Can an object moving away from you travel farther than 1 light year after 1 year?

[tommac]

Alternatively can light travelling in a straight line away from you travel less than 1 light year in 1 year?

I think the answer is yes for both but want to make sure.

Of course as with all of my other questions we need to start with a black hole.

The key to the following logic is that C ( the speed of light ) is constant however neither time nor space is constant. By that I mean that in different reference frames two clocks wont necessarily stay syncronized. So if an observer passes through a strong gravitational field the speed of his clock relative to a clock in empty space will signifigantly vary. If the speed of his clock varies and his perception of distance varies then the distance that he traveled in the past can appear differently to what he currently percieves.

Here is the example.

You are hovering very close to the event horizon of a black hole. You shoot lasers then wait a few seconds then hit your boosters to travel in the direction that you shot the lasers. Peculiarly you notice that the lasers are now much farther away than they should be. In fact after a year you may notice that the light travelled 20 light years away from you.


So now you find that strange shoot 2 move lasers in the same direction and then put your ship into reverse back to hovering near the EH. You see that these lasers after a year really are only 1/2 a light year away from you.

However at any moment if you measured the speed of the lasers away from you they will be travelling at the speed of light away.

They key here is moment. Within a year ( or even a second ) the percieved flow of time can change as one passes into or out of a gravitational field. While this is happening percieved distances are also changing. What was your last year was really 20 years to everything else that is in your current gravitational well.

However at an instant light never travels away from you at any other speed than C.

[01101001]

Alternatively can light travelling in a straight line away from you travel less than 1 light year in 1 year?

Relative to what? You/me?

In what environment? A vacuum?

[Zamise]

I"m thinking the actual distance the light can travel may vary but one light year is one light year not twenty or less than 1. So, even if you were within the event horiozon and some how shot the laser straight up and it came back down to you a year later it still traveled 1 light year not zero even if it only went five inches away from you. Or maybe I'm not getting it.

[WayneFrancis]

Alternatively can light travelling in a straight line away from you travel less than 1 light year in 1 year?

In a vacuum light will always travel 1 light year in 1 year relative to you ...because relative to you it always travels at C.

In a non vacuum then light will always travel less then 1 light year in 1 year

I think the answer is yes for both but want to make sure.

Of course as with all of my other questions we need to start with a black hole.

The key to the following logic is that C ( the speed of light ) is constant however neither time nor space is constant. By that I mean that in different reference frames two clocks wont necessarily stay syncronized. So if an observer passes through a strong gravitational field the speed of his clock relative to a clock in empty space will signifigantly vary. If the speed of his clock varies and his perception of distance varies then the distance that he traveled in the past can appear differently to what he currently percieves.

Here is the example.

You are hovering very close to the event horizon of a black hole. You shoot lasers then wait a few seconds then hit your boosters to travel in the direction that you shot the lasers. Peculiarly you notice that the lasers are now much farther away than they should be. In fact after a year you may notice that the light travelled 20 light years away from you.


So now you find that strange shoot 2 move lasers in the same direction and then put your ship into reverse back to hovering near the EH. You see that these lasers after a year really are only 1/2 a light year away from you.

However at any moment if you measured the speed of the lasers away from you they will be travelling at the speed of light away.

They key here is moment. Within a year ( or even a second ) the percieved flow of time can change as one passes into or out of a gravitational field. While this is happening percieved distances are also changing. What was your last year was really 20 years to everything else that is in your current gravitational well.

However at an instant light never travels away from you at any other speed than C.

I was writing up a big thought experiment but simply put as you accelerate away from something your experience of time dilates but so does your experience of distances. You are standing next to a friend then accelerate away from him instantly at .99C and you travel for what you believe is 1 light year and stop instantly at .99C. You are now 6.93 light years away from your friend and to your friend you traveled for 7 years. If you tried to communicate to each other during the trip your then any messages you receive would come in 7x faster and any you send your friends would get 7x slower then they where sent. When you decelerate you shift your time dilation back to your friends frame of reference.

Now yes if you bring in gravity wells then the equations get a bit more complicated but nothing that is outside the reach of a average kid that knows algebra. They might say it is to hard but they have the knowledge to solve the equations.

