Light, The Big Bang, And Inflation Theories

 

 

By

 

Rodney W. Peterson’

 

 

Math G, Section: 16814. M.W. 5-7 PM Professor Ian Walton

 

 

            Contemporary cosmologists are as fixated with the origins of the universe as were the ancient Egyptians and Greeks; in point of fact, since prehistoric Homo sapiens focused their binocular vision on towards the heavens and observed the impenetrable radiant constellations (comprised of some 3,000 visible extraterrestrial bodies), the Cosmos has continued to enrapture and flummox all who ponder its splendor and genesis; and, despite the ingenious contributions of Isaac Newton, James Clerk Maxwell, Max Planck, and Albert Einstein, humankind is only somewhat closer to answering the fundamental question: From where did the visible universe originate from?

            The aforementioned men, along with their predecessors Copernicus, Galileo, and Kepler, shared one common passion—the habitual observance and notation of celestial light. Centuries passed between the Greeks and Einstein before the elemental question: What is light?—did acquire a comprehensible answer.

The first individual for consideration, regarding the properties of light, is Sir Isaac Newton (1643-1727). Newton is accredited with one of the first scientific clues regarding the properties of light, “[when] In 1672, in the first paper that he submitted to the Royal Society, Newton described an experiment in which he permitted sunlight to pass through a small hole and then through a prism. Newton [discovered] that sunlight, which gives the impression of being white, is actually made up of a mixture of all colors of the rainbow” (Voyages, 86). Newton’s experiment demonstrated that the visible “white” light the Sun emits is in actuality bands of light. In our present day Newton’s light bands are known as spectral light and are a segment of electromagnetic radiation, and whose particular wave lengths are approximately between 400 and 750 nm (nanometers), however, the entire electromagnetic spectrum is made up of gamma rays, X-rays, Ultra-violate, visible (or white light), infrared, microwaves VHF/UFH, short-wave radio, and long-wave radio.

            The second individual for consideration, regarding the properties of visible light, is James Clerk Maxwell (1831-1879). Maxwell is accredited with the discovery of light’s “electromagnetic” properties, and his discovery is analogous to Newton’s laws of mechanics (or Newtonian relativity), the propounded explanation for the moon’s orbit about the earth (as well as all planetary systems). Maxwell’s experiments with electric charges demonstrated that magnetism was the result of moving charged particles. According to Maxwell there existed a fundamental connection between electrical charges and magnetism, that is, moving charged particles produced magnetism. Maxwell adroitly amalgamated, hitherto, separate rules for electricity and magnetism into one consistent theory. “In the vicinity of an electric charge, another charge feels a force of attraction or repulsion: Opposite charges attract; like charges repel. When charges are not in motion, we observe only this electric attraction or repulsion. If charges are in motion, however … we measure another force, called magnetism” (Voyages, 82).

And, as any contemporary college physics text book will explain, typical atoms are these above-referenced particles, which possess a universal blueprint—positively charged proton(s) (comprising the nucleus) and negatively charged orbiting electron(s). Maxwell investigated the oscillation “and found that the resulting pattern of electric and magnetic fields would spread out and travel rapidly through space … all atoms [which consist of charged particles] oscillate back and forth … The resulting electromagnetic disturbances are among the most common phenomena in the universe” (Voyages, 82).

Inventively, “Maxwell was able to calculate the speed at which an electromagnetic disturbance moves through space; he found that it is equal to the speed of light, which had been measured experimentally. On that basis, he speculated that light was one form of a family of possible electric and magnetic disturbances called electromagnetic radiation” (Voyages, 83). Maxwell’s experiments demonstrated that the phenomena of changing fields could produce electric currents and changing electric currents could produce changing magnetic fields and once started, electric and magnetic field changes simultaneously generated the other. “Because of his contributions, the set of equations are known as Maxwell’s equations … Essentially, Maxwell’s equations combine the electric and the magnetic fields into a single electromagnetic field … [which are] separate fields … symmetrically related in the sense that either one can create the other” (College physics, 649).

