Decoding the Cosmic Background Radiation
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In devising theories to organize data that we obtain from our observations of Reality we must employ imagery that our minds can comprehend, so we use similes and metaphors, images that bear a kind of likeness to the phenomena we wish to describe. But, of necessity, we have only imperfect likenesses available to us, so we must take care to examine our reasoning closely lest our similes and our metaphors subtly lead us astray. Our current Cosmogony offers an excellent example of what that statement means.
According to the story, as we presently have it, the Universe exploded into existence ex nihilo 13.7 billion years ago (give or take 200 million years) and filled itself with matter and energy so thickly that the plasma coupled to the radiation tightly enough to make the Universe opaque. As the Universe expanded, the plasma/radiation mix expanded adiabatically (that is, without absorbing heat from or losing it to some other body) and, thus, cooled. After an elapse of 379,000 years from the beginning (give or take 8000 years) the plasma/radiation mix had cooled enough for the plasma to begin neutralizing itself and thereby freeing the trapped radiation. Over the next 118,000 years (give or take 3000 years) the Universe became transparent and the radiation flew free, leaving the gas and plasma to condense into galaxies.
We gained that story largely from Edwin Hubble, for whom NASA named its space telescope. Hubble determined from his measurements that the Universe=s other galaxies are largely flying away from ours, the farther galaxies receding faster than the nearer ones. Based on that picture, Hubble likened the Universe to an exploding bomb, the galaxies analogous to the shrapnel thrown out by the bursting shell.
The exploding bomb metaphor seems like a good one. We even refer to our cosmogony as The Big Bang in recognition of it (though the term was originally presented by Fred Hoyle as a term of derision). But how can we make certain that our metaphor matches Reality properly?
Simple. We ask a question.
We may properly claim that the well-devised question marks the beginning of all good science; for without the question we can have no answer and, thus, no advance of knowledge. Through the endless process of raising questions, answering them, raising new questions on those answers, and answering those in turn, natural philosophers and scientists have built up the knowledge that comprises modern science. And of all the questions that scientists have asked, those reflecting the deepest insights have caused the most profound truths to be fished up out of the sea of ignorance: AWhat if Earth revolves about the sun instead of vice versa?@; AHow does Ampere=s law apply to the gap between the plates of a charging capacitor?@; or AHow do Maxwell=s Equations work for different observers if the luminiferous Šther does not actually exist?@
Scientists may labor for years, decades, even centuries without conceiving such questions. They advance their science slowly, painstakingly, sometimes in wrong directions. Then one day someone raises a question whose answer sends a beliefquake shuddering through the sciences and out into the wider culture. Thus we find our culture adorned with such treasures as Koppernigk=s heliocentric solar system, Maxwell=s electromagnetic theory, and Einstein=s Relativity.
The askings of such questions give us events to cherish, though we must, perforce, appreciate them in hindsight. But those askings also give us opportunities to study the ways of human thought. I now present what I believe to be a beautiful example of such an opportunity.
I: Gulko=s Question
In a paper titled AIs Big Bang Cosmology a Science?@ published in the Journal of the British-American Scientific Research Association, a now-defunct group of amateur scientists, Arnold G. Gulko asked,
AHow does radiation from an obviously very high temperature equilibrium taking place billions of years ago reach us today as a microwave radiation which has a temperature level below 3 degrees Kelvin?@
In the next paragraph he implies a further question by commenting,
AIf the universe is expanding, then it must have started small and the blackbody radiation might have been released when the universe was much smaller than it is now. If that were so, those radiations should have moved outwardly past us so as to no longer be received by us.@
I combine the gist of those two quotes into a paraphrase, a singe question that I call Gulko=s Question:
Given the cosmologists= belief that radiation decoupled from matter between 300,000 and 600,000 P.I. (Latin: Post Initium, After The Beginning) at a temperature of 3000 Kelvin, what makes it possible for us to detect any of that radiation today and why at a temperature of 2.725 Kelvin (Centigrade degrees above Absolute Zero)?
Having thus recast Gulko=s Question, I then examined cosmology texts drawn from my own library and from the library of the UCLA Department of Physics (see Appendix One). I took a sample that I regarded as just large enough, though certainly not exhaustive, to provide a consistent picture: most of the authors ignore the first part of Gulko=s Question (why do we detect any of the primordial radiation at all?) and give answers to the second part (why does the radiation come to us at such a cold temperature?) that seem clearly wrong. That picture, however fuzzy it looks to us, represents a serious problem in the study of cosmology; for if cosmologists do not correctly understand the cosmic background radiation, then the validity of the standard cosmological model, for which they make the cosmic background radiation the key piece of evidence, comes into serious question. And yet for over four decades no cosmologist seems to have noticed the existence of that problem, much less solved it.
What makes that possible? How can cosmologists possibly remain unaware of a flaw as subtle as a supernova in the foundation underlying their prime theory of the Universe and its history? I believe that the answer to that question lies in the way that we use language (and its similes and metaphors), but I want to look at the correct answer to Gulko=s Question before I confront that question and try to devise an answer.
