JesseM
Science Advisor
- 8,519
- 16
JDoolin said:Two people traveling at different speeds that are co-located will see exactly the same events, but they will see them at different places.
JesseM said:By "see" do you mean visual appearances,
JDoolin said:Yes
JesseM said:or do you mean calculations of distances and times in his own rest frame?
So you mean your statement to apply to both apparent visual distance and also to distance in each observer's rest frame? But in terms of apparent visual distance, it's not true that "two people traveling at different speeds that are co-located will see exactly the same events, but they will see them at different places"--if they are co-located, both will see exactly the same thing, so naturally the apparent visual distance of different objects (i.e. their visual size) and their visual arrangement relative to one another will be identical for both of the co-located observers at that instant.JDoolin said:Yes.
JesseM said:-do you think they will be unable to perform measurements that determine the position and times of events in a frame other than their rest frame,
Why would the speed of the frame affect how hard it is to determine the position and time of an event? (which might be on the worldline of an object moving fast or slow relative to yourself)JDoolin said:Yes. (If it is a fast moving frame.)
What do you mean "no use"? The problem of the object appearing suddenly in your view is a visual issue which applies regardless of what coordinate system you use. I don't see why for any given object, whatever its visual appearance as it passes within range of your instruments, it should be harder to assign position and time coordinates in one imaginary coordinate grid than in another imaginary coordinate grid. Can you explain further, give a numerical example or something?JDoolin said:It depends on how fast the objects are moving. If you happen to be in a system where another planet is going by at, say a rapidity=10. That planet will appear so suddenly in your view, and then be so time-dilated after it passes by; there would be absolutely no use whatsoever in defining your coordinates in terms of that planet's coordinate system.
What would look like a diagonal smear? The visual appearance of the object passing by you, or your drawing of the object's worldline in a diagram which uses the frame moving rapidly relative to the Earth, or the drawing of the Earth's own worldline in a diagram in that frame?JDoolin said:I can tell you what it would look like: It would look like one big diagonal smear
How does that make it hard to calculate the coordinates of any events? You just did the calculation yourself, showing that two events on the worldline of a clock on Earth which have 1 second of proper time between them must have occurred 11,013 seconds apart in the coordinate time of this frame. Piece of cake!JDoolin said:with each second on Earth stretching out for cosh(10)=11,013 seconds on the diagram.
What do "rounding errors" have to do with the speed of the Earth in this frame? Again, a frame is a purely imaginary thing, we can define the frame to be the one where the Earth is moving at some precisely specified velocity if we wish, rather than defining it in some other way and then trying to measure the speed of the Earth in this frame. And even if we do define the frame in some other way that requires us to measure the speed of the Earth in this frame, this is a practical issue, not a theoretical argument for why we must use a frame with low velocity relative to ourselves regardless of the precision of our measuring instruments.JDoolin said:but rounding errors would creep up very quickly because everything in your diagram for Earth would be just a smidgeon off the line x=c*t.