In spite of Maxwell’s symmetrical wave-like electromagnetic field, visible light possesses a somewhat contradictory second property, which cannot be fully explained by his wave model. In addition to possessing wave-like properties light also possesses particle-like properties. Contemporary physicists know these self-contained bundles of energy as packets of electromagnetic energy, or photons. The scientific method has repeatedly confirmed that visible light has a dual nature and can behave wave-like and particle-like at the same time.

Attempting to contemplate light as possessing dual properties, can be difficult, but what must be kept upper most in mind is that visible light is visible light; and each photon (a particle composed of even smaller particles) possesses a certain, or constant, amount of energy, and this “energy is proportional to the frequency of the wave it represents” (Voyages, 96). And the above-referenced proportionality leads to the next individual and his contribution.

The third individual for consideration, regarding the properties of light, is the German physicist Max Planck (1858-1947). In or about the year 1900, Planck scrutinized the inability of classical electromagnetic theory to explain the characteristics of thermal radiation and devised a radical explanation which correctly predicted that atoms emitting radiation “have only discrete energy rather than continuous distribution of energies” (College Physics, 842). Planck’s theoretical detection facilitated supplanting the inherent discrepancies of classical electromagnetic theory’s continuous quantity energy with quantized energy, occurring in discrete amounts, and said quantity is mathematically represented as hf, which in English is known as quantum energy.

Quantum energy, according to Planck’s definition, is “the energy [that] occurs only in integral multiples of hf. The symbol h represents a constant known as Planck’s constant and has a value of h = 6.63 X 10^-34 J·s” (College Physics, 842). Planck’s pioneering work gave astronomers “Planck’s constant” and his hypothesis of quantum energy won Planck the 1918 Nobel Prize. However, outside the scientific community, Planck does not possess the public awareness that Albert Einstein achieved, but Einstein’s two postulates, which form the basis for his special theory of relativity, will be for all time linked with Planck’s quantum energy hypothesis.

The fourth and final individual for consideration, regarding the properties of light, is mathematician and physicist Albert Einstein (1879-1955). Inarguably, Einstein was the most gifted mathematician and physicist of the Twentieth Century, and is accredited for his General Relativity (the very large scale at the Cosmological level) equation E=mc². In particular, it is the second postulate of his special theory of relativity that contributively elaborates upon another property of light, that is, the consistency of its speed. Einstein stated: “The speed of light in a vacuum has the same value in all inertial fields.” Einstein built upon Planck’s quantum energy hypothesis and ingeniously “reasoned … that energy quantization is a fundamental property of electromagnetic waves … He suggested … that to conserve energy, the emitted radiation should also be quantized. [Einstein proposed] … The radiant energy from a point source is not distributed continuously throughout an increasingly larger region, but, instead, this energy consists of a finite number of spatially localized energy quanta which, moving without subdividing, can only be adsorbed and created in whole units” (College Physics, 842).

Einstein, in 1905, published a paper on his Special Theory of Relativity regarding light absorption and emission, and in so doing laid down the most profound mathematical concept for the property of light; that is its speed, the c in his General Relativity equation: E=mc² (where E = energy, m = mass, and c = equals the speed of light, that is to say, energy equals mass times the speed of light squared).

Having now considered the contributions of Newton, Maxwell, Planck, and Einstein, as they pertain to the multiple properties of light, the math behind these theories can, perhaps, be comprehensible for the layperson. From Newton we now know visible light is actually comprised of rainbow-colored bands; and, from Maxwell we now know visible light is comprised of charged particles, photons, that have wave-like electromagnetic properties; and, from Planck we now know visible light radiates discrete “quantized” energy; and, from Einstein we now know light possess a universal constant speed of 300,000 km/s. If confusion persists, it is not necessarily the layperson’s fault, because “The confusion that [Maxwell’s electromagnetic model] this wave-particle duality of light caused in physics was eventually resolved by the introduction of a more complicated theory of waves and particles, now called quantum mechanics” (Voyages, 84). However, quantum mechanics (the very small scale at the subatomic level), in scope, is beyond the purpose of this essay because only the elementary properties of visible light, particle, wave, and speed, are considered herein.

