Ships Passing According to Bob (gray ship) and to Anna (red ship)

With these animations you'll see how each observer can see the other's ship shorter and the other's clocks running slowly. You need grasp only two ideas: First is the idea of simultaneity being relative, that two events­bservations of clocks­simultaneous in one frame won't be simultaneous in the other; second, that when two clocks pass--a single event--the observers there on the spot in both frames agree on what both passing clocks read. Note: Bob's ship is the lower/gray one and Anna's the upper/red one. Also, for the most convenient control of events, it's easiest just to drag the sliders.

Length Contraction according to Bob In the left animation, stop Anna's ship at the point where her back clock aligns with Bob's back clock. At this time, zero in Bob's frame, observers at his back and middle look across and see the back and front of Anna's ship. They observe these two clocks in Anna's ship reading zero and -60, but the main point is that at this single time in Bob's frame, Anna's ship stretches only from Bob's back to his middle--it's only half as long as Bob's. The right animation confirms Bob's conclusion, because observers do always agree on what their passing clocks read. But to see the same two observation events from Annna's perspectve you have to stop Bob's ship at two times: first, when Bob's middle aligns with Anna's front (when Bob's middle clock reads zero and Anna's front reads -60); and second, when the back clocks align (and both observers see zero on both these clocks).

Length Contraction according to Anna From Anna's point of view, Bob is moving, so she should see his ship contracted. She does! In the left animation, if you stop Anna's ship when the ships' backs are aligned (all Bob's clocks read zero) then stop it when its middle aligns with Bob's front (Bob's clocks read +60), you see that Anna's clocks both read zero at these two events. In her frame observers see Bob's back and front at the same time (zero) and it stretches only from Anna's back to her middle. In the right animation, Anna's perspective, these two observation events clearly occur at the same time (though again at two times, zero and +60, on the relevant clocks in Bob's frame).

Time Dilation according to Bob The effect of time dilation is to see less time pass on a moving clock than on your own. Does Bob see Anna's moving clocks running slowly? Yes, all of them! But to be quantitatively correct, he must always look at the same clock in Anna's frame, for Bob sees her clocks as unsynchronized. In the left animation, stop Anna's ship when her front clock aligns with Bob's middle and then later when her front aligns with Bob's front. When the observers in the two frames look across at each other's clocks, they'll agree that the first observation occurs at zero on Bob's middle clock and -60 on Anna's front. In the second observation, Bob's time is +40 and the Anna's front clock reads -40. According to those in Bob's frame, a time interval of 40 has elapsed, and they've seen only 20 elapse on the same (front) clock in Anna's frame. (It isn't fair to say that Anna sees more time, i.e., 40, go by on Bob's clocks than on her own between these two observation events, because they're at two different places/clocks in Bob's frame, and Anna says that these two clocks weren't synchronized in the first place.) The same two observation events--Bob's middle and front clocks passing Anna's front--can be viewed in the right animation, and they confirm that the observations are at zero and +40 on Bob's middle and front clocks and at -60 and -40 on Anna's front clock.

Time Dilation according to Anna Anna has to watch a single clock on Bob's ship. Suppose she watches Bob's middle clock. In the left animation, stop Anna's ship when her front clock aligns with Bob's middle clock and then when her middle clock aligns with Bob's middle. These observation events occur at times -60 and -20 on the clocks at the front and middle of Anna's ship, and at zero and +20 on the clock at Bob's middle. Observers on Anna's ship have seen an interval of 40 go by in their frame and only 20 go by on a single (middle) clock in Bob's. As always, the same two observation events, when viewed in the right animation, confirm the effect--less time passing on a single clock in Bob's frame when seen by observers (at different locations) in Anna's.