Everything is always relative to you. For the photons in any laser you use they experience no time and no distance. You can't ask a photon "How far did you travel?" or "How long have you been in existence" These questions have no answer to a photon who doesn't experience space or time as we do.

Time and space dilation are easily correlated. You speed up and your time gets dilated by 7x then your perception of distance along the axis you have accelerated on is dilated by 7x. It is Rocket away from the earth at .99c then earth stops looking like a sphere

and looks more like a pancake

but when you "slow" back down then it pops back to the sphere.

So to your original questions. In your given frame of reference an object can not travel further away from you then 1 light year. If you change your reference frame then you are changing both your perception of time and distance and your question doesn't cover that. If you do the math you'll see that the object in your new frame of reference will only approach C but never get there.

The actual equation is

V1 + V2
______________ = Apparent V

1 + ( V1V2/C^2)

When you take everything into account V < C if both of the objects are not massless and if one or both of them are then V = C

[kzb]

Distant galaxies with red-shifts more than a certain value are apparently moving away from us at more than 1 light year per year.

[AndrewJ]

Distant galaxies with red-shifts more than a certain value are apparently moving away from us at more than 1 light year per year.

Is that an allusion to the "ant on a rubber rope" phenomenon? Wouldn't mind reading another explanation of that if it's not too off topic.

[01101001]

Is that an allusion to the "ant on a rubber rope" phenomenon? Wouldn't mind reading another explanation of that if it's not too off topic.

If this isn't enough, think about starting your own topic so the current question can have its own life -- or researching the many that have gone before.

Sean Carroll's Cosmology Primer FAQ: Are distant galaxies moving faster than the speed of light? Wouldn't that violate relativity?

The "velocity" that cosmologists speak of between distant galaxies is really just a shorthand for the expansion of the universe; it's not that the galaxies are moving, it's that the space between them is expanding. If the distance isn't too great, this expansion looks and feels just like a recession velocity, but when the distance becomes very large that resemblance breaks down. In particular, it's perfectly plausible to have distant galaxies whose "recession velocity" is greater than the speed of light.

More there.

See also Ned Wright's Cosmology FAQ: Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR.

[yelram]

If two objects move away from each other each moving the speed of light, and they both turn around and look where they came from, are they moving away from each other at the speed of light, or twice the speed of light? The area they would travel over the same amount of time would make it seem like twice the speed, but I know GR would say the speed of light. Isnt this a bit of a conundrum?

[01101001]

If two objects move away from each other each moving the speed of light [...]

Relative to what?

[yelram]

Relative to what?

Each other.

[grant hutchison]

Relative to what?

Each other.

Speed of light relative to each other means that they each measure their separation as one light year at the end of one year, so that's all internally consistent. (Neglecting for the moment that it's physically impossible for material objects to move at the speed of light relative to anything.)

Grant Hutchison

[yelram]

Speed of light relative to each other means that they each measure their separation as one light year at the end of one year, so that's all internally consistent. (Neglecting for the moment that it's physically impossible for material objects to move at the speed of light relative to anything.)

Grant Hutchison

But they were moving in opposite directions. Their distance between one another should be TWO light years. Okay we'll do it with lasers then. You fire one laser the opposite direction from the other, in a year, what is the distance between the ends that both lasers have traveled? If the lasers were able to turn around and look back, would they see eachother as 1 lightyear apart, or 2? And if its 2, wouldnt that then infer that the lasers were moving away from each other at TWICE the speed of light?

[Argos]

'well, the answer to that question is quite simple, I bet that my driver, sitting up at the back, there, could answer it...'

[tommac]

Relative to what? You/me?

In what environment? A vacuum?

Relative to you, and yes in a vacuum. The thing that I am hinting at is your reality is changing. You only aged one year, but someone standing right next to you aged 50 years in that one year that you percieved. Light travelled 50 light years from the person standing next to you + in your current perspective ( but you only aged one year ). But at no time did you ever see light travelling faster than the speed of light, it is just your perception of space and time that have changed.

[tommac]

Sorry can we get back on track to my question?

I am at( jsut outside ) the event horizon of a black hole. An observer is out in empty space ( lets consider a vacuum for simplicity ). He detects that the black hole is 2 light-years away

I shoot the laser and wait 1 year what the observer also waits one year. I can see his clock and it is really spinning. It is clear that his time is moving much faster than my time.

The observer sees my clock and my clock appears stuck ... he realizes that my time is running much slower than his time.

Is everything OK so far?

so after 1 year of his time, the light is 1/2 way. However, 1 year of his time, is like 1 minute of my time. So I must percieve that light has made it half way to him in 1 minute. Since light travels as C ... I must percieve him as much closer to me than he percieves. Right? He is only 2 light minutes away from me.

Is this correct so far?

Now I hit my jets and leave lets say I just waited 1 minute ( light was halfway there ) and then left. I start to lose the effects of space-time dilation and get to a point where I am in the exact same reference frame as the distant observer. Our clocks are now running at the same speed. For me 1 minute + whatever time it took me to travel back to him , for him it was 1 year + whatever time it took for me to travel to him. We notice that our clocks are off by 1 year - 1 minute ( maybe slightly more because of the time dilation when travelling ).

For me I see the lasers that I shot being much farther from me than they should be. It fact by my calculations using straight C ... the light it exactly 1 year - 1 minute ( +- ) further along in its journey than I predicted using C.

[NEOWatcher]

I am at( jsut outside ) the event horizon of a black hole. An observer is out in empty space ( lets consider a vacuum for simplicity ). He detects that the black hole is 2 light-years away

I think it already went astray here. You are each observing a different distance because your units of measurement and time are not equal.

[tommac]

I think it already went astray here. You are each observing a different distance because your units of measurement and time are not equal.

No I dont think this is where it went astray ... it is actually the heart of my question. The starting points of the two observers are distant but the at the end (t2) they are the same.

So yes the initial units of meausement are different. But at T2 they are the same. So for the one who experienced the change of units of measurement could make it appear to him over the course of time that light travelled faster than the speed of light.

For any instant of time the speed of light is measured at C .... however over the course of a year ( because now experiences a different unit of measurement ( compared to when he was near the EH )) light could have travelled further away from him than his current perception of 1 light year.

[grant hutchison]

But they were moving in opposite directions. Their distance between one another should be TWO light years.

Nope. You just specified that they were moving at lightspeed relative to each other. That's one light year in one year.

Okay we'll do it with lasers then. You fire one laser the opposite direction from the other, in a year, what is the distance between the ends that both lasers have traveled? If the lasers were able to turn around and look back, would they see eachother as 1 lightyear apart, or 2? And if its 2, wouldnt that then infer that the lasers were moving away from each other at TWICE the speed of light?

You're going to keep getting nonsense if you talk about photons that can measure the behaviour of other photons.
An observer who watches both lasers (for instance by recording the time at which they light up targets at a known distance) will of course figure out that they illuminate targets two light years apart after one year, but that has nothing to do with what would be measured by an (impossible) observer travelling with one of the laser beams.

Grant Hutchison

[WayneFrancis]

If two objects move away from each other each moving the speed of light, and they both turn around and look where they came from, are they moving away from each other at the speed of light, or twice the speed of light? The area they would travel over the same amount of time would make it seem like twice the speed, but I know GR would say the speed of light. Isnt this a bit of a conundrum?

No it isn't a conundrum or a paradox. Because of the

V1 + V2
______________ = Apparent V

1 + ( V1V2/C^2)

formula you would see that they are moving away, relative to each other at C, If you take 2 objects travelling at .99C then
you get
1.98
_____ C
1.9801

or 0.99994949750012625624968435937579C

You'll never get to C unless at least one of the objects is already traveling at C in which it will always work out to C.

Now to an external observer, say at the point the 2 object started flying away from each other, it might appear that they are traveling apart at 2xC but neither object is traveling faster then C relative to any other point in the universe, again forgetting expansion which isn't really having an object move any faster.

[WayneFrancis]

But they were moving in opposite directions. Their distance between one another should be TWO light years. Okay we'll do it with lasers then. You fire one laser the opposite direction from the other, in a year, what is the distance between the ends that both lasers have traveled? If the lasers were able to turn around and look back, would they see eachother as 1 lightyear apart, or 2? And if its 2, wouldnt that then infer that the lasers were moving away from each other at TWICE the speed of light?

