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Date:  2459352.18
2020-2021: CXXXI

THE DAILY ASTRONOMER
Tuesday, May 18, 2021
Seeking Space-Time  Part II

Space-time: physical reality's pervasive tapestry. This two part article
shall vainly attempt to demystify that which is both pervasive, yet
intangible. It encompasses everything, but is, itself, uncontainable. That
has been the challenge confronting those inquiring into its nature, for it
is not merely void, but something even deeper in character, even if not
more readily observable.

Until its conclusion, yesterday's article pertained more to philosophical
conjecture instead of scientific investigation. Debate as to its nature
began in ancient Greece, with Zeno believing space to be nonexistent as
material objects could not act onto it. Later, Aristotle advanced the more
widely accepted theory that space defined itself according to the objects
occupying it. It was regarded as being similar to a fluid conforming itself
to whatever vessel contained it. Centuries later, Kepler, Galileo and
Newton, the patriarchs of mathematical physics and astronomy, managed to
determine the order of our solar system and the means by which the planets
interact gravitationally. However, they had little to say about space-time,
itself, apart from Newton, whose rigid, deterministic models merely
affirmed that which was already assumed -that space and time existed
separately and independently. Neither affected the other and both were
immutable. Space and time were distinct
'[image: 220px-Joseph_Louis_Lagrange2.jpg]
*Joseph-Louis LaGrange*

Although we often credit Albert Einstein (1871-1955) with space and time's
unification, the fusion truly began two centuries earlier with Joseph-Louis
LaGrange (1738-1813). In his book, The Theory of Analytic Functions (1797),
he refers to the science of mechanics as involving four dimensional
geometry: three spatial dimensions (width, breadth, and length) and the
other of time (duration.) LaGrange reasoned that all mechanical and
physical motion necessarily required the time dimension for any situation.
A situation changed through time. Were time extracted from the system,
change would be rendered impossible. With a few decades, Edgar Allan Poe
-yes, the horror story author- mentioned space-time fusion in his
remarkable essay entitled "Eureka!" (1848)* He regarded space and time as
being 'as one,' about a half century before H.G. Wells' time traveling
protagonist in the "Time Machine" posited the same notion when explaining
the philosophy of his temporal transport craft.

While Poe and Wells' assertion is now deemed prescient, their models were
more descriptive than analytical. It would be left to Albert Einstein in
his two relativity theories to furnish the model with the quantitative
basis, just as Isaac Newton's "Principia" conferred mathematical formalism
onto what had hitherto been merely an intuitive sense of space and time's
distinctness and immutability.

A BRIEF HISTORY OF LIGHT

Einstein did not merely conjure these theories out of nothing. It arose
from what was, in the late 19th century, a paradigm shift in humanity's
view of light and its propagation through space. Ever since Ole Roemer
(1644-1710) performed the first measurement of light speed based on
observations of Jupiter,** it was assumed that light moved at a finite
speed. Until that time, no experiment was devised to ascertain light
velocity. Having established that light moved at a specific speed, a
question remained concerning its means of propagation. Did it travel as a
particle or wave? (Spoiler: it turns out to be both, hence the advent of
quantum physics.) Newton developed a corpuscular theory of light, citing
the precise linearity of reflected beams -behavior that other waves do not
exhibit in contrast with Christian Huygens (1629-1695) wave front theory.
As Newton was the more eminent of the two, his theory became predominant
for more than a century until light phenomena such as refraction was seen
to be inexplicable were light beams composed of particles, not waves. When
James Clerk Maxwell (1831-1879) published his famous equations in 1861 and
1862***, he demonstrated that light was an electromagnetic wave, which, for
a while, demolished the particle-theory and made the wave model apparently
unassailable.

As often happens in science, one solution spawns other problems. Principal
amongst the problems the Maxwell equations precipitated was how light waves
traveled. Once they determined that light traveled as a wave, it was
wondered through which medium these waves propagated. All other wave
phenomena, such as ocean and sound waves,require a medium. Ocean waves need
water just as sound waves need material, preferably gases. Presumably,
light required a material which permitted its conveyance: a hypothetical
substance dubbed the "aether," after the air that the Gods breathed on
Olympus, as opposed to the befouled oxygen we unwashed mortals inhale.

In 1871, Albert Michelson and Edward Morley performed the now-famous
Michelson-Morley experiment by which they attempted to measure Earth's
motion through this aether, more properly known as the luminiferous aether.
Through arduous effort, they constructed an interferometer capable of
measuring how light beams directed perpendicularly would shift as Earth
revolved and rotated through this aether wind. By this time, humanity knew
Earth's orbital speed, which, at the time of the experiment, was measured
to be i30 kilometers per second. As Earth revolved and rotated, they would
know how the light beam's wavelength, which was 600 nm**** for experiment,
would experience shifting due to the wind the mobile Earth generated. To
their surprise, and chagrin, they detected no displacement at all.


