Perception

This is a blog post I've been thinking about for a long time.  I have been fascinated about ways in which we percieve the world around us affects our interpretation of physical reality.  I am planning for this to be a long post that I will add to several times. 

This may be cliched, but let's start off with the allegory of Plato's cave.  In it people ("prisoners") are restrained so that all they see their entire lives are shadows upon the wall of a cave in front of them, cast by the light from a fire behind them.  Of course they come to believe that the shadows represent the whole of reality.  In this allegory the people are only able to perceive a limited form of reality that falls far short of what other people can normally perceive.  This is extended further to imply that some people (philosophers in Plato's version) can see deeper truths of our universe than the typical person, etc.  However, the point I want to make with this is that sometimes a more "accurate" view of the world can be more misleading.  The earth looks relatively flat.  The sun and moon "rise" and "set".  However, like the prisoner in the cave we can see a shadow of the earth on the moon cast by the sun during a lunar eclipse, and the shadow is not flat but round like the earth (link).  Sometimes a more restricted view like a shadow in Plato's cave can give a more accurate version of physical reality then the version we are used to.  I had a roommate from Shanghai, China my first year of college and he knew a lot of maxims.  One of these comes to mind with this example: "(the shape of) a mountain is better (more accurately) seen from a distance (rather than walking closer to see all the detail)".

Okay, now let's switch gears and talk about antimatter.  If matter and antimatter interact they annihilate each other in a tremendous release of energy.  To pick a specific example if an electron and positron (the antimatter version of an electron) run into each other they disappear and a high energy light wave (gamma radiation) photon or two are produced.  Alternatively, since energy and mass are interchangeable (recall the famous E=mc^2), a sufficient amount of energy could result in an electron positron pair.  What is a positron?  It is like an electron but everything is reversed.  Instead of a negative electric charge it has a positive charge; other qualities like "spin" are also reversed.  Feynman came up with a way to diagram the abstracted interactions of particles in time and space (called a Feynman diagram) and we could draw the annihilation of an electron (e-) with a positron (e+) like this.

The electron and positron moving forward in time run into each other in space and annihilate each other releasing energy.  We could also diagram the convergence of energy in time and space to a sufficient amount to produce mass. 

If we combined these two diagrams we could draw something like this.

Now, this change is very subtle and strange but it is not false.  It all depends on how you decide to view the process.  I'm going to make a small change to the diagram. 

I've made the positron an electron moving backward in time.  What would an electron moving backward in time look like?  Well, for example, negative charges repel each other, so backward in time a negative charge would appear to be attracted to another negative charge.  In other words it would appear to be positively charged, etc.  Antimatter is equivalent to matter except that it is, strangely enough, moving in the opposite direction in time.  (I did not create this idea; Feynman proposed it.)  Note that it takes a tremendous amount of energy to make even a small amount of matter reflect through time.  This brings up several interesting points.  Why are the mass, charge, etc. of all electrons in the universe exactly the same?  Could it be that there is only one electron and that it has just bounced back and fourth through time?  The same goes for protons, etc.  (I thought I had come up with this idea but I just read it was proposed by Wheeler.  Although, I suspect it might also have something to do with resonance of certain combinations of mass, charge, spin, etc.)  One way to build the ultimate doomsday machine is to completely destroy a single electron.  This might wipe out all atoms (as we know it) in the universe back and fourth through time and matter everywhere would fly apart because of the repulsive positive charge of protons.  (Although, how you would do this is another question.)  Also, might time be cyclical and the universe alternates through phases dominated by matter or energy, as the two reflect off of each other?  ...or a more fun question; why isn't time travel possible?  I'll save that one for later.  Anyway, this view of the universe, the realization that matter and antimatter are traveling in opposite directions through time, is only limited by our perception of the process. 

Okay, let's switch gears again and talk about mirrors.  I've blogged about this before.  It is a subtle but profound way our assumptions affect our view of physical reality.   When we see our reflection in a mirror everything seems normal, unless we have writing on our t-shirt.  Then we realize the mirror flips things left to right---but not up and down.  Thinking about this for a while we realize this is very strange.  There is no physical reason a mirror would "know" left and right and only flip that instead of up and down.  The answer lies in the realization that the mirror doesn't actually flip anything.  It all lies with what we are used to seeing and doing in our everyday world that leads us to be mislead into believing the rule that mirrors reverse objects left to right but not up and down.  What we view the mirror as doing is related to how we interact with horizontal and vertical planes.  At first they seem equivalent to each other---a horizontal plane is the same as a vertical plane except rotated 90 degrees---but this is not really true.  If you don't believe me then why can vertical planes intersect and horizontal planes cannot; there is a fundamental difference.  In our everyday lives we are used to operating in space on a horizontal plane.  When we turn something around we tend to do it left to right---this seems normal and in fact it is so normal it is difficult for us to recognize how limited this is.  We very rarely rotate things top to bottom to flip them around; especially objects containing text on them ("this side up" packages notwithstanding).  Part of the difficulty in seeing this is in our interpretation of the letters in the words.  When I used to work in a print shop we would hold the text upside down to see if it was aligned square with the edges of the page.  If it was right-side up our mind would work on interpreting the text and interfere with our ability to look at the dimensions of the page (until "stage two" and we  could read just fine upside down, then "stage three" and we could teach our self to ignore interpreting the words---then it wouldn't matter if it was right-side up or upside down).  So let's make up some new text symbols that look like this.

