Physics 12

MODERN PHYSICS: AN INTRODUCTION

http://www.youtube.com/watch?v=ajhFNcUTJI0

QUOTE AND CLIP OF THE DAY:

Bodies and forces, especially Newton's laws of motion and the principles of mechanics based on them

Physics that does not make use of quantum mechanics or the theory of relativity.

But many theories in classical physics break down when applied to extremely small objects such as atoms or to objects moving near the speed of light.

At the end of the 19th century it looked as if Physics was pretty well “wrapped up”!?

CLASSICAL PHYSICS

Since roughly 1900, new discoveries have caused significant paradigm shifts

Includes the advent of quantum mechanics (QM) and of Einsteinian relativity (ER).

Physics that incorporates elements of either QM or ER (or both) is said to be modern physics.

MODERN PHYSICS:

Modern physics is often encountered when dealing with extreme conditions. Quantum mechanical effects tend to appear when dealing with "lows" (low temperatures, small distances)

Relativistic effects tend to appear when dealing with "highs" (high velocities, large distances)

The "middles" being classical behaviour.

MODERN PHYSICS:

Special Theory of RelativityGeneral Theory of RelativityQuantum Theory

MAJOR MODERN PHYSICS THEORIES

EINSTEIN

Perimeter Institute Everyday Einstein: GPS and Relativity Complete WS # 3 and 4

A PRACTICAL APPLICATION:

are just a way of saying that sometimes different people will say different things about the motion of the same object

http://www.amnh.org/learn/pd/physical_science/week2/frame_reference.html

There are two types of frames of reference often referred to in physics: Inertial and Non Inertial

(Inertia: resistance of an object to change its state of motion)

KEY CONCEPT: FRAMES OF REFERENCE

Non accelerating Newton’s 1st law and other laws of physics are valid For example:

Inside a bus moving at constant velocity with a ball inside

INERTIAL FRAME OF REFERENCE

Accelerating Newton’s 1st law does not hold For example:

If you are in the bus when it starts to slow down (accelerating backward) the ball seems to be accelerating forward inside the bus. No external force has acted on the ball so how can it be accelerating?

There appears to be an external force because we see it from an accelerated frame of reference inside the bus (non inertial frame).

NON-INERTIAL FRAME OF REFERENCE

Einstein Physical theory of space and time developed based on the

postulates that all the laws of physics are equally valid in all frames of reference moving at a uniform velocity and that the speed of light from a uniformly moving source is always the same, regardless of how fast or slow the source or its observer is moving.

Introduced a new way to view: Space Time Simultaneity

SPECIAL THEORY OF RELATIVITY

Once upon a time……

FIRST A BIT OF BACKGROUND:

MAXWELL’S EQUATIONS:

Maxwell demonstrated that electric and magnetic fields travel through space in the form of waves at the speed of light in 1865

When scientists (other than Maxwell) were originally looking at electric and magnetic fields generated by charges (in a vacuum), they came up with some equations to predict the strength and direction of these fields.  It turned out that some constants were required in the equations to get the field strengths right. 

Maxwell came along and (in addition to fixing one equation), he put them together and realized that combining the equations resulted in two "wave equation" which predicted that the electric and magnetic fields were waves.

Maxwell continued….

The important idea is that the speed of light is independent of the velocity of the sources of light!

Prior to experiments by Michelson and Morley, it was assumed that light needed a medium to propagate through

This medium was called the “luminiferous ether” and Michelson and Morely set out to test for the presence of this ether

They used an interferometer, which is a device designed to measure wavelengths of light

MICHELSON-MORLEY EXPERIMENT

Prevailing theories held that ether formed an absolute reference frame with respect to which the rest of the universe was stationary.

It would therefore follow that it should appear to be moving from the perspective of an observer on the sun-orbiting Earth.

As a result, light would sometimes travel in the same direction of the ether, and others times in the opposite direction.

