How Does Time Dilation Affect Colony Ships A and B in Relativity Theory?

[Dropout]

Been asking this since 1994.



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50,000 years have passed since Colony spaceship A and Colony spaceship B launched from Earth. Like in a star trek episode, they all reverted to barbarism, and then regrew a new technological society. Forgot where they came from, and what theyre doing. Theyre big colony ships.

Colony ship A gets on the radio and finds out that they are 1 light-year away from Colony ship B. They start commmunicating with each other, and discover they are also at rest with each other. They decide to join forces, but Colony ship B's propulsion system is broke. So Colony Ship A then accelerates REAL FAST at 99.99999999999999% the speed of light in 1 minute to dock with Colony ship B, 1 year later Colony Ship A decelerates and then docks with the other colony ship.

So according to relativity colony ship A only aged a few hours, while Colony Ship B aged an entire year.

WRONG!



------B ----------A

C

Some guy on Planet C that's monitoring the entire situation, notices that Colony ship A and B are wizzing by at 99.9999999999999999999999% the speed of light. Planet C sees that A decelerates to zero, then reaccelerates to 99.99999999999999999% the speed of light to dock with B. PLanet C notes that B experienced time dilation the entire time.

So what is it?

A) A new universe is created for Planet C that says Colony Ship B experienced time dialation.

B) Each particle in the universe has a history log showing every velocity change, so paradoxes like this can't happen.

 

[Janus]

Neither. You need to take the Relativity of Simultaneity into account for planet C and length contraction into account. Assume that Ship A and B synchronize their clocks before A leaves to join B. Now As the ships fly by planet C, Planet C takes note of the Times on the Clocks. He will note that ship B's clock runs about 1 year ahead of Clock A, And that they are only about one light minute apart.

So A stops (His clock now run at the same rate as C), for 1 min to let B catch up, then speeds back up to B's speed. B's clock, which undergoes time dilation during this time, changes very little, so that when they meet up, B's clock is one year minus 1 minute ahead of A's clock. The same result seen by the ships. No paradox.

 

[Dropout]

According to A and B, what they see is that they are 1 lightyear apart. C may see length contraction as entirely different thing.

I meant acceleration and deceleration is an unrealistic 0-c in 1 minute, for mathematical simplicity. The trip though is 1 year, for mathematical simplicity 99.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% the speed of light.

The ships have no windows and don't see the outside universe, only radio contact with each other, and being at rest with each other.

 

[Dropout]

Relativity states that Ships A and B being at rest with each other are a universe unto themselves, being that there is no universal speed of light or speed of rest, and every frame of reference for every particle at rest with each other is a universe unto itself. So therefore ship A being at lightspeed for a year should experience the time dialation.

 

[JesseM]

Dropout, did you read Janus' response? The answer is that different frames define "simultaneity" differently, which means that two events which happened simultaneously in one frame happened at different times in another frame. In A and B's rest frame, up until the moment A accelerated their clocks were synchronized--the event of A's clock striking 12 happened simultaneously with the event of B's clock striking 12, for example. But in C's frame the two clocks were not synchronized--instead he sees B's clock ahead of A's clock, so for example, he might see B's clock strike 12 at the same moment that A's clock strikes 10. So even though he does see A's clock speed up after it accelerates (because A's velocity has decreased rather than increased), A will still be behind B when they meet, simply because B started out so far ahead of A...even though A narrowed the gap by ticking faster, it still did not catch up with B, from the perspective of C's frame. If you like, I can work out an actual numerical example to show just how this works, and why both frames will predict exactly the same answer about what A and B's clocks will read at the moment they meet.

 

[Dropout]

Ok, planet C is monitoring the radio transmissions of both ships A and B. When the ships A and B dock and start talking to each other what will planet C hear them say?


Ship A, "I experienced time dialation."

Ship B, "I experienced time dialation."

 

[Janus]

Neither. No one ever "experiences" time dilation, it is always measured as happening to the other frame.

 

[Dropout]

Neither. No one ever "experiences" time dilation, it is always measured as happening to the other frame.

Im not being anal about simultaneouty, and exactly what time they have at their clocks at one particular point in time. I want to know what they said to each other when they docked. What did they SAY?

Ship A verbalized something to Ship B, and Planet C was monitoring the entire situation. What did Ship A say?

 

[Dropout]

drawing in ASCII don't work very well

 

[Janus]

Im not being anal about simultaneouty, and exactly what time they have at their clocks at one particular point in time. I want to know what they said to each other when they docked. What did they SAY?

Ship A verbalized something to Ship B, and Planet C was monitoring the entire situation. What did Ship A say?

Ship A: While I was accelerating towards Ship B, Ship B's clock jumped about a year forward in time.(Ship B's clock ran fast.) While I was traveling at a constant speed towards Ship B and braking to to a stop, Ship B's clock ran slow.
Ship B: While Ship A acclerated towards me, traveled at a constant speed and braked to a stop, Ship A's clock ran slow by varying amounts depending on its relative velocity WRT to me at the moment.

Planet C: Both ships Clocks ran slow until Ship A decelerated to a stop and its clock clock kept the same time as mine. Ship B's clock continued to run slow. When Ship B caught up to ship A, ship A accelerated back up to speed with ship B and its clock started to run slow again.