II: The Relativity of Creation
Edwin Hubble=s inference in 1929, from measured redshifts and inferred distances, that the galaxies all recede from each other at speeds more or less proportional to their distances from each other Alike fragments of an exploded bomb@ leads inevitably to the idea that at some instant in the past the Universe originated in a single point that expanded, filling itself with matter and radiation, to become the galaxy-filled void that we inhabit now. Beginning as a super-hot, heavily-dense plasma that completely filled space, matter and radiation comprised a jelly-like body that expanded opportunistically with the expanding space, the matter and radiation cooling together. At some stage in the expansion the plasma cooled enough for the matter and the radiation to decouple from each other; that is, the radiation, which had begun its existence trapped in the ionized gas, its electric and magnetic fields entangled with the ions and electrons of the plasma, became free to fly through the thinned gas and through space as it does today. The gas, which the pressure exerted by the trapped radiation had kept free of nonuniformities, became free to evolve into galaxies, stars, and planets. Those statements describe the main features of the standard cosmological model, popularly known as the Big Bang theory.
The cosmic background radiation comprises the radiation that came free in the decoupling event. From the uniformity in its observed temperature cosmologists have inferred that the Universe expanded uniformly and, thus, that decoupling happened at the same time everywhere. Unfortunately, that last inference tends to imply subtly that decoupling happened simultaneously at all points in one inertial frame B ours. However, we can disabuse ourselves of that implication by way of a subtlety from the theory of Relativity, one that no cosmologist ought to have missed: the time that was the same everywhere was proper time, the time that would elapse on clocks at rest in the inertial reference frames occupied and marked by portions of the expanding plasma. As seen from any given point, then, portions of the plasma progressively farther from that point fly away from the given point ever faster (in accordance with Hubble=s law), at speeds up to but not including the speed of light, thereby marking the full array of available inertial reference frames. In those frames clocks mark time dilated relative to time elapsed in the frame marked by the given point. Consequently, decoupling occurred at the point occupied by a hypothetical observer and then, as measured in that observer=s frame of reference, occurred progressively later (not counting the time lag due to the distance that the light must cross at a finite speed) at points ever farther from that initial point, the times ranging from the presumed 300,000 years P.I. to Šternity. For our hypothetical observer, then, there will never come a time when they won=t detect the primordial radiation glowing in the sky. That analysis answers the first part of Gulko=s Question. The radiation that we detect today decoupled from the primordial plasma when the Universe was roughly half its current age.
Time dilation also answers the second part of Gulko=s Question, though to understand why we must invoke it we must first examine the currently accepted answer to see why it goes wrong. In the conventional model cosmologists explain the low temperature of the cosmic background radiation by modeling it as a photon gas cooling adiabatically in an expanding container. George Gamow provided a good description of that model in an article that appeared in Scientific American in 1954: he compared the radiation in the primordial fireball to light trapped inside a cylinder with perfectly reflecting walls and a movable piston at one end. In that model, when the piston moves outward, the trapped light becomes cooler by losing energy through the work that it does upon the moving piston. That model provides an accurate description of the cooling of the primordial radiation prior to its decoupling from matter, because during that time the radiation lost energy through doing work upon the expanding gas. But after matter and radiation decoupled from each other, Gamow=s model no longer describes the fate of the radiation correctly: since the time of its release, the radiation has done no work upon moving walls (or their equivalent) simply because the Universe has none.
We correctly describe the cosmic background radiation not as Acooled@ , but rather as Acold@ ; that is, the radiation had a temperature of 2.725K, in our frame of reference, from the very instant it decoupled from matter and that temperature has not changed since that time. Time dilation, as part of the relativistic Doppler shift, interpreted through the kinetic theory of heat, gives us the explanation we need for that fact. We know that time dilation slows down the motions occurring in a moving object and we know that the temperature of an object reflects the motions of the atoms that comprise the object, so we can infer that in a reference frame in which it moves an object will appear colder than it does in the frame in which it floats at rest. Likewise, processes that take place at a given temperature in the rest frame take place at lower temperatures in frames in which the components are moving: in a rocket moving past us at 87.7 percent of lightspeed, for example, we would observe water boiling at 86.6 degrees below zero on the Celsius scale, instead of at the conventional 100 degrees above zero. Thus, instead of decoupling at the proper temperature of 2900K, the cosmic background radiation that we detect today decoupled at 5.45K (the remaining reduction to 2.725K coming from the motion part of the Doppler shift).
By exploiting Wien=s displacement law, cosmologists have related the assumed proper temperature of decoupling to the temperature inferred from observations of the cosmic background radiation, taking the ratio 2990K/2.725K = 1064 to give us the z-factor (representing the degree of redshift in the radiation=s spectrum) associated with the recession of the decoupling plasma. I have taken that calculation a step further and used the relativistic Doppler shift (on which, see Appendix Two of this essay) to calculate the Lorentz factor (the factor by which the relative motion between Earth and the primordial plasma we observe via the cosmic background radiation dilates time) associated with that z-factor as equaling about 532.
