Trying to Understand Relativity (part 8)

In the Principia Mathematica, Issac Newton laid out his revolutionary theory of gravity.  He laid out with incredible precision exactly how gravity worked.  His formulas were used to calculate the exact orbits of the planets with an accuracy that stood for hundreds of years.  Say the word "gravity" and Newton's name is probably the first to come to mind.  His work is a milestone in the history of physics.  But although Newton literally wrote the book on gravity, he left out one little piece of information.  He never made a clear statement of exactly what gravity is.  Sure, he demonstrated how it worked in complex, intricate, mathematical detail, but he never really delved into what it was, beyond the idea that it was a force of attraction between objects that depended on mass and distance.  But what was this force?  How did the sun reach across the millions of miles of empty space and hold the Earth in it's place?  It was like a puppet master moving a puppet, but no one could find the strings.  Newton provided precise calculations of how the puppet master's hands control the puppet, and he basically left it to someone else to figure out the nature of the strings.

The someone else was Albert Einstein.  With his theory of General Relativity, Einstein showed that gravity was caused by the fabric of space-time being warped by the mass of an object.  The heavier the mass of an object the bigger and deeper the warp it caused in the fabric.  Imagine you have a blanket stretched out tight in the air.  If someone sets a baseball on it, it causes a dip around it in the blanket.  If someone sets a bowling ball on it, it causes a wider, deeper dip.  If you bring the baseball close enough to the bowling ball, it will fall into the bowling ball's dip and hit it.  This is what causes gravity.  This concept corresponds exactly with Newton's calculations of his "force" which varied according to mass and distance, but in a way he probably never imagined.

After spending the past month discussing time and time travel, it's got me wondering if there isn't a point at which Einstein's theory runs up against the same sort of wall that Newton did.  In case you missed it, I added a rather long edit to the last relativity post.  It starts about halfway down with the word "EDIT".  If you're actually making a serious attempt to follow this mess, then I suggest going back and looking it over.  I start with an explanation of the concept of relative motion, and then the constancy of the speed of light, and then I get into a thought experiment demonstrating how the time distortion effect can be inferred from these facts.  It's a rudimentary explanation of Special Relativity, and it's about as far as I've gotten at this point.  

Now, I'm told that I need to bring General Relativity into the picture to solve our Bob and Ann problem, but I'm not quite done with Special Relativity.  For one thing, I feel like I've barely got a finger hold on the idea.  I certainly don't feel confident that I have my mind completely wrapped around it, and I'm not ready to move on just yet.  But something else bothers me as well.  I kind of get how you look at the constant speed of light and you're forced to draw the conclusion that time distorts to compensate, but I'm not quite sure what this tells us about the nature of time.  This is where I feel like Relativity begins to run into that Newtonian wall.  Maybe it's my own limited understanding.  I spent some time yesterday, looking up "space-time" and "Minkowski space" and found a lot of equations that might as well have been written in ancient Sanskrit, for all that I was able to understand them.  But yet, I couldn't quite find what I was looking for.

I get the sense that Relativity looks at relative velocity and the constant speed of light, and then simply demonstrates the mathematical fact of time dilation, in the same way Newtonian physics looks at mass, motion, and attraction and then demonstrates the mathematical fact of gravity.  It's like, you point to where they show up in the calculations, but you're not really explaining them beyond the math.  Perhaps I'm being presumptuous.  Maybe the answer has just gone completely over my head.  Still, I can't help but wonder:  What is the significance of the fact that time can be distorted?  Why are mass and velocity the defining factors in this distortion?  What does this tell us about the nature of time?  Suppose time is the "dynamic flux", the constant change and motion of all matter in the universe that I proposed earlier.  Then, what does it mean that an observer can see this flux slow at high velocity?  If anyone has any answers, feel free to speak up.

