[Physics Class Notes] on Time Dilation Pdf for Exam

We define time as an ordered arrangement of defined events, rather than a continuous flow of experience in an indivisible continuity.

Time dilation meaning in the theory of special relativity is the “slowing down” of a clock as seen by an observer who is in relative motion with respect to that clock.

As we are all familiar with the concept of time; however, very few know about time dilation. 

On this page, we will discuss time dilation theory with the time dilation equation and time dilation formula.

Time Dilation Definition

As we know that time is something that we all are familiar with. For instance, 60 seconds is one minute and 80 minutes is 1hr 20 min, 24 hours in a day, and so on. This is called linear time, which is something we are familiar with and agree with.

Also, in the above text, we understand that in terms of Physics and Einstein’s theory of relativity, the difference in the time elapsed between two clocks is the ”time dilation.”

We also say that time dilation refers to a special relative state that time can pass at varying rates in diverse reference frames. Also, it depends upon the velocity of one frame of reference comparative to another.

In simple words, in terms of Physics and Relativity, time dilation is a measure of the elapsed (passed) time that we measure using two clocks. 

In the time dilation theory, we refer to two reference frames, the first is the proper time, i.e., one-position time, and observer time or two-position time. Besides, both of them are interconnected and we can find the time dilation of one frame reference if we know the velocity and speed of another frame.

Time Dilation

Do you know how time dilation occurs? Or do you know the concept of time dilation and length contraction? If not, let’s understand how.

Time dilation occurs either because of the relative velocity between the two frames of reference or due to a difference in gravitational potential between their locations (gravitational time dilation taken from general relativity). When undetermined, “time dilation” refers to the effect due to velocity.

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Time Dilation Formula

Let’s suppose that in a reference frame, the time between the events is called proper time or one-position time and is labeled as Δt0.

Now, in another reference frame, the observer sees the two events occurring in a different position. Furthermore, in the observer’s reference frame the time between two events is known as observer time or two-position time, which is labeled as Δt. 

Besides, the observer time will always be greater than the proper time. We consider this effect of time as time dilation. Most noteworthy, we can measure both Δt0 and Δt.

The time dilation formula is given as;

[text{Observer Time }= frac{text{Proper Time (Two – Position Time)}}{sqrt{1-(frac{v^{2}}{c^{2}})}}]…..(1)

Here,

Δt = the two-position time or observer time, measured in seconds

​Δt0 = the one-position time or proper time, measured in seconds

v = is the velocity in meter per second, measured in m/s.

c = refers to the speed of light that is equal to 3 x 10⁸m/s.

The time dilation equation (1), expresses the fact that the moving observer’s period of the clock  Δt0 is longer than the period Δt in the frame of the clock itself.

Because all clocks that have the prevalent period in the resting frame should have a common period when observed from the moving frame reference, while all other clocks, like the mechanical, electronic, optical should exhibit the identical velocity-dependent time dilation.

Black Hole Time Dilation

This has consistently been something troublesome for us to comprehend. The way we consider it is that even though we can’t see past the event horizon, we realize that black holes or dark openings exist because of the properties, for example, gravitational lensing, which is identified with time dilation. 

This time dilation identifies with how we legitimize/justify not having the option to see past the event horizon of a dark opening/black hole. To the extent of data misfortune, it references the matter that the actual black hole body is shaped from.

Also, the outside observer would see the star begin to collapse and then evaporate without ever seeing a black hole shape if they wait long enough. Since the information initially found in the star has been transformed into thermal radiation, the information issue still remains.

Fun Fact

In the wake of compensating for varying signal delays because of the changing distance between an eyewitness and a moving clock (for example Doppler impact), the spectator will quantify the moving clock is ticking more slowly than a clock that is very still in the observers’/eyewitness’ own reference outline. Likewise, a clock that is near an enormous body (and which hence is at lower gravitational potential) will record less slipped by time than a clock arranged further from the said gigantic body (and which is at a higher gravitational potential). 

These forecasts of the hypothesis of relativity have been over and over affirmed by tests, and they are of common sense worry, for example in the activity of satellite route frameworks, for example, GPS and Galileo. Time dilation has likewise been the subject of sci-fi works.