A perusal through current Astronomy textbooks supports the above thesis. Here is a partial listing of instruments and detectors used by astronomers to sample radiation inherent to different regions of the electromagnetic spectrum (note the general similarity to Earth-directed sensors): Conventional Optical Telescopes (refractors and reflectors); Optical Interferometers; Photographic plates; Photomultipliers (photons --> electrons); Image Intensifiers; Vidicons; Semiconductor detectors; Scintillation detectors; Charge-Coupled Devices (CCDs); Bolometers; Prism, Filter, and Grating Spectrometers; Polarimeters; Radiotelescopes; Infrared Telescopes; Gamma Ray and X-ray Telescopes
The illustration below demonstrates
the power and versatility of multispectral measurements that continue to provide
important, often critical information pertinent to astronomy, and by extention,
to the higher levels that underlie cosmological thinking. Shown are composite
images of the Milky Way galaxy acquired over different parts of the spectrum
using satellite- mounted sensors. Because the labelling is likely be blurred on
your screen, from the top these spectral regions are: Light from the excitation
of atomic hydrogen; the same, for molecular hydrogen; infrared; near infrared;
optical; x-ray radiation; gamma rays; a "reference" or "finder" image.
These panels were assembled at NASA
Goddard Space Flight Center's Astrophysics Data Center using results from
satellites developed there and elsewhere. Enlarged versions of each of these,
and several more at different wavelengths appear near the beginning of page page 20-4.
Astronomers have found interpretive
benefits in combining images made by sensing radiation at different wavelengths
collected by telescopes that are ground-based and/or on space observatories. Of
course, information in any of the input images is itself usually revelatory and
important in understanding stellar processes. Here is a composite of a Chandra
X-ray image, a visible image, and two images at different radio wavelengths of
the Galaxy Centaurus A that illustrates these points:
Cosmology is one of the writer's
(NMS) hobbies and special interests - has been since his high school days and
first acquaintance with the sciences. It was once a tentative choice as a career
until it became obvious that my mathematical abilities were too limited to allow
me to master the essential concepts of Physics to the degree needed to excel in
Astronomy and Cosmology. But, I have over the years "devoured" a number of texts
and popular accounts (starting with Isaac Azimov paperbacks) that deal with the
three main areas of Physics - Quantum Mechanics, which deals with the
very small; Newtonian Physics, which covers the physics of "everyday
world" scales, and Relativity/Astrophysics, which examines the very large
(scales at cosmological sizes), especially under relativistic conditions
in which measurements are made on objects traveling at speeds near that of
light. This has endowed me with enough elementary expertise to attempt this
Section, which is an condensed survey of current knowledge of the fundamentals
of Cosmology presented in a generalized descriptive narration rather than a
rigorous, mathematically-developed synopsis and supported by numerous
illustrations. I have sought - but not yet obtained - reviews by professional
astro-scientists in hopes of validating and improving its content (your
critique, if you are so qualified, would be much appreciated and changes made
accordingly). But, for now, I accept full responsibility for the errors of
commission and omission that inevitably have made their way into this write-up.
When I first began this Section, I
already knew that the majority of Astronomers/Cosmologists/Physicists had
accepted two fundamental ideas about the Universe: it was expanding and
it seems to have had a finite beginning involving the "explosion" of a very
small primeval particle (containing almost unimaginatively huge energy) referred
to as the Big Bang. My starting point in preparing the Section (back in
early 1997) was to re-read The Big Bang, by Joseph Silk, 2nd Ed., 1989,
W.H. Freeman Co., which I outlined in toto. (note: the 3rd edition has
been released in late 2000; this is the one book [in paperback] I would urge you
to acquire if you wish to delve in depth into Cosmology). As I proceeded to
organize this survey of Cosmology, I "discovered" a number of magnificent
illustrations made through the Hubble Space Telescope on the Space Telescope
Science Institute's Home Page on
the Internet, Many of these I downloaded and incorporated into the text of this
Section, which has been expanded and repeatedly rewritten. In Fall of 1997, I
found The Whole Shebang: A State-of-the-Universe(s), by Timothy Ferris,
1997, Simon & Schuster in a bookstore during a visit to the Washington, D.C.
area. After a full reading - it is a highly recommended account in layman's
language - more revisions were made.
Yet another trip there led to
finding a just published textbook Foundations of Modern Cosmology, by J.
Hawley and K. Holcomb, 1998, Oxford Press, scoped as a survey at the College
Senior-Graduate School level, which I went through at a cautious pace although
consistently fascinated. I judge it to be the one of the best science books of
any kind I have ever perused. It treats Cosmology in a proper way, from the
viewpoint of Einsteinian Special and General Relativity. (Special Relativity,
which came first, deals with spacetime in terms of the electrodynamics of moving
systems; General Relativity is a refinement that brings in the proper role of
gravity.)
Rather than recasting the entire
Section 20 in terms of relativistic Cosmology - which would have greatly
enlarged its length - I have extracted some of the important ideas and
information from their book and incorporated these by splicing into the text.
But, if you have - or develop from this Section - an abiding curiosity about
Cosmology in its fullest scope and want to learn more using a treatise that
contains rather straightforward and manageable mathematics, I strongly urge you
to order Foundations of Modern Cosmology (it is not likely to be found at the
usual bookstores) and put aside the month or so that will be needed to
investigate the "foundations" of Cosmology (about 10 pages a day is the limit I
advise, since you need to digest and ponder its many significances). Or, if you
want a rather rigorous (mathematical) but quicker synopsis of
Astronomy/Cosmology on the Internet, then try the lecture
notes, prepared by the University of Pennsylvania Physics Dept.; especially
helpful are Lectures 24-26.
I have deliberately avoided
detailed explanatory coverage in Section 20 of some of the more avant
garde aspects of Cosmology, such as: Theories of Everything (a unified model
including all physical aspects of the Universe's origin); Spontaneous Self
Creation; Hawking radiation (which draws upon quantum mechanics, thermodynamics,
and relativity); Hyperdimensional (greater than 3 and up to at least 10
dimensions) Space; Supersymmetry; Superstrings (go to this site for a good summary of this
new, perhaps revolutionary field); Magnetic Monopoles; Wormholes and Time
Travel. However, some of these topics are touched upon briefly where pertinent
to the ideas being considered. Perhaps key answers will come from observations
made by the Planck Explorer spacecraft and the James Webb Space Telescope to be
launched in the early 21st Century. Meanwhile, a paperback that considers most
of these ideas is Hyperspace by Michio Kaku, Anchor Books. 1994
(Doubleday) treats many of the above topics in a clear exposition and is another
recommended read. Another, more recent hardback that covers many of the above
topics, with emphasis on Superstrings, is Brian Greene's The Elegant
Universe, W.W. Norton & Co., 1999; this book has been summarized on the
Internet by M.
McGoodwin..
Michio Kaku has revised his
Beyond Einstein: The Cosmic Quest for the Theory of the Universe, Anchor
Books, 1995, which includes an extended section on Superstrings. Also
recommended along these lines is God's Equation: Einstein, Relativity, and
the Expanding Universe, by Amir Anzel, Dell Publ., 1998.The role of
Inflation in the early Universe is presented as an odyssey of discovery by Alan
Guth in The Inflationary Universe, Perseus Books, 1997. An outstanding
paperback that clearly illuminates Cosmology from the quantum viewpoint is
Other Worlds by Paul Davies, Penquin Science, 1988.