It's like "dark matter", which is a theoretical construct that scientists use to make the calculations work in astrophysics.  They really have no idea what it is.  It's just something that shows up in the calculations.  Or consider the puzzling results of the double slit experiment that show up in quantum physics.  There is an old fable about three blind men stumbling across an elephant.  One of them grabs the trunk, and declares that the elephant is like a long snake.  Another grabs the leg, and declares that the elephant is like a thick tree trunk.  Still another feels the side of the animal, and declares that the elephant is like a wall.  I get the sense that these scientists are like these blind men.  There's something there.  It reveals its presence in the equations, but what it is remains a mystery, seen through a formula darkly.  I don't mean this to be derogatory to scientists, by the way.  They'd be the first to admit to being mystified.

The philosopher Immanuel Kant proposed that time and space were simply products of the mind, concepts that we filter reality through to make sense of it.  Frankly, I've always been appalled by this idea.  If time and space aren't objectively "real", then how can we hope to establish any sort of solid reality beyond ourselves?  The slightest flirtation with this idea and it feels as though the vast universe is about to collapse into my brain and become some sort of flat non-entity, like an image on paper with no depth.  It's likely that my understanding of Kant is as flawed as my understanding of Einstein.  But this idea that the speed of time's passing is relative to the speed of the observer forces me to at least consider if there isn't an element of perception involved in the nature of time.

And on that confusing note, I bring my contribution to "Time Travel Month" to an end.  I hope you've all had fun.  I enjoyed it, but I feel like I could go another ten years without talking about time travel and its strange paradoxes again.  It's been a little exhausting.  Oh...And hey, Doug, if you followed the link here from the first post of the month and you're reading this on February 1st, don't forget to mention something about the timetravelfund.com in the comments below that first post.  I don't want to waste any time getting on the ground floor of that amazing opportunity.  I'll thank you for it later.

(This post also available in extra cheesy version.) 

Trying to Understand Relativity (part 7)

I had planned to start off this post by correcting an error I made in the last relativity post.  I had said that a trip across a light year at 75% the speed of light would take 18 months, when actually it would be 16 months.  I was going to go into a lengthy explanation of how to figure this, but a lot has changed since then, and pursuing this mistake would be a waste of time.  You see, I've come to the conclusion that I've gotten completely off the track with this, and I need to approach the problem from a fresh angle.  I'm pretty sure that everything I've said up this point, and every piece of progress that I've thought I made is completely wrong.  So not only have I been making your brains hurt, I've been doing so with gross errors in logic and my ignorance of the concepts I've been trying to deal with.  For this I apologize.

But I'm getting ahead of myself here.  I've really been trying to put some genuine effort into figuring this out lately, and I want to give you some kind of idea where I'm at with this.  The best place to start would be with a comment I left on the last relativity post:

I was doing some actual reading on this today, and I came across an interesting explanation. Imagine you have a clock that works by bouncing a beam of light between two mirrors stacked on top of each other and facing each other. The interval between each bounce is one second. If you started to move the clock to the right, then it would look like the beam of light was traveling at an angle to a stationary observer because the position of one mirror would always be slightly to the right of where the other had been when the beam hits it. So from the stationary observer's perspective the beam of light would be traveling a farther distance between the mirrors. Since the speed of light is constant then the time it takes the light to reach each mirror is actually extended and therefore time becomes distorted. One second becomes 1.3 then 2 then 6 and so on, as the clock is pushed faster to the right. The exact amount of distortion can actually be calculated from the angle that the beam is skewed. But, if you were to run along side the clock, keeping pace with it, the beam would be straight up and down again and bouncing at perfect one second intervals. It's not just a matter of appearances. The distance the beam is traveling is actually relative to the observer.

So see, THIS I understand. It's the best explanation of relativity I've found. For the first time it gives me a perfectly clear idea of not only how but why relativity works. I just have to figure out how this relates to my scenario. Or maybe I need to come up with a new scenario. I don't know.

