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9.2 Space: 4. Current and emerging understanding about time and space

Syllabus reference (October 2002 version)
4. Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light	Students learn to: outline the features of the aether model for the transmission of light describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether discuss the role of the Michelson-Morley experiments in making determinations about competing theories outline the nature of inertial frames of reference discuss the principle of relativity describe the significance of Einstein’s assumption of the constancy of the speed of light identify that if c is constant then space and time become relative discuss the concept that length standards are defined in terms of time in contrast to the original metre standard explain qualitatively and quantitatively the consequence of special relativity in relation to: the relativity of simultaneity the equivalence between mass and energy length contraction time dilation mass dilation discuss the implications of time dilation and length contraction for space travel	Students: gather and process information to intrepret the results of the Michelson-Morley experiment perform an investigation to help distinguish between non-inertial and inertial frames of reference analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and discuss the relationship between thought and reality analyse 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 solve problems and analyse information using:

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 28 Aug 03]

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.

outline the features of the aether model for the transmission of light

• 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 luminiferous aether.
  
  
• The list of properties included the following. The aether should:
  • 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 light waves.

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.

describe and evaluate 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 interference.
  
  
• 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.

discuss 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 theory.
  
  
• 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 correct.
  
  
• 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).

perform an 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 as follows:
  • 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 accelerometer.

outline 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.

discuss 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, your velocity.

analyse and interpret 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:

describe 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.

identify that if c is constant then space and time become relative

• 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.

discuss 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 platinum-iridium alloy.
  
  
• 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.

analyse 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 theory.
  
  
• 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 became testable.
  
  
• 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.

explain qualitatively and quantitatively the consequence of special relativity in relation to:

• the relativity of simultaneity
• the equivalence between mass and energy
• 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 waves.

The equivalence between mass and energy

• 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 Mass-Energy.

Length contraction

• The length of an object measured within its rest frame is called its proper length (L_o). Observers in different reference frames in relative motion will always measure the length (L_v) 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.

Time dilation

• The time taken for an event to occur within its rest frame is called the proper time (t_o). Observers in different reference frames in relative motion will always judge the time taken (t_v) to be longer.
  
• The equation that expresses this is
  
• For example: A traveller on a train with a speed of 0.8 c, picks up and opens a newspaper. The event takes 1.0 second as measured by the train traveller. As observed by a person standing by the side of the track the event takes 1.7 seconds.

Mass dilation

• 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 as:
  
  
  where
  • m = relativistic mass of particle,
  • m₀ = rest mass of particle,
  • 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 Tutoria Ned Wright, UCLA Astronomy Faculty, California, USA

C-ship: Relativistic ray traced images Fourmilab, Switzerland

solve problems and analyse information using:

• 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 rest.
  
  Calculate:
  1. the length of the spacecraft as observed from Earth, and
  2. the time for which the sign flashed as observed from Earth.

  Solution
  
  

• Sample problem 2 – Mass dilation and Energy
  
  A space probe has a rest mass of 2000 kg.
  1. Calculate its mass after acceleration to 0.75 c and after further acceleration to 0.90 c.
  2. Calculate the amount of energy that has been converted to mass in accelerating the probe to 0.90c.

  Solution

discuss the implications of time dilation and length contraction for space travel

• 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 into mass.