Could someone use the Crab Nebula as an example with whatever this half shell spiral thing is about?
Exactly. It forms an Archimedean spiral:
As it rotates, intersections between the spiral and some axis move away from the center at a fixed rate (c). But the angle between the curve and the axes gets closer to 90 degrees as you get farther away, because it’s moving faster.
Well, the Crab nebula pulsar doesn’t need a rotating half shell; it has an off-centre rotating beam, which draws two very quick spirals in the nebula (one at each pole). In X-Rays this looks like a cone, but close-up it would look like a conical spring.
That’s it; so it is a regular spiral, but it does get steeper as the spiral moves outward. Note that the spiral would only have moved halfway round a complete circuit by the time it gets to Pluto, as Pluto is five and a half light-hours away.
And another way of looking at it is that the portion of the shadow which reaches Pluto would have moved in a straight line directly from the Sun, despite the spiral movements of the rest of the shadow.
Interesting. So my sister on the orbiting platform over Venus would see the shadow of the shell moving past east to west, but since it is moving about 2c at Pluto, I would see it pass from west to east, and if I look through my powerful telescope at the sun, the shell would appear to be rotating in the opposite direction compared to what my sister reports. The whole galaxy must be moving increasingly backwards with respect to what we think it is doing.
Ok, turns out there is an Oyster Nebula. Let’s try it with that one.
So if we imagine this spiral propagating outward from a rotating source (which will look the same as the spiral simply rotating - I’m tempted to animate it but I think it would be hard on the eyes).
If you draw a circle concentric with the spiral, as the spiral propagates out, it will intersect the circle in one place only and that intersection will traverse the entire circumference of the circle once for each period of the spiral’s rotation/emission.
If you enlarge the circle, the intersection will still only happen in one place, and will still traverse the circle once per period, but since a larger circle must have a larger circumference, the speed that the intersection point sweeps the circle MUST be faster than for a smaller circle.
The spiral, if composed of radiation emitted from a pulsar, is only propagating radially at the speed of light, but the movement of the intersection MUST increase as the radius of the circle increases (which ‘movement’ as previously laboured, is not actual movement of a thing - it is a series of positions being illuminated in sequence by different photons every moment)
Or it could pass at the same rate over a longer period of time. The shadow terminator at Pluto would appear to be much larger than it does at Venus, in much the same way as a pinpoint laser beam appears to be a ten-mile-wide spot when you shine it on the moon. And it seems to correlate with the Lorentz Contraction described in Special Relativity.
If it has to pass around the circumference of a circle once per period, that has to happen faster on a larger circle - if you’re saying that it widens in order to avoid exceeding c, then as the circle widens, there would have to be a point where the intersection point encompasses the entire circumference at once, then more than once, and so on.
Which would make it impossible to detect pulsars at any sort of long distance, because the signal would just be continuous.
Except, as your spiral gets larger, your enclosing circle also gets larger. Pulsar signals are extremely ridiculously powerful, which is why we can detect them: if they were as strong as our most powerful radar beams, they would be diffused to imperceptibility over just a few parsecs, but they are thousands or millions of times more intense than all our radar emitters on Earth put together.
If there is a detectable ‘pulse’ created by a propagating spiral intersecting a theoretical circle where we are sitting on the circumference, then other people sitting on other positions on the circumference of the same circle must experience the pulse before or after us, as it traverses the circle. Do you agree?
If it did, it would distort the Archimedean spiral into something else. But it has to be an Archimedean spiral, because that’s what you get when you have particles radiating away from a central point at a fixed speed, with a phase equal to the angle.
The spiral doesn’t even have to be made of light. It could be made from non-relativistic particles, like bullets shot from a central gun. You can’t assume relativity has any effect here.
From several previous posts:
"propagation of a shadow"
"the shadow travels"
(similar phrases)
What the heck does that even mean? There’s nothing there!
Nope; you’d still see the shell rotating from west to east. But you’d see light echoes coming from distant moons and planets. We should always be aware of light travel time when observing distant objects - even Mars has moved about two and a half times its own diameter since the light we see was reflected from its surface.
When you turn on light source, light propagates away from the light source at the speed of light.
When you turn it off, the absence of light also has to propagate out. It’s not a thing in its own right - it’s a gap - a hole, but it follows the trailing edge of the last bit of light, at the speed of that light.
Right, exactly. If it were limited to the speed of light, it wouldn’t be.
Well, “detectable” is the keyword there. The effective wavelength of the “pulse” would be much greater. Almost as if it had been, idk, red-shifted. I seem to recall hearing that term before sowewhere, “red-shift”. Let me see if I can remember where …
Here’s a way to visualise it: shadows, even though they are not made of anything, can form rays, as depicted below:
If the cloud casting that shadow were to magically and instantly vanish, the shadow ray that it is casting does not disappear all at once - it disappears as the light fills it from the direction of the source, at the speed of light.
Please would you answer the question?
For a pulsar such as we have been discussing, hundreds of light years distant, and with a period of multiple rotations per second, and which IS detectable as a sharp periodic spike of signal*. Will a person who is on a different position on the same circumference as us, experience the pulse at a different time from us?
*This part isn’t in any way hypothetical. Numerous examples of such pulsars have been measured.