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Length Contraction causes Time Dilation?

by Max™
Tags: contraction, dilation, length, time
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Max™
#37
Mar30-11, 12:04 AM
P: 242
Quote Quote by Passionflower View Post
Max™ that statement is absolutely true.

Frankly I am still not convinced you fully accepted the implications of special relativity.
No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.

If you crossed 640 light years fast enough that it was contracted down to 2 light years in your frame, while avoiding any time dilation strangely, and you then crossed THAT distance fast enough that you took just a little over 2 years to do so, wouldn't you then experience time dilation on THAT duration, and observe quite a bit less than 2 years during your trip?



If the 2 light years in your frame was 640 light years for a signal laser you fired on the same trajectory when you left, then your trip would take more than the 640 years required for a detector at your destination to receive the signal.


Yes, in your frame, you'd only experience/age/observe 2~ years, and claim your laser beam only crossed 2 light years.



If you then turned around and fired a reply laser while going fast enough that you again measure the beam traveling for only 2 years as it crossed 2 light years, you would return 1280+ years after you left, roughly 4 years older.


If the contraction observed from your frame meant you only took 2 years to cross that distance without any effects from time dilation, you'd arrive at Betelgeuse 638~ years before the signal laser, and you'd make it home a thousand years or so before you even left!
Rap
#38
Mar30-11, 05:22 AM
P: 789
Quote Quote by Max™ View Post
No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.
It is true.

Quote Quote by Max™ View Post
If you crossed 640 light years fast enough that it was contracted down to 2 light years in your frame, while avoiding any time dilation strangely, and you then crossed THAT distance fast enough that you took just a little over 2 years to do so, wouldn't you then experience time dilation on THAT duration, and observe quite a bit less than 2 years during your trip?
Sorry, I don't understand. Anyway, lets not suspend time dilation while keeping Lorentz contraction, it totally confuses everything.

Quote Quote by Max™ View Post
If the 2 light years in your frame was 640 light years for a signal laser you fired on the same trajectory when you left, then your trip would take more than the 640 years required for a detector at your destination to receive the signal.
Betelguese is 640 light years away according to Earth. It takes 640 years for the light beam to travel there *according to Earth*, not according to the light beam. According to the spaceship, it is 2 light years away, and the light takes 2 years to make the trip.

Quote Quote by Max™ View Post
If you then turned around and fired a reply laser while going fast enough that you again measure the beam traveling for only 2 years as it crossed 2 light years, you would return 1280+ years after you left, roughly 4 years older.
Right - this is the twin "paradox".

Quote Quote by Max™ View Post
If the contraction observed from your frame meant you only took 2 years to cross that distance without any effects from time dilation, you'd arrive at Betelgeuse 638~ years before the signal laser, and you'd make it home a thousand years or so before you even left!
This is what the Earth experiences - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 640 years, you get there in 640+ years. This is what you experience - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 2 years, you get there in 2+ years. If you turn around and head back, along with a light beam, Earth will say that second light beam took 640 years to make the trip, got to Earth 1280+ years after you left. Earth will say you arrived back at Earth 1280++ years after you left. You will say that second light beam took 2 years to reach Earth, and you took 2+ years to get back to Earth, arriving 4++ years after you left. (Here I am using + to mean x+>x and ++ to mean x++ > x+).

The fact that you have only aged 4++ years while those on Earth have aged 1280++ years is called the twin "paradox".
harrylin
#39
Mar30-11, 06:00 AM
P: 3,187
In addition:
Quote Quote by Max™ View Post
[..]
Yes, in your frame, you'd only experience/age/observe 2~ years, and claim your laser beam only crossed 2 light years.
Again: not in "your frame" but in the inertial frame in which you happen to be in rest at that time. That may sound picky but it becomes essential in a continuation of discussion, as now happened:
If you then turned around and fired a reply laser while going fast enough that you again measure the beam traveling for only 2 years as it crossed 2 light years, you would return 1280+ years after you left, roughly 4 years older. [..]
From the experience of the traveler, indeed this will be the case, and he may have difficulty in explaining - based on that experience - why the stay-at home aged so much. You may next want to argue that this proves that the inertial frame of the Earth is something like a True Rest frame - but that's wrong. In relativity all inertial frames are equally valid in the sense that no such frame can be identified from observations.
Here you switched from using one inertial frame to another for one observer. For a reality-like description that is not allowed; in that sense, the class of inertial frames is preferred in special relativity.

