Notes to a video lecture on UNIZOR.COM
Is Time Absolute?
Since we discuss the Relativity in this course, let's discuss what exactly the term relativity means.
It is easy to see that a concept of a position is relative.
Consider a traveler on a cruise ship around the world who every day takes tea in the tea room at 5 o'clock.
From his perspective he takes his tea at the same place - in the tea room. But from a viewpoint of a person who lives in London the places are different because a cruise ship is moving along its course.
Another easy concept is a relativity of a movement. If an object A is attached to the ground, it's not absolutely at rest, as some observers might say, because the Earth is rotating around its own axis and around Sun.
If object A is positioned somewhere in space and object B is passing it, an observer at A might say that he is at rest and B is moving, while an observer at B can say that he is at rest and object A is moving.
Isaac Newton has built his theory of Mechanics with these principles in mind.
At the same time, to put his theory on a solid mathematical base he needed such entities as trajectory, speed, acceleration etc. - all those where we need to use time as a major component in calculations.
The time was understood then as something absolute, independent of position or motion, and the only progress in its understanding was to be able to measure it as precisely as possible.
Everybody intuitively understood that...
...except Einstein.
First of all, Einstein accepted as postulates two main principles developed by physicists up to 19th century:
Principle of Relativity which states that all physical processes, laws and equations must be identical in all inertial reference frames uniformly moving relative to each other
and
Principle of constancy of the speed of light in all inertial reference frames independently of their relative movements.
In other interpretation, the speed of light is independent of the speed of its source. It depends only on the properties of medium through which light propagates, like vacuum, air, glass etc.
Based on these principles, common sense logic and simple mathematics Einstein came to a conclusion that, if we continue considering time as absolute and identical in all reference frames, the second principle of constancy of the speed of light contradicts the Principle of Relativity.
This topic was discussed in the previous lecture Postulates of Theory of Relativity.
Here we will try to dig a little deeper into what time is.
Consider the following example.
A spaceship is flying with a speed of v=150,000,000 meters per second (m/s) away from the Earth.
Speed of light in the air inside a spaceship is c=300,000,000 m/s.
In the middle of a cabin of this spaceship we place a source of light capable to produce a short flash in all directions.
On two walls of this cabin, the front and the back, we install sensors that register the time the light reaches the wall. The distance from the center of a cabin to either wall is L=90 meters (m).
We do assume that all clocks are absolutely synchronous and show the same time on a spaceship.
According to the Principle of Relativity, an observer inside a spaceship should have no difference in timing of a ray of light reaching the front or the back of the spaceship walls, whether a spaceship is moving or not, and this time to the front wall Tfront should be the same as to the back Tback and equal to the length covered by a ray of light (90m) divided by a speed of light (300,000,000m/s), which is equal to 0.3 microsecond (μs). Both rays, issued towards the front and to the back, should reach the sensors simultaneously.
Tfront = Tback = 0.3μs
Observer on Earth sees it differently.
In his view the front of a spaceship moves away from the source of light, while the back of a spaceship moves toward it.
Therefore, by the time Tfront needed for light to reach the front wall, this front wall will cover the extra distance
Dfront = v·Tfront
During this same time Tfront the ray of light has covered the initial distance of L=90(m) to the wall plus extra distance Dfront that wall moved away from it because a spaceship moves, which brings us to an equation
c·Tfront = L + Dfront or
c·Tfront = L + v·Tfront or
Tfront = L/(c−v) =
= 90/150,000,000(s) = 0.6μs
Analogously,
Dback = V·Tback
c·Tback = L − Dback or
c·Tback = L − v·Tfront or
Tfront = L/(c+v) =
= 90/450,000,000(s) = 0.2μs
Times for light to reach the front and the back walls of a cabin are different
Tfront = 0.6μs
Tback = 0.2μs
The same two events, light hitting the front and the back walls of a cabin in a spaceship, that seemed simultaneous for an observer inside a spaceship, are not simultaneous from an Earth observer's viewpoint.
Let's make a small modification in our experiment and change the functionality of a sensor attached to the back wall of a cabin in a spaceship.
The time it's supposed to register will be registered with a delay of 0.1μs.
An observer on a spaceship will see that the timing for the light to reach the front wall is still 0.3μs, but the timing for the back wall will be greater by 0.1μs, that is
Tfront = 0.3μs
Tback = 0.4μs
The back wall sensor will show greater time than the front wall one.
Let's see it from the Earth observer's view point.
The front wall sensor functions as before,
Tfront = 0.6μs
The same delay in the back wall sensor will register time by 0.1μs greater than before, that is
Tback = 0.3μs
We have an interesting situation.
The same two processes happening on a spaceship (the light reaching the front and the back walls) take different time with one (the light reaching the back wall) taking longer (Tback=0.4μs) than another (Tfront=0.3μs) from the spaceship observer, but the opposite inequality (Tback=0.3μs is shorter than Tfront=0.6μs) between timing is observed from the Earth.
What is a longer process for a spaceship is taking shorter time for an observer on Earth.
Summary
Time is relative.
One observer can see two events as simultaneous, while another might see them as occurring at different times.
A process can take one time from one observer's viewpoint, but another observer might see it as taking longer or shorter time.
If one even precedes another from one perspective, from another perspective might be seen as occurring in reverse order.
TIME IS RELATIVE, as everything else in our Universe.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment