Re: [Phys-L] Relativity Games

[John Denker <jsd@av8n.com>]

On 11/08/2012 06:20 AM, Chuck Britton wrote:
> http://gamelab.mit.edu/games/a-slower-speed-of-light/
>
> http://www.testtubegames.com/velocityraptor.html

1) Thanks for the links.

2) I changed the Subject: line because I'm pretty sure the testtubegames
 site is not associated with MIT.

Let me speak about the velocityraptor thing.  (I can't get the MIT
things to run on my computer.)

A positive remark:  The idea of building a gamemaker-style game with
relativistically correct kinematics is interesting and valuable.

On the other hand:  Maybe I'm just being dense, but I'm having a hard
time figuring out a correct, consistent interpretation of what I'm
seeing in this game.

There are at least three different reference frame in use, one of which
is not explicitly shown:
  a) The "scenery" frame, including the background tiles, the water hazards,
   riveted-metal walls, et cetera.  This frame has its own [x, y] coordinates.
   It presumably has its own t coordinate as well.
  b) The "screen" frame, i.e. the actual pixels on your computer screen.  The
   "reset" button, "menu" button, etc. are attached to this frame.  I assume
   the time coordinate for this frame is real-world wall-clock time.
  c) The frame instantaneously comoving with the protagonist creature.

Frame (c) is definitely different from (a) and (b), because the creature is
quite obviously moving relative to them.

Note that players are being asked to identify with the protagonist creature.
The game purports to show what the creature is seeing in frame (c).  My first
problem is that AFAICT we have no handle on frame (c) ... other than the depiction 
of the creature itself.  There is no coordinate grid to help us perceive x and 
y coordinates in this frame ... and (!) no clue as to what the t coordinate is 
doing.

As a related point, I cannot figure out the relationship between the screen 
frame (b) and the other frames.  This seems kinda important, since the screen
frame is the one most directly experienced by the user.

Last but not least, I have not been able to come up with any interpretation
of the screen frame that is relativistically correct.  Maybe I'm just not
interpreting it correctly, but at the very least we should consider it a
bug that the game is so difficult to interpret correctly.  Specifically, try
this:  Work your way to level 7.  This doesn't take long.  Walk over to the
right side.  Then start moving towards the left.  Ramp up the velocity to 2.7
(out of 3) and then leave it there, so there are no more acceleration effects.
You will observe that relative to the screen frame, the creature is moving
leftward at one speed and the scenery as a whole is moving leftward at a much
slower speed.  AFAICT relative to the screen frame, the scenery is contracted
by a large amount, even though it is moving with only a small velocity.  It
may be that it is contracted by an amount appropriate to the Vc-Va difference,
but it is moving at the much smaller Va-Vb rate.

As a related point, relative to the screen frame, in this situation the bullets 
are moving backwards i.e. right-to-left!  WTF?  The small leftward motion of 
the cannon is not sufficient to explain this.

I would be quite happy to be wrong about this, i.e. quite happy if somebody
could provide a consistent explanation of what we are seeing.  OTOH it seems 
like poor pedagogy to present something where the correct interpretation is 
so hard to find.

Constructive suggestion:  Some of these problems go away if you push the
"panning" button and thereby switch to "centered" mode, i.e.  the "first 
person" point of view.  That seems to make the creature frame and the screen 
frame be the same.  The creature remains fixed in the screen frame.  That 
makes sense, given that the creature cannot be moving relative to its own 
reference frame.  If the scenery is moving relative to the creature, it just
scrolls past our point of view.

There is some incomprehensible discussion of this issue at
  http://www.testtubegames.com/srel101.html#frames

============================

Undocumented feature:  If you click anywhere outside the game frame, it pauses
the game action.  There is a separate button to turn off the annoying music.

============================

Speaking of bad pedagogy, on the associated page
 http://www.testtubegames.com/srel101.html#sr
it begins by saying

> Special Relativity is based on two ideas:
>
>     The laws of physics are the same in all Reference Frames.
>     The speed of light through empty space is c=300,000,000 m/s.
>
> That's it! How hard could it be?

Well, if you insist on taking that approach, special relativity is very hard
indeed.  Given that starting point, it is highly non-obvious how to formulate 
the laws of physics so as to make them the same in all reference frames, while
leaving the speed of light invariant.  Circa 1900, several of the smartest guys 
in the world worked on this for many years before they figured it out.

The good news is that things don't have to be hard.  If you choose a better
starting point, things are very much simpler.  Specifically, if you start with
the idea that time is the fourth dimension, you can derive the constancy of
the speed of light as an easy corollary.  You don't need to take it as a 
postulate.  This is worked out in detail at
  http://www.av8n.com/physics/spacetime-welcome.htm