 

[Dropout]

Ship A: While I was accelerating towards Ship B, Ship B's clock jumped about a year forward in time.(Ship B's clock ran fast.) While I was traveling at a constant speed towards Ship B and braking to to a stop, Ship B's clock ran slow.
Ship B: While Ship A acclerated towards me, traveled at a constant speed and braked to a stop, Ship A's clock ran slow by varying amounts depending on its relative velocity WRT to me at the moment.

Planet C: Both ships Clocks ran slow until Ship A decelerated to a stop and its clock clock kept the same time as mine. Ship B's clock continued to run slow. When Ship B caught up to ship A, ship A accelerated back up to speed with ship B and its clock started to run slow again.

So your saying ship B verbalized to Ship A, "You aged 1 year, while we only aged a few minutes."

 

[Dropout]

From the colony's ship point of view during that 1 year. Colony Ship B gets on the radio and transmits across space to Colony Ship A, "Hey that's amazing, our scientists were correct about time dialation, your clock is running slow Colony ship A, since you accelerated towards us and are now traveling at 99.99999999999999% the speed of light."

PLanet C listens to Colony Ship B's transmission and starts to think, "WTF are they talking about? Colony Ship B is suppose to experience time dialation." A great debate begins on Planet C about the validity of their theories on time dilation after listening to that broadcast.



















From the colony's ship point of view during that 1 year. Colony Ship B gets on the radio and transmits across space to Colony Ship A, "What is going on Colony ship A? We are reading you accelerated towards us at 99.99999999999999% the speed of light, you should be experiencing time dialation, but we are actually the ones experiencing time dialation. We must already be traveling at 99.99999999999999% the speed of light and you actually slowed down to the universal speed of stop. We will build a telescope to see if we are passing any galaxies up, oh look we just passed a planet C."

PLanet C listens to Colony Ship B's transmission and starts to think, "Yeah that's right, our scientists were right about relativity."















I used three numbers for mathematical simplicity.

A) They are 1 lightyear apart from their point of view, so if they traveled at the speed of light it would take 1 year to get there.

B) Acceleration is nearly isntant, for simplicity purposes I wouldn't have to get anal about exactly how much time passes during acceleration. Make it 0 to light speed in 1 minute, yeah it would make mush of their bodies but its not theoretically impossible.

C) Top speed is 99.9999999999999999999999999999999999999999999% the speed of light after acceleration, again its not theoretically impossible for matter to travel that fast.

So one or the other will age 1 year. Its either one or the other that experiences time dialation. It doesn't really matter what happens enroute, simultaneuty doesn't matter, what matters is after they meet up and determine who experienced time dialation. Once those ships broadcast over the universe a radio wave about what they said, then its written in stone what exactly happened otherwise 2 universes are created each one with different radio waves transmitted across the universe.

 

[Dropout]

Im specifically asking what they VERBALIZED to each other because verbalization is something that can't get bogged down in simultaneouty of events or mathematics. I remember physics classes and the way they bent space in that cone of light in different frames. It was all fine and dandy when dealing with with pulses of light, in fact it made perfect sense.

What is impossible is for one observer to see this ---.--

and another observer to see this ...-..

 

[Dropout]

OH yeah, and another thing that is strange, length contraction.

Brownian motion on a nuclear scale. In the sun at its hottest spot, you got Hydrogen atoms going close to the speed of light because of speed. Maybe not OUR sun, but atoms in very hot places are being bounced around in a brownian motion that are close to the speed of light.

At any particular point in time, you can have a Hydrogen atom in one galaxy going 99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% the speed of light in exactly the same direction of another Hydrogen atom in another galaxy going just as fast.

According to length contraction, from an outsiders point of view, those two hydrogen atoms will be right next to each other, not separated by millions of light years, but right next to each other. Most of matter is made up of empty space anyways, our bodies are mostly made up of space, even lead is made up of mostly empty space. What makes length contract? Dont know, but solid matter doesn't exist in the universe anyways, so I am guessing that if your traveling in the same direction your part of the same body that can shrink.

 

[Janus]

So your saying ship B verbalized to Ship A, "You aged 1 year, while we only aged a few minutes."

No, read it again.

 

[Janus]

From the colony's ship point of view during that 1 year. Colony Ship B gets on the radio and transmits across space to Colony Ship A, "Hey that's amazing, our scientists were correct about time dialation, your clock is running slow Colony ship A, since you accelerated towards us and are now traveling at 99.99999999999999% the speed of light."

PLanet C listens to Colony Ship B's transmission and starts to think, "WTF are they talking about? Colony Ship B is suppose to experience time dialation." A great debate begins on Planet C about the validity of their theories on time dilation after listening to that broadcast.

Only if the inhabitants of planet C had no understanding of Relativity. If they understood Relativity and what it predicts, they would have no problem with this at all.

From the colony's ship point of view during that 1 year. Colony Ship B gets on the radio and transmits across space to Colony Ship A, "What is going on Colony ship A? We are reading you accelerated towards us at 99.99999999999999% the speed of light, you should be experiencing time dialation, but we are actually the ones experiencing time dialation. We must already be traveling at 99.99999999999999% the speed of light and you actually slowed down to the universal speed of stop. We will build a telescope to see if we are passing any galaxies up, oh look we just passed a planet C."