That calculation means that the cosmic background radiation that astronomers detect today decoupled from the plasma at a time, in our reference frame, 532 times longer after the instant in which the Universe came into being than the proper time of decoupling. To achieve a Lorentz factor of 532 that plasma must move away from the Milky Way at a speed close to that of light and we know that the radiation has come back to us at the speed of light, so we can see clearly that in our frame the cosmic background radiation decoupled from matter when the Universe was about half its present age. The ongoing process of refining the value of Hubble=s constant over the past sixty plus years implies at present that the Universe has a proper age of about 13.7 billion years. If we divide that age by two and then by 532, we obtain the proper date of decoupling as 12.86 million years P.I., not the currently assumed 389,000 years P.I. That calculation thus shows us a quotience of over 1.5 orders of magnitude between the conventional age of decoupling and the age calculated from the relativistic Doppler shift.
Of course we can conceive the possibility that decoupling happened at a proper temperature higher than 2900K. Indeed, we know of numerous examples of plasmas in which decoupling happens at higher temperatures; among them we find the photospheres of Sol (6000K), Altair (8600K), Sirius A (11,000K), Vega (11,200K), and Beta Centauri (21,000K). The stars with the coldest photospheres, stars of spectral class M, such as Antares (3100K), come closest to modeling the conventional picture of the decoupling of the cosmic background. If the proper temperature of the cosmic background radiation turns out to go higher than 2900K, then we must calculate both the z-factor and the Lorentz factor associated with it proportionately higher and the proper date of decoupling will turn out to have occurred earlier than 12.86 million years P.I.
Whatever proper temperature the primordial plasma may have had at decoupling, we can say for certain that the temperature of any point in the Universe had not fallen to anything near 2900K prior to one million years P.I. The inference that the proper temperature of the Universe remained above any given value far longer than the current model proposes effectively invalidates that model. Cosmologists will have to go back and recalculate the features of that model (the creation of the elementary particles, the amount of nucleosynthesis that occurs, the proportion of the dark matter that consists of baryonic matter, the processes of galaxy formation, etc.) and may very well have to change the mathematical descriptions that comprise the model as well. The current standard cosmological model simply does not hold true to Reality.
We must feel dismayed, to say the least. How can a modern scientific theory, one that has attracted considerable attention and intellectual effort for over half a century, remain vulnerable to such a shocking blow? In the forty years since Penzias and Wilson=s discovery of the cosmic background radiation transformed the Big Bang hypothesis into the Big Bang theory, no one, to the best of my knowledge, has carried out the simple and obvious relativistic calculation that I displayed above, even though cosmologists have acknowledged from the beginning that the source of the radiation moves away from Earth at relativistic speed. What made the cosmologists all miss that relativistic analysis for four decades?
III: The Sapir-Whorf Hypothesis
Also known as the theory of linguistic relativity, in clear analogy with Einstein= s Relativity, the Sapir-Whorf Hypothesis consists essentially in the claim that how we comprehend a phenomenon depends as much upon our cultural frame of reference as it does upon the phenomenon itself. In linguistic relativity the frame of reference comprises the language that we use to describe the phenomenon. As Benjamin Lee Whorf (1897 Apr 24 - 1941 Jul 26) put it:
AWe are thus introduced to a new principle of relativity, which holds that all observers are not led by the same physical evidence to the same picture of the universe, unless their linguistic backgrounds are similar, or can in some way be calibrated.@
Thus, while we all perceive the same features in any given scene, our different languages translate those same percepts into different concepts. Put a different way, the Sapir-Whorf hypothesis tells us that a society=s choices in constructing a language, which reflect that society=s experiences, constrain the individual conversion of percepts into concepts. You can find a more disturbing version of the hypothesis expressed in George Orwell= s famous novel A1984", especially in the appendix on Newspeak.
The famous example in linguistics compares the way in which English speakers and I˝uit apply names to bulk quantities of frozen-water flakes. English has only one noun that names the stuff (snow), though skiers have taken to using adjectives as if they were nouns in order to make many of the same distinctions that the I˝uit make. I˝upiatun, a language spoken on Alaska=s North Slope, also has a generic word for snow (apun), but it also has over half a dozen other nouns that name varieties of snow distinguished from each other by their mechanical properties. Among those nouns we find names for fresh or powder snow (nutagaq), packed snow (anui), melting snow (auksalaq), and hard crusty snow (silliq). In addition, I˝upiatun has words that we cannot easily calibrate with English; the word Aqunguq@, for example, refers to Abrightness on the horizon indicating the presence of ice on the ocean@. Their language thus gives the I˝upiaq people ready reference to concepts that make devising thoughts appropriate to participation in a Neolithic culture in a land dominated by ice and snow convenient in ways that the concepts named in English are inadequate to do.
Whorf further expressed his ideas on linguistic relativity in two subhypotheses; 1) all higher levels of thinking depend on language and 2) the structure of the language one habitually uses influences the manner in which one understands their environment.
