# Relativity and “light years”

As I understand relativity, time is relative to your velocity, meaning your watch moves slower relative to those who are stationary when moving at great speeds.

1. So if that's true, then when we talk about "light years", is that a distance based on year at some average Earth velocity?

2. Furthermore if we got in a spacecraft and traveled at near light speeds, for a journey say 5 light years away, would it not seem much shorter than 5 years for those traveling?

There are some misconceptions in your question, and you are really asking two different things.

First, remember that if you are on a spaceship moving at high speeds, Earth people will measure your watch as moving slower than theirs and you will measure their watches as moving slower than yours! Relativity works boths ways, that's why it's called relativity.

A light year is a unit of distance, just like a meter or a mile. It is defined as the distance that light travels in a year; this definition implicitly assumes that the same observer will measure both distance and time, and that this observer is inertial. One important point is that you do not actually have to go out and measure a light year to know what it is! Earth's velocity doesn't matter, because a light year is defined assuming you are in some inertial frame, it doesn't matter which one.

If distance and time are measured by different observers, things will change: If one of the observers gets on a rocket ship and travels at $0.9999c$ for a year proper time, someone else standing on Earth will measure the travelled distance to be much more than $0.9999$ light years (around 70 light years, in fact).

This is also the answer for the last part of your question. If you travel 5 light years (as measured from Earth!) at a speed practically equal to $c$, when you get there your clocks will read much less than 5 years.

When we talk about distances in light-years we mean the distance from the Earth to some other object in terms of the distance that light travels as measured in any inertial frame of reference. It really doesn't matter which particular inertial frame of reference you use because light always travels at the speed c with respect to any inertial reference frame. Also, for all practical purposes you can regard the passage of time as being the same for all planets and objects in our solar system since their relative speeds with respect to each other are all much less than c.

As for the spacecraft question, yes the journey would seem to take less than 5 years for the traveling astronauts. The total time of the journey would be reduced by the time dilation factor.

The speed of light is a constant of nature in all inertial frames, so in any inertial frame you will measure the same distance that light travels in a given unit of time. That's to say, the speed of light is the same for you and your buddy measuring the distance light travels in a set unit of time (according you own individual clocks). This raises a seeming paradox, since if we were to be talking about measuring the distance that sound travels in a unit of time, a person travelling relative to the sound wave(s) would definitely measure a different unit of time (if they were to be travelling at the speed of sound, the sound wave would be standing still!), so we must then conclude that your buddies time must be changed.

For your second question, absolutely yes. To get an even better example of it, if you were a photon travelling to a galaxy millions of light-years away, you would get there in the blink of an eye! Time would stay still, and so you'd literally get there "instantaneously".

A fun exercise I recommend is the following: go on the internet and look up a nearby star/galaxy you would like your species to visit. Then think of a time-duration you would consider bearable for the time-scale of the journey over there. Now, use basic special relativity to calculate how fast you would need to travel in order to get over there in that amount of time.

• The "light experiences no time" thing, while fun to throw around on the internet to impress people, doesn't belong in an answer here. You can't have an inertial frame moving at the speed of light. – Javier Oct 17 '15 at 2:52
• True, but I don't think it shouldn't belong in an answer here. The concept I was trying to convey was time dilation in the situation he was talking about, and I felt the limiting case of light itself would get this across the easiest. I haven't said that it's possible to boost to such a reference frame. – Arturo don Juan Oct 17 '15 at 3:11

As I understand relativity, time is relative to your velocity,

Not at all.
Neither are your indications ("positions of the little hand of your watch" etc.) relative to or depending on the description of anyone else moving with respect to you,
nor your ordering these indications of yours into a sequence,
nor the determination of your durations between pairs of these indications of yours (or at least, the determination of your duration ratios, between pairs of pairs of your indications).

What can be said, however, is that geometric relations between participants (such as mutual speeds) must be determined and taken into account when trying to compare a duration of one participant (between two indications of this one participant) to a duration of another participant (between two indications of that other participant).

meaning your watch moves slower relative to those who are stationary (relatively) when moving at great speeds.

That's an improper assertion; namely attempting to characterize the rate of "your watch" not by durations of "your watch" itself (between its indications) but by durations of other participants (between indications or readings of their watches).

The correct, well-established characterization and comparison of rates, mean lives, etc. is instead to first determine rates (or life durations) individually, properly, and then to compare and to summarize these individual results.

So if that's true then when we talk about "light years", is that a distance based on year at some average earth velocity?

When we speak of (non-zero) distance values, and of the determination of distance values in the first place, we're characterizing and attributing the distance value to two distinct participants (also called the "two ends") who were and remained at rest to each other.

Consequently, the notion of velocity is involved in this sense: If a (non-zero) distance value is attributed to two particular ends, in some particular trial, then their velocity with respect to each other was zero, in this trial.

Furthermore if we got in a spacecraft and traveled at near light speeds

... with respect to Earth, or the Sun, I presume; let's say at speed $v := \beta~c$ ...

for a journey say 5 light years away

... from the Sun, let's say; i.e. to some (hypothetical) participant (e.g. some star) as destination, who was and remained as good as at rest wrt. the Sun, for the entire trial; such that the ping dutation between the Sun and this (hypothetical) participant was found throughout the trial as 10 years ...

would it not seem much shorter than 5 years for those traveling?

Well, if these participants who travelled from the Sun to the destination uniformly at speed $\beta +c$ then say that their journey took them $$\frac{5}{\beta}~\left(\sqrt{1 - \beta^2}\right)~\text{years},$$ then everyone can conclude that the duration they mean by "$1~\text{year}$" is equal to the duration we (Earth, Sun) mean by "$1~\text{year}$". (How else could we possibly compare and confirm which of their durations they might mean by "$1~\text{year}$"?.)

Besides, it would be improper to attribute to the Sun and the (hypothetical) destination considered here any other distance value than the 5 light years which they determined themselves of each other.

p.s.

The definition of determining distance values, between pairs of ends which were and remained at rest to each other, in terms of the (half of) ping duration, as $$\text{distance} := c~\frac{\tau_{\text{ping}}}{2},$$ where the ping duration of each such pair is of course mutually equal, is called the "chronometric" (definition of) "distance".

It is of course an essential feature of Einstein's Theory of Relativity, but its importance was perhaps only fully recognized by the 1960s, by physicists such as J. L. Synge.