Still another superb review is
The Cosmic Blueprint, also by Paul Davies, Touchstone Books, 1992; three
of his more philosophical tomes that attempt to reconcile the modern world of
science with metaphysical questions (including the role of God in creation) are
listed at the end of this Section. Two other excellent reviews, both published
by the Oxford Press, are The Left Hand of Creation by John Barrow and
Joseph Silk, updated edition, 1993, and The Life of the Cosmos by Lee
Smolin, 1997. Another thorough treatise is Before the Beginning: Our Universe
and Others by Martin Rees, Addison-Wesley, 1997. A very recent paperback,
The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and
the Beauty of the Cosmos, by Mario Livio, 2000, J. Wiley & Sons, is
highly recommended for its in-depth treatment of many basic cosmological
concepts and its survey of the idea strongly supported by observation that the
Universe's expansion is now accelerating.
In addition to the U. Penn site
mentioned above, the Internet has a plethora of interesting sites that come up
when "Astronomy" and "Cosmology" are entered as the keywords in any of the
popular search engines. The best I have found (and strongly recommend
visiting) are the three courses taught by, and condensed on the Internet, Dr.
James Schombert of the Dept. of Physics at the University of Oregon. The links
here are to Ast122 on stars,
and Ast123 on galaxies and
expansion. And, more recently, Dr. Schombert has put a new course on the Web,
entitled 21st
Century Science, which focuses on three themes: 1) Classical and Einsteinian
Physics; 2) The quantum World; and 3) Some first order ideas about
Cosmology. Also quite informative is the Astronomy Notes web site prepared by
Nick Strobel.
Here are five more that I found
informative: (1),
prepared by Dr. E. Wright of UCLA, which has four key sections, a News of the
Universe section which updates these sections with major new discoveries or
announcements, and a very enlightening FAQ page at (2), (3),
an excellent synopsis by J. Hawley of parts of the book cited above on Cosmology
that he co-authored with K. Holcomb, (4), a good general
summary of some key ideas in Cosmology included in the Astronomy Today site, and
(5), a
summary of a program on Cosmology shown on PBS. Two more sites, with a somewhat
advanced treatment of the subject are the Cosmology review prepared by the National Research
Council and by Cambridge
University astronomers. And I can also recommend a site prepared by Dr. Sten Oldenwald
which is in the form of numerous questions arranged in a FAC format; click on
any of the categories in the COSMOS group (note the other interesting
space-related subjects). Another informative Web Site that reviews some
fundamentals of Cosmology: Goddard's MAP program.
Here is the latest source update:
Four informative articles on "..Keys to Cosmology" appear in the February 2002
issue of Scientific American. These touch upon several major developing concepts
(sound wave action; cosmic structures; supernovae and acceleration of expansion;
gravity as a fundamental control) that are either omitted or not fully treated
in the rest of this Section). In the remainder of this Preface, I
can't resist the temptation to touch upon (actually summarized in a bevy of
paragraphs) some of the most basic ideas that underlie Relativity and Quantum
Mechanics. Relativity is the concept that best describes the physics of
"mega-space"; it is not deterministic in the sense of Newtonian
mechanics. Instead it is relativistic in that the values and meanings of
such concepts as space (three-dimensional), time, and gravity are relative to
the conditions in which movements associated with them occur. Thus, as treated
by Special Relativity, length of a body in motion, for example, is not absolute
but varies according to the speed of that body in relation a reference frame at
rest or moving at a different speed, with the length being assessed by the usual
means of measurement - namely, one that depends on visible light and other
electromagnetic radiation to obtain its values. For normal conditions, such as
mobile activities in terrestrial environments, the lengths as measured show no
discernible variations. Relativity's principal realm of applicability is under
conditions in which a body under scrutiny is traveling at speeds near that of
light and in which gravity is so strong that space itself becomes warped.
Quantum Mechanics, on the other hand, concerns "micro-space", at (sub)atomic
levels; it is probabilistic in nature. In between, scalewise, is the classical
physics view of motion established by Newton, Galileo and others in the 17th
Century; this Newtonian physics, as it is often called, is what we humans tend
to use in our everyday lives.
What is treated in the next
sequence of paragraphs is a synoptic review of Relativity which the writer (NMS)
has developed by reading 4 textbooks on the subject (the best is the Hawley and
Holcomb "Fundamentals of Modern Cosmology", Chapters 6-9, cited above), and by
reading through a number of Web sites. Of these, the one to visit at some stage
of your understanding of Relativity is the famous book written in 1920 by Albert Einstein, now online in its
entirety. Prior to that, after reading through the material presented below, two
Web sites that give a nice overview are 1) Nick Strobel's
treatment; and 2)
Ed Wright's version. Relativity is an outgrowth of
Einstein's thoughts, in the early 1900s, about motion and gravity in a
non-Newtonian framework. He was also trying to reconcile (or integrate) 1) some
fundamental concepts in the field of electromagnetic forces established earlier
as Maxwell's Laws with 2) the Newtonian mechanical Universe. Newton's physics -
especially in the realm of mechanics - works well in the dynamics of three
dimensional space (especially at the local scales for earth-sized bodies and
smaller) and at velocities common to everyday experience. Instead of the
Absolute view of fundamental parameters such as space and time envisioned
in Newtonian physics, space, time, energy and mass can vary in their perceived
nature in a Relative sense, depending on the inertia frame(s) of
reference used to measure and monitor them. Both the history of his discoveries
and an excellent portrayal of how they affect Cosmology is given in Amir Aczel's
book God's Equation: Einstein, Relativity, and the Expanding Universe,
1999, Dell Publishing. However, because of the inherent "greatness" of Einstein
as a scientist and humanitarian (selected by Time Magazine as the "Man of the
20th Century), the writer strongly recommends this splendid biography:
Einstein: The Life and Times, by Ronald W. Clark, 1971, Avon Books. Two
excellent Internet sites that include many Links to other sources about him and
his work are: (1) and (2). Here is a
typical photo of Albert Einstein in his later years:
Einstein's theory of Special
Relativity (SR) was first published in the Annalen der Physik in the
summer of 1905. In the same issue of that magazine, he also had significant
papers on Brownian motion and on the photoelectric effect (which helped confirm
the dual nature of light [exists simultaneously as waves and particles], for
which he later was awarded a Nobel Prize; ironically, it was a key early finding
that led to quantum indeterminancy which Einstein could never accept). Thus,
three revolutionary papers appear in one volume (copies of which now sell at
high prices to collectors who, like the scientists, recognize that this feat of
triple masterpieces was extraordinary and unique).
Einstein was not the first to
realize that physical properties should, theoretically, change significantly
when their measurements are made under conditions where the observer is
traveling at high speeds relative to that of light. In 1889, the Irish physicist
George FitzGerald suggested that objects moving very fast (at significant
fractions of light speed would appear to "shrink" in length according to the
equation:
where L is length, v is the speed
of the object, and c is the speed of light. That notion was later picked up by
Henrik Lorenz and developed in more mathematical terms. (But it was Hermann
Minkowski, Einstein's math instructor at the Swiss Federal Polytechnic School in
Zurich, who is credited with placing the theory of Special Relativity on a firm
mathematical foundation.) Einstein was aware of the FitzGerald-Lorenz ideas but
during several years of deep thinking (independent of communications with these
other physicists) he explored the implications in much greater depth, finally
developing what has come to be called Special Relativity and demonstrating its
many consequences. He, in effect, showed the limitations of Newtonian physics
whenever motions involved move at high speeds. Special Relativity is derived from
the premise that the speed of light is truly a constant - an absolute value -
which determines how one must approach the measurements of the physical
phenomena of the Universe. The principle from which many conclusions about the
relative aspects of time and motion in the physical universe are formulated
springs from this simple statement: "The speed of light * is the same when measured
from all moving (inertial) frames of reference, regardless of their (relative)
speeds."
