Trying to Understand Relativity (part 10)

If the flow of time can be affected or altered by a physical phenomenon, then it seems necessary to establish some point of contact between time and physical matter.  For instance, if we say that the weight of an object here on Earth would be 1/16th of that weight if we were to move that object to the Moon, we are able to state this with the utmost confidence because we understand precisely how weight is a physical property of the object, and because we understand precisely how this property expresses itself through the object.  We understand that weight is a measurement of the force of gravity's interaction between the mass of the object and the mass of the Earth or the Moon.  Likewise, if we are to stake the claim that an object's duration can be affected by its velocity, then in the same manner, we need to either understand time as a property of the object, or understand how time can be affected by the object.  In either case, some connection between time and the object needs to be established.

Relativity addresses this problem by tying time to space, forming the unified concept of space-time.  According to Relativity, the mass of an object warps the space around it, and other objects caught in this curvature fall towards the object, creating the appearance of attraction which we call gravity.  Since time is interwoven with space, this warping of space causes a warping in time as well.  In the special circumstances of Relativity this seems to make a certain amount of intuitive sense.  We picture space as a flat plane, and time as a perpendicular dimension to that plane, represented perhaps by an arrow.  Normally, they pass at right angles to one another without disturbing each other, but when there is a warp in the plane of space, it causes a warp in the passage of time as well.

Evidence backs up the facts of this as well.  The warping of space was proven by taking photographs of the stars surrounding the sun during a solar eclipse.  The stars appeared to be slightly shifted in their positions because their light was passing through the warped region of space around the sun.  From the warping of space follows the warping of time.  The Earth is certainly a massive object, and as such, it warps space to a considerable degree, fortunately holding us and the atmosphere snugly to its surface.  In addition to warping space, it also warps time to an almost imperceptible degree.  The GPS satellites in orbit have to be recalibrated on a daily basis to account for the discrepancy.  These aren't just formulas on a chalkboard; these are genuine realities.  Due to the mass of the Earth, time really does run slightly slower here than it does out in space.

So where does this leave us?  In the previous post I brought the wave model to bear on all of this.  With this wave model I proposed that time existed entirely in change and motion.  I went on to speculate that the time dilation effect predicted by Relativity was really a uniform slowing of all motion.  Relativity, however, seems to have returned us to the notion that time exists independently of matter, as something aloof, as a dimension or medium through which change and motion occurs, rather than arising out of the change and motion itself.  Relativity couples time with space, rather than with the matter occupying that space, and there is plenty of evidence to support this union.

Once again, I'm thrown for a loop.  The wave model seemed to neatly provide the point of contact mentioned above.  If time was in the motion, then it seemed to make sense that accelerating one frame of reference to near the speed of light relative to another would cause a uniform regress of motion within the frames to account for the constancy of light.  The next step was to try and figure out exactly how this uniform regress could be caused by acceleration.  It seemed to a matter of calculating how the external and internal velocities balanced to compensate for the speed of light, and then time dilation would arise up out of this balance.  It would all be an adjustment of motion.

It all has an appealing simplicity, but that doesn't necessarily make it right.  I can't deny the connection between space and time.  It has been demonstrated clearly in theory, and in practice, and I'm not here to rewrite Relativity, but rather to understand it.  At the most, I would only propose a reinterpretation of the conclusions drawn from the theory.  So I pose the questions to you, the reader.  Does the space-time concept invalidate the wave model?  Is the hypothesis still worth pursuing anyway?  Is it possible that instead of space stealing time away from matter, perhaps space exists through matter in a similar way as I've proposed that time exists through matter?  The wave model suggests that change doesn't pass through time, but rather that time passes through change.  Likewise, is it possible that objects don't exist in space, but rather that space exists in objects?  Can space and time be unified on the ground of physical matter, as properties of that matter?  In other words, where do we go from here?

Trying to Understand Relativity (part 9)

You might recall a while back that I proposed a wave model of time as opposed to the more traditional linear model.  The idea was that time wasn't a line that we traveled on, but rather a wave that swept us along with a crest composed of all the dynamic changes through-out the universe.  Another way of putting it would be to say that time isn't a line or a medium in which these changes occur, but rather that time is the changes themselves and nothing more.  Things are happening in the universe and we are witnessing them, and we call these happenings and the fact of our witness, "time."  In this view, if everything was cleared out of the universe or if all changes in the universe could suddenly be stopped, then time itself would stop.  In this view, there is no time without change and motion.

