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Re: My mistake or Einstein's

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On 09.08.2016 20:04, sepp623@yahoo.com wrote:
> This scenario of this simple problem ends up with contradictory
> results. Please identify the mistake.
>
> In this problem, I use c = 3 * 10**8 meters/second as the speed of
> light.


> Consider an inertial reference frame, F0, that has an object A moving
> along the x-axis at -2.8 * 10**8 meters/second. If this object starts
> accelerating in the positive x direction at a constant rate of 28
> meters / second**2 as measured in F0, how long does it take for this
> object to reach a speed of 2.8 * 10**8 meters/second as measured in
> F0? When I do the calculation, I find that it takes 2 * 10**7
> seconds. This based on the simple formula v = a * t


This is the source of the error;-)
Seriously, it is all right, but it will lead to the error.

You can think of object that have constant "coordinate" acceleration,
but it is probably not what you think.
A passenger on such object will feel bigger and bigger "g force".
In his local (temporary) inertial reference frame the acceleration
will grown.

But until it reach c, such object could exist.

> Now, when this object accelerates from -2.8 * 10**8 meters/second to
> 2.8 * 10**8 meters/second at the constant rate of 28 meters /
> second**2 as measured in F0, how far does this object travel along
> the x-axis during this time interval as measured in frame F0? Since
> the acceleration rate is constant, I used the formula d = 0.5 * (a *
> t**2) to determine the distance, along with the initial velocity
> before the acceleration starts of -2.8 * 10**8 meters / second. This
> resulted in:
>
> d = ((-2.8 * 10**8) * (2 * 10**7)) + (0.5 * 28 * (2 * 10**7) * (2 *
> 10**7)) meters

The idea is sound, I did not check your calcultaions.


> I run into a problem when I use Einstein's simultaneous events
> concept in conjunction with these numbers.


> Let there be a second inertial reference frame, F1, that is moving
> with a relative velocity with magnitude of sqrt(3)/2 * c with respect
> to F0. And let there be a second object in space, object B, that
> initially has the same velocity as object A. When object B
> accelerates, its pattern of acceleration is identical to object A's
> pattern of acceleration.

Og, lets remember this assumption (*).

> Let observers in frame F1 measure the
> distance between object A and object B to be sqrt(3) light-seconds.
> At time t0, observers in frame F1, simultaneously, start both object
> A and object B accelerating in the positive x direction. Observers in
> frame F1, measure that the distance between object A and object B
> remains constant at sqrt(3) light-seconds.

Yes...

> The distance between
> object A and object B remains constant as measured in frame F1
> because both objects had the same initial velocity (the relative
> velocity of object A to object B was zero before the acceleration
> started), they accelerate in the identical manner (just at different
> locations in space) and both objects started accelerating
> simultaneously (as measured in frame F1).


> Now in frame F0, prior to the start of any acceleration, let object B
> have a greater x coordinate than object A at any point in time, as

Do not do this! I do not know if that is a new assumption.
I do not known if it contradicts earlier assumptions
(which starts earlier)
This is messy and unreadable!

Just create the scene, tell us that F1 have velocity v
in F0. And the sign of v will tell us if F1 is going in the direction
of greater or smaller 'x'. It is your task to think through
what you want to achieve and create a clear situation.

Tell us that in one of the freme they have such and such position,
The velocity is directed in that direction...
The rest have to be conclusions (preferbly backed by calculations:)


> they both move with velocity -2.8 * 10**8 meters/second along the
> x-axis of F0. And let the direction of the acceleration of both
> objects be in the positive x direction when the acceleration of each
> object starts. Per Einstein, frame F0 measures that one of the
> objects starts accelerating 3 seconds before the other object starts
> accelerating.

Not 3s.

In F0 the starts have coordinates (t,x):
(0,0)
and
(0,3)

velocity of F1 is v = sqrt(3)/2,
so gamma = 1/sqrt(1-3/4) = 1/(1/2)=2

The first start is still at (0,0),
th second is at time
t' = gamma t +- gamma x v = +-2*sqrt(3)/2 *3 = +-3*sqrt(3) s



> Let the direction of relative velocity between frame F0
> and F1 be such that object A starts accelerating 3 seconds before
> object B starts accelerating, as measured in frame F0.
>
> Since object A started accelerating 3 seconds before object B, object
> A gets closer and closer to object B as function of time. During the
> acceleration as the velocity of object A goes from -2.8 * 10**8
> meters/second as measured in F0 to 2.8 * 10**8 meters/second, how
> close does object A get to object B as measured in frame F0?

The closest approach will be at the end. When both spaceship
stops accelerating, transfer to its reference frame and
compute the distance.

> Previously I computed that during that acceleration object A moves a
> distance of ((-2.8 * 10**8) * (2 * 10**7)) + (0.5 * 28 * (2 * 10**7)
> * (2 * 10**7)) meters
>
> During that same time interval, with object B starting its
> acceleration 3 seconds later, object B moves a distance of ((-2.8 *
> 10**8) * (2 * 10**7)) + (0.5 * 28 * ((2 * 10**7) - 3) * ((2 * 10**7)
> - 3) meters


This is bunch of numbers, not equation?
What does it mean?

