# Help Applying SR to Calculate Time Dilation

• Palpatine
In summary, the conversation discusses the concept of time dilation in relativity and how it leads to different rates of clock ticking for different observers due to the lack of absolute simultaneity. This causes an illogical situation where two observers both see the other's clocks running slower. The issue arises from assuming the existence of an absolute simultaneity, which is no longer applicable in relativity.
Palpatine
I made this pic to illustrate my problem.

A spaceship (labeled B) departs from a space station (labeled A) at 80% the speed of light (0.8c). A applies the time dilation principle and calculates that B's clocks are running slower than his.

Some time later a smaller craft (labeled C) detaches from B and travels at 80% the speed of light in the opposite direction. B applies the time dilation principle and calculates that C's clocks are running slower than his.

But this results in an illogical situation. B's clocks are slower than A's and C's clocks are slower than B's but C is stationary in A's reference frame so C's clocks are running at the same rate as A's.

What am i doing wrong?

You are implicitly assuming the existence of an absolute simultaneity. This no longer holds in relativity. Instead, you must be aware that events that are simultaneous for one observer are not necessarily simultaneous for another. Since the rate at which clocks tick in an inertial frame is based on the notion of simultaneity in that frame, you will get different results as different frames have different definitions of simultaneity.

## What is time dilation?

Time dilation is a phenomenon predicted by Einstein's theory of Special Relativity, where time appears to move slower for an object that is moving at a high velocity compared to a stationary observer. This is due to the fact that the speed of light is constant and time is relative.

## How is time dilation calculated using Special Relativity?

The formula for calculating time dilation is t' = t√(1-(v^2/c^2)), where t is the time measured by the stationary observer, t' is the time measured by the moving object, v is the velocity of the moving object, and c is the speed of light. This formula takes into account the relative velocity and the constant speed of light.

## What are some real-life examples of time dilation?

One example of time dilation is the time difference between a clock on Earth and a clock on a satellite orbiting Earth. The clock on the satellite will appear to run slower due to its high velocity. Another example is astronauts on the International Space Station experiencing time dilation due to their high speeds.

## How does time dilation affect GPS systems?

GPS systems must take into account the time dilation of satellites orbiting Earth in order to accurately calculate location and time. Without this adjustment, GPS systems would be off by several meters, making them unreliable for navigation.

## Does time dilation only occur at high speeds?

Time dilation occurs at any speed, but it is most noticeable at high velocities close to the speed of light. At everyday speeds, the effects of time dilation are too small to be measured. However, it is still a fundamental principle of Special Relativity that applies in all situations.

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