The following seems contradictory. There are two identical rockets separated a distance L as measured on the x-axis in an inertial reference frame. Let the two rockets be on parallel lines to the x-axis. An observer in a frame moving at V relative to the x-axis turns on the thrusters of both rockets simultaneously as measured in his frame. As viewed in this frame the tip of each rocket remains a distance L away from the tip of the other rocket even as the rockets accelerate. This occurs because both rockets undergo identical simultaneous accelerations, so as one rocket changes position the other does the identical motion at a different location in space as measured in this frame. How do people on board the rockets view things? In the inertial reference frame the rockets were initially in, the turning on of the thrusters of each of the two rockets were not simultaneous events. The thrusters of one rocket were turned on before the thrusters of the other rocket. Let's say you are in the rocket where the thruster was turned on first, and you start accelerating toward the other rocket at some constant acceleration rate. After T seconds as measured in your accelerating rocket, the thrusters of the other rocket are turned on so that both of you are now accelerating in the same direction. You note that at this time you had a closing velocity of V (you and the other rocket were approaching each other). You know the other rocket is identical to yours, and you are still accelerating at the same constant rate. If the closing rate continues at least at V or greater, after some point in time the tip of your rocket will pass the tip of the other rocket. But we've already established that as measured in the inertial reference frame where turning on the thrusters were simultaneous events, the tips of the two rockets never are at the same point in space at the same time, and hence can never pass each other. It seems to me at some point in time the rocket that started accelerating first must pass the other rocket. Thanks for explaining this from the point of view of someone in the first rocket. David Seppala Bastrop Texas
Whoah... so many errors in the formulation of your question.
On Nov 8, 8:25 am, DSeppala <dsepp...@austin.rr.com> wrote:
> The following seems contradictory.
Yes, "seems".
> There are two identical rockets separated a distance L as measured on > the x-axis in an inertial reference frame.
Ok, so both are ON the x axis. The usual config.
>Let the two rockets be on > parallel lines to the x-axis.
? Now you mean that they are both NOT on the x axis but on parallel lines *to* the x axis?
>An observer in a frame moving at V > relative to the x-axis turns on the thrusters of both rockets > simultaneously as measured in his frame. As viewed in this frame the > tip of each rocket remains a distance L away
? They are a distance L in which frame, the "initial" frame you referenced or this new frame V ? make up your mind.
At this point, you must completely rephrase your problem because it is too badly posed.
On Nov 8, 8:23 am, eric gisse <jowr.pi.nos...@gmail.com> wrote:
> DSeppala wrote: > > The following seems contradictory.
> Wow! David Seppala doesn't understand an example that slightly different > from the last 50,000 he has posted in the previous decade. Imagine that!
> [...]
You're moving ahaed faster so light has more distance to travel to reach you. Accelerate toward light in absolute space and you get closer so light has to travel a shorter distance. This is the cause of the appearence of the relativity of simultaneity.
To clarify your confusion caused by my phrasing. The two identical rockets are positioned to travel along lines parallel to the x-axis (as if they were racing side by side once they start accelerating). The tip of one rocket is at x = 0, and the tip of the other is at x = L'. In another inertial reference frame that is traveling at velocity V with respect to the inertial reference frame the two rockets are initially in, the distance between the tips of the rockets is measured as L. At time t0 in this moving reference frame, observers in this frame turn the the thrusters on both rockets simultaneously. The accelerometers on board each rocket show a constant and identical acceleration. As measured in the moving frame (where the thrusters were simultaneously turned on) at any instant of time, the tips of the two rockets are always L meters apart since both rockets simultaneously go through identical motions (but at different points along the x-axis). Now in the original rocket inertial frame, the thrusters weren't turned on simultaneously. The thrusters of one rocket was turned on before the thrusters of the other rocket. From the point of view an observer in the first rocket, how does he describe what happens during the constant acceleration? First he starts accelerating toward the other rocket. Then at some point in time as measured by the first rocket's clocks, the other rocket starts to accelerate. At time t1 (as measured by the first rocket's clocks) when the other rocket begins its acceleration, the two rockets were approaching each other with some velocity. As they both continue to accelerate along the x- axis, why doesn't the tip of the first rocket ever reach the same x position in space as the tip of the second rocket and eventually pass the second rocket? Hope that clarification removes your confusion. David On Nov 8, 9:54 am, rotchm <rot...@gmail.com> wrote:
> Whoah... so many errors in the formulation of your question.