For "twin-paradox" scenarios in which one observer switches inertial frames (or in which he uses a non-inertial frame), only* the description of the other observer who does not switch frames provides a consistent and realistic explanation in SR (loosely said: "frame-hopping" leads to inconsistent or unreal descriptions).

Cheers,
Harald

*Einstein tried to get rid of that with GR, but most people nowadays don't appreciate the reality of "induced gravitational fields".
Max™
#40
Mar30-11, 09:23 AM
P: 242
Quote Quote by Rap View Post
It is true.



Sorry, I don't understand. Anyway, lets not suspend time dilation while keeping Lorentz contraction, it totally confuses everything.
This is why that statement wasn't true, the thread was started in response to someone insisting that you don't just suspend time dilation, but that it was caused by the shorter Lortenz contracted distance.



Betelguese is 640 light years away according to Earth. It takes 640 years for the light beam to travel there *according to Earth*, not according to the light beam. According to the spaceship, it is 2 light years away, and the light takes 2 years to make the trip.
A lightlike path connecting Earth and Betelgeuse is 640 light years long and takes 640 years to travel.



There are two events at the start of the thought experiment, we'll just assume the ship was flying past the Earth to confirm that it is not simply a confusion on my part due to an admitted preference for background star reference frames, and to take acceleration out of the equation entirely.


The ship flies past the Earth at the spacetime event: (x+y+z=0, t=2011 CE), and fired a signal laser towards Betelgeuse, the ship synchronized their clocks as they passed by, so they're now tallying up information which they can perform a measurement with. A bored astronomer decides to tally up measurement as well, he records the ship hauling off along the x axis (for simplicity), with the laser inching further and further ahead of it.


In the ships frame the Earth whizzed past at nearly the speed of light, and continued receding along the x axis, while the laser the ship fired races away at the speed of light towards Betelgeuse.


There is another event of note here, Betelgeuse, located at (x=+640 light years from the Earth/Ship rendezvous point, t=3/30/2011 CE) along a spacelike trajectory oriented along the ships flight path.


In the Earth frame it is just sitting there, 640 years away at the speed of light, picking it's red supergiant nose.

In the ship frame it is hurtling towards the point where the Earth was when the ship passed it at nearly the speed of light.



In 2 years, Earth frame, the astronomer notes that the beam of light has traveled 2 light years, the ship has traveled 1.9999999~ whatever light years, and that Betelgeuse flicked a massive coronal booger roughly in the direction of Rigel... but otherwise did nothing of interest.


At the spacetime event (x=+2 light years from the Earth/Ship rendezvous point, t=3/30/2013 CE), the passenger on the ship checks his instruments and determines that he is at (x=+.011~ or so light years from the E/SrP, t=4/3/2011), a mere 3 days have passed since the Earth flew past him... for some reason, probably a sale at the interstellar mall... and he notes that since his signal laser can't be more than 3 light days ahead of him at this point, he inputs that measurement into his super parallax measuring doohickie and it tells him Betelgeuse is a bit more than 200 times as far away from him as his signal laser, so it must be just under 2 light years away!



Is he correct?

Well yeah, I guess, in a sense, as he has no reason to think he's actually in a frame experiencing major relativistic effects. He did measure the correct distances/duration as far as his frame is concerned.



The question here is, is there any manner in which his completely real and accurate measurements can be reconciled with any frame besides his (besides the arbitrary selection of suitably chosen frames which someone would point out exist if I didn't mention them)?


Is he doomed to watch the squished up universe hurtle past him, Unable to consider that perhaps he was in a boosted frame, and that just maybe his measurements were distorted by it?


