BurtJordaan » 27 Apr 2017, 22:16 wrote:So how did isotropy 'magically' return after the acceleration stopped? In order to understand that, we must turn to the spacetime structure  not to time (yet), because we did not really use time in the interferometer experiment. Spacetime structure will be topic of the next part.

Dave_Oblad » April 29th, 2017, 1:37 pm wrote:Hi all,
Given:
Ship(A) & Ship(B) are at right angles with Zero Velocity. (Ref=CMB)
Ships are separated by 300,000 Km (one light second).
Ship(A) shoots Laser Beam at Right Angle Mirror.
Beam hits Mirror and bounces 90' to Ship(B) perfectly on Target.
Given:
Both ships then accelerate identically to 86% Light Speed simultaneously and go inertial.
Both ships are still at a perfect 90' angle from each other, coasting, on perfect parallel paths.
...
So let's start the discussion on a SHARED FRAME with this simple example provided.
Question1: Why does Ship(A) observe Ship(B) to still be located at a perfect right angle?
Dave_Oblad » April 29th, 2017, 1:37 pm wrote:Question2: Why does Ship(A) not need to lead the Target to make up for the Light Transit Delay?
mitchellmckain » April 29th, 2017, 10:03 pm wrote:The interesting thing to ask in special relativity is what does someone in a different inertial frame see? So introduce another observer C who is watching these two ships pass him at that 86% of the speed of light. According to C, Ship A DOES lead the target in order for his beam of light to reach ship B. How is this possible? Lorentz contraction shortens the lengths of ship A in the direction of motion (according to observer C) and thus changes the angle of the mirror, and thus the direction of the beam of light according to observer C.
bangstrom » 30 Apr 2017, 11:55 wrote:Lorentz contraction is essentially a rotation through space so, if observer C is between the two passing ships, C should observe both ships to be rotated as if traveling a bit sideways with the tail ends of the ships closer and the nose ends pointed away. From that perspective, both ships would appear shorter and the rotation would redirect the mirror.
BurtJordaan » April 30th, 2017, 10:51 am wrote:
Lorentz contraction is not a rotation through space, but can be viewed as a rotation in spacetime. There is huge difference between the two. Lorentz contraction do not "redirect" any mirrors.
BurtJordaan » 29 Apr 2017, 22:03 wrote:If we take the blue structure as Bob's and the red structure as Alice's, it is easy to see that we could just rotate both of them around the origin so that Alice's +cT points upwards on the page and Bob's more to the left, and things will essentially 'look' the same. In fact, we can rotate the two structures together in any direction, through any angle and as long as we do not change the angle between them, things will still essentially look the same, wherever we leave them to point.

Dave_O wrote:Question1: Why does Ship(A) observe Ship(B) to still be located at a perfect right angle?

Dave_Oblad wrote: since the speed of light didn't change and the diagonal path would have to take longer, we might say that a local stationary observer would say it took a bit longer than a second for the light to bridge the diagonal gap between Ships.
Dave_Oblad wrote:if both Ships synced their personal clocks at the start, then both Ship's clocks would still be in sync.
Dave_Oblad wrote:If Ship(A) send a signal on his Laser Beam that had a TimeStamp, the receiver at Ship(B) would see that their Local Time is a bit ahead of that from Ship(A). The same would be true in reverse.
Faradave wrote:To the extent you accept the synchronization scheme, you would have done a "oneway speed of light" measurement.
Dave_Oblad » 30 Apr 2017, 23:55 wrote:Jorrie introduced Alice and Bob. Both are heading towards a starting line. When they cross the line at the same time, the Race starts and both Alice and Bob click their start/stop watches (get their clocks in sync). While Bob, who is going very slow, continues straight on towards the Finish Line, Alice (who was gong very fast) takes the long scenic route. Ultimately.. Alice returns and manages to cross the Finish Line at the exact same time as Bob. They both click their stop watches at the same time when they cross the Finish Line.
Faradave » 01 May 2017, 00:38 wrote:If Earth and Mars happen to be close and aligned at a point where instantaneous velocities are essentially equal (parallel), it will still take about 14 minutes to get a signal from either one to the other. In a situation where the bodies are (momentarily) relatively at rest, they can point their antennae directly at each other.
BurtJordaan » 29 Apr 2017, 22:03 wrote:The moment we rotate one structure relative to the other, we lose the perfect symmetry, because now we will have a curved cT axes for at least one of the participants. This is what acceleration does. It is the process of changing the angle between two structures. Once the acceleration stops, the asymmetry remains, unless we erase this history and set up a new structure with a new constant angle between the two structures.