The interferometer consists of a: Light source Beam splitter (half silvered mirror) Mirrors (one fixed, one adjustable) Screen

The goal was to observe interference patterns between light waves

INTERFEROMETER

Michelson and Morley set the apparatus so that one beam was travelling parallel to the ether and the other was travelling perpendicular to the ether

They then rotated the apparatus and attempted to measure changes in the interference patterns

Unfortunately, they were unable to observe a change in interference patterns that they expected due to the motion of the earth

Michelson and Morley’s results remained a mystery until Einstein published his special theory of relativity

MICHELSON-MORLEY RESULTS

In 1905 Albert Einstein proposed that we accept the fact that the speed of light was the same in all reference systems

Einstein’s theory of special relativity requires giving up some long held “common sense” ideas about space and time that we have held over the centuries.

But it had the advantage that it embodies both theory (Maxwell) and experimental results (Michelson and Morley) in rejecting an absolute reference frame.

ENTER EINSTEIN: 1905

Based on his consideration of Maxwell’s lack of a frame of reference, Einstein proposed his special theory of relativity based on two postulates:

1. All physical laws must be equally valid in all inertial (non-accelerated) frames of reference

2. The speed of light through a vacuum will be measured to be the same in all inertial frames of reference

THE SPECIAL THEORY OF RELATIVITY

Time Dilation:

The term time dilation applies to situations in which time intervals appear different to observers in different inertial frames of reference.

It is only when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light) that time dilation becomes important.

2

2

0

1cv

tt

As a result, we end up with two times:Δt – dilated time (seconds)

Δt0 – proper time (seconds)

v – velocity of moving frame of reference (m/s)

c – speed of light (m/s)

TIME DILATION

The proper time could be thought of it as the “rest time,” where the event is at rest, although this term is not generally used. Another way to picture it is as the “one-point” time, the time for an observer who sees the clock as staying at only one point.

Example 1:

A rocket speeds past an asteroid at 0.800 c. If an observer in the rocket sees 10.0 s pass on her watch, how long would that time interval be as seen by an observer on the asteroid?

Proper time!

Lorentz Factor:

Is the factor by which time, length, and "relativistic mass" change for an object while that object is moving

is often written as gamma to SAVE TIME!!!

This number is determined by the object's speed in the following way:

2

2

1

1

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Note: that for small speeds, γ is approximately 1 thus, no time dilation

So…..

0tt

Page 819 Questions 1-3

TRY IT :

Another Relativistic Effect: Length Contraction

In a way that is similar to time changes depending on the frame of reference, length is also affected

An observer at rest (relative to the moving object) would observe the moving object to be shorter in length.

Length Contraction:

http://www.physicsclassroom.com/mmedia/specrel/lc.cfm

Note: only affects distances parallel to motion!

Muon

is an elementary particle similar to the electronOn Earth, most naturally occurring muons are created by

cosmic rays, which consist mostly of protons, many arriving from deep space at very high energy

About 10,000 muons reach every square meter of the earth's surface a minute; these charged particles form as by-products of cosmic rays colliding with molecules in the upper atmosphere.

These particles are created about 9000m above the surface of the Earth and travel at about 0.998c

Example: Muon

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scd

tvd

stcc

st

cv

tt

9000

)30(998.

30

)998(.1

2

1

2

2

2

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The muon is an unstable subatomic particle with a mean lifetime of 2.0 µs (measured from earth). These particles travel at about 0.998c. What distance does the muon travel over its lifetime?

According to time dilation, the muon’s half-life should be 30μs in the muon’s frame

As a result, the muon can travel a .998c for 30μs covering a distance of 9000m

stcc

st

cv

tt

30

)998(.1

2

1

2

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Example: Muon

According to length contraction, the distance that the muon needs to move through (measured in the frame of reference of the Earth) should be 600m in the muon’s frame.

Use the info from the previous slide to prove this!

Thus, the Earth rushes towards the muon at .998c for 2μs covering a distance of 600m

md

scd

tvd

mLc

cmL

c

vLL

600

)2(998.

600

)998(.19000

1

2

2

2

2

0

mLc

cmL

c

vLL

600

)998(.19000

1

2

2

2

2

0

Try it

Page 824 Questions 4-6

http://www.youtube.com/watch?v=30KfPtHec4shttp://www.youtube.com/watch?v=G-R8LGy-OVs

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