# Travelling to the Nearest Star and Time Dilation

## Main Question or Discussion Point

I was reading some articles on the internet, about scientists being able create space ships capable of nearing the speed of light, some time in the future. So say they did do this and managed to reach around 0.9999999% of the speed of light and wanted to travel to the nearest star which, to keep it simple, is 1 light year away. Meaning it would take one year to reach the star. But my question is; is this one earth year, or one year from the crews point of view. Because at such speeds time dilation would mean that 1 day for the crew would be nearly 20,000 years on earth. Hence, if it is one earth year then surely the journey time for the crew, to get to the nearest star, would be only 4.32seconds. Assuming that one day is 86,400 seconds and that lasts 20,000 years, then proportionatly one year lasts 4.32 seconds. Obviously, if the journey was a year from the crews perspective then 7.3 million years would have passed by the time they reached the star which would be very impractical.
So if you could travel one light year to the nearest star would the journey last a year in earth time or a year from the space ships view?

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In earth time.

Janus
Staff Emeritus
Gold Member
First off. 0.9999999c gets you a time dilation factor of 2236, not 20,000.

Secondly the 1 year would be Earth time. For the crew it would take 3.91 hrs.

ISo if you could travel one light year to the nearest star would the journey last a year in earth time or a year from the space ships view?
Suppose the distance from Earth to the nearest start is one light year and both are at rest with respect to each other. Then the distance for the traveler will shrink depending on how much he accelerates in the direction of the star. For instance the traveler may only have to travel 1/2 light year to get to the star due to length contraction.

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Suppose the distance from Earth to the nearest start is one light year and both are at rest with respect to each other. Then the distance for the traveler will shrink depending on how much he accelerates in the direction of the star. For instance the traveler may only have to travel 1/2 light year to get to the star due to length contraction.
Do you really think the travelers motion causes the rest of the universe to shrink?
If so, then what physical forces/effects accomplish this, and do it nearly instantaneously?

Do you really think the travelers motion causes the rest of the universe to shrink?
From the universe perspective distance and duration are interrelated, they don't exist by themselves.

Remember Minkowski's catchy statement: "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

Ken G
Gold Member
Yes, the distance shrinks instantaneously, yet another reason to not consider distance as something "real", but rather something contingent. It's more like, if you are driving a car to your Aunt Tillie's house, and you have 30 miles to go at a speed of 30 mph (apologies to the metric folks), you are looking at a 1 hour drive. If you decide you need to get there in 1/2 hour, you accelerate to 60 mph. When you do that, the time you are looking at instantaneously changes from 1 hour to 1/2 hour-- and we now see that distance is not so very different from that.

Indeed, what is particularly "cute" is that at low speeds, the distance stays fixed and you get there sooner by covering that distance faster, but at speeds close to c, you basically shorten your trip by reducing the distance moreso than by covering it faster. So when someone says "shorten your commute by taking a faster road", if you are nearing c, they mean it quite literally!

Indeed, what is particularly "cute" is that at low speeds, the distance stays fixed and you get there sooner by covering that distance faster, but at speeds close to c, you basically shorten your trip by reducing the distance moreso than by covering it faster. So when someone says "shorten your commute by taking a faster road", if you are nearing c, they mean it quite literally!
Indeed.

You can say that if the distance between two objects A and B at relative rest with each other is X then a traveler going from A to B travels always less than X.

Gives a different spin on Zeno's paradox doesn't it jtbell
Mentor
Do you really think the travelers motion causes the rest of the universe to shrink?
If so, then what physical forces/effects accomplish this, and do it nearly instantaneously?
To make an analogy:

MeJennifer:
Remember Minkowski's catchy statement: "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
Fortunately for us, the world does not work via catchy statements.

Ken G
Indeed, what is particularly "cute" is that at low speeds, the distance stays fixed and you get there sooner by covering that distance faster,
There you have answered the question!

jtbell
In the coordinate system that is fixed to your head, that star moves thousands of light-years in the blink of an eye. What physical forces accomplished this? Did the inhabitants of a planet orbiting that star notice any effects from this?
Not according to the currently known rules of physics, i.e., his moving does not make his perception about real events, and no one else would share his experience .
That's the point being made. If a traveler is affected by time dilation, destinations arrive earlier than expected, and it's a subjective choice to interpret this as space contraction.

Dale
Mentor
Do you really think the travelers motion causes the rest of the universe to shrink?
If so, then what physical forces/effects accomplish this, and do it nearly instantaneously?
It is real, but there is no force involved. It is simply geometry. The geometry of the universe is more interesting than the geometry you learned in high-school.

