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Science
Physics
Quiz 4 Notes
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Terms in this set (34)
Einstein's Theory of Relativity
Very fast moving objects (special & general relativity)
Principles of Relativity
Laws of nature does not depend on where you are or how fast you move.
Example: The speed of light is the same everywhere (300,000 km/s)
Consequences: Time, Length, and Mass depend on where you are and how fast you move.
Galilean Relativity
Suppose the ball is moving 20m/s forward in the airplane reference frame, and the plane is moving at 300m/s in the ground reference frame.
How fast is the ball moving measured from the ground?
The ball & airplane are in relative motion - they move at different speeds with respect to the ground.
A: 300 m/s + 20 m/s = 320 m/s
The Principle of Relativity
Every non-accelerated observer observes the same laws of nature. In other words, no experiment performed within a sealed room moving at an unchanging velocity can tell you whether you are standing still or moving.
Example: If you were in an airplane without windows, and it was moving at a STEADY SPEED, you would not be able to tell if you were moving or not.
Principle of the Constancy of Lightspeed
The speed of light (and of other electromagnetic radiation) in empty space is the same for all non-accelerated observers, regardless of the motion of the light source or of the observer.
Every observer has to see a light beam move at speed c regardless of observer's motion.
Special Theory vs. General Theory
General theory allows for accelerated observers, while special theory only allows for non-accelerated observers.
Special Theory of Relativity
Made up of the two principles: principle of relativity, and the constancy of light.
Relativity of time
Time is relative to the observer, there is no single "real" or "universal" time in the universe.
Ex: Light clock - Velma and Mort both have a light clock, but Velma is moving and Mort is at rest. From Velma's perspective the light travels at speed c. From Mort's perspective, the light in Velma's spaceship travels slower than his light clock. This is because the time moves slower when moving than stationary.
Time Dilation
Moving clocks run slower from the perspective of an observer at rest. Moving light clock takes more time to tick than one at rest.
Time Travel
If time slows down when you're moving close to the speed of light, time should go backwards if you move faster than the speed of light aka travel back in time. If you fly as the speed of light, you can even travel to the future.
Twin Paradox
Measuring time from different perspectives.
Example: Mort and Velma have identical 10-minute ice-cream cones. Velma passes Mort at 75% of light speed. Times measured by Mort for his and Velma's cone to melt is 10 minutes for him, and 15 minutes for her.
Relativity of Simultaneity
Simultaneity is relative, not absolute. Observer riding on a train will see the light reaches the front and end at the same time. Observer outside the train will see the light reaches the front and end at a different time.
In order to measure a distance, we need to measure two positions simultaneously (otherwise things might shift positions.) This theory tells us that distance is relative.
Spacetime
Space and time are intertwined within each other.
Event - is a point in spacetime (position and time)
Length Contraction
Things in motion looks shorter than when at rest.
Length Contraction + Time Dilation
These two combined explain why time seems to "slow down" in the light clock.
Because the moving light clock is actually a shorter distance, it may seem like it's traveling a bigger distance (since light travels at the same speed) but it doesn't. Watch the video to clarify this.
https://www.youtube.com/watch?v=ttZCKAMpcAo
Relativistic Mass
Relativity predicts that the amount of inertia (mass) is larger for a moving object. Mass is relative to rest mass.
Rest Mass
Light has a zero rest mass - anything that moves at the speed of light has zero rest mass. Anything that has rest mass move always slower than the speed of light.
When v = c, m is infinite.
Simultaneity
Time - Time Dilation
Space - Length Contractions
Mass - Relativistic Mass
Energy & Mass
Energy has mass, and mass has energy. Any kind of energy you put into an object will increase it's mass. (Stretching a rubber band, lifting an object, etc.) As an object speeds up, we get kinetic energy, and the MASS of the object increases as well.
You can increase a system's mass by lifting it (giving it grav. e), stretching it (elastic e), and warming it (therm. e).
Einstein's Formula: E = mc^2
The Principle of Mass-Energy Equivalence
Energy has mass in the form of inertia. And mass has energy in the ability to do work.
Special Relativity Summary
1) moving clocks run slow (time dilation)
2) moving objects are shorter (length contraction)
3) moving objects have more mass
4) mass is energy and vice versa (E=mc2)
Quiz Question: You are in a spaceship moving past Earth at nearly light speed and you observe Mort, who is on Earth. You measure his mass, pulse rate, and size. How are they different from the values measured by Mort himself?
A: Mass has increased, pulse rate has slowed down, and size is reduced along the direction of motion.
Tips on Relativity
1) Consider the observer or measurer is always in
the rest frame. (even if he/she is riding a
spaceship!)
2) "The moving object" has to be moving relative to
the observer. (even if he/she is waiting on Earth!)
3) Then find the time/length/mass/energy of a
moving object measured by the observer.
Equivalence Principle
No experiment performed inside a closed room can tell you whether you are at rest in the presence of gravity or accelerating in the absence of gravity.
An acceleration is equivalent to the force of gravity. The effects of an accelerating reference frame cannot be distinguished from the effects of gravity.
The basic principle of general relativity.
General Relativity
Theory of gravitation, that observed gravitational effect between masses results from their warping of spacetime.
Answers the question about what accelerated observers experience.
Gravity bends light
Acceleration cannot be distinguished from gravity. In an accelerated frame, light pathways can be bent.
Therefore: Gravity should bend light - gravitational lensing.
The path of light is described as the "straightest possible" path.
Curved Spacetime
Space and Time are measured in terms of light. However, light can bend as well - Spacetime itself is bent/curved/warped by gravity.
The path of a light beam is the straightest possible path.
Curved Space
In curved space, the notion of straightness is different from the flat space.
For example, on the surface of a sphere, two lines start out parallel and extend as "straight" lines will meet.
Mass/Energy in Spacetime
Mass or Energy warps the fabric of spacetime. Light follow the "straight line" inside the warped fabric of spacetime.
Ex: The mass of the sun causes spacetime to curve, so freely moving objects (such as planets and comets) follow the straightest possible paths allowed by the curvature of spacetime. This explains why planets move in circles around the earth - not because of gravity holding them in their orbits, but because Earth simply falls freely along the warped spacetime.
Einstein's Equation
Matter tells space how to curve, and space tells matter how to move.
General relativity tells us that the spacetime is not just a fixed passive background in nature. But it is an active participant of the universe.
Quiz Question: Since accelerations are equivalent to gravity, a person could cancel the effect of Earth's gravity by...
1. Orbiting Earth
2. Falling from a high place, such as a diving board or airplane.
Earth's gravity does not cancel out completely, but you can cancel out the feel of the gravitational pull.
Gravitational Time Dilation
Gravity wards spacetime - clocks run slowly in a strong gravitational field. THEREFORE, clocks in satellites run faster than clocks on Earth.
Near stars, clocks run slowly.
Black Holes
It is a region of spacetime having a very strong
gravitational field so that nothing (even light) can
escape.
(Small) Black holes are formed from a dead body of
a massive star. (>30 solar mass) First form a
supernova, and then gravitationally collapse to a
BH.
It is believed that every galaxies has supermassive
black hole (million solar mass) in the center.
Event Horizon
Event horizon: "point of no return." Beyond the event horizon, nothing can escape. It can be considered as a 'surface' of a black hole.
As one approaches the event horizon, body gets stretched by huge tidal force.
The clock runs slower and slower as it gets near the horizon, compared to the far outside. It becomes infinitely slower when the clock is at the horizon!
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