Bell Ringer If you were to wake up on the bus and could not see out any of the windows, would you be able to tell if you were moving or not?

Special Relativity

Special Relativity vs General Relativity In 1905, Albert Einstein developed his Theory of Special Relativity –How we move through a space changes on how we move through time Special relativity refers to motion through a space at constant velocity General relativity refers to accelerated motion through a space

Space-Time Einstein reasoned that space and time are two parts of one whole called space-time From the viewpoint of special relativity, we travel through a combination space and time –When we stand still, we are only traveling through the time portion of space-time –When we move a bit, we travel through both aspects of space-time

Space-Time If we could somehow travel through space at the speed of light, no time would elapse in our own perspective Whenever we move through space, we alter our rate of moving through time –Time Dilation: The stretching of time an object experiences as it approaches the speed of light

Summary of Space-TIme When you stand still, you are traveling at the maximum rate in time: 24 hours per day If you traveled at the maximum rate through space (the speed of light), time would stand still

Motion is Relative Whenever we discuss motion, we must pick a reference point –Usually we refer to motion relative to the surface of the earth –Example: On a bus, you may travel 0 mi/h relative to the seat, but 60 mi/h relative to the road outside Speed is a relative quantity, meaning its value changes based on location, or frame of reference

Motion is Relative The speed of an object coming from a moving reference frame: –Add the speed of the object itself to the speed of the reference frame v ball = 40 mph (relative to the ground) v truck = 0 mph (relative to the ground) Catcher catches ball at 40 mph

Motion is Relative The speed of an object coming from a moving reference frame: –Add the speed of the object itself to the speed of the reference frame v ball = 40 mph (relative to the ground) v truck = 20 mph (relative to the ground) Catcher catches ball at 60 mph

Motion is Relative The speed of an object coming from a moving reference frame: –Add the speed of the object itself to the speed of the reference frame v ball = 40 mph (relative to the ground) v truck = -20 mph (opposite direction of ball) Catcher catches ball at 20 mph

The Speed of Light is Constant Light does not behave like the baseball thrown from the truck No matter what the speed of the source of the light, light will always travel toward an observer at the same speed –If light is a constant, then space and time must be a single unit –Altering the rate of one will alter the rate of the other

The Speed of Light is Constant The speed of light is found to be the same in all frames of reference, moving or not Represented by the variable, c c = 3 x 10 8 m/s (in a vacuum)

Postulates of Special Relativity First Postulate: All laws of nature are the same in all uniformly moving frames of reference –i.e. The behavior of a coin when flipped on a plane that is moving at constant velocity is no different than if flipped while standing still No experiment confined in the moving reference frame itself can determine whether or not there is uniform motion

Postulates of Special Relativity Second Postulate: The speed of light, c, in empty space will always have the same value regardless of the motion of the source or observer.

Time Dilation Light Clock: A flash of light bounces back and forth between parallel mirrors and “ticks” equal intervals of time

Time Dilation Consider a light clock observed from someone inside a fast-moving space ship –This observer would see the light bouncing vertically up and down Consider a light clock observed from someone outside a fast-moving space ship –This observer would see the light moving along a diagonal path, which is therefore longer

The Twin Trip Consider identical twins: –One twin takes a high speed round-trip journey –The other twin stays on Earth When he returns, the traveling twin will be younger than his stay-at-home twin –i.e.) Traveling at 50% c, 1.15 years will elapse on earth –i.e.) Traveling at 99.5% c, 10 years will elapse on earth

The Twin Trip If motion is relative, why wouldn’t the traveling twin come home to find the Earth twin younger than himself?

The Twin Trip The light flashes have less distance to travel as the ship gets closer to the receiver

The Twin Trip The light flashes have more distance to travel as the ship gets farther from the receiver

The Twin Trip

Therefore, both twins agree on the same results: –The Earth twin has aged more than the traveling twin The traveling twin experiences two frames of reference: One on the way out and one on the way back The Earth twin experienced a single, different reference frame They meet again at the same point in space, but never the same point in time

Space and Time Travel Before the theory of relativity, no one thought we could ever travel great distances in space –Our life span is too short to cover such great distances Today, because of time dilation, we know that time for a person on Earth is different than time for a person in a high-speed spacecraft –Problem: The amount of energy needed to propel a spacecraft near the speed of light is too great.

Space and Time Travel In the future, people may have the option to travel into space and return to a future century of their choosing These people could never come back to the same era they left –Time travels only one way – FORWARD Time and space, and therefore space-time, exist in the universe, not vice versa –Without the universe, there would be no space or time