Ah, but now you've found a flaw in my logic, right?  If the universe was stopped and completely static, wouldn't it be so for a certain amount of time?  The problem is that this question presupposes an observer, who can witness the static universe and perhaps even measure its frozen state with the one working stopwatch in all of existence.  In such an event, it would be the observer and their stopwatch that would be in a state of flux, changing and happening.  The passage of time that the universe remains static could only be measured relative to the observer and the watch.  If we remove them from the scenario, then the universe could stop ...now...and then start again without any of us knowing about it, and the question of "how long" it was stopped becomes meaningless.  There would be no sense in which you could say that it was a fraction of a second or a million years without something else in a state of flux to reference it against.  At any moment, at any prior state of the flux considered in isolation and pulled from existence like a still photograph, we could claim that the universe "stopped" for an indefinite interval and it would alter nothing.  The claim itself would be nonsense.  We would simply being saying, "The universe was like this, and then it moved again."  In the wave model, there would be no point in trying to look for time between the gaps in these changes.  In the wave model, time is defined by the changes. 

Now, in that same post where I introduced this wave model, I also wondered, if it was true that I was on to something with this idea, then how did Relativity relate to it?  If time was nothing more than a changing, moving universe, then how could speed affect this? How did the constancy of the speed of light factor into this scenario?  How could extreme velocity actually bend time itself?  Well, I think I might possibly have an answer for that.  At the very least, I think I may be on the right track.

Let's say that you have a box on your desk.  This box is completely empty.  It's an absolute void inside, and let's say that the box is made from some hypothetical material that experiences no atomic processes whatsoever.  The box is completely static.  There is no change, no decay, no entropy.  Like our example of the static universe, time can only be measured for this box relative to the changes in the flux you experience.  You go to bed; you wake up; you go to work; you come home, and you say that the box has aged a day simply because it has arrived at this same moment in time with you.  It has endured changes in the flux that you have experienced as a day.  Time is not happening to the box itself.  Nothing is happening to the box.  Time is happening outside the box, and the box is merely persisting through these changes.  We can measure the duration of this persistence only in relation to what has occurred outside the box.  The sun goes up; the sun goes down.  Seasons change.  People grow old and grey.  And all the while the box...just...sits there.

Suppose we were to look at this box from a different perspective, say from the perspective of an observer standing on the sun.  To them, the box is not sitting still, but rather it is being transported around the sun by a different frame of reference.  This observer would have the additional benefit of marking the box's passage through time by tracking its course around the sun.  If you recall my addendum to part 7, then you'll remember the scheme of interlocking frames of motion I established, the Earth round the sun, the sun round the galaxy, the the galaxies speeding away from one another, and so on.  Just as an observer in any one of these frames of reference would calculate the speed and the position of the box's transport relative to themselves, so too would they calculate the box's duration by measuring it against the changes in the universe's dynamic flux as they observe them from their vantage point.

This is where we bring Relativity into the picture.  Suppose we took this box and placed it aboard a rocket racing away from you and the Earth at near the speed of light, and let's say that given the speed it's going and the time dilation effect predicted by relativity, that as a year passes here on Earth, you see only a day pass aboard the rocket.  Stop to closely consider how you would interpret this experience.  You wouldn't look at the rocket and say a day has passed.  You would look at the universe from your perspective and say that a year has passed, and you have observed a day aboard the rocket span the length of that year.  This is how you would draw the conclusion that time was running slower aboard the rocket.  You would literally see things happening slower there.

Something curious happens though, if you focus exclusively on the box.  Considered in isolation, there is no meaningful way that you can say time is happening slower for the box.  There is no meaningful way that you can say that only a day has passed for the box.  As we established above, time is not happening to the box at all.  The only meaningful way that you can measure the box's duration is by comparing it to the passage of time that you've witnessed its persistence.  So, whether the box is sitting here at your desk, or rocketing away from you at the speed of light, you're forced to reach the same conclusion.  You've witnessed the persistence of this box for a year.  The only difference is that the box on the rocket has the misfortune of being imbedded in an extremely slowed environment.  The box itself has avoided the time dilation effect by virtue of its own immobility.  Possibly this is because technically you haven't witnessed time slowing down aboard the rocket, but rather you've witnessed the uniform slowing of all motion within that frame of reference to compensate for the relative velocity.  However, since, in the wave model, time and motion are interdependent, and the slowing is completely uniform and consistently even throughout the frame of reference from the tiniest particle to the most fleeting thought, you would still be completely accurate in saying that time aboard the rocket has slowed relative to you.  You might see a clock slowing down aboard the rocket, but that is literally and exactly what you're seeing, just a slowed clock.  And yet, you're also seeing it as evidence of slowed time.  A clock tracks the passage of time, but yet the motion of the clock itself is also a manifestation of time.