There is always a horizontal bar at the top and a circle to the right.  If we turned the page around to face away from us (and if we could see through the paper) it would look like this.

Now the bar at the top is in the same place, but the circle is always to the left of each character.  This is what we see in a mirror.  However, nothing is really flipped.  The mirror is reflecting what is actually on the page as it faces away from us.  The key is how did we turn it away from us.  We are used to turning things left to right and rotating around vertical planes in daily life. 

However, if we get away from what we are used to in daily life, it is also perfectly equivalent to flip something up and down in a horizontal plane. 

Now the bar is on the bottom, but the circle is still to the right.  If we flip the page this way (up and down) and look at it in the mirror this is what we see.  ...the mirror flipped the text up and down but not left and right!  ...the mirror is still doing the same thing according to the laws of physics and light rays reflect from objects off its surface to our eyes.  The only thing that changed was our expectation of how images should be rotated to look at them.

A truly reverse text image would be flipped both up and down and left and right, a sort of "animatter" text.

This is not something a (regular flat) mirror is capable of, because it doesn't really flip the direction of anything.  Note the rotational symmetry, which is probably more apparent in a standard text example:

The true reversal is equivalent to just rotating the text still facing toward us.  Okay, now that we have talked through this the process might seem trivial.  However, I have seen people completely stumped when I ask them why the rule, that mirrors flip left and right and not up and down, is true---at the risk of being repetitive, the confusion only comes from what we are used to experiencing in our everyday lives and how this affects our view of physical reality. 

As a side note I was drawing these kinds of figures on napkins and reflecting them in silverware, at a restaurant, for my brother to look at when he was visiting recently.  The waitress probably thought we were nuts. 

Okay,  next I plan to switch gears again and talk about something a little different: order, disorder, and entropy. Anyone that has taken thermodynamics knows the rules about order proceeding to disorder in a closed system and that it takes energy to locally increase order.  This is the increase of entropy in a system.  When I took thermodynamics I thought a lot about just what was entropy really.  There are some states that we expect to occur in a system and some that are unexpected.  If we flip a quarter 10 times and see H,H,T,H,T,H,T,T,T,H for the sequence of "heads" and "tails" this seems fairly normal and expected.  However, if we see T,T,T,T,T,T,T,T,T,T this is surprising and unexpected.  In fact, if the probability of "tails" is 1/2 each flip and each flip is an independent event the probability of seeing 10 tails in a row is (1/2)^10 or one out of 1,024.  If this were a row of 10 quarters we might say the system is in a highly ordered state.  If each hour a quarter is randomly picked and flipped again then after a few days the disorder of the system naturally increases.  After a few days we would expect to see something like the first example: H,H,T,H,T,H,T,T,T,H.  We smile and nod and feel like we understand what is going on ... to prove it we can calculate the probability of the disordered state.  There is a 1/2 chance of each heads or tails so if all are independent we can multiply the probabilities and we get (1/2)^10 or one out of 1,024 ... so, the disordered state is just as highly improbable as the ordered state.  Where was the increase in entropy? 

We tend to not recognize either  H,H,T,H,T,H,T,T,T,H or T,T,T,H,H,T,H,H,T,H as being that different from each other and lump them together as "expected."  It is true that there are many more ways to get a mix of heads and tails, rather than all tails (there is only one way to do that).  However, we would probably recognize H,T,H,T,H,T,H,T,H,T as also being very unusual.  Again, the probability of any single outcome is the same and just as unlikely.  We just notice some as "rare" and lump the others together as "common", but it is our perception and expectation that is doing this.  Really what we are doing is defining a "specific" state and contrasting this to a larger class of "general" states.  If we took seven sheets of paper and write E N T R O P Y down in large letters one to each page and laid them down next to each other in a mowed field (with high paper proof/repellant fences), the wind would blow them around and make them disordered.  Only very, very rarely would they rearrange in order on the ground and spell out E N T R O P Y again.  However, if we started from any of the other possible arrangements, it would be just as unlikely for the wind to blow the pages around and arrive at the alternative state again.  How much of the concept of entropy, a fundamental concept in physics, is based on our own arbitrary human definitions of what we are used to expecting to see?  It is just as likely for a drop of ink dissolved in and diffused throughout a cup of water to spontaneously reform into a drop of ink suspended in the water as it is to move to any other specific diffuse configuration of atoms in the water.  We say this is impossible according to the laws of thermodynamics because there would be a reduction of entropy in the system---but is this just because it would result in a state that we could observe as being different and distinct from a larger group of states that appear to be equivalent to each other (but in fact are not and just as unique from each other in a precise physical sense). 

For fun I suggest you read about "Maxwell's demon" which is a classic thought experiment in thermodynamics about the change in entropy of a system and about how this might be related to the use of gravitational slingshots to take advantage of the orbits of large objects to accelerate spacecraft to high speeds (higher than the average speed of bodies in the system) through the solar system. 

Okay, now should I switch gears to time travel?  
  (to be continued...)