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

[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 acceleration) 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?