The part of relativity I never got, reference frame

[Mr.Bigg]

So I was pondering long distance space travel. As I understand it, if you can accelerate a vessel, say over the course of a year, to near light speeds, you can cover very very long distances in a very short period of time(as measured on your on space ship) due to the effects of relativity. Depending on the speed achieved, you can travel thousands of light years on a few years worth of life support, yes?

What I don't understand is where reference frames come into the question. Say you took the reference frame of the other planet you are trying to reach. If you hold the spaceship constant, and travel towards it at the same speeds. Thousands of years would pass before you(the planet), reached the ship. Accordingly, everyone on board is dead and gone. Since there is no 'true' reference frame, which is correct? Are both somehow correct?

Let me know if I am being unclear in my scenario/question.

 

[marcus]

It depends on who does the accelerating.

 

[tiny-tim]

Hi Mr.Bigg!

Say you took the reference frame of the other planet you are trying to reach. If you hold the spaceship constant, and travel towards it at the same speeds. Thousands of years would pass before you(the planet), reached the ship. Accordingly, everyone on board is dead and gone.

To simplify matters, we'll assume there is no acceleration …

the ship was already at cruising speed before it passed the Earth, and doesn't brake until after it passes the planet.

So it passes Earth in 2011 and passes the planet in 3011, but everyone on board is only a few years older.

ok, in the spaceship's frame, the distance is much shorter, enabling the planet to reach them in only a few years.

But the date on the planet in the spaceship's frame of reference when the Earth passes the spaceship is 3011 (minus a few minutes), not 2011 (ie, that's what the calendar on the planet says at the time which the spaceship regarded as the present), and of course it's 3011 when the planet passes the spaceship, so everyone on the planet ages only a few minutes … far less than the few years on the spaceship!

 

[Antiphon]

Tiny, this doesn't seem right to me. Suppose the planet and Earth had synchronized calendars as you assume. If the planet were broadcasting it's present date the Earth and the spaceship would both read the remote date from their signal as 1011 as the ship passed earth, not 2011 or 3011. During the couple of years it took the ship to get there, they would read the calendar broadcast as traversing 2000 years of remote planet time in just a few spaceship years, right?

 

[ghwellsjr]

So I was pondering long distance space travel. As I understand it, if you can accelerate a vessel, say over the course of a year, to near light speeds, you can cover very very long distances in a very short period of time(as measured on your on space ship) due to the effects of relativity. Depending on the speed achieved, you can travel thousands of light years on a few years worth of life support, yes?

What I don't understand is where reference frames come into the question. Say you took the reference frame of the other planet you are trying to reach. If you hold the spaceship constant, and travel towards it at the same speeds. Thousands of years would pass before you(the planet), reached the ship. Accordingly, everyone on board is dead and gone. Since there is no 'true' reference frame, which is correct? Are both somehow correct?

Let me know if I am being unclear in my scenario/question.

Your first paragraph is an adequate description of your scenario without regard to any frame of reference, but if you want to assign your scenario to a reference frame, it would be easiest to pick one in which the two planets are at rest and in which the traveler starts and ends at rest. Remember, a frame of reference is merely a coordinate system involving three components of space (X, Y, and Z) and one component of time (T). You can then state the locations of the two planets and the path of the traveler as a function of time. Then, if you want to see what the components would be in any other reference frame, you should use the Lorentz Transform to convert them from the one frame to the other frame. This will prevent you from concluding that the traveler survives the trip when assigned to one frame of reference and dies in another frame.

 

[Rap]

So I was pondering long distance space travel. As I understand it, if you can accelerate a vessel, say over the course of a year, to near light speeds, you can cover very very long distances in a very short period of time(as measured on your on space ship) due to the effects of relativity. Depending on the speed achieved, you can travel thousands of light years on a few years worth of life support, yes?

What I don't understand is where reference frames come into the question. Say you took the reference frame of the other planet you are trying to reach. If you hold the spaceship constant, and travel towards it at the same speeds. Thousands of years would pass before you(the planet), reached the ship. Accordingly, everyone on board is dead and gone. Since there is no 'true' reference frame, which is correct? Are both somehow correct?

Let me know if I am being unclear in my scenario/question.

