# Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light

 BikiCrumbs: Current and em…ission of light

## Students learn to:

#### 1. Outline the features of the aether model for the transmission of light

• The aether was thought to be the medium that light travelled trough.
• The aether filled all space.

In the 2003 HSC Notes from the Examination Centre - Physics, Question 18(a) the examiners comment on the difference between features and properties of the aether.

#### 2. Describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether

• Michelson and Morley attempted to measure the ether wind, similar to the wind caused when a car travels through still air. The experiment was set up as shown above, with an interference pattern showing up on the inferometer. The experiment was then rotated 90 degrees with the idea being that the aether wind would affect the path of at least one of the light beams causing a different interference pattern to appear. The interference pattern observed was the same. This null result meant that the aether was not acting in this experiment and as such was not necessary for light to propagate.

• Michelson and Morley attempted to measure the relative speed of the earth through the aether, a substance conjectured to be the medium in which light is propagated, that filled all space. Their method involved splitting a beam of light, from a single source into two beams that travelled perpendicular to each other. The two beams were brought together and shown on a screen, creating an interference pattern. If the earth moves relative to the aether, then the speed of one beam will be different from that of the other, just as the speed of a boat going first upstream and then downstream is different from that of a boat travelling across the stream. The difference in speed of the two beams would alter the interference pattern, when the apparatus is rotated through 90degrees. No such alteration was found. This and similar failures to detect the motion of the earth through the aether led later to the development by Einstein of the special theory of relativity, and the subsequent abolishment of the aether theory.

#### 3. Discuss the role of the Michelson-Morley experiment in making determinations about competing theories

The Michelson-Morley experiment made determinations about the aether theory because they provided evidence against it. It was not until Einstein, however, that the null result was explained and the aether model disproven.

#### 4. Outline the nature of inertial frames of reference

It is a non-accelerating frame of reference where Newton’s First Law is obeyed.

#### 5. Discuss the principle of relativity

Galilean relativity states that the same laws of physics apply in stationary frames of reference and frames of reference with a constant velocity.

Newtonian relativity states that in an inertial frame of it is impossible to disinguish between moving at a constant velocity and being stationary.

Einstein’s special relativity had two postulates: -the laws of physics are the same in all inertial frames of reference -the speed of light is constant and is independent of the velocity of the source or the observer

#### 6. Describe the significance of Einstein’s assumption of the constancy of the speed of light

This assumption explained the null result of Michelson-Morley and showed that the aether was not necessary. It also suggests that nothing can travel faster than the speed of light. This assumption also allowed Einstein to propose his theories of time dilation, length contraction and mass dilation.

#### 7. Identify that if c is constant then space and time become relative

In classical physics space is relative to the observer, but time is constant. In the theory of relativity, time becomes relative as well as space. This means that time passes differently for different observers, depending upon their velocity. If a man is sitting in a train travelling at c and looks into a mirror he will see his reflection. If an outside observer looks into the train they will see the light travel twice as far to reach the mirror. If c is constant this means that time slows down inside the train according to the outside observer as c=distance/time.

#### 8. Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard

Up until recently the metre was defined as the distance between two marks on a platinum-iridium bar in Paris. But now the definition of the speed of light as well as the definition of a second have become more accurate than our definition of the metre. So now the metre is defined as the distance travelled by a beam of light in a vacuum in 1/c seconds. As such the speed of light has been set at a given number of metres per second, so as our measurements become more accurate our definition of the metre will be revised, while c will remain constant. This also means that the metre is the same for any frame of reference, meaning that it is unaffected by length contraction and time dilation.

#### 9. Explain qualitatively and quantitatively the consequences of special relativity in relation to:

##### -Relativity of simultaneity

The Relativity of Simultaneity

If two flashes of light occur at the same distance from a person, that person will judge these two events to be simultaneous. Another person standing in another position may not judge these events to be simultaneous. Therefore simultaneity is dependent upon the frame of reference.

When a flash of light is emitted from person A, they should see the light hit the two ends at the same time. This is because the speed of light is constant irrelevant of the frame of references motion. However person B will see things differently, he will see the light reach the back of the train before it hits the start of the train, this is because the back of the train has moved closer to the source and the front of the train has moved away from the source.

