Tomahoc said:
There is the assumption that the tachyon velocity is not frame dependent, meaning not fixed relative to Earth but fixed relative to the aether which can be anywhere.
In other words, you don't know what the tachyon's velocity is in any frame, because you don't know which frame is the aether frame.
Tomahoc said:
In this example, if we send aborting signal after 30 seconds. It should arrive at the missile 30 seconds?
Since you don't know the tachyon's velocity in any frame, you can't predict when it will reach the missile. However, you can still draw some conclusions just by working the problem in the Earth frame. See below.
Tomahoc said:
Also ignore the distance is tau ceti. Imagine it is so far off that light speed is not enough to reach it because it is far. I thought tau ceti is hundreds of light years away and I'm assuming 0.99999999999c (or put any 9 where it is far enough)
In other words, you want a scenario where the President's order goes out too late for a light pulse to reach the missile before it hits Tau Ceti, correct? I'll assume that's your intent in what follows.
In my last post, I said we can figure out everything in the Earth frame; I was hoping you would pick up on that, but I'll go ahead and do it now. All quantities are relative to the Earth frame in what follows. We have a distance D to Tau Ceti, a speed v < 1 for the missile (I'm using units in which c = 1), and a time t after the missile launch when the President's order goes out. We want t to be large enough that the radio pulse emitted then from Earth can't reach the missile before it hits Tau Ceti.
We assume that the missile is launched at time t_0 = 0. The time the missile reaches Tau Ceti is:
t_m = \frac{D}{v}
The time the radio pulse reaches Tau Ceti is (the pulse is sent at time t and travels at speed 1):
t_r = t + D
We want t_r > t_m, which gives
t + D > \frac{D}{v}
or, rearranging terms,
t > D \frac{1 - v}{v}
Now suppose we have a tachyon pulse that travels at speed w > 1 in the Earth frame (we don't know w's exact value, but we can still work with it as an unknown variable). We can run the same type of analysis as above to find the time t_y that a tachyon pulse emitted at t will reach Tau Ceti:
t_y = t + \frac{D}{w}
If we want the tachyon pulse to catch the missile before it reaches Tau Ceti, we must have t_y < t_m, which gives
t + \frac{D}{w} < \frac{D}{v}
or, rearranging terms,
t < D \frac{w - v}{w v}
So if the time t lies between the two limits given above, i.e., if we have:
D \frac{1 - v}{v} < t < D \frac{w - v}{w v}
then the tachyon pulse will be able to catch the missile before it hits Tau Ceti, but a radio pulse will not.
I'll stop here to let you digest the above; it should give you an idea of how to calculate when each pulse will reach the missile, as well as when it will reach Tau Ceti.
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