I guess it is s(t) = v0*t + 0.5 at^2

And We have the error.

You have assumed that in F1 both rockets have the same
'acceleration pattern' (so the same trajectory).
This was the assumption I labelled (*).

They do not have the same pattern in F0!

The coordinate acceleration of the second rocket is not
even constant in F0.


The A rocket have acceleration pattern
v = v0+a*t
s = s0 + v0*t+0.5 a t^2
in F0.

this mean, as I mentioned, that proper acceleration
(acceleration measured by instruments on rocket A)
is changing.

In F1 the movement is not v' = v0'+a'*t',
but both rocket have the same trajectory (only
shifted in space by 3 light seconds).

Proper acceleration is changing, but at the same time
in F1 both rocket have the same proper acceleration.

Now, we are going back to F0. The surface of simultaneity
"rotate" and now at the same time both rocket have
different proper accelerations!

So them have (most of the time:) different coordinate accelerations.

The B rocket do not have constant acceleration equal to
A's acceleration.


There is no crash, you have used wrong trajectory for rocket B.



You can get the trajectory of B in F0 by transfering
trajectory of A to F1, shifting (x'->x' +3) and
transfering back to F0.

The result is not a nice equation;-)


You can also use the motion with constant proper acceleration:
https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)
It looks the same in every reference frame.


bartekltg

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My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 11:04 -0700
  Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-09 12:26 -0700
  Re: My mistake or Einstein's pcardinale@volcanomail.com - 2016-08-09 12:57 -0700
  Re: My mistake or Einstein's pcardinale@volcanomail.com - 2016-08-09 13:04 -0700
  Re: My mistake or Einstein's "Paul B. Andersen" <relativity@paulba.no> - 2016-08-09 22:39 +0200
    Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 13:56 -0700
      Re: My mistake or Einstein's "Paul B. Andersen" <relativity@paulba.no> - 2016-08-10 10:51 +0200
  Re: My mistake or Einstein's JanPB <filmart@gmail.com> - 2016-08-09 15:15 -0700
    Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 15:38 -0700
      Re: My mistake or Einstein's JanPB <filmart@gmail.com> - 2016-08-09 15:53 -0700
        Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 16:21 -0700
          Re: My mistake or Einstein's JanPB <filmart@gmail.com> - 2016-08-09 23:05 -0700
            Re: My mistake or Einstein's Maciej Woźniak <mlwozniak@wp.pl> - 2016-08-10 11:56 +0200
          Re: My mistake or Einstein's bartekltg <bartekltg@gmail.com> - 2016-08-10 14:17 +0200
    Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-10 01:39 -0700
  Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-09 17:26 -0700
    Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 17:38 -0700
      Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-09 17:53 -0700
        Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 17:59 -0700
          Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-09 18:26 -0700
            Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 19:05 -0700
              Re: My mistake or Einstein's moroney@world.std.spaamtrap.com (Michael Moroney) - 2016-08-10 02:59 +0000
              Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-09 20:06 -0700
  Re: My mistake or Einstein's Sylvia Else <sylvia@not.at.this.address> - 2016-08-10 13:16 +1000
    Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 21:11 -0700
      Re: My mistake or Einstein's Sylvia Else <sylvia@not.at.this.address> - 2016-08-10 14:15 +1000
        Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 21:31 -0700
          Re: My mistake or Einstein's Sylvia Else <sylvia@not.at.this.address> - 2016-08-10 14:48 +1000
            Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-09 22:56 -0700
              Re: My mistake or Einstein's The Starmaker <starmaker@ix.netcom.com> - 2016-08-10 01:36 -0700
  Re: My mistake or Einstein's Sylvia Else <sylvia@not.at.this.address> - 2016-08-10 20:35 +1000
  Re: My mistake or Einstein's bartekltg <bartekltg@gmail.com> - 2016-08-10 14:04 +0200
    Re: My mistake or Einstein's Maciej Woźniak <mlwozniak@wp.pl> - 2016-08-10 14:29 +0200
      Re: My mistake or Einstein's bartekltg <bartekltg@gmail.com> - 2016-08-10 15:29 +0200
        Re: My mistake or Einstein's sepp623@yahoo.com - 2016-08-10 06:36 -0700
          Re: My mistake or Einstein's Sylvia Else <sylvia@not.at.this.address> - 2016-08-11 11:16 +1000
        Re: My mistake or Einstein's Maciej Woźniak <mlwozniak@wp.pl> - 2016-08-10 15:36 +0200
    Re: My mistake or Einstein's bartekltg <bartekltg@gmail.com> - 2016-08-10 15:49 +0200
      Re: My mistake or Einstein's Maciej Woźniak <mlwozniak@wp.pl> - 2016-08-10 16:14 +0200

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