PLanet C listens to Colony Ship B's transmission and starts to think, "Yeah that's right, our scientists were right about relativity."

Again, this would happen only if all the participants did not understand Relativity. For one, in SR there is no such thing as a "universal speed of stop", or absolute frame of rest. If these "scientist's" version of Relativity includes such a frame, then it is not SR.

I used three numbers for mathematical simplicity.

A) They are 1 lightyear apart from their point of view, so if they traveled at the speed of light it would take 1 year to get there.

B) Acceleration is nearly isntant, for simplicity purposes I wouldn't have to get anal about exactly how much time passes during acceleration. Make it 0 to light speed in 1 minute, yeah it would make mush of their bodies but its not theoretically impossible.

C) Top speed is 99.9999999999999999999999999999999999999999999% the speed of light after acceleration, again its not theoretically impossible for matter to travel that fast.

So one or the other will age 1 year. Its either one or the other that experiences time dialation. It doesn't really matter what happens enroute, simultaneuty doesn't matter, what matters is after they meet up and determine who experienced time dialation. Once those ships broadcast over the universe a radio wave about what they said, then its written in stone what exactly happened otherwise 2 universes are created each one with different radio waves transmitted across the universe.

You just can't disregard simultaneity, nor the observations of the participants during the trip like that, as they are integral to understanding Relativity. And Relativity says: That while all the participants will agree to what the respective clocks on ship A and B will read when they meet, They will not agree on how they got that way.

 

[Janus]

Im specifically asking what they VERBALIZED to each other because verbalization is something that can't get bogged down in simultaneouty of events or mathematics. I remember physics classes and the way they bent space in that cone of light in different frames. It was all fine and dandy when dealing with with pulses of light, in fact it made perfect sense.

What is impossible is for one observer to see this ---.--

and another observer to see this ...-..

Why?

Let's use an analogy:

Person A is standing next to a tree and decides to judge its height by comparing to the thumb of his outstretched arm. It is 20 "thumbs" high.

Person B is standing a fair distance from the tree and makes the same measurement, he measures the tree to be 2 'thumbs' high.

To someone not used to the concept of perspective, this would seem impossible. How can two people see two different heights in the same tree?

The same thing happens with Relativity, in this case our Observers are viewing the same space-time interval from different perspectives. They are seeing the same "Reality", but are just seeing it from different viewpoints.

 

[Janus]

OH yeah, and another thing that is strange, length contraction.

Brownian motion on a nuclear scale. In the sun at its hottest spot, you got Hydrogen atoms going close to the speed of light because of speed. Maybe not OUR sun, but atoms in very hot places are being bounced around in a brownian motion that are close to the speed of light.

At any particular point in time, you can have a Hydrogen atom in one galaxy going 99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% the speed of light in exactly the same direction of another Hydrogen atom in another galaxy going just as fast.

The amount of energy it would take to get a hydrogen atom up this speed would rival the entire energy output of a total galaxy.

According to length contraction, from an outsiders point of view, those two hydrogen atoms will be right next to each other, not separated by millions of light years, but right next to each other.

From an outsiders point of view they are millions of light years apart. From their own point of view, they are much further apart. and it is the galaxies that are close together. This brings up the point of Simultaneity again. If particle A is passing through galaxy A at same time as particle B is passing through Galaxy B according to the inhabitant of the Galaxies, then according to the particles, they do not. One particle passes through its galaxy before the other does.

Most of matter is made up of empty space anyways, our bodies are mostly made up of space, even lead is made up of mostly empty space. What makes length contract? Dont know, but solid matter doesn't exist in the universe anyways, so I am guessing that if your traveling in the same direction your part of the same body that can shrink.

Length contracts because it is a measurement, and in SR it is measurements made between frames that have relative motion WRT each other that are effected.

 

[Dropout]

So your saying Planet C is going to hear a totally different radio transmission then Ships A and B.

So planet C's going to hear Ship A say, "Hey B, you experienced time dialation."

And Ship A is going to say to Ship B, "Hey I experienced time dialation."


Only one radio transmission can be transmitted across the universe for all to hear, it may be received slow to some or fast to others, but there can only be one radio transmission.

 

[Chronos]

Dropout, read a book. If you don't understand the question, it is unlikely you will understand the answer.

 

[Dropout]

See, been asking this for years, nobody has an answer. I am not asking whos clocks were running slower at this piont in time, in this guys frame of reference, I am simply asking what did they say to each other when they docked. And the rest of the universe is listening into their conversation.

 

[pervect]

That's not what he's saying at all.

Where did you get the idea that the laws of physics controlled what people said, anyay? That's a very strange idea. At the risk of getting a bit philosophical, the laws of physics control the outcome of experiments that people perform, and what people observe - the laws of physics do not (directly!) control what people say about the results. Unless one views people as a machine - but even then, people-as-machines are so complicated that it is very difficult to predict exactly what they will do or say.


We could spend a lot of time describing what people in the two spaceships saw, but at this point it doesn't seem worth it, because it doesn't seem to me like you're really paying any attention to what people are trying to tell you.