This is kind of like the twin paradox. The situation is not symmetric. The person taking off from Earth accelerates, the other planet does not. After the acceleration phase, the person on the ship will see the other planets population has aged significantly. To people on the planet, they will not see the same effect on the people in the rocket.

 

[HallsofIvy]

But taking the scenario tiny tim suggested where the spaceship is already at full speed relative to the target planet) when it passes Earth and maintains that speed until after it has passed the planet, it is symmetric. From the "reference frame" of the planet (and the Earth since even planets around different stars will not have relative speeds near c), it will take a thousand years for the ship to reach the other star but you would observe time to have slowed down for people on the starship so they will arrive while still alive. Frome the "reference frame" of the ship, the distance between the Earth and the planet will have been compressed so, even at speeds below the speed of light, they will arrive while they are still alive. No "paradox".

 

[Rap]

But taking the scenario tiny tim suggested where the spaceship is already at full speed relative to the target planet) when it passes Earth and maintains that speed until after it has passed the planet, it is symmetric. From the "reference frame" of the planet (and the Earth since even planets around different stars will not have relative speeds near c), it will take a thousand years for the ship to reach the other star but you would observe time to have slowed down for people on the starship so they will arrive while still alive. Frome the "reference frame" of the ship, the distance between the Earth and the planet will have been compressed so, even at speeds below the speed of light, they will arrive while they are still alive. No "paradox".

Yes. The twin paradox (I know, not being considered here) always involves acceleration when the other twin turns to come back, and that's where the other twin sees people aging rapidly on earth.

 

[tiny-tim]

Hi Antiphon!

Tiny, this doesn't seem right to me. Suppose the planet and Earth had synchronized calendars as you assume. If the planet were broadcasting it's present date the Earth and the spaceship would both read the remote date from their signal as 1011 as the ship passed earth, not 2011 or 3011. During the couple of years it took the ship to get there, they would read the calendar broadcast as traversing 2000 years of remote planet time in just a few spaceship years, right?

At the moment the spaceship passes the Earth, the spaceship's present and the Earth's present do not coincide.

If the planet's calendar shows 2011 at what Earth (at that moment) calls the present, then it shows 3011 at what the spaceship (at that same moment) calls the present.

(and btw the broadcast signal will not reach Earth until just before 3011)

 

[Mr.Bigg]

Hi Mr.Bigg!


To simplify matters, we'll assume there is no acceleration …

the ship was already at cruising speed before it passed the Earth, and doesn't brake until after it passes the planet.

So it passes Earth in 2011 and passes the planet in 3011, but everyone on board is only a few years older.

ok, in the spaceship's frame, the distance is much shorter, enabling the planet to reach them in only a few years.

But the date on the planet in the spaceship's frame of reference when the Earth passes the spaceship is 3011 (minus a few minutes), not 2011 (ie, that's what the calendar on the planet says at the time which the spaceship regarded as the present), and of course it's 3011 when the planet passes the spaceship, so everyone on the planet ages only a few minutes … far less than the few years on the spaceship!

Thanks, that makes sense. I guess I get caught up thinking, one can leave Earth and get to the planet (for the sake of argument with zero relative speed to the earth) 1000 years later and it would be 1000 years later for both planets. But that distinction doesn't really hold up when you have to send 1000 year old information between the two. Anyway, whether my reasoning there makes sense, I understand what you've posted.

 

[ghwellsjr]

I found this thread to be quite remarkable. That's why I'm going to make some remarks about it.

At first glance, it appears that there is a lot of disagreement going on here but after studying very carefully what each contributor is saying and where they are coming from, I can see that they are all making valid statements.

But before I comment on the individual posts, let me summarize the scenario that seems to have been agreed upon by everyone:

A spaceship leaves the vicinity of Earth at a very high speed bound for a planet 1000 light-years away. The space travelers age only about a year or so during the trip.

Mr. Bigg asked about how "reference frames come into question". It's important to realize that if you want to "take the reference frame of the other planet", what is commonly understood by this phraseology, is a frame in which the planet is at rest. But there are an infinite number of them, as they can vary in the orientations (directions) of the three axes and the origin of the three axes. They can also vary in when you call the time "zero". Also, it's important to realize that just because the planet is at rest in whichever frame is selected, all the other objects are also in that same reference frame. So in this case, the Earth is also at rest and the spaceship is moving.

