Spacetime
By Thomas Knierim
Table of Contents
Intr

oduction

.....................................................................................................................2
R
elativity

.......................................................................................................................... 4
T
ime Dilation

....................................................................................................................7
S
pacetime

....................................................................................................................... 10

Q
uantum Theory

............................................................................................................ 13

T
he Uncertainty Principle

.............................................................................................. 17

T
he Universe

..................................................................................................................2 0
O
pen Questions

..............................................................................................................2 5
F
requently Asked Questions

..........................................................................................2 9
Spacetime, Thomas Knierim, www.thebigview.com
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Introduction
"Do not take the lecture too seriously . . . just relax and enjoy it. I am going to tell you
what nature behaves like. If you will simply admit that maybe she does behave like
this, you will find her a delightful, entrancing thing. Do not keep saying to yourself
"But how can it be like that?" because you will get . . . into a blind alley from which
nobody has yet escaped. Nobody knows how it can be like that."
(Richard Feynman introducing a lecture about quantum theory)
Natural sciences always had a great influence on philosophy and on the way we see
the world. Until the age of the Renaissance there was no clear distinction between
philosophy and science. Speculations about physics and astronomy were among the
favourite topics of the natural philosophers of antiquity and continued to flourish
until the time of Copernicus. The desire to explore the starry heavens and to reveal its
secrets is probably as old as mankind itself. However, notable advances in this
discipline were made only fairly recently, after the invention of the telescope in the
17th century. This section deals with the accomplishments of 20th century physics in
the world of the largest structures, such as galaxies and stars, and that of the smallest
structures, such as atoms and particles. We take a closer look at Relativity and
Quantum Physics in particular, both of which have given us amazing new insights
into what we call creation.
Newton: the three laws of motion.
In the eyes of physics, the world used to be a predictable place. Aristotle and Ptolemy
laid the foundation for the scientific understanding of the universe, which remained
authoritative for one-and-a-half thousand years. Until the time of Galileo, the Greeks
were undisputed in natural science and astronomy. Galileo, Copernicus, and Newton
changed this. Isaac Newton (1642-1727) revolutionised physics with his proposition
that all bodies are governed by the three laws of motion. The first law of motion states
that a body continues in a state of rest or continues to be moving uniformly in a
straight line unless a force is applied to the object. The second law states that the
force applied to an object is proportional to its mass multiplied by acceleration
(F=ma). The third law states that for every action there is an equal opposite reaction.
With these three simple laws, Newton created a whole new model of the universe,
superseding Ptolemy's model of epicycles. Eighty years before, Galileo (1564-1642)
had pointed out that the Earth rotates around the Sun. The mechanics developed by
Newton and Galileo provided the basis for 17th to 19th century cosmology. In this
view, planets revolved in well-defined orbits around stars, where the rotational force
is balanced by the gravitational force. According to the universal law of gravitation,
bodies attract each other with a force F=m1*m2/r², which means that the force
increases with mass and decreases (squared) with distance.
Laplace: the mechanistic universe.
Given these natural laws, mankind derived a picture of the universe that accounts
neatly for mass, position, and the motion of the celestial bodies while it interprets the
latter as dynamic elements of a celestial apparatus, not unlike that of a mechanical
apparatus. It is therefore called the mechanistic worldview. It was elaborated in its
purest form by Marquis de Laplace (1749-1827) in his writing Mécanique Céleste. The
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mechanistic view sees the universe as an arrangement in which stars and planets
interact with each other like springs and cogs in a clockwork, while God is watching