Equivalence between mass and energy

The rest mass of an object is equal to a certain quantity of energy. In nuclear reactions this mass can be converted into energy, and conversely energy can be converted into mass according to E = mc2. The Laws of Conservation of Mass and Energy are now replaced by the Law of Conservation of Mass-Energy in special relativity.

Length contraction

The length of an object at rest is known as its proper length (L0), and this length is contracted (Lv) when the object’s velocity approaches the speed of light. This is expressed by the equation:

$l_v = l_0 \sqrt{1 - \frac {v^2}{c^2}}$

Time dilation

The time for an event to occur in the rest from is called to, but observers in different frames of reference will judge this time to be longer (tv). This is expressed by the equation:

$t_v = \frac {t_0}{\sqrt{1 - \frac {v^2}{c^2}}}$

Mass dilation

As the velocity of an object increases, so does its mass. This mass change is only really noticeable at speeds close to c. The mass varies according to the equation:

$m_v = \frac {m_0}{\sqrt{1 - \frac {v^2}{c^2}}}$

Where:

m0 = rest mass

mv = relativistic mass

#### 10. Discuss the implications of mass increase, time dilation and length contraction for space travel

Mass increase means that if a particle was accelerated to the speed of light it would have infinite mass, so to accelerate it to this point would require infinite energy, which is an impossibility. Therefore an object cannot be accelerated to the speed of light.

Time dilation means that if someone were to take a journey to a distant star at say 0.8c and the trip seemed to take 17 years on the Earth, the man in the spacecraft would only experience 10 years passing. This means that it is theoretically possible to travel to stars thousands of light years away within a lifetime of an astronaut if a spacecraft can be accelerated close to the speed of light, however, when they returned to earth, they would find that hundreds of years would have passed.

As the spacecraft accelerates to faster and faster speeds the length it has to travel becomes shorter.

## Students:

#### 1. Perform an investigation and gather first-hand or secondary data to model the Michelson-Morley experiment

This may have reference to a boat analogy where boats travel in different directions but the current of the water will affect their velocity. A swimmer swimming with the current would have trouble returning, whereas a swimmer swimming perpendicular to the current would have trouble on both the way to and back. An observer on a riverbank would thus see that the swimmer swimming perpendicular would have traced an open triangular path.

#### 2. Perform an investigation to help distinguish between inertial and non-inertial frames of reference

This can be determined by allowing a pendulum to hang, and then dropping an object from the pivot of the pendulum, if there is an angle between the two then your frame of reference is non-inertial.

#### 3. Analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and discuss the relationship between thought and relativity

One limitation of thought experiments is that their outcomes often rely upon common sense, and sometimes new areas of science don’t make immediate sense. This was particularly true in Einstein’s case, but his only choice to experiment at near light velocities was thought experiments.

The following is one of Einstein’s most famous thought experiments:

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? There are two possible outcomes:

• No. This answer is in keeping with the aether model because light can only travel at a set speed, but violates the principle of relativity which states that when in inertial frame of reference you cannot conduct any experiment to tell if you are stationary or moving at a constant velocity.
• Yes. Because according to Newtonian relativity, in an inertial frame of reference it is impossible
• since light moves at a constant velocity time must pass differently inside and outside the train
• the aether is superflous

#### 4. 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

Any theory, no matter how logical it may seem, cannot stand without experimental evidence. This also holds true in Einstein’s case, where proof for his theory of relativity only came later with particle accelerators and nuclear reactors. Examples of proof include:

• Two extremely accurate atomic clocks were sycronised. One remained on the Earth’s surface while the other was flown around the world in jet aeroplanes. When the second clock returned there was found to be a slight difference in time between the two. This indicates that time dilation has occurred.
• Many muons can be detected at sea level, but the trip from the upper atmosphere to the surface would take longer than the muon’s lifetime at the speed it is travelling. This also suggests that time dilation and length contraction have occurred.
• The fact that energy can be produced from fission reactions verifies energy-mass equivalence.

#### 5. Solve problems and analyse information using:

E = mc2

$l_v = l_0 \sqrt{1 - \frac {v^2}{c^2}}$

$t_v = \frac {t_0}{\sqrt{1 - \frac {v^2}{c^2}}}$

$m_v = \frac {m_0}{\sqrt{1 - \frac {v^2}{c^2}}}$