4. Current and emerging understanding about time and space

has been dependent upon earlier models of the transmission of light

Light travels as a wave so it needs a medium - the ‘aether’

The luminiferous aether:

•filled all of space, low density, transparent

•permeated all matter, but was completely permeable

•great elasticity to support and propogate light waves

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

It was not thought that waves could be transmitted through a vacuum. It was proposed that throughout the universe permeated an aether, through which light waves could travel. Michelson and Morley set out to measure the speed of light waves through the aether. They set up an apparatus that emitted in phase light waves that were split in two by a half-sivered mirror. The waves then travelled along two perpendicular paths and returned to a detector where they observed the interference pattern. Under the aether model the interference pattern should not have resembled that of light waves in phase. It did and the conclusion was that no observable difference in the speed of light through the aether could be determined.This method of comparing light waves involves the very sensitive effect of interference so it should accurately indicate any difference in velocity. Michelson and Morley further enhanced the validity by repeating the experiments many times and by investigating variables such as differing times of the day and year - all with the same result.

The null results in the Michelson-Morley experiments were a major factor in the acceptance by Physicists that the aether does not exist. The scientific community had accepted the aether theory and suggestions were even made that planets could drag the aether along with them and that objects contract in the direction of the aether wind. These suggestions did not survive closer scrutiny and the null result obtained by Michelson and Morley (and repeated by others since) provided the evidence to dispel the aether theory. This experiment also helped people accept Einstein’s idea that the aether was not necessary.

Michelson and Morley helped to dispel the aether model for the transmission of light. Explain what the aether model was and how they helped to dispel it.

5 3 marks

It was not thought that waves could be transmitted through a vacuum. It was proposed that throughout

the universe permeated an aether, through which light waves could travel. Michelson and Morley set

out to measure the speed of light waves through the aether. They set up an apparatus that emitted in

phase light waves that travelled along two perpendicular paths and observed the interference pattern.

Under the aether model the interference pattern should not have resembled that of light waves in phase.

It did and the conclusion was that no observable difference in the speed of light through the aether

could be determined. Einstein proposed that there is no aether and that the speed of light is constant

regardless of the frame of reference. Whilst he did not draw his conclusions from Michelson and

Morley’s experiment, their experiment helped the scientific community accept Einstein’s theory.

Jacaranda Experiment 5.1

Tennis balls and fan from Zealey

Lasers and mirrors

Interpret the results of the Michelson-Morley experiment

Using the telescope on an interferometer to view the returning light rays, an interference pattern is evident. The pattern observed indicated no shift of phase so the light rays had travelled at the same speed, showing no effect or existence of any ‘aether wind’.

an inertial reference frame is one which is stationary or moving at a constant velocity, so we expect all our laws of Physics to hold when we are stationary or at constant v. e.g. drop a ball in a stationary bus or bus moving at constant v and it will fall straight down.

We expect things to behave differently when we are in an accelerating reference frame - e.g. a dropped ball will not fall straight down if the bus you are in is accelerating or turning.

Jacaranda Experiment 5.2 using data-logger and motion sensor

Outline the nature of inertialframes of reference

Outline an investigation to help distinguish between non-inertial and inertial frames of reference

The plug and retort stand - stationary, constant v, accelerating, decelerating, rotating platform

Galileo put forward the idea that all steady motion is relative and cannot be detected without reference to an outside point.

Einstein's special theory of relativity deals with how we observe events, particularly how objects and events are observed from different frames of reference.

(1)(The relativity principle): The laws of Physics have the same form in all inertial reference frames

(1) makes perfect sense: an inertial reference frame is one which is stationary or moving at a constant velocity, so we expect all our laws of Physics to hold when we are stationary or at constant v. e'g. drop a ball in a stationary bus or bus moving at constant v and it will fall straight down.

We expect things to behave differently when we are in an accelerating reference frame - e.g. a dropped ball will not fall straight down if the bus you are in is accelerating or turning.