Right - this is the twin "paradox".
Uh... no, it's just an aspect of relativity, make no mistake, my issue has nothing to do with a false paradox.


If there was no way for the guy in the ship to determine that he had been in motion, that would give the appearance of a paradox, and this often confuses people upon first hearing it.


If you can't tell by now, my problem is being all too aware of how that "paradox" is resolved. The only way the passenger on the ship can claim the universe is contracted around him is if he can't break the symmetry between his frame and another observers frame.


Setting aside the issue that he would remember accelerating, and putting him in the above described flyby scenario, then yes, he could claim that his frame was inertial and undistorted.

It's a rather scary place, his choice of coordinates, what with stars and planets hurtling past at nearly the speed of light... I mean, yes, we're whirling around along several different axes at anything from a few hundred, to a several thousands, all the way up to a million or so miles an hour depending on which motion you want to consider... but that's pretty far from sitting there with gigantic balls of nuclear fire hurtling towards you at 670 million mph.


This is what the Earth experiences - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 640 years, you get there in 640+ years. This is what you experience - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 2 years, you get there in 2+ years. If you turn around and head back, along with a light beam, Earth will say that second light beam took 640 years to make the trip, got to Earth 1280+ years after you left. Earth will say you arrived back at Earth 1280++ years after you left. You will say that second light beam took 2 years to reach Earth, and you took 2+ years to get back to Earth, arriving 4++ years after you left. (Here I am using + to mean x+>x and ++ to mean x++ > x+).

The fact that you have only aged 4++ years while those on Earth have aged 1280++ years is called the twin "paradox".
...

/sigh

Again, my issue is in no way related to an inability to understand an example I put forth in an effort to be understood, though the irony is rich enough that it could smother the heart of a massive star and cause it to supernova.



Technically, the twin paradox ONLY arises if you neglect acceleration completely, ANY change in direction breaks the symmetry between the frames, resolving the apparent paradox to be nothing but a quirky result of the way spacetime rotations work.
harrylin
#41
Mar30-11, 10:02 AM
P: 3,187
Quote Quote by Max™ View Post
[...]
If there was no way for the guy in the ship to determine that he had been in motion, that would give the appearance of a paradox, and this often confuses people upon first hearing it.
If you can't tell by now, my problem is being all too aware of how that "paradox" is resolved. The only way the passenger on the ship can claim the universe is contracted around him is if he can't break the symmetry between his frame and another observers frame.
That's the heart of relativity - the PoR or symmetry of inertial frames! No need to start talking about twin paradoxes, this is more straightforward. According to relativity there is no way for the guy in the ship to determine that he is "truly" in motion at a certain time, other than a mere assumption about the likely state of "true" motion of the stars. Do you find the Lorentz transformation paradoxical? Did you understand Tiny-tim's explanation in the parallel thread that I linked to (his post #3)?
Passionflower
#42
Mar30-11, 10:56 AM
P: 1,555
Quote Quote by Max™ View Post
No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.
Well the statement is true. It takes the traveler a little over 2 years to reach the destination which is 2 lights years away.
Max™
#43
Mar30-11, 11:58 AM
P: 242
I know all about that, but there is a way for him to determine his frame is not symmetrical with all others, he accelerated.

The "true" motion of the stars doesn't require a mere assumption if you notice they all have a significant vector and velocity relative to you. At rest or not, it pushes the limits of realistic explanations, plus he would notice the blue shift/red shift and aberration of the CMBR... but those are all far above the level of this conversation.

For the record, I first learned about relativity back in the mid 80's, and am well versed in not just the stripped down explanations of the theory as usually provided to laymen, but also the mathematical underpinnings, as well as the rich scientific principles upon which the whole theoretical structure was built almost a hundred years ago.