In other words, the speed of light
is invariant, and will always have its precise value of 299,792 km/sec (186,282
miles/sec; or expressed in terms more familiar to Earth's people, a speed of
670,579,200 miles/hour [mph]) whether it is measured from a point on Earth
moving at its celestial velocity or from a spaceship traveling at
hypervelocities. Unlike a Newtonian description of relative motion (e.g. a
person walking at a velocity X on a train moving at velocity Y is seen by an
external observer to be moving at a speed of X + Y if walking forward in the
direction of train motion, or X - Y if walking opposite to train motion),
Einstein showed that the additive Newtonian case cannot apply when an object
moving at a speed 'v' less than that of light 'c' in a framework common to both
(say, a person walking in a spacecraft that has attained light speed); that is
to say c + v is impossible and nothing in the Universe can appear to move at
speeds great than light. This constancy of light speed (and its limiting value)
is a cornerstone of Einstein's Special Relativity. A corollary drawn from this
principle is that, for any two systems moving at different uniform velocities,
all the laws of Mechanics (in Physics) operate in the same way in both systems,
i.e., are not influenced or moderated by their relative speeds. However,
Relativity is most relevant and applicable for phenomena in which very high
speeds are involved as well as aspects of Physics involving the quantum state of
matter and energy.
At the low speeds (compared to
light) that we travel in Earth life, we have all experienced the effects of
small differential speeds in our auto on an Interstate relative to a car
traveling at slightly lower speeds in the next lane (we actually sense that we
are going fast because our eyes are aware of features off the highway that are
standing still). But, relative to each other, the feeling of motion differences
is minimal. But, an observer (say, a pedestrian) off to the side notes both cars
as going fast. However, our sense of relative motions is accentuated when we
compare our forward motion with autos moving against our direction in opposing
lanes.
Let's consider another aspect of
relative motion. This is referred to as the "Relativity of Simultaneity".
Suppose we are on a very long single car train with glass sides, and you are
situated at its middle lengthwise. Suppose also that the train is moving
very rapidly. Let a lamp encased in a container but with slits that
outwardly direct two beams, one forward and the other to the rear, be suddenly
switched on. Two reference photons of light (to simplify this thought
experiment, we will ignore all the other photons in the beam signal) leave in
opposite directions from the middle of the train simultaneously towards
reflecting convex mirrors at both ends of the train. You will see the light
signal arrive at the front and back of the train at the same time, since the
frame of reference (you, the observer) is moving at train speed. But, to someone
off the train and at its side directly perpendicular to the light source at the
instant it passes, the photon from the back will arrive earlier (the distance to
the back mirror has shortened as the train moves forward) whereas the
simultaneous photon from the front mirror has traveled both the distance from
the center and the added distance covered during travel at the speed of light
represented by the distance the train has moved since the photon event began. To
the external observer, the photon from the front arrives after the photon from
the back of the fast-moving train and thus the dual mirror reflection events are
not simultaneous, i.e., seem to occur at slightly different times. (Of course,
in reality this experiment would not be feasible to conduct since trains move
much much slower than light speed.)
Now, looking at this with another
example, assume we occupy a spacecraft moving at extreme speeds (approaching the
speed of light), from which we send forth a light signal to an external
observer. If we somehow can measure that light as it moves outside the
spacecraft, regardless of our speed the light is found to be moving at its fixed
value of almost 300,000 km/sec. From our frame of reference onboard, the
relative motion of ourselves within the spacecraft is that of standing still
with respect to the spacecraft itself but moving quite fast with respect to
external objects and observers. For the rapidly moving spacecraft passenger,
clocks onboard seem to move normally (no change in the length of a second) and
lengths remain the same. For stationary observers located elsewhere (say, on
Earth) or alternatively observers in constant motion at a speed lower than the
spacecraft, clocks in the spacecraft appear to tell time more slowly so that
time dilates (interval between seconds increases) (intense gravitational fields
produce the same effects). Not only do the people in the spacecraft as seen from
the outside look as though they are slowing down but they are dimensionally
shortening in the direction of motion. To a distant observer, our spacecraft
will appear distorted owing to the differences in time when light left different
parts of the rapidly advancing vehicle. In effect, for anyone moving at high
relativistic speeds, time stretches out (called time dilation), space
shrinks, and mass and inertia greatly increase relative to
external observers.
In a sense, these relativistic
effects will seem "illusory" to external observers. For instance, length as a
dimension does not really decrease (contract) in terms of the spacing of atoms
in a real meter stick moving near the speed of light. To the observer moving in
sync with the stick (as held by an astronaut on the fast-moving spacecraft), its
length would remain the same in appearance as it did before launch. The high
rate of speed does not force the atoms to crunch together in the direction of
motion. But, to an observer off to the side, the shortening of the length occurs
because light seems to have left one end of the meter stick before the other
owing to the great contrast in relative speeds. So, for both dimensions and
time, no actual changes take place; the apparent spatial contracts and
time dilations are the consequence of the modes of measurement. To many, the time effects owing to
relativity seem even weirder than those associated with spatial dimension
shifts. If the above-mentioned spacecraft's occupants were to return to Earth
after 20 years of high speed travel, they will have aged only at some shorter
time compared with the 20 years that the observer left behind has added to his
life from the beginning of our journey. The best example of this is found in
Einstein's Twin Paradox. Start with two brothers born on the same day.
Now, as young adults they separate in this manner: The ground twin remains on
Earth; the space twin takes a journey such as described in the last paragraph.
Upon return, the space twin finds his brother to have aged beyond that of
himself according to the record of time (the calendar), 20 years, elapsed since
the space trip began. The Earth twin is thus 20 years older. But, time has
shortened for the space twin and his bodily functions (in aging) have proceeded
more slowly, so that he upon return appears to have aged just a few years (say,
3). (Two obvious questions might be: 1) does the space traveler see his return
as a step into the future; 2) can the shortening of time go negative so that a
traveler can somehow move backward in time from "now" to the past? Both
prospects have been subjects of science-fiction movies.)
Let's carry this spacecraft motion
a step further. In the October 2002 issue of Scientific American which
features a single topic - Time, Paul Davies discusses this mode of travel in his
article That Mysterious Flow (referring to concepts and perceptions of
time, in which he demonstrates that the steady flow of time is an illusion). In
a box on Simultaneity entitled "It's All Relative", he reviews the case of a
spacecraft traveling at 80% light speed towards Earth and then continues on a
direct line to and past Mars. I shall summarize his scenarios in the following 4
paragraphs:
To people on the spacecraft, at any
time interval they feel as though they are standing still while both Earth and
Mars move toward them. In the two reference-frame examples Davies develops, he
cites actual calculated times for different events as measured on Earth and in
the rocket. In the scenario, the starting point is high Noon, which has been
sychronized accurately to be simultaneous for both Earth and Moon observers; at
the beginning of the experiment, the clock on the spacecraft was also set at
Noon. At precisely that time, the Mars observer sends a light signal directed at
the Earth observer. Its transit time is given as 20 light-minutes, as
predetermined by the actual (known) distance to Mars. First, from the frame of reference
set as the Earth station, at Noon, the Earthling assumes the Martian has just
sent a light pulse to Earth at the prearranged time also of Noon. Sure enough,
that signal arrives on Earth at 12:20 PM. At just this time, the rocket passes
by the Earth, but some distance away, at 80% light speed. Using calculations,
the Earthling determines that the rocket sees the Mars signal at 12:11 PM -
earlier than Earth because the spaceship is moving so fast. But, because time
slows down from the Earthlings perspective, he records the arrival of the space
ship just past the zeneth point above Mars to be at 12:25 PM. Now, from the rocket's perspective,
these events unfold. First, at the Earth approach, the spaceship personnel
measure the distance between Earth and Mars, find this to be 12 light-minutes
(owing to length contraction as a high speed object looks externally at
apparently moving targets). After the rocketpeople pass above the Earth at
precisely noontime, knowing that the Martians were scheduled to signal Earth at
Noon, they now look for that signal as they enter the space between the two
planets. They expect to see it at 12:12 (the transit time they deduce from the
distance measurement they made. But, because of time dilation, the rocket clock
runs at a different rate from Earth and Mars clocks. Oddly (but valid) the Earth
and Mars people determine that the spacecraft's clock is running slower than
their clocks even as the rocketpeople in turn think their spaceship time runs
slower. The Mars noontime signal arrives at the spacecraft at 12:07 PM on its
clock, and without thinking in Relativity terms they wonder if it had been sent
prematurely. At 12:15 spaceship time, Mars "appears" as though it has arrived at
the spacecraft above it (when actually the spaceship has done the traveling). It
signals both Mars (below) and Earth (behind it) at this arrival point. That
signal reaches Earth at 12:35 PM.