Let us begin with the math symbol for the frequency of light (wave-like property), which is ƒ; and, ƒ = c/λ. The math symbol “c” represents the speed of light, and the math symbol “λ” (meaning 1) represents the wavelength of light. Now let us recall that the h in Planck’s constant represents a constant that equals 6.626 X 10^-34 J·s (the math symbol “J·s” represents Joule second, the metric unit of energy). The math symbol representing a photon (light’s particle property) is Eø. Review of the aforesaid accords a formula to express visible light’s dual properties: Eø = hƒ. And let us not forget the “rest” mass of a photon, which in math notation is represented as mø; and, mø equals c²/Eø. What the above math connotes is visible light is composed of photons (a discrete packet of energy), particles that can, at times, also behave like electromagnetic waves—both of which travel at the universal speed of light, 300,000 km/s.

Consequently, the frequency and wavelength of visible light are inversely proportional, their product always being the speed of light in a vacuum; and the energy conveyed by an individual photon is directly proportional to the light’s frequency, the constant of proportionality being Planck’s constant (h) = 6.63 X 10^-34 J·s; and if an equivalent “rest” mass can be spoken of for a photon, then it would be found by equating the energy of that photon Eø with the famous rest energy equation of Einstein’s Special Theory of Relativity: Eø ≡ Eо = mо c². Hence, mо = c²/Eø.

Acquiring an elementary comprehension of visible light, its simultaneous dual properties, proved itself a perplexing conundrum for centuries. Yet visible light, the continuous electromagnetic spectrum human eyes detect without difficulty, distinguishes only a small segment of the entire electromagnetic spectrum—a diverse spectrum that includes Gamma rays, X-rays, Ultra-violate light, Visible, Infrared, Microwaves, VHF/UHF, Short-wave radio, and Long-wave radio radiation, proved to be Kinderspiel compared to the origins of The Cosmos.

Nineteenth and early Twentieth Century astronomers, like their ancient counterparts the Egyptians and Greeks, were no less challenged when contemplating the origins of the universe. The evolutionary processes of the Cosmos presented humankind with Sphinx-like conundrums within conundrums until the pantheon of mathematical genius provided humankind with Albert Einstein, who possessed the mathematical prowess to grapple with the Cosmos and its probable origins. Einstein’s Relativistic models, adequately measuring objects traveling at the speed of light, opened the heavens vanitas (emptiness), instabilitas (instability), and vertibilitas (mutability) to theoretical consideration hitherto unimaginable.

Coincidently, subsequent observations made by Edwin Hubble (1889-1953) confirmed an expanding endless universe, and “set the stage for today’s studies of galaxy formation when he discovered that the Milky Way was not alone ... The known universe suddenly ballooned in size” (National Geographic, 16). Drawing this conclusion from his October 6, 1923, observations he thereby did substantiate Einstein’s theoretical equations and transformed the current theory of a static “unchanging” universe into a dynamic changing endless entity—rife with the malevolent throws of birth, life, and death. Consequently, by virtue of Einstein and Hubble, mathematically contemplating scientific theories on the origins of the universe are, quite possibly, unique to the late Twentieth and early Twenty-first centuries.

Presently, there are two concurrent theories regarding the origin of the universe, and they are known as the Big Bang and Inflation Theories. However, when contemplating the origins of the Cosmos, what is meant by the term “Big Bang? And, when contemplating the evolution of the universe, what is meant by the term Inflation theory?

In the past several decades the prevailing theory on how the Cosmos began is commonly referred to as the BIG BANG. In essence, this theory suggest that there was nothing and then there was something as result a tumultuous effulgent explosion, all of which resulted in what Cosmologist call the present “observable universe”—some fifteen billions years later. Observable universe is meant to construe a comprehension that the light (the visible particle wave-like properties of photons) emitted by galaxies billions of light years distant from earth are collected and studied, and some of this light may well be near the beginnings of the Cosmos. However, Cosmologist do not limit their studies by observing only the properties of visible light, because the primordial electromagnetic spectrum is composed of many differing forms of radiant energy, radiant energies that include Gamma rays, X-rays, Ultraviolet, Visible, Infrared, Microwaves, VHF/UHF, Shortwave radio, and Long wave radio waves, as mentioned earlier.

