5 ms·
Yes, yes, you have shown you know what relativity is. But the relative velocity of earth and mars — which I can't convince Wolfram Alpha to tell me, but it's go
by unanswered 6y ago
Yes, yes, you have shown you know what relativity is. But the relative velocity of earth and mars — which I can't convince Wolfram Alpha to tell me, but it's got to be on the order of their orbital velocity so let's say 5x10^4 mph — is a tiny tiny fraction of c so their inertial reference frames are essentially identical. So sitting in our reference frame, we can make inferences about what's happening "now" on mars,such that these inferences are consistent (to within that tiny fraction of c) with all of our current and future observations in this reference frame; i.e., consistent with a classical(+ finite speed of light) model of the universe. Which is why I left this out of my question and only asked about the consequences of a finite speed of light.
Put another way, simultaneity is perfectly well defined in a single inertial reference frame, and for purposes of my question, earth and mars can be considered to be relatively motionless.
- johncolanduoni 6y agoNow is the part where someone brings up even with the low relative velocity, you haven’t accounted for the simultaneity issues we’d have if the earth collided with a black hole while the rover landing was happening.
- unanswered 6y agoOr the fact that mars is not as deep in the gravity well of the Sun! I wonder if they have to account for that one when programming, like, antenna aiming or something.
- minitoar 6y agoIIRC gps suffers about 1hz of blueshift due to descending into earths gravity. I think the velocity (Doppler) shift of the spacecraft is a way bigger factor than the gravitational shifting.
- jtsiskin 6y agoNo, I don’t think you’re quiet understanding what they are saying. They aren’t talking about the different speeds of earth or Mars. Simultaneity is not “perfectly well defined in a single intertidal reference frame”. That is just a convention. If the RTT of earth to Mars is 20 minutes, then we can say that it takes us 20 minutes for our message to reach the rover, and the rover’s message arrives instantly, and that’s a consistent definition of simultaneity. https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/significance_conv_sim/index.html https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/si...
- unanswered 6y agoExcept that an observer located in the (hypothetical/approximate) common reference frame, but situated halfway to Mars, will report observations inconsistent with this definition (NB of course we receive their report at a time consistent with the definition, but the contents of the report are not consistent). So yes, you can play games with your definition of simultaneity, but you will win stupid prizes like observers in the same reference frame no longer agreeing about simultaneity when such a result is worse than what relativity requires. Your link points this out. You can play these games; I don't dispute it. But it's a separate matter entirely from anything to do with relativity, as your link points out, which is itself separate from the classical problem I originally posed. So we are now two steps removed from anything relevant to the Mars rover; I guess we get a sense of pride and accomplishment?
- DiogenesKynikos 6y agoIt doesn't depend on the relative velocity of Earth and Mars. It depends on your coordinate system. You can use Schwarzschild coordinates centered on the Sun and use the time coordinate to define simultaneity, but that's an arbitrary choice.