Two light years in YOUR frame of reference. Not 2 light years in THEIR frame of reference. You can think of light as having no real frame of reference. There is no distance and no time so lets talk about sub light speed.

I shoot 2 rockets off in opposite directions at .99C and let them travel for 1 year. How far apart are they?

To me they are 1.98 light years apart.
How far apart are they relative to each other? They are
0.1428 light years away from each other. Of coarse to them they have only been traveling for about 52 days and not 1 year.

Don't mistake and external frame of reference's perception as the on of the objects frame of reference.

[WayneFrancis]

Relative to you, and yes in a vacuum. The thing that I am hinting at is your reality is changing. You only aged one year, but someone standing right next to you aged 50 years in that one year that you percieved. Light travelled 50 light years from the person standing next to you + in your current perspective ( but you only aged one year ). But at no time did you ever see light travelling faster than the speed of light, it is just your perception of space and time that have changed.

Ummm you can not travel 1 light year and have someone right next to you age 50x more then you....they would have to be left far behind.

lets take your example and work backwards. How fast, to an external observer, would you need to travel to age 50x slower?

50 = 1/√1-(V^2/C2)
since the velocity I'm looking for can be in units of C then C =1 and C^2 = 1

50 = 1/√1-V^2

.02 = √1-V^2
0.0004 = 1 - V^2
V^2 = 1 - 0.0004
V = √0.9996
V = 0.99979997999599899971991597359142C
So Person A accelerates away from person B at 0.9997999...C
Person A's time dilates by 50x. Their perception of distance also dilates by 50x
In person's B's reference A traveled for 50 years.
In person's A's reference they traveled for only 1 year.
In person's A's reference they traveled ~49.99 light years
In person's B's accelerated reference they traveled fro ~0.9998 light years.
If person B slowed back down, relative to A then they would see that they had traveled for the ~49.99 light years and while they perceived time to only pass at 1/50th the rate of person A they are now back in that space/time reference frame.

If person B shined a laser at the destination just after launching and reaching their top speed Both person A and B would observe that laser traveling towards the destination at C. For person A it would get there in ~364 days 22 hours 14 min 52.1691538244 seconds For person B it would get there in 50 years.

When you say "your reality is changing" if you mean your perception of time and distance, along the axis of acceleration, is changing then yes. But things are still self consistent when you look at them through the proper formulas.

[WayneFrancis]

Sorry can we get back on track to my question?

I am at( jsut outside ) the event horizon of a black hole. An observer is out in empty space ( lets consider a vacuum for simplicity ). He detects that the black hole is 2 light-years away

I shoot the laser and wait 1 year what the observer also waits one year. I can see his clock and it is really spinning. It is clear that his time is moving much faster than my time.

The observer sees my clock and my clock appears stuck ... he realizes that my time is running much slower than his time.

Is everything OK so far?

so after 1 year of his time, the light is 1/2 way. However, 1 year of his time, is like 1 minute of my time. So I must percieve that light has made it half way to him in 1 minute. Since light travels as C ... I must percieve him as much closer to me than he percieves. Right? He is only 2 light minutes away from me.

Is this correct so far?

Now I hit my jets and leave lets say I just waited 1 minute ( light was halfway there ) and then left. I start to lose the effects of space-time dilation and get to a point where I am in the exact same reference frame as the distant observer. Our clocks are now running at the same speed. For me 1 minute + whatever time it took me to travel back to him , for him it was 1 year + whatever time it took for me to travel to him. We notice that our clocks are off by 1 year - 1 minute ( maybe slightly more because of the time dilation when travelling ).

For me I see the lasers that I shot being much farther from me than they should be. It fact by my calculations using straight C ... the light it exactly 1 year - 1 minute ( +- ) further along in its journey than I predicted using C.

I think you need to start using real numbers to get an idea of what is going on.
For 1 you can never be just outside the EH in your frame of reference. As you approach the EH it will slowly recede from you. Not as fast as you are traveling towards it but at a rate that you'll never actually hit it.