from above. If the initial positions and states of all objects in a mechanically
determined universe are known, all events can be predicted until the end of time,
simply by applying the laws of mechanics. It was further thought that this kind of
knowledge is available only to an omniscient God.
The mechanistic view does not make any statements about the creation of the
universe. Things were taken as preestablished by the creator. From a mechanistic
standpoint, solar systems like our own are in a delicate balance, because only a slight
increase or decrease in mass or velocity of the planets would let the planets either
spiral into the Sun or wander into outer space. There had to be a construction plan.
There was a necessity for a creator God who initially put balance into the universe.
Needless to say that the church was comfortable with this theory, despite the earlier
quarrels with Galileo, and in spite of the fact that it generally viewed scientific
progress with great suspicion.
Discovery of the speed of light.
In 1676 the Danish astronomer Ole Roemer (1644-1710) announced a remarkable
discovery. He observed seasonal variations in the disappearances of Jupiter's moons
behind Jupiter. Because the distance between Earth and Jupiter varies with the
seasons, while the Earth travels on its path around the Sun, this means that the light
from Jupiter's moons travels either shorter or longer distances throughout the year.
The changes in Roemer's observation corresponded with the distances between Earth
and Jupiter, which implied that the speed of light is finite. Roemer's observation did,
however, not directly contradict the mechanistic worldview. In the mechanistic view,
light waves travel through the ether, just as sound waves travel through air. - Yet,
there was a problem with the concept of "ether". Its existence could never be
detected.
At the end of the 19th century, the mechanistic view was in trouble. Astronomers
noticed that Mercury's perihelion (the closest point to the Sun in its orbit) changed
slightly with every orbit. This observation shattered the notion of immutable orbits.
Astronomers tried to solve this problem by predicting a mystery planet they called
Vulcan, which would account for the observed gravitational variations. Needless to
say that it was never found.
The American physicists Michelson and Morley brought the mechanistic worldview
into even more trouble. In an experiment, which was designed to measure the
velocity of the Earth, they found that the speed of light is constant, contrary to what
they had expected. They found this characteristic of light to be in disagreement with
the Galilean velocity addition formula v'=v1+v2, which means their observation
contradicted classical mechanics.
Einstein changes everything.
At the beginning of the 20th century, a formerly unknown clerk of the Swiss patent
office by the name of Albert Einstein thought to himself: "Falling objects don't feel
gravity." He imagined what it would be like to ride through space on a beam of light
and came to the conclusion that space and time can be visualised as coordinate
systems, or "reference frames", relative to the observer. This was the basis for his
Relativity Theory. At about the same time, other physicists pondered on equally
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fundamental problems, which concerned interactions of matter and radiation, but
came to totally different conclusions than Einstein. The result of their collective
thought, quantum theory, explained the behaviour of subatomic particles.
With this being written in the year 1999 it is safe to say that Relativity was the single
most influential physical theory of the 20th century for the way it has changed our
view of the universe. Not that other discoveries in physics were less significant, but
few of them have been so well received by the general public. Relativity has grabbed
people's imagination and sparked discussions in philosophy and religion which last
until the present day. Quantum physics, although perhaps more pertinent to daily
life, is a close second.
Is causality questioned by modern physics?
Relativity and Quantum Theory have implications on cosmology, epistemology, and
metaphysics. We only begin to understand their impact on our traditional ways of
seeing the world. How does God fit into our new picture of the universe? Can the stuff
the world is made of be explained by physics alone? What is space and time? Does
quantum physics contradict causality? To find out more about these questions and to
learn about the findings of Einstein, Heisenberg, and others, take a closer look at the
fascinating world of modern physics.
Relativity
The notion of relativity is not as revolutionary as many believe. In fact, spatial
relativity is part of our everyday experience. Spatial relativity, also called Galilean
relativity in honour of Galileo who first formulated the concept of relative motion, is
often confused with Einstein's theories. Galileo simply described the fact that an
