A reader writes in with a question about the physics of Star Trek:
When the Enterprise goes into warp speed (which as I take it are multiples of the speed of light, warp 5, 5x the speed of light, etc.) and they show the ship zooming through the cosmos, they always show the stars its passing as elongated. In the special theory of relativity, is it not true that moving near the speed of light objects will appear to actually contract? But then again, according to relativity one can’t go faster than the speed of light, so perhaps there is some other physical phenomena going on here. Or maybe I should just enjoy the show for what it is.
I’m not nearly as conversant in Trek as I am in Star Wars, but I’ll give it a shot.
It’s my understanding that warp speed was originally meant to be polynomial in nature. For a speed of “warp n”, the velocity of the Enterprise was v = c(n^2) or something of that nature. Thus warp 5 is actually 25 times the speed of light. Actually I had better look this up… ok, Wikipedia tells me that in fact the equation is v = c(n^3) so warp 5 is 125 times the speed of light. Which is fast, but still puts travel times between even nearby stars in the region of several days.
Later they changed the formula and now the exponent is 3.333… except for speeds greater than warp 9. That’s an unspecified function with a vertical asymptote so that warp 10 is actually infinite.
Now for relativistic speeds there is length contraction. Objects outside your fast-moving spacecraft will be contracted along your direction of motion in your reference frame. But the Enterprise is moving much faster than light. Special relativity is clearly already out the window because faster-than-light travel is not possible in that theory. The more general version of the theory – general relativity – is a little more lax. You can’t travel faster than light, but theoretically it may be possible to distort space in such a way that the Neutral Zone is only a few million miles away in your reference frame. You can then travel across the distorted space at an normal speed and arrive in a reasonable time.
This is wildly far-fetched and I’m using the word “theoretically” in the loosest possible sense. But it’s TV, so we’ll go with it.
Will it make things appear to be elongated or contracted? I couldn’t say, but there are circumstance in which we actually can directly observe distorted space elongating the appearance of objects. Gravity bends space, and even comparatively modest bending over a long distance can create visually observable effects. If you have a cluster of galaxies between you and some very distant other galaxies, the cluster can act as a gravitational lens. In the picture below you can see the bright galaxy cluster dominating the image, and you can also see background galaxies elongated into distorted arcs by the gravitational distortion on the light moving through the cluster:
Perhaps not exactly the same thing, but certainly in the same spirit. It’s distorted starlight occurring directly from the gravitational warping of space. Close enough for me.