moving light bulb sphere of photons

Dreads

If you have a moving light bulb and an observer at rest wrt the light bulb. The observer is tiny and he is inside the light bulb. The light bulb is travelling along the x axis. The light is then turned on what will the observer see..a sphere of photons travelling outwards from the observer?

Keep in mind if you are in a space ship travelling in the direction of the x axis and there is a a laser trained on a spot along the Y axis . Regardless of the velocity of the frame of reference the laser will always remain trained on the spot.

so if the frame goes faster the photons from the laser will "bend" more so they remain on the spot

Therefore photons travelling perpendicular to the direction of travell MUST bend more than non perpendicular photons. The amount a photons bends is propriotional to the angle the photons makes wrt the x axis. Photons travelling along the x axis will not bend at all.

Therefore the photons cannot form a sphere around the observer as they are not all bending by the same amount. The shape formed wiil be a skewed sphere or a shapes that is NOT an sphere... is there something I am missing here?

CompuChip

Yes, you are missing that photons propagate at the same velocity to all observers (assuming that the inside of the light bulb is a vacuum, i.e. there is no argon, neon or nitrogen inside).

ZikZak

If you are on the light bulb, you see an expanding sphere of photons.
On the other hand, if you are any other observer, you see an expanding sphere of photons.

You are missing that the speed of light is c in all reference frames.

In a frame in which the light bulb is moving, you will also observe doppler shifting and relativistic beaming, but the wavefront is always a sphere.

lightarrow

It's not only frequence to be different because of the moving frame, but amplitude too, so I can't understand how the wavefront can stay spherical.

ZikZak

The wavefront remains spherical because the speed of light is c. Frequency and amplitude aren't speed.

lightarrow

Yes, it's correct, sorry.

DaleSpam

The equation of the sphere of light in the stationary frame is:
c²t² = x² + y² + z²

Transforming to the moving frame is:
(ct'γ-vx'γ/c)² = γ²(x'-vt')² + y'² + z'²

Which simplifies to:
c²t'² = x'² + y'² + z'²

robphy

My animations at
physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#circularlightclocks
might help you visualize the situation.

The intersection of
the light rays emitted by an event on an inertial observer's worldline
and the worldtube traced out by a circular array of mirrors around that observer
is, according to that observer,
a set of simultaneous events that are equidistant in space from the observer
(i.e. a circular wavefront).

The analogous situation is constructed for
an inertial observer moving with respect to this first observer.

phyti

Could he see a sphere of photons travelling outwards?

CompuChip

... which is rather obvious, because the transformation
ct = ct'γ-vx'γ/c
x = γ(x'-vt')
is derived precisely from the requirement that the speed of light be constant to any observer (i.e. from c²t² = x² + y² + z² holding in any Lorentz-equivalent frame).

lightarrow

Thanks, DaleSpam, robphy, CompuChip.

Dreads

Assume we have the stroy above with the globe moving along the x axis yadda yadda yadda

so you have the observer at the centre of photons moving out in all directions. Imagine the photons as lines of equal length raditiang from a central point. Imagine for now just in 2D. A perfect analogy is a wagon wheel with lots of spokes. But some of the spokes are straight( the photons moving along the x axis) and some of the spokes are bent with the amount of bending being propotional to the angle the spoke makes with the x axis. Spokes at 90 degrees to the x axis bend the most.

With some of the spokes straight and others bent, and they are all the same lenght they will NOT form a circle. Rotate this malformed wagon wheel thru 360 degrees around the x axs and it is not a sphere

Dreads

the lines will be equal length as all photons are moving at C. The wagon wheel analogy is what the photons will look like at a snap shot in time say T0

Dreads

When I say that the spokes are bent I mean they will not be radiating out from the central point, perpendicular to a tangent of that central point.

if you draw a circle around the central point with the central point as the centre of the circle, the radiating lines will not be perpendicular to the tangent of that circle.

Only the photons moving along the x axis will be perpendiular to a tangent to the aformetioned circle.

Dreads

the only way the spokes of a wagon wheel, bike wheel etc, with equal length spokes, can form a circle is if all the spokes are perpendicular to the tangent to a second circle, where the tangent is taken at the point where the spoke intersects the second circle. With the centre of the second circle being the centre of the spokes.

Move any spoke the tiniest amount away from perpendicular and the spokes will no longer form a perfect circle

JesseM

If all the spokes radiate out from a single center point, they will automatically be tangent to a circle with that point at its center, no? There's no way you could have a bunch of equal-length spokes that all radiate from a single point that don't all end in points on a circle. After all, every radius of a circle is just a straight line segment going from the center to a point on the circle, it's impossible to draw a straight line going from the center that doesn't lie along one of the radial lines.

DaleSpam

Yes it is a sphere; I derived it above.

Since your conclusion is demonstrably wrong, why don't you go back and see if you can spot the mistake.