 

[Dropout]

That's not what he's saying at all.

Where did you get the idea that the laws of physics controlled what people said, anyay? That's a very strange idea. At the risk of getting a bit philosophical, the laws of physics control the outcome of experiments that people perform, and what people observe - the laws of physics do not (directly!) control what people say about the results. Unless one views people as a machine - but even then, people-as-machines are so complicated that it is very difficult to predict exactly what they will do or say.


We could spend a lot of time describing what people in the two spaceships saw, but at this point it doesn't seem worth it, because it doesn't seem to me like you're really paying any attention to what people are trying to tell you.

What people are telling me is the special relativity party line I've heard 100 times before. Do people in the ships only communicate with 1 flash of light? I think not, I think they would talk to each other. I am simply asking what Ship A and Ship B said to each other, and what planet C heard they say to each other. Its actually a very simple scenario, exactly like the twin paradox with a 3rd frame of reference thrown in. Is that's what's throwing you all off, a 3rd frame of reference?

The twin paradox works perfectly A-ok when dealing with 2 frames of reference, but can the relativity withstand a 3rd frame of reference? This isn't a complex scenario here, its pretty simple.

 

[JesseM]

What people are telling me is the special relativity party line I've heard 100 times before. Do people in the ships only communicate with 1 flash of light? I think not, I think they would talk to each other. I am simply asking what Ship A and Ship B said to each other, and what planet C heard they say to each other.

When they dock and compare clocks, every single person will hear them say that A's clock is now way behind B's clock, assuming their clocks were synchronized in their own frame before A accelerated.

 

[Dropout]

Colony Ship A and Colony Ship B are 1 light year apart and at rest with each other. They begin radio contact with each other, Colony Ship A accelerates towards Colony Ship B, from zero to the speed of light in under one minute. 1 year later from Colony Ship B's perspective, Colony Ship A decelerates in under 1 minute and docks with the other ship. Colony Ship A says to B, "WOW, you aged 1 year, we only aged a few minutes."


WRONG!

What Colony Ship A and B don't realize is that they are already traveling at the speed of light, and therefore Colony ship A didnt accelerate towards Colony Ship B, it decelerated to ZERO while Colony Ship B continued along its merry way at the speed of light. Planet C sees all this and hears Colony Ship A say on the AM radio, "WOW, you aged 1 year, we only aged a few minutes."



You telling me this ^^^^^^^^^^^^^^^^^ isn't a paradox?

 

[Dropout]

When they dock and compare clocks, every single person will hear them say that A's clock is now way behind B's clock, assuming their clocks were synchronized in their own frame before A accelerated.

And A gets on the AM radio and transmits across the universe, "We only aged a few minutes you aged 1 year."

The rest of the universe meanwhile is shaking its head wondering how this is possible since one of the big points about general relativity says that there is no universal speed limit, every universe unto themselves.

 

[JesseM]

Colony Ship A and Colony Ship B are 1 light year apart and at rest with each other. They begin radio contact with each other, Colony Ship A accelerates towards Colony Ship B, from zero to the speed of light in under one minute. 1 year later from Colony Ship B's perspective, Colony Ship A decelerates in under 1 minute and docks with the other ship. Colony Ship A says to B, "WOW, you aged 1 year, we only aged a few minutes."

Ship A doesn't say that he "aged less", he just observes that his clock is behind that of ship B's. This doesn't necessarily mean he aged less, it might just mean that his clock started out being way behind ship B's, then while he was moving towards ship B it began to catch up (because ship B was aging less during that interval), but his clock was still behind ship B's at the moment they met. The question of "who aged less" is meaningless unless they started out at the same point in space and compared ages, then moved around, then reunited to compare ages again. If they didn't start out at the same place, there is no frame-independent way to decide how their ages compared to begin with--different frames disagree about how old A was "at the same time" that B was a given age, because that depends how you define simultaneity. So likewise, there's no frame-independent way to decide who aged less as A approached B if they didn't start out at the same point in space earlier.

 

[Dropout]

If I see your clock is going half as mine, your going to age half as me.

They started out at rest with each other, so they started out at the same frame of reference with each other. Just because they didnt occupy the same space doesn't mean they have the same relative frame of reference. The only matter that occupies the same space are black holes. Just cause they are separated by 1 light year doesn't mean anything.

 

[JesseM]

If I see your clock is going half as mine, your going to age half as me.

But this isn't about the rate the two clocks go (which depends on the reference frame, so the inertial observers B and C will disagree on whether A's clock was going slower than B or vice versa), this is about the time on each clock at the moment they meet. In C's frame, it's B's clock that's going slower, but since A's clock started out way behind B's clock, A's clock is still behind B's clock when they meet. If in my frame your clock starts out reading 5:00 and my clock starts out reading 4:00, and then you travel towards me for an hour while your clock only ticks at half the normal rate, then when we meet my clock will read 5:00 while yours will read 5:30. So, even though you only aged half as much as me (in my frame), my clock is still behind yours.

They started out at rest with each other, so they started out at the same frame of reference with each other.

Sure, they start out in the same frame of reference, but other frames observing them will not agree on their relative ages at the moment before A accelerates, and every frame is equally valid. There can be no absolute, frame-independent truth about who "aged less" unless there is an absolute, frame-independent truth about how their ages compared at some initial time.

