4. Current and emerging understanding about time and space

has been dependent upon earlier models of the transmission of light

Outline the features of the aether model for the transmission of lightLight 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

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

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.

Question 5Michelson 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.

Gather and process information to interpret the results of the Michelson-Morley

experiment

Jacaranda Experiment 5.1

Tennis balls and fan from Zealey

Lasers and mirrors

Outline the nature of inertialframes of reference

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.

Perform an investigation to helpdistinguish between non-inertialand inertial frames of reference

Jacaranda Experiment 5.2 using data-logger and motion sensor

All steady motion is relative and cannot be detected without reference to an outside point

Discuss the principleof relativity

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 objectthen 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 luminiferous aether

is superfluous

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– the equivalence between mass and energy– length contraction– time dilation

Analyse and interpret some ofEinstein’s thought experiments involving mirrors and trains

anddiscuss the relationship between thought and reality

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.

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!

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

Analyse information to discussthe relationship between theoryand the evidence supporting it,

using Einstein’s predictionsbased on relativity that were

made many years beforeevidence was available to

support it

Discuss the concept that length

standards are defined in terms

of time with reference to theoriginal meter

Originally 1x10-7 times lengthof Earth’s quadrant passing through Paris then two marks on a bar. Now uses constancy of c and accuracy of second to define:

Does a theory need evidence to support it?

How long after Einstein’s theories wereatomic clocks able to verify them?

Identify the usefulness of discussing space/time, rather than

simple space

Account for the need, when considering space/time, to define

events using four dimensions

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

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 (gets bigger) (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.

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.

Solve problems and analyseinformation using:

Lv = L0(1- v2/c2)

and

tv = t0 / (1 – v2/c2)

Where

L0 = the length of an object measured from its rest frame

Lv = 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 time

tv = time taken as seen from the frame of reference in relative motion to the rest frame

Discuss the implications of 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.

Solve problems and analyse

information using:

Lv = L0(1- v2/c2)

and

tv = t0 / (1 – v2/c2)

L0 = the length of an object measured from its rest frame

Lv = 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 time

tv = time taken as seen from the frame of reference in relative motion to the rest frame

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

Gather, process, analyseinformation and use available evidence to discuss the relative

energy costs associated with

space travel