Now, I was a little datasponge of a 6 year old Aspie, between the bookshelf full of various out of date encyclopedias (I still pull up random factoids from the old white cover 1963 Britannica at the strangest times, my favorites were the A's, M's, P's, and the S's!), and my precious books on Relativity (Black Holes and Warped Spacetime, and Einstein: the Life and Times)... so while it may sound a little improbable for someone to say they've been studying something like Relativity since they were a little kid... it isn't that odd if you've ever met a 6 year old with Asperger's Syndrome. If it wasn't the rock collection, dinosaur trivia, or Legos... I was talking your ear off about how awesome Wheeler and Kerr metrics were.
Passionflower
#44
Mar30-11, 12:20 PM
P: 1,555
Quote Quote by Max™ View Post
I know all about that, but there is a way for him to determine his frame is not symmetrical with all others, he accelerated.
Ok, how does that invalidate anything?

Quote Quote by Max™ View Post
The "true" motion of the stars doesn't require a mere assumption if you notice they all have a significant vector and velocity relative to you. At rest or not, it pushes the limits of realistic explanations, plus he would notice the blue shift/red shift and aberration of the CMBR... but those are all far above the level of this conversation.
If your point is absolute motion then it is really back to square one. Motion is relative.

You wrote:
Quote Quote by Max™ View Post
No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.
And here is another statement that is true but one that you consider is false:
Quote Quote by Max™ View Post
"since I can make the distance shorter by going faster, it takes less time to get there",
You keep putting wagers out that some statement is false or you don't understand relativity. Then when people say the statement is actually true, you just come up with other statements and the process repeats.
Max™
#45
Mar30-11, 01:14 PM
P: 242
Quote Quote by Passionflower View Post
Well the statement is true. It takes the traveler a little over 2 years to reach the destination which is 2 lights years away.
Except they don't take 2 years because the distance is contracted, they are in a significantly dilated frame of reference performing distance measurements which are skewed by their reduced motion through time.


You observe a beam of light moving away from you at the speed of light, even if you're going .99999999999999999999~ c, it still races off at full speed, rather than gradually creeping ahead due to you ALMOST being at light speed yourself.


If you're in a Ferrari 458 doing 198 mph side by side with a McLaren MP4-12c doing 200 mph, he's going to ever so slightly nudge out in front and continue crawling further and further ahead.


If you're racing along at almost the speed of light, to an observer as you rush past, you're going to lag bit by bit behind a beam of light. Yet you see the beam zoom off like you were standing still... why?


When you're moving faster through space, you're moving slower through time. What you register as being a second in which the beam of light gains nearly 300,000 kilometers on you is a much longer time for an observer who isn't scooting along quite so quickly as you are.


Note that they don't have to be at rest, if you're doing .99999999999999999999995 c and I'm doing .99995 c, we'll each observe the other appearing to slow down, the clocks we're conveniently holding both seem to tick slower for the other guy, as we've all established repeatedly.


Once we come to a stop though, my clock will have ticked more than yours, I'll have aged a bit quicker than you did, though we both hardly aged compared to someone waiting for us back at Earth.



This is why you can't say "the distances contract, so you take less time to cross them", it's completely backwards. You experience less time because of your velocity, which causes you to claim everything else is contracted.

http://www.phys.unsw.edu.au/einstein...ation.htm#true

So Jasper observes Zoe's clock to tick more slowly by a factor γ, which is always greater than or equal to one. This factor γ occurs regularly in special relativity, so we have plotted it at right. (The dashed line plots 1/γ.) We notice that, unless v is a substantial fraction of c, γ is approximately 1. This of course is why we don't notice time dilation at ordinary speeds. For an airplane travelling near the speed of sound, γ = 1.0000000000005.

Note that 1/γ(v/c) is the equation of a circle, although we have stretched the horizontal axis so that the dashed line looks like an elipse. So γ (the solid line) is conveniently remembered as the reciprocal of a circle.

In the animations, Zoe's car travels at 0.8c, so γ = 1.67, so Jasper measures Zoe's clock to have ticks that are 60% of the time that Zoe measures.
Length contraction
You have probably noticed that, in Jasper's version of events, Zoe's car has shrunk. And vice versa. We haven't proved that yet, but it's logically simple. Suppose that Zoe and Jasper choose to measure lengths in lightyears, lightseconds, lightnanoseconds* etc: ie they measure distance by how long light takes to cover the distance. If they agree on the speed of light, but disagree on measurements of time, they must inevitably disagree on length as well. If you observe someone's clocks run slowly by a factor γ, you will also observe her rulers to be short by a factor of γ: that's the only way that she can measure the speed of light to have the same value you get.

