Re imagining the trampoline analogy

[geordief]

Suppose we have a trampoline  moving through the vacuum of space 

At any snapshot in time (so not 4d) the trampoline will look to us in it's normal flat shape

 

Now  let us say that a region of the trampoline is subject to an acceleration (for simplicity perpendicular  to the surface) so that that region  is stretched into the shape all trampoline analogists  are familiar  with  except  that there is no heavy metal object  producing the "well"  but rather the shape is produced "internally " by the local acceleration.**

 

So an observer at a remove from the "flying trampoline" will see a flat surface with a protrusion  a bit reminiscent of Sigourney  Weaver's belly in Alien.

If we now  put ourselves in the frame of reference  of the flat part of the surface  and look around at  what we can see from that  frame  then we will see whatever we will see.

But if we similarly look around from the region of the protuberance  (if the acceleration has  been significant) then the same scenes will  be visually distorted  and light coming from the same place as was seen by the people on the flat ,unaccelerated  region of the trampoline  will be coming  from a different  direction  and either sped up or slowed down.(am a little unclear here)

Does the trampoline viewed this way provide a good model, not of gravity but of the effect of how light is curved  when a frame of reference is accelerated  wrt  a source of light?

Does the trampoline analogy work better for acceleration than gravity?

 

,**it is just a small,local region of the trampoline that is accelerated and not all of the trampoline.

[Markus Hanke]

On 3/19/2023 at 2:38 AM, geordief said:

Does the trampoline viewed this way provide a good model, not of gravity but of the effect of how light is curved  when a frame of reference is accelerated  wrt  a source of light?

I wasn’t able to find a visualisation of what you’d see if you were to look out the front window of a relativistic rocket, but I found a visualisation of how your visual field gets distorted at a constant v=0.9c:

The accelerated version would be similar, just…well…accelerated. The angular size of your visual field would shrink more and more as you keep accelerating (“tunnel vision”). You would also notice something strange happening behind the rocket - things would at first seem to recede fast, but then they’d appear to slow down and eventually “freeze” into place at some apparent distance, while all the way being redshifted away into invisibility. It’s as if a horizon forms behind your rocket - this is called a Rindler horizon.

Looking at the above animation, I don’t know if you would consider the trampoline to be a good analogy for this. Mathematically the coordinates used to model accelerating frames are those that describe hyperbolas, so I guess there is some justification for it.