For the purpose of this essay, Subhypothesis One gives us an obvious tautology. Higher levels of thinking require language because they involve the use of abstractions. We certainly count modern physics and cosmology as entities that require heavy use of abstractions, so we need concern ourselves no more with Subhypothesis One.
In Subhypothesis Two we have a different matter. How the structure of language influences understanding gives us the key to discovering how cosmologists missed using Relativity to describe decoupling. Again, Whorf provided what has become a famous example to illustrate his point.
From 1919, shortly after receiving his Bachelor of Science degree in Chemical Engineering from MIT, to 1941, Whorf worked as a fire prevention inspector for the Hartford Fire Insurance Company in Hartford, Connecticut. He had taken a course in linguistics from Edward Sapir (1884 - 1939) while he was at MIT and after graduating pursued the further study of linguistics as an amateur. He soon discovered that his hobby gave him useful insights into the problems he encountered on his job, a fact that he noted in a paper that he wrote in the summer of 1939 in memory of Sapir (with whom he had remained in contact). In that paper, AThe Relation of Habitual Thought and Behavior to Language@, he wrote that he had analyzed hundreds of reports on the circumstances surrounding the start of fires and he provided an example of one such analysis;
ABut in due course it became evident that not only a physical situation qua physics, but the meaning of that situation to people, was sometimes a factor, through the behavior of the people, in the start of the fire. And this factor of meaning was clearest when it was a LINGUISTIC MEANING, residing in the name or the linguistic description commonly applied to the situation. Thus, around a storage of what are called Agasoline drums@, behavior will tend to a certain type, that is, great care will be exercised; while around a storage of what are called Aempty gasoline drums@, it will tend to be different B careless, with little repression of smoking or of tossing cigarette stubs about. Yet the Aempty@ drums are perhaps the more dangerous, since they contain explosive vapor. Physically the situation is hazardous, but the linguistic analysis according to regular analogy must employ the word >empty=, which inevitably suggests lack of hazard. The word >empty= is used in two linguistic patterns: (1) as a virtual synonym for >null and void, negative, inert@, (2) applied in analysis of physical situations without regard to, e.g., vapor, liquid vestiges, or stray rubbish, in the container. The situation is named in one pattern (2) and the name is then Aacted out@ or Alived up to@ in the other (1), this being a general formula for the linguistic conditioning of behavior into hazardous form.@
Put another way, the denotation of a word (empty = contains none of X) is associated with or logically entails a set of connotations (the identity of X, if not stated, is implied by the name of the container; contains no useful quantities of X; whatever X does or may be made to do won=t occur; etc.) that condition the translation of percept into concept. Thus, a person who knows that gasoline is a fire hazard can perceive a storage area labeled Aempty gasoline drums@ and conceive the area as a safe place for smoking cigarettes. We can infer that someone must have received a serious jolt to provide Whorf with fodder for that report.
If our description of a concrete situation can mislead us into life-threatening behavior, then how much farther afield can our description of an abstract theory lead us? In those realms of thought where we reason by analogy, using similes and metaphors that may have connotations totally inappropriate to the phenomena under consideration, we can apparently become easily lost. With that thought in mind, we can now examine the central thesis of modern cosmology.
IV: Hubble=s Bomb
In 1929 Edwin Hubble revealed his discovery that the galaxies= motions away from the Milky Way have a rough proportion to their distances from the Milky Way, a relationship now known as Hubble=s law. Invoking a compelling image, Hubble described the galaxies as flying away from each other Alike the fragments of an exploded bomb@. Cosmologists subsequently reinforced that imagery through their perverse adoption of Fred Hoyle=s sarcastic remark about Aa very big bang@. Thus, in spite of some use of alternative imagery (as, for example, by comparing the galaxies to dots painted on an inflating rubber balloon), cosmologists still regard the creation of the Universe as a kind of explosion.
We see that conception reflected in the use of a single word. Cosmologists typically describe the cosmic background radiation as Acooled@, which carries the connotation of a cooling process, rather than as Acold@, which carries no such connotation. Thus the cosmologists subtly bias their conversion of percepts (their observations of the Universe) into concepts (their theory of the Big Bang) in a way that further reinforces the explosion metaphor.
In denotation we have Aexplosion = suddenly hot, highly pressurized gas expanding rapidly@. The connotations associated with that denotation include Aexpels fragments at high speed@ and Agases cool adiabatically@. The first of those connotations connects the denotation to the data that provide the source of Hubble=s simile. The second connotation reinforced the appeal of the simile when Penzias and Wilson discovered the cosmic background radiation: an originally hot Universe, including its primordial radiation, appears to have cooled to 2.725 Kelvin.
