3 ms·

Is there a somewhat longer (maybe illustrated) example of this principle somewhere? You've captured my interest and I want to read more

jfoutz 6y ago
maybe this one? https://en.wikipedia.org/wiki/Ladder_paradox https://en.wikipedia.org/wiki/Ladder_paradox depending on where you stand, the ladder can fit in the garage, or it can't. If I remember right, it's from the original special relativity paper, which is super accessible. General was always beyond me, but special is just high school math.
alephu5 6y ago
https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity
d_tr 6y ago
The links provided are nice but I will leave a comment here in case it is useful. If I measure the temporal (dt) and spatial (dx) distance between two events A and B, then I can calculate what another observer would measure (dt' and dx') using the so-called Lorentz transformation, provided that I know his velocity relatively to me (v). The Lorentz transformation is a linear operator, written down as a matrix. Now, the spacetime interval (ds) between A and B, is computed with the formula ds^2 = dx^2 - c^2 dt^2. The interesting property here is that the Lorentz transformation leaves ds^2 unchanged, i.e. dx^2 - c^2 dt^2 = dx'^2 - c^2 dt'^2. So, it also does not change the sign of ds^2, which determines whether light is fast enough to travel a distance dx within time dt. The animation in the Wikipedia link by alephu5 shows the Lorentz transformation in action for a smoothly varying value of relative velocity. The events A B C are all separated by positive ('spacelike', light not fast enough) intervals, which graphically means that the line connecting them has a slope of less than 45 degrees in that graph, and the Lorentz transformation can tilt that line both ways and change the ordering of the events in the t axis. If two of these events on that graph were separated by a negative ('timelike') interval, the line connecting them would have a slope larger than 45 degrees and the Lorentz transformation could not alter their relative ordering in the t axis, meaning that all observers would agree on the ordering.
shaunpersad 6y ago
Light cones helped me understand causality from a slightly different perspective: https://en.wikipedia.org/wiki/Light_cone https://en.wikipedia.org/wiki/Light_cone https://www.youtube.com/watch?v=OZv3ycr6Jxg https://www.youtube.com/watch?v=OZv3ycr6Jxg

jfoutz 6y ago

maybe this one? https://en.wikipedia.org/wiki/Ladder_paradox https://en.wikipedia.org/wiki/Ladder_paradox depending on where you stand, the ladder can fit in the garage, or it can't. If I remember right, it's from the original special relativity paper, which is super accessible. General was always beyond me, but special is just high school math.

alephu5 6y ago

https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity

d_tr 6y ago

The links provided are nice but I will leave a comment here in case it is useful. If I measure the temporal (dt) and spatial (dx) distance between two events A and B, then I can calculate what another observer would measure (dt' and dx') using the so-called Lorentz transformation, provided that I know his velocity relatively to me (v). The Lorentz transformation is a linear operator, written down as a matrix. Now, the spacetime interval (ds) between A and B, is computed with the formula ds^2 = dx^2 - c^2 dt^2. The interesting property here is that the Lorentz transformation leaves ds^2 unchanged, i.e. dx^2 - c^2 dt^2 = dx'^2 - c^2 dt'^2. So, it also does not change the sign of ds^2, which determines whether light is fast enough to travel a distance dx within time dt. The animation in the Wikipedia link by alephu5 shows the Lorentz transformation in action for a smoothly varying value of relative velocity. The events A B C are all separated by positive ('spacelike', light not fast enough) intervals, which graphically means that the line connecting them has a slope of less than 45 degrees in that graph, and the Lorentz transformation can tilt that line both ways and change the ordering of the events in the t axis. If two of these events on that graph were separated by a negative ('timelike') interval, the line connecting them would have a slope larger than 45 degrees and the Lorentz transformation could not alter their relative ordering in the t axis, meaning that all observers would agree on the ordering.

shaunpersad 6y ago

Light cones helped me understand causality from a slightly different perspective: https://en.wikipedia.org/wiki/Light_cone https://en.wikipedia.org/wiki/Light_cone https://www.youtube.com/watch?v=OZv3ycr6Jxg https://www.youtube.com/watch?v=OZv3ycr6Jxg