Now I suggested that after you select your reference frame, if you want to see what the X, Y, Z, and T components look like in another reference frame, you should use the Lorentz Transform to do the conversion. But it should be noted that the LT does not automatically do everything for you. Instead, you have to pick events in your starting frame and convert them individually to the final frame. An event is any coordinate of time plus the three coordinates of space (whether or not anything is located at that defined point in space and at that specific time). So two obvious events would be when the spaceship leaves Earth and when it arrives at the planet.

So now let's say you want to use a frame in which the spaceship is at rest. You could use the LT to get from your previous one to this new one or you could pick another one of the infinite frames that are available to you.

That's what tiny-tim did in his first post. He picked a frame for the spaceship such that the calendar on the spaceship had the same date as the planet had when the spaceship arrived at the planet (approximately 3011). This, of course, made the date on the spaceship calendar way different from the date on the Earth calendar at the time when the spaceship left the vicinity of earth.

Then Antiphon questioned tiny-tim's dates and posted some dates that seemed to be correct to him. However, Antiphon was talking about dates that the Earth and spaceship travelers see of the distant planet's calendar, so we have to now take into account the fact that images are in transit at the speed of light from the planet to Earth and the spaceship. In particular, since it takes a thousand years for light to get from the planet to earth, anyone viewing the planet would see it as it appeared one thousand years ago, that is, the calendar would be displaying 1011. Then as the spaceship made its trip, it would observe the years on the planet's calendar progressing through 200+ years in a very short time according to its own clock/calendar.

After that, Rap posted that the situation was not symmetrical because the space travelers would be seeing time on the planet advancing at a rapid constant pace, right from the beginning to the end of the trip, whereas, the planet would not see a similar thing concerning the spaceship. As a matter of fact, they will not even be able to see the spaceship until a year or so before the spaceship arrives around 3011 and then they will see its calendar advancing at the same rate that the spaceship saw the planet's calendar advancing.

Next, HallsofIvy defended tiny-tim's assessment, disagreeing with the lack of symmetry that Rap noted, but he was talking, again, about what is determined by the two reference frames and not what was viewable by the various participants in the scenario.

And then Rap defended his observation, again re-iterating that it had to do with what people see and tiny-tim defended his reference frame position.

So what is the lesson to be learned here? Obviously, if you're going to talk about what the various participants actually see as they go through the various stages of the scenario, you cannot expect them to have the same kind of information that is provided by a frame of reference, where clocks have been previously synchronized across the entire domain of the scenario. Instead, their observations are of necessity delayed by the light transit time. Posters should make it clear whether they are talking about what observers can see when looking at remote objects, or whether they are talking about co-ordinate times which the observers do not see when looking at remote objects.

 

[Rap]

After that, Rap posted that the situation was not symmetrical because the space travelers would be seeing time on the planet advancing at a rapid constant pace, right from the beginning to the end of the trip, whereas, the planet would not see a similar thing concerning the spaceship. As a matter of fact, they will not even be able to see the spaceship until a year or so before the spaceship arrives around 3011 and then they will see its calendar advancing at the same rate that the spaceship saw the planet's calendar advancing.

Next, HallsofIvy defended tiny-tim's assessment, disagreeing with the lack of symmetry that Rap noted, but he was talking, again, about what is determined by the two reference frames and not what was viewable by the various participants in the scenario.

And then Rap defended his observation, again re-iterating that it had to do with what people see and tiny-tim defended his reference frame position.