I was thrilled when I first discovered this illustration.  Finally, an explanation of relativity I understood.  I spend pretty much the entire shift at work that night bouncing that beam of light around between those two mirrors in my head as I went about the business of filling the machines and mopping the floor.  It actually made sense.  I just had to figure out how to apply this to Bob and Ann and I was home free.  

Unfortunately, as always, it turns out that none of this was going to be easy.  A few days later I had some quiet time to really think and dig into the situation.  It wasn't long before I came face to face with another huge problem.  You see, although the above illustration does a great job of explaining how an observer in one frame of reference can see time moving differently in another frame of reference that's in motion relative to his own, it doesn't help me understand how that time distortion affects the motion itself between the two frames.  That's the issue that I think is really at the heart of my thought experiment.  A message I sent to my friend, secondscout, who assured me he has the answers to all this, will demonstrate what I mean: 

Hey, since you're throwing your hat into the ring on this, I figured out something you can help me with. I found a good thought experiment the other day that explained the time dilation effect. I described it in the comments of my last post on my blog. It might be one you're already familiar with. Anyway, I think I have a good idea how and why the clock would look like it's running slower on a ship speeding away from you at near light speed. I'm having a problem now with the speed and distance the ship itself would appear to be going. Would it look like it's going it's actual speed, or would it look like it's traveling slower to the same degree as the time is slowed on board? Either way, I'm coming up with a problem.

I'll explain with a simpler version of my experiment that's closer to the classic twin paradox. Let's say Bob and his mother live in the same house. Bob hops aboard his rocket and takes off at 75% the speed of light. Now, to his mother watching at the window time appears to run slower aboard the ship. For every minute that passes aboard the ship, she sees 90 seconds pass on her clock at home. Now, if Bob looks back at his house, he sees the same thing. From his point of view, it looks like he's standing still and the house is zipping away from him at 75% the speed of light with a slower clock. From a relative standpoint it doesn't matter who's in a ship and who's in a house, it just matters that there's a gap widening between them and the speed that it's widening. It only makes sense to say he's going 75% the speed of light away from the house. His speed has to be calculated from a reference point.

Okay, so after Bob has traveled for a year, he stops. At 75% the speed of light, he's now 9 light months from the house. So when he looks back at the house, I would think it would appear that only three months have passed there since he left. At this point, I'd almost be willing to chalk all this business of slowing clocks and time dilation up to the most elaborate optical illusion of all time, caused simply by the delay in the light's travel time, and go take a nap, if it wasn't for one thing: The Mother.

See, it doesn't work out the same from her point of view. She can't look across the 9 light months and see him as he was 3 months after he left the house, because he wasn't stopped on the 9 light month spot 3 months after he left. He didn't stop there until a year after he left. So, supposedly she shouldn't see him reach that point and stop until 21 months after he's left the house.

But how can this be? They're both traveling at 75% the speed of light relative to each other. When Bob stops, they both stop. When they both look back, shouldn't they both see the same distance and difference between each other? Yet, it seems for the mother that she has to see Bob's speed slowed to the same degree as the time distortion. Meanwhile, Bob has to see the house move away from him at it's actual speed. At one year, he is 9 light months from the house. How could he truly say he was traveling at 75% the speed of light otherwise?

Now, you could try to look at from the opposite point of view. You could say the house was speeding away from Bob, and the mother looked back after a year across the 9 light month distance and saw Bob as he was three months after they parted. But the problem is that Bob stopping the ship is an event that happened at a specific position in time and space. It was that action that stopped the widening of the gap. It seems like everything would have to add up in agreement with exactly when and where it happened.

So, I hope this makes sense? I'm totally stumped. If you can help me out of this one, then I think I can figure the rest out. I think it's all a matter of flipping it around for his approach to House A. I think I was actually closer to the answer in my first couple of posts. If time on the ship appears to slow as it speeds away, shouldn't it appear to go faster as the ship approaches? I don't know. Maybe you can answer that one too.

