Home > Physics > Core > Space > Space: 4. Current and emerging understanding about time and space
9.2 Space: 4. Current and emerging understanding about
time and space
Extract from Physics Stage 6 Syllabus (Amended
October 2002). © Board of Studies, NSW.
[Edit: 11 June 10]
Prior Learning: HSC modules 9.2
(subsections 2 and 3)
Background: The theory of relativity came
out of considerations about the way that light travels, but
to do so physicists had to overcome a long held belief in a
theory that eventually proved to be incorrect. The relativity
effects considered here apply to circumstances that we do not
normally experience — travelling at a significant
fraction of the speed of light. Application of the theory
suggests some tantalising possibilities for space travel.
the features of the aether model for the transmission of
- During the nineteenth century, physicists were certain
that light was a waveform. They assumed that, like all
other known waveforms, light waves needed a medium through
which to travel to us from the Sun and other stars.
- No medium could be found, and so one was hypothesised,
along with a set of expected properties. It was called the
The list of properties included the following. The aether
- fill all of space and be stationary in space
- be perfectly transparent
- permeate all matter
- have a low density
- have great elasticity in order to propagate the
gather and process
information to interpret the results of the Michelson-Morley experiment
- Gather information from reputable web sources or from encyclopedias or journals.
If you use the Internet use a search engine to find out about the results
of the experiment.
The web page below will give you a start.
- Process information by comparing the results from several different sources.
Skim through the background information of the web page listed below until
you get to the experiment. Note that the author has already done some interpretation
of the experiment. Compare this with other sources.
- The Michelson-Morley experiment a
web page of the Department of Physics, University of Virginia, that describes
the Michelson-Morley experiment in some detail.
the Michelson-Morley attempt to measure the relative velocity
of the Earth through the aether
- The Michelson-Morley experiment was devised to detect
the aether using light and an effect called
- As the Earth was supposed to be moving through a
stationary aether, there should have been an apparent
aether wind. The speed of light was supposed to be
constant in the aether, so this aether wind should
slow down light heading into it, as seen by us. The
Michelson-Morley experiment compared the speed of such a
light ray with another light ray directed across the
aether wind. The two rays were compared using an
interferometer, a device that displays interference
effects. No significant difference was found between the
two light rays.
- The experiment was of sufficient sensitivity according to the aether model,
yet failed to detect any presence of the aether. No matter who did the experiment,
where it was done or when it was done, no one was able to physically demonstrate
the interference effect that would prove the existence of the aether.
the role of the Michelson-Morley experiments in making
determinations about competing theories
- From theory come predictions that can be tested.
Experiments are performed to test the predictions, and from
the results of the experiments, judgements can be made
regarding the validity of the theory. The Michelson-Morley
experiments were performed to test the prediction, based on
the aether model, that an aether wind should exist.
- The Michelson-Morley experiments were performed in 1887
and had null results, despite satisfying all requirements
regarding sensitivity. This did not, however, disprove the
- Various modifications of the aether theory were offered
over the following years. Each modified theory resulted in
new predictions to be tested. Each test failed.
- Almost twenty years after the Michelson-Morley
experiments, Einstein proposed the theory of relativity, in
which the aether model was not needed. The theory of
relativity produced its own set of predictions, not all of
which were testable at that time. As technology has
improved, the predictions have been tested and found to be
- The choice for scientists was as follows: continue to
follow a theory for which no predictions proved true
(aether) OR follow an alternative theory for which
prediction do prove true (relativity).
investigation to help distinguish between non-inertial and
inertial frames of reference
- Perform the investigation that may be
planned by your teacher, by carrying out the procedures
efficiently and safely.
A sample investigation that can be easily carried out is
- A plumb bob will only hang directly down in an
inertial (or non-accelerated) frame of reference; it
will hang in other directions in non-inertial (or
accelerated) frames of reference. Try letting one hang
from your hand while you are standing still or walking
with a steady velocity (that is, a steady speed in a
straight line). Next, try accelerating to a run,
stopping quickly or changing direction. How did the
plumb bob react under each of these conditions?
- You should be able to test these observations by
taking your plumb bob on a ride in a car or bus. Do not
look out the window, but only observe the plumb bob.
Can you deduce the motion of the vehicle from the
direction in which the plumb bob hangs?
- The plumb bob in this activity has been used as an
the nature of inertial frames of reference
- A frame of reference is a rigid framework relative to
which position, displacement, velocity, etc, can be
measured. For example, the interior of a car, train, plane,
on the ground, the Earth, the Sun.