Click to Enlarge

This is just a first step, and it's all just speculation at this point, and to be clear I'm not trying to claim that there is some error or misconception in the theory of relativity.  I'm not trying to second guess Einstein.  I think even he would agree that slowed time would manifest itself to the observer as slowed motion.  Imagine being on Earth and watching a single day aboard that rocket transpire over a year.  Imagine how slowly you'd see someone perform their morning shave.  But the questions remain.  Is the time dilation caused by the slowed motion, or is the slowed motion encapsulated by the time dilation?  Is there more to it than than this, other factors?  How does near light travel relate to this? If time is interconnected with motion, then doesn't it made a certain sense that extreme motion might affect time?  Anyway, we'll see what happens down the road.        

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 5)

It was suggested to me that I read Einstein's own book on Relativity.  Well, I tried to follow up on this suggestion, but I found myself a little in over my head.  I've read difficult books before, Freud, Kant, Sartre, Nietzsche, and so on.  It took some effort to get through those books (Sartre especially), but at least I never felt completely bogged down in the rougher patches, and I was always fascinated enough by their ideas that I was compelled to continue.  I'm not sure why I should find myself having more trouble with this Einstein book, but I do.  I would read a couple of pages, re-reading most of the paragraphs a few times, and then I would set it aside at the point when I felt like I was going to pass out.  Then, when I'd go back and try to pick up where I left off, I'd be completely lost and I'd have to start over.  After several times of doing that, I think I've about had it.  But don't just take my word for it, check it out:

IN your schooldays most of you who read this book made acquaintance with the noble building of Euclid’s geometry, and you remember—perhaps with more respect than love—the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. By reason of your past experience, you would certainly regard every one with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue. But perhaps this feeling of proud certainty would leave you immediately if some one were to ask you: “What, then, do you mean by the assertion that these propositions are true?” Let us proceed to give this question a little consideration.

Geometry sets out from certain conceptions such as “plane,” “point,” and “straight line,” with which we are able to associate more or less definite ideas, and from certain simple propositions (axioms) which, in virtue of these ideas, we are inclined to accept as “true.” Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven. A proposition is then correct (“true”) when it has been derived in the recognised manner from the axioms. The question of the “truth” of the individual geometrical propositions is thus reduced to one of the “truth” of the axioms. Now it has long been known that the last question is not only unanswerable by the methods of geometry, but that it is in itself entirely without meaning. We cannot ask whether it is true that only one straight line goes through two points. We can only say that Euclidean geometry deals with things called “straight line,” to each of which is ascribed the property of being uniquely determined by two points situated on it. The concept “true” does not tally with the assertions of pure geometry, because by the word “true” we are eventually in the habit of designating always the correspondence with a “real” object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.

Now, I have really no idea what he's talking about here.  I know what "Euclidean Geometry" is, and I'm familiar with the concepts he's talking about, but I have no clue what he's getting at here.  Is he saying that the truth of the principles of geometry are only verifiable by their own internal logic and not by empirical observation?  Is he's saying that they ought to be only verified in this manner to be more "pure"?  This is only the first two paragraphs and I'm totally lost.  I would argue that the principles of geometry are empirically verifiable, because the shapes that geometry deals with are abstract forms of shapes that occur in natural observable reality.  I would argue that "2+2=4" is as abstract as it gets, but a person can take four buttons and empirically observe the truth for themselves.  I would argue this, but I'd probably be arguing with nothing but my own confusion.  I'm probably not even in the same ballpark where Einstein is pitching this particular game.  It's probably not even the right sport or even the right season.  I'm alone on the field, yelling at the empty stands. 

Maybe the problem is that I've been trying to read the book online.  Maybe I need to get a hard copy of it.  I don't know.  I would have liked to have more to say, and more progress to report.  I'm sure you would have liked something more interesting to read than a story of how someone threw a book against a wall.  I know people are trying to help with their suggestions, and I do appreciate it, but I think I make the most progress when I stick to my original plan and don't allow myself to get sidetracked.  I may return to the Einstein book, and if I run across a copy of it at the book store, I'll pick it up.  For now, I'm going to stick with my houses and their neighborly inhabitants.  See you next time.        

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.