Lets just take your example from before of 50x
You, person A, are in the gravity well far enough that your time is 50x slower then the external person, B. Person B sees the distance from you to them as 2 light years. You see the distance as .04 light years. You flash the laser at person B and wait 1 year, in your frame of reference. You'll see that the laser flew past your friend in just over 1 week of your time. If you travel towards your friend you'll actually see time slow down because of your acceleration but as you climb out of the gravity well it will also speed up. IE if you did a constant burn then over all your time would even slow down even more when compared to your friend. So while you think it only took a week to get to your friend more then 2 years would have passed for them. When you slow down, accelerate in the opposite direction, you shift your frame of reference back to your friend. Now you'll see that the laser pulse you sent off about 2 weeks ago is now over 4 light years away.

Where you start to not make sense is

Now I hit my jets and leave lets say I just waited 1 minute ( light was halfway there ) and then left. I start to lose the effects of space-time dilation and get to a point where I am in the exact same reference frame as the distant observer. Our clocks are now running at the same speed. For me 1 minute + whatever time it took me to travel back to him , for him it was 1 year + whatever time it took for me to travel to him. We notice that our clocks are off by 1 year - 1 minute ( maybe slightly more because of the time dilation when travelling ).

If we use actual numbers and go back to my example where you just shined the laser and waited 1 minute then fired your rockets here is what has happened.

That 1 minute was 50 minutes to your friend. The relative distance the light traveled for both of you is the same. IE the fraction of the distance between the two of you is the same.

What happens from here is entirely dependent on how fast you traveled to your friend. Remember in your frame of reference you are only .04 light years from your friend. While your rockets are already burning to keep your position above the BH you are not actually accelerating yet. As soon as you boost your rocket to go to your friend then you start accelerating towards them and your clock will slow down even more relative to them. Thus that light pulse is getting further and further from you and you are also experiencing less time in relation to your friend. Say you travel at what you perceive to be .99C to your friend. How long would it take you?

well your apparent velocity is .99C to you. That .04 light years now appears to you as only 0.005642694 light years. Your friend doesn't see you traveling at .99C but at about 0.99999899477C It still take you, according to him just over 2 years passed.

So if you flashed the laser then immediately hit your boosters to .99C then you would get to your friend in about 2 days of your time. The light would have still passed your friend when you get there. As you traveled toward your friend your Lorentz factor relative to your friend jumped from 50x to over 700x so sure you observed the laser only travel 2 days, while you where flying towards your friend but when you slowed down that 2 days dilates out to 1400 days. You and your friend at any point in time would see the laser pulse at the same location what differs is your perception of the actual distance.

[R.A.F.]

Can an object moving away from you travel farther than 1 light year after 1 year?

No.

[WayneFrancis]

...So for the one who experienced the change of units of measurement could make it appear to him over the course of time that light travelled faster than the speed of light. ...

No for the person who experienced the change in units of measurement the light always travels at C.

Lets look at this another way.

You are on earth and shine a laser at Alpha Centauri. You wait 1 year then blast off toward Alpha Centauri at .99C how far has that light traveled?

Well to you the light has now only traveled 1/7th of a light year. Does this mean that it is traveling slower then C? Nope because you are in a reference frame that is slowed down by 7x. Just because you where not in that frame for a year doesn't mean that the speed of C appeared to change. In every frame of reference you are in the light appears to be traveling at C. It also doesn't seem to have been going slower before. The problem comes from you not shifting everything when you change reference frames. Remember for the actual light beam there is no time or distance. So you can't ask the light "How long have you been traveling?" or "How far have you traveled?" To light these questions don't make sense.

[WayneFrancis]

Nope. You just specified that they were moving at lightspeed relative to each other. That's one light year in one year.

You're going to keep getting nonsense if you talk about photons that can measure the behaviour of other photons.
An observer who watches both lasers (for instance by recording the time at which they light up targets at a known distance) will of course figure out that they illuminate targets two light years apart after one year, but that has nothing to do with what would be measured by an (impossible) observer travelling with one of the laser beams.

Grant Hutchison

Well put. If you talk about traveling at C then time and distance are meaningless.

If you talk about sub light speed then everything is also consistent as long as you understand the reference frames.

[WayneFrancis]

No I dont think this is where it went astray ... it is actually the heart of my question. The starting points of the two observers are distant but the at the end (t2) they are the same.

So yes the initial units of meausement are different. But at T2 they are the same. So for the one who experienced the change of units of measurement could make it appear to him over the course of time that light travelled faster than the speed of light.

