[image: 800px-Damocles-WestallPC20080120-8842A.jpg]
*Damocles: Parable of the Sword*
Though we're almost two decades into the 21st century, many of our cultural
references are still derived from mythological sources. "The Midas
Touch," indicating a person gifted with the ability to succeed at
every endeavor, is one. "The Sword of Damocles," in reference to a
terrible threat, is another. Ironically, we often misuse both phrases,
for their presumed meaning differs considerably from their original one.
We know from a previous encounter with Midas (April 22) that he didn't
succeed at everything. In fact, the buffoonish, but kindly, king generally
made a mess of most matters. The Sword of Damocles doesn't refer to a
horrible threat at all, but instead was something of a parable, as we
shall see. The story begins with Dionysius, the Sicilian king, not the
god of wine and merriment. Dionysius II ruled the Sicilian kingdom of
Syracuse. From most accounts, his was a cruel reign of harsh laws brutally
enforced. Moreover, he implemented a draconian tax code that all but
impoverished most of his subjects, including many of those in his royal
court. One courtier, named Damocles, particularly detested his poverty.
Though he spent the greater part of the day surrounded by palatial
opulence, Damocles' lodgings were Spartan, his meals meagre, and his life
seemed little more than a series of drudgeries. One morning he felt so
desperate about his life that he dared to address King Dionysius II,
himself. "My liege," he said audaciously, "your life is so blessed and
abundant in riches. How I wish my home was so luxurious and my larder so
well stocked." Apart from being affronted by this impertinent statement,
Dionysius gently replied, "Would you care to trade places with me?"
Damocles beamed. "Oh, if only I could. It is my greatest wish of all.
How happy I would be!" Saying no more, Dionysius turned away from
Damocles and attended to other matters. The next morning, Damocles
reported to the court and started at once to attend to his duties. However,
on seeing Damocles, a soldier bowed low in his direction and said, "Good
morning, your majesty." Damocles thought the soldier was behaving in jest
until all the other court attendants treated him in a similar vein. They
all bowed low, diverted their eyes and referred to him as "your majesty."
The chef brought out a tray laden with the finest foods. "Your breakfast
is ready, your majesty. Pray be seated." Damocles suddenly felt quite
uncomfortable and looked around nervously for King Dionysius II. A moment
later the king appeared. To Damocles' astonishment, the King said, "Please
sit down to eat...your majesty." Still standing, Damocles regarded him
frightfully. "I don't understand." Dionysius approached him. "You are
the King, now, Damocles I. I have relinquished my throne to you."
"W...w...why did you d...do that?!" Damocles asked with a stammer.
Dionysius replied with a smile, a sight very few had ever seen. "Because
you told me that you desired my life above all other things. I have
grown weary of ruling and have chosen you as my successor. Rejoice! Rule
well. But, first of all, eat! The food is growing cold." Damocles
uneasily sat down and while the others looked on admiringly, he partook of
the finest breakfast he had ever eaten. He was so enthralled by the
delicacies that at first he didn't notice that he was seated on the softest
cushion he had ever felt. Though still bewildered by this abrupt
lifestyle change, Damocles was beginning to truly enjoy his new situation.
He relished the food and reclined on the cushion. Soon he experienced a
sudden drowsiness and said, "I would love to take a nap now." Dionysius
answered, "By all means, please do so. You are the king and may do as you
please." Damocles leaned back and as he drifted off to sleep
murmured, "I am the happiest person in the world." Damocles awoke a
couple hours later and after a moment remembered his new good fortune. "I
am awake!" he announced, his voice noticeably more stentorian than it had
ever been. "Impeccable timing, sire," the chef said. "Lunch is about
to be served." Damocles rubbed his hands together and prepared to dine
when he suddenly looked up and to his horror saw a sword dangling
precariously by a single strand of horsehair. Not only did it point
downward, but its tip was only slightly above his head. "What is
that?!" he demanded, his voice much more high pitched than usual. "A
sword," Dionysius explained calmly. "Why is it there?" Damocles asked,
staring frightfully at the glittering blade. "Because you are king,"
Dionysius answered. "You occupy the pinnacle of our world. Many
people, actually most people, desire to have your position now. Some
of them would love to kill you and usurp your throne. One never knows
who might harbor such ambitions. Many of those in your own court secretly
covet the throne and would think nothing of slitting your throat in your
sleep. In fact, the next time you decide to nap during the day, be
sure to be locked in your bedroom with your most loyal soldiers standing
guard." Damocles scanned the room. "Which are the most loyal ones?"