That second connotation necessarily entails a reference to the kinetic theory of gases. In that modern theory of thermodynamics, gases held in containers that expand cool adiabatically (i.e. by losing thermal energy in doing work) when they push against the containers= moving walls. In the case of gases from an exploding bomb, the ambient air provides the container, against which the bomb=s hot gases do work by pushing it outward and thereby creating a shock wave. In the newborn Universe the still-coupled radiation and plasma cooled in that way, by each parcel of gas doing work against the pressure of the surrounding gas as space expanded. The plasma continued to cool by that means after decoupling until it broke up in the initial stage of galaxy formation. As George Gamow noted, even light, seen quantum-mechanically as a gas made up of photons held inside a container with perfectly reflecting walls, can cool adiabatically as the container expands (that is, the spectrum of the light will change from that of light emitted from a hot blackbody to that of light emitted from a cooler blackbody). Hubble=s bomb imagery strongly implied that image of light as a photon gas cooling by expanding adiabatically with the Universe, even though we know that the photons in the cosmic background radiation have not interacted with anything like a moving wall since they decoupled from the plasma.
To borrow Whorf=s analysis, we can see that Hubble=s simile with one connotation led cosmologists to name the origin of the Universe with the denotation Aexplosion@ and then to describe it theoretically through another one of the connotations, that of Agases expanding adiabatically@, which subtly implies that the physics of the newborn Universe differed little from that of an empty gasoline drum ignited by a smoldering cigarette.
I believe that we can support that analysis by our observation that the cosmologists= interpretation of the temperature of the cosmic background radiation does not include relativistic considerations. The connotations associated with Aexplosion@ do not include Relativity, so our unconscious translation of the percepts pertaining to the cosmic background radiation into the concepts of the Big Bang theory excludes it. And we can find further support for the analysis in another conceptual exclusion from the Big Bang theory, one involving the physics of plasmas.
The relevant percept in this case comes to us through the observation that the energy flux that comprises the cosmic background radiation has an exceptionally smooth distribution across space; that is, across the sky the observed temperature of the radiation, corrected for the peculiar motions of Earth, Sol, and the Milky Way, varies by less than one part in ten thousand. That fact necessarily means that at the time of decoupling the density of matter had a similar smoothness throughout the Universe. Yet soon after decoupling, on the cosmological time scale, the matter had clumped into galaxies arrayed in clusters that, according to maps like those first drawn by Margaret Geller, John Huchra, and Valerie de Lapparent, sketch huge filaments throughout space. The intervening transformation of the density of matter, from a smooth distribution to a lumpy one, still stands as a mystery, called the galaxy problem, in the Big Bang theory. Indeed, the excitement over George Smoot=s announcement, in 1991, that he and his team had found in data from the Cosmic Background Explorer evidence of slight density fluctuations that might serve as seeds for a gravitational breakup of the plasma strongly suggests that cosmologists still don= t have a proper clue with which they can solve the mystery of the galaxy problem.
And yet someone familiar with the physics of plasmas would suggest an obvious solution based on the instabilities for which plasmas are infamous among physicists, instabilities that have for half a century frustrated efforts to devise reactors that use controlled thermonuclear fusion to produce energy for the generation of electricity. Prior to decoupling, that someone would claim, the radiation, through its pressure, provided a negative feedback mechanism that opposed the growth of density fluctuations in the plasma. After decoupling, when that mechanism was gone, the positive feedback effects, such as magnetic pinch, would have swept the plasma into the filaments that subsequently broke up into protogalaxies. We can actually see a beautiful example of that kind of process in the Crab Nebula, a cloud of plasma that was blown outward in the smooth explosion of a supernova (SN1054) and yet now, less than a thousand years later, displays a prominent filamentary structure reminiscent of the maps drawn by Geller, Huchra, and de Lapparent.
Why does the Big Bang theory not show the galaxy problem dissolved in such mechanisms? I can only point out that we don= t find Aplasma instability@ among the connotations of Aexplosion@, but does that fact, interpreted through the Sapir-Whorf hypothesis, give us sufficient evidence to explain the unconscious suppression of discovery of a solution to an important problem in cosmology?
Can we possibly believe that a single analogy can so monopolize the translation of perceptions of objective Reality into conceptions of subjective understanding as to exclude other relevant thoughts from our minds? Can the quirks of language so easily prevent us from discerning things that we should properly regard as obvious? We can answer those questions, I believe, but doing so requires a bit of roundabout reasoning that begins with the recollection of the quaint story of AColumbus and the Egg@.
According to the story, Christopher Columbus attended a feast celebrating his discovery of what we now call America, in the course of which feast another guest opined that the voyage was merely a simple and obvious stunt that anybody could have performed. Columbus agreed, pointing out that the world has in it many simple and obvious stunts that anybody can perform. As an example he offered the guest a hard-boiled egg and asked him to stand it upright on its blunter end. After fumbling with the egg for several minutes, the guest handed it back to Columbus and commented that the trick could not be as simple as Columbus had claimed. Columbus then poured a small amount of salt into a pile on the table and set the egg in it (or, as an alternative version has it, he rapped the egg=s blunter end on the table and balanced the egg on the resulting dent in its shell). The chagrined guest admitted that Columbus what had just demonstrated was, indeed, simple and obvious. AYes,@ Columbus said, Abut only after I have shown it to you.@
Does that mean that the posting of this essay on the Internet will lead cosmologists to exploit the simple and obvious tricks of applying Relativity and the knowledge of plasma instabilities to the information they have obtained from the cosmic background radiation? Not necessarily and probably not likely. The reason supporting that rather depressing statement follows from the recognition that the Sapir-Whorf hypothesis must be founded as much upon deep-flowing emotional undercurrents as upon the cognitive contents associated with our words and phrases. Among the strongest of those undercurrents we find simple human vanity, especially in the form of an abhorrence we all have of others seeing us in the wrong about anything. That abhorrence gains strength from any significant investment of personal resources (e.g. time, effort, reputation, love, etc.) that we may put into the thing about which we are wrong. Lurking in the unconscious mind, where most of our thinking takes place, such emotional undercurrents can indeed prevent thoughts from coming into consciousness and may even contribute to the forgetting or dismissal of thoughts of which we have been made aware.