Before pressing forward with the primal Big Bang theory, however, an analogy of a VCR and a VHS tape would be helpful in illustrating the aforementioned. Think of rewinding a VHS tape of your favorite movie in a VCR from its ending to its beginning—all the while watching the images progress backwards in real-time. Now think of the universe as we observe it here and now, and ask the question: How would it look if the evolution of the Cosmos had been recorded and we could watch it run backwards in spacetime? Simplification applied, this thought model allows you and I, as well as Cosmologists, to intellectually approach the question from where did everything, the Cosmos, originate?

Pursuant to Big Bang theorists, “Eventually, we would find that all matter was once concentrated in an infinitesimally small volume. [Cosmologists] identify this time with the beginning of the universe … The violent explosion of that concentrated universe at the beginning of time is called the Big Bang” (Fraknoi, et al., 600). However, there are inherent flaws with this theory. For example, the theory does little to “explain why there is [not] more matter than antimatter in the universe, nor does it account for the origin of the density fluctuations that ultimately grew into galaxies … It also does not explain the remarkable uniformity of the universe” (Fraknoi, et al., 617).

To assist answering these theoretical questions, we return to Einstein’s eloquent intellectual achievement, his theory of General Relativity: E=mc², which was published in 1916. E=mc² fundamentally transmogrified physics; and, in 1925, the scientific method substantiated Einstein’s theory of general relativity. With Einstein’s relativistic theories substantiated, Cosmologists could now quantitatively begin investigating the origins of, not just our solar system and/or our galaxy—the Milky Way, but, the Cosmos at large because they now possessed the means to hypothetically explore the what, when, and how questions of the Big Bang theory; scientifically affirming that “… energy cannot be created or destroyed, but only converted from one form to another” (Fraknoi, et al., 321). Understood correctly, conversion of energy into matter is the basis or premise that something “matter’ can evolve from “energy”—something from nothing.

As the Big Bang theory suggests “The expansion of the universe began everywhere at once throughout the universe we can see” (Fraknoi, et al., 605). The first mathematician to hypothesize the physical processes of the Big Bang was not Einstein but, rather, Abbé Georges Lemaître (1894-1966). According to Lemaître, the universe originated from what he called “the primeval atom” which cataclysmicly detonated, as the consequence of radioactive disintegration, into pieces of atoms as result the inherent splitting processes of nuclear fission. Although the 1927 theory of cataclysmic eruption held, the fission process did not.

In 1948, physicists George Gamow, Ralph Alpher, and Hans Bethe, published their theory suggesting the beginning of the universe came about as result of the processes of fusion, wherein “… fundamental particles … built up the heavy elements by fusion in the Big Bang … The result of their efforts is now considered the standard model of the Big Bang” (Fraknoi, et al., 612); although Astronomer Fred Hoyle is credited for coining the term Big Bang. Be as that may, does the Big Bang answer the question from what and/or where did everything come from, that is, the stuff that went bang? In short, the answer is yes and no.

Remember, there are flaws; flaws that do not explain why there is more matter than antimatter, the origin of density fluctuations that evolved into galaxies, and the remarkable uniformity of the universe, as a whole.

As it turns out, coincidentally, Lemaître’s theory was more accurate than inaccurate, and the search to explain the evolution of the universe leads us to Lemaître’s alma mater, MIT, and Alan Guth, Ph.D., a contemporary man who postulates a plausible theory which grapples with the seeming inconsistencies of the Big Bang theory; and who, in April 2001, was awarded the Benjamin Franklin Medal in physics (the precursor to the Nobel Prize) for his effort.