> On Nov 8, 8:25 am, DSeppala <dsepp...@austin.rr.com> wrote:
> > The following seems contradictory.
> Yes, "seems".
> > There are two identical rockets separated a distance L as measured on > > the x-axis in an inertial reference frame.
> Ok, so both are ON the x axis. The usual config.
> >Let the two rockets be on > > parallel lines to the x-axis.
> ? Now you mean that they are both NOT on the x axis but on parallel > lines *to* the x axis?
> >An observer in a frame moving at V > > relative to the x-axis turns on the thrusters of both rockets > > simultaneously as measured in his frame. As viewed in this frame the > > tip of each rocket remains a distance L away
> ? They are a distance L in which frame, the "initial" frame you > referenced or this new frame V ? make up your mind.
> At this point, you must completely rephrase your problem because it is > too badly posed.
On Nov 8, 12:55 pm, DSeppala <dsepp...@austin.rr.com> wrote:
> To clarify your confusion caused by my phrasing. > The two identical rockets are positioned to travel along lines > parallel to the x-axis (as if they were racing side by side once they > start accelerating).
SIDE by SIDE...ok
>The tip of one rocket is at x = 0, and the tip > of the other is at x = L'.
Thus they are NOT side by side???
Make up your mind. Try again.
Eg. Let S be an ( 2 dim) i-frame.
Two rockets ( or their tips) initially ar rest at locations ( x=0, y = 1) and ( x=0, y = -1). They are thus SIDE by SIDE, understand ???
Ok trying to understand what you meant... You are just citing a different variant of the Boughn identical accelerated twins. Read it and similar material. We have explained those situations to you befeore..for the past many years!
We explained to you how to s olve "1+2" We explained to you how to s olve "1+3" We explained to you how to s olve "1+4" We explained to you how to s olve "1+5"
Now you are asking to explain "1+6". No. Figure it out yourself or learn how to read...its all explained somewhere on the net and books.
On Nov 8, 12:55 pm, DSeppala <dsepp...@austin.rr.com> wrote:
> To clarify your confusion caused by my phrasing. > The two identical rockets are positioned to travel along lines > parallel to the x-axis (as if they were racing side by side once they > start accelerating). The tip of one rocket is at x = 0, and the tip > of the other is at x = L'. In another inertial reference frame that > is traveling at velocity V with respect to the inertial reference > frame the two rockets are initially in, the distance between the tips > of the rockets is measured as L. At time t0 in this moving reference > frame, observers in this frame turn the the thrusters on both rockets > simultaneously. The accelerometers on board each rocket show a > constant and identical acceleration. As measured in the moving frame > (where the thrusters were simultaneously turned on) at any instant of > time, the tips of the two rockets are always L meters apart since both > rockets simultaneously go through identical motions (but at different > points along the x-axis). > Now in the original rocket inertial frame, the thrusters weren't > turned on simultaneously. The thrusters of one rocket was turned on > before the thrusters of the other rocket. From the point of view an > observer in the first rocket, how does he describe what happens during > the constant acceleration? First he starts accelerating toward the > other rocket. Then at some point in time as measured by the first > rocket's clocks, the other rocket starts to accelerate. At time t1 > (as measured by the first rocket's clocks) when the other rocket > begins its acceleration, the two rockets were approaching each other > with some velocity. As they both continue to accelerate along the x- > axis, why doesn't the tip of the first rocket ever reach the same x > position in space as the tip of the second rocket and eventually pass > the second rocket? > Hope that clarification removes your confusion. > David > On Nov 8, 9:54 am, rotchm <rot...@gmail.com> wrote:
> > Whoah... so many errors in the formulation of your question.
