I Relativistic Effect of Time Dilation: What is it Called?

[Gerinski]

Let's take a star 500 light years away from Earth, let's call it Star X. To make round numbers let's say we are in Earth year 2000.
We set a manned space mission to Star X, the spaceship will travel at 0.5 light-years per year (0.5 c) so it will reach there in 1000 years. Let's not worry about the longevity of the travellers, let's assume they are superhumans who live more than 1000 years.

Upon departure in year 2000, the travellers obviously see Star X how it was 500 years earlier, in Earth year 1500. When they will arrive there 1000 years later, in year 3000, they will see how Star X looks like in year 3000.
So if they look forward towards Star X during the trip, in 1000 years of travel they will see the evolution of Star X in 1500 years. The travel time plus "catching up the delay" in light travel time from Star X to Earth. In other words they will perceive time running faster than normal, precisely 1.5 times faster than normal (while looking towards Star X, they will see 1500 years of the star's history condensed in 1000 years of their time).

Oppositely, if they look back towards Earth during the trip, on departure they see how Earth looks like in year 2000. When they arrive at Star X in year 3000, the Earth is 500 light years away so its light takes 500 years to reach them. They will see how Earth looked like in year 2500.
So they will perceive time running slower than normal, in the 1000 years of travel time they will see the evolution of Earth during 500 years. Time will appear to run at half its normal rate while looking back towards Earth.

This perception of time running faster or slower than normal, due to one's velocity towards / away from the light source, what is this effect called? Is it just time dilation? Is it relativistic Doppler effect? Does it have another name?

Thanks,

 

[PeterDonis]

Is it relativistic Doppler effect?

Yes.

 

[Gerinski]

Thank you, I checked "Relativistic Doppler effect" on Wiki and it only talks about the redshifting or blueshifting of light frequency, it does not mention anything about the alteration of the perceived rate of the passage of time, so that confused me.

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

 

[Nugatory]

it only talks about the redshifting or blueshifting of light frequency, it does not mention anything about the alteration of the perceived rate of the passage of time, so that confused me.

That’s just two ways of saying the same thing. Imagine that there are radio transmitters on Earth and the remote destination, both sending out a one cycle per second signal (as measured by someone at rest relative to the transmitter). Now we can make a clock just by counting successive peaks in the signal; they’re one second apart so each peak is one tick of the clock.

And if we’re moving relative to the clocks/transmitters? The red or blue shift will mean a difference in the clock rate.

 

[pervect]

Thank you, I checked "Relativistic Doppler effect" on Wiki and it only talks about the redshifting or blueshifting of light frequency, it does not mention anything about the alteration of the perceived rate of the passage of time, so that confused me.

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

The effect you are describing is indeed the relativistic doppler shift. The bit about it being an "alteration of the preceived time" is your own personal interpretation as far as I know. Since you're leaving some relativistic effects out of your calculation, it's not entirely correct as stated. However, the basic idea is not entirely wrong, but it's also not quite complete or correct as stated.

Let's fill in the missing effect with the exact relativistic fomula. Your normalized velocity is called $\beta$, and is equal to .5 since $\beta = v/c$.

The duration of the journey as measured by a clock on the ship is not 1000 years, but 1000 years / $\gamma$, where $\gamma = 1 / \sqrt{1-\beta2} = 2/\sqrt{3}$. This means that the duration of the journey for a traveler on the ship is only about 866 years, $1000 * \sqrt{3} / 2$. This effect is usually called "relativistic time dilation".

Your calculation that the travelers see 1500 years of history of the star on the journey is correct, but they see the 1500 years of history in 866 years, not 1000 years. This means that the relativistic doppler shift is not 1500/1000 = 1.5 but given by the wiki formula for relativistic doppler shift.

$\sqrt{1+\beta}/\sqrt{1-\beta} = \sqrt{3} = 1.73$, to two significant figures.

If you multiply the doppler factor of 1.73 by the length of the journey , 866 years, you do indeed get the 1500 year figure that you calculated earlier, ignoring rounding errors. What you were missing from your calculation is the relativistic correction to the duration of the journey, which is usually called "relativistic time dilation".