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Halc

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- TL;DR Summary
- Exploration of how something moving faster than light speed would appear.

This topic assumes special relativity only, so no gravity is involved. I wanted to know how a superluminal thing would appear to an observer, and two of the 'things' I thought of were a moiré pattern and the red dot projected by a laser pointer. The former can be discussed, but this post will focus on the dot.

Suppose we have a spherical projection screen of radius 3 million km. Our laser pointer is at the center, and it projects a dot somewhere on the screen, which gets there 10 seconds after being emitted. Furthermore, if you look close at the dot, it is encoded with a 32 bit integer that takes a minute to loop. The dot can be made to move at arbitrarily high speeds around the screen. There is a cat that cat move very fast, up to 0.9c. The cat is the observer, and is named Felinestein.

First thing to note is that relative to the inertial frame of the sphere, the dot is in exactly one location at any time and the 'clock' it projects runs at normal rate. Relative to different inertial frames, this is not the case, and the dot might appear in multiple places at once, and some of them might count faster or slower or even backwards.

First scenario is a stationary cat. Felinestein is nearsighted up to only 100 km and cannot see the dot move all the way across the sky, so observation is local and very close to being flat. Let's say we put the laser at the end of a second hand and have it go around once a minute so the dot moves at just over c. Felinestein, who is right at the screen where the dot passes, will not see the dot coming just like you don't hear a supersonic jet coming. But he notices it immediately upon it passing, when it coincidentally projects time t0. Which way does it go? Turns out Felinestein sees two dots, both receding. Looking 'upstream', the dot appears to move away very quickly (over 21 c), is blue shifted, and counts backwards to ~228000 very quickly. Looking in the other direction the dot moves away at just over 0.5c, is red shifted, and counts upward to about 228000 at about half speed.

If the laser rotation rate is increased to say 10 seconds, the dot will be moving at 6.3c and the stationary cat will see the upstream dot move away slower. The downstream dot will appear to move away at around .85c and both will count slower to +/- ~38000.

The redshift I am basing on the fact that the numbers observed count faster or slower than the normal rate (of a stationary dot). In the upstream case, the dot appear to be receding, but also counting backwards, so the double negative results in a blue shift, not a red shift. That's the first unintuitive thing, that an approaching superluminal object would still be blueshifted despite appearing to recede from the observer.

I don't thing there will by any equivalent of a sonic boom. Felinestein is right at the screen and there's no particular bright flash as the dot moves by, but I suspect that if he's off to the side by say a km, there would be one, and the points at which the dot first appears and subsequently splits are not directly opposite him.

What about the moiré pattern? Is there any redshift at all to such a phenomenon? I'd think not since it is effectively a pattern of holes in a screen with a stationary (everywhere uniform) light source behind. There's no moving light to shift.

I'll have Felinestein start to chase the dot in a subsequent post. This seems to have been enough for an intro so far.

Suppose we have a spherical projection screen of radius 3 million km. Our laser pointer is at the center, and it projects a dot somewhere on the screen, which gets there 10 seconds after being emitted. Furthermore, if you look close at the dot, it is encoded with a 32 bit integer that takes a minute to loop. The dot can be made to move at arbitrarily high speeds around the screen. There is a cat that cat move very fast, up to 0.9c. The cat is the observer, and is named Felinestein.

First thing to note is that relative to the inertial frame of the sphere, the dot is in exactly one location at any time and the 'clock' it projects runs at normal rate. Relative to different inertial frames, this is not the case, and the dot might appear in multiple places at once, and some of them might count faster or slower or even backwards.

First scenario is a stationary cat. Felinestein is nearsighted up to only 100 km and cannot see the dot move all the way across the sky, so observation is local and very close to being flat. Let's say we put the laser at the end of a second hand and have it go around once a minute so the dot moves at just over c. Felinestein, who is right at the screen where the dot passes, will not see the dot coming just like you don't hear a supersonic jet coming. But he notices it immediately upon it passing, when it coincidentally projects time t0. Which way does it go? Turns out Felinestein sees two dots, both receding. Looking 'upstream', the dot appears to move away very quickly (over 21 c), is blue shifted, and counts backwards to ~228000 very quickly. Looking in the other direction the dot moves away at just over 0.5c, is red shifted, and counts upward to about 228000 at about half speed.

If the laser rotation rate is increased to say 10 seconds, the dot will be moving at 6.3c and the stationary cat will see the upstream dot move away slower. The downstream dot will appear to move away at around .85c and both will count slower to +/- ~38000.

The redshift I am basing on the fact that the numbers observed count faster or slower than the normal rate (of a stationary dot). In the upstream case, the dot appear to be receding, but also counting backwards, so the double negative results in a blue shift, not a red shift. That's the first unintuitive thing, that an approaching superluminal object would still be blueshifted despite appearing to recede from the observer.

I don't thing there will by any equivalent of a sonic boom. Felinestein is right at the screen and there's no particular bright flash as the dot moves by, but I suspect that if he's off to the side by say a km, there would be one, and the points at which the dot first appears and subsequently splits are not directly opposite him.

What about the moiré pattern? Is there any redshift at all to such a phenomenon? I'd think not since it is effectively a pattern of holes in a screen with a stationary (everywhere uniform) light source behind. There's no moving light to shift.

I'll have Felinestein start to chase the dot in a subsequent post. This seems to have been enough for an intro so far.

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