BurtJordaan » May 1st, 2017, 1:15 am wrote:Faradave » 01 May 2017, 00:38 wrote:Given that there is a 14 lightminutes distance between them, wouldn't they have to be at relative rest for at least that 14 minutes?
BurtJordaan » 01 May 2017, 10:49 wrote:Epstein diagrams and acceleration (Continued)
Before we go on to discuss that, (as "homework" ;)) please consider what would have happened if, instead of switching off the rocket, Alice has rapidly turned around and applied the exact same (reverse) acceleration for exactly the same time on her clock. And then switched off the rocket to coast again.
Jorrie wrote:The 'normal' orthogonal axes x and ct, with the squares formed by the dotted lines represents the spacetime structure for the reference observer (say it is Bob). The oblique axes x' and ct', with the 'parallelograms' instead of squares are the spacetime structure for the relatively moving observer (say Alice), as seen by Bob. This is a crucial caveat, because Alice could just as well have been chosen as the reference observer, because she would have seen her own structure as orthognal and Bob's as parallelograms, just slanted in the opposite direction.
Jorrie wrote:Most readers have probably seen Minkowski spacetime diagrams, which are an attempt to show spacetime structures for two relatively moving inertial observers. It is noncontroversial, scientifically correct, but at the same time very intimidating to many readers, so I do not want to dwell on them too much.
Jorrie wrote:Logical conclusion: their clocks ran the same, but they recorded different times because their SPt vertical displacements were different.
Jorrie wrote:For me the best (nonmathematical) answer lurks in the change in spacetime structure.
Dave_Oblad » 01 May 2017, 23:02 wrote: Remember the Title of the OP?
If your intention was to teach Relativity to College Graduates, you are doing fine. But if your Target audience was middle school children, then the sudden introduction of such large words and concepts kind of exemplifies the OP.
Dave_O wrote:Even I didn't get you were jumping directly into Acceleration and Deceleration, which are usually avoided in SR.. until the basics are better understood. How did we get from a "Lab floating in Space" to your "Minkowski spacetime diagrams" in one sudden post leap?
Dave_O wrote:Jorrie wrote:Logical conclusion: their clocks ran the same, but they recorded different times because their SPt vertical displacements were different.
From the above quote I would have to conclude that we are not comparing Alice's Clock to Alice's Clock, as that would be silly. So.. we must be comparing Alice's Clock to Bob's Clock. So how can they run the same and yet be different?
Dave_Oblad » 01 May 2017, 23:18 wrote:Did the structure of SpaceTime itself physically change because Alice accelerated? Or was it Alice and her clocks that changed structure because she accelerated through SpaceTime?
Jorrie wrote:The larger structure of spacetime can't change due to whatever Alice does, but isn't it reasonable to argue that her own, private spacetime structure has changed relative to Bob's?

Faradave » 02 May 2017, 15:08 wrote:The continuum provides separation of events, which are then mapped according to each observer's reference frame.

Braininvat » 02 May 2017, 16:00 wrote: A continuum provides a certain kind of separation (non"jumpy") without dictating anything about a personal FoR. It is not observable, because it's really only a nebulous kind of "permission" to move smoothly.
BurtJordaan » 01 May 2017, 22:20 wrote:It is easy to see that before the acceleration, Alice and Bob have shared the same spacetime structure. During the acceleration, only Alice's spacetime is distorted and her measures of space and time are changed. She now measures less time and less distance between events than what Bob does.
Dave_Oblad » 02 May 2017, 19:48 wrote:To describe this structure on a more simple level, we might start by agreeing both SpaceTime and Matter have real structure, and such is interactive between them.
Dave_O wrote:Both Balls adopt some of the SpaceTime curvature from each other and take on the internal Structure of Acceleration.. towards each other.. where the curvature becomes greater (gradient) the closer they become.
So what is this Curvature? Specifically.. it is the Gradient effect each Ball is having on the local SpaceTime Structure that surrounds the Balls. Bottom line.. if SpaceTime didn't have a Structure of its own, there would be no Gravity effects.
BurtJordaan » May 2nd, 2017, 11:45 am wrote:
Not so  Alice's clock was not influenced by the acceleration and still ticks like Bob's. But her spacetime structure is different in the sense that she had less distance to cover and did it in less ticks of her clock. Her INS computer would have been programmed to automatically adjust the scale of the map in its memory and would have told her exactly at what time on her clock she arrives at her destination. How cool is that?
Jordaan wrote:The larger structure of spacetime can't change due to whatever Alice does, but isn't it reasonable to argue that her own, private spacetime structure has changed relative to Bob's? Remember that they have started with identical structures. These "identical structures" could have been different to the universe's spacetime structure, which happens to be undetectable.
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