[image: aether_wind.svg.png]
*The Michelson-Morley experiment was designed to detect*
*the aether, a substance that scientists believed pervaded*
*the cosmos.  *

This 'failure,' and other lesser known experiments, led directly to Albert
Einstein's formulation of the Special Theory of Relativity (1905), in which
he determined that light speed was constant in all inertial reference
frames. Or, to phrase it differently, one's measurement of light speed
doesn't change if one is stationary or in motion. This theory might not
seem staggering, until one realizes that one would measure a light beam's
speed as being the same if one were standing on the ground or traveling in
a spacecraft at 90% light speed! So, the only result is that time, itself,
must change. Time dilates at higher speeds! For the very first time, time,
itself, was seen as mutable. One's time frame changes merely by moving and
as we occupy a Universe full of motion, "everyone has their own clock," as
Einstein asserted. Newton's notion of time existing independently of space
was shattered. Finally, through special relativity, space and time were
truly united into Space-time.

In 1916, Einstein published the sequel: General Relativity. Here, the focus
was not speed, but gravitation: the fundamental 'force' mediated between
all massive objects. This action-at-a-distance force confounded Newton
metaphysically. While he developed a working model to explain how gravity
affected materials, he could not explain its nature. He included something
of a disclaimer in his writings by acknowledging that such remote influence
between bodies was irrational. Einstein provided a new means by which to
explain gravitational attraction. He quite cleverly divorced gravity from
matter and concluded it was a property of space-time, itself, not of
objects. Any massive object distorts its local space-time geometry, much
like a bowling ball would deform a taut rubber sheet. If one were to toss
ball bearings across the sheet, those closest to the bowling ball would
'fall' into its indentation. Similarly, any proximate objects to the Sun,
such as planets, would be inextricably bound to it gravitationally. Earth
is lodged in the Sun's gravity well, just as we are trapped in Earth's.

Gravity is shown not only to distort space, but time as well. Gravitational
time dilation causes clocks to run at different rates depending on the
matter nearby. Clocks on the ground have been shown to run more slowly than
those in airplanes, as the grounded clock is in a more powerful
gravitational field. The timing mechanisms associated with the Global
Positioning System satellites must take this gravitational time dilation
into account. In theory, time will be faster for you even if you climb up a
ladder, though the difference is practically negligible.

Relativity didn't destroy Newtonian determinism, which still works quite
well in describing how boulders fall off cliffs and how spacecraft like the
Pioneer probes can still move through outer space without the necessity of
continued impulses. However, Einstein's relativity demonstrated that
Newtonian physics was only valid in regions of weak gravity and low
velocities. Make the gravitational fields too powerful or the speeds too
high, and relativistic effects become increasingly more important.
[image: warping-spacetime-ligo.jpg]

By relativistic reckoning, Earth shouldn't just produce an indentation,
but, instead, must create a spinning space-time vortex around itself as it
rotates on its axis and revolves around the Sun. Of course, how can one
ever attain supporting evidence? Amazingly, NASA's gravity probe B mission
did exactly that in an experiment requiring many years of the most precise
measurement possible. The Gravity B probe uses gyroscopes oriented toward a
distant star. While in orbit around Earth, the probe's ultra-fine spherical
gyroscopes***** maintained a constant orientation on the star. As Earth
moved through space, the space-time experienced twists and distortions that
caused the gyroscope to shift ever so slightly: a phenomenon called
"geodetic precession." After many years, the Gravity Probe B yielded the
results researchers expected: the gyroscope's precession resulted from
Earth's space-time vortex.

More confirmation for General Relativity, which hardly requires it. We
accept that space isn't rigid; time isn't a rigid progression, and that
they are both woven together into the space-time grid that stretches to all
corners of the Universe. As we commemorate the 50th anniversary of the Time
Lords, we understand that perhaps such unconstrained travel to all space-
time coordinates is unlikely. Then again, the more we learn about the
cosmos, the more fantastic it becomes. Today's impossibility is tomorrow's
commonplace. Maybe our descendants will puzzle out space-time deepest
mysteries and in so doing, will believe that we in the 21st century had
barely fathomed anything.

*We've encountered "Eureka" before in our astronomical wanderings, most
notably during discussions about Olber's Paradox: the one that asked the
deceptively simple question, "If the Universe is infinite and contains an
infinite quantity of stars, why is the night sky dark?" Heinrich Olbers
(1758-1840) posed this question as a challenge to the model that the
Universe was of infinite age and extent. Were it so, then every single
sight line would extend to a star, making the sky uniformly bright. In
"Eureka," Poe suggested that the Universe's finiteness in space and
duration was the only solution to this paradox, as astronomers now believe
it to be.

**Ole Roemer first estimated light's speed by observing Jupiter's moon Io,
one of the four Galilean satellites -Io, Europa, Ganymede and Callisto-
that Galileo discovered in 1610. Roemer realized that eclipses of Io
(called immersions) were slightly off predictions. He reasoned that this
error resulted from light's finite travel time: the eclipse would happen
sooner around opposition (when Earth and Jupiter were close together) and
later when Earth was much farther from Jupiter. Though Roemer's first light
speed estimate was 28% lower than the accepted value today, his work served
to establish that light speed was not infinite.

***These four equations are considered some of the most beautiful ever
written, for they conjoin what had been considered the disparate phenomena
of electricity and magnetism, thereafter known by the married name
'electromagnetism

****nm = nanometers (one billionth of a meter) 600 nm is in the orange-red
part of the visible light spectrum. (Wavelength is related directly to
color.)

*****These gyroscopes are as close to perfectly spherical as possible. With
an 1.5 inch diameter, they are within 40-60 atomic layers of perfect
sphericity. Such precision is necessary, since any imbalance within the
sphere would cause a precession larger than that General Relativistic
effects would induce.



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