I'm expecting a reply on this before too long.  I might copy it into the next post, with secondscout's permission, of course.  In the meantime, if anyone sees what I'm talking about and has any ideas, as always your contributions are quite welcome.  As you can see, it's two steps back and maybe half a step forward.  Now I can't even get Bob to leave his house without running into problems, let alone get him over to Ann.  Don't worry, we'll get these two crazy kids together yet.

EDIT: At the risk of making this the longest post ever, I'm going to go ahead with the edit I mentioned below.  Although the concept of relative motion is fundamental to the understanding of relativity, I haven't really delved too deeply into the matter in these posts.  Perhaps in the past I didn't fully appreciate what an important element it was.  Perhaps I took for granted that more people were familiar with the concept.  Either way, I think it's time to spare a few moments for a basic explanation of the concept.

In the comments below, Chanel was confused about how the house could be moving at 75% the speed of light in the scenario I laid out above.  I explained that it was a matter of relative motion.  We put some cars on a highway and I explained how their speeds calculated relative to one another.  If you're going 50 MPH and the car in front of you is traveling at 40 MPH, then from your perspective the car ahead of you is backing up towards you at 10 MPH.

Now, all this might seem needless confusing and a complete waste of time, but the fact of the matter is that the speed of nearly everything with one crucial exception is calculated from a reference point.  Generally we use the Earth itself as a reference point, and since most of our experience is confined to the surface of the Earth, this works out nicely and we never give it another thought.  When we're driving at 50 MPH in our car we never consider that this is 50 MPH relative to the Earth.  We just figure that's the speed we're moving.  But now let's say we stop at red light.  At that point, we figure we're standing still, and someone standing at the side of the road would agree.  They would look at our car and say it's stopped.  However, the Earth itself rotates at about 1,000 MPH give or take.  So, to someone out in space, they would say you're spinning at 1,000 MPH on the surface of the Earth.  The guy standing by the roadside thinks you're stopped because he's spinning at 1,000 MPH along with you.  Now, suppose there was a guy further out in space.  He would say, no, you're spinning at 1,000 miles an hour AND orbiting the sun at 67, 062 MPH.  Standing still indeed!  Now, suppose there was someone even further out in space.  He would say, no, again.  He would say you're spinning at 1,000 MPH, orbiting the sun at 67,062 MPH AND orbiting the galaxy at 447,000 MPH.  Finally, if you asked someone in another galaxy how fast you were moving, they would say you're spinning at 1,000 MPH, orbiting the sun at 67,062 MPH, orbiting the galaxy at 447,000 MPH and all the while you'd also be speeding away from them at 2,250,000 MPH (depending on which galaxy you talk to.)  So you see, the question of how fast you're going depends entirely on the reference point you're figuring your speed from.  In reference to the Earth, you're standing still.  In reference to the sun, you're spinning at 1,000 MPH and orbiting it at 67,062 MPH.  In reference to the center of the galaxy....you get the point.

Here's another example that doesn't involve a trip to deep space.  Let's say you're on a bus.  You're sitting in the back, and your friend is sitting up front.  You throw a tennis ball to your friend.  A guy sitting across the aisle clocks of the speed of this tennis ball, using a radar gun or something.  He gets a result of 5 MPH.  From his point of view, that's how fast the ball is moving.  Okay, now let's say you pass a guy standing on the street just as you throw the ball, and let's say the bus is going 50 MPH.  If he also had a radar gun and he had the slightest interest in knowing how fast the tennis ball was moving, he would get a result of 55MPH.  From his point of view, that's how fast the ball is moving, because the frame of reference that the ball is being throw at 5 MPH is itself moving at 50 MPH, so the results are compounded.

