what's wrong with these pictures?

nitsuj

I'm gunna point out the "fallacy" with the scenario as presented.

yes micheal c is right regarding relative motion, but it does matter as far as the shape of the light pulse. This is because of RoS.

Because A is in motion & is the one who emits the light pulse to make a circular light pulse image, it would not be seen as circular to any other observer in relative motion with A.

The fallacy of the scenario is in both FoR the image is presented as a circle, which is incorrect due to RoS. Interestingly, there is no spatial seperation or two seperate events in this demonstration of RoS.

To the point thats been made here already, c is invariant.

ghwellsjr

Well, I can see it is not going to be productive to try to lead you in the right direction. I'm just going to show you the bottom line:

\

The red guy is your observer A and the green guy is your observer B. When A meets B, a flash of light is emitted (as MichaelC said, it doesn't matter who emits it). Each of the observers carries with them their own set of mirrors that they have measured to be in a perfect circle but because of length contraction along the direction of motion, A's mirrors form an ellipse. Neither one of them can see the circle of light as it is expanding, they will only be able to tell its presummed position away from them when they see the reflections from all their own mirrors collapsing on them simultaneously. Note how they each see a different set of reflections (but only at the moment of collapse) and B's form a circle centered on the original location of the flash while A's form a displaced circle that coincides with the future location of A when he arrives at the location of the collapse at the moment of the collapse.

All of this is from the Frame of Reference in which B is stationary. Remember, Frames of Reference do not provide the observers in them with any more knowledge or insight into what is happening with the propagation of light or the motion of other observers, rather, they provide us with instantaneous knowledge of where the light and both observers are throughout the scenario because we define the propagation of light and the motion of the observers to be as such.

You need to watch this over and over again and then pretend that you are observer A (the red guy) and see if his experience is any different than the experience of observer B (the green guy.

By the way, this is exactly the scenario that yuiop asked you to imagine in post #2.

nitsuj

That's cute Hmmm... well I can see it is not going to be productive for me to try and lead you to understand this very simple scenario, Im just gunna tell you the bottom line.


Because of RoS, the two observers would not see the shape of the light pulse the same.

The scenario misrepresented this; the light pulse being circular from perspective of each FoR, it could not be.

Yes I have seen your annimation before, even reffered others to it. It's a really cool one. Mine is two still images of nearly the same scenario.

Michael C

No, that cannot be. c is a contant, the same for all observers. For any observer, the light emanating from a single flash will be seen as a growing circle (or sphere).

nitsuj

Cool, how does A measure themselves in the centre of the circle? (c being constant is another "reason" why the issue with the scenario is misrepresentation of RoS)

ghwellsjr

The same way B does--with mirrors placed a measured distance away in a circular pattern. Both A and B are doing exactly the same thing as far as they are concerned. It only looks different to us because we are viewing both of them from a single Frame of Reference. But it won't matter which FoR we decide to use, it will still illustrate the same experience for them.

Michael C

A measures himself at the centre of the circle, but sees B moving away from this centre. B measures himself at the centre of the circle, but sees A moving away from this centre.

Look at the animation that was just posted. Read ghwellsjr's explanation.

Michael C

You still need to answer this: how can you define "in motion" or "stationary" relative to an event?

nitsuj

Very clearly, as seen in the first image, givin the details of the scenario clearly B is at "rest" relative to the event, since he sees the light pulse as circular. ( as I pointed out now, A would not see the light pulse as circular.

I'll post an image showing what A sees, if B sees the light pulse as a circle. It might make it more clear.

nitsuj

Yes & length contraction accounts for the measure from the "top" of the light pulse circle, how is the measure to the bottom of the light pulse circle accounted for in the first image?

Note intervals are invariant. The interval between observer A and the bottom of the light circle is not the same as the interval with A in the centre of the circle.

Alright, so if A immits a light pulse in a perfect circle from their PoV, then here is the shape of the light pulse circle from B's PoV.



Note because of the invariance of c, "length contraction" is visable as the shape of the light pulse, of course this not actually length contraction but merely shows that A did not fire the light pulse as one event from B's PoV, from A's PoV it was a single event.

[IMG][/IMG]

The suggested image below from B's PoV is wrong.

[IMG][/IMG]

Michael C

You're assuming that A doesn't see the light pulse as circular and using this to produce your "definition". It doesn't make sense. An event has no velocity, it doesn't define an inertial frame. You can define motion relative to a particle, but not relative to an event.

Try this: A and B both carry a light source. When A and B coincide, both A and B send a light pulse. Two light pulses are sent, at the same time and from the same place. How can A see the light from his own source expanding in a circle and the light from the other source not expanding in a circle? That would mean that A sees the light from one source moving at a different speed to that of the light from the other source.

nitsuj

What I thought was going to give it up for sure was A not being in the centre of the circle for both images. as clearly would be the case since there is no spatial seperation and it is a "single" event. the only other thing to account for RoS is simply a disagreement on when the light was emitted from the souce, which in turn effects the shape of the light pulse.

you're assuming they both actually see a circle, because of RoS and invariant c, it cannot be the case.

Michael C

The length contraction formula is for rigid objects. The light circle is not a rigid object: the "bottom of the circle" and the "top of the circle" do not happen at the same times for A and for B. If B is surrounded by a circular mirror (as in the animation), he sees the light hit the "top" and the "bottom" of the mirror at the same time (in the animation, it's the right side and the left side of the mirror). For A, these two events are not simultaneous: A sees the light hit the top of B's mirror before it hits the bottom if B's mirror. Note that A sees B's circular mirror as an oval (length contraction) but A sees the light from the flash emanating in a circle.

Once more, any observer must see the light from a flash emanating in a circle, precisely because c is invariant.

nitsuj

1. And vice versa. But A emitts the light and has determind what makes a circle, B disagrees, says its an oval that A made. This is because the light pulse that A emmits is not simultaneous from B's perspective.


Length contraction "is for" measuremnt. Distance can be measured as length, for example the "contracted" distance infront & behind A in the direction of motion. And, the non contracted length that is perpendicular to the direction of motion.


Once more no they don;t micheal. The creation of a circular light pulse is observer dependent. Don't forget that A is in motion and is the one that determines the circular light pulse. Because A's measure of length / time is different from B's it will not look like a circle to B. Both measure the speed of the light pulse as c, that is the shape never changes.

robphy

As Michael C says... "The length contraction formula is for rigid objects. "

More precisely, "length contraction" essentially refers to the apparent spatial-separation between two parallel [in spacetime] timelike-worldlines (like two ends of a meterstick).... not the spatial-separation between a timelike worldline and a lightlike line (which, if you are about to emit another light flash, is more like [but not quite] a wavelength ).

robphy

Can you clarify something for me?

Suppose observers Alice and Bob each carry a flashlight.
When Alice and Bob meet at event O, both momentarily turn on their flash lights.
On a spacetime diagram,
are the events on the light-cone of Alice's flash
the same events as those on the light-cone of Bob's flash?

nitsuj

lol, oh okay, yes it is for Rigid objects, like a ruler, that measures non rigid things like distance. A great point that clairifies....

So Rob, you're saying that if A is travelling at 0.5 c and emits a circular light pulse, that "at rest" observer B sees it as a circle as well?