Trying to Understand Relativity (part 4)

So, let's return to our thought experiment.  I mentioned last time that I found a flaw in the scenario I laid out in part 2.  I had my houses a light year apart and I put the guy from house B aboard a rocket on Jan. 1st 2010 and sent him to visit his neighbor in house A at nearly the speed of light (figure 1).  Considering the constancy of the speed of light, I thought I had found a clue to the time dilation effect of special relativity.  I said that if the guy in house A watched from his window, he wouldn't see guy B leave from his house until 2011 because of the time it took the light to reach him.  Furthermore, I said if guy A stayed at his window and continued to watch the journey, he wouldn't see guy B at the midpoint of his trip until June of 2011, because from his vantage point the trip began on Jan. 1st 2011 and it would take another six months for guy B to reach the midpoint.  Therefore, I concluded that guy B couldn't arrive on Jan. 1st. 2011, as I had originally thought, because he couldn't be sitting in guy A's house while guy A was still at the window watching him make the trip.  He couldn't arrive until 2012, after guy A had spent a year watching him make the trip.  So guy B would leave on Jan. 1st 2010, fly for a year at near the speed of light, but yet he wouldn't arrive at his destination until 2012.  

Figure 1.

However, I soon found a problem with this.  If guy B leaves for his journey on Jan. 1st 2010, then he reaches the midpoint of his trip in June of 2010.  At that point he is half a light year from house A, so the light from his ship will take six months to reach house A arriving on...yep, Jan. 1st 2011 not June as I had figured last time.  In fact, if you consider guy B's position at any point in his trip, the light will always arrive at house A on Jan. 1st 2011.  For instance, guy B will reach the 3/4 mark in September 2010.  He will be a quarter of a light year away, and the light will reach house A once again on Jan. 1st. 2011.  So it seems that guy B can still arrive on Jan. 1st 2011 and not beat the light there.  It seems that we're right back where we started from.

Will my efforts to understand Relativity be forever frustrated by my inadequate abilities to use the MS Paint program???

But yet there's a fundamental contradiction here.  What would guy A see from his window then?  He can't see guy B zip across the distance between their houses in a matter of seconds.  That would violate the whole idea of light traveling at a constant speed.  Guy A can't see guy B coming towards him faster than the speed of light.  It's impossible.  As I explained last time, light travels at the same speed regardless of its source.  So guy A's persistent vision of guy B's ship absolutely cannot look like it's traveling across the space between their houses at faster than the speed of light.  

For the sake of argument, let's say that guy B is traveling at a percentage of the speed of light that would land him at guy A's doorstep at the very last minute of the day on Jan. 1st 2011.  In other words, he's traveling at a speed where he crosses a light year in a year and one day.  If guy A were watching this from his window, and the light were reaching him from the different points in guy B's journey in the manner laid out above, he would see the rocket cross the distance of a light year in one day.  The persistent vision of the ship would have to reach him at 365 times the speed of light!   

Wow, that pickle is really Cruising!!!

So here you have two seemingly logical explanations that are yielding different results.  If you consider it from a static viewpoint, if you consider guy B at any one specific point in his journey, then you have the light reaching guy A on Jan. 1st 2011.  But if you look at it from dynamic viewpoint, if you put guy A at the window watching the whole thing in motion from the window then...then time has to expand to accommodate the speed of light!  In fact, the faster guy B races over to meet his neighbor, the more time will expand to compensate.  If guy B travels at the speed suggested above, a light year in a year and one day, then for guy A to watch the trip from his window and not have his persistent vision of the ship exceed the speed of light, then I believe that the trip would have to take 365 years from his point of view.  Yes, quite a long beard indeed!

Alright, so I may have it, and I may not.  It's a little early to pop the cork on the champagne just yet.  I'm still going to go back and read Einstein's original work as fellow blogger Martin Redford suggested yesterday.  A suggestion so obvious, I feel like an idiot for not doing it before.  Still, I thank him for his help.  Anyway, I'll read Einstein, see what I find, see if I've really made a break-through here or whether I'm still completely lost.