(2) is a bit more difficult to accept, because we would think that if light comes from a moving object then it would have more or less velocity depending on which way the source was moving. Well, it doesn't! - the speed of light is constant regardless of the motion of the source.

(2) (Constancy of the speed of light): Light propogates through empty space with a definite speed c independent of the speed of the observer

This principle applies only for inertial frames of reference and states that, from within such a reference frame, you cannot perform any experiment or observation to detect motion. The inference from this is that you could not perform an experiment to detect motion through the ether.

The luminiferous aether

is superfluous

Discuss the principleof relativity

Simultaneity

Two events which are simultaneous to one observer are not necessarily simultaneous to another observer.

e.g. A stationary train is passed by a very fast moving train.

You are standing in the middle of the stationary train.

Martin stands in the middle of the very fast moving train.

At the exact moment that Martin's train is in line with your train, one bolt of lightning hits the front of your train and another hits the back of your train.

You see both bolts at the same time (simultaneous).

Martin sees the bolt he is travelling towards slightly before the one he is travelling away from.

So simultaneity is relative, not absolute, suggesting that time is also not an absolute quantity.

Explain qualitatively and quantitatively the consequence of special relativity in relation to the relativity of simultaneity

Einstein used thought experiments involving mirrors and trains to illustrate relativity concepts. This allowed the reader to envision and understand ideas were not able to be investigated experimentally. Thought is thus used to model and analyse a reality which is not achievable with the technology of the day.

Martin sees the beam travel from Rebecca's starting point in space to where the mirror is in space (when the spaceship has moved along a bit) back to where Rebecca has moved to in space (when the spaceship has moved along even more).

The time that this takes is longer because it was a longer distance at the speed of light.

So time is relative.

Rebecca sees the beam travel a short distance to mirror and back.The time this takes is short, because it was a short distance at the speed of light.

Remember speed = dist/time so time = dist/speed

Martin on earth observes the beam travelling to the mirror and back.

e.g. Rebecca on the spaceship flashes a light beam to a mirror on the roof and back.

The constant speed of light means that for a spacecraft travelling near the speed of light, time passes more slowly when observed from outside the spaceship.

Explain qualitatively and quantitatively the consequence of special relativity in relation to time dilation

tv = t0 / (1 – v2/c2)

Now, since the speed of light is constant and time is relative, length must also change.

In fact as speed of an object increases, it appears to contract along the direction of motion.In the time it takes to register the rear of Rebecca's spacecraft, it will have moved a distance, d, so it appears to be not as long horizontally. There is no vertical motion so it is not shorter vertically.

For Rebecca on her spacecraft, she measure less time to travel from one point to another than Martin observes. If the speed of light is constant, Rebecca measures less distance from one point to another!

Explain qualitatively and quantitatively the consequence of special relativity in relation to length contraction

Lv = L0(1- v2/c2)

Explain qualitatively and quantitatively the consequence of special relativity in relation to mass dilation

The mass of an object appears to change when measured by someone in a different frame of reference. The relativistic mass does not increase much from the rest mass until light speed is approached, when the mass quickly becomes infinite. Further input of energy results in further mass increase, to the extent that enough energy can never be input to cause velocity to go past the speed of light. The force required to accelerate this amount of mass requires enormous amounts of energy - which creates even more mass!

The relativistic mass can be calculated using this equation:mv = m0 / (1 –

v2/c2)

Explain qualitatively and quantitatively the consequence of special relativity in relation to the equivalence between mass and energy

E = mc2

Objects travelling near the speed of light acquire extra mass as energy is input, so Einstein inferred that the mass contained the extra energy. So relativity gives the energy of a moving body as

E = K.E. + mc2

and for a stationary body (no kinetic energy)

E = mc2

This equation clearly shows that mass has an energy equivalent which can be calculated and that energy has a mass equivalent.

Question 2

The following diagram shows a train with a mirror attached to the roof. A flash gun on

the floor of the train explodes. A person is outside observing all that happens.