 

[wisp]

It is possibe to exlpain what happens using the ether as a reference frame. The ones moving faster through the ether age slower. This avoids all the complications that relativity throws up.

 

[JesseM]

It is possibe to exlpain what happens using the ether as a reference frame. The ones moving faster through the ether age slower. This avoids all the complications that relativity throws up.

But unless we modify the laws of physics, there will be no way to measure what the ether's rest frame is. Also, see this usenet post for more reasons why this is an extremely inelegant solution.

 

[Janus]

So your saying Planet C is going to hear a totally different radio transmission then Ships A and B.

So planet C's going to hear Ship A say, "Hey B, you experienced time dialation."

And Ship A is going to say to Ship B, "Hey I experienced time dialation."


Only one radio transmission can be transmitted across the universe for all to hear, it may be received slow to some or fast to others, but there can only be one radio transmission.

No. I'm saying nothing of the sort.

If ship A makes the only transmission, it might go something like this:

"As I accelerated, Time on ship B jumped forward about a year, and the distance separating us contracted to 1 light min. Then for the one min it took, by my clock, for us to come together at a relative velocity of near c, ship B's time ran slow. When we matched velocities again, 1 year had passed for ship B, (as reckoned from before I started my accleration) and 1 min had passed for me. "

Ship B and planet C receive this exact same message. While they will agree as to the final outcome, they will not agree with A's message of how that outcome was arrived at.

To ship B, Ship A took one year to cross 1 lightyear of distance, during which time Ship A's time ran so slowly that only 1 min passed for its inhabitants.

To planet C, The time on Ship B was already 1 year ahead of the time on ship A before ship A did anything. The distance between the two ships is also only 1 light min. Ship A comes to a stop, and for the one minute it takes for ship B to catch up, the time on Ship A ran at the same rate as the Planet's, while time on Ship B ran so slow that hardly any time accumulated on it during this time. Then ship A accelerates back up to speed with Ship B and their time rate match again.

The fact that events followed a different sequence for them than that reported to them by the mesage received from Ship A, does not bother them A bit as long as they understand Relativity. In fact, this is what they would expect ship A to say, As it is exactly what Relativity predicts that ship A will record as happening.

 

[Janus]

What people are telling me is the special relativity party line I've heard 100 times before. Do people in the ships only communicate with 1 flash of light? I think not, I think they would talk to each other. I am simply asking what Ship A and Ship B said to each other, and what planet C heard they say to each other. Its actually a very simple scenario, exactly like the twin paradox with a 3rd frame of reference thrown in. Is that's what's throwing you all off, a 3rd frame of reference?

The twin paradox works perfectly A-ok when dealing with 2 frames of reference, but can the relativity withstand a 3rd frame of reference? This isn't a complex scenario here, its pretty simple.

It doesn't matter how many many frames of reference you include, the Twin Paradox works.

BTW, the Twin paradox requires a minimum of 3 frames of refernce in its standard form:
1.The frame of the Earth twin.
2. The outbound trip frame of the second twin
3. the Return trip frame of the second twin

If you take into consideration a finite acceleration during the turn around, the TP includes an infinite number of frames of reference. (one for each instantaneous velocity the second twin passes through while acclerating.)

 

[Dropout]

Step 1: Colony Ships A and B POV: They are at rest with each other so therefore each clock on each ship are going the same speed, they are in radio contact with each other and talk to each other. ShipA, "Hi." ShipB, "How you doing?", ShipA, "Ok." Both ships are also separated by 1 light year.

Step 1: Planet C POV: Ship A and Ship B are at rest with each other, they are both going the speed of light exactly in X-direction. I hear their radio transmissions going REAAAALLLLY SLoooowwwww. I hear Ship A say really slow, "Hi." ShipB, "How you doing?", ShipA, "Ok." Both ships are right next to each other, Planet C hears them both talking about being separated by 1 light year and they start laughing about Relativity and their POV and how weird it sounds, funny but true.





Step 2: Colony Ship B POV: Colony Ship A accelerates toward Ship B, in one minute Ship A is going the speed of light. Ship A says reaaaallly Slow, "Hi Ship B."

Step 2: Planet C POV: Colony ship A Decelerates while Ship B continues on a collision course towards Ship A. After a few minutes, they hear ship A say in normal speed, "Hi, ship B."



Step 3: Colony Ship B POV: Colony Ship A decelerates in one minute to dock with Colony Ship B. They dock, and Ship A says in normal time, "Hi Ship B, you aged 1 year, I aged a couple minutes." Ship B says, "Yup."

Step 3: Planet C POV: Immediately after Ship A decelerates it begins to accelerate again to dock with Ship B. Being that they are right next to each other, length contraction. Both ships dock. Ship A says reaaallllly slow, "Hi ship B, you aged 1 year, I aged a couple of minutes." Ship B says, "Yup." <-------------paradox.

From Planet C's POV, the opposite should have happened. Ship A should have aged 1 year, because they were the ones whos clock was going faster, whereas Ship B was going the speed of light the entire time.

