Free Spinspace: The Space of Spins (The Metaspace Chronicles Book 2) by Matthew Kennedy

by the direction their heads are pointing in.  But in fact, it is a little more complex, because while in pathspace you might imagine slowing down and heading back the other way, in spinspace the spins can actually flip while staying in the same place.”
    He picked up one of the tops, halting it, and then turned it over and set the point of its “hat” into the dimple of the board.  A little leg now stuck up from the upward-pointing “bottom” of the top.  
    He gave the inverted top a twist to start it spinning.   After a few seconds something remarkable happened.  The top blurred out horizontally and then recovered with its hat pointing back up again.  “Whereas in pathspace , a particle's momentum will keep  it moving forward until it hits something, in spinspace the direction of spin can be reversed without hitting anything.”
    Lester looked at the now right side up top.  “But it didn't,” he noticed.  “The top is not upside down any more but it is still spinning in the same direction.”
    “Yes and no.”  Xander held out his hands and curled his fingers letting his thumbs both point toward the ceiling. “Both of my hands now illustrate spins pointing 'up'. But the curling of my fingers goes in opposite directions. They used to be called 'clockwise' and 'counter-clockwise' because the way my left hand fingers curl is the same direction the hands move on an old-fashioned clock.”
    Now he rotated his right hand so that his right thumb pointed down toward the floor.  “For convenience, we could just as well call these spin directions plus and minus, and stop referring to clocks.
    “With particles, spin tends to be quantized, but we'll talk more about that later. For now you can imagine spin as a quantity that can be larger or smaller, and positive and negative.  The convenience of using  + and – to describe it is now you only need one hand.”
    “All right,” said Lester.  “So we can imagine spinspace as the same as coordinate space, with the addition of a value of spin for every point in space that can be positive or negative.”
    “Almost,” said Xander.   “But there is a bit more to it. On this board the only stable configurations are spin up or spin down.  In real space, however, there is no board to constrain motion, so in real space the spins can all be positive or negative or zero, and their spin axes can point in any direction in 3-space.”
    He passed a hand over the tops and they all slowed to a stop and fell over on their squares.  “Now let's get back to the spinometer.  The first thing you have to learn is crude manipulation of spinspace. “
    Lester tried to imagine reaching out and grabbing the cone to set it spinning.  This had no effect other than making it rock slightly on its support.
    “You will need to remember how you solved the swizzle,” said Xander.  “I imagine your first efforts were like imagining pushing the air down the middle of a tube.”
    “Yes,” said Lester.  “Didn't work.”
    “But I imagine what did work was imagining the total pattern of the pathspace around the tube – part of which was the motion outside the tube.”
    “Yes,” said Lester.  I finally got the pattern I wanted when I saw one of the guards at the prison blow a smoke ring.”
    “Very good,” said Xander.  We must remember to use that image with the students.  For the spinometer, what I have found works better than imagining it twisting is to imagine all the spin you want distributed in the space around the cone, and then gathering all of that spin into the cone, like you are focusing it.”
    “I don't understand,” said Lester.
    Xander reached into the box again and came out holding a circular piece of glass in a metal rim with a handle.  “By now,” he said, “you may have learned how to manipulate light paths to do more than make yourself invisible.”
    “Well, yes.  I learned how to use it to see though walls and  to make distant objects look