* The lightnanosecond is a convenient unit. c is about 3 x10^8 metres per second, and a nanosecond is 10^-9 seconds, so a lightnanosecond is 0.3 metres. (Americans, who use British imperial units, can therefore remember that the speed of light is about one foot per nanosecond. The rest of us can remember it as 30 centimetres per nanosecond.)

Zoe, who is a graffiti artist in her spare time, will demonstrate this: she decides to tag the two ends of the verandah. (The paint can is green, and it sprays purple paint.) For Jasper, the distance between the tags will be his proper length, ie the length measured in his frame, because they are stationary with respect to him. Zoe can measure the time between the two tags, and thus get her measurement of the length of the verandah.
Passionflower
#46
Mar30-11, 01:23 PM
P: 1,555
Quote Quote by Max™ View Post
Except they don't take 2 years because the distance is contracted,
Well then it seems we can agree to disagree. The travelers clock is still going at one second per second. No changes for him at all.

Quote Quote by Max™ View Post
distance measurements which are skewed by their reduced motion through time.
Their distance measurements are as real as can be.

Quote Quote by Max™ View Post
you're going .99999999999999999999~ c,
There is no such thing as absolute speed. You can measure the speed of something that has mass only wrt something else that has mass.
Max™
#47
Mar30-11, 02:07 PM
P: 242
I never said he would notice any changes, his clock ticks off one second every time he expects it should, like... clockwork.


Another observer watching his clock tick from a slower moving frame would see it tick slower (and vice versa), but if the faster moving traveler came to rest beside the slower moving observer it would be obvious that the traveler's clock had ticked less.


I actually was using velocity, and never said anything about absolute speed.

If we were both at rest together in an inertial frame and pulled out two completely identical stopwatches, started them at exactly the same moment, then we both accelerated up to particular fraction of the speed of light, except you got much closer to c than I did, when we came to a stop afterwards your watch would read a shorter duration for your trip than mine would.


Where is the confusion here?
DaleSpam
#48
Mar30-11, 02:42 PM
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Quote Quote by Max™ View Post
A lightlike path connecting Earth and Betelgeuse is 640 light years long and takes 640 years to travel.
This is an example of some sloppy writing which I think is betraying some sloppy thinking that may be the source of your confusion. The quoted sentence is MEANINGLESS as written because the reference frame for the distance and the time measurement are not specified. In order for this statement to be meaningful it would have to be amended as follows:

A lightlike path connecting Earth and Betelgeuse is 640 light years long in the Earth frame and takes 640 years to travel in the Earth frame.

Distance and time are relative quantities, and like all relative quantities, you must identify the reference frame to which they refer. The following statements are also correct for your scenario.

There exists some frame in which a lightlike path connecting Earth and Betelgeuse is 2 light years long and takes 2 years to travel.

In a frame moving 0.999995 c wrt Earth in the direction from Earth to Betelgeuse the distance between Earth and Betelgeuse is 2 light years. In this frame it takes light 1.000002 years to go from Earth to Betelgeuse or 409599 years to go from Betelgeuse to Earth. In this frame it takes 2.00001 years from the time that Earth passes the origin for Betelgeuse to pass the origin.

Notice how relative quantities are always referenced to some specific frame. You make other comments like "they are in a significantly dilated frame of reference" and "he's actually in a frame experiencing major relativistic effects" which lead me to believe that the omission I point out above is not simply a gaffe, but is a basic misunderstanding.
Max™
#49
Mar30-11, 04:44 PM
P: 242
See, here's the problem, you're saying the effects are real in that they do happen, I'm saying that as well, but that the cause is due to measurement from a particular frame, not the universe actually smushing up around you.

