Time Dilation Graph: Variables & Lorentz Contraction

[nicekarmajobs]

Can anyone tell me what exactly do the variables "Time Dilation" and "Velocity of a fraction of the speed of light" represent (in this graph) from the lorentz contraction?

http://www.fourmilab.ch/cship/figures/gr_timedial.gif

Does the x-axis represent "v/c" or is it "v^2/c^2"? What does the y-axis represent? Which "t"? Or is it one "t" over another?

 

[kuruman]

Both axes represent dimensionless quantities. The x-axis is v/c, what some textbooks call β. The y-axis is, as you say, "one t over another". More simply, it is the relativistic factor

[tex]\gamma=\frac{1}{\sqrt{1-v^2/c^2}}[/tex]

I guess what you are supposed to take home from this graph is that when v/c is greater than 0.95 or so, the time dilation factor starts getting really noticeable.

 

[kerimek]

The variables "Time Dilation" and "Velocity of a fraction of the speed of light" in the graph represent two important concepts in Einstein's theory of relativity: time dilation and Lorentz contraction.

Time dilation refers to the phenomenon where time appears to pass slower for an object moving at high speeds compared to an observer at rest. This is represented by the y-axis in the graph, which shows the ratio of the time experienced by the moving object (t) to the time experienced by the observer at rest (t0). As the velocity of the object increases, the time dilation also increases, meaning that time appears to pass slower for the moving object.

The x-axis in the graph represents the velocity of the object (v) as a fraction of the speed of light (c). This is commonly referred to as the "beta" factor, where beta = v/c. The x-axis can also be interpreted as the ratio of the velocity squared (v^2) to the speed of light squared (c^2). This is because the time dilation and Lorentz contraction equations involve the square root of 1 - (v/c)^2.

Lorentz contraction, also known as length contraction, is the phenomenon where an object moving at high speeds appears to be shorter in the direction of motion compared to an observer at rest. This is represented by the ratio of the length of the moving object (L) to the length of the object at rest (L0) on the y-axis. As the velocity of the object increases, the Lorentz contraction also increases, meaning that the object appears to be shorter in the direction of motion.

In summary, the x-axis represents the velocity of the object as a fraction of the speed of light and the y-axis represents the ratio of time or length experienced by the moving object compared to an observer at rest. Both of these concepts are important in understanding the effects of high velocities on time and space, as described by the theory of relativity.