Professor Guth developed a hypothesis he coined the “inflationary” theory. Encapsulated, the theory posits that the universe began from a marble size of extremely dense hot matter which exploded, and from this explosion the universe rapidly inflated and, thereafter with uniformity, expand and cooled, permitting the evolutionary formation of galaxies, stars, solar systems, and planets (as we have come to know them). Commensurate with the Big Bang, inflation theory attempts an explanatory narration of what was before, during, and/or after the cosmic marble exploded, addressing some of the propounded eccentricities of the Big Bang; from zero, the “era of quantum gravity”, to the period comprising inflation—between 10^37s through 10^34s.

It is in the interval between 10^37s and 10^34s (the period of time comprising the inflationary theory) that, according to Guth, “ … the universe expanded at a rate that kept doubling before beginning to settle down to the more sedate expansion originally described by the Big Bang theory” (B. Lemley, Discover, April 2002).

In other words, “The universe … began in the era of quantum gravity [0 to 10^37s], a time when all four forces of the universe—gravity, electromagnetism, the strong (nuclear) and weak forces—may have been unified. Energy boiling out of this unstable stew grew during the brief inflationary period at an ever-doubling rate, and then decayed into an electronquark soup [10-34s to 10-6s] as those forces began splitting apart. The soup’s fundamental particles [10-6s to 3.5 minutes] combined into ever-more-complex forms as the universe cooled and expanded” (B. Lemley, Discover, April 2002). As theorized, something, matter (particles), developed from nothing, a vacuum.

However, one must bear in mind that Guth’s inflationary theory is firmly anchored upon the bedrock foundation of quantum mechanics, whereby “… nothing is something. Quantum theory holds that probability, not absolutes, rules any physical system. It is impossible … to predict the behavior of any single atom; all physicists can do is predict the average properties of a large collection of atoms. Quantum theory also holds that a vacuum, like atoms, is subject to quantum uncertainties. This means that things can materialize out of the vacuum, although they tend to vanish back into it quickly” (B. Lemley, Discover, April 2002). Physicists refer to this phenomenon as quantum fluctuation, the realm of particle physics (matter), and Guth’s “inflationary theory suggests that what erupted was a ‘false vacuum’, a peculiar from of matter … ”; and, according to inflation theory—“a false vacuum is characterized by a repulsive gravitational field, one so strong it can explode into a universe” (B. Lemley, Discover, April 2002).

Being the aforesaid found true, then for the average individual, with an average intellect, trying to conceptualize something from nothing is tantamount to “… imagining nothing, a pure vacuum. Imagine no space at all and no matter all”, which is all but impossible to comprehend; but, Guth cautions, “Don’t imagine outer space without matter in it” (B. Lemley, Discover, April 2002). But that is exactly what Guth requires anyone contemplating the Big Bang and/or inflationary theories to think—a “false” vacuum with and without “things” (particles) popping in and out of material existence.

To recapitulate the above-mentioned paragraphs, it is helpful to bear in mind what inflation theory attempts to establish, namely, an evolutionary time line, between the era of quantum gravity (wherein matter did not exist) 0 and 300,000 years (when negative and positive subatomic particles organized into stable atoms of hydrogen, helium, and lithium). How matter evolved from energy and became the observable universe is abridged in the subsequent paragraph.

Following the era of quantum gravity (when the marble size universe exploded and was simultaneously profoundly hot, hotter than our Sun’s 15 million° K core, and, only the four forces—gravity, electromagnetism, the strong and weak nuclear forces—existed concordantly) is the period of inflation (10^37s – 10^34s), when the false vacuum acted as a repelling force. Following inflationary expansion is the Quark soup period (10^34s – 10^6s); followed by the period between 10^6s and 3.5 minutes, wherein the radioactive quark soup cooled and emitted photons (tiny packets of electromagnetic energy). And here is when, in the evolutionary process, light became visible.

Accordingly, the quark soup period is followed by the period between 3.5 minutes to 300,000 years, wherein the origin of light atomic nuclei coalesce. And from 300,000 years to 1 billion years atoms evolved (the universe cooled permitting protons, neutrons, electrons, and neutrinos to built up, stabilize, and form deuterium or heavy hydrogen); and from 1 billion years to 12-15 billion years, the first galaxies evolved, organized, and expanded to their present day position and appearance. Viola! We have not only the evolution time line of the universe (its inflation-expansion)—but the evolutionary conversion processes of matter materialized from energy: The manifestation of something from nothing!

What has simplistically been presented here, energy becoming matter, in of its self—is a relatively new theory. However, the premise that energy can become matter has been scientifically observed and documented in particle accelerators around the world. Subsequently, therefore, one can think of the primeval universe, between 3 and 4 minutes old, functioning like a star—nuclear fusion of simpler elements into more complex elements.

Guth’s inflationary theory reiterates what GUTs (Grand Unified Theory: a model that unites three of the four forces of nature as a single force as result tremendous temperatures) predict, that an “incredible event occurred when the universe was about 10^35s old … The equation of general relativity, combined with the special state of matter at that time, predict that gravity could briefly have been a repulsive force” not the force that Cosmologist observe in the universe today; and, it’s this repulsive force that Guth conceptualizes in his inflation theory—“an extraordinary rapid expansion or inflation during which the scale of the universe increased by a factor of about ten to the fiftieth power times more than predicted by standard Big Bang models” (Fraknoi, et al., 619). Accordingly, Guth’s inflationary model marginally differs from the Big Bang only in the seconds from the era of quantum gravity to 10^-35s. After 10^-35s, the two theoretical models are identical.

In his own words, Guth states: “The inflationary universe theory is an add-on to the standard Big Bang theory, and basically what it adds on is a description of what drove the universe into expansion in the first place ... Inflation theory takes advantage of results from modern particle physics, which predict that at very high energies there should exist peculiar kinds of substances which actually turn gravity on its head and produce repulsive gravitational forces … The inflationary theory gives a simple explanation for the uniformity of the observed universe, because in the inflationary model the universe starts out incredibly small … the inflation takes over and magnifies this tiny region to become large enough to encompass the entire universe, maintaining this uniformity as the expansion takes place.” But, Guth cautions, “… everything has to be described in terms of probabilities” (Brockman, www.edge.org, 2002).

For the back yard astronomer, a different manner in which to simplify inflation theory is to think of said theoretical model as several pieces added to a jigsaw puzzle. Although Guth’s propounded theory accords more comprehension applied to the Big Bang, it also suggests plausible explanations (but not absolute answers) as to why there exists more dark matter than matter, how galaxies evolved from the origins of density fluctuations, as well as, explain (in part) the present uniformity of the current observable universe. More pieces, however, are required before the Cosmological puzzle becomes complete. The challenge standing remains our continued acquisition of the fundamental scientific knowledge to explain observable cosmological phenomena.

Unlike our predecessors, the Egyptians and Greeks, celestial bodies themselves may no longer elicit idolatrous veneration, but they assuredly continue to capture our acute watchfulness. Undoubtedly humankind’s fascination with the origins of the universe will not abate, but continue to compel us to seek answers to its riddles. Apparently what was true for Aristotle continues to remain true “The beginning of anything is the most important part, being indeed half of the whole.” And therein lies a maxim holds humans, we are obsessed with not knowing the beginnings of anything, knowing only that nothing precedes a beginning and everything proceeds from its beginning.

 

Works Cited

 

1. “Alan Guth: The Golden Age of Cosmology.” edge.org. 2001. 07/06/2002

<http://www.edge.org/documents/day/day_guth.html>.

 

 

2. Cowen, Ron. “Galaxy Hunters: The Search for Cosmic Dawn”. National

Geographic. February 2003: 2-29.

           

           

3. Fraknoi, Morrison, and Wolff. Voyages Through The Universe. 2nd ed.

Harcourt: Philadelphia, 2001.

                       

 

4. Lemley, Brad. “Guth’s Grand Guess.” Discover. April 2002: 33-38.

                       

                       

5. Newton, Sir Isaac: Mathematicians. Accessed 03/11/03; available from

            <http://www-goups.dcs.st-ac.uk/~hisory/Mathematicians/Newton.html>.

                       

                       

6. Wilson, Jerry, D., And Anthony J. Buffa. College Physics. 4^th ed.

NJ: Prentice Hall, 2000.