> > On Nov 8, 8:25 am, DSeppala <dsepp...@austin.rr.com> wrote:
> > > The following seems contradictory.
> > Yes, "seems".
> > > There are two identical rockets separated a distance L as measured on > > > the x-axis in an inertial reference frame.
> > Ok, so both are ON the x axis. The usual config.
> > >Let the two rockets be on > > > parallel lines to the x-axis.
> > ? Now you mean that they are both NOT on the x axis but on parallel > > lines *to* the x axis?
> > >An observer in a frame moving at V > > > relative to the x-axis turns on the thrusters of both rockets > > > simultaneously as measured in his frame. As viewed in this frame the > > > tip of each rocket remains a distance L away
> > ? They are a distance L in which frame, the "initial" frame you > > referenced or this new frame V ? make up your mind.
> > At this point, you must completely rephrase your problem because it is > > too badly posed.- Hide quoted text -
> The following seems contradictory. > There are two identical rockets separated a distance L as measured on > the x-axis in an inertial reference frame. Let the two rockets be on > parallel lines to the x-axis. An observer in a frame moving at V > relative to the x-axis turns on the thrusters of both rockets > simultaneously as measured in his frame. As viewed in this frame the > tip of each rocket remains a distance L away from the tip of the other > rocket even as the rockets accelerate. This occurs because both > rockets undergo identical simultaneous accelerations, so as one rocket > changes position the other does the identical motion at a different > location in space as measured in this frame. > How do people on board the rockets view things? In the inertial > reference frame the rockets were initially in, the turning on of the > thrusters of each of the two rockets were not simultaneous events. > The thrusters of one rocket were turned on before the thrusters of the > other rocket. Let's say you are in the rocket where the thruster was > turned on first, and you start accelerating toward the other rocket at > some constant acceleration rate. After T seconds as measured in your > accelerating rocket, the thrusters of the other rocket are turned on > so that both of you are now accelerating in the same direction. You > note that at this time you had a closing velocity of V (you and the > other rocket were approaching each other). You know the other rocket > is identical to yours, and you are still accelerating at the same > constant rate. If the closing rate continues at least at V or > greater, after some point in time the tip of your rocket will pass the > tip of the other rocket. But we've already established that as > measured in the inertial reference frame where turning on the > thrusters were simultaneous events, the tips of the two rockets never > are at the same point in space at the same time, and hence can never > pass each other. It seems to me at some point in time the rocket that > started accelerating first must pass the other rocket. > Thanks for explaining this from the point of view of someone in the > first rocket. > David Seppala > Bastrop Texas
xxein: The rockets proceed at distance L from one another. What you 'see' is the front rocket appearing closer because you are in waiting on the light to see it move as you move toward it. Just the opposite occurs for the front rocket to 'see' you. It is already moving away from you before it sees your light arrive when you appear stationary.
But that is only the beginning of the explanation. Suppose you both pass through the same instantaneous velocity of .2c during this acceleration. The light travel time from front rocket to rear rocket diminishes. But light travel time will increase for light to get to the front rocket from the rear one. Iow, the front rocket will appear increasingly closer to the rear rocket while the rear rocket appears increasingly further away as your speeds increase. C is a finite velocity.
If they were point particles able to observe each other, they would show limits to this observability. As they got to c in velocity, the rear one would view the front one as being 1/2 L away (if both on the same axis instead of parallel axes) because the time for light to get there would be c/2. Light has doubled it's speed to get to you because you are approaching that light at c velocity (2c for the effect). Otoh, for the front to view the rear, the rear would disappear because the light would never get to it. This is the basis for a physical explanation for velocity addition.
This is not nearly the end of the explanation either. This is reflected light between observers with co-moving clocks. Not generated light by the movers (that gives a different measurement and remain as L because of time dilation).
The end of the explanation goes seamlessly to the Pioneer (so-called) anomaly. Yeah. Right through gravity and cosmology.
I could only wish that there is a non-brainwashed person who could persue the physic instead of the taught physics.
