Special Relativity

Time Dilation, The Twins Paradoxand Mass-Energy Equivalence.

Classical Relativity

1,000,000 ms-1 1,000,000 ms-1

■ How fast is Spaceship A approaching Spaceship B?

■ Both Spaceships see the other approaching at 2,000,000 ms-1.

■ This is Classical Relativity.

Einstein Postulates that c is a universal constant

• All measurements of Light Speed gave same value.

• Did not seem to matter whether we were moving towards or away from light source.

• This means that you will ALWAYS measure light at same speed.

• You cannot ride along with the light beam.• He also derives the equation E = mc2

Einstein’s Special Relativity

1,000,000 ms-1

0 ms-1

300,000,000 ms-1

Both spacemen measure the speed of the approaching ray of light. How fast do they measure the speed of light to be?

Special Relativity

• Stationary man– 300,000,000 ms-1

• Man travelling at 1,000,000 ms-1

– 301,000,000 ms-1?– Wrong!

• The Speed of Light is the same for all observers

Time Travel!

• Time between ‘ticks’ = distance / speed of light

• Light in the moving clock covers more distance…– …but the speed of light is constant…– …so the clock ticks slower!

• Moving clocks run more slowly!V

7

v = 0.8c

v = 0.9c

v = 0.99c

v = 0.9999c

Relativistic Mass• E = mc2

• Objects have energy due to their mass!• If objects get more energy the mass must

increase!• TRUE OR FALSE:– An object has more mass when you heat it up.– An object has more mass when you lift it up high.– An object has more mass when it is moving.

Relativistic Mass• E = mc2

• Objects have energy due to their mass!• If objects get more energy the mass must

increase!• TRUE OR FALSE:– An object has more mass when you heat it up.– An object has more mass when you lift it up high.– An object has more mass when it is moving.

ALL TRUE!

Relativistic Mass• When you fuse hydrogen to make helium the

resulting nucleus is lighter than the parts used• When you break Uranium apart the resulting

products are lighter than the original nucleus.• This “Mass Defect” accounts for energy

released in nuclear reactions.• Also explains why you cannot accelerate

objects to light speed.

Explanation of the Lorentz Transformations

• Man on the train sees light take this path:

Explanation of the Lorentz Transformations

• Man on the train sees light take this path:

• We see the light take this path

Explanation of the Lorentz Transformations

• Man on the train sees light take this path:

• We see the light take this path• Which is longer because of the train’s motion

Explanation of the Lorentz Transformations

• Man on the train sees light take this path:

• We see the light take this path• Which is longer because of the train’s motion

ct2

vt1

ct1

• Light always travels at c• We see train moving (hence t1)• Pythagoras’ theorem tells us:

Derivation of Time Dilation.

OR

OK, so this is WRONGBUT…

The Lorentz Transformations

• Time does appear to slow down for travellers:

The Lorentz Transformations

• Time does appear to slow down for travellers:

• You always “think” that your reference frame is stationary!

• You will never see see another person move faster – they always appear slower.

Let’s try an example

• Suppose a muon is created in the upper atmosphere (they are, btw).

• It has a lifetime of 2.2 x 10-6 seconds.

• How far can it travel? (assume it travels at c)

Let’s try an example

• Suppose a muon is created in the upper atmosphere (they are, btw).

• It has a lifetime of 2.2 x 10-6 seconds.

• How far can it travel? (assume it travels at c)

• So how come we see them 100,000 meters below?

“I wish I was a muon too”

• If a muon knows it is travelling fast…

• And It travels through the atmosphere (which is 100,000 meters thick)

• And it has already had the diagnosis (that it only has 2.2 μs to live)

• Does it “think” that it can exceed light speed?