Time dilation and length contraction are not just optical illusions, but neither do they represent a physical contraction. These effects are the result of a measurement from a given inertial frame that is performed on body moving with respect to that frame. We assume that the measurements always take into account the finite travel time of light. Consider two observers moving relative to one another. You have no difficulty with the idea of their velocities being relative - each thinks the other is "really moving." In SR, time intervals and space intervals are also relative. You don't shrink or see your own clock run slow. The other observer sees your clocks slow and meter sticks contracted from his frame. Similarly you will observe his clocks slow and meters sticks short from your frame. The time dilation and length contraction are inherent properties of the way measurements must be performed in spacetime.
http://www.astro.virginia.edu/~jh8h/..._1/quest7.html


I do admit that I'm a bit overly insistent about the broken symmetry, but the length required to treat someone flying from here to another star as an intertial frame leaves a bad taste in my mouth.

I know his frame is accelerated, he knows his frame is accelerated, thinking about the hypothetical inertial frame is one thing, but it is another to claim the particular details of measurement within said hypothetical inertial frame are the cause of the effects you experience in an accelerated frame.

At that point it isn't just a matter of "earth and betelgeuse went flying past me", unless you're pretending GR doesn't exist, and topping it off by pretending that you can't handle acceleration at all in SR (you can, it just doesn't do it very easily).
Passionflower
#50
Mar30-11, 05:49 PM
P: 1,555
Quote Quote by Max™ View Post
At that point it isn't just a matter of "earth and betelgeuse went flying past me", unless you're pretending GR doesn't exist, and topping it off by pretending that you can't handle acceleration at all in SR (you can, it just doesn't do it very easily).
What has GR to do with this?
DaleSpam
#51
Mar30-11, 06:59 PM
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Quote Quote by Max™ View Post
thinking about the hypothetical inertial frame is one thing
There is nothing hypothetical about the inertial reference frame.

Quote Quote by Max™ View Post
thinking about the hypothetical inertial frame is one thing, but it is another to claim the particular details of measurement within said hypothetical inertial frame are the cause of the effects you experience in an accelerated frame.
Nobody claimed that. The explanations would be different in a non-inertial frame, but equally valid.
Max™
#52
Mar30-11, 08:29 PM
P: 242
Quote Quote by Passionflower View Post
What has GR to do with this?
Well, working with just SR is kinda like me telling you calculate integrals and differentials, but not letting you use the fundamental theorem of calculus to flesh the structure out properly.

SR is great because the mathematical form doesn't require you to keep track of multi-dimensional tensor systems, but it's just not the same as the richer understanding you gain when you include GR into the structure.



As for the inertial frame, if you were flying from here to Betelgeuse you would need to accelerate until the halfway point and then decelerate the rest of the way in order to reach relativistic speeds such as we're discussing, presumably some sort of nuke-pusher drive or maybe an anti-matter pulse engine.


In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.
Passionflower
#53
Mar30-11, 09:18 PM
P: 1,555
Quote Quote by Max™ View Post
Well, working with just SR is kinda like me telling you calculate integrals and differentials, but not letting you use the fundamental theorem of calculus to flesh the structure out properly.

SR is great because the mathematical form doesn't require you to keep track of multi-dimensional tensor systems, but it's just not the same as the richer understanding you gain when you include GR into the structure.



As for the inertial frame, if you were flying from here to Betelgeuse you would need to accelerate until the halfway point and then decelerate the rest of the way in order to reach relativistic speeds such as we're discussing, presumably some sort of nuke-pusher drive or maybe an anti-matter pulse engine.


In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.
Sorry Max I lost you completely here.
DaleSpam
#54
Mar30-11, 09:33 PM
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P: 17,318
Quote Quote by Max™ View Post
In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.
No, the inertial frame is not hypothetical in any way regardless of whether or not the ship is ever at rest in it.

In addition to the sloppy language I pointed out above you seem to have this mistaken notion that there is a requirement for some object to be at rest in order for a reference frame to be valid. That is simply not the case. We need not restrict our analysis to frames where some object is at rest and we need not restrict our analysis to objects which are at rest in our chosen frame.


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