observer in motion sees things differently from a stationary observer, because he has
a different spatial coordinate system, or "reference frame" in Relativity speak. It
might sound more complicated than it actually is. Consider the following example:
Galilean relativity: the train example (courtesy of Stephen Hawking).
Two people riding on a train from New York to San Francisco play a game of ping-
pong in the sport compartment of the train. Lets say, the train moves at 100 km per
hour (= 27.8 m/s) and the two players hit the ball at a speed of two meters per
second. In the reference frame of the players, the ball moves back and forth at this
particular speed. For a stationary observer standing beside the railroad, however,
things look quite different. In his reference frame the ball moves at 29.8 m/s when it
is played forward in the direction where the train is heading, while it moves at 25.8
m/s in the same direction when it is played backwards. Thus he doesn't see the ball
moving backward at all, but always moving towards San Francisco. For an observer in
outer space, things look again totally different because of the Earth's rotation, which
is opposite to the train's movement; therefore the outer space observer always sees
the ball moving East.
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Einstein's new concept of Relativity.
Einstein's Relativity differs from classical relativity, because of the way he looked at
time. Before Einstein, people thought time to be absolute, which is to say that one big
clock measures the time for the entire universe. Consequently one hour on Earth
would be one hour on Mars, or one hour in another galaxy. However, there was a
problem with this concept. In an absolute time frame the speed of light cannot be
constant. Roemer found that the speed of light is finite and has a certain, quantifiable
velocity (usually abbreviated with "c"), which at first implies Galilean relativity. This
would mean that while the Earth rotates at a velocity of v, light emitted in the
direction of the Earth rotation must be c + v, while light emitted in the opposite
direction would travel at c - v, relative to an outside observer.
In 1881, A. Michelson conducted an experiment which proved that this is not the
case. With the help of an apparatus that allowed measuring minute differences in the
speed of light by changes in the resulting interference patterns, Michelson observed
that the speed of light is always the same. No changes whatsoever. The experiment
has been repeated later with greater precision by Michelson and E.W. Morley.
Special Relativity published in 1905.
Numerous attempts were made at reconciling these discrepancies, yet they were all
unsuccessful, until Einstein solved the dilemma with his famous paper On the
Electrodynamics of Moving Bodies in 1905, in which he developed his Special
Relativity Theory. Special Relativity is an extremely elegant construct that deals with
things moving near or at the speed of light. Surprisingly, the new concept of space
and time that arises from Relativity is based only on two simple postulates: 1. The
laws of physics are the same in all inertial (=non-accelerating) reference frames, and
2. The speed of light in free space is constant.
It is a matter of common experience that one can describe the position of a point in
space by three numbers, or coordinates. For the purpose of explaining the relativistic
model, Einstein added time as a fourth component to the coordinate system, and the
resulting construct is called spacetime. Just as there is an infinite number of 3-D
reference frames in Galilean relativity, there is an infinite number of 4-D spacetime
reference frames in Einstein's theory. This is to say that Einstein put an end to
absolute time. The revolutionary insight lies in the conclusion that the flow of time in
the universe does indeed differ depending on one's reference frame.
Albert Einstein (1879-1955)
German physicist Albert Einstein published his papers on
Relativity Theory between 1905 and 1916. He became
internationally noted after 1919 and was awarded the Nobel Prize
in 1921. Einstein emigrated to the USA when Hitler came to power
in Germany.
Einstein: "Relativity teaches us the connection between the different
descriptions of one and the same reality."
In his usual humble way, Einstein explained how he reinvented physics: "I sometimes
ask myself how it came about that I was the one to develop the theory of Relativity.
The reason, I think, is that a normal adult stops to think about problems of space and
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time. These are things which he has thought about as a child. But my intellectual
development was retarded, as a result of which I began to wonder about space and
time only when I had already grown up." On Relativity, he said: "Relativity teaches us
the connection between the different descriptions of one and the same reality."