Ken G
Gold Member
If a traveler is affected by time dilation, destinations arrive earlier than expected, and it's a subjective choice to interpret this as space contraction.
It's not a "subjective choice", it is an axiom of relativity. Of course, all axioms are subjective choices in some sense, but it is quite misleading to describe them as such. Is it a "subjective choice" that the axioms work? We don't have to adopt any axiom of physics, no one is twisting our arm-- the issue is whether or not we benefit by doing so. In the case of special relativity, Einstein's conventions have not been improved on. If you are steering this into the philosophy of "do lengths really contract instantaneously", you have left the realm of science-- in science, it serves us well to imagine that indeed they do.

Science explains the physical world and the illusory world.
If space contracts for a traveler leaving the earth, why doesn't anyone else perceive it?
This is the difference. The choice of longer time intervals or shorter spatial intervals is with the traveler only and no one else, i.e. it's subjective. SR is a theory of transformations of one subjective observer to another ('relativity') as a result of their motion.

Hello phyti.

How does the traveller choose. The only choice he has is whether to travel or not.

Matheinste

good evening matheinste;

Art leaves earth in a spacecan, circles back to fly along a path parallel to the earth and moon centers which are 1.2 light seconds apart. The earth and moon send continuous signals perpendicular to his path. At .6c, his clock records .8 of earth time (time dilation).
He records a time interval of (1.2/.6)*.8=1.6 secs between signals. He calculates the time should be 1.2/.6=2.0 secs. SR says he can assume he is not moving, so he chooses this option and explains the time difference as a shortening of the earth-moon separation, or so the popular opinion would have it.
This is the tradeoff, if he cannot determine his state of motion, or chooses to ignore it (the earth is moving), he must accept the anomaly of length contraction.
To show it's fictional, he knowing SR, and knowing the earth-moon separation from previous measurements, divides his clock time by .8, and the anomaly is gone!
He would also have at least one other clue, events ahead of him would be occurring faster, and events behind occurring slower, other than dopplershifted light.

JesseM
Science explains the physical world and the illusory world.
If space contracts for a traveler leaving the earth, why doesn't anyone else perceive it?
This is the difference. The choice of longer time intervals or shorter spatial intervals is with the traveler only and no one else, i.e. it's subjective. SR is a theory of transformations of one subjective observer to another ('relativity') as a result of their motion.
You can't talk about space "contracting" unless you're dealing with a non-inertial coordinate system, but the laws of physics don't work the same way in this coordinate system as they would in inertial ones. However, if you have an inertial system of rulers and clocks at rest relative to the Earth which measure the distance from Earth to Alpha Centauri as 4 light-years, and you also have a different set of inertial rulers and clocks moving at 0.8c relative to the Earth, then according to the measurements of the second set the distance from Earth to Alpha Centauri is only 2.4 light years. There is no physical basis for saying one of these distances is "more correct" than the other since the laws of physics work exactly the same in the coordinate systems defined by these two different ruler/clock systems, and so if the accelerating guy on the ship always uses a ruler/clock system at rest relative to himself at that moment to measure distance at that moment, then after accelerating to 0.8c relative to the Earth he'll say the distance from Earth to Alpha Centauri is now only 2.4 light years.
phyti said:
To show it's fictional, he knowing SR, and knowing the earth-moon separation from previous measurements, divides his clock time by .8, and the anomaly is gone!
But you could equally well say that he could prove the previous measurements (made on a ruler/clock system at rest relative to the Earth) were "fictional" by an analogous method. If we pretend the frame in which Earth and Alpha Centauri are moving at 0.6c represents the "real truth" about lengths and distances and simultaneity, then we can note that in this frame a clock at Alpha Centauri is 3.2 years ahead of a clock at Earth at any given moment, and both are ticking at 0.6 the "correct" rate, so if the "true" distance between them is 2.4 light years and it takes 2.4/0.8 = 3 years between the moment the ship passes Earth and the moment the ship passes Alpha Centauri (here we assume the ship is 'really' at rest while Earth and Alpha Centauri move past it at 0.8c), then in that time the clock on Alpha Centauri has advanced by 3 * 0.6 = 1.8 years. But since the clock on Alpha Centauri was ahead of the clock on Earth by 3.2 years, this means the time on the Alpha Centauri clock when it passes the ship will be 3.2 + 1.8 = 5 years greater than the time on the Earth clock when it passed the ship (for example, if the Earth clock read 2000 when it passed the ship, then the Alpha Centauri clock read 2003.2 at that moment, and 3 years later the clock on Alpha Centauri read 2005). So, here we have neatly explained the "fiction" that the trip seemed to have taken 5 years according to clocks on Earth and Alpha Centauri, even though it "really" only took 3 years, using both the fact that clocks on Earth and Alpha Centauri are slowed down by time dilation, and also the fact that they are out-of-sync by 3.2 years thanks to the relativity of simultaneity.