You'll remember though, that I said above that there was one crucial exception to all this.  That's the speed that light travels.  Light stands apart from all these interlocking frames of reference.  It travels at the same speed regardless of who is looking at it.  Let's say that instead of throwing a tennis ball, you shined a flash light up at your friend.  The guy across the aisle would clock the beam as traveling at the speed of light.  The guy standing on the street would also clock it as the speed of light, not the speed of light plus 50 MPH like the tennis ball.  The movement of the bus isn't a factor.  The light travels the same speed regardless.  Hell, even the guy in the other galaxy would agree on the speed.

Well, this created a problem.  Light is so much faster than the speeds we usually deal with (186, 282 miles per second) that it isn't real an everyday problem, but it was a problem nonetheless.  How could light cut through all these frames of relative motion and always end up being the same?  Something had to give.  Einstein came along and figured out that that something was space and time itself.  Why is that?  Well, that brings up back to the clock experiment I mentioned way up at the top of this post.

Fig. 1

The clock (fig. 1) operates by bouncing a beam of light between two mirrors.  The beam of light is represented by the yellow lines going up and down.  For the sake of argument, we'll say that the interval between each bounce is one second.  That would make the mirrors 186,282 miles apart.  That would be one huge friggin' clock, but again, for the sake of argument.  Every time the beam hits the mirror, it makes the clock tick one second.  Up, down, tick, tock.   It's a clock; it measures time; yawn...whatever.

Fig. 2

But, let's say you started to watch the clock move to the right.  Fig. 2 is suppose to represent the clock in motion, but you know how my Paint skills are.  The grey clocks are the same clock as it's moving, alright?  So, since the clock is moving, when the beam of light bounces from the bottom mirror to the top one, the top mirror is no longer in the same spot directly above where the bottom mirror was when the beam of light left it.  During the time the beam of light is traveling from bottom mirror to the top, the top has shifted to the right, because the clock is moving to the right.  From where you stand the light traveling in a zig-zag pattern of angles (fig. 2) which means it's traveling a farther distance.  It's not only covering the distance between the mirrors up and down.  It's also covering the distance that the clock has moved.  If we were dealing with tennis balls, there wouldn't be a problem.  We would just add the speed that the clock is moving to it's bouncing speed, and everything would fall nicely into place.  But light is different.  We still measure it traveling at the same speed.  So, since it's traveling a farther distance, but yet going the same speed, that means it takes longer to travel between the mirrors.  Since the clock is still ticking a second for each bounce, you begin to see it take longer and longer to tick a second as the clock moves faster and faster and the beam of light has to travel a farther distance and a more acute angle to keep up with it.  The clock begins to slowwww dowwwwnnn.  Tiiiiicccccckkkkk.....tooooooocccccckkkkk.  Gradually you notice that the time on the clock is falling behind the time on your watch.  Time is moving slower for the moving clock.

Now, suppose your friend was standing there with you.  They don't feel like just standing there watching the clock, so they run to catch up with it.  As they reach a speed where they're keeping a perfect pace with the clock, they look over and see fig.1 again, because relative to them, the clock is once again standing still.  So the years pass, and you stand there watching your friend and you grow old, but they stay young because time has slowed for them relative to you.

This "relative to you" is the crucial point.  If your friend looks back at you, it seems that you are receding from them.  If you're leaning against another one of these fancy clocks, they'll see the zig-zag effect on your clock and they'll think time is slowed for you.  You see, it's all relative.  So, who's growing the long white beard here?  Well, that brings you to the Twin Paradox.  The problem I propose above is a little different.  

Let's say your friend runs for a year.  They run at speed that will put them at a distance where the light will take 9 months to travel the distance between you after a year.  Then they stop and look back.  Now, you're both standing still relative to each other and time is ticking the same.  The light that reaches your friend has taken nine months to travel from you to the spot they're standing on, so they see you as you were nine months in the past.  But you can't look across that same distance and see your friend as they were nine months in the past, because they weren't stopped on that spot nine months ago.  They were still running with the clock.  This is where I'm stuck.

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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.                            

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.