This view of Relativity, that there are different realities, has been picked up
unanimously by the public, and hence, has taken on a far greater meaning than that
of the original scientific theory, the focus of which was -strictly speaking- on
mechanics and electrodynamics. This astonishing success was at least in part due to
Einstein's personality. He understood himself as a philosopher as much as a scientist,
and he was ready to discuss philosophical issues at any time, particularly matters
involving Relativity. The philosophical aspect of Relativity forced people to think
differently about the universe. Suddenly, the cosmos was not a God-created
clockwork anymore, but a totality of disparate realities with the same basic natural
laws.
E=mc² - Energy equals mass times the speed of light squared.
An outstanding feature of Special Relativity is its mass-energy relation, which is
expressed in the well-known formula: E=mc².
Einstein derived this relation in an attempt to reconcile Maxwell's electromagnetic
theory with the conservation of energy and momentum. Maxwell said that light
carries a momentum, which is to say that a wave carries an amount of energy. Due to
the principle of conservation of momentum, if a body emits energy in the form of
radiation, the body loses an equivalent amount of mass that is given by E/c². This
describes the relation between energy and mass.
According to the conservation principle, in a closed system the sum of mass and its
energy equivalent is always the same. The mass-energy relation tells us that any
change in the energy level of an object necessarily involves a change in the object's
mass and vice-versa. The most dramatic consequences of this law are observed in
nature, for example in nuclear fission and fusion processes, in which stars like the
Sun emit energy and lose mass. The same law also applies to the forces set free in the
detonation of an atomic bomb.
Was Einstein involved in the development of the atomic bomb?
Einstein was not directly involved in the creation of the atomic bomb, as some people
assume. His credits are rather being the one who provided the theoretical framework.
In 1939, Einstein and several other physicists wrote a letter to President Franklin D.
Roosevelt, pointing out the possibility of making an atomic bomb and the peril that
the German government was embarking on such a course. The letter, signed only by
Einstein, helped lending urgency to efforts in the creation of the atomic bomb, but
Einstein himself played no role in the work and knew nothing about it at the time.
General Relativity published in 1916.
Eleven years after On the Electrodynamics of Moving Bodies, Einstein published his
second groundbreaking work on General Relativity, which continues and expands
the original theory. A preeminent feature of General Relativity is its view of
gravitation. Einstein held that the forces of acceleration and gravity are equivalent.
Again, the single premise that General Relativity is based on is surprisingly simple. It
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states that all physical laws can be formulated so as to be valid for any observer,
regardless of the observer's motion. Consequently, due to the equivalence of
acceleration and gravitation, in an accelerated reference frame, observations are
equivalent to those in a uniform gravitational field.
This led Einstein to redefine the concept of space itself. In contrast to the Euclidean
space in which Newton’s laws apply, he proposed that space itself might be curved.
The curvature of space, or better spacetime, is due to massive objects in it, such as the
Sun, which warp space around their gravitational centre. In such a space, the motion
of objects can be described in terms of geometry rather than in terms of external
forces. For example, a planet orbiting the Sun can be thought of as moving along a
"straight" trajectory in a curved space that is bent around the Sun.
On the following pages we will examine spacetime and other fascinating aspects of
Relativity in some detail and see how Relativity leads us to new insights about the
structure and the creation of the universe.
Time Dilation
One of the most enthralling aspects of Relativity is its new understanding of time. The
term "time dilation" might evoke images of Salvadore Dali's timepieces hanging on
twigs, however, time dilation is all but surrealistic. As stated earlier, if the speed of
light is constant, time cannot be constant. In fact, it doesn't make sense to speak of
time as being constant or absolute, when we think of it as one dimension of
spacetime. Special Relativity states that time is measured according to the relative
velocity of the reference frame it is measured in. Despite of the simplicity of this
statement, the relativistic connection between time and space are hard to fathom.
There are numerous ways to illustrate this:
The four dimensions of spacetime.
In Relativity the world has four dimensions: three space dimensions and one
