what is the shape of the worldline of an object at rest, when time is plotted on the vertical axis? This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you Relativity 103a: Galilean Relativity – Spacetime Diagrams. Following along are instructions in the video below:
To relativity 103 galilean relativity in depth in relativity 103. Well cover space time time diagrams the space time separation vector. The galilean transform and the euclidean metric tensor.
Later in the series. The metric tensor will help us understand black holes the expansion of the universe gravitational waves. And much more.
But for now were just going to study the simple metric tensor in euclidean geometry. Remember that in relativity. 101.
We stated the principle of galilean relativity. Which means that the laws of motion are the same in all inertial reference frames. An inertial reference frame is just a non accelerating.
Reference frame such as a scientist standing still on the ground or a car or a plane. Traveling by at a constant speed in galilean relativity. Different inertial frames.
Will disagree on an objects velocity momentum and kinetic energy. But they will agree on time space and size and mass as well as newtons laws of motion. And gravity.
Now i should mention that even though different observers will agree on the size of objects and. The space between objects denoted delta x . Different observers.
Will disagree on the position of objects denoted by x on its own the main goal of galilean relativity is to calculate the different quantities that people disagree on in different reference frames that way even if a scientist is doing a physics calculations while standing still on the ground. Other observers in different reference frames. Will still be able to agree on how the laws of motion cause objects to move even if they are doing calculations from different perspectives and end up with different numbers now of all these quantities that people in different reference frames will.
Disagree on the most important is the position of objects x . And to understand how observers disagree on position in galilean relativity. Well begin by studying spacetime diagrams.
A spacetime diagram is a tool for visualizing. The motion of objects in different frames of reference in this video. Were going to be using spacetime diagrams to study galilean relativity.
A spacetime diagram has time along the vertical axis increasing upward and position along the horizontal axis increasing to the right you might think this is pretty strange since most physics. Classes put time on the horizontal axis. But in relativity.
Were often interested in tracking the motion of objects to the left and right so it makes sense to have position on the horizontal axis. So that we can track left and right motion also whether you like it or not putting time on the vertical axis has become a standard convention in just about every relativity. Textbook.
At this point. So. Ill be following along with this convention.
And ill be putting time on the vertical axis lets look at our first example of motion in a spacetime diagram observer. 1. Is a scientist who is standing still lets say that the scientist starts at the origin at a position of zero meters.
If he stand still then 1 second later in time hell still be at a position of zero meters. Hell continue to stay at the same position at 2 seconds 3 seconds 4 seconds and so on so in this spacetime diagram. An observer who is standing still will simply travel in a vertical line.
They are traveling through time. But they are not traveling through space. And this path that the scientist follows in the spacetime diagram is called its world line .
Heres another example observer. 2. Is a car moving at a speed of 25 meters per second to the right if the car starts at the origin at a position of zero meters.
After 1 second. The car will have traveled 25 meters to the right. After 2 seconds.
Its position will be 50 meters to the right.
After 3 seconds. 75 meters to the right and so on and so forth. So we can see that in a spacetime diagram.
An object traveling to the right is represented by a diagonal world line pointing to the upper right now in our last example observer. 3. Is a plane is moving at 200 meters per second to the left this time.
Ive given myself more room on the left of the space time diagram to show the planes world line again. Lets say that the plane starts at the origin after one 1 second. It will have moved 200 meters to the left or in other words.
It has a position of negative 200 meters after 2 seconds. It has a position of negative 400 meters. So we can see that the plane is traveling very fast to the left and the world line follows.
A diagonal path moving up and to the left and because the plane is traveling so fast. The planes world line is closer to the horizontal than the cars world line. So to summarize spacetime diagrams objects that are not moving will have a completely vertical world line and objects that are moving at a constant speed will have a diagonal world line objects that are moving more slowly will have a world line.
Thats closer to the vertical and objects that are moving more quickly will have a world line thats closer to the horizontal. So hopefully you now understand how to use spacetime diagrams and world lines to help visualize the motions of objects through space and time. But there is one last.
Very important point i need to mention earlier. I said that when a world line is vertical it means the object is stationary and not moving. However.
According to galilean relativity. All motion is relative to something else and there is no special stationary reference frame. Thats at rest from the point of view of the scientist.
The scientist is stationary and the car is driving by to the right but from the point of view of the car. The car is stationary and the scientist is going by to the left along with the road and the entire neighborhood. So this spacetime diagram.
Where the scientist has the vertical world line and the car is moving off to the right is drawn from the scientists frame of reference. But it would be equally correct to draw a spacetime diagram from the cars frame of reference. Where the car is stationary with a vertical world line and the scientist is moving off to the left.
Even though these two spacetime diagrams look different they represent the exact same situation and the exact same physics just from different points of view. Heres another way to think about motion in different reference frames. In spacetime diagrams.
Lets say that as time passes by at each second. We take a photograph of all the objects in space as the seconds go by we end up with a series of photographs or time slices that can help us trace out the world lines of all the different moving objects. We can see here that the scientist has a vertical world line.
So this spacetime diagram represents. The frame of reference of the scientist since he is standing still now watch what happens if we slide all these photographs over to the left. We have managed to arrange the photographs so that the cars world line is now vertical.
The spacetime diagram is now drawn from the cars frame of reference here. The car is stationary and the scientist is moving to the left and the plane is traveling to the left even faster and we can also arrange the photographs so that the planes world line is vertical this shows the planes frame of reference where the plane is stationary. The scientist is traveling fast off to the right and the car is traveling to the right even faster.
So remember that we can always rearrange a space time diagram so that any object of our choice is stationary. All we have to do is rearrange the time slices to make that objects world line vertical remember that in galilean relativity. There is no special stationary frame of reference we can always change reference frames by sliding the time slices in our spacetime diagram back and forth.
So in summary. A spacetime diagram helps us track the motion of objects through space and time a vertical world line. Means.
The object is stationary and a diagonal world line means. The object is moving at a constant speed. A world line closer to the vertical.
Means. The object is traveling slower and world line closer to the horizontal means. The object is traveling faster also remember that there is no such thing as a special stationary frame of reference and we can always change the frame of reference in a galilean space time diagram by moving the time slices back and forth.
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