The "moral" of this story is that
the same instantaneous events appear to observers located at different places at
different times, thus confirming Einstein's deduction that there is no measuring
system that can register an event as happening at the same time everywhere - the
same motions seem relative with respect to "when" at different locales,
each with its own observation conditions, for multiple, separate, and moving
observers, and thus time is not an absolute as once affirmed by Newton and
others. For a person onboard a spaceship traveling at high relativistic speeds,
on contacting Earth he/she would learn that the clocks back there appear as
though they would be running faster, i.e., have speeded up. Conversely, the
passage of time on the spaceship relative to those on Earth would seem to have
slowed down. Likewise dimensionality in space is not absolute.
Thus, from such reasoning, Einstein
concluded that the proper number of dimensions needed to explain the unusual
phenomena that result from relativistic motions must be four rather than the
traditional three (space: length, width, and depth or height). The Universe is
fundamentally in a 4-D state. The fourth dimension, that of time, is considered
independent of spatial dimensions in Newtonian mechanics but is closely
interrelated in the Einsteinian system. (Note: the time used in Newtonian
physics to measure velocities, accelerations, momentum, etc. is of the ordinary
or fixed variety.) Under relativistic conditions, the role of time becomes
paramount in measuring the positions of objects in motion: time enters in
because locations are changing even as time is consumed as the light travels
from source to observer and hence when the signal reaches the observing device
the object has now changed position.
In one of his thought
experiments, Einstein envisioned what would happen to a beam of light moving
beyond the interior of a space vehicle accelerating at relativistic speeds.
Applying Special Relativity concepts, to the onboard observer the light is
transmitted along a straight line, since both the light source and the vehicle
are traveling at the same speeds. But to an outside observer at rest, the light
beam would appear to curve, inasmuch as the paths of its photons are shifted
progressively as they travel out from the high speeding vehicle. Thus, under the
influence of gravity-acceleration, the light which must travel the shortest
distance between two points (A, source; B, target) will be subject to A's having
moved a finite distance during the transit time relative to the observer at B -
thus the light traces a curved line, from which it follows that space itself
is curved in the sense that light traveling across it follows a curved path
that still represents the shortest distance between points. (Any segment of a
longitudinal line on a sphere is curved but nevertheless remains the shortest
distance between the points at each end of the segment.)
One corollary drawn from this
aspect of Special Relativity is that the huge dimensions of the Universe require
that we always consider time in measuring distances. We see any distant galaxy
as it was then, not as it really is now (it may in fact by now have greatly
evolved and has lost and gained many stars). Likewise, its position then
relative to us is not the same as now.
Let us expand upon this last
paragraph. This distribution of objects throughout the vastness of space, which
gives information as we observe them today that represents different times and
locales in the past, embodies the concept of Spacetime. At cosmic
levels, all event actions (along what are termed "worldlines"), together with
relative changes in sizes and distances, are embedded in spacetime. Thus, as we
shall see later in the Cosmology Section, this is one consequence of Spacetime:
light from a source (e.g., a galaxy) located at this time 5 billion light years
away (or, approximately at a distance of 47 x 1021 kilometers) left
the galaxy that many years ago and shows the appearance or state of evolution
reached by that galaxy then. What is actually happening at (and to) that galaxy
today will be received (perceived) as an event or state transmitted at this
moment only at some distant future time, during which the galaxy has since moved
farther from Earth (actually, both galaxy and Earth are drawing apart) and has
evolved beyond what is described for it during early 21st Century cosmological
observations.
To get a mental picture of what it
means to visualize in Spacetime on a cosmic scale: Imagine you are somewhere
inside (for convenience, say, near the middle) of a huge sphere in which are
randomly distributed a huge number of points (for the Universe Model, these
would be galaxies that contain inhabited planets as observation points); you now
gaze outward to see various galaxies at different distances from your local
observation site); if this were actually just a real world model of finite
dimensions, e.g., a few hundred feet, then every other point would send you
light at essentially the same instant, so the view is static and just
three-dimensional; but if you are really looking out at all the detectable
galaxies in a 3-D Universe, at any given moment, the light received from any one
would have taken a finite (long by comparison to your local framework) time to
get there, and different points (galaxies) at different distances sent their
light received now at different times in the past; thus you see a
three-dimensional array of points in cosmic space that represent objects whose
ages vary (farthest are oldest, since light had to travel longer to get to you
and hence had to leave earlier; nearest are youngest). This is a spacetime
panorama, in that the 3-D assemblage of points at different distances actually
consist also of points that differ in age and time of transmission. In such an
array, another characteristic is that NOW (the present moment) those
points are different (in distance, in stage of evolution, etc.) than they were
as you now observe them, i.e., they have moved on with expansion and have
changed to new states, the extent of which depends on their distance from your
observation point.
One of the paradoxical spinoffs of
Special Relativity as applied to Cosmology concerns the perception of
past and future. If a burst of photons leaves a distant galaxy at
some particular time and then arrives at our observation point, we have indeed
seen "into the past" to specify that moment in time. This is refered to as the
Lookback Time - the time required for photons from a source to reach and
be received at an observation point (as from a star to an Earth telescope). But,
for an observer in a galaxy "beyond" us in a direction that the light would
travel if it had not been intercepted by Earth, that moment has not yet
happened. It belongs to some time in the "future" (measured for our framework in
terms of Earth time) for that observer but when he/she eventually sees it, it
will be represented as the same moment that we have witnessed in the "now" time
of reception on Earth. Nevertheless, for any pair of events separated in time
but causally connected (light signals can mutually pass between them) the order
of reception of evidence for these two events will always follow the
before-after sequence. Another of Einstein's conclusions
then was that mass and energy obey the Principle of Equivalence, such that under
certain conditions, energy can "condense" to mass and, conversely, that mass is
convertible to energy (hence the famed equation: E = mc2, with
c being the speed of light]). From this equation, one can deduce that as an
object moves faster up to speeds approaching that of light its energy (and the
mass equivalent) will begin to increase notably. In principle then, the maximum
energy a given amount of mass can release is determined by c2. This
mass-energy equivalence ranks with the space-time equivalence at the top of the
list of his achievements. It also forms the basis for schemes to recover huge
amounts of energy from "tapping" into the nuclei of atoms; the energy released
from the explosion of an atomic bomb derives from this relationship (nuclear
explosions produce only a fraction of this total energy).
This principle of relativistic mass
increase is used in the particle accelerators that physicists have built to
"smash the atom", or more precisely, to penetrate the nucleus to learn its
nature and to determine the types of subatomic particles that can exist in
nature. As particles such as electrons, protons, neutrons, muons, etc. are
accelerated (by moving through magnetic fields) to near-maximum relativistic
speeds, their masses greatly increase (approach infinity), making them much more
powerful and effective "bullets" that impart sufficient energy upon colliding
with a nucleus to break it apart or otherwise modify it. To summarize the essence of Special
Relativity, simply remember that to a slow moving or fixed observer, on a fast
moving object (think of some futuristic spacecraft) time will appear (to the
slower observer) to slow down (clocks tick slower), three-dimensional
objects will appear to shorten, and mass will increase whereas
these metrics remain unchanged for anyone on or in the object. Various
experiments have repeatedly proved the validity of Special Relativity.
Relativistic effects are noted in objects moving at as slowly as 40% of the
speed of light, and are dramatic above 70% as they rise exponentially. To quote
from Ronald Clark's book on Einstein (op. cit. above), "Einstein had showed that
time and space were not the inelastic things which they were thought to be, but
were relative to the sum total of circumstances in which they were considered.
Thus he changed the meaning attached to the word "reality"." (p. 755). The theory of General Relativity
(GR), of which the first elements were put forth by Einstein in 1913 and 1915
followed by his "Foundations" paper in 1916, after about a ten year gestation,
was his effort to fit gravity into the spacetime picture. Since 1905, Einstein
had grown more adept as a mathematician; he found that tensor calculus and
Riemann geometry were particularly suited to developing the quantitative
relationships in the theory.
General Relativity has more direct
relevance to Cosmology than the more esoteric Special Relativity. GR is
concerned with frames of reference that accelerate relative to some one
frame which itself can be moving or still. Special Relativity is applicable to
frames that are traveling at uniform velocities (or one may be at
apparent rest; apparent because if it is on Earth [say, a fixed telescope] it is
actually in motion because of the Earth's rotation, its orbit around the Sun,
the Sun's motion in its galactic arm, and the movement of the galaxy relative to
the whole expanding Universe). General Relativity is concerned with the effects
of accelerating velocities, and their relationships to a proper
understanding of Gravity and to a rethinking of the geometry of cosmic space
(overthrowing the Euclidian framework [three orthogonal axes] for one of a
curved nature). General Relativity's concepts, together with certain facets of
Special Relativity, have allowed scientists to predict such things as
relativistic redshifts, cosmic expansion, quasars, neutron stars, Black Holes,
gravitational waves and the age recession of components in expanding space
(remember from above: objects near the edge show themselves as they were early
in Universe history; those closer to Earth are normally in an advanced age).
Gravity, from our experience, is
strongly dependent on mass. Einstein recognized that gravity is also dependent
on motion and the geometry of space. He thus postulated still another
equivalence: that of acceleration and gravity. This is confirmed by the
following thought experiment: Place yourself in an elevator that is initially at
rest in a building (or on the ground). You drop a ball and it naturally falls to
the floor (at an acceleration of 9.8 meters/second2 or 32
ft/sec2. In this conventional case, gravity is the "cause" of the
ball's acceleration; the value of acceleration is related to the Earth's total
mass (remember the Newtonian equation F = ma). Now, imagine this elevator and
you inside are transported to some point in outer space so far from large bodies
that any gravitation effect due to the Earth or other massive bodies is close to
zero. Let some power source (such as a rocket engine) act on the elevator to
move it upwards at an acceleration rate of 9.8 m/sec. You will feel
just like you did in the Earth-based elevator: you feet are planted on the
elevator floor and if you release the ball it will fall as it did on Earth.
Since no gravity is acting, you would conclude that the gravity-like conditions
you experience must be due to the imposed acceleration.
From this experiment Einstein
concluded that gravity and acceleration obey the Principle of Equivalence (i.e.,
are equivalent), being just two variants of the same fundamental physical
effect. Thus, anyone enclosed in a windowless box, such that this person cannot
look outside to see if the surroundings are either moving or not, will not be
able to distinguish whether the box is being acted upon by gravity or is instead
accelerating outward in space far from any mass source of a gravitational field.
This conclusion is the basis for further deductions about gravity and the gross
shape of space that led Einstein to the rvolutionary ideas that arise from
General Relativity. Returning briefly to the falling
ball in the elevator scenario, we illustrate another aspect of the role of
gravity/acceleration. If the elevator is stopped and a ball is dropped, it will
move straight down at the acceleration appropriate to Earth's gravity. If,
instead, it is released in a fast dropping (thus accelerating) elevator, when
the elevator's rate of speed change just balances that of standard gravity, the
ball will "hang" suspended in the elevator rather than falling. (This is similar
to the effect of inducing weightlessness for a short period when an airplane
accelerates into a fast dive; this effect, evidenced by free floating, is also
experienced by astronauts in the Space Shuttle when it orbits at angular
velocities that balance [offset] Earth's gravity.)
Still a third elevator example:
Start with this illustration.
Imagine the elevator to have glass
sides and to contain an observer inside. A person exterior to it shines a light
horizontally through the elevator. When at rest, both the internal and the
external observer see that the light beam maintains its direct horizontal path.
Then put the elevator into motion upward at a constant velocity and have the
exterior individual again aim the beam at it. The outside person sees no change
in beam direction but the inside person sees it bent down at some constant angle
(thus, stays straight but depressed). If instead, the elevator is accelerating,
the beam passing within becomes curved downward. (Such a sequence of beam path
behaviors is impossible at present to duplicate experimentally since the
velocities and accelerations must be greater than can be acquired by moving
vehicles [i.e., "elevators"], although space probes orbit or recede fast enough
to participate in relativity experiments.) The third case, the accelerating
elevator, which by equivalence is a gravity-producing analog, demonstrates that
a light beam will follow a curved path when influenced by a powerful gravitation
field. Gravity, on the grand scale (stars
and galaxies), can be conceived as a force field that influences geometry: in
other words, gravity bends or distorts the fabric of spacetime. Matter/energy
determines the curvature of spacetime and is said to "warp" space (this can be
visualized as follows: consider a fastened rubber sheet on which a grid pattern
is drawn; a heavy object, such as a round rock, if allowed to drop on the sheet,
will create a depression and distort the grid around that indentation). This can
be visualized in the drawing below:
One can use this diagram to imagine
how gravity affects an object that comes into its neighborhood. As it approaches
the high mass (pictured here as a sphere that could be a Giant star), while
moving along the grid representing the "fabric" of spacetime in two dimensions,
it will start to follow the distortion of that grid that produces a depression.
As its motion continues, the object (not shown in this diagram) must eventually
end up "trapped" as it reaches the sphere (this is just analogous to being drawn
to the sphere by ever-increasing gravity). In this Einsteinian depiction it is
the local curvature of space by mass rather than the Newtonian force that
delivers objects to the mass itself. (The incoming object can escape this "trap"
by exerting enough energy (force) to steer away from, or out of, the
depression.) In a sense, gravity adds another
"spatial" dimension by inducing this curvature. Gravity then, in Einstein's
view, is just the effect of masses imposing curvature in the four-dimensional
extension of space, i.e., spacetime. The physicist John Wheeler summed the
concept succinctly: "Space tells matter [mass] how to move; matter tells space
how to curve".