(a) Explain how this scenario supports the concept of time dilation.

(b) Describe an actual experiment that supports the concept of time dilation.

2 (a) 3 marks

Using the train as a reference frame, the light travels the distance from the flash gun

(f) to the mirror (m) and back again (f).

The person who is observing the train from the outside is in a different reference

frame. The train is moving forwards so that the position of the flash gun when the

light leaves is different to the position of the flash gun when it returns.

It has a greater distance to travel.

Given that the light is travelling at c in both reference frames, the time it takes for the

light to return to the flash gun will be longer in the person’s reference frame than in

the trains.

(b) 2 marks

Two very accurate hydrogen maser clocks were synchronised. One was flown around the world while the other

remained in the same spot on Earth. When the one that was flown around the world was compared with the one which had

remained on Earth, the one that remained on Earth had experienced a very small amount of time more

A theory can be postulated based on reason without supporting evidence and may exist until such time as it is proved or disproved. If a theory is proved it may become the accepted scientific teaching or law.

If it is disproved it may be discarded and a new theory may be postulated.

Einsteins predictions as to time dilation, for example, were not supported by evidence for many years until a maser clock could be flown around the world and compared to a clock which remained on

Earth.

Using the relationship that speed=distance/time

and the constant speed of light in a vacuum, any length can be precisely defined as the distance light travels in a vacuum during a

given time period.The meter was originally 1x10-7 times the length of the Earth’s quadrant passing through Paris, then it was two marks on a bar. Now the definition uses the constancy of c and accuracy of second to define:

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

Discuss the concept that length standards are defined in terms of time in contrast to theoriginal meter standard

Einstein’s assumption of the constancy of the speed of light is significant because it changes our perception of space and time.

Newtonian physics attributes the achievement of different distances observed in different reference frames to different relative velocities. But a constant speed of light

means that different distances must now be attributed to different times (TIME DILATION).

Similarly, different times in different frames of reference must now be attributed to different distances travelled (LENGTH CONTRACTION).

Ordinarily at low speed if we observe a change in the distance that an object travels in a certain time, it is because the relative velocity is different.

e.g. a bouncing ball on a high speed plane has a different relative velocity to someone on the plane and someone on earth watching it.

But light has no different relative velocities- it is constant! -- so time changes instead! The light observed on the plane travels a short distance so time is short (passed more slowly) . The light observed from the ground travelled a large distance so time was longer (passed more quickly).

Conversely, if we travel a distance in a shorter time, it's usually because we travel faster, but c is constant so d is less!

Time and space are not constant, but dependent on the motion of the observer. There is a continuum, where if one changes, the other is affected. The speed of light is the constant.

Four-dimensional spacetime

To the observer, it seems that when time dilates (i.e.gets bigger) (i.e.passes more slowly), length gets shorter, so time and space are intimately connected - space gets exchanged for time and vice-versa.

So any object is specified by four quantities, 3 to describe where in space and one to describe when in time. Although space and time are not the same, they are not independent of one another.

Describe the significance of Einstein’s assumption of the constancy of the speed of light and identify that if c is constant then space and time become relative

Question 5

Describe a thought experiment that illustrates time dilation. Discuss how

Einstein’s Theory of Relativity has led to a revision of the conservation of energy.

5 4 marks

Consider a flash gun in a fast moving vehicle with an observer inside and an observer outside. There is a mirror directly

above the flash gun. When the gun explodes, the observer inside will see the flash and then see it again once the image

has bounced off the mirror. It follows the path illustrated below and takes a certain amount of time to do this.

The observer outside will see the flash but since the vehicle is moving, the flash must travel a greater distance before it

is reflected off the mirror and back to the observer.

This will take a longer time, thus time is relative to the reference frame of an event. The difference between the times is

the time dilation.

This is part of Einstein’s theory of relativity. Einstein’s theory also describes that mass can be converted into energy.