> The following seems contradictory. > There are two identical rockets separated a distance L as measured on > the x-axis in an inertial reference frame. Let the two rockets be on > parallel lines to the x-axis. An observer in a frame moving at V > relative to the x-axis turns on the thrusters of both rockets > simultaneously as measured in his frame. As viewed in this frame the > tip of each rocket remains a distance L away from the tip of the other > rocket even as the rockets accelerate. This occurs because both > rockets undergo identical simultaneous accelerations, so as one rocket > changes position the other does the identical motion at a different > location in space as measured in this frame. > How do people on board the rockets view things? In the inertial > reference frame the rockets were initially in, the turning on of the > thrusters of each of the two rockets were not simultaneous events. > The thrusters of one rocket were turned on before the thrusters of the > other rocket. Let's say you are in the rocket where the thruster was > turned on first, and you start accelerating toward the other rocket at > some constant acceleration rate. After T seconds as measured in your > accelerating rocket, the thrusters of the other rocket are turned on > so that both of you are now accelerating in the same direction. You > note that at this time you had a closing velocity of V (you and the > other rocket were approaching each other). You know the other rocket > is identical to yours, and you are still accelerating at the same > constant rate. If the closing rate continues at least at V or > greater, after some point in time the tip of your rocket will pass the > tip of the other rocket. But we've already established that as > measured in the inertial reference frame where turning on the > thrusters were simultaneous events, the tips of the two rockets never > are at the same point in space at the same time, and hence can never > pass each other. It seems to me at some point in time the rocket that > started accelerating first must pass the other rocket. > Thanks for explaining this from the point of view of someone in the > first rocket. > David Seppala > Bastrop Texas
You are saying that contraction would effect simultaneity by changing distances for light.
> On Nov 8, 12:55 pm, DSeppala <dsepp...@austin.rr.com> wrote:
> > To clarify your confusion caused by my phrasing. > > The two identical rockets are positioned to travel along lines > > parallel to the x-axis (as if they were racing side by side once they > > start accelerating).
> SIDE by SIDE...ok
> >The tip of one rocket is at x = 0, and the tip > > of the other is at x = L'.
> Thus they are NOT side by side???
> Make up your mind. Try again.
> Eg. Let S be an ( 2 dim) i-frame.
> Two rockets ( or their tips) initially ar rest at locations ( x=0, y > = 1) and ( x=0, y = -1). > They are thus SIDE by SIDE, understand ???
okay, I will be more pedantic for you. Initially one rocket tip is at x = 0, y = 0. The other rocket tip is at x = L' and y = D where D is greater than the diameter of the rocket so that they never can crash into each other if they travel at different velocities along those lines parallel to the x-axis. In this frame at time t0, the rocket at x = 0, y = 0 starts accelerating in the positive x direction at some constant acceleration rate, which I'll call g. At some time t1 where t1 > t0 the second rocket starts accelerating in an identical fashion in the positive x direction. As viewed from the first rocket, why do the observers on board the first rocket say that they can never catch up to the second rocket even though their speed along the x-axis is always greater than the second rocket's speed along the x-axis? David
On Nov 8, 12:26 pm, rotchm <rot...@gmail.com> wrote:
> Ok trying to understand what you meant... You are just citing a > different variant of the Boughn identical accelerated twins. Read it > and similar material. We have explained those situations to you > befeore..for the past many years!
In the Boughn identical accelerated twins variant the twins eventually return to the same frame. In my question, the first rocket is continually is approaching the second rocket but can never catch up to the second rocket, even if they accelerate for all eternity (by that I mean as t becomes infinite). I don't understand why. David
> We explained to you how to s olve "1+2" > We explained to you how to s olve "1+3" > We explained to you how to s olve "1+4" > We explained to you how to s olve "1+5"
> Now you are asking to explain "1+6". No. Figure it out yourself or > learn how to read...its all explained somewhere on the net and books.
