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Chapter 15 – Special Relativity Space and Time

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Chapter 15 – Special Relativity Space and Time

- The Nature of the Universe
- The universe began 13.8 billion years ago with the “big bang”. At this moment in time, all of the matter and energy in the universe was confined to a single point of unimaginable density.
- Evidence for this:
- * cosmic radiation background
- * measurements of the expansion
- rate of the universe
- * mathematical models
- The “big bang”, referred to as inflation by physicists, was the moment that both time and space began in our universe. Inflation of space continues to this day.

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- Space-Time
- Newton and others believed that the universe was uniform and infinite.
- Einstein reasoned that space and time are two parts of a whole called space-time
- “ When you stand still, then all your traveling is through time. When you move a bit, then some of your travel is through space and most of it is still through time. If you were somehow able to travel through space at the speed of light…all your traveling would be through space, with no travel through time!”
- (p. 213-214)

- The Speed of Light
- How fast does light travel?
- 300,000 km/sec
- or
- 186,000 miles/sec
- At this speed you would make 7.5 trips around the earth in one second!
- However, space is vast and distances are very large. The time it takes for light to travel from our sun to the earth is about 8 minutes. Light takes 4.2 years to travel from the nearest star (Alpha Centauri) to the earth.

Relative Motion

- The speed at which a baseball catcher catches a baseball thrown from a truck depends on the relative motion of the truck. The combined velocity of the baseball + truck is greater when the truck moves moves towards the catcher and less when the truck moves away from the catcher.
- This is NOT TRUE FOR LIGHT. A beam of light will always travel at 300,000 km/s, regardless of how fast the source is moving towards or away from the observer!

Postulates of Special Relativity

1) “All the laws of nature are the same in all uniformly moving frames of reference” – p. 217

2) “The speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer” – p. 218

Consequences of Special Relativity

Time Dilation:

Time slows down for a traveler the faster you go.

The twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.

Consequences of Special Relativity

2) Length Contraction:

A traveler moving near the speed

of light holds a meter stick. A

stationary observer will see the

traveler’s meter stick to be less

than 1 meter long.

A baseball that travels at near the

speed of light will become shorter

in the direction that it travels.

Consequences of Special Relativity

2) Increased mass:

As a traveler moves faster

And faster, the mass of the

traveler increases.

At the speed of light, the mass

of an object becomes infinite.

This is the reason you cannot

travel faster than the speed of

light, since it would take an

infinite amount of energy to

accelerate an object with infinite

mass beyond the speed of light.

Summary:

Postulates of Special Relativity:

1) “All the laws of nature are the same in all uniformly moving frames of reference” – p. 217

2) “The speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer” – p. 218

Consequences of Special Relativity:

Time Dilation

Length Contraction

Increased Mass