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JesseM
If we pretend the frame in which Earth and Alpha Centauri are moving at 0.6c represents the "real truth" about lengths and distances and simultaneity
Sorry, that should be 0.8c.

Hello phyti.

I have nothing to add to what Jessem has written.

Matheinste.

Ken G
Gold Member
Science explains the physical world and the illusory world.
You have a way of defining a difference?
The choice of longer time intervals or shorter spatial intervals is with the traveler only and no one else, i.e. it's subjective. SR is a theory of transformations of one subjective observer to another ('relativity') as a result of their motion.
That isn't the sense of "subjective" you used above. Above you said the axioms of relativity were subjective, now you say the length contraction is subjective. That is very different. The length contraction that any particular observer infers is subjective because it depends on their motion-- that the axioms of relativity agree with experimental tests is objectively true.

JesseM
If we pretend the frame in which Earth and Alpha Centauri are moving at 0.8c represents the "real truth" about lengths and distances and simultaneity, then we can note that in this frame a clock at Alpha Centauri is 3.2 years ahead of a clock at Earth at any given moment, and both are ticking at 0.6 the "correct" rate
Incidentally, if phyti isn't too familiar with the relativity of simultaneity I should explain why these two clocks at Earth and Alpha Centauri would be out-of-sync by 3.2 years. When building inertial coordinate systems in SR, the idea is that each observer synchronizes clocks at different locations by assuming that light moves at the same speed in both directions relative to himself; so, an observer in the Earth/Alpha Centauri rest frame could synchronize clocks at Earth and Alpha Centauri by setting off a flash at the midpoint between them, and setting clocks at each location to read the same time at the moment the light from the flash reaches them.

So if we assume that Earth and Alpha Centauri are "really" moving at 0.8c with a distance of 2.4 light years between them, assume that at time t=0 in this "true" frame, Earth is at position x= +1.2 light years, Alpha Centauri is at position x= -1.2 light years (both moving in the + direction on the x-axis), and a flash is set off between them at the origin, x = 0 light years. If light "really" moves at c in both directions in this "true" frame, then after 0.666... years, the light moving in the -x direction will be at position x = -0.666... light years, while Alpha Centauri will have moved 0.8 * 0.666... = 0.5333... light years in the + direction, so it'll be at x = -1.2 + 0.5333... = -0.666... light years as well. So at this time the clock at Alpha Centauri is set to a time of zero. Then, 5.333... years later at t=6 years in the "true" frame, the light moving in the +x direction will be at position x = 6 light years, and Earth will have moved 0.8 * 6 = 4.8 light years from its position at t=0, so it'll now be at x = 1.2 + 4.8 = 6 light years as well. This will be when the clock at Earth is set to zero, 5.333... years after the Alpha Centauri clock was set to zero. Keeping in mind that the Alpha Centauri clock was ticking at 0.6 the normal rate this whole time thanks to time dilation, the Alpha Centauri clock now reads 0.6 * 5.333... = 3.2 years at the moment the Earth clock is set to 0 years, and since both clocks tick at the same slowed-down rate forever after, the Alpha Centauri clock will always be 3.2 years ahead of the Earth clock.

Hi JesseM;
But you could equally well say that he could prove the previous measurements (made on a ruler/clock system at rest relative to the Earth) were "fictional" by an analogous method.
Those were measurements in his own frame, no dilation, no contraction.

(here we assume the ship is 'really' at rest while Earth and Alpha Centauri move past it at 0.8c), then in that time the clock on Alpha Centauri has advanced by 3 * 0.6 = 1.8 years. But since the clock on Alpha Centauri was ahead of the clock on Earth by 3.2 years, this means the time on the Alpha Centauri clock when it passes the ship will be 3.2 + 1.8 = 5 years
time for spacecan-earth event: s=0 e=0 a=3.2
time for spacecan-alpha event: s=3 e=1.8 a=5.0
Here you show the spacecan time for the trip is 3 yr, the same as when it moves at .8c!

If you synchronize the clocks in the e-a frame, they use the 'rest' distance of 4 lyr. They do not detect a length contraction in their own system. The contraction is an assumption by the spacecan observer in response to the reduced time on his clock to travel the 4 ltyr.

The time difference for earth and alpha-c is 2sbg=5.33 yr., with s= spatial separation (2), b=v/c (.8) and g=gamma factor (1/.6) This includes time dilation.

