# Proper Time and Time Dilatation

• LCSphysicist
In summary, proper time is the time measured by a moving clock. The expression ##d \tau = \frac{d t}{\gamma}## shows that the proper time is less than the coordinate time, which may seem paradoxical. However, this is because in the frame where you are moving, time is dilated. In your rest frame, there is no such thing as an inherently "moving frame" and thus ##d \tau = d t##.
LCSphysicist
Homework Statement
I am a little confused with the concept of proper time
Relevant Equations
.
I am a little confused with the concept of proper time: Using the invariance of the distance square in the Minkowski space, we can get the expression ##d \tau = \frac{d t}{ \gamma}## Now the problem:

Aren't the proper time the time measured by a moving clock? That is, if i am moving with speed v and carries with me a clock, "my" proper time is the time elapsed in my clock, right?

But, to the best of my knowledge, the time elapsed in a moving frame shouldn't be dilated? The so called time dilatation, so why the proper time in the expression above is lesser than the coordinate time?

The expression above has a special frame?

In your rest frame, you are not moving, and thus ##\gamma = 1## and ##d\tau = dt##. There is no such thing as an inherently "moving frame", frames can only move relative to each other and you have to be careful in how you reference this.

In the frame where you move with speed ##v##, you indeed have ##d\tau = dt/\gamma## with ##dt## being the coordinate time differential in that frame.

docnet

## What is proper time?

Proper time is the time measured by an observer who is at rest relative to the event being observed. It is the time experienced by an object or person in its own frame of reference.

## How is proper time different from coordinate time?

Coordinate time is the time measured by an observer who is moving relative to the event being observed. It is the time measured by a clock that is synchronized with other clocks in the same frame of reference. Proper time takes into account the effects of time dilation due to relative motion.

## Why is proper time important in relativity?

Proper time is important in relativity because it is a fundamental concept that helps us understand the effects of time dilation and the relativity of simultaneity. It allows us to accurately measure time in different frames of reference and make predictions about how time is experienced by different observers.

## How is proper time related to the speed of light?

According to Einstein's theory of relativity, the speed of light is constant in all frames of reference. This means that the measurement of time is relative to an observer's frame of reference. As an object approaches the speed of light, its proper time slows down relative to a stationary observer.

## Can proper time be measured?

Yes, proper time can be measured using a clock that is at rest relative to the event being observed. This clock will measure the proper time of the object or person in its own frame of reference. However, measuring proper time for objects moving at high speeds may require precise and sophisticated instruments.

Replies
21
Views
4K
Replies
6
Views
2K
Replies
12
Views
2K
Replies
9
Views
2K
Replies
54
Views
2K
Replies
37
Views
3K
Replies
1
Views
958
Replies
67
Views
3K
Replies
4
Views
805
Replies
10
Views
2K