For any instant of time the speed of light is measured at C .... however over the course of a year ( because now experiences a different unit of measurement ( compared to when he was near the EH )) light could have travelled further away from him than his current perception of 1 light year.

No it won't The math is a bit hard because it really depends on the size of the black hole and the positions of the 2 observers. But taking out the slope of the gravity well

Take the example of 2 observers
Observer A is further outside the gravity well then B
Observer A sees the distance as 2ly
Observer B sees the distance as 0.04ly
Observer B shoots laser pulse at Observer B and waits until it is half way to Observer B this takes 7.3 days to Observer B and take 1 year to the Observer A
Observer B then fires their rocket and instantly accelerates to .99C and travels to Observer A and instantly decelerates.
The distance from Observer B to A from B's frame of reference then collapses to 0.002836ly The laser pulse then appears to have only travel 0.001418ly.
Observer B travels for 1 day 50 min 30 seconds in their frame of reference to reach Observer B.
Total time for the laser pulse, in B's reference frames is 8 days 8 hours 2 min and change
The distance that B observed the light to travel is also 7.3 light days + 1.035 light days

If you talk about B's frame of reference when it comes to a stop beside A then B has to use A's clock and acknowledge that the light was emitted 2 years ago not just over 8 days. If you try to say "Where was the laser pulse 8 days ago?" after stopping beside the A then you are talking about 8 days in A's reference frame not the past 8 days in B's reference frame. If you do talk about B's reference frames when considering time then you must ALSO consider B's reference frames when it comes to distance in which case the light only has traveled just over 8 light days.




then ignites their engine instantly bringing them to .99C and flies to Observer B.

[NEOWatcher]

No I dont think this is where it went astray ... it is actually the heart of my question....

It seems that I have some back up here. Of course I'm not using math just like you're not using math, so we are both speaking in terms of intuition. The difference is that I do have a strong math background, so I can envision it in those terms. I'm just too lazy to work it out.

[rommel543]

I have a question and a comment:

The question is more a hmm I wonder type of thing. If I was traveling at .99 c (hypothetically saying that I could) and I pointed a laser in the direction I was traveling what would happen to the light? Would I see the point of light slowly moving away or would I see anything at all?

The comment is regarding the two object traveling away from each other at the speed of light for 1 year (traveling 1 light year) .

If the lasers were able to turn around and look back, would they see eachother as 1 lightyear apart, or 2? And if its 2, wouldnt that then infer that the lasers were moving away from each other at TWICE the speed of light?

The problem here is that the two lasers are traveling from a relative starting point, not each other and you need to calculate from that point.

If two people were standing back to back then walked for 1 hour at 1 mile per hour away from each other, they would be 2 miles apart. That doesn't mean their speed doubled, only the distance apart. Calculating their speed is from a relative starting point, not each other. Even relative to each other you still need to take into account that both bodies are in motion.

If the two lasers traveled in the same direction instead of opposite directions they would have still traveled 1 light year, not 0, its just that they distance between them is different than the original posting.

[grant hutchison]

The question is more a hmm I wonder type of thing. If I was traveling at .99 c (hypothetically saying that I could) and I pointed a laser in the direction I was traveling what would happen to the light? Would I see the point of light slowly moving away or would I see anything at all?

Any experiment you could do to measure the speed of light in your rapidly moving laboratory would give the same result as if you were standing still: light would move at lightspeed relative to your experimental apparatus. In fact, there's no experiment you could do to tell whether you were "moving" or "standing still", because these conditions can only be measured relative to another observer.

Grant Hutchison

[rommel543]

Any experiment you could do to measure the speed of light in your rapidly moving laboratory would give the same result as if you were standing still: light would move at lightspeed relative to your experimental apparatus. In fact, there's no experiment you could do to tell whether you were "moving" or "standing still", because these conditions can only be measured relative to another observer.

Grant Hutchison

That's if I am in a enclosed area (kind of like the whole jumping on a moving train experiment). I'm talking hypothetically that I have the ability to travel at close to speed of light myself (dun da dun.. what's that up in the sky?..is it a bird? Is it a plane? No its a hypothetical flying computer programmer with an over active imagination!).