 

[JesseM]

Dropout, why are you still ignoring the point that C will see their clocks (or biological ages) as being different to begin with? If you're going to have an example involving their radio transmissions, you need to include as part of the transmission their clock-readings or ages. Taking that into account, your story might look like this:

Step 1: Colony Ships A and B POV: They are at rest with respect to each other, and separated by 1 light year. Ship A's captain broadcasts a message immediately before accelerating towards B: "At the tone, I will be exactly 35 years old--beeeep." Ship B's captain broadcasts a similar message on his own 35th birthday. Then on his 36th birthday, ship B's captain receives A's message. Since ship A was exactly 1 light year away, he reasons that the message must have taken 1 year to get to him, so they both must have been 35 years old when the message was sent.

Step 1: Planet C POV: Ship A and Ship B are at rest with each other, they are both going at 0.9999995c in X-direction. Before Ship A accelerates, a Planet C observer sees them separated by a distance of only 0.001 light years. On the Planet C observer's 36th birthday, he looks through his telescope and sees that ship B appears to be exactly 1 light year away, so he reasons that that's how far ship B must have been 1 year ago (which means ship B would currently be 1.9999995 light years away). Around the same time, he receives a slowed-down radio broadcast from Ship B, saying "At the tone, I will be exactly 35 years old--beeeep." The beginning of the beep falls exactly on his 36th birthday, so taking into account Ship B was 1 light year away at that moment, he concludes that he and the Ship B captain must have turned 35 at exactly the same moment.

Now, the Planet C observer is a member of a very-long lived species, so at the ripe old age of 2035.9995 years old, he receives a slowed-down message from ship A saying "At the tone, I will be exactly 35 years old--beeeep." Using his telescope, he can see that ship A was 1001 light-years away at the moment this message was broadcast, so it must have been sent when he was 1034.9995 years old. So for him, 999.9995 years passed between ship B sending his message and ship A sending his message. But knowing that ship B only ages at 0.001 his own rate, he reasons that only 0.9999995 years passed on ship B in that time, so ship B must have been 35.9999995 years old at the same moment that ship A was exactly 35 years old.

Step 2: Colony Ship B POV: Colony Ship A accelerates almost instantaneously until it is moving at 0.9999995c towards Ship B, then when A reaches B's position it decelerates almost instantaneously to dock. Since A started out 1 light-year away, it takes 1/0.9999995 = 1.0000005 years to reach B, so B is 36.0000005 years old at the moment A reaches him (about 16 seconds after B turned 36). Ship A's captain was only aging at 0.001 his own rate during this trip, so Ship A's captain will only be (1.0000005)*(0.001) + 35 = 35.001000001 years old when he arrives. So at the moment they dock, they broadcast a message saying "At the tone, Ship A's captain will be 35.001000001 years old and ship B's captain will be 36.0000005 years old--beeeep."

Step 2: Planet C POV: Colony ship A decelerates almost instantaneously while Ship B continues on a collision course towards Ship A, then at the moment B reaches A, A accelerates almost instantaneously to dock. Since they were initially 0.001 light years apart, it takes 0.001/0.9999995 = 0.001000001 years for ship B to reach A. Ship A's captain was exactly 35 when his ship decelerated, and he aged at the normal rate afterwards, so he was 35.001000001 years old when Ship B caught up to him. Ship B's captain was 35.9999995 at the moment that A decelerated, and he aged at 0.001 the normal rate as he approached B, so 0.001000001 years later he'd be 35.9999995 + (0.001)*(0.001000001) = 36.0000005 years old when he caught up to A. So when the Planet C observer is 2036.0005 years old, he receives a slowed-down message from 1001 light years away (which must have been sent when he was 1035.005 years old, or 1034.9995 + 0.001000001 years) saying "At the tone, Ship A's captain will be 35.001000001 years old and ship B's captain will be 36.0000005 years old--beeeep."

So, you see? No paradox. Ship B's captain thinks that A aged at 0.001 times his own rate as A moved towards him, while the Planet C observer thinks that B aged at 0.001 times A's rate after A decelerated, but it still makes sense for both of them to think that A will be 35.001000001 years old and B will be 36.0000005 years old when they meet, because B thinks that both him and A were 35 years old at the moment A accelerated, while C thinks that B was already 35.9999995 years old at the moment A accelerated, so even though A aged faster as B approached him, B was still older when they met because of this head start. There is no unique frame-independent truth about how old B was "at the same moment" that A turned 35 and accelerated, thus there can be no unique frame-independent truth about who "aged less" as A and B rushed towards each other.

 

[pervect]

What people are telling me is the special relativity party line I've heard 100 times before. Do people in the ships only communicate with 1 flash of light? I think not, I think they would talk to each other. I am simply asking what Ship A and Ship B said to each other, and what planet C heard they say to each other. Its actually a very simple scenario, exactly like the twin paradox with a 3rd frame of reference thrown in. Is that's what's throwing you all off, a 3rd frame of reference?

The twin paradox works perfectly A-ok when dealing with 2 frames of reference, but can the relativity withstand a 3rd frame of reference? This isn't a complex scenario here, its pretty simple.

The twin paradox can easily withstand a third frame of reference.

Your question, however, remains ill-posed. What sort of conversations are you imagining that people have when it takes a year to get a reply to one's message?