Alpha Centauri clock now reads 0.6 * 5.333... = 3.2 years
Here because you used the contracted distance (2.4, a result of time dilation), you have shortened the time twice.

With the traveler on earth, all three agree on a 4 lyr distance.
The synchronization of earth-alpha clocks is irrelevant because they are in the same frame.
With s not moving:
time for spacecan-earth event: s=0 e=0 a=u
time for spacecan-alpha event: s=5 e=3 a=u+3
With s moving:
time for spacecan-earth event: s=0 e=0 a=0
time for spacecan-alpha event: s=3 e=5 a=5

If you don't already use them, the Minkowski space-time diagrams are very helpful in maintaining clarity for exercises like these.

Einstein was intelligent enough to know that merely moving did not affect distant clocks or spatial intervals physically, i.e. alter physical processes elsewhere. He felt confident enough to state this as postulate one of the SR theory. He also realized that perception works differently, thus his theory transforms one observers description of (perceived) events to that of another.
I call it a 'black box' theory because you put in a set of values and a different set comes out, without explaining the details of how it works. The main source of confusion is in my opinion, the distinction between the physical event and the perception of the event. A simple observation, you see a star. You don't see the star 'now' as a coincident/synchronous event, you see it as it was, e.g., 1 million yrs ago. That's the time difference between the event and its perception.
The issue is not what is real or imaginary, it's what is consistent with known rules of science. The synchronization of two clocks in the same moving frame involves forming an asynchronous system, but it will work within that system.
My scenarios regarding a moving observer are intended to show the effect of time dilation, which is an experimentally verified fact, doesn't require length contraction as an explanation for results.

JesseM
JesseM said:
But you could equally well say that he could prove the previous measurements (made on a ruler/clock system at rest relative to the Earth) were "fictional" by an analogous method.
Hi JesseM;

Those were measurements in his own frame, no dilation, no contraction.
What does that matter? If we were talking about an alien planet which moved path Earth at 0.8c inertially, and which had always been moving at that speed relative to Earth rather than accelerating away from Earth like the ship, would that somehow change your answer about whose measurements are "fictional"?
phyti said:
time for spacecan-earth event: s=0 e=0 a=3.2
time for spacecan-alpha event: s=3 e=1.8 a=5.0
Yes, these are the simultaneous clock-readings in the frame where the ship is at rest and Earth and Alpha Centauri are moving at 0.8c.
phyti said:
Here you show the spacecan time for the trip is 3 yr, the same as when it moves at .8c!
Of course, all frames must agree that if the relative velocity between the ship and Earth+Alpha Centauri is 0.8c, and the distance between Earth and Alpha Centauri is 4 ly in their own rest frame, then the ship's clock will have advanced 3 years between the moment it passes Earth and the moment it passes Alpha Centauri. That's just how relativity works, all frames must always make the same predictions about local physical events like what a clock reads at the moment it passes right next to some landmark. The point is that there is no real basis for calling one frame's measurements "real" and the other's "fictional".
phyti said:
If you synchronize the clocks in the e-a frame, they use the 'rest' distance of 4 lyr.
What are you talking about? They don't use "distance" at all, they just set off a flash at the midpoint, and zero their clocks at the moment the light from the flash reaches each one.
phyti said:
The time difference for earth and alpha-c is 2sbg=5.33 yr., with s= spatial separation (2), b=v/c (.8) and g=gamma factor (1/.6) This includes time dilation.
If you're talking about the time difference between clocks at Alpha Centauri and Earth as seen in the frame where they are moving at 0.8c, it's 3.2 years.
JesseM said:
Alpha Centauri clock now reads 0.6 * 5.333... = 3.2 years
phyti said:
Here because you used the contracted distance (2.4, a result of time dilation), you have shortened the time twice.
The contracted distance is not "a result of time dilation", they are separate phenomena. If the spaceship-observer looks at an enormous ruler which is at rest with respect to himself, and there are clocks at the 0 light-year mark and the 2.4 light-year mark which are synchronized in the ruler rest frame, then the reading on the 0 light-year mark clock as Earth passes it will be the same as the reading on the 2.4 light-year mark as Alpha Centauri passes it; thus at the "same moment" (in this frame) that Earth is at the location of one clock, Alpha Centauri is at the location of the other clock, 2.4 light years away.
phyti said:
With the traveler on earth, all three agree on a 4 lyr distance.
The synchronization of earth-alpha clocks is irrelevant because they are in the same frame.
Yes, but if they are synchronized in their own frame, then when viewed in another frame they will be out-of-sync. Do you disagree?
phyti said:
With s not moving:
time for spacecan-earth event: s=0 e=0 a=u
time for spacecan-alpha event: s=5 e=3 a=u+3

