Trying to Understand Relativity (part 3)

Before taking yet another crack at Relativity, I tried to do a little "research" this time, which basically means I Googled "understanding relativity" and clicked on a bunch of links, read a bunch of articles, followed some of Google's suggested, related searches, and so on.  Not that I've always taken such a lazy, haphazard approach to the subject.  I've actually read a few books on relativity in the past.  But the problem has always been the same.  It's this problem that lead me to writing these posts in the first place.  All of these sources do a fine job of explaining the way that relativity works, but they never really tell me how or why it works that way....At least, not to my satisfaction.  Maybe I'm just missing something. Examples like the Twin Paradox merely demonstrate the fact of time dilation.  Yes, when the twin in the ship gets home his brother is older than him, I get it.  Yes, it's amazing and mind blowing and all that, but I want to know why.  

Maybe I need to have a clearer definition of what I mean by that.  I'm sure someone could sit me down and explain the math to me with a bunch of crazy equations involving triangles and italic letters until I was sure that I was about to have a brain aneurysm, and who knows, maybe that's what it takes to even have a basic understanding of it.  Maybe I'm totally out of my league on this one.  But I'm hoping that there's a way to comprehend the concept itself without getting deep into the technical details.  I'd like to imagine that someone could give me a satisfying explanation of how an air conditioner works without having to resort to wiring schematics and a chart showing the molecular configuration and chemical composition of the refrigerating agent.  I just want a brief description of how the damn thing makes cold air.  Am I asking too much?

Of course relativity is a bit more complicated that an air conditioner, I realize that.  I guess I'm trying to understand how the idea first occurred to Einstein.  There had to be a moment before he worked out all the math and the details when he looked at the constant speed of light, relative motion, space, and time and saw the first hints of his theory.  There had to be a moment when the simple genesis of the idea made sense, and he knew he was on to something.  I guess that's the moment I'm trying to return to.  I want to take those same elements and figure out how someone could see relativity there.  Nowadays relativity has been tested and confirmed and it has a solid place in the annals of scientific history.  But what if somehow all evidence of it completely disappeared and it somehow vanished from the public consciousness?  How could someone rediscover the idea from scratch?  How could they work it out from the elements involved?

This may seem like a pointless line of speculation and waste of time.  It must sound odd the way I'm putting it.  I'm not talking about reinventing relativity, or trying to forensically recreate Einstein's mental processes.  I'm talking about the core understanding of a basic idea.  Let me put it like this, let's say you wanted to understand how fire is made.  You read some books, you search the internet, and yet you keep seeing the same thing.  They all just keep saying, "Rub two sticks together and voila!"  But that's not what you want to know.  You want to know why rubbing the two sticks together makes fire.  So then they tell you, "Well it's all based on this guy's theory of rubbing sticks together."  So at that point, you say, "Well, what if that guy never existed.  What would make a person look at two sticks and think that rubbing them together would make fire?  What if we had to figure it out for ourselves?"  

This is where I feel like I'm at with relativity.  I don't know why I bother.  It just frustrates me not to be able to understand it.  Like I said, maybe I'm just in over my head.  Maybe I should just humbly accept my limitations and move on.  Really, it's not even the whole theory I'm trying to grasp.  Obviously, most of my speculation has focused on the time-dilation effect, which is only a very small part of the theory.  Not that the concept of gravity being caused by mass warping space is any picnic to try to understand either, but I'm not even close to ready to open that can of worms yet.                                            

Anyway, I hope to get things back on track with my next post on the subject.  I guess I got off on a bit of a tangent here.  I'll return to my two neighboring houses next time, and maybe have some new ideas on how to approach the whole thing.  Almost immediately upon hitting the "publish" button on my last relativity post, I noticed a possible flaw in my scenario.  At first glance it seemed as though this flaw might undo any progress I might have made and put me right back at square one with guy B's trip seeming instantaneous to the guy in house A.  However, after considering the matter, I think this "flaw" might actually point to a way through, rather than a step back.  I'm still working it out, though.  

Next time?

Trying to Understand Relativity (part 2)

At the risk of my sanity, I'm taking another crack at trying to understand relativity.  Last time I set up a thought experiment (figure 1) that involved two neighboring houses that were a light year apart.  I placed the guy in house B aboard a spaceship and sent him to visit the guy in house A.  The end result was that it appeared (to my limited understanding at least) that the trip would seem instantaneous to the guy in house A.  Because of the time it would take for the light from house B to reach him, the guy in house A wouldn't see his neighbor board his ship until 2011. Seconds later the neighbor would be knocking at the door.  This result seemed to be the direct opposite of what I've always been told about relativity.  

Figure 1.

I think that one problem is that I failed to take the constancy of the speed of light into consideration.  Basically, I left the relativity out of relativity.  Light behaves strangely when it comes to the speed at which it travels.  This behavior seems to run contrary to common sense.  If you're in your car at night and you have the headlights on, the light from those bulbs travels at the speed of light.  Now, as you press on the gas and speed up to sixty miles an hour, it would appear that the light should travel at the speed of the light PLUS the sixty miles an hour that the car is going.  Since the source of the light itself is being propelled at sixty miles an hour, then the light should reach an observer, say someone standing on a hill a mile down the road, that much faster...right?  But that's not what happens.  It turns out that the light travels at the exact same speed regardless of the velocity of its source.  So something has to give....time.   

