More Time for Nothing...

More Time for Nothing...

OK, Time travelers... ready for the ultimate skinny? Suppose someone asks you how far it is around a lake while you are running.  You may be tempted to say something like "Oh, it is about 1-and-a-half miles." That would not be any fun! So, instead answer with a question, like "Gee, mister, how big a ruler should I use?"   Assuming you do not get punched out, you will probably be ignored and left alone, permanently... by that person anyway.   However, on the rare occasion that some brave soul rises to the bait... "How about paces." I gladly answer "Just about 1800."

Now suppose we ask a more serious question.   How far is it around the lake if I use a meter stick? How about a 1 Foot ruler?  How about a 1" measure? A 1/2" measure? A 1/4" measure?... A .0000001" measure?  Would all of those come out the same?  You are measuring the same lake - right?  But, do you get the same answer?  No.   Now wait a minute... what do we mean by "around the lake"?  Clearly if I drew a line around the lake and just measured the same line with different measures it might be pretty simple... so lets keep it interesting and say that you measure as close to the water line as possible... now answer the question... Visualize it... Not so easy.   Not even if you froze te water so that it stood still!  If you read my earlier posts about existance you know that I think there is no right answer because neither the pond, nor the ruler, nor I exist.   However, aside from that, lets talk about what we perceive to be real.   Is there a right answer to how far is it around the lake? I suppose you can chew on that a while... ya'know that little pebble you ignored with the 1' ruler? Don't forget to measure around it with the .1' ruler! Tricky!

Mathematicians spend a lot of time thinking about really big and really small numbers... sort of the ultimate extreme athletes!  Maybe we could get a "right" answer to the above question if we had the ultimate shortest measure. Some gague and string theories adopt the Plank length (1.616252(81)×10^35 meters) as the ultimately shortest short... Which is related via the speed of light to the shortest time interval, the chron.  To illustrate, think about thin tall things.   Take a square that is 1" by 1".  By definition, it has an area of 1 square inch.   Now, lets squish it so that it is only 1/2" wide, but with the same area... sure, it has to be 2" tall (2 * .5 = 1). Now squeeze it until it is 1/4" wide... yep, it will be 4" tall.   See the game? So, let's get really crazy and squeeze it until it is 1/10000000000" wide.  Sure, simple, it is 10000000000" tall.  Seems easy, but can you answer this question... How tall is it if I squeeze it to 0" wide? Is that even possible? Is there a "Tallness" that would still give 1 square inch? Well... generally we just avoid that question... Some like to talk about infinity, but usually the answer is "You give me the width and I will give you the height."  The hight gets as tall as it needs to get - See?  So, if we use the Plank length as the utimate skinny, that little square would be 1.616252x10^35 meters tall! (About 10^32 miles!)

Lets take our ultimate skinny measure and travel back to the 1880's to see what our Flatland friend is up to...

E. Abbot Abbot's stories of the Flatland folk had to deal with an issue of thinness in regard to the 3D visitor who reveals himself to them. Lets just talk about me and my pencil the day after I put it through my 2D friends living room and then pulled it out! He thought he was going crazy!   From my perspective, it seemed very easy!   But I had a different problem... I could not seem to see him very well in his space.   When I got down close to the pond surface, everything just seemed to disappear! Try this experiment... get a piece of paper and a pencil. Draw a light, straight, inch-or-so pencil line on the paper and look at it... any trouble seeing that?  Nope. Ok, now lay the paper on the table and get down close to the surface... can you still see it easily? yes? OK, get closer... Closer... you see? After a bit you can not see the line at all!

I had that trouble with my friend!  If I entered his space I saw nothing!   So, answer me this... How thin is that pencil line?  The thickness of the image on the Shroud of Turin is 200-600 nanometers (http://www.shroudstory.com/) - Is a pencil line that thin?  However thin it is it is too thin to be viewed easliy from the surface it is on.  So, as EAA said in Flatland, the creatures had a little thickness. OK, that is cool! Let's say that!

Lets think about me in my 3D world and about some 4D creature coming to visit me. Lets also suppose that the 4th dimension we both have but that I do not perceive the same, is time! If he comes into my world will he be able to see me? I think not, or at least not easily.   I think that if he is "above" or "below" my time he can see me just fine, but as he gets close to my 3D "brane" he would have more and more trouble seeing me! Just like I have trouble seeing the pencil line on the paper or seeing my Flatland friend.  (We will talk more about time as a space dimension next post.)

Now, that leads to an interesting question... do I have a little thickness in 4D just like the Flatlander has a little thickness in 3D?   I often visualize our universe as the surface of a slice through time where the stuff "below" is the past and the stuff "above" is the future.   After our above discussion, maybe it can not be a surface, but rather a thin wafer. Hummmm... does that mean that I exist now but also a bit in the past and a bit in the future? Maybe that is how we are able to remember things and predict events.

If we only preceived "Now" what would the past mean?  See?   Wouldn't it be hard to live in a world where we could not infer where a ball would go when we threw it?   Heisenberg's famous Uncertainty Principal says about the same thing... you can not know both the location and the momentum of a particle with ultimate precision.   If I slice the location of the particle too thinly, I can not measure it's velocity! I can not predict it's path. I need a little thickness to take the measurement.   Similarly, in time-talk, we can infer instantaneous velocity, but we can not measure it - we need a little time to do the measurement.

If the Plank-length-chron is an actual smallest thickness in time, then I have a thickness in time! Then what happens if I leave my 3D prison brane and learn to fly in the 4th dimension? Am I traveling in time?  EAA's Flatlander learned to fly in 3D... maybe there is hope for me in 4!    Nois