So let me talk about relativity for a second, because relativity is a fucked up subject to think about.
I wouldn't call myself an expert in the idea of relativity other than a few basic equations and concepts, but I love thought experiments and this is one of the craziest things in the universe once you start to understand it.
Here's the central idea: The speed of light is the same everywhere. If light is coming to the solar system from a distant star, it doesn't matter how fast that star is moving toward us or away from us, the speed of light that you measure will be exactly the same. You would expect that incoming stars would emit faster light and that stars moving away would see the light slightly slower, but this was proven not to be the case by experiment. Relative velocity doesn't affect how fast light moves, it is measured the same from anywhere in the universe. This discovery leads to the conclusion that nothing can go faster than the speed of light.
First off: Time dilation and length contraction. If you see somebody moving relative to where you are at close to the speed of light, they will appear to be physically compressed in their direction of motion. Time will also appear to be moving slower for them. Also, events that appear to be happening simultaneously to you will appear to happen at slightly different times relative to the other person, and vice versa.
Why does a constant speed of light lead to time dilation? This is the way it was explained to me, and it makes some sense. Imagine you have a beam of light reflecting between two mirrors. From a stationary point of view, the light takes a certain amount of time to get from one side to the other.
Now suppose this mirror is in motion. The light would appear to move back & forth and bounce between the mirrors, but now it also has sideways motion. The total path is now longer. If it were something moving at normal everyday speeds, the horizontal motion would add to the overall speed and it would appear to take the same amount of time but travel faster than the stationary light. But because the light must travel further while moving at the same speed, it takes longer to traverse the path, and therefore the passage of time in the other frame of reference is actually slower.
Length contraction is a different subject, but I think I found a way to explain why it would have to happen.
Astronaut B is floating in space. He looks to both sides and can see Astronaut A and Astronaut C on opposite sides, speeding toward him at close to the speed of light. They are going to zoom past him without hitting and continue moving at full speed. At the exact moment that they pass him, he takes a flash photo of their journey.
The light from the flash is emitted as a sphere. Astronaut B looks out after he takes the picture and "sees" (or would somehow measure) the light emitted as an expanding sphere. Astronauts A and C are speeding away from him at almost the speed of light, appearing to almost reach the edge of that sphere.
But then look at it from astronaut A's point of view. He sees B speeding away at almost the speed of light, and C moving ahead further than that. Without relativity, you'd conclude that astronaut C is moving twice the speed of light, but remember the flash of light, because that's the critical thing: Because the light is always moving at the same speed, it's the same shape for everybody, so everyone sees it as a sphere with all the astronauts inside of it. The astronaut at the far edge of the sphere still fits inside, and A sees B moving almost the speed of light with C moving slightly faster. C sees the same situation, but in reverse.
This image goes a little bit of the way to explaining why it takes more and more energy to go close to the speed of light. Adding more energy makes it go closer and closer to the speed of light, but there will always be more space between the object and that event horizon in which light is still propagating and space is expanding in the same pattern. We could continue this example with more astronauts going past at even greater speeds, and if you added more and more objects in a row they would appear closer and closer to the edge of the sphere from your perspective, but there would still be more space where you could add another one.
There are some weird things that happen in relativistic conditions. Simultaneity gets messed up. Suppose you have the same situation as the first example with light reflecting off a mirror, only make it perpendicular, so the mirrors are moving in the direction in which they are separated. Imagine you have a flashing thing in the middle, and suppose the mirrors are stationary from the point of view of the center. You emit light from the center, then you "see" the light hit the mirror on both sides at the same time and then reflect back to hit the center point at the same time.
Now imagine you're looking at this from somewhere that is moving sideways relative to the mirrors. One beam will appear to go backwards and immediately run into the mirror behind it. The other beam will move forwards, but because the mirror is receding faster and the light still appears to move at the same local speed, it takes longer to reach the other mirror. Eventually it hits the mirror and is quickly reflected back, just in time to meet up with the other photon which has been traveling forward most of the time.
This is bizarre and counterintuitive, because from one person's vantage point, the order of events completely changes; the light bouncing off the sides of the mirror is no longer simultaneous, but one happens before the other.
It is possible to trace out the path of these particles by visualizing the time as a space axis (i.e. each horizontal row represents a moment in time) in which case the situation looks like this:
Notice how these two transformations show the exact same event, just from two different points of view. There is no absolute time to which all observers in the universe can be synchronized, but whatever vantage point you are looking from there is still one single universe that is consistent with itself. If two particles collide, then they will always collide in that same position in timespace, even if it get projected in different ways depending on relative velocity. It just might not look the same from all angles.
What confuses most people about this is that it's symmetrical. You'd think, if I see time slowed down from their perspective they must be seeing your time sped up with you stretched out. But that's wrong. There is no state of absolute rest, and no vantage point is more valid than any other. So if you see an object coming at you at a certain speed, there's no difference in saying you're standing still and the other person is moving, or you are moving and the other person is standing still. If you're moving close to the speed of light relative to someone else, you see what the other person also sees. So from the vantage point of the other person traveling close to the speed of light, your length is also contracted and your time is also slowed down.
This leads to an apparent paradox, which Wikipedia calls the
ladder paradox.
Imagine you have a ladder moving at almost the speed of light. (It could be any object, but somehow people decided it was going to be called the ladder paradox.) You also have a garage with two doors on opposite sides. The ladder is normally too big to fit in the garage, but because it is moving so fast and is length contracted it is small enough. The doors stay open until the ladder is inside, at which point they shut instantly for a brief moment while it fits inside and then open again. (Or I guess another way to look at it would be if it started with only the left door open, then the left door closed and then the right one opened.)
From the ladder's perspective, the garage is now much shorter for it to fit inside. How can both of these situations be consistent?
It works, because the ladder sees a completely different order of events. From the ladder's point of view, it flies in, the door in front closes, then it passes through the garage, and then the door behind it closes. If the doors were to actually touch the ladder it would feel the collisions at different times.
This situation can be diagrammed with a timeline the same way we did the particles bouncing off the mirrors. If you look at the way it's stretched out you see it's stretched diagonally in the same way.
Other crazy shit about relativity: The speed of light is the arbiter of causality. For any two events that appear to happen close enough that you could reach one from the other going less than the speed of light, there is some frame of reference in which both of those events happened in the same place at different points in time. For any two events that happen far enough away that you couldn't possibly reach them