By Don Koks, 2018.

Are the Lorentz Contraction and Time Dilation Real?

Yes, they most certainly are. They are both a result of what we measure—and what we measure is as real as things get.

Time dilation is easier to understand: we can easily measure if, say, a fast-moving particle is decaying after a longer time than it would if it were at rest. But Lorentz contraction still confuses people. Consider that simple discussions in relativity can go awry when the distinction between "seeing" and "observing" (or "measuring") is not made clear. What we see is what we really see with our eyes or cameras: this has visual perspective, and can contain optical illusions due to the distances of objects, such as the apparently faster-than-light motion seen of matter that is being ejected from some galaxies. "Seeing" can contain the Doppler effect, which is due to changing arrival times of signals at our eyes or measuring gear. Contrast this seeing with what we observe or measure, which you can envisage as the end result of seeing after we have subtracted all the complications caused by signal travel times and distances of objects. For example, even outside the realm of relativity, if you hear two explosions at different times, this does not mean they really happened at different times. Once you have corrected for the travel times of the sound from possibly different distances, you might conclude that they really occurred at the same time. So, you heard them happening at different times, but you observed that they happened at the same time.

In fact, in relativity we seldom analyse a situation on paper by asking what is seen and then accounting for signal travel times. Instead, we invoke the properties of a frame. A frame is a collection of observers, each equipped with all manner of measuring devices, and who each measure only what is happening in their own immediate vicinity. What makes them a frame are two properties:

They all share a common standard of simultaneity: that is, they all agree on the times of events. This is actually not something that can be guaranteed for any old set of observers, but it is certainly true for inertial frames and "uniformly accelerated frames". Sharing a common standard of simultaneity allows them to allocate times to events in a meaningful way: it allows them all to agree on when an event took place.
They all share a common standard of distance: that is, they all agree that they are not moving relative to each other. This also is not something that can be trivially guaranteed, but again it is certainly true for inertial frames and uniformly accelerated frames. Agreeing that they have no relative motion allows them all to agree on where an event took place.

When I wish to make an observation of an event or a series of events, I ask all of these observers who make up my frame to record what happens in—and only in—their immediate vicinity for some time interval. Then, later, they send me their observations, which I collate to construct a description of the scenario. This procedure means that I will never been fooled by, say, the Doppler effect. For example, it is still commonly believed (and even taught by some non-physicists) that relativity is all about what is seen: you will find it said that time dilation is all about the fact that when a clock moves away from you, the signals you receive from it are Doppler shifted such that you see it ticking slowly. This is supposed to prove that "moving clocks tick slowly", but is a completely (and trivially) invalid proof. Relativity says that all moving clocks tick slowly in an inertial frame, but the presence of the Doppler shift is an unnecessary complication when we wish to understand what is going on. When we analyse a moving clock with the above set of observers, the Doppler shift doesn't appear, and so what is left is true time dilation.

(I presume that those who make the above incorrect statement about a receding clock have never thought about the case when the clock is moving toward you: when it's moving toward you, the Doppler effect means that you will see it ticking quickly, even though relativity says it is actually ticking slowly.)

Similarly, this kind of analysis makes it clear that when we observe a moving object, its length is contracted. What we see is more complicated: see the FAQ entry on Penrose–Terrell Rotation for a discussion of that. The fact that this contraction is frame dependent is neither here nor there. As an analogy, consider the air flow over an aircraft's wings that makes it fly: this is frame dependent too—it changes as the plane flies faster—but if you insist that this air flow is not real in the aircraft's frame, then while you might still be able to crunch numbers in an aircraft-engineer exam, you will forever be wondering how aircraft can fly. So, don't think that the Lorentz contraction is not real. It's as real as anything else.

The fact that the air flow over an aircraft's wings does change in a particular well-defined way when we change frame is a reflection of the fact that the whole scenario of the aircraft flying through air is "real", and this can be described using the elegant maths of vectors. Similarly, when certain measurements of an object change in a particular well-defined way when we change frame in relativity, this is also an indicator that what is going on is real. And that is the idea behind using tensor notation in the maths of advanced relativity.