Well, I would not characterize my exchange with HallsOfIvy that way. I always talk about what one "sees" at a particular instant as what they will calculate to have happened at that instant, taking into account the speed of light. In my first post, I was assuming the spaceship to be at rest with respect to the Earth, then experiencing a short acceleration phase, after which it completed most of the journey at constant velocity to the other planet. When at the Earth, and at rest with respect to the Earth, the spaceship would "see" its calendar and the calendars on both planets set to 2011. After the short acceleration phase (a day in duration, I know, not realistic) the spaceship would "see" both its calendar and Earth's calendar to be set at ~2011, but would see the other planets calendar set to ~3011. That was the "rapid ageing" I was speaking about, and the asymmetry was the acceleration of the spaceship, absent in both planets. At this point, things go about the same as if the spaceship had passed the Earth without acceleration assuming both the Earth and spaceship calendar coincided at 2011 as the spaceship passed the Earth. This was what HallsOfIvy stated - no acceleration, and I agreed, there would be no rapid ageing of the people on the other planet (actually they would age more slowly) as the rocket sped towards the other planet. Still, when the rocket passed Earth, it would "see" the other planet's calendar as set to 3011. I remarked that this was like the twin paradox, where the twin that turns around, "sees" the population of the Earth age rapidly during the turnaround phase of the trip, while ageing more slowly during the constant-velocity phases.

 

[ghwellsjr]

Well, I would not characterize my exchange with HallsOfIvy that way. I always talk about what one "sees" at a particular instant as what they will calculate to have happened at that instant, taking into account the speed of light. In my first post, I was assuming the spaceship to be at rest with respect to the Earth, then experiencing a short acceleration phase, after which it completed most of the journey at constant velocity to the other planet. When at the Earth, and at rest with respect to the Earth, the spaceship would "see" its calendar and the calendars on both planets set to 2011. After the short acceleration phase (a day in duration, I know, not realistic) the spaceship would "see" both its calendar and Earth's calendar to be set at ~2011, but would see the other planets calendar set to ~3011. That was the "rapid ageing" I was speaking about, and the asymmetry was the acceleration of the spaceship, absent in both planets. At this point, things go about the same as if the spaceship had passed the Earth without acceleration assuming both the Earth and spaceship calendar coincided at 2011 as the spaceship passed the Earth. This was what HallsOfIvy stated - no acceleration, and I agreed, there would be no rapid ageing of the people on the other planet (actually they would age more slowly) as the rocket sped towards the other planet. Still, when the rocket passed Earth, it would "see" the other planet's calendar as set to 3011. I remarked that this was like the twin paradox, where the twin that turns around, "sees" the population of the Earth age rapidly during the turnaround phase of the trip, while ageing more slowly during the constant-velocity phases.

Why do you now put quotes around the word 'see' when you didn't do that before? Why do you give yourself permission to redefine a perfectly good English word to fit your own arbitrary definition without telling anybody?

Your concept of the traveler being able to calculate what happens at some instant is based on arbitrarily selected (by you) frames of reference. There are always an infinite number of frames of reference in which any observer is at rest and you happened to have picked two, one before acceleration and one after acceleration, in which the planet ends up having aged suddenly between the two and you think this is something so significant that you can justify claiming that this is what the traveler sees, quotes or no quotes.

Did you notice that tiny-tim arbitrarily selected a reference frame for the traveler so that his calendar would correlate to the planet's calendar when the traveler arrived there so that at the beginning of the trip when the traveler was still near earth, there was a big difference between the Earth's calendar and the traveler's calendar? He could just as easily have picked a frame of reference in which the two calendars had the same date at the start of the trip and different dates at the end. There is no preferred way to pick a frame.

If we had used the Lorentz Transform to get from our earth/planet rest frame in which both of them had calendars set to the year 2011 and then calculated the year in the rest frame of the traveler, the year would be no where near 2011 or 3011.

Your problem, Rap, is that you haven't learned that time is relative and that you cannot talk about a common instant between observers in relative motion. You need to learn this. Why don't you try to use your scheme to analyze what the traveler "sees" of both the Earth's calendar and the planet's calendar at the same time?

Furthermore, frames of reference are essentially useless when trying to determine what observers actually see and I mean this in the ordinary English sense of the word (as in "seeing is believing", not as in "I see, said the blind man"). You cannot remove the speed of light and the time delay between when an image is sent on its way from a source to the observer. It won't matter which arbitrarly selected frame of reference is used or even switching between frames of reference, there is only one answer to the question of what an observer sees and on this thread, Antiphon is the one who correctly described what the traveler sees. Everybody else was talking about frames of reference, which is what the OP asked about, but at least no one else claimed that their arbitrarily selected frames of reference provided a clue as to what the traveler sees, except you.

 

[Rap]

Why do you now put quotes around the word 'see' when you didn't do that before? Why do you give yourself permission to redefine a perfectly good English word to fit your own arbitrary definition without telling anybody?