- An inertial frame of reference involves no
acceleration. It allows for uniform velocity motion or a
state of rest only.
the principle of relativity
- The principle of relativity was first stated by Galileo
and embodied in Newton’s first law. It states that it
is not possible to perform an experiment within an inertial
frame of reference to detect the motion of the frame of
reference. The only way to detect the motion of an inertial
frame of reference is by referring to another frame of
reference. For example, if you are in a spacecraft far from
any planet, star or other object, then you cannot tell if
you are moving. Your rockets have long been turned off and
you are coasting along to your destination with uniform
velocity. However, without referring to outside objects
(for example, triangulating off certain stars over a long
time period), it is impossible to measure, or even detect,
some of Einstein’s thought experiments involving
mirrors and trains and discuss
the relationship between thought and reality
- A limitation of thought experiments is that what you
imagine as the outcome is based upon your common
sense, that is, your collective experiences of the way
things normally happen. Einstein used thought experiments
to investigate situations that could not be tested in
reality. In some cases, that inability to test, stems from
limitations in current technology.
- The following outlines one of Einstein’s most
famous thought experiments. It is this scenario, in
particular, that occupied his thoughts during the period
1895 to 1905 when he was formulating his theory:
Imagine that you are sitting in a train facing
forwards. The train is moving at the speed of light. You
hold up a mirror in front of you, at arm’s length.
Will you be able to see your reflection in the mirror?
The experiment could have one of two possible outcomes,
each of which involves a dilemma for the scientific
community of the time that believed in the aether
- No, the reflection will not appear. This is the
result predicted by the aether model, since light can
only travel at a set speed (3 × 108 m
s-1) through the aether. If the train is
travelling at that speed then the light cannot catch the
mirror to return as a reflection. Unfortunately, this
violates the principle of relativity, which states that
in an inertial frame of reference you cannot perform any
experiment to tell that you are moving.
- Yes, the reflection will be seen because, according
to the principle of relativity, it would not be possible
for the person in the train to do anything to detect the
constant motion with which he or she is travelling.
However, a person watching this from the side of the
track should see the light from your face travelling at
twice its normal speed!
Einstein decided that:
- the reflection will be seen as normal, because he
believed that the principle of relativity should always
- the person at the side of the track sees the light
travelling normally. BUT, this means that time passes
differently for you on the train and for the person at
the side of the track
- the aether mode; has nothing to do with it. Einstein
described it as superfluous.
the significance of Einstein’s assumption of the
constancy of the speed of light
- One of the fundamental postulates of the theory of
relativity is that all observers see light travelling at
the same speed c (3 ×
108 m s-1), regardless of their
motion. In the thought experiment described above, he
emphasised that the train traveller and the observer at the
side of the track must both see light travelling at the
same speed. This, however, means that time passes
differently for each observer.
that if c is constant then space and time become
- In classical physics, space (that is, position,
displacement and velocity, including the speed of light)
can be relative to an observer, but time is an absolute
quantity, passing identically for everybody.
In the theory of relativity, which assumes that
c is constant for all
observers, then time is relative as well as space. In
other words, time passes differently for different
observers, depending upon how fast they are moving.
In the thought experiment described above, both
observers see light travelling at the same speed,
c. However, the observer on the
ground sees the light travel twice as far to reach the
mirror. Since c = distance /
time, this must mean that the observer
outside the train saw the light take twice as long to
reach the mirror. In other words, as seen from outside
the train, time inside the train has slowed down.
the concept that length standards are defined in terms of
time in contrast to the original metre standard
- The metre was defined in 1793 for the first
time, when the French government decreed it to be one
ten-millionth of the length of the Earth's quadrant
passing through Paris. After this arc was surveyed
(incorrectly), three platinum standards were made along
with several iron copies.
- When the Systeme Internationale (SI) of units was set
up in 1875, the metre was defined to be the distance
between two lines scribed on a single bar of
- The current definition of the metre is much more
precise and accessible. One metre is defined as the length
of the path travelled by light in a vacuum during the time
interval of 1/299 792 458 th of a second. This modern
definition takes advantage of the constancy of the speed of
light, as well as the capability technology has given us to
measure time and the speed of light with great precision.
- The light-year is another length standard defined in
terms of time and the speed of light. It is equal to 9.47
× 1012 km.
information to discuss the relationship between theory
and the evidence supporting it, using Einstein’s
predictions based on relativity that were made many years
before evidence was available to support it
- When analysing this information you should identify and
explain how data supports or refutes the predictions that flow from a proposed
- A proposed theory usually needs experimental evidence before it is taken
seriously. An example of this from the preliminary course, also mentioned
in HSC topic 9.4, is Maxwell’s theory of electromagnetic radiation,
proposed in 1865 and not really adopted until Heinrich Hertz provided some
experimental evidence more than twenty years later, in 1887.
- When Einstein proposed his special theory of relativity in 1905, the experimental
and technological capability to verify the predictions did not exist. When
he proposed his general theory of relativity (this theory included gravity
and acceleration) in 1915, there was no evidence available to support it.
Only four years later in 1919 the general theory of relativity was able to
be used to explain the anomalous perihelion precession of Mercury. The British
astronomer, Eddington announced that observations of stars near the eclipsed
Sun confirmed general relativity's prediction that massive objects bend light.
It arose from observations of star light passing close to the sun, possible
only at the time of total solar eclipse. An slight apparent shift in the position
of a star could be accounted for by applying the general theory.