With s moving:
time for spacecan-earth event: s=0 e=0 a=0
time for spacecan-alpha event: s=3 e=5 a=5
You seem to be completely confused about the relativity of simultaneity. If Earth and Alpha Centauri clocks are synchronized in their own rest frame, then when s is not moving relative to them, of course they will be synchronized in the current rest frame of s (since this is the same as their own rest frame), so if e reads 0 then a should read 0 as well, not "u". Then when s is moving relative to them, Earth and Alpha Centauri's clocks will be out-of-sync in the current rest frame of s, so if e reads 0 then a reads 3.2.
phyti said:
If you don't already use them, the Minkowski space-time diagrams are very helpful in maintaining clarity for exercises like these.
Minkowski diagrams simply illustrate the coordinates assigned to events by different frames which are related to one another by the Lorentz transformation. Let's call frame A the rest frame of Earth and Alpha Centauri, and the coordinates of that frame x and t, while frame A' is the frame where they are moving at 0.8c and the ship is at rest (after it has accelerated), and the coordinates of that frame x' and t'. In the A frame, say that Earth is always at position x = 0 light years, Alpha Centauri is always at position x = 4 light years. Their clocks match the coordinate time of this frame, so that at t=0 years the Earth clock reads 0 and the Alpha Centauri clock reads 0, at t=5 years the Earth clock reads 5 and the Alpha Centauri clock read 5, etc.

Now, let's look at the event of the Earth clock reading 0, and also look at the event of the Alpha Centauri clock reading 3.2. Event #1 has coordinates x=0, t=0, while event #2 has coordinates x=4, t=3.2. Now we can use the Lorentz transformation to find the coordinates x' and t' of both events in the A' frame. The Lorentz transformation equations are:

x' = gamma*(x - vt)
t' = gamma*(t - vx/c^2)
where gamma = 1/sqrt(1 - v^2/c^2).

With v=0.8c, gamma = 1.6666...

So for event #1 we have:
x' = 1.666... * (0 - 0.8*0) = 0
t' = 1.666... * (0 - 0.8*0) = 0

And for event #2 we have:
x' = 1.666... * (4 - 0.8*3.2) = 2.4
t' = 1.666... * (3.2 - 0.8*4) = 0

So, you can see that in this frame, both events--the Earth clock reading 0, and the Alpha Centauri clock reading 3.2--happen simultaneously at time t'=0. You can also see that in this frame, event 1 happens at x'=0 while event 2 happens at x'=2.4, showing that they are 2.4 light years apart in this frame.
phyti said:
Einstein was intelligent enough to know that merely moving did not affect distant clocks or spatial intervals physically, i.e. alter physical processes elsewhere. He felt confident enough to state this as postulate one of the SR theory.
Er, where did he say that? The first postulate of SR is that the laws of physics work the same in every frame.
phyti said:
I call it a 'black box' theory because you put in a set of values and a different set comes out, without explaining the details of how it works. The main source of confusion is in my opinion, the distinction between the physical event and the perception of the event. A simple observation, you see a star. You don't see the star 'now' as a coincident/synchronous event, you see it as it was, e.g., 1 million yrs ago. That's the time difference between the event and its perception.
When I see an event has nothing to do with what coordinate I assign it in my reference frame. If I look through my telescope and see a star exploding at the same time I drop a quarter in the ground, and the star is 1 million light-years away in my frame, then this means that in my frame the event of the star exploding has a t-coordinate 1 million years less than the t-coordinate of my dropping the quarter on the ground. The Lorentz transformation deals with the time-coordinates assigned to events in this way, not with the times that I see events.

Originally Posted by phyti
time for spacecan-earth event: s=0 e=0 a=3.2
time for spacecan-alpha event: s=3 e=1.8 a=5.0

Yes, these are the simultaneous clock-readings in the frame where the ship is at rest and Earth and Alpha Centauri are moving at 0.8c.
The ship/can is moving.

Originally Posted by phyti
Here you show the spacecan time for the trip is 3 yr, the same as when it moves at .8c!

Of course, all frames must agree that if the relative velocity between the ship and Earth+Alpha Centauri is 0.8c, and the distance between Earth and Alpha Centauri is 4 ly in their own rest frame, then the ship's clock will have advanced 3 years between the moment it passes Earth and the moment it passes Alpha Centauri.
If the ship/can is not moving, alpha-c cannot reach him in 3yrs if light requires 4 yrs!

JesseM