As physicists, it's really not our job to write dialog for characters. If you can re-think your question in more physical grounds, we can probably provide an answer.

For instance, it's possible for us to imagine that each spaceship is sending regular pulses at 1 second intervals. (or 1 minute, or 1 hour, or whatever). And that all spacehsips each announce via a broadcast when some specific event is occurring - for instance, the spaceship that accelerates can announce "I am starting to accelerate".

The stationary spaceship cannot announce when the accelerating spaceship starts to accelerate, but it can announce when it actually sees the event hapen, so it can say "I see you start to move".

Both spaceships can announce, together "We're docked".

It's reasonably straightforwards, knowing the velocity, and the doppler shift formula

time ratio = \sqrt{\frac{c-v}{c+v}} to find out how many pulses each observer receives.

So we can ask "How many pulses does the stationary spaceship receive from the time it sends the "I see the other spaceship start to accelerate" and the time that it sends the "We are docked" message.

And we can ask "How many pulses does the accelerating spaceship receive from the stationary spaceship from the time it turns on its engines until the time the two spaceships dock.

And we can point out that everyone agrees on these facts, including the planet-based observers.

And we can point out that the first number is lower than the second.

Other than that, we would need some more specific input on what your question was.

 

[HallsofIvy]

What people are telling me is the special relativity party line I've heard 100 times before.

Another name for "the special relativity party line" is reality- it's passed all the experimental tests so far which is "all ye know of this world and all ye need to know".

That's why you've heard it 100 times before!

 

[Dropout]

"So, you see? No paradox. Ship B's captain thinks that A aged at 0.001 times his own rate as A moved towards him, while the Planet C observer thinks that B aged at 0.001 times A's rate after A decelerated, but it still makes sense for both of them to think that A will be 35.001000001 years old and B will be 36.0000005 years old when they meet, because B thinks that both him and A were 35 years old at the moment A accelerated, while C thinks that B was already 35.9999995 years old at the moment A accelerated, so even though A aged faster as B approached him, B was still older when they met because of this head start. There is no unique frame-independent truth about how old B was "at the same moment" that A turned 35 and accelerated, thus there can be no unique frame-independent truth about who "aged less" as A and B rushed towards each other."

It doesn't matter what planet C "THINKS" what will happen, as soon as A and B dock and transmit over the radio, the transmission will conflict with C's theory.

 

[Dropout]

In this experiment with 2 colony ships and a planet, I purposefully started and stopped the experiment with ShipA and ShipB in equal frames of reference so nobody could say, "Simultaneouty is why this or that happens."

It doesn't matter when, how fast, or how slow Planet C receives a radio transmission from ShipA or ShipB. A message is a message nomatter how slow it plays back, when you hear it, or how weak the signal is. If the radio message says at 0.000000000000000000000000000000001 normal speed that, "THE COLOR OF THE PEN IS BLUE!" Then the color of the pen is blue nomatter if the signal came out of a black hole, from a different galaxy, or was played backwards.

 

[JesseM]

"So, you see? No paradox. Ship B's captain thinks that A aged at 0.001 times his own rate as A moved towards him, while the Planet C observer thinks that B aged at 0.001 times A's rate after A decelerated, but it still makes sense for both of them to think that A will be 35.001000001 years old and B will be 36.0000005 years old when they meet, because B thinks that both him and A were 35 years old at the moment A accelerated, while C thinks that B was already 35.9999995 years old at the moment A accelerated, so even though A aged faster as B approached him, B was still older when they met because of this head start. There is no unique frame-independent truth about how old B was "at the same moment" that A turned 35 and accelerated, thus there can be no unique frame-independent truth about who "aged less" as A and B rushed towards each other."

It doesn't matter what planet C "THINKS" what will happen, as soon as A and B dock and transmit over the radio, the transmission will conflict with C's theory.

No it doesn't. C's theory is that when they dock, A will be 35.001000001 years old and B will be 36.0000005 years old, which is exactly the same thing B predicted (and is what actually happens). Read my Step 1 and Step 2 from C's point of view to understand why he will predict this.

 

[JesseM]

In this experiment with 2 colony ships and a planet, I purposefully started and stopped the experiment with ShipA and ShipB in equal frames of reference so nobody could say, "Simultaneouty is why this or that happens."

I think you're confused here--just because everyone agrees that they share the same reference frame, that doesn't mean you can't analyze things from the perspective of a reference frame where both are moving at the same nonzero velocity. And if their ages are the same in their own rest frame, their ages will be different in a reference frame where they are moving.

It doesn't matter when, how fast, or how slow Planet C receives a radio transmission from ShipA or ShipB. A message is a message nomatter how slow it plays back, when you hear it, or how weak the signal is. If the radio message says at 0.000000000000000000000000000000001 normal speed that, "THE COLOR OF THE PEN IS BLUE!" Then the color of the pen is blue nomatter if the signal came out of a black hole, from a different galaxy, or was played backwards.

