Relativistic effects when passing through a sphere

[md65536]

I'm trying to reason about the effects of aberration when passing through the center of a spherical shell. Suppose we do this at near c and describe what we see when we pass through the center point of the sphere. Suppose we enter at the south pole heading for the north.

 

- The sphere will appear perfectly spherical. Every great circle inscribed on its surface will appear as a perfect circle (though not all appear the same size).

 

- The south pole will appear much closer than the north. The equator will appear "squished forward", so that the southern hemisphere looks much bigger than the northern.

 

- We experience no aberration of gravity, so if we suppose that the sphere is massless but there is a massive gravitational body at a single point on the equator, then as we pass the center we feel a gravitational pull directly to our side even though we see the mass ahead of us???

 

Is this correct?

[Spyman]

I don't understand the need of a massless sperical shell? A spaceship without windows is passing through a stars gravity field at high speed and the pilot needs to keep a straight course, he pinpoints the star with his telescope but should he correct for the apparent angle or the true angle?

 

AFAIK the apparent angle is only an illusion due to the finite speed of light and the speed of the observer.

(There is no gravitational pulls from illusions but the true location of the body radiates a real force.)

 

Light from location 1 will appear to be coming from location 2 for a moving telescope due to the finite speed of light, a phenomenon known as the aberration of light. As light propagates down the telescope, the telescope moves requiring a tilt to the telescope that depends on the speed of light. The apparent angle of the star φ differs from its true angle θ

http://en.wikipedia.org/wiki/Aberration_of_light

 

I interpret aberration as that the observed photons are coming from point 1 and going straight down to the observer at the true angle, (simultaneously with gravity), while the telescope moves to the right with matching speed and angle such that the photons can get inside but don't hit its walls.

[md65536]

I don't understand the need of a massless sperical shell?

 

I was thinking about the apparent mass distribution of a spherical shell, and whether or not the interior of a massive shell would have a net 0 gravitational force as with Newtonian gravity, but I switched to a point mass as a simpler case to figure out first. If there's no apparent distortion of a gravitational field, then the interior should have no net gravitational force --- or would relativistic mass affect this?

 

Edit: Thinking too much about aberration I forgot about length contraction. Would a sphere behave gravitationally like it was flattened (and closer) in the direction of relative velocity, regardless of how it appears?

 

Mainly I'm considering how aberration preserves the apparent shape of a circle, and considering that this is true for any orientation of a circle relative to a ship's position and velocity. Is it???? Or am I wrong, and it's only the 2-dimensional outline of a sphere that appears circular?

 

A sphere should be distorted in a similar way to this: Imagine you have a rigid glass sphere, and over it is a slippery, stretched rubber skin. You can pull on the skin, stretching it more and pulling it to one side of the sphere (the far side, effectively) but the skin remains spherical. This is what aberration would look like.

 

Also, aberration can cause the size of the sphere to look different, but not the shape. As you move directly away from a sphere, it will appear smaller? Ahead of you it should appear bigger -- stretched in a forward direction???

 

And inside a sphere, I have no idea. Perhaps the forward-facing and backward-facing aberration scaling effect would be reciprocal, so the sphere appears to be the correct size?

 

 

I need to find a relativistic 3d modelling program, or make one...

Edited November 9, 2012 by md65536

[Spyman]

I think objects on the inside would be weightless as with Newtonian gravity but relative an outside view, time would appear to tick more slowly on the inside and light passing out through the walls of the sphere would be redshifted due to coming from a deeper gravitational potential.

 

Length contraction is something real for the observer and not an illusion like aberration, if the pilot in the ship measures a shorter distance then gravity should behave as emitted from this measured distance.

 

Is it not the other way around? When you move towards an object you have to angle the left and right telescope closer together to see the boundaries of the object in view, making it look smaller. Looking behind you you would have to angle the telescopes in a more forward direction to see the boundaries of the object which should make it look bigger.

 

Aberration does not tell you how far away the walls are, so it can't be used to measure a size. You can see that you are inside a sphere where the skin is compressed in forward view and stretched looking out at the rear, like the rubber skin on that glass sphere you described.

 

If there would be syncronized beacons on the inside sending signals so the ship can calculate the distance to the point of the wall it is looking at, then it should be possible to calculate what angle the ship will see the equator at and which diameter it would appear to have.

[md65536]

Is it not the other way around? When you move towards an object you have to angle the left and right telescope closer together to see the boundaries of the object in view, making it look smaller. Looking behind you you would have to angle the telescopes in a more forward direction to see the boundaries of the object which should make it look bigger.

Well uh, yes and no...

 

Approaching objects take up a reduced portion of your field of view but they also look farther away, giving them the appearance of being stretched. Receding objects cover a greater portion of your field of view but they also look like they're close up, giving the appearance of being compressed. If every circle appears circular then the approaching stretched circle will have to appear stretched in all directions. -- sorta.

 

But like you point out, that doesn't give you a meaningful measure of size. If you place rulers across the circles (at rest relative to them) then the rulers appear to stretch or shrink too, and the diameter of the circle remains fixed relative to that ruler. If you've placed two rulers across the center of an approaching circle, one parallel to your velocity and one perpendicular, then the parallel ruler will appear be perceived to be stretched while the endpoints of the perpendicular one appears to shrink, and yet the circle remains perfectly circular-looking! This is possible because the endpoints of the perpendicular ruler also appears to move forward around the edge of the circle (like the stretched skin we've been talking about) so it no longer appears to bisect the "apparent" circle. Also the perpendicular ruler happens to not appear straight, with its middle appearing to curve toward you.

 

 

I understand that there's a distinction between how things look and how they are, and I'm mixing it up a little, but I'm still interested in understanding how things look.

 

Anyway, the illusion of approaching objects appearing to stretch away from you really is apparent. Things really do appear to move away. However if you realize that they are also appearing smaller in your field of view then you no longer accept that they are farther away, and then the illusion becomes clearer.

 

Here's a video of the effect, from MIT's recently released relativistic game:

 

Around this point in the video, the player is usually moving forward (and you can see it is so around the edges of the screen), yet the higher the velocity, the farther the center of the view appears to move away. However, if you measured the size of anything in pixels, nothing that "appears stretched" away from you should ever actually take up an increased length in pixels.

 

Also interesting in the video, the spheres that you collect never appear to be distorted by relativistic effects. (Not that this is a perfect measure, especially considering that just by projecting a game-world view angle onto a screen with a different view angle -- depending on how big your screen is and how close you are but typically games have an exaggerated view angle -- the spheres will be distorted by this projection, as they would be also in non-relativistic games, more so toward the edges of the screen).

 

 

So I suppose you are right, by most measures even the appearance of approaching circles would seem smaller. Except for the illusion by which their smaller appearance makes them seem farther away, and that the brain perceives distant objects as bigger, ... well I guess you might say that approaching objects appear smaller yet are perceived to be bigger.

 

 

This brings up more questions but I think we've figured out the main thing I was interested in, thanks.