Matter and Energy

Unit 4: Matter and EnergyChapter 11: Relativity

11.1 Relationship between Matter and Energy

11.2 Special Relativity

11.3 General Relativity

11.1 Investigation: Frames of ReferenceKey Question:

How does your frame of reference affect what you observe?

Objectives:

Explain how physicists define a frame of reference.

Set up an experiment to analyze frames of reference from the perspective of different observers.

The Relationship between Matter and Energy

According to Einstein’s formula, in a nuclear reaction, some mass is converted to energy.

The c2 factor means that even a tiny amount of mass is equivalent to a huge amount of energy.

Matter and energy

The speed of light (c) is 3 × 108 m/s, so the speed of light squared (c2) is 9 × 1016 m2/s2.

During the radioactive decay of carbon-14, a tiny amount of mass is converted to a relatively large amount of energy.

Einstein's formula

mc2

Mass (kg)

Energy (J) Speed of light

3.0 x108 m/sec

This equation tells us that matter and energy are really two forms of the same thing.

The speed of lightThe speed of light is so important in physics

that it is given its own symbol, a lowercase “c”.

When you see this symbol, remember that “c” is 300 million m/s, or 3 × 108 m/s.

The speed of light

Einstein’s theory of relativity says that nothing in the universe can travel faster than the speed of light.

If the Sun was to vanish, we would still see it in the sky for 8 minutes and 19 seconds.

Antimatter Up until the 1930s, scientists were confident that they

could explain all the elements with three subatomic particles, then they discovered antimatter.

Antimatter is the same as regular matter, except properties like electric charge are reversed.

Antimatter When antimatter meets an

equal amount of normal matter, both the matter and antimatter are converted to pure energy.

A bit of antimatter the size of a grain of sand would release enough energy to power a city for a week if it combined with an equal amount of normal matter.

Strange particles: neutrinos

Huge numbers of neutrinos are created by nuclear reactions in the Sun.

Neutrinos are lighter than electrons and are very difficult to detect.

Neutrinos are affected only by the weak force, so most neutrinos pass right through Earth without interacting with a single atom.

Particle accelerators

Other particles even heavier than the proton and neutron have also been found.

Physicists use high-energy accelerators to produce the heavy particles so we can study them.

Strange particles: quarks

Quarks come in different types and the lightest two are named the up quark and the down quark.

The six kinds of quarks are named: up, down, strange, charm, top, and bottom.

Today, we know that protons and neutrons are made of even smaller particles called quarks.

Unit 4: Matter and EnergyChapter 11: Relativity

11.1 Relationship between Matter and Energy

11.2 Special Relativity

11.3 General Relativity

11.2 Investigation: Special Relativity

Key Question:

What are some of the implications of special relativity?

Objectives:

Explore consequences of time dilation.

Calculate the equivalence of mass and energy using Einstein’s formula, E = mc2.

Special Relativity

The theory of special relativity describes what happens to matter, energy, time, and space at speeds close to the speed of light.

Simultaneity

When we say that two events are simultaneous, we mean they happen at the same time.

Since time is not constant for all observers, whether two events are simultaneous depends on the relative motion of the observers.

SimultaneityTwo lightning strikes

are simultaneous to the observer at rest, but the observer moving with the train sees the lightning strike the front of the train first.

Special Relativity

These effects are observed in physics labs:

1. Time moves more slowly for an object in motion than it does for objects that are not in motion. This is called time dilation.

2. As objects move faster, their mass increases.

3. The definition of the word “simultaneous” changes.

4. Space itself gets smaller for an observer moving near the speed of light.

Special Relativity1. Clocks run slower on moving

vehicles compared with clocks on the ground. By moving very fast, it is possible for one year to pass on a spaceship while 100 years have passed on the ground.

2. The closer the speed of an object gets to the speed of light, the more of its kinetic energy becomes mass instead of motion.

3. The length of an object measured by one person at rest will not be the same as the length measured by another person who is moving close to the speed of light.

Speed of light paradox

A paradox is a situation that does not seem to make sense.

A ball thrown from a moving train approaches you at the speed of the ball relative to the train plus the speed of the train relative to you.

The speed of light appears the same to all observers independent of their relative motion.

Speed of light paradox If the person on the train

were to shine a flashlight toward you, you would expect the light to approach you faster.

The light should come toward you at 3 × 108 m/sec plus the speed of the train.

