If we were to return to Sheldon's first time on
the couch and saw Penny riding a skateboard past the scene,
Sheldon would see her in his reference frame.
Would Penny see the first moment he sits in that spot followed by
a 40-minute episode of Star Trek in the same order Sheldon experiences it?
Considering our previous discussion about slicing of space-time,
do you think all observers see the two events in
the same order or with the same time interval between the events?
Let's explore this further using one of Sheldon's favorite objects, trains.
Sheldon is preparing for a trip on
the Napa Valley Wine Train in his favorite 1915 Pullman-Standard lounge car.
Ever the physicist, Sheldon would like to conduct
an experiment to test the consequences of a constant speed of light.
To do this, he sets up a light source in the center train car and has two of
his friends standing in his light detectors in
the caboose and the engine at either ends of the train.
While the train is in the station,
we say that it is at rest.
Here in the station,
Sheldon conducts his first experiment by flashing the light and
recording the arrival times that his friends measure at each end of the train.
Since the distance to the light source is the same from both friends,
they each detect the light at the same time.
We call this a simultaneous detection.
The train then leaves the station and begins
its journey traveling at a constant speed through the mountains.
Sheldon prepares the experiment again,
this time with the train in motion.
Since the train is traveling at a constant speed, once again,
the flash of light arrives at each of his friends at precisely the same time.
In both the stationary case and the one with the moving train,
the observers are at rest with respect to Sheldon and the light source.
As a result, they observe the pulses arriving simultaneously on each occasion.
Sheldon wants to know what his experiment would look like
if he was stationary with respect to a moving train,
so he gets off at the next stop.
He gets ahead of the train and get set up to redo
his experiment as the train passes at a constant velocity.
This time, the light source flashes the moment that it passes Sheldon.
Since the train is moving from left to right,
Sheldon observes the light pulse arrive at the caboose of the train
first followed by the arrival of the pulse at the engine of the train second.
Sheldon is puzzled, he observed the light pulse arrive at the back of the train first,
while his friends on board report that the light pulse arrives simultaneously.
In Sheldon's frame of reference,
the light pulses do not arrive
simultaneously even though his friend's frame of reference, they do.
This disagreement between observers is a result of light traveling at
a constant speed no matter how quickly the source of light moves.
This is called the relativity of simultaneity and it describes that
stationary and moving observers will report the order of
events differently depending on their proper motion with respect to one another.
As strange as it seems,
both Sheldon and his friends on the train are right.
In some cases, the order of events depends on the motion of the observer.
Einstein explained this through the concepts of length contraction and time dilation.
So, why don't observers in different reference frames agree on the order of events?
Well, think back to our block of cheese space-time analogy.
A moving observer relative to another observer actually slices up space-time differently.
Not only can they potentially see events in different order than other observers,
but they also measure length and time differently.
Have a look at this graph which represents space-time for a stationary observer.
A stationary observer sees objects as they naturally are and clocks run as expected.
However, a moving observer sees space-time through a different slice.
Here's what space-time looks like to a moving observer.
Both the moving observer's time axis and distance axis have shifted.
Physicists say that the time and space coordinates
are rotated due to the motion of the observer.
This is a convenient picture to paint,
but what other real observable effects of this skewed reference frame?
Well, earlier we mentioned that moving observers measure changes in length and time.
Length contraction is given by the equation,
L is equal to L zero times the square root of
one minus the velocity of the observer divided by the speed of light squared.
Well, this equation describes is how
the length of the object appears to a moving observer.
If I jump into a spacecraft,
and I'm moving at nearly the speed of light,
objects I observe will appear to shrink in my direction of motion.
Something like the [inaudible] would pass by the ship appearing to be almost as flat as a pancake.
It's not just length that changes though, time also changes.
Time dilation is given by the equation t is equals to t zero divided
by the square root of one minus the velocity
of the observer divided by the speed of light squared.
In this case, time is modified by dividing by these terms under the square root sign.
So, instead of decreasing,
the time observed by the moving observer increases.
So, the moving observers see all external clocks slowing down the faster they move.
Both length contraction and time
dilation are effects that are measured by a moving observer,
the faster the observer moves with respect to any object such as a clock,
the thinner it appears and the slower it ticks.
Hopefully, your head isn't spinning too much
yet because we have to discuss an important issue with special relativity.
Since a moving observer appears to be stationary in their own frame of reference,
who can we trust when we say that the lengths
have been contracted and the clocks have been slowed?
To illustrate this problem,
we need to introduce you to the twin paradox.