> On Nov 8, 12:55 pm, DSeppala <dsepp...@austin.rr.com> wrote:
> > To clarify your confusion caused by my phrasing. > > The two identical rockets are positioned to travel along lines > > parallel to the x-axis (as if they were racing side by side once they > > start accelerating). The tip of one rocket is at x = 0, and the tip > > of the other is at x = L'. In another inertial reference frame that > > is traveling at velocity V with respect to the inertial reference > > frame the two rockets are initially in, the distance between the tips > > of the rockets is measured as L. At time t0 in this moving reference > > frame, observers in this frame turn the the thrusters on both rockets > > simultaneously. The accelerometers on board each rocket show a > > constant and identical acceleration. As measured in the moving frame > > (where the thrusters were simultaneously turned on) at any instant of > > time, the tips of the two rockets are always L meters apart since both > > rockets simultaneously go through identical motions (but at different > > points along the x-axis). > > Now in the original rocket inertial frame, the thrusters weren't > > turned on simultaneously. The thrusters of one rocket was turned on > > before the thrusters of the other rocket. From the point of view an > > observer in the first rocket, how does he describe what happens during > > the constant acceleration? First he starts accelerating toward the > > other rocket. Then at some point in time as measured by the first > > rocket's clocks, the other rocket starts to accelerate. At time t1 > > (as measured by the first rocket's clocks) when the other rocket > > begins its acceleration, the two rockets were approaching each other > > with some velocity. As they both continue to accelerate along the x- > > axis, why doesn't the tip of the first rocket ever reach the same x > > position in space as the tip of the second rocket and eventually pass > > the second rocket? > > Hope that clarification removes your confusion. > > David > > On Nov 8, 9:54 am, rotchm <rot...@gmail.com> wrote:
> > > Whoah... so many errors in the formulation of your question.
> > > On Nov 8, 8:25 am, DSeppala <dsepp...@austin.rr.com> wrote:
> > > > The following seems contradictory.
> > > Yes, "seems".
> > > > There are two identical rockets separated a distance L as measured on > > > > the x-axis in an inertial reference frame.
> > > Ok, so both are ON the x axis. The usual config.
> > > >Let the two rockets be on > > > > parallel lines to the x-axis.
> > > ? Now you mean that they are both NOT on the x axis but on parallel > > > lines *to* the x axis?
> > > >An observer in a frame moving at V > > > > relative to the x-axis turns on the thrusters of both rockets > > > > simultaneously as measured in his frame. As viewed in this frame the > > > > tip of each rocket remains a distance L away
> > > ? They are a distance L in which frame, the "initial" frame you > > > referenced or this new frame V ? make up your mind.
> > > At this point, you must completely rephrase your problem because it is > > > too badly posed.- Hide quoted text -
DSeppala wrote: > On Nov 8, 12:26 pm, rotchm <rot...@gmail.com> wrote: >> Ok trying to understand what you meant... You are just citing a >> different variant of the Boughn identical accelerated twins. Read it >> and similar material. We have explained those situations to you >> befeore..for the past many years! > In the Boughn identical accelerated twins variant the twins eventually > return to the same frame. In my question, the first rocket is > continually is approaching the second rocket but can never catch up to > the second rocket, even if they accelerate for all eternity (by that I > mean as t becomes infinite). I don't understand why.
Of COURSE you don't understand. The real mystery is why you persist.
> On Nov 8, 12:26 pm, rotchm <rot...@gmail.com> wrote: >> Ok trying to understand what you meant... You are just citing a >> different variant of the Boughn identical accelerated twins. Read it >> and similar material. We have explained those situations to you >> befeore..for the past many years! > In the Boughn identical accelerated twins variant the twins eventually > return to the same frame.
Depends on the version of it .. some have them eventually stopping accelerating, some do not
> In my question, the first rocket is > continually is approaching the second rocket
the rockets get further apart, not closer together
> but can never catch up to > the second rocket, even if they accelerate for all eternity (by that I > mean as t becomes infinite). I don't understand why.
Do some more reading on borne rigid motion, and bells spaceship 'paradox'
> > On Nov 8, 12:26 pm, rotchm <rot...@gmail.com> wrote: > >> Ok trying to understand what you meant... You are just citing a > >> different variant of the Boughn identical accelerated twins. Read it > >> and similar material. We have explained those situations to you > >> befeore..for the past many years! > > In the Boughn identical accelerated twins variant the twins eventually > > return to the same frame.