The "acid test" of the validity of
General Relativity is the actual observation of light from distant stars being
bent (slightly, but measurable) during a full solar eclipse, so that the stars
just beyond the edge of the Sun appear to shift in position relative their usual
position in the sky. This test (done by English astromers under Sir Arthur
Eddington's direction) was first successfully conducted during a May, 1919 solar
eclipse, resulting in a small but measured displacement of stars near the
darkened Sun; this now famous experiment marked the widespread acceptance of
General Relativity among physicists and astronomers. Afterwards, the test has
been repeated many time, always confirming to within experimental error the
predicted amount of displacement based on the mathematics of General Relativity.
The test led to worldwide notoriety for Einstein, so that his name became known
to the "man in the street". Once his fame was established, he was persuaded to
become involved in Peace groups, and as a promoter of the (ill-fated) League of
Nations; his preeminence as a top scientist also gave him leverage as a
spokesman for the Zionist effort to gain a homeland in Palestine (some years
after Israel was established in 1947 by UN mandate, he was offered the honorific
position as its first President but had to decline because of health).
Now the principle is used to
explain the gravitational lens effect. Light from, for example, a very distant
quasar that passes a massive galaxy closer to Earth can be bent to produce
double (rarely triple) images.In other words, gravitational attraction causes a
slight but measurable curvature of the path of a light beam wherever the beam
passes near a massive object. Sometimes the distant object's lensed image is
spread out in an arc pattern. This Hubble Space Telescope image shows an example
of this effect.
Perhaps the most "spectacular"
display of gravitational lensing is the Einstein Cross, in which a quasar
image (G2237-0305, as seen by the HST)is repeated 4 times owing to intervening
objects (probably galaxies) that bend its light:
Einstein also showed that gravity
can affect time as well as space. Experiments have proved that time runs faster
when the gravity field weakens as a clock is moved away from the source of the
gravitational pull. One specific test to verify this notion: When a rocket was
launched away from Earth following a straight vertical trajectory, a maser
signal was transmitted to Earth for a monitoring period of 100 minutes during
the experiment. A systematic shift in signal frequency (thus time-dependent)
occurred compared with the time units that this maser clock produced back on
Earth. Although the change to higher rates of time progression was small (at a
distance of 10000 kilometers it was 0.02% faster than on Earth), it exceeded by
fifty times the experimental error below which the real speeding up would have
been inconclusive. The observed change values enroute agreed closely with
predicted ones based on relativity theory. An early outgrowth of the
consequences of General Relativity is the model devised by Einstein and others
of the type of Universe that would be predicted from its tenets: Thus, the
so-called Einstein Universe is closed, finite, curved and unbounded. This is
covered in more detailed on page 20-9; suffice for now to say that the evidence
based on expansion rates and the amount of total matter/energy found or deduced
for the Universe we have studied argue against this type, and Einstein himself
abandoned this model after Hubble and others showed the Universe to be
expanding. Regardless, the concept of General Relativity still applies to the
actual Universe as we are coming to know and understand it. And, another
consequence of Relativity of interest to those seeking equations to define the
Universe's behavior (type of expansion, etc.) is that these must meet the
conditions (or restrictions) that Relativity imposes on any mathematical model
they propose, i.e., the equations must be compatible with (cannot violate) the
precepts deduced from Relativity as applied to cosmic scales.
These, then, are some rudiments of
Relativity, hopefully not expressed here so superficially in this condensation
that only a vague insight into its characteristics, properties, and influences
will be implanted. Consult any of the references cited above for more details.
Also, you may wish to work through another challenging review of this subject
placed on the Internet by J. Schombert.
Keep in mind also that much of relativity is unfamiliar in terms of everyday
life experiences, so that it is hard to picture the consequences of physical
processes taking place at high speeds. Gravity is weak on Earth and the motions
we are subjected to are quite slow by comparison.
For us , Newtonian Physics -
particularly the Second Law which describes acceleration and determines a
Constant of Proportionality - works well for most everyday activities on Earth
and for the Keplerian Laws that govern motions in the Solar System. But there is
growing evidence that motions within and between galaxies involve rates of
movement greater than predicted by Newton's Laws and require some adjustment of
the acceleration values at cosmic scales. The concepts of Dark Matter and MOND
(see the bottom of page
20-9 for details) may explain this discrepancy from Newton's Laws.
For the Universe as a whole
Einsteinian Physics, perhaps MOND, and Quantum Mechanics are
needed to gain a proper, more complete picture of its operations. Because of
Quantum Physics' importance in understanding the achievements of Science at the
small scales below the normal environments - on Earth and in Space - we deal
with in everyday life, some additional paragraphs on this vital subject are
presented below.
Quantum Mechanics (QM) or Quantum
Physics is complementary to Newtonian (Classical) Physics (NP); whereas the
latter applies to macroscopic and normally rigid bodies, QM operates in the
realm of atomic and subatomic particles and radiation (often called the
microcosm). You may find helpful this Internet site containing some Classroom
notes dealing with the physics that led up to Quantum Physics. A more
specific review of QP is found in this review by Prof. Sobottka of the
University of Virginia in his Chapter 3;
go on to Chapter 4 in that reference - to do this click on Home at the bottom of
the Ch.3 page and then on the first part of Ch. 4 in his left margin.
Much of what we experience in NP
fails to work in the same way in QM, in which the behavior of matter and energy
seemingly acts in "strange" ways. A hallmark of QM is that the description of
the action of particles that comprise matter and radiation must be treated as
probabilistic - that is, with some degree of uncertainty which requires
statistical analysis. Thus, knowledge of the nature and behavior of atomic and
subatomic particles falls (both physically and metaphysically) in the category
of indeterminancy, which implies that we can never know precisely the
real state and nature of the material "thing" being examined.
The foundation of QM was laid near
the beginning of the 20th century by two of Science?s greats: Max Planck and
Albert Einstein. (Ironically, in later life Einstein never could accept the main
ideas of Quantum Mechanics, in large part because he believed that
indeterminancy has no place in the natural order.) Planck was intrigued by the
distribution of radiant energy (light in the visible range and beyond) coming
from a perfect radiatior or blackbody, for which he derived the Planck Blackbody
Law (page 9-1). For
such a body at some temperature, it was known that the intensity of radiation
varied with wavelength, with measurable energy confined to a continuous but
finite range of emitted wavelengths. This can be plotted as a spectral curve, as
we observed in the Section on Thermal Remote Sensing (see page 9-2). The shape of
the curve and total energy involved shifts with temperature (Wien?s Displacement
Law; same page). In 1900, Planck provided an explanation for this energy
distribution, and also the discrete locations of discontinuous spectra observed
in emission spectroscopy (see page 13-6), by
postulating that radiant energy is quantized in the sense that it is
corpuscular, consisting of tiny packets of energy called quanta (a
quantum is the smallest possible unit of energy). From this concept, he deduced
one of the fundamental formulae in both remote sensing and, more generally,
physics, which we first encountered in the Introduction (page I-2): E = hf (where
h is the Planck constant [~ 10-27- erg sec]- and f is the frequency
of the quantum [treated as an oscillator, i.e., a particle that vibrates]).
Thus, an excited atom (e.g., heated in an electric arc, as is done in emission
spectroscopy) gives off radiation at different discrete energies that correspond
to narrow, discontinuous, specific wavelengths (inverse of frequency). Likewise,
an object heated to a certain temperature emits continuous radiation over some
spectral range. In each case, the radiation consists of a stream of quanta with
particular properties tied to an energy-wavelength relationship.