Generally, this doesn't make much difference in our everyday lives and at the normal speeds that we travel, but when you're talking about a craft moving at near light velocities, this point becomes significant.  So that brings me back to my thought experiment.  Now let's suppose that the guy in house A stands at his window, watching the entire trip as his neighbor crosses the distance between their houses.  

Is that a Flying Pickle?

Now, as I mentioned last time, although the guy in house B leaves in 2010, the guy in house A doesn't see him leave and start his journey until 2011.  Since the guy from house B was travelling at 99.99999% the speed of light, and since the distance between the houses was exactly one light year, I figured that the trip would take just a little over a year.  So you have the guy in house A seeing the trip begin in 2011, and then guy from house B arriving in 2011 just a few seconds later. Quick trip, right?  But again, let's put the guy from house A at his window, watching the trip.  Now, at any certain point along the line, the light from the ship is travelling at the speed of light and it takes that amount of time to reach guy A at his window.  So, at let's say...the half point of the journey, the light from the ship is going to take 6 months to reach guy A at his window.

Now, at this point, it's at least June 2011 when guy A sees his neighbor at the half point of his journey.  So the guy from house B can't arrive at his doorstep in January 2011 if the guy from house A is still standing at his window watching him make the trip.  Guy B can't exceed the speed of light, so he can't reach his destination before the light does.  He can't be sitting in guy A's living room, sipping coffee and reminiscing about old times, while his ship is still out there making the trip.  This, I think, is where the time dilation comes into effect.

It would seem then, that at the very earliest, the guy from house B can't arrive on the doorstep of house A until January 2012.  As you recall, this would be 2 years after he started out from his driveway, even though only a year passed for him aboard the ship.  So while Guy A is two years older, his neighbor has only aged one.  I think I'm getting closer to understanding it all, but I don't think I'm quite there yet. 

For one thing, I believe that relativity suggests that the time dilation would be far more extreme that what I've laid out in this scenario.  I think that maybe the guy in house A should have a long white beard when his neighbor finally arrives.  I'm not sure.  At that close to the speed of light, guy A should perhaps see time aboard the ship slow down to almost a halt as it speeds along the cutting edge of light itself.  Maybe that one year aboard the ship would stretch and span across guy A's time line exponentially.  I don't know.  I've taken the matter as far as I can at the moment.

Am I making progress?

To be continued?

    

Trying to Understand Relativity (part 1)

I've always been intrigued by the theory of relativity, but I really have a hard time wrapping my head around the whole concept.  I'd like to think I'm smart enough to understand it, but after ten minutes of thinking about it, I start to feel like that famous railroad worker that had a tamping rod driven through his skull.  I understand how it all works to some degree, but I don't understand why.  I know that the discovery that light travels at a constant rate irregardless of the velocity of the source emitting or reflecting the light contributed to Einstein's development of the theory in some way.  I know all about the time dilation and the Twin Paradox and everything.  I just can't quite grasp the way it all works.  I've tried to devise a kind of thought experiment to help me understand, but I think I'm clearly missing something.

Figure 1.

Alright, so you have these two houses.  They are both separated by a distance of one light year (figure 1).  It's 2010 at both houses, but because of the time it takes for the light to reach each neighbor, when they look out at each other they're both seeing the state that each existed in back in 2009.  

Figure 2

Okay, so now let's say that in 2010 the guy in house B decides to visit the guy in house A.  He gets into his spaceship and travels at as near the speed of light as it's possible to get (figure 2).  Since the distance is one light year, it will take him just over a year to make the trip.  So he'll arrive at house A in 2011.  Okay, now let's say that the guy in house A has been standing at his window watching all this.  Again, since it takes a year for the light to travel, the guy in house A doesn't see his neighbor in house B pull his spaceship out of his garage until 2011.  Then, a mere few minutes later, he gets a knock at his door.  His neighbor from house B has just arrived on his doorstep.

So doesn't it seem like the trip would seem nearly instantaneous to the guy in house A?  Yet, everything I've ever heard about relativity seems to suggest the opposite.  They say that if the guy in house A could see a clock aboard his neighbor's spaceship it would seem to slow down.  If the guy from house B could see a clock in the living room of house A from aboard his ship, it would seem to race by.  But it seems almost like it would be the other way around.  House A would see the clock zip along, spinning through a year of days in a matter of seconds.  Meanwhile, from the ship, the clock in house A would seem to slow down to compensate for the extra year.  (Remember, that the guy in house B sees house A as it was in 2009 when he climbs aboard his ship.)

I don't know.  The problem's obviously not with relativity, but rather with my understanding of it.  There's either something fundamentally flawed or missing in my experiment, or my idea of relativity itself is completely backward.  I don't get it.

I need some aspirin.