That process extends into the social realm, since language gives us fundamentally a means of communication among people. In the creation of any consensus that we shall associate these connotations and not those connotations with this given denotation, we grant authorities in the relevant fields almost sole responsibility in both the inclusionary and exclusionary decisions, presumably because most of us assume that those authorities will least likely lead us wrong through their interpretations. Social status thus plays a strong role in the Sapir-Whorf hypothesis. As elders of the scientific tribe, mainstream cosmologists established and still maintain the imagery of the Big Bang theory, mainly through their influence upon their students and upon the peer-review process. In that influence we can see the basic mechanism of ideosclerosis, the hardening of thought into dogma.
Established orthodoxies rarely change in any significant way through action by members of the institutions that hold them and maintain them, however well those members may intend their actions. Radical change properly comes from outsiders, from amateurs and misfits. Think of Niklas Koppernigk studying astronomy in rural Poland; think of James Clerk Maxwell, whose bizarre sense of humor, by his own account, put a wall of estrangement between him and his colleagues; and think of Albert Einstein working in the Swiss Patent Office while dreaming of light and of the secrets it has to tell of space and time. Such heretics transform orthodoxy by discerning its hidden structure and correcting its flaws. An awareness of the influence of the Sapir-Whorf hypothesis may enable us similarly to transcend the limitations of that hypothesis to correct current scientific orthodoxies. No, we won= t change the world, only the way in which people conceive it.
1) Carroll, John B. (Editor), ALanguage, Thought, and Reality, selected writings of Benjamin Lee Whorf@, MIT Press, 1956. LCCCN 56-5367.
2) Gamow, George, AModern Cosmology@, Scientific American, Vol. 190, No. 3, pp 55 - 63, March 1954.
3) Gulko, Arnold G., AIs Big Bang Cosmology a Science?@, Journal of the British-American Scientific Research Association, Vol. XIV, No. 5, pp 14 - 22, March 1993.
4) Whorf, Benjamin L., AThe Relation of Habitual Thought and Behavior to Language@, pp 75 - 93 in ALanguage, culture, and personality, essays in memory of Edward Sapir@, edited by Leslie Spier, 1941 by Sapir Memorial Publication Fund, Menasha, WI.
The Cosmology Texts
The following list describes the texts that I searched for answers to Gulko=s Question. Under the publishing information I list for each text 1) the time and proper temperature of decoupling given by the author, 2) the answer the author provides to the first part of Gulko=s Question, and 3) the answer that the author gives to the second part of Gulko=s Question. Though I have used a small sample, I believe that it is broad enough and the answers are consistent enough to imply strongly that the ongoing search of other texts will turn up essentially the same answers. (See Appendix Three to see how some of those answers stood as of 2003).
A) Abell, George O., ARealm of the Universe, 2nd Ed.@, 1980, Saunders College/Holt, Rhinehart and Winston, Philadelphia, ISBN 0-03-056796-3.
1) Approximately 1,000,000 years P.I. and 3000K.
2) Not explicitly addressed. The diagram on Pg 376 depicts decoupling as a horizontal line on a space-time plot, thus representing decoupling as having occurred simultaneously everywhere in a space that was effectively infinite from the instant of Creation. The cosmic background radiation is thus presented as radiation emitted from matter that was 17 billion lightyears from the Milky Way=s position at the time of decoupling. The diagram, however, is inconsistent with Relativity in that it depicts a Universe with an inertial frame of absolute rest filled with matter, most of which is flying away from any given position faster than light.
3) The temperature is transformed by the Doppler shift to resemble that of radiation from a cold blackbody.
B) Dykla, John J., ACosmology@, pp 167 - 182 in AEncyclopedia of Astronomy and Astrophysics@, Robert A. Meyers, Editor, 1989, Academic Press, Inc., San Diego, CA, ISBN 0-12-226690-0.
1) 700,000 years P.I. and 3000K.
2) Not addressed.
3) Ashifted to the radio spectrum by the expansion of the universe.@
C) Kipperhahn, Rudolf, ALight from the Depths of Time@, 1987, Springer-Verlag, New York, ISBN 0-387-17119-3.
1) 300,000 years P.I. and 3000K.