he asked. "That," Dionysius said, "is a matter you must decide for
yourself. You must trust your instincts as to who you may trust and who
you cannot trust." Damocles looked back up at the sword. "What if I'm
wrong?" "You'll probably be assassinated." Damocles sat bolt
upright. "How long will that sword be above me?" Dionysius looked
slightly sad. "Every day for the remainder of your life."
Damolces gulped. "That long?" Dionysius smiled again. "It might not be
long at all." Even though the lunch set before him was even more
delectable than the breakfast, Damocles suddenly had no appetite. He
remained silent for a few moments. During that time, he cast furtive
glances at both the sword point above him and the previous king in front of
him. Finally, he said, "Your majesty, would you care to become your
majesty, again? I don't think I desire to be king any longer."
Dionysius frowned. "You proclaimed to have been the happiest person a few
hours ago." Damocles sighed. "That was before the sword arrived." So,
Dionysius II remained Dionysius II. Damocles rose from the table and
promptly attended to his duties. It was said that on that very evening,
Damocles returned to his humble domicile. He dined on lukewarm porridge and
then curled into his hard, unkempt bed and, by his own account, never slept
more soundly in his life.
THE SOUTHWORTH PLANETARIUM
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Founded January 1970
Julian Date: 24591120.16
2020-2021: XIX
THE DAILY ASTRONOMER
Monday, September 28, 2020
Remote Planetarium 97: Special Relativity I
As we progress further into outer space, it is incumbent on us to delve
more deeply into many of the physical laws governing the Universe. Two
of the most important theories related to space-time are the Special Theory
of Relativity (1905) and the General Theory of Relativity (1916). The
first pertains to the speed of light, the second to gravitation. Before
we continue with our cosmic tour, we'll devote some time to the Special
Theory of Relativity and its astonishing precepts. We'll cover
General Relativity next week.
We begin with a rapid review of Newtonian mechanics, named for Sir Isaac
Newton (1643-1727), the patriarch of physical sciences. Newtonian laws
viewed space and time as disparate forces that did not influence each
other. Objects moved from one point in space to another in a fixed
amount of time. The image below depicts a projectile motion diagram of
a young person kicking a soccer ball.
[image: 9e3e2eafa36aebeff3bd348ccfddf01346266851.jpg]
The motion laws derived from Newtonian mechanics enable us to predict a
macroscopic object's position provided we know its initial conditions. The
above diagram shows a soccer player kicking a ball. As the ball is moving
under gravity's influence, it describes a parabolic arc from the kicking
location to its landing point. Although Newton's laws yield accurate
results at low velocities and in weak gravitational fields,* they are far
less accurate at high speeds or in regions of strong gravity.
From a Newtonian standpoint, we can know the location and speed of that
ball at any given moment provided we have information related to the
initial conditions, such as the applied force, the angle of the kick and
the planet's surface gravity. We can then perform a series of
mathematical operations to determine the object's speed and position at any
given time. While these calculations become somewhat dodgy when one
includes details such as air resistance, the principle remains the same:
a ball moves through space in a given amount of time. The ball's motion
exerts no influence over the progression of time.
Classical mechanics, those based on Newtonian laws, withstood scrutiny
quite well for the two centuries following Newton's 1687 publication of
"Philosophiae Naturalis Principia Mathematica" (Mathematical Principles of
Natural Philosophy). Then, in 1881, Albert Michelson performed an
experiment to detect the *aether,* the substance believed to have pervaded
the Universe and through which light was believed to propagate.
Scientists based the notion of the ether on the behaviour of Earth-bound
waves, such as those traveling through air and water. For instance,
sound waves require a medium through which to move. Light, being
wave-like, was also thought to have required its own medium.