Because I made the incorrect assumption that this was what people meant by "see". The English word "see" can cause confusion by blurring the distinction between what one observes at an instant and what happens at that instant, by assuming Galilean invariant time. We need to distinguish between what one observes and what one calculates as being simultaneous, given the finite speed of light. I am not interested in semantic arguments, only that we have well defined terms when we converse. I am happy to use the word "see" to mean what we observe, and refer to simultaneous events as what we calculate to be simultaneous given the finite speed of light.

Your concept of the traveler being able to calculate what happens at some instant is based on arbitrarily selected (by you) frames of reference. There are always an infinite number of frames of reference in which any observer is at rest and you happened to have picked two, one before acceleration and one after acceleration, in which the planet ends up having aged suddenly between the two and you think this is something so significant that you can justify claiming that this is what the traveler sees, quotes or no quotes.

If two firecrackers go off on the other planet, one in 2011, one in 3011 and a day, the rocket ship on earth, taking a day to accelerate, will observe by observing the flash, after accounting for the speed of light, that the first one went off as he began his acceleration in 2011, the second one went off a day later by his calendar, after his acceleration was complete, in the frame of reference stationary with respect to him. He will not see these events as they happen, but when he does, he will see someone setting off the first firecracker, and their ancestor a thousand years later setting off the second one.

Did you notice that tiny-tim arbitrarily selected a reference frame for the traveler so that his calendar would correlate to the planet's calendar when the traveler arrived there so that at the beginning of the trip when the traveler was still near earth, there was a big difference between the Earth's calendar and the traveler's calendar? He could just as easily have picked a frame of reference in which the two calendars had the same date at the start of the trip and different dates at the end. There is no preferred way to pick a frame.

Yes. I was assuming, and stated explicitly, that the calendars of both planets, stationary with respect to each other, and the rocket ship before acceleration, stationary with respect to the Earth, had their calendars synchronized to 2011. In other words, they would agree, after taking the speed of light into account, that all three had flipped their calendars to January 1, 2011 simultaneously. This is possible because all three share the same inertial frame, but with different origins.

If we had used the Lorentz Transform to get from our earth/planet rest frame in which both of them had calendars set to the year 2011 and then calculated the year in the rest frame of the traveler, the year would be no where near 2011 or 3011.

Yes, under tiny tim's assumptions, not under mine.

Your problem, Rap, is that you haven't learned that time is relative and that you cannot talk about a common instant between observers in relative motion. You need to learn this. Why don't you try to use your scheme to analyze what the traveler "sees" of both the Earth's calendar and the planet's calendar at the same time?

Our problem is that we sometimes do not communicate well. Two observers in relative motion can agree on a common instant in time for one event, all they have to do is set their clocks to agree on the time that they calculate that that event occurred, taking into account the finite speed of light. After that, their clocks will not agree on the time coordinate for any event. If you still think I need to use my scheme to analyze the problem you stated, I will.

Furthermore, frames of reference are essentially useless when trying to determine what observers actually see and I mean this in the ordinary English sense of the word (as in "seeing is believing", not as in "I see, said the blind man"). You cannot remove the speed of light and the time delay between when an image is sent on its way from a source to the observer. It won't matter which arbitrarly selected frame of reference is used or even switching between frames of reference, there is only one answer to the question of what an observer sees and on this thread, Antiphon is the one who correctly described what the traveler sees. Everybody else was talking about frames of reference, which is what the OP asked about, but at least no one else claimed that their arbitrarily selected frames of reference provided a clue as to what the traveler sees, except you.

Again, my reference frames were not arbitrarily selected. I totally agree that there is only one answer to what an observer sees, but I never meant that seeing two events occur simultaneously means that the observer will calculate those events as having occurred simultaneously.

 

[tiny-tim]

That's what tiny-tim did in his first post. He picked a frame for the spaceship such that the calendar on the spaceship had the same date as the planet had when the spaceship arrived at the planet (approximately 3011). This, of course, made the date on the spaceship calendar way different from the date on the Earth calendar at the time when the spaceship left the vicinity of earth.