dimension that is not exactly time but related to time. In fact, it is time multiplied by
the square root of -1. Say, you move through one space dimension from point A to
point B. When you move to another space coordinate, you automatically cause your
position on the time coordinate to change, even if you don't notice. This causes time
to elapse. Of course, you are always travelling through time, but when you travel
through space you travel through time by less than you expect. Consider the following
example:
Time dilation; the twin paradox.
There are two twin brothers. On their thirtieth birthday, one of the brothers goes on a
space journey in a superfast rocket that travels at 99% of the speed of light. The space
traveller stays on his journey for precisely one year, whereupon he returns to Earth
on his 31st birthday. On Earth, however, seven years have elapsed, so his twin brother
is 37 years old at the time of his arrival. This is due to the fact that time is stretched
by factor 7 at approx. 99% of the speed of light, which means that in the space
traveller’s reference frame, one year is equivalent to seven years on earth. Yet, time
appears to have passed normally to both brothers, i.e. both still need five minutes to
shave each morning in their respective reference frame.
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Time in the moving system will be observed by a stationary observer to be running
slower by the factor t':
As it can be seen from the above function, the effect of time dilation is negligible for
common speeds, such as that of a car or even a jet plane, but it increases dramatically
when one gets close to the speed of light. Very close to c, time virtually stands still for
the outside observer.
Time expands, space contracts.
Interestingly, while time expands from the perspective of the stationary observer,
space contracts from the perspective of the moving observer. This phenomenon is
known as Lorentz contraction, which is exactly the reciprocal of the above time
dilation formula: l'=l*sqr(1-v²/c²). Thus the space traveller passing by Earth at a
speed of 0.99c would see it's shape as an ellipsis with the axis parallel to his flight
direction contracted to a seventh of its original diameter. That is of course, if he sees
it at all, given the enormous speed. Therefore, space travel is shortened with the
velocity of the traveller. A journey to the 4.3 light-years distant Alpha Centauri C, the
closest star to our Sun, would take only 7.4 months in a space ship moving at 0.99c.
The effect of time dilation has been experimentally confirmed thanks to very precise
caesium clocks that can measure extremely small periods of time. Unfortunately,
time dilation is completely outside of human experience, because we have not yet
devised a way of travelling at speeds where relativistic effects become noticeable.
Even if you spent your whole life in a jet plane that moves at supersonic speed, you
would barely win a second over your contemporaries on the ground. And, not even
today's astronauts can perceive the Lorentz contraction. Imagine you are a
cosmonaut on board of space station Mir, moving at 7700 meters per second relative
to Earth. Looking down upon Europe from space, you would see the entire 270
kilometre east to west extent of Switzerland contracted by a mere 0.08 millimetres.
Can we travel at the speed of light?
The hope that one day mankind will be able to travel at near-to-speed-of-light
velocities seems farfetched, because of the incredible amounts of energy needed to
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accelerate a spacecraft to these speeds. The forces are likely to destroy any vehicle
before it comes even close to the required speed. In addition, the navigational
problems of near-to-speed-of-light travel pose another tremendous difficulty.
Therefore, when people say they have to hurry in order to "win time", they probably
don’t mean it in a relativistic way.
Kant: Space and time are properties of thought.
The German philosopher, Immanuel Kant (1724-1804), maintained that time and
space are a priori particulars, which is to say they are properties of perception and
thought imposed on the human mind by nature. This subtle position allowed Kant to
straddle the well-known differences about the reality of space and time that existed
between Newton and Leibniz. Newton held that space and time have an absolute
reality, in the sense of being quantifiable objects. Leibniz held against this that space
and time weren't really "things", such as cup and a table, and that space and time
have a different quality of being. Kant's position agrees with Newton in the sense that
space and time are absolute and real objects of perception, hence, science can make
valid propositions about them. At the same time, he agrees with Leibniz by saying
that time and space are not "things in themselves," which means they are
fundamentally different from cups and tables. Of course, this view of space and time
