To Stretch or Not To Stretch

Physics has the distinction of hosting the one of the weirdest concept hierarchies  Don’t get me wrong: physics is beautiful in its intricate connections. But sometimes, especially in the case of modern physics, one feels something like:

WTF_1

So, most of us know about special relativity. A quick summary for the unfortunate: Special relativity establishes the speed of light as constant in all inertial reference frames (that is, for all observers who are either at rest or moving at a constant velocity). One of its implications is that information (in the layman’s case:anything) cannot travel faster than light. This means that as one starts approaching the speed of light, stuff starts happening. Time slows down (according to an outside observer looking at you), your mass increases and weird lighting effects start taking place. I am concerned with length contraction: the shortening of length of objects which are moving at relativistic velocities.

After an unexpected abortion of its hiatus, my conscience prevented me from playing Ace Combat.  And so I was looking for something productive to do when I found this website. According to the article, even though relativistic speeds may cause measurable shortening of length, it most certainly is not observable. Instead the fast travelling object will actually “appear” elongated, while actually being “contracted” at the same time (Schrodinger’s cat, anyone?).  The more I progressed into the article, the more I was like:

WTF_2

But then, I went into scientist mode…

inception_meme__1_…and decided to do a little calculation of my own.

 Imagine there is an object moving towards you at a velocity ‘v’. The stationary length of the object is ‘l’. The distance between you and the farthest part of the object is ‘x’.

rel_exp_1

Just by looking at the image we can see that light from the back of the object takes longer to reach the observer. Mathematically:

t_back_eqnt_front_eqn

We also know that we see an image when photons belonging to the same “plane” reach our eyes. From the equations above, we can see that photons reflected from the front “l/c” seconds later will arrive at the same time (i.e. on the same “plane”) as photons reflected from the back. However in ‘l/c’ seconds, the object will have moved by the distance:

dist_eqn

So the image that will reach our eyes will be like:

rel_exp_2

The apparent length of the object will be:

obs_enlrg_fac_eqn

Let us now assume that the object’s velocity is actually relativistic. So the measured length of the object will shrink to:

rel_len_eqn

And it is this length that will undergo apparent distortion:

final_stretch_eqn

Where l(measured) is the stationary length of the object. The relativistic factor shrinks whereas the observational factor stretches the object. It all comes down to which one of those functions is more powerful. This is a graph of enlargement vs. speed. ‘1’ on the y axis represents no distortion.

plot_rel_factors

Back to Ace Combat. ibrahim2016 out.

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One thought on “To Stretch or Not To Stretch

  1. I like this explanation. Its interesting to me that this seems like a pretty simple solution to an extremely confusing circumstance, but I guess science that goes a bit further than what we can perceive is always inherently so. Also interesting are the attempts at demonstrating this effect in Sci-Fi pop culture. I wonder how accurate these representations are?

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