How slow it plays back is indeed irrelevant, but when you hear it is not. Suppose in 2005 you look through your telescope and see an explosion 100 light years away--would you say that in your frame, the date the explosion happened was 2005? Of course not, you'd take into account the finite speed of light and retroactively assign it a date of 1905. Then if you saw another explosion in 2025 from a distance of 120 light years away, you'd say this explosion happened in 1905, and thus that the two explosions happened simultaneously in your frame. But if an observer in a different frame also assumes that light travels at the same speed in all directions in his frame, then he will assign different dates to these explosions, and say that they did not happen simultaneously.

It would also be possible to assign dates to events using only local measurements made right next to the event. Suppose I am sitting on a giant ruler which is at rest relative to me, and mounted along the ruler is a series of clocks, which are all "synchronized" in my frame (more on what this means in a second). Then if an explosion happens right next to the ruler, I can just look at what marking on the ruler this explosion happened next to, and what the reading on the clock at that marking was at the moment it happened. Another observer may also be riding on a ruler that's at rest relative to him, and which is moving parallel to my ruler alongside of it, so he can assign coordinates to the event using the same procedure. But the key here is that according to Einstein, each observer should "synchronize" the clocks along their own ruler using the assumption that light travels at the same speed in all directions in their own frame--but if each observer uses this assumption, than each observer will see the other observer's clocks as being out-of-sync. To see this, suppose I set off a flash at the exact midpoint of two clocks. If I assume light travels at the same speed in all directions in my frame, then I should define the clocks to be "synchronized" if each one reads the same time at the moment the light from the flash hits it. But if another observer who sees the two clocks moving also assumes light moves at the same speed in all directions in his frame, then from his point of view the light must hit the two clocks at different times, since one clock is moving towards the point where the flash was set off and the other is moving away from that point. So, if each clock reads the same time when the light hits it, this other observer will say the two clocks are out-of-sync (I drew some diagrams of two rulers moving alongside each other in this thread, illustrating how each one thinks the other one's clocks are running slower and are out-of-sync, yet they are consistent in their predictions about physical events in the same local neighborhood). The end result is that each observer will get the same result for the coordinates of different events if he relies on local measurements on a system of synchronized clocks that he would if he relied on the idea I outlined in the previous paragraph, where you look at the time you received light from an event and then subtract the time the light took to get to you. Either way, if two events (such as A and B celebrating their 35th birthday) happen "at the same time" in one frame, that means that in another frame the two events happened at "different times".

 

[pervect]

In this experiment with 2 colony ships and a planet, I purposefully started and stopped the experiment with ShipA and ShipB in equal frames of reference so nobody could say, "Simultaneouty is why this or that happens."

It doesn't matter when, how fast, or how slow Planet C receives a radio transmission from ShipA or ShipB. A message is a message nomatter how slow it plays back, when you hear it, or how weak the signal is. If the radio message says at 0.000000000000000000000000000000001 normal speed that, "THE COLOR OF THE PEN IS BLUE!" Then the color of the pen is blue nomatter if the signal came out of a black hole, from a different galaxy, or was played backwards.

But simultaneity IS important to the problem, becaue the planet's notion of simultaneity is different from the ships notion of simultaneity.

You may have heard this 100 times before, but one can always hope that this time (the 101 time) that you will listen...

[add]
To explain a little further...

Let's suppose that A and B decide to make a big cerimonial event for the time when ship B lights its engines up.

A and B carefully synchorinze their clocks. Rather than worry about how this is accomplished, let's describe the result. When A sends a signal "It's now Jan 1, 2500 Ad", it arrives on ship B exactly on Jan 1, 2501 Ad, one year later. (One year later being the difference betweent the time contained in the transmission, based on A's clock, and the time it arrives, based on B's clock.)

Similarly, when B sends a signal to A, if they send the signal on Jan 1 2501 Ad (B's clock) iit will arrive on Jan 1, 2502 Ad (A's clock).

The planet will see things differently however - in the planet's coorinate system, A and B's clocks will not be synchronized. This is the key point that you've been missing.

 

[wisp]

But unless we modify the laws of physics, there will be no way to measure what the ether's rest frame is. Also, see this usenet post for more reasons why this is an extremely inelegant solution.

I don't rate his views on the ether, as he misses key points. I posted a response to his work in an earlier link
https://www.physicsforums.com/archive/topic/t-58050_Aether_theories_which_are_experimentally_indistinguishable_from_SR..html
about an important third class of ether, which Tom Roberts missed.

No one has yet put a good case to forward to dismiss the ether.

 

[russ_watters]

No one has yet put a good case to forward to dismiss the ether.

How 'bout - there is no evidence that it exists and our theories work extrordinarily well without it? Isn't that good enough reason not to pursue it?

 

[wisp]

How 'bout - there is no evidence that it exists and our theories work extrordinarily well without it? Isn't that good enough reason not to pursue it?

Russ

No. I believe that the detection of the ether will become routine once techniques are developed to detect it using instruments of proper sensitivity. An article published in the New Scientist today "Catching the cosmic wind" explains how the ether wind can be measured. I believe there are simpler ways to detect the ether, but this method looks hopeful.

 

[jdavel]

Russ

No. I believe that the detection of the ether will become routine once techniques are developed to detect it using instruments of proper sensitivity...

wisp,

How sensitive do the instruments need to be? And can "sensitivity" be described in terms of the minimum variation in light speed that can be resolved?