2) Implies that we exist in a region in infinite space, which region is defined by a horizon moving away from us at the speed of light, the Universe still being opaque in those regions that could only be reached by something flying faster than light. The cosmic background is radiation coming to us from those other regions.
3) The radiation has Acooled down@, being Doppler shifted from the instant of emission.
D) Kolb, Edward W., and Michael S. Turner, AThe Early Universe@, 1990, Addison-Wesley Publishing Company, ISBN 0-201-11603-0.
1) Approximately 200,000 years P.I. and 3000K.
2) Not addressed.
3) Radiation redshifted by the expansion of the Universe.
E) Silk, Joseph, AThe Big Bang B Revised and Updated Edition@, 1989, W.H. Freeman and Company, New York, ISBN 0-7167-1812-X.
1) 300,000 years P.I. and 3000K
2) Not explicitly addressed. The diagram on Pg 165 implies that the expansion of space carried radiation away from the Milky Way, thereby retarding its arrival. That implication violates Einstein=s second postulate of Relativity, by which postulate the time required for light to reach an observer from some point depends only upon the distance between the observer and that point at the time the light was emitted (as measured in the observer=s frame of reference) and not upon any motions of the source or any other intervening reference frames.
3) After decoupling the radiation was cooled by the expansion of space. The process is equivalent to the adiabatic expansion of a gas, but is attributed to the stretching of the photons by the expansion of the space through which they are flying, a process that violates conservation of energy. On Pg 397 the author acknowledges that time dilation plays a role in shaping the cosmic background radiation, but assigns that role to controlling the radiation=s energy flux and not its temperature.
The Relativistic Doppler Shift
Since the last part of the Nineteenth Century astronomers have had a way (and only one way) to discover a portion of the motions of distant stars and galaxies. Astronomers infer the motion of a star toward or away from Earth by calculating the relative velocity from the measured displacement of the bright and dark lines that appear in the star=s spectrum relative to the corresponding lines in light coming from a stationary source. Those lines, discovered by Joseph von Fraunhofer (1787 Mar 06 - 1826 Jun 07) in 1814, comprise ghostmarks on the rainbow-colored band of light that emerges from a glass prism, ghostmarks whose significance was discerned around 1860 by Robert Wilhelm von Bunsen (1811 Mar 31 - 1899 Aug 16) and Gustav Robert Kirchhoff (1824 Mar 12 - 1887 Oct 17). Astrophysicists base the use of relative displacements of spectral lines to calculate relative velocities upon a discovery made concerning wave phenomena in 1842 by Christian Johann Doppler (1803 Nov 29 - 1853 Mar 17) and verified for light by Armand Hippolyte Louis Fizeau (1819 Sep 23 - 1896 Sep 18), the man whose first measured the speed of light.
If a star moves, at least in part, away from Earth, then the part of the star=s motion that=s oriented directly away from Earth causes the wavelengths in the star=s emitted light to appear to observers on Earth to be lengthened over what they would be if the star were not moving, thereby making the Fraunhofer lines appear to be shifted toward the red end of the visible spectrum. Astronomers use that redshift (also called the Doppler shift), then, to calculate the radial component of the star=s velocity relative to Earth. Astronomers also use it to measure the recession speeds of galaxies and quasars away from Earth.
But we have another ghostmark on light that we can use to discern Doppler shifts. If we have the spectrum of light emitted from a perfectly black body, then Wien=s displacement law tells us that the wavelength at which the body emits the greatest proportion of its radiated energy stands in inverse proportion to the absolute temperature of the blackbody. Thus, if we know the absolute temperature of a body emitting blackbody radiation and can measure the peak wavelength of its spectrum, we can then exploit Wien=s law to calculate the size of the Doppler shift and from that number calculate the relative velocity of the body. To a good approximation stars and galaxies radiate like blackbodies, so there we have the method that astrophysicists use to calculate the recession speed of the source of the cosmic background radiation, though it requires of us that we calculate the proper temperature of the source from theories of radiation/plasma decoupling.
We can work out a mathematical description of the Doppler shift by exploiting the electromagnetic theory of light first created by James Clerk Maxwell (1831 - 1879) in 1861. According to Maxwell=s theory, light consists of electric and magnetic fields that create wave patterns by tracing out mutually perpendicular sinusoidal arrays of force that propagate away from their source as oscillating electric currents in the source generate them. We take the wavelength to denote the distance between two successive points on the wave, in the direction of propagation, at which one of the fields has the same magnitude and orientation; thus, if we let blip represent the interval of time that the source takes to repeat one of its electric oscillations, then the wavelength of the electromagnetic pattern rippling away from the source equals the product of blip and the speed of light.
Now imagine that the source moves to the right with a certain speed, so that in the elapsed time blip it will have crossed a distance, left to right, equal to the product of that speed and blip. Because it moves, in the course of emitting one wave, measured from crest to crest, the source will partly overtake the leading crest on the part of the wave emitted toward the right and will move away from the leading crest on the part of the wave emitted toward the left; thus, relative to a wave that the source would emit while at rest, the distance between the leading and trailing crests will be shorter on the part of the wave propagating toward the right and longer on the part of the wave propagating toward the left. A simple geometric consideration then lets us modify the above boldfaced statement to calculate the wavelengths of the rightward and leftward propagating parts of the wave, giving us, respectively,
1. The wavelength going to the right equals blip times the speed of light minus blip times the source speed.
2. The wavelength going to the left equals blip times the speed of light plus blip times the source speed.
The first of those statements represents a blueshifted wavelength and the second of them represents a redshifted wavelength.