Joule had proposed that energy is always conserved. Einstein introduced the concept that mass can be converted into

energy and vice versa.

Relativistic mass does not increase dramatically above the rest mass until near light speed, when the mass quickly heads towards infinity. Space

travel is thus unable to pass light speed because a great energy input is required to

cause acceleration and this energy input converts to even more mass.

Solve problems and analyseinformation using:

E = mc2

Lv = L0(1- v2/c2)

tv = t0 / (1 – v2/c2)

mv = m0 / (1 – v2/c2)

Where

L0 = the length of an object measured from its rest frameLv = the length of an object measured from a different frame of reference

v = relative speed of the two frames of referencec = speed of light

t0 = time taken in the rest frame of reference = proper timetv = time taken as seen from the frame of reference in relative motion

to the rest framem0 = the mass of an object measured from its rest framemv = the mass of an object measured from a different frame of reference

E = Energym = change in massDescribe

each of the quantities in the formulae above

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

Question 3 Hal is undertaking a return trip to Procyon which is 11.4 light years away to drop off some Cargo. He plans on travelling at a speed of 0.7c (where c is the speed of light).

(a) Discuss the difficulty of obtaining this speed with current technology. (b) Determine how much time Hal’s mother Beverley would have experienced while he was away (assume

that Hal’s space craft can achieve its maximum velocity very quickly and that he does not spend any significant time on Procyon).

(c) Determine how much time Hal would have experienced whilst on his return trip. (d) The time that Beverley experienced and the time that Hal experienced are different. However, if the

frame of reference is changed so that Beverley on the Earth is moving at 0.7c and Hal is stationary, it could be considered that Beverley has experienced less time than Hal. Discuss why this reference frame cannot be considered.

3 (a) 1 mark

The difficulty in obtaining this speed is the amount of fuel that would need to be

carried. Hydrogen and oxygen are currently used. The more fuel that is placed on the

rocket, the more mass the rocket has and that mass must be accelerated also. A speed

of 0.7c is not achievable because no rocket would be able to carry all the required

fuel.

(b) 1 mark

t = 11.4 x 2/0.7

t = 33 yrs

(c) 1 mark

tv = to/(1 – v2/c2)0.5

to = tv(1 – v2/c2)0.5

to = 33(1 – 0.72c2/c2)0.5

t0 = 23 yrs

(d) 1 mark

Hal does experience a longer time than Beverley because Beverley’s reference

frame is inertial. Hal’s reference frame is non-inertial and the general theory of relativity

must be applied to it. Only then can time from Hal’s reference frame be considered.

(b) 1 markLv = L0(1-v2/c2)0.5

Lv = 11.9(1 – 0.82c2/c2)0.5

Lv = 7.2 light years

Question 4

A rocket is travelling to the star Tau Ceti which is a distance of 11.90 light years away.

The rocket travels at a speed of 0.8c and the time taken to accelerate and decelerate is

negligible.

(a) Determine how many years the crew of the rocket will age as they travel to Tau Ceti.

(b) Determine the distance the crew will have travelled in light years.

4 (a) 2 marks

tv = s/v

tv = 11.9/0.8 = 14.9 yrs

t0 = tv(1-v2/c2) 0.5

t0 = 14.9(1 – 0.82c2/c2)0.5

t0 = 8.9 years

Solve problems and analyse

information using:

E = mc2

Lv = L0(1- v2/c2)

tv = t0 / (1 – v2/c2)

mv = m0 / (1 – v2/c2)

Where

L0 = the length of an object measured from its rest frameLv = the length of an object measured from a different frame of reference

v = relative speed of the two frames of reference

c = speed of light

t0 = time taken in the rest frame of reference = proper timetv = time taken as seen from the frame of reference in relative motion to the rest framem0 = the mass of an object measured from its rest framemv = the mass of an object measured from a different frame of reference

E = Energym = change in mass

Discuss the relative energy costs associated withspace travel