This Planck hypothesis languished
until 1905 when Einstein recognized its applicability to his attempt to explain
the previously discovered (by Heinrich Hertz in 1987) photoelectric effect - the
phenomenon in which light striking certain types of metals caused generation of
a stream of electrons (whose existence was verified by J.J. Thomson in 1897)
that could be extracted as an electric flow. The maximum kinetic energy released
is related to the frequency of light in a (monochromatic) beam but this
frequency must be at or above a characteristic (for the metal) frequency that
represents an energy value called the work function φ. The Planck equation for
this effect becomes: K.E. = hf - φ. Einstein deduced that the light consists of
"lumps" or "bundles", which he called photons and surmised were a
manifestation of what Plank had named quanta. These photons are capable
of knocking off electrons (in this use, photoelectrons) from their host atoms
that could then be collected as a current. A specific photon, which Einstein
demonstrated to be the physical entity that Maxwell had postulated earlier to
make up electromagnetic radiation that travels both as a wave and a particle, at
a specific wavelength &lamda; (or frequency) yields a corresponding finite
energy (K.E.) value (usually given in electron volts [eV]) for a released
photoelectron. His explanation eventually (in 1922) won the Nobel Prize in
Physics for Einstein.
In 1913, Niels Bohr published his
"picture" of an atom, consisting of a nucleus (proposed earlier by Ernest
Rutherford) and a series of orbits at different (minute) distances from the
center within which electrons at particular energy states for each orbit moved
at high velocities. When some process, such as heating or electrical excitation,
caused an electron to move from one orbital energy level to another, and then
the electron moved back to its initial state, a photon of some specific
wavelength was emitted, according to the relation: E2 -
E1= hf. Thus, this transition from one energy level to another is
quantized, i.e., has a discrete value. Bohr also found that the levels could be
assigned integer quantum numbers that account for the angular momentum L of an
electron such that L = n (h/2p) where n can form a series 1,2,3,4,?. With this
concept, the spectral lines for elements like hydrogen could be explained.
However, the Bohr atom, elegant
though it be as a concept, had limitations when atoms of elements of higher
atomic number were investigated in terms of their spectral outputs when excited.
In the "golden age" of QM, these discoveries were made: 1) when x-rays
(energetic photons with much shorter wavelengths than visible light) acting as
particles collide with others (for example, electrons), some of their momentum
is transferred to the recoiling electrons, with both having new momentums (the
Compton Effect) (1923); this partition of momentum further established that
radiation consists of particles; 2) Louis de Broglie (1924) determined that
since radiation particles could be described as also having wavelengths, they
must travel as moving waves - thus, photons have a dual nature, behaving
under certain observational conditions as particles and under other conditions
functioning as waves (this wave-particle duality is a fundamental concept in
subatomic or quantum physics; although hinted at by Planck, it was Einstein's
photoelectric effect hypothesis that set the idea on firm experimental and
theoretical grounds); the so-called de Broglie wavelength for a moving subatomic
particle is given by l = h/p where p = the particle?s momentum mv; 3) W. Pauli
announced his Exclusion Principle (1925), that no two electrons in the same atom
can have the same 4 principal quantum numbers; 4) E. Schroedinger in 1926
published his famed wave equation (see the parenthetical next paragraph) which
better described the movement of free electrons but applies to other particles
including photons, and includes an important term Ψ called the wave function; 5)
Werner Heisenberg in 1927 enunciated the famous Uncertainty Principle which
states that it is not possible to fix both the momentum and the instantaneous
position of a moving particle such as an electron simultaneously with high
precision for both; 6) also in 1927, several investigators conducted experiments
that found diffraction effects when electrons pass through 1 or 2 tiny slits
onto a recording screen; the electrons are not directed to either slit
specifically but will pass through one or the other in a manner controlled by
probabilities (see 8 paragraphs below).
The Uncertainty Principle brings
into play the fact (mentioned in Discovery 6 above) that in the quantum world
every event or process cannot be specified exactly. The characterization must be
that of probabilities in the statistical sense. As an example, the
precise orbit and location of an electron around its nucleus can never be known
with certainty - one can only surmise its various possibilities in terms of a
range of probabilities. This means that the electron's position and velocity are
indeterminant. If this is valid, then we must conclude that a purely
deterministic Universe (an idea that goes back to the ancient Greek philosophers
and was much debated in philosophic schools even into the 20th Century) does not
fit the evidence, at least at the quantum level. The Schroedinger Equation is
inherently a probablistic one. We elect here just to show [without elaboration]
this Equation, one of the fundamental mathematical expressions that defines the
wave-particle duality at the heart of Quantum Physics. It can be written in a
variety of ways. First, it is shown in its differential equation form for the
basic case of one-dimensional time-independent functionality:
In this expression, m is the mass
of the particle (Schroedinger's original derivation was for the wave behavior of
the electron), h is the Planck constant, E is the total particle energy, V is
its potential energy, x is the one-dimensional position locator, and Ψ is the
wave function [analogous to amplitude measure for the classical wave equation].
For the three dimensional [using spherical geometry; hence radius r]
time-dependent case, the Schroedinger partial differential equation can be
stated as:
We do not expect you to "fully
fathom" the meaning and use of this equation (unless you have had the proper
physics/math background) but simply wish to present it as an elegant statement
of how subatomic particles move in the reality of the micro-world. Most of the essentials of QM were
thus formulated from 1900 into the decade of the 1920s but further insights and
applications have continued thereafter, including extrapolations to what is
often referred to as Quantum Cosmology. As quantum concepts are applied to
Cosmology, their principal application is tied to the first minute or so of the
Universe when 1) the singularity came into being and 2) the various particles
relevant to atoms were first generated. There are other application later in
cosmic time including formation of the elements within stars.
In the early 20th century, much of
the accruing knowledge came from the study of the electron, with emphasis on its
interaction with light. As a particle, initial concepts perceived it as having a
discrete shape and a sharp boundary and considered it to orbit in a plane at a
precise distance. Instead, it now is conceived to have an indistinct boundary
(its edges are "smeared" out) and to travel with its own electrical field; when
bound to an atom it moves in pathways having an average distance from the
nucleus that can follow any of the innumerable possible orbits along a sphere of
reference. When some apparatus attempts to locate it and determine its velocity,
the measuring method, say a beam of photons, interacts with the electron and in
effect disturbs its motion. Because of the Heisenberg uncertainty, if at any
instant information about its position is reliable (high precision), then
corresponding information about its movement has through the interaction become
less well known. This translates into some degree of unpredictability in any
attempt to specify the state of particles whether within or free of atoms with
which they may associate; therefore, certitude about the location and motion of
a particle is denied because of this mutual incompatibility. Thus, the electron
cannot be made to behave as though static to fix a location without influencing
its actual motion. This is true for any particle or wave at atomic scales. The
uncertainty principle can be expressed as an inequality in the form ΔxΔp is
equal to or greater than h, where the product of the Delta increments
(uncertainty limits) for location (x) and momentum (p) is as large or larger
than the value of the Planck constant. A similar argument (ΔEΔt is equal to or
greater than h) concludes that as the time needed to measure the energy of a
moving particle increases, the uncertainty about the energy value E also
increases. One consequence of the Uncertainty Principle is that the behavior of
electrons surrounding the nucleus cannot be described by Newtonian Physics,
which depend on laws of mechanics that work on "rigid" bodies that follow
precise (planetlike) orbits around that nucleus. This requires modification of
the Bohr atom model which is just too simplistic to describe the microscopic
realities in the world of atoms.
