wacky implications of relativity

Wacky Implications of Relativity

SPH4U – Grade 12 Physics

Unit 5

Relativity is strange…

Video link:http://www.youtube.com/watch?v=ev9zrt__lec

Time Dilation

Time is an interesting thing. What exactly is it? And how exactly does it work?

There is no such thing as absolute time.

Yet Another Thought Experiment

To illustrate, let us perform a thought experiment where two observers measure different time intervals for the same sequence of events.


A spaceship contains two parallel mirrors (which we call “top” and “bottom”) and a method of sending a pulse of light from the bottom mirror to the top, at right angles to the mirrors. Inside, on the bottom mirror the Lady of Physics has placed a clock that records a “tick” at the instant the pulse leaves the mirror and a “tock” when the pulse returns.


To the Lady of Physics, who is stationary next to the clock, the pulse of light goes up and down and she hears and “tick” and then a “tock”.


This happens whether or not the space ship is moving or at rest relative to the Earth.

We will choose this frame of reference as our ‘stationary’ frame and call it reference frame S. We will say it takes Δts seconds for the light pulse to travel from the bottom mirror to the top. Thus the distance between the mirrors is cΔts.


Now, let’s say the spaceship moves with speed v relative to an observer on Earth, Ms. Moncrief.

How will Ms. Moncrief see this event as occurring? Will she measure the time between a “tick-tock” to be the same length, shorter, or longer than the Lady of Physics measured it?


From Ms. Moncrief’s viewpoint the pulse takes a longer time interval to travel from the bottom mirror to the

top.


This is because in the same time that the pulse moves to the mirror, the spaceship moves a distance of vΔtm relative to Ms. Moncrief (We write Δtm because that is the time interval to go from the bottom mirror to the top in the moving reference frame).

Einstein’s Equations

According to Einstein’s second postulate, light has the same speed, c, for both observers. Using the Pythagorean theorem we can know that:


Thus, if we isolate Δtm we would get:


This tells us that for a v such that 0 < v < c, (ie: a non-zero velocity that is less than the speed of light) Δtm > Δts, or in other words the time as measured in the moving reference frame is greater than the time as measured in the stationary reference frame.


So the time interval observed by Ms. Moncrief moving relative to the mirrors is greater than the corresponding time interval seen by the Lady of Physics inside the ship. So… it’s as if more time passes on Earth than passed on the ship.

Ms. Moncrief would say that time slowed down on the spaceship.

The duration of a process as measured by an observer who sees the process begin and end in the same position is called the proper time.

The observation that time on a clock that is stationary with respect to an observer is seen to run slower than time on the clock that is stationary with respect to that observer is called time dilation.

It is called time dilation because it would appear to Ms. Moncrief that what started as a swift process (the tick and tock of a clock) slowed down significantly (ie. took longer) when the clock started moving at near the speed of light.

The Speed Limit

Notice that in the equation the denominator is only going to be a real number if we know that is positive.

In order for that to happen…

2

2

1c

v

tt sm

2

2

1c

v

The Speed Limit

The Speed Limit

Thus, Einstein could say that no material object can have a speed that is equal to or greater than the speed of light.

The Twin Paradox

Suppose one pair of young identical twins takes off from Earth and travels to a star and back approaching the speed of light.

The other twin remains on Earth.

The Twin Paradox

When the traveling twin returns to Earth, will he be older, the same age, or younger than the twin he left behind? Why?

The Twin Paradox

The twin in the spaceship will be younger than the twin on Earth. The twin on Earth is in the same frame of reference for the other twin’s whole trip. It isn’t a symmetrical situation because the twin that is traveling has to slow down, stop, turn around and speed up again – when he is accelerating or decelerating he is in a non-inertial frame of reference.

Read more about this on pg. 593

Length Contraction

Just as time is not the same in all frames of reference, length is not the same in all frames of reference.

Length Contraction

Relativistic Momentum

Homework

Read section 11.2 & 11.3 in your text. Add information from your reading into your notes.

Answer the following questions:Pg. 587 # 2, 3, 4Pg. 597 # 1, 2, 4

wacky implications of relativity

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