Michelson and Morley found experimentally that the light comes toward you at a speed of 3 × 108 m/sec no matter how fast the train approaches you!

Speed, time, and clocks Einstein thought about

a clock that measures time by counting the trips made by a beam of light going back and forth between two mirrors.

A person standing next to the clock sees the light go back and forth straight up and down.

The time it takes to make one trip is the distance between the mirrors divided by the speed of light.

Speed, time, and clocks To the observer in the

space ship, the path of light is straight up and down.

To someone observing the spaceship, the light appears to make a zigzag because the mirrors move with the spaceship.

The speed of light must be the same for both observers, yet the person on the ground sees the light move a longer distance!

Speed, Time and Clocks

Atomic clocks In the early 1970s an experiment was performed

by synchronizing two precise atomic clocks.

One was put on a plane and flown around the world, the other was left on the ground.

When the flying clock returned home, the clocks were compared.

The clock on the plane measured less time than the clock on the ground. The difference agreed precisely with special relativity.

The twin paradox A well-known thought

experiment in relativity is known as the twin paradox.

Two twins are born on Earth.

They grow up, and one of the twins goes on a mission into space and travels at the speed of light.

Upon returning from a 2-year (ship time) trip, the astronaut is 2 years older than when she left.

However, her twin brother is 20 years older now!

Unit 4: Matter and EnergyChapter 11: Relativity

11.1 Relationship between Matter and Energy

11.2 Special Relativity

11.3 General Relativity

11.3 Investigation: General Relativity

Key Question:

What is Einstein’s theory of general relativity?

Objectives: Describe how the theory of general relativity builds

upon Einstein’s earlier explanation of special relativity.

Compare and contrast Newton’s ideas to Einstein’s explanations about the effects of gravity.

Research applications of general relativity

General relativity Einstein’s theory of general

relativity describes gravity in a very different way than does Newton’s law of universal gravitation.

Imagine a boy and girl who jump into a bottomless canyon, where there is no air friction.

On the way down, they throw a ball back and forth.

Reference frame

In physics, the box containing the boy and girl is called a reference frame.

No experiment the boy or girl do inside the box can tell whether they are feeling the force of gravity or they are in a reference frame that is accelerating.

Curved space-time

This equivalence of acceleration and gravity must also be true for experiments that measure the speed of light.

In order to meet both these conditions, Einstein deduced two strange things which must also be true.— 1. Space itself must be curved.— 2. The path of light must be deflected by

gravity, even though light has no mass.

Curved space-time

Consider rolling a ball across a sheet of graph paper.

If the graph paper is flat the ball rolls along a straight line.

A flat sheet of graph paper is like “flat space.”

Curved space-time

A large mass, like a star, curves space nearby.

If you roll a ball along this graph, its path bends as it rolls near this place where the graph is stretched by the mass.

Curved space-time If you look straight down on

the graph, the path of the ball appears to be deflected by a force pulling it toward the large mass.

You might say the ball “felt” a force of gravity which deflected its motion.

This effect of curved space is identical to the force of gravity.

Black holesTo understand a black hole, consider a

rocket trying to leave Earth.

If the rocket does not go fast enough, Earth’s gravity pulls it back.

If gravity becomes strong enough, the escape velocity can reach the speed of light.

A black hole is an object with such strong gravity that its escape velocity equals or exceeds the speed of light.

Black holes

The name black hole comes from the fact that no light can get out, so the object appears “black”. Because

Earth’s escape velocity is much less than the speed of light, light easily escapes its gravity.

Black holes and light

Black holesYou might think it would

be impossible to see a black hole but you can see what happens around a black hole.

Any matter that falls into a black hole gives off so much energy it creates incredibly “bright” (intense) radiation as it falls in.

Astronomers believe our own Milky Way Galaxy has a huge black hole at its center.

The Big Bang The best evidence indicates that

the age of the universe is about 13 billion years, plus or minus a few billion years.

If the universe is expanding, then it must have been smaller in the past.

Sixteen billion years ago, scientists estimate that cataclysmic explosion occurred and the universe started growing from a tiny point into the incredible vastness we now see.

Traveling Faster than Light

Some physicists are looking for loopholes in the laws of physics in the hope that one day, science fiction will become reality.

One idea being explored to bypass the light-speed barrier involves Einstein’s concept that space can be distorted into structures called wormholes.