Did you notice that tiny-tim arbitrarily selected a reference frame for the traveler so that his calendar would correlate to the planet's calendar when the traveler arrived there so that at the beginning of the trip when the traveler was still near earth, there was a big difference between the Earth's calendar and the traveler's calendar? He could just as easily have picked a frame of reference in which the two calendars had the same date at the start of the trip and different dates at the end. There is no preferred way to pick a frame.

no, this is wrong (and it's not what i said)

i didn't actually choose a frame for the spaceship (or, to be more precise, a clock start-time … the velocity of the spaceship's frame is fixed, and we can only choose the start-time of the clock) …

i only talked about the spaceship's "present" …

when the (non-accelerating) spaceship is passing the Earth, both the Earth and the spaceship agree about what is the "present" on Earth …

but they wildly disagree about what is the "present" on the other planet: the Earth says that the "present" is planet calendar-year 2011, but the spaceship says that the "present" is planet calendar-year 3011 …

(of course, neither of them can see the planet's calendar "at the present" … the light will take nearly 1000 years to reach the Earth, and several hours to reach the spaceship … this is just a calculation )

the spaceship's "present" goes wildly into the Earth's "future" for large distances forward, and wildly into the Earth's "past" for large distances backward

But the date on the planet in the spaceship's frame of reference when the Earth passes the spaceship is 3011 (minus a few minutes), not 2011 (ie, that's what the calendar on the planet says at the time which the spaceship regarded as the present), and of course it's 3011 when the planet passes the spaceship, so everyone on the planet ages only a few minutes … far less than the few years on the spaceship!

 

[Rap]

when the (non-accelerating) spaceship is passing the Earth, both the Earth and the spaceship agree about what is the "present" on Earth …

but they wildly disagree about what is the "present" on the other planet: the Earth says that the "present" is planet calendar-year 2011, but the spaceship says that the "present" is planet calendar-year 3011 …

(of course, neither of them can see the planet's calendar "at the present" … the light will take nearly 1000 years to reach the Earth, and several hours to reach the spaceship … this is just a calculation )

Right, and for a spaceship that is at rest on Earth, Earth and spaceship will agree that at present, the other planet's calendar reads 2011. Yet, a day later, when the spaceship has accelerated and attained its final velocity, it will say that at present, the calendar on the other planet reads 3011, the same as it would if it had passed the Earth at that velocity, as described in your second paragraph above. This is the "rapid aging"on the second planet (according to the spaceship) that I was referring to. And again, the spaceship cannot see the other planet's calendar "at present" because it takes time for the light from the other planet to reach the spaceship. This is a conclusion it will draw at that time.

 

[tiny-tim]

Hi Rap!

Right, and for a spaceship that is at rest on Earth, Earth and spaceship will agree that at present, the other planet's calendar reads 2011. Yet, a day later, when the spaceship has accelerated and attained its final velocity, it will say that at present, the calendar on the other planet reads 3011, the same as it would if it had passed the Earth at that velocity, as described in your second paragraph above. This is the "rapid aging"on the second planet (according to the spaceship) that I was referring to.

Actually, you said the opposite …

… This was what HallsOfIvy stated - no acceleration, and I agreed, there would be no rapid ageing of the people on the other planet (actually they would age more slowly) as the rocket sped towards the other planet.

Still, when the rocket passed Earth, it would "see" the other planet's calendar as set to 3011. I remarked that this was like the twin paradox, where the twin that turns around, "sees" the population of the Earth age rapidly during the turnaround phase of the trip, while ageing more slowly during the constant-velocity phases.

… "no rapid ageing of the people on the other planet" .

You're now referring to the "ageing" after acceleration …

you can't do that … the spaceship knows perfectly well that it has accelerated, and will
not attribute any ageing to the planet.

 

[Rap]

Hi tiny-tim!

Sorry for the deleted post, I thought It was in error, but I was mistaken. LOL

Actually, you said the opposite …

I don't believe I did - I was responding to HallsOfIvy who said no acceleration, and I agreed that in that case there would be no ageing.

… "no rapid ageing of the people on the other planet" .

You're now referring to the "ageing" after acceleration …

you can't do that … the spaceship knows perfectly well that it has accelerated, and will
not attribute any ageing to the planet.