> Depends on the version of it .. some have them eventually stopping > accelerating, some do not
> > In my question, the first rocket is > > continually is approaching the second rocket
> the rockets get further apart, not closer together
> > but can never catch up to > > the second rocket, even if they accelerate for all eternity (by that I > > mean as t becomes infinite). I don't understand why.
> Do some more reading on borne rigid motion, and bells spaceship 'paradox'
Whats the speed of light for a rocket moving directly behind it?
> okay, I will be more pedantic for you. > Initially one rocket tip is at x = 0, y = 0. The other rocket tip is > at x = L' and y = D where D is greater than the diameter of the rocket > so that they never can crash into each other if they travel at > different velocities along those lines parallel to the x-axis.
So R1 cannot coincide ( touch, catch up ?) with R2 ? ( R = rockets) The diameters are irrelevant. And since the rockets travel along parallel paths, they cannot conincide ( crash). Your velocity argument seems irrelevant.
Start over.
> In this frame at time t0, the rocket at x = 0, y = 0 starts > accelerating in the positive x direction at some constant acceleration > rate, which I'll call g. At some time t1 where t1 > t0 the second > rocket starts accelerating in an identical fashion in the positive x > direction. As viewed from the first rocket, why do the observers on > board the first rocket say that they can never catch up to the second > rocket even though their speed along the x-axis is always greater than > the second rocket's speed along the x-axis?
They cannot catch up because you posed the scenario that way !! R1 and R2 travel on ( non-touching) parallel paths !! DuH!
You mean catch up as in, to have the same x coordinate? Then,
??? Observers onboard the first rocket would not say that they can never catch up. In fact, they can catch up to the second rocket.
Let R2 be at L', = 1 cm. Let t0 = 0 and t1 = 3600 sec ( 1 hour btw!). Let g = 1. Within a fraction of a second, R1 would catch up with R2 and pass it. Only an hour later will R2 start to move...
You description is again totally confusing and does not make sense. Go read, ALOT. See how the authors write and explain scenarios. Once you learnt how to be fully clear in your descriptions, then you can start to worry about the math and physics.
> The following seems contradictory. > There are two identical rockets separated a distance L as measured on > the x-axis in an inertial reference frame. Let the two rockets be on > parallel lines to the x-axis. An observer in a frame moving at V > relative to the x-axis turns on the thrusters of both rockets > simultaneously as measured in his frame. As viewed in this frame the > tip of each rocket remains a distance L away from the tip of the other > rocket even as the rockets accelerate. This occurs because both > rockets undergo identical simultaneous accelerations, so as one rocket > changes position the other does the identical motion at a different > location in space as measured in this frame. > How do people on board the rockets view things? In the inertial > reference frame the rockets were initially in, the turning on of the > thrusters of each of the two rockets were not simultaneous events. > The thrusters of one rocket were turned on before the thrusters of the > other rocket. Let's say you are in the rocket where the thruster was > turned on first, and you start accelerating toward the other rocket at > some constant acceleration rate. After T seconds as measured in your > accelerating rocket, the thrusters of the other rocket are turned on > so that both of you are now accelerating in the same direction. >You > note that at this time you had a closing velocity of V (you and the > other rocket were approaching each other).
If you perform the LTs for the simultaneous events from the simultaneous frame to either rocket frame, you'll find that the rocket in front is always turned on first and there is no closing velocity.
> You know the other rocket > is identical to yours, and you are still accelerating at the same > constant rate. If the closing rate continues at least at V or > greater, after some point in time the tip of your rocket will pass the > tip of the other rocket. But we've already established that as > measured in the inertial reference frame where turning on the > thrusters were simultaneous events, the tips of the two rockets never > are at the same point in space at the same time, and hence can never > pass each other. It seems to me at some point in time the rocket that > started accelerating first must pass the other rocket. > Thanks for explaining this from the point of view of someone in the > first rocket. > David Seppala > Bastrop Texas
Have a go at using the LTs for transforming the simultaneous events to the frame of either rocket.
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