# Time dilation in special relativity

Suppose a star ship is moving with some velocity. Two light pulses one in direction similar to star ship another opposite to it is shot towards the space ship. Then how time inside space ship adjust to make velocity of light constant?

• Are you looking for the boost for the time dilation, or something else? Commented Apr 9, 2014 at 16:33

Then how time inside space ship adjust to make velocity of light constant?

To make a measurement of the one-way speed of light within the starship, two stationary, spatially separated, synchronized clocks must be used.

When the measurement of the speed of the two oppositely directed light pulses is made, the measured speed is $c$ for both.

However, in the frame of reference in which the starship is moving with speed $v$, the clock at the rear of the starship is not synchronized with the clock in the front of the starship.

It is this difference in synchronization, this relativity of simultaneity, that accounts for the fact that, in both directions, the speed of the light pulses measures $c$.

• what if at the centre of spae ship suppose a sensor measures the speed of light in both diretions Commented Apr 11, 2014 at 0:59
• does if at single point in space time appears to flow in different rates Commented Apr 11, 2014 at 1:02
• @user44250, you need to read some more and do some thinking about the two questions you asked in these comments. (1) to measure the one way speed of something requires two spatially separated, synchronized clocks (2) an event (a 'point') in spacetime is a where and a when. Time 'flows' at a point in space, not a point in spacetime. Commented Apr 11, 2014 at 1:14

All clocks in the star ship may be synchronized, this is not the problem. But the problem is to measure speed of a light beam coming right towards the observer.

Imagine any observer outside of the starship - you will agree that he will measure both beams at c. And inside the starship, the speed of light c is not modified, just it is not possible to measure it.

First, to make things simpler to understand, imagine that the spaceship is 300,000 km's long. Now let's assume the spaceship is at rest in space and a clock at one end of the spaceship is synchronized with another clock located at the opposite end.

Here, if we send a burst of light from one end to the other at say 12:00 noon, if done in either direction it will reach the opposite end when the opposite clock says 12:00 noon plus one second. Thus the light will have traveled across 300,000 km's in 1 second, hence the speed of light is measured as being the expected speed of light.

Now this spaceship exists within a 4 dimensional environment known today as the Space-Time continuum. Also, as stated by physicist Brian Greene, when the space ship is at rest in space, the spaceship is in actual fact still in motion, but instead it's constant motion is now confined to moving across the dimension of time only, and is doing so at the speed of light. This is the maximum speed at which one can move across time.

In this case the entire spaceship is extending across space while it's constant motion is entirely across the dimension of time.

However, if you change your direction of travel within the Space-Time continuum, then the spaceship is no longer extending across merely space. Rotation has occurred, thus less of the spaceship is extending across space, and partially it is now also extending across the dimension of time. Thus the two clocks are no longer located at the same point in time, thus the two clocks are no longer synchronized.

If the spaceship was traveling at 260,000 km's per second, the clock at the rear would be ahead of the clock at the front by 0.866 of a second ( 300,000 km's spaceship length * v/cSQRD ). Also, based upon the Time dilation equation, both clocks would now be ticking at half speed. Also, based upon the Lorentz-Fitzgerald contraction equation, the spaceship has shrunk to a spatial length of only 150,000 km's long.

If a burst of light is sent from the rear to the front, to a stationary observer who is at rest in space, he sees that the light is only moving 40,000 kps faster than the spaceship and thus the observer sees that it takes the light 3.73 seconds to go from the rear to the front. ( 150,000 km's / 40,000 kps = 3.73 sec. ) However, onboard the spaceship time is ticking at half speed and so their clocks would only tick a total of 1.866 sec.

But not to forget that the clocks are not in sync. So if the burst of light is released from the rear at 12:00 noon, it will reach the front at 12:00 noon plus 1.866 sec, but the clock at the front is lagging behind by 0.866 sec. Thus when the light reaches this clock the clock will read ( 12:00 noon + 1.866 - 0.866 = 12:00 noon + 1 second ). Therefore it will seem as though it only took one second for the light to have traveled from one end of the spaceship to the other, since only 1 second seems to have been measured. Also, they are completely unaware that their spaceship has shrunk to half of its original spatial length. Thus to them it appears as though light had traveled across 300,000 km's in 1 second, hence the speed of light.

If a burst of light is sent from the front to the rear, to a stationary observer who is at rest in space, he sees that the light is moving at 560,000 kps relative to the spaceship since the light and the spaceship are moving in opposite directions ( 260,000 kps + 300,000 kps = 560,000 kps ). Thus the observer sees that it takes the light only 0.268 of a second to go from the front to the rear. ( 150,000 km's / 560,000 kps = 0.268 sec. ) However, onboard the spaceship time is ticking at half speed and so their clocks would only tick a total of 0.134 sec.

But not to forget that the clocks are not in sync. So if the burst of light is released from the front at 12:00 noon, it will reach the rear at 12:00 noon plus 0.134 sec, but the clock at the rear is ahead of the opposite clock by 0.866 sec. Thus when the light reaches this clock the clock will read ( 12:00 noon + 0.134 + 0.866 = 12:00 noon + 1 second ). Therefore it will seem as though it took one second for the light to have traveled from one end of the spaceship to the other, since only 1 second seems to have been measured. Again, they are completely unaware that their spaceship has shrunk to half of its original spatial length. Thus once again, to them it appears as though light had traveled across 300,000 km's in 1 second, hence the speed of light.