3.12.3 Special Relativity

Question 1

Describe the Michelson-Morley interferometer setup.

Answer 1

Monochromatic light sent through a semi-silvered mirror at 45 degrees, splitting the light into 2 beams, both sent to their own mirror to be reflected back to the semi-silvered mirror, to both be sent to a detector to show an interference pattern of fringes.

Question 2

What is the role of the compensator in the Michelson-Morley experiment?

Answer 2

It makes up for the extra distance travelled by the beam of light reflected by 90 degrees at the semi-silvered mirror

Question 3

What is the ‘ether’?

Answer 3

A medium in space proposed to carry light waves.

Question 4

What was the point of the Michelson-Morley experiment?

Answer 4

To test the existence of an ‘ether’, by testing the speed of light waves travelling in different directions with the same distance to see if there was a motion changing the speed of one of the light waves.

Question 5

What was the result of the Michelson-Morley experiment?

Answer 5

After rotating the setup 90 degrees, the interference pattern did not change, showing the time taken for light to travel was unaffected by rotation of the apparatus.

Question 6

What conclusions were drawn from the result of the Michelson-Morley experiment?

Answer 6

1. The ether doesn’t exist (or the Earth drags the ether along with it as it moves)
2. The speed of light is invariant in free space

Question 7

What are inertial frames of reference?

Answer 7

Those which move at constant velocity relative to each other, so a frame accelerating or rotating cannot be an inertial frame of reference.

Question 8

What does Einstein’s theory of special relativity apply to?

Answer 8

Inertial frames of reference.

Question 9

What are the two postulates of Einstein’s theory of special relativity?

Answer 9

1. The speed of light in free space is invariant
2. The laws of physics have the same form in all inertial frames

Question 10

Explain what is meant by the postulate ‘the speed of light in free space is invariant’.

Answer 10

The speed of light is independent of the motion of the source or the observer.

Question 11

Explain what is meant by the postulate ‘the laws of physics have the same form in all inertial frames’.

Answer 11

The laws of physics will act in the same way in all inertial frames of reference.

Question 12

What is time dilation?

Answer 12

A consequence of special relativity, meaning it only occurs in inertial frames, and causes time to run at different speeds depending on the motion of an observer.

Question 13

What is meant by a stationary observer?

Answer 13

Someone stationary relative to the frame of reference where an event is occurring.

Question 14

What is meant by an external observer?

Answer 14

The perspective where the frame of reference is in motion.

Question 15

What is the proper time (t0)?

Answer 15

The amount of time passed experienced by the stationary observer during an event.

Question 16

What does v represent in the special relativity equations?

Answer 16

The velocity at which the stationary observer is travelling.

Question 17

Which will always be smaller, the proper time or the time measured by an external observer?

Answer 17

The proper time will always be shorter than the time measured by an external observer.

Question 18

What provides experimental evidence for time dilation?

Answer 18

Muon decay, as muons enter the atmosphere at very high speeds and so experience significant time dilation, affecting how quickly they decay.

Question 19

What is length contraction?

Answer 19

A consequence of special relativity, meaning it only occurs in inertial frames, and causes the length of objects moving at high speeds to appear shorter to an external observer.

Question 20

What is the proper length (l0)?

Answer 20

An objects length as measured by an observer who is at rest relative to the object.

Question 21

What property of an object remains constant during length contraction?

Answer 21

The width.

Question 22

What provides experimental evidence for length contraction?

Answer 22

Muon decay, as the muons are travelling at such a high speed the distance they travel will appear shorter than the distance as viewed by an external observer.

Question 23

What is the relationship between energy and mass as proved by the theory of special relativity?

Answer 23

Mass and energy are interchangeable, E=mc^2.

Question 24

Explain how the mass of an object is relative, in terms of energy transfer.

Answer 24

• Transferring energy to object will cause its mass to increase, while transferring energy away from an object will cause its mass to decrease
• Because of this, the faster an object travels, the more massive it becomes

Question 25

What does m0 represent?

Answer 25

The rest mass.

Question 26

When does the classical calculation of kinetic energy by using the formula 1/2mv^2 not apply to objects?

Answer 26

When objects are moving at relativistic speeds, over 1/10th of the speed of light.

Question 27

Why does the classical calculation of kinetic energy by using the formula 1/2mv^2 not apply to objects moving at relativistic speeds?

Answer 27

The mass of the object changes significantly.

Question 28

What does the total energy of a relativistic object consist of?

Answer 28

Kinetic energy and rest energy, E = Ek + E0

Question 29

What is the formula for the kinetic energy of a relativistic object?

Answer 29

• Ek = E - E0
• Ek = (m0c^2)/√(1-v^2/c^2) - m0c^2

Question 30

What did Bertozzi’s experiment provide experimental evidence for?

Answer 30

The increase in mass of an object with speed.

Question 31

Describe the setup of Bertozzi’s experiment.

Answer 31

• Particle accelerator which could emit electrons at varying kinetic energies
• Two detectors, A and B, connected to an oscilloscope
• Aluminium plate connected to a temperature sensor

Question 32

Describe Bertozzi’s experiment.

Answer 32

1. Electrons released in pulses, the time taken for them to travel between detectors A and B calculated using oscilloscope by measuring distance between peaks on the display (and multiplying by the time base)
2. Distance between A and B measured and speed of the electrons calculated
3. Electrons directed at aluminium target, colliding with it to transfer their kinetic energy to the target in the form of heat
4. Change in temperature of the target measured using temperature sensor, so the kinetic energy of the electrons could be directly measured

Question 33

What is the formula for the kinetic energy of one electron?

Answer 33

Ek = mc∆θ/n

Question 34

What was the result of Bertozzi’s experiment?

Answer 34

When the results were plotted as a graph of kinetic energy against speed, the values were very close to those predicted by Einstein’s theory of special relativity, so the experiment provided evidence to support it.

Question 35

Why can an object not reach the speed of light according to special relativity?

Answer 35

As an object’s speed approaches the speed of light, its mass approaches infinity, so its energy approaches infinity, which is impossible as you cannot have an infinite amount of energy.