I How things appear to an accelerated observer

[PeterDonis]

the same setup but from Alice's viewpoint:

Alice is not at rest in this diagram (her worldline is not a vertical line), so I don't see how this represents "Alice's viewpoint", for the reason I've already given: changing frames from event to event on Alice's worldline does not give "Alice's viewpoint", since it does not result in a single valid coordinate chart covering the region of spacetime of interest, in which Alice is at rest.

 

[PeterDonis]

red is Alice's worldline.

Isn't Alice supposed to have been at rest, co-located with Bob, until she starts accelerating at time $t = 0$ in the "Bob's viewpoint" diagram?

If so, that diagram only shows her worldline correctly after $t = 0$, not before it. Before it her worldline should be a vertical line co-located with Bob's.

 

[jartsa]

Not immediately, no, because of the finite speed of light. But once the light from the time the distant object abruptly accelerated reaches Alice, she will see an apparent size change.

Nah. Light ray goes from a point on the object to the eye of Alice. No change of angle of the light ray in this case. I mean light ray that reaches Alice's eye must have a certain direction.

 

[PAllen]

Nah. Light ray goes from a point on the object to the eye of Alice. No change of angle of the light ray in this case. I mean light ray that reaches Alice's eye must have a certain direction.

No, look up relativistic aberration. If a distant object suddenly starts moving rapidly toward you, then when light emitted right after the change reaches you, it will have a more horizontal angle, which looks like it got smaller, thus further away.

 

[PeterDonis]

Nah.

The relativistic beaming effect is frame independent; it doesn't matter whether you consider the source or the observer to be moving.

 

[jartsa]

No, look up relativistic aberration. If a distant object suddenly starts moving rapidly toward you, then when light emitted right after the change reaches you, it will have a more horizontal angle, which looks like it got smaller, thus further away.

Relativistic beaming effect is frame independent. But the change of the size of the image works as I explained earlier. Let me explain second time:

Let's say a distant object emits rays equally to all directions. If said distant object suddenly starts moving rapidly toward you, then when light emitted right after the change reaches you, more of those emitted rays reach you ("headlight effect"), which would have the effect of rays with more different angles reaching you, if there was not the effect of rays becoming more parallel.

The maximum angle between those rays emitted by the object that reach you depends on the size of the object and the distance. Not velocity of the object.

 

[PAllen]

The maximum angle between those rays emitted by the object that reach you depends on the size of the object and the distance. Not velocity of the object.

Distance is frame dependent. Consider light reaching you from right after the far away object has started moving rapidly towards you. Consider another observer, colocated with you, moving with the same direction and speed as the far away object, after it changed speed. That observer sees the 'standard' angular diameter of the object. By aberration (derivable directly from Lorentz transform), you must see a smaller angular diameter for the object than that colocated, comoving observer.

 

[PeterDonis]

Relativistic beaming effect is frame independent. But the change of the size of the image

Must also be frame independent, since it's part of relativistic beaming.

 

[lemelinm]

I've been working on a Minkowsky spacetime diagram generator. The software is probably way overkill, but I'm retired and it keeps my brain active. I am no physicist, but I am a pretty good programmer.

Side note: if you have any interesting things to diagram on a 2D Minkowsky spacetime diagram, let me know. I need good test cases.

The software is complete enough that I can draw diagrams, but I'm still hunting for bugs. The software has the ability to define a problem with respect to one inertial frame and draw it with respect to another. It also allows for animations, and I can set up animations where every frame is drawn relative to a different inertial frame. This makes it possible to view things from the point of view of an accelerated observer in a variety of ways.

Here is a simple setup I tried. An observer accelerating at 1g travels 4 light years. At (0,0), the accelerating observer's velocity is 0. We'll call her Alice. There are two other observers, one at (0,0) (Bob)and one at (4,0) (Ted), both at rest with respect to each other and to Alice (at time 0). Here is a diagram that includes just Alice's worldline.

View attachment 294211​

The solid colors represent where Alice sees Bob (black) and Ted (blue). The solid numbers represent the times she would see if Bob and Ted displayed huge clocks and Alice had a powerful telescope. The faded colors represent the calculated position (per Alice) of Bob and Ted, and the faded numbers are their calculated clock times. For example, Alice starts out seeing Ted 4 light years away and displaying a clock time of -4.

Here is an animation of the scenario, from Alice's point of view, from time 0 until she reaches Ted.

View attachment 294212​

Since we are viewing this from Alice's point of view, her position doesn't change. I believe this animation is correct, but it surprised me. As Alice accelerates toward Ted, Alice sees Ted receding into the distance—at least, until his clock reaches 0.

Let me know if this animation looks wrong and in what way.

Could you tell me what software yoiu are talking about?

 

[jartsa]

Distance is frame dependent. Consider light reaching you from right after the far away object has started moving rapidly towards you. Consider another observer, colocated with you, moving with the same direction and speed as the far away object, after it changed speed. That observer sees the 'standard' angular diameter of the object. By aberration (derivable directly from Lorentz transform), you must see a smaller angular diameter for the object than that colocated, comoving observer.

If the other observer is standing still next to me and starts co-moving with the faraway object when she sees that the far away object has started moving, then the observer-object system is put into motion in a non-Born-rigid way, so the observer sees a change in that system.

I guess your idea was that there will be no change, because effects of object starting to move and observer starting to move cancel out. But there is a change.

I had to change the scenario, because the original is just too confusing for me. I hope the basic idea did not change too much.

 

[PeterDonis]

I had to change the scenario, because the original is just too confusing for me.

It's not your scenario and it's not your thread, so if you cannot respond to the scenario as the OP of the thread formulated it, you should not try to change the scenario; you should just not post in the thread since you have nothing of interest to contribute.