ability to re-engineer entire galaxies. The natural course of events will change course.
If intelligent life did not intervene, the Universe would end up filled with neutron stars, black dwarf stars, and frozen planets. Intelligent life will alter that picture. There will be cities instead of planets and the vacuum will be perfected by the removal of all debris that can be used for construction, the Universe ultimately swept clean. Stars will be taken apart for fusion fuel and construction material. Even neutron stars will not escape the attentions of God=s apprentices. Described so briefly, such actions seem more desperate than grand, a pathetic staving off of the inevitable, though the people whose lives play out in that time might disagree.
But just suppose that the Map of Physics, which I have been assembling on another part of this website, is itself only a crude beginning. Assume that, just as Ancient Egyptian surveying rules presaged the deeper understanding of Euclid=s plane geometry, this Rationalist flowchart presages something that we cannot yet conceive, an understanding that goes deeper into Reality than our simple logic and mathematics can do. The people who hold that successor to the Map of Physics may no longer merely obey the laws of Nature, but may also have the ability to amend them. Imagine that our far descendants do just that.
Long before the lights of Nature=s Creation have begun to fade away, new lights will begin to shine in the galaxy. Drawing inexhaustible energy from the process of Creation itself and taking matter from dead stars and lifeless planets, people of the future will create worlds yet undreamed and build civilizations as incomprehensible to us as ours would be to a Paleolithic mammoth hunter. Far from being a doomed Golden Age, our own time may be merely the faintest predawn glow presaging an Age of Ęternal Light.
Cosmological Parameters from WMAP Data
John Cramer= s Alternate View
Analog, October 2003
Proper Temp. of Decoupling 2,900 K
Total Density* 1.02 " 0.02
Baryon Density* 0.044 " 0.004
Matter Density* 0.27 " 0.008
Dark Energy Density* 0.73 " 0.04
Neutrino Density* <0.015 @ 95% CL
CMB Temperature 2.725 " 0.002 K
CMB Photon Density 410.4 " 0.9 photons/cm cubed
Proper Temp/CMB Temp 1089
Baryon-to-Photon ratio 6.1 " 0.3 E-10 baryons/photon
Baryon-to-Matter ratio 0.17 " 0.01
Hubble Constant 71 " 4 km/sec/Mpc
Age of Universe (corrected for accel.) 13.7 " 0.2 billion years
Age at Decoupling 379 " 8 thousand years
Decoupling Duration 118 " 3 thousand years
Age at Reionization 180 + 220 - 80 million years
* as a fraction of the whole.
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