The wave-particle duality of quanta
is demonstrated by shooting a beam of electrons at a plate containing a narrow
slit and then recording the summed pathways over time of these electrons after
they are diffracted at the slit and then travel to a recording medium such as a
fluorescent screen. The result is a pattern typical of that predicted by wave
theory, with a buildup of screen "hits" (persistent light dots on the screen)
that resembles this figure:
Most hits are distributed along the
axis of line of sight of the electrons that got through the slit. But there is a
periodic and symmetric series of highs and lows on either side: these are the
summed numbers of hits from electrons diffracted at different angles. The hit
events result from a probability distribution that arises from the quantum
behavior of electrons (or photons, or other particles) subject to the wave
aspect of their movement (if the particles had not had a wave nature only those
electrons moving in a straight line through the narrow slit would have struck
the screen, reproducing the slit as a thin image.
A more puzzling behavior is
observed when the electron beam encounters two slits close to each other. A
somewhat different interference pattern of highs/lows (light/dark if film is
used to record the diffraction waves) is the outcome. Treating each electron
passage as an individual event, it is not possible to predict or deduce which
slit accepted it - each electron acts as though it is unaware of the other slit
it did not pass through. The one and two slit examples are controlled by
different wave functions in the Schroedinger equation. In either case, for each
event the electron (or other particle) went through only one of the slits but
its surrounding field passed through both as a manifestation of its wave nature.
There is, of course, much more to
QM than this brief summary of its salient features. Here are a few more comments
that may clarify some points.
1) The various forces associated
with the atom (Strong; Weak; Electromagnetic; see page 20-1) act on the
particles that they control by exchange of quanta. (There is at least one school
of thought in Nuclear Physics that speculates that the Strong Force is similar
in some respects to gravitational forces.) The protons and neutrons in the
atomic nucleus are held together through the Strong force by gluons which
provide the binding force. Radioactivity involves statistically random decay
within the nucleus that depends on W bosons to actuate the Weak force;
individual nuclear particles (electrons, protons, others) that cannot be
predicted as to any specific atom will escape when that force is overcome,
causing any decayed atom either to become a different isotope of the element
involved or to change into one or more new element species. Electrons, held
around an atomic nucleus by the Electromagnetic force, upon changing energy
states as they are jumped into higher electron shell levels, upon decaying to
lower energy states exude photons that can interact with more electrons or other
particles. These several forces as they act and interact are alternately
describable by Field theory: specifically, at the quantum level, the Yang-Mills
field (an expansion or variant of the Maxwell field that pertains to
electromagnetic waves) describes the operative mode of force exchange at the
nuclear level.
2) Quantum theory allows for some
truly strange activities by particles. One is the "tunneling" phenomenon in
which a particle, e.g., the electron, can move across a physical barrier within
which it is confined to appear outside that barrier; this happens
probabilistically and may occur only after a long time. Another activity is even
more exotic: there appears to exist in so-called empty space some form of energy
(as yet undetected and undefined) that allows intermittent "creation" of
anti-particles and particles that last for brief instants before mutually
annihilating (see page
20-10).
3) Despite the imprecision or
probabilistic nature of matter and energy at the microscopic levels of space, QM
does not negate our approach to physical phenomena at the more traditional
macroscopic levels. It operates on things at the cosmic scale (atoms in galaxies
and starts) and on processes described in other than quantum terms, such as
chemical bonding, electrical conductivity, thermal properties, and nuclear
power, Classical physics, with its formulae that do not include quantum factors,
provides valid explanations which are functional and allow calculations that
describe workable and meaningful results in a world setting sensible to human
scales.
4) QM, which was to mature after
Einstein?s theories of Special and General Relativity, seemed to conflict with
those ideas and for a while eclipsed the conclusions drawn from Relativity.
Einstein had at first conceived of a static, grossly unchanging Universe whose
physics was determined by its geometric properties. He extrapolated the rigidity
of macroscopic behavior according to NP to the atom itself but the evidence from
QM showed conclusively that in the microscopic world Newtonian Laws had to be
replaced by Probabilistic Laws. Despite his major contribution to QM from his
explanation of the Photoelectric effect, Einstein, who remained dubious about
aspects of QM throughout his life. He remained firmly convinced that the
physical world was deterministic (operating under Laws set forth by some
external intelligence - a Creator similar to the philosopher Spinoza's
impersonal God). He refused to accept the indeterminancy of a Quantum microworld
(his most famous quote: "God does not play dice with the World"). Einstein spent
his last 35 years (without success) trying to find equations that integrated
gravity and electromagnetic forces in a single Law that governs all of the
physical Universe (physicists still haven't reached that goal). Eventually, both
QM and Relativity were accepted but now the attention is focused on combining
them in the Theory of Everything (written as TOE), in which the gravitational
force (in its relativistic form) is integrated (reconciled) with quantum forces.
Progress in this endeavor has been made but a verified Theory of Everything
remains elusive.
Assuming you have read the above synopsis of Quantum Mechanics and still want
more insight, try this Web
site which is written to be user-friendly to the uninitiated. A good review
of Quantum Cosmology including the implications of the Instanton concept are
examined at this Cambridge University
site. To recapitulate the above
paragraphs about Special and General Relativity (SGR), Quantum Physics (QP), and
Newtonian Physics (NP) as they apply to Cosmology: QP is most relevant in the
first minutes after the birth of the Universe but continues to apply to all
matter and energy since then; SGR is pertinent to those initial minutes but has
its greatest role as space grows thereafter; NP functions most effectively when
applied and restricted to actions and movements in scales perceptible to
ordinary observations in human experience. The treatment over the next 13
lengthy pages covers a wide scope and much relevant information but is still
only likely to give a broad-picture comprehension if you, like most, lack the
advanced knowledge and training so esoteric to cosmologists and astrophysicists.
The "worlds" of Quantum Physics and Relativity lie well beyond the experience of
ordinary living and can only be properly fathomed through their mathematical
precepts. The realms of the extremely small and the extremely
large are indeed bizarre. They are however interrelated (determining just
how is a work in progress) through the action of gravity. But one notable
difference: for Relativity, the gravitational fields are continuous; whereas for
the subatomic realm, the quantum fields are discontinuous.
As a parting thought, keep in mind
that Cosmology, like Astronomy and all Science, is still growing as it solves
old and discovers new problems and uncovers principles that will inevitably
modify the basic concepts already developed as working ideas. Thus, there are
today competing models for Universe expansion, precepts for the early moments of
"creation" are still being debated, and even the Big Bang itself is being
questioned both in its details and, by a few, in its essential correctness.
Cosmology remains a somewhat inexact science and is still a work in progress.
Here endeth the Preface. Press the
Back button on your browser or, if that doesn't work, press the Previous flag or
Next flag below (depending on how you accessed the Preface) now to return to the
first page of the Cosmology Section.
* The speed of light was first estimated in
1678 by Christiaan Huygens. He started time difference measurements made two
years earlier by the astronomer Ole Roemer (credited with establishing that
light travels at a finite speed) of systematic variations of the time intervals
in which moons of Jupiter were eclipsed as the Earth moved in its orbit from
position 1 to position 2 six months later. The difference of 22 minutes was
combined with the then estimated value of the mean Earth-Sun distance to arrive
at a speed of light value of 2.3 x 108 m/sec, about 77% of the
currently accepted value. In 1849, Armand Fizeau (in Paris) used laboratory
apparatus to improve the measurement, obtaining a speed of 3.15 x 108
m/sec. Later measurements closed in on the present value (2.998 x 108
m/sec); this most precise value has been determined with timing based on use of
the cesium-beam atomic clock.
Primary Author: Nicholas M.
Short, Sr. email: mailto:%20nmshort@ptd.net