- As technology improved in the twentieth century, relativity theory predictions
- Some other pieces of experimental evidence that became available in the
years that followed are:
- the flying of atomic clocks to determine the existence of time dilation
- the dilated lifetimes of mesons penetrating the Earth’s atmosphere
- the energy yield from converted mass in nuclear reactions
- the observed increase in the mass of particles accelerated to near-light
speed, in devices such as particle accelerators.
- As a consequence of relativity theory successes, and the continuing failure
of any experiments to demonstrate the existence of the aether, its existence
was no longer required.
qualitatively and quantitatively the consequence of special
relativity in relation to:
- the relativity of simultaneity
- the equivalence between mass and
- length contraction
- time dilation
- mass dilation
The relativity of simultaneity
- If two events in different places are judged by one
observer to be simultaneous then they will not generally be
judged to be simultaneous by another observer in a
different reference frame in relative motion. In other
words, whether or not two events are seen by you to be
simultaneous depends upon where you are standing.
- Try this thought experiment offered by Einstein:
A train is fitted with light operated doors. The light
fitting is in the centre of the roof, and is operated by a
train traveller standing in the middle of the floor. When
the train is travelling at half the speed of light, the
train traveller turns on the light. The light travels
forwards and backwards with equal speed and reaches both
doors at the same time. The doors then open, and the train
traveller sees them opening simultaneously. An observer
standing outside the train watches this happen, but sees
the back door opening before the front. This is because the
back door is advancing on the light waves coming from the
light, while the front door is moving away from the light
The equivalence between mass and
- The rest mass of an object is equivalent to a certain
quantity of energy. Mass can be converted into energy under
extraordinary circumstances and, conversely, energy can be
converted into mass. For example, part of the mass is
converted into energy in nuclear fission reactions. When a
particle and its anti-particle collide, the entire mass is
converted into energy.
- Einstein’s famous equation expresses the
equivalence between energy, E and
mass, m: E =
mc2. The amount of energy given
off in a nuclear transmutation is related by this equation
to the amount of mass “lost”.
- In Special Relativity, the Law of Conservation of
Energy and the Law of Conservation of Mass have been
replaced by the Law of Conservation of
- The length of an object measured within its rest frame
is called its proper length (Lo). Observers in
different reference frames in relative motion will always
measure the length (Lv) to be shorter.
- The equation that expresses this is
- For example: A train that is measured to be 100 metres
long when at rest, travels at 80% of the speed of light
(0.8 c). A person inside the
train will measure the length of the train to be 100 m. A
person standing by the side of the track will observe the
train to be just 60 metres long.
Another consequence of the theory of Special Relativity
is that the mass of a moving object increases as its
velocity increases. This is the phenomenon of mass
dilation. It is another expression of the
mass-energy equivalence and is represented mathematically
- m = relativistic mass of particle,
- m0 = rest mass of
- v is the velocity of the particle relative
to a stationary observer and
- c = speed of light.
- This effect is noticeable only at relativistic speeds.
As an object is accelerated close to the speed of light its
mass increases. The more massive it becomes, the more
energy that has to be used to give it the same
acceleration, making further accelerations more and more
difficult. The energy that is put into attempted
acceleration is instead converted into mass. The total
energy of an object is then its kinetic energy plus the
energy embodied in its mass.
- To accelerate even the smallest body to the speed of
light would require an infinite amount of energy, all the
energy of the universe, plus a whole lot
“more”. Thus material objects are limited to
speeds less than the speed of light.
Web sites that demonstrate the
consequences of relativity:
Relativity Tutorial Ned Wright, UCLA Astronomy
Faculty, California, USA
C-ship: Relativistic ray traced
images Fourmilab, Switzerland
Sample problem 1 – Length
contraction and Time dilation
An alien spacecraft streaks past the Earth at 0.90
c. As it does so it flashes a
sign that reads, “We come in peace”, for 2.0
seconds. The spacecraft measures 55 metres long when at
- the length of the spacecraft as observed from
- the time for which the sign flashed as observed
Sample problem 2 – Mass
dilation and Energy
A space probe has a rest mass of 2000 kg.
- Calculate its mass after acceleration to 0.75 c and
after further acceleration to 0.90 c.
- Calculate the amount of energy that has been
converted to mass in accelerating the probe to
the implications of time dilation and length contraction for
- Recall from part 3 of this topic that current maximum
velocities do not allow for viable interstellar travel
because the travel times are prohibitively long.
- Provided that relativistic speeds could be reached, the
nearest stars should be able to be reached in several
years. For example, travelling to Alpha Centauri at half
the speed of light should take a little over eight years.
However, due to time dilation and length contraction, the
journey would take significantly less time.
- From the Earth’s point of view the clocks on the
spacecraft are moving slowly, so that less time passes on
the spacecraft compared to the Earth. From the point of
view of the spacecraft occupants, the length of the journey
has contracted to a significantly shorter distance, which
they cover in less time. In the example above, the
occupants record approximately seven years passing before
they arrive at their destination, rather than eight years.
- Accelerating to relativistic speeds would incur
considerable energy costs, due to the conversion of energy