what's wrong with these pictures?

nitsuj

It took me a while to finally see where the following scenario is wrong.

I found it a "fun one" to consider.


Scenario
Observer A moving at 0.5c compared to observer B.

Observer A sends out an idealized light pulse in a perfect circle. Perhaps by using a single light source & through diffraction of sorts is redirected in a perfect circle, expanding outwards at c.

Image one is from the PoV of observer B who I'll say is at rest.

Image two is from the PoV of A who is moving at 0.5c compared to B.




two




Ignore the difference in diameter (timing of the image).

I had always been confused how observer A could determine that B measures them self at the centre of the circle. Given observer A sees them near the "top" of the circle, I was able to explain the "contracted" length that is "seen" near to top of the circle, but had no clue what explains the "elongation" at the bottom.

After sometime, I finally realize that my scenario is a fallacy. ( at least I think it is)

yuiop

I am not sure why you are referring to elongation. Each observer would see themselves as being at the centre of an expanding perfect circle of light. One way to demonstrate this is with the following thought experiment. Imagine A has a circle of mirrors attached to him with a radius of 1 light second and B is attached to a similar circle of mirrors. When they pass close by each other at a relative velocity of 0.5c a static electricity spark between them causes a flash of light to be emitted. Exactly 2 seconds later (by A's clock), A will see the reflected flash return simultaneously from all A's mirrors and B will also see a flash reflected back from all B's mirrors simultaneously, (exactly 2 seconds later as measured by B's clock). The situation is perfectly symmetrical.

nitsuj

The ruler is contracted in the direction of motion. Please explain how observer A measures themselves in the centre.

robphy

It might help to draw a spacetime diagram of the lightcone of flash event,
and each inertial observer's worldline (through that event)
and that observer's [hyper]plane of simultaneity.

On each observer's plane of simultaneity,
the lightcone events on that plane are equidistant from that observer's worldline event on that plane.

nitsuj

Are you saying there is nothing wrong with the above scenario & pictures?

How is it both observer A & B would measure the idealized light pulse as a perfect circle?

robphy

Can you see your pictures in my avatar?

nitsuj

yea, It's a good one!


In the "rest frame" image below I can "see" length contraction (A). That is I know, since c is constant Observer A would measure themselves in the centre of the light pulse circle, I can understand that due to a contracted ruler observer A measures a longer distance to the light pulse in front then the "contracted" space seen from the "rest" FoR image.

How can observer B account for observer A's measure of length to the "rear" of the circle (B) that would place them in the centre? (this is practically giving up the fallacy of the scenario)

These images are like spacetime diagrams. These images have spatial axis, numerous time axis (depending on how you "cut it") and an event. The image below is the boosted/primed one. Actually the more I think of it this is very similar to a light cone, this image is from the top looking down on the event (which is an observer in this case, the event was the pulse of light which happens to originate with the observer). Simply treat the Circle of the light pulse as the null line (which it is).

nitsuj

Kinda misunderstood the scenario, A is in motion and only A generates the pulse.

The first image is how observer B sees the scenario (this is why I can say observer B is at rest)

The second image is how Observer A measures the scenario.

How can you account for the measure of the "bottom" length as performed by observer A; who measures them self in the centre of the circle.

Just to be crystal clear the letters A & B in the above image are just for identifying two measurements; not the two observers.

ghwellsjr

None of your images are crystal clear. I have no idea what you are trying to portray. Why do you think anyone looking at your drawings and with the help of you explanations would have any idea what you are trying to convey?

For example, in your first and last images, there is a faint line going up from the bottom of the picture into the circle but not in your second image. What does it represent and why is it not in the second image?

Next to the top of this faint line, there is something that looks like text in a font so tiny that it is unreadable. What is that? And why in the second image does similar feature appear a little below and to the right of the center of the circle?

In your last image you explain that A and B are not the observers called A and B. Can you understand why this could be confusing? In any case, it's still confusing because in your first post, you said the first image, which looks like something is moving, is for B, who is at rest and the second image, which looks stationary, is for A, who is moving. Then in your last image, it looks like you have added detail to the first image, but again, this is for B, who is not moving.

You said in your first post that this issue is a "fun one". I can help you maximize your fun by directing you step by step how to arrive at the correct images and conclusions but it will take a lot of work on your part and it will take a lot of time, but it will be a lot of fun and you will learn a lot. Or I could just show you the bottom line (image) and it will be all over in one post. Which do you prefer?

nitsuj

I preffer you just tell me why you think the above scenario is not correct. I already know why it is not correct.

The main thing to consider with this scenario is that both observer A & B see the image as a perfect circle.


"Why do you think anyone looking at your drawings and with the help of you explanations would have any idea what you are trying to convey?"

You an ***. How about because it is clear what the scenario is. What about it confuses you? the irrelevant line in one image but not the other, the fact the two different measures & two different observers are both identified with A / B. yea that's super complicated.

The scenario is describe with two sentences. And what each observer measures is in two images. Info overload!!

ghwellsjr

Your first image looks to me like it is for observer A who is traveling, not observer B. That's one thing wrong.

Your second image looks to me like it is for observer B who is at rest. That's two things wrong.

You indicated that each observer is determining that the other observer is at the center of the circle of light. That's wrong. Each observer determines that he himself is at the center of the circle of light, he has no opinion about the other observer.

You indicated that one of the observers concludes that he is near the top of the circle and far from the bottom of the circle but you have not explained how he makes that determination. It's wrong for you to make such statements without telling us how the observer is supposed to figure this out.

Justin, I'm trying to help you. Please cooperate with me.

Michael C

It makes no difference who generates the pulse. The pulse could be generated by A, by B, or by somebody else moving relative to both of them.

It's also misleading to say that A is in motion and B is at rest: A is in motion relative to B and B is in motion relative to A.

The situation is, as others have remarked symmetric: each observer sees himself as the centre of the circle (or sphere, is we are in a world with 3 spatial dimensions) and each observer sees the other observer moving away from the centre.

In order to understand why this is so, you need to think about relativity of simultaneity. Imagine that observer B is standing at the midpoint between two trees, one "below" and one "above" him in your diagram. He sees the light hit both trees at the same time. Observer A, moving relative to B and the trees, does not see the light hitting the two trees at the same time.

nitsuj

k, so only Observer A makes a light pulse. Both images are of Observer A.

Image one is what Observer B sees when looking at A. This is because A is moving, B sees A in the position shown in the first image. I hear ya ghwellsjr about the pictures not being very clear. In the first image, observer B is seen near the top of the circle, at the end of the blue line that indicates the motion of A.


Image two, is how Observer A would see them self.


In the second image A observes them self in the centre of the circle.



For you to spot the "fallacy" in the scenario, you have to understand which frame each image is observed from. Is it clear now?

nitsuj

Actually it does matter, what a lame response. How about you understand from the description of the scenario that only A makes the pulse, relative to the event of generating the pulse A is in motion. B relative the event of generating the pulse is stationary.

So tell me why it doesn't matter who is moving? That doesn't even makes sense in this scenario. Your analysis of this scenario is way off.

nitsuj

In order to see the fallacy in the scenario you need to think about relativity of simultaneity.

Michael C

How can you define "in motion" or "stationary" relative to an event?

robphy

That is correct for special relativity.
The speed of light is independent of the source.

In other words, the light cone of the flash event is a property of the event... not of any worldline meeting that event.

It's best to simply say that there is a flash event when the two objects meet.