also introduces new problems. It divides the world into a phenomenal (inner) reality
sphere and an noumenal (outer) reality sphere. From this academic separation arise
many contradictions in epistemology. We will, however, not deal with this particular
problem at this point.
Life in a spacetime cubicle.
From Relativity we learn that time and space is seemingly independent of human
experience, as the example of time dilation suggests. Since our own perception of
time and space is bound to a single reference frame, time appears to be constant and
absolute to us. Physics teaches us that this is an illusion and that our perception
deceived us within living memory. Thanks to Einstein, we are now able to draw
relativistic spacetime diagrams, compute gravitational fields, and predict trajectories
through the four-dimensional spacetime continuum. Still, we are hardly able to
visualise this spacetime continuum, or deal with it in practical terms, because human
consciousness is bound to the human body, which is in turn bound to a single
reference frame. We live within the confinements of our own spacetime cubicle.
Considering that in Relativity, spacetime is independent of human perception, the
Kantian understanding of space and time as a priori particulars seems to be obsolete.
They are no longer properties of perception, but properties of nature itself. But, there
is more trouble looming for Kant. Relativity stretches the distinction between
phenomenal reality, i.e. that which can be experienced, and noumenal reality, i.e. that
which is purely intelligible and non-sensory, to a degree where these concepts almost
appear grotesque. For example, the question arises, whether time dilation falls into
the noumenal or phenomenal category? Since it can be measured, it must be
phenomenal, however, since human perception is bound to a single reference frame,
it must also be noumenal. The distinction between noumenon and phenomenon is
thus blurred and possibly invalidated.
We can attempt to imagine relativistic models with the help of appropriate
mathematical models, but cannot experience it directly, at least not until someone
builds a near-to-speed-of-light spacecraft. Thanks to Einstein, we are able to look
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beyond the phenomenal reality of space and time, and we understand that there is
more to it than commonsense perception tells us. In a way, Einstein has freed our
minds from the spacetime cubicle.
Spacetime
From the preceding reflections on time dilation, we learn that Albert Einstein has
overthrown commonsense assumptions about space and time that were valid for
centuries. Relative to the observer, distances appear to contract while clocks tick
more slowly when moving at velocities close to the speed of light. These are the
practical consequences of Special Relativity, the work for which Einstein became
famous. Einstein did not stop at this point. In 1916, he published his General
Relativity, which further challenged conventional wisdom. The paper proposed that
matter causes spacetime to curve. Gravitation is understood as the warping of
spacetime, not a force acting at a distance, as Newton had suggested.
A massive object causes spacetime to curve, which is often illustrated with the picture
of a bowling ball lying on a stretched rubber sheet:
Contrary to appearance, the diagram does not depict the three-dimensional space of
everyday experience. Instead it shows how a 2-D slice through familiar 3-D space is
curved downwards when embedded in flattened hyperspace. We cannot fully envision
this hyperspace. Flattening it to 3-D allows us to represent the curvature and helps us
visualise the implications of Einstein's General Theory of Relativity.
Gravitation bends light rays.
Since light has no mass, it is not subject to Newton's law of gravity, and hence, in
Newtonian physics gravity has no effect on light. If space is curved, however, it
follows that a ray of light seemingly moving in a straight line really travels in a curved
line following the curvature of space. This is comparable, in some way, to the
itinerary of a plane. Because the Earth is a sphere, the shortest path between two
points on Earth is described by a geodesic, a curved line. While moving along the
geodesic it would appear to the passengers of the plane that they are moving in a
straight line, although they are not. Similarly, the light of distant stars travels through
the curved geometry of space before it reaches Earth. This proposition is supported
by observation.
When the light of a star passes close to the Sun, it is deflected by the Sun's
gravitational field, which causes it to appear slightly displaced. The star appears to be
farther from the Sun than it should be. The displacement has been measured by
photographing the apparent position of stars during a solar eclipse and comparing
these positions with those observed in the night some time later. Apparent shifts of
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