TestTube Lesson: ‘Seen’ Distances

May 19, 2013

I just got a great question about Special Relativity. (And I imagine this might kick off a series, so do ask any physics questions prompted by the games/point out cool physics you come across)

The Problem

A player (‘BARP’) commented on a previous post, wondering:

“In the seen view of VR, the room shrinks/gets closer behind the raptor. But light should take longer to reach the raptor from behind him, so the view behind the raptor should be stretched out.”

So what’s up?  A great question, and since it cuts to the core of the ‘Seen’ view (and requires some images) I thought I’d answer it in post form.  If you haven’t played Velocity Raptor yet, do that first.  This post will make a lot more sense once you reach level 25.

The basis for the ‘Seen’ view is that when you see something, the light from it didn’t reach your eyes instantly.  Light travels fast, sure, but it takes time to reach you.  So when you look at a star that’s many light-years away, you’re seeing it as it was many years ago.  In Velocity Raptor, with slower light, you notice this even with nearby objects.

The commenter makes a perfectly intuitive point.  If the light from an object takes longer to reach you, it would make sense that the object appears further away.  The light from the moon takes longer to reach you than the light from your computer monitor, and it certainly appears further away.  When you (as Velocity Raptor) are running away from, say, the left hand wall, there’s some extra lag for the light to reach you (check out Level 26, and keep the Doppler shift firmly in mind).  So shouldn’t the wall appear further away?  And yet on the screen, it appears much closer to you.

On the left, the raptor standing still. On the right, the raptor running to the right.

Why that doesn’t happen

It turns out that how far away an object appears to be doesn’t depend at all on how long the photons have been traveling towards you.  Truly, your eyes can’t detect the ‘age’ of a photon.  All your eyes detect are things like the color, and the angle the light is coming from.  It’s that second one that tells our brain how big an object appears…

What’s really going on

You can think of your eye like a pinhole camera.  Light rays from an object come in and get projected on the back wall (aka your retina).  The closer — or bigger — an object is, the bigger the image on your retina.

The further the blue bar, the smaller the image cast on the retina.

When the raptor is running away from the wall, the eyeball is now moving away from the incoming light.  That means the light that enters the eye has to travel further before it reaches the retina.

A stationary eye at the top, and a moving one on the bottom.

In the bottom image, the dotted-line box shows where the camera was when the light passed through the pinhole.  The solid box shows where the camera is when the light finally hits the retina.  It keeps the same angle of attack the whole time, but has longer to spread out, and makes a bigger image on the retina.  Thus, the wall appears bigger.  (Keep in mind that we should take length contraction into account… but that ends up being a second order issue.  The effect I’ve described exists with or without length contraction.)  This explanation, by the way, relies heavily on the great site spacetimetravel.org, which you should definitely check out if you want to learn more.

Now in 3D!

The question remains… does that mean the wall is closer, or does it mean the wall is bigger?  If Velocity Raptor were from a first-person perspective (like A Slower Speed of Light), it wouldn’t make a big difference.  In such a game you don’t see the distance of objects.  An object could be small, or it could be far away.  But with the bird’s-eye-perspective in Velocity Raptor, the distance needs to be drawn right on the screen.

It turns out the wall appears closer, instead of bigger.  You can think about the true path of an object… if it is traveling in a straight line, you should always see it at some point along that path.  Imagine standing on train tracks and watching the train race away from you.  Should it appear bigger (wider and taller) than it is, or closer than it is?  If it appeared wider, then the train would no longer seem to fit on the tracks.  The wheels would be spaced to far apart.  But the contact point of the wheel and the newly-run-over track must appear to be at the same place.  The photons, after all, are emerging from the same location.  Thus, the train cannot seem wider, and must seem closer.

So, excellent question, BARP, I hope this helps explain the ‘Seen’ view just a bit.  Lingering questions/qualms with this explanation?  Ask away in the comments below.

-Andy