Those statements, of course, stand only approximately true to Reality and only when the source moves relative to the observer at a speed very much smaller than the speed of light. We can make those statements precisely true to Reality by acknowledging that its oscillating electric current makes the source a kind of clock, which is subject to time dilation. We must thus multiply blip by the Lorentz factor to calculate the correct time interval over which the source emits the wave, the dilated blip. If we divide the source=s speed by the speed of light and call the resulting fraction haste, then we get the Lorentz factor between our observers and the source when we divide one by the square root of (one minus the square of haste). Because we want to consider only the cosmological redshift, I will modify only the second statement above.
When we multiply blip by the Lorentz factor, Statement 2 tells us that the wavelength that we receive from the receding source equals the Lorentz factor times (blip times the speed of light plus blip times the speed of the source). The parentheses in that statement indicate that we must carry out the sum before we multiply the result by the Lorentz factor. Next we work a little algebraic magic on that statement:
1. We get the received wavelength when we multiply (blip times the speed of light plus blip times the speed of the source) by the Lorentz factor;
2. We get the same result when we multiply (one plus the haste of the source) by the Lorentz factor times blip times the speed of light, because blip times the speed of the source gives us the same result as does blip times the speed of light times the haste of the source;
3. Because blip times the speed of light gives us the wavelength as emitted by the source, we get the same result when we multiply (one plus the haste) by the Lorentz factor times the emitted wavelength;
4. Now we use a special trick based on the fact that (one minus the square of the haste) gives the same result as multiplying (one plus the haste) by (one minus the haste). The square root of that product appears in our calculation of the Lorentz factor, so we can cancel the square root of (one plus the haste) from our calculation without changing the result. Thus we get the received wavelength when we multiply the emitted wavelength by the square root of (one plus the haste) and divide the result by the square root of (one minus the haste). Thus we get the calculation describing the relativistic Doppler redshift.
Astronomers define the redshift factor (or z-factor, because they represent it in their algebraic representations with the letter zee) as the calculation (observed wavelength divided by proper wavelength) minus one. That makes the redshift factor of a stationary source equal to zero, which makes sense because the radiation that we get from that source does not display a shift in its ghostmarks. We can use Statement 4 in the paragraph above to work out the arithmetic recipe that lets us calculate that redshift factor in terms of the haste of the receding source. We find that adding one to the redshift factor gives us the same result as we get from dividing the square root of (one plus the haste) by the square root of (one minus the haste). Using some rather clever algebraic tricks we can turn that calculation inside out and thereby devise a way to calculate the haste from any given redshift factor. We can then use that haste to calculate the corresponding Lorentz factor. Thus, we calculate the Lorentz factor that corresponds to a given redshift factor by adding (one plus the redshift factor) to one divided by (one plus the redshift factor) and then dividing that sum by two.
As I noted above, we can use Wien=s displacement law to calculate the redshift factor of the cosmic background radiation. By that law the ratio of the peak wavelengths of the blackbody spectrum, observed wavelength divided by proper wavelength, equals the ratio of the absolute temperatures of the background, proper temperature (absolute temperature of the radiation as emitted) divided measured temperature (absolute temperature of the radiation as received). We take the proper temperature of the cosmic background to equal 2900K and the measured temperature to equal 2.725K, so we have a redshift factor of 1064 and a Lorentz factor of 532.5.
Adapted from WMAP Data presented in A The Alternate View@ ,
John G. Cramer, Analog Science Fiction and Fact, Oct 2003,
Vol. CXXIII, No. 10, Pgs 75 - 79.
Proper Temperature of Decoupling =2900 Kelvin
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 = 2.725K"0.002K
CMB Photon Density = 410.4"0.9 photons/cm cubed
Proper Temp/CMB Temp. = 1064 (Cramer gives 1089)
Baryon-to-Photon ratio = 6.1"0.3 x 10-10 baryons/photon
Baryon-to-Matter ratio = 0.17"0.01
Hubble= s Constant = 71"4 km/sec/Megaparsec
Age of Universe (corrected for acceleration) =13.7"0.2 billion years
Age at Decoupling = 379"8 thousand years
Age at Decoupling by relativistic Doppler shift = 12.86 million years
Decoupling Duration = 118"3 thousand years
Age at Reionization = 180 + 220 - 80 million years
Local Mass Density** = 9.7 x 10-27 kg/cubic meter
*As a fraction of the whole.
**To calculate the Local Mass Density we have the photon density multiplied by the Baryon-to-Photon ratio multiplied by the ratio of total density to baryon density multiplied by the mass of the proton (1.67 x 10-27 kg.).
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