Physicists reasoned that Earth would produce an "aether wind" as it moved
through space, akin to the disturbances a ship induces in water. The aim
was to compare light speed as measured along the direction of Earth's
motion to that in a direction perpendicular to it. Michelson found no
difference at all when he first conducted the experiment and again in 1887
when he repeated it with the assistance of Edward Morley. Aether was
found not to exist. Light waves move through a vacuum.
This famous Michelson-Morley experiment, as it is now called, was one of
the principal findings that led a patent clerk named Albert Einstein to
formulate his "Special Theory of Relativity," in 1905. The theory's
fundamental postulate states that:
* The speed of light is the same in all inertial reference
frames.*
* [Speed of light = **299,792,458 metres per second.]*
The statement, itself, seems simple enough. However, its ramifications
are incredible, almost preposterous. Not only did Special Relativity
constitute a tectonic shift of the Newtonian paradigm, it forever after wed
space and time to form a hyperdimensional continuum called "Space-time."
The first aspect of relativity we'll discuss is the most startling one,
that of *time dilation*. A moving vessel's velocity can literally dilate
time. To understand the correlation between this postulate and
time, we'll conduct a thought experiment. We're going to place you in
a train car. Glass covers both sides of the car. A mirror is attached
to the floor and another mirror is directly above it on the ceiling. A
light source shoots a beam directly up from the floor toward the ceiling
mirror. The reflected light then moves toward the floor mirror. A
friend, named Bob, stands next to the train tracks and watches you as your
train moves past him. Refer to the diagram below.
[image: main-qimg-68a69f65d36babb6b2d26fc8a91f23c0.webp]
As the train moves, the light beam moves up and down between the mirrors.
From your perspective, the beam consists of two straight vertical lines
connecting the mirrors. However, from Bob's perspective, the light beam
forms a triangle, the base of which is parallel to the train tracks.
Because this scenario is a thought experiment, we can imagine that Bob can
actually see the entire triangular path as the train travels. We know
the distance of the two vertical beams you see is less than the distance
along the triangle that Bob observes. We now remember that:
[image: 12_062_a_00_005.png]
Einstein's postulate states that light speed is constant in all inertial
reference frames. So, Bob measures the same speed of light as you would
measure. We have already established that the light beam distance is
greater for Bob than for you. Since the rate is constant, but the
distances differ, time, itself, must change, itself. Your time frame is
not the same as Bob's. In fact, the faster you move, the greater the
time dilation becomes. Practically, this time dilation effect is
very slight for velocities below half the speed of light. However,
once the speeds exceed this threshold, the time dilation effects become
quite significant:
-If you're moving at 50% light speed, a stationary observer will experience
1 day, three hours and 36 minutes for every single day you experience.
-If you're traveling at 90% light speed, a stationary observer such as Bob
will experience two and one quarter days for every single day you
experience.
-Accelerate up to 99.9999% light speed and a stationary observer will
experience about TWO YEARS for every since you experience.
-If -and, Kirk, this seems to be an impossible if- you could travel at
light speed, time aboard your vessel will stop entirely. So, for
instance, an entire century could elapse for a stationary observer in what
to you would literally be an instant! One would experience immense
difficulties when trying to accelerate to this speed, as we shall learn
tomorrow.
At this point, we must address a very popular misconception: one cannot go
backward in time by moving faster than light speed simple because:
* Nothing can exceed the speed of light in a vacuum! *
Light speed is the ultimate speed limit. Nothing can move faster than
light propagating through a vacuum according to Special Relativity.
Scientists have found no evidence to contradict this tenet, either.**
Tomorrow, we'll continue this discussion about Special Relativity. Its
effect on time, space, matter and, of course, energy.
*Yes, Earth's gravitational field is quite weak compared to the fields
around stars and negligibly weak when compared to those surrounding neutron
stars and black holes.
**Light speed is lower when it passes through other media, such as water.
Some objects such as electrons can exceed this speed. When they do they
produce a strange bluish glow called "Cherenkov Radiation."
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