What I am saying is this - in one case you have a spaceship passing the Earth going towards the other planet. The other planet is at rest with respect to Earth. When the spaceship passes the Earth, its calendar and Earth's calendar coincide at 2011. Earth says, at that time, its calendar agrees with that of the other planet, at 2011. The spaceship, however, says that at that time the other planet's calendar reads 3011. No rapid ageing on the other planet, according to the spaceship, but a disagreement with Earth as to the reading of the other planet's calendar.

In the accelerated case, you start with all three at rest with respect to each other, the spaceship is sitting on Earth, and all three agree that all calendars read 2011. Then the spaceship accelerates for a time that is quite small compared to the time it takes for it to travel to the other planet. Its acceleration stops when its velocity reaches that value that it had in the first case. At this point, the spaceship says the same thing as in the first case: that the calendar on the other planet reads 3011. This is what I mean by the rapid aging of the second planet, from the point of view of the spaceship. In a time very small with respect to its total travel time to the other planet, the other planet's calendar has gone from 2011 to 3011.

All of these conclusions are, of course, subject to delays due to the finite speed of information.

(I will be offline for a few days, so if you prove me wrong, hold on)

 

[ghwellsjr]

Because I made the incorrect assumption that this was what people meant by "see". The English word "see" can cause confusion by blurring the distinction between what one observes at an instant and what happens at that instant, by assuming Galilean invariant time. We need to distinguish between what one observes and what one calculates as being simultaneous, given the finite speed of light. I am not interested in semantic arguments, only that we have well defined terms when we converse. I am happy to use the word "see" to mean what we observe, and refer to simultaneous events as what we calculate to be simultaneous given the finite speed of light.

Thank you for making this admission.

Now I'd like to summarize from various posts what you are saying about the spaceship:

When at the Earth, and at rest with respect to the Earth, the spaceship would "see" its calendar and the calendars on both planets set to 2011. After the short acceleration phase (a day in duration, I know, not realistic) the spaceship would "see" both its calendar and Earth's calendar to be set at ~2011, but would see the other planets calendar set to ~3011.

If two firecrackers go off on the other planet, one in 2011, one in 3011 and a day, the rocket ship on earth, taking a day to accelerate, will observe by observing the flash, after accounting for the speed of light, that the first one went off as he began his acceleration in 2011, the second one went off a day later by his calendar, after his acceleration was complete, in the frame of reference stationary with respect to him. He will not see these events as they happen, but when he does, he will see someone setting off the first firecracker, and their ancestor a thousand years later setting off the second one.

Yes. I was assuming, and stated explicitly, that the calendars of both planets, stationary with respect to each other, and the rocket ship before acceleration, stationary with respect to the Earth, had their calendars synchronized to 2011. In other words, they would agree, after taking the speed of light into account, that all three had flipped their calendars to January 1, 2011 simultaneously. This is possible because all three share the same inertial frame, but with different origins.

What I am saying is this - in one case you have a spaceship passing the Earth going towards the other planet. The other planet is at rest with respect to Earth. When the spaceship passes the Earth, its calendar and Earth's calendar coincide at 2011. Earth says, at that time, its calendar agrees with that of the other planet, at 2011. The spaceship, however, says that at that time the other planet's calendar reads 3011. No rapid ageing on the other planet, according to the spaceship, but a disagreement with Earth as to the reading of the other planet's calendar.

In the accelerated case, you start with all three at rest with respect to each other, the spaceship is sitting on Earth, and all three agree that all calendars read 2011. Then the spaceship accelerates for a time that is quite small compared to the time it takes for it to travel to the other planet. Its acceleration stops when its velocity reaches that value that it had in the first case. At this point, the spaceship says the same thing as in the first case: that the calendar on the other planet reads 3011. This is what I mean by the rapid aging of the second planet, from the point of view of the spaceship. In a time very small with respect to its total travel time to the other planet, the other planet's calendar has gone from 2011 to 3011.

You have made it clear that all three, the earth, the spaceship, and the planet have their own calendars synchronized while the spaceship is in the vicinity of earth, both before and after the short acceleration phase.

But what I don't understand is how you conclude that the spaceship calculates the planet's calendar is at 3011 while still in the vicinity of earth.

