Two major predictions of Special Relativity- time dialation and the increase of relativistic “mass” (technically, momentum)- have been directly observed. Has foreshortening in the direction of travel, the third major prediction of Special Relativity, ever been observed?
Not sure, but I think analysis of results from the Relativistic Heavy Ion Collider on Long Island is only consistent with the atoms being flattened into thin disks along their travel direction.
Close enough to direct observation for me. My question was because I was wondering if something like a nucleus or small molecule whose properties were dependent on it being spherically symmetrical showed altered behavior at relativistic speeds. Sounds like heavy ions fit the bill.
Its properties will only depend on its dimensions in its own reference frame, which won’t change.
It’s worth mentioning that, if you accept time dilation, then length contraction is a logical consequence. If time dilation has been observed, then length contraction follows inevitably.
Here is how time dilation implies length contraction. Suppose that you are floating serenely in space. At a certain distance away from you, there floats a space-buoy. The space-buoy is stationary with respect to you. Let’s say that, in your reference frame, the distance between you and the space-buoy is d[sub]your frame[/sub].
Then I fly by you in a rocket, just barely missing you, heading straight for the space-buoy. Let E[sub]1[/sub] be this event where you and I are practically in the same place at the same time. Let r be the speed that you measure me as having.
Of course, in my frame, it is you who passes me with speed r. And you just barely missed me! Hey! Why don’t you watch where you’re going! 
Since you and the space-buoy are stationary with respect to each other, I see the space-buoy approaching me with speed r. Let d[sub]my frame[/sub] be the distance between you and the space-buoy in my reference frame. Eventually, I collide with the space-buoy and my ship explodes. Call this event E[sub]2[/sub].
You already accept time dilation as having been observed. Now, in your frame, you measure a duration of t[sub]your frame[/sub] between events E[sub]1[/sub] and E[sub]2[/sub]. But, because of time dilation, you see the clock in my frame as running slow. It makes fewer ticks between passing you and being destroyed in the collision with the space-buoy. That is, I measure a shorter duration t[sub]my frame[/sub] between events E[sub]1[/sub] and E[sub]2[/sub]. This gives us
t[sub]my frame[/sub] < t[sub]your frame[/sub].
Now, in your frame, you see me travel a distance of d[sub]your frame[/sub] in time t[sub]your frame[/sub]. Since my speed in your frame is r, we must have that
r = d[sub]your frame[/sub] / t[sub]your frame[/sub].
Meanwhile, in my frame, I see the space-buoy travel a distance of d[sub]my frame[/sub] in time t[sub]my frame[/sub]. Since, in my frame, the space-buoy is approaching me with speed r, we must also have that
r = d[sub]my frame[/sub] / t[sub]my frame[/sub].
Since the value of r is the same in these two equations, we get that
d[sub]your frame[/sub] / t[sub]your frame[/sub] = d[sub]my frame[/sub] / t[sub]my frame[/sub],
or, equivalently,
d[sub]your frame[/sub] ⋅ t[sub]my frame[/sub] = d[sub]my frame[/sub] ⋅ t[sub]your frame[/sub].
But recall that t[sub]my frame[/sub] < t[sub]your frame[/sub]. Thus, the only way that the above equation can hold is if
d[sub]my frame[/sub] < d[sub]your frame[/sub].
That is, I measure a shorter distance between you and the space-buoy than you do. The interval from you to the buoy appears contracted (compared to its “rest-length”) as it passes me by at speed r. And this is exactly the phenomenon of length contraction.
Indirectly yes, since length contraction is necessary to get everything else to balance. But I’d been wondering if some more direct observation had been made. The linked to references say yes, so question answered.