- #36
Doc Al
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Only with respect to itself! Its velocity with respect to something else can certainly be non-zero.vilas said:No! For the ship v=x=0, because any uniform velocity is zero velocity for the ship.
Physically equivalent, but not 'the same'. Velocity matters, especially if you want to get somewhere.Therefore all frames are equivalent for the ship.
Again, your 'velocity meter' only shows what you've programmed it to show. What you actually measure directly is acceleration and time; you've got to calculate your speed with respect to some frame of interest. If you want the correct relative velocity, you'd better use SR formulas.Treating this as an experiment, let the ship start from frame #1 and add velocity of 0.001c (my previous assumption of 0.00099c has no meaning as in this case I have just applied correction factor and not SR factor). Suppose we assume it to be true. So velocity meter will show 0.001c.
Velocity is frame-dependent, of course.Ship is now in the frame #2. I refuse to buy an argument that the ship has velocity of 0.001c. Of course it has this velocity with respect to frame #1. But it is at rest in the frame #2.
The velocity with respect to what frame? Since frame #1 and #2 are physically equivalent, the same burst when in frame #2 will give you a velocity of 0.001c with respect to frame #2. You mistakenly think that that means you have a velocity of 0.001c + 0.001c = 0.002c with respect to frame #1. Not so!Now frame #1 and #2 are equivalent and if they are treated as such, then as an experimental fact, in the frame #3 velocity must be 0.002c.
Assuming you've correctly programmed it--using SR formulas--to show the velocity with respect to frame #1, it will not show 0.002c.If velocity meter doesn’t show velocity as 0.002c, then experiment conducted in frame #2 is not same as that conducted in frame #1.
Of course we are, since we want results that agree with experiment. Note that you had to use SR formulas to get each burst of 0.001c. If you didn't, then those speeds are not reflecting of reality either. It's SR all the way, baby!We are now talking on subtle concepts. According to you all inertial frames are equivalent and so the ship will get 0.001c, in moving from frame 1 to frame 2. Similarly the ship will gain 0.001c, in moving from frame 2 to frame 3. However, according to you, velocity in the frame 3 will be different than that as measured from frame 1. With this you are presupposing correctness of SR velocity addition equation.
Only if you program it wrong!But as I said earlier, for the ship, frame 1 doesn’t exist. Every time it gets a boost, it is in its own rest frame, as if nothing as happened before. No way to calculate its own uniform velocity. Therefore an astronaut in the ship has to rely on the velocity meter. Since every frame is as good as the starting frame, velocity meter must add 0.001c with every boost.
You still seem to think that your accelerometer somehow measures speed directly without the need to program it. But it looks like you've programmed your 'velocity meter' with incorrect Newtonian formulas. Good luck in planning your travels, as your calculated relative velocity with respect to various frames is incorrect.With respect to frame 1, if SR is considered, then the velocity meter reading is false. But there is no reason why it should be false.
Of course if you measured your relative velocity directly, then you'd always get the correct SR results. (Look out the window!)