As Antiphon pointed out in post #4 and as I affirmed in post #11, prior to the spaceship's acceleration, he and the Earth see the planet's calendar set to 1011 but they know, because of a prior synchronization of the calendars that it is actually at 2011. But it will take another thousand years before the year 3011 shows up on the Earth's calendar and on the planet's calendar, according to their common rest frame. I don't see how a day of spaceship acceleration can cause 1000 years of time to be made available to the spaceship.

If a firecracker were set off in the year 2011 on the planet and another one in 3011, the spaceship would not see the first one until half way through its trip and it would see the second one just about the time it arrived at the planet. Even if you take into account the light travel time, it doesn't allow you to say in any sense that the second firecracker went off when the spaceship was near earth, at least as far as I can tell.

So could up please help me understand the calculation that the spaceship makes that allows him, after the fact, of course, to conclude that he was near the Earth when the second firecracker went off.

 

[Rap]

You have made it clear that all three, the earth, the spaceship, and the planet have their own calendars synchronized while the spaceship is in the vicinity of earth, both before and after the short acceleration phase.

But what I don't understand is how you conclude that the spaceship calculates the planet's calendar is at 3011 while still in the vicinity of earth.

As Antiphon pointed out in post #4 and as I affirmed in post #11, prior to the spaceship's acceleration, he and the Earth see the planet's calendar set to 1011 but they know, because of a prior synchronization of the calendars that it is actually at 2011. But it will take another thousand years before the year 3011 shows up on the Earth's calendar and on the planet's calendar, according to their common rest frame. I don't see how a day of spaceship acceleration can cause 1000 years of time to be made available to the spaceship.

Maybe we are again confusing "see" (as in "observe now") and "calculate to be happening now". As you said, prior to the spaceship's acceleration (at rest on Earth), the Earth and spaceship "see" the other planet's calendar to be set at 1011, and calculate that 2011 is "happening now" on the other planet. I agree with tiny-tim's statement in #9, regarding a spaceship which passes by the Earth (rather than accelerating from it), with calendars set to 2011 at passing:

If the planet's calendar shows 2011 at what Earth (at that moment) calls the present, then it shows 3011 at what the spaceship (at that same moment) calls the present.

In other words, if the spaceship did not accelerate, but rather passed the Earth at its final velocity, and its calendar and Earth's calendar agreed at 2011 when it passed, then Earth would, at that instant, see the other planet's calendar as reading 1011, and calculate that 2011 was happening now on the other planet. The spaceship would see the other planet's calendar as reading 1011 also, of course, but would calculate that 3011 was happening now on the other planet.

When the spaceship is at rest on Earth, its calendar will be at 2011, same as Earth, and the same as the other planet. After the spaceship accelerates, it will be in (roughly) the same inertial frame as the rocket that did not accelerate, and so it will see things roughly the same as the rocket that did not accelerate: i.e. its calendar will still be set to roughly 2011 and, like the spaceship passing the Earth, it will calculate 3011 to be happening now on the other planet. In other words, during the acceleration phase, it will calculate the other planet's calendar to move from 2011 to 3011, while seeing it at 1011.

If a firecracker were set off in the year 2011 on the planet and another one in 3011, the spaceship would not see the first one until half way through its trip and it would see the second one just about the time it arrived at the planet. Even if you take into account the light travel time, it doesn't allow you to say in any sense that the second firecracker went off when the spaceship was near earth, at least as far as I can tell.

So could up please help me understand the calculation that the spaceship makes that allows him, after the fact, of course, to conclude that he was near the Earth when the second firecracker went off.

Hmm - we have been assuming that the spaceship is traveling nearly the speed of light, and glossing over the small differences. If the other planet is 1000 light years from Earth, and the spaceship makes the trip in 2 years, by its reckoning, then it will reach the other planet at 2013 by its own calendar, 3011 plus a small amount, according to the other planet's calendar. That small amount is the thing. The spaceship will see the first firecracker go off, 2011 by the other planet's calendar, about half way through its trip, as you say. It will see the second firecracker go off a bit before it passes the second planet, 3011 plus a little by the second planet's calendar, a bit before 2013 by the spaceship's calendar. At that point, the spaceship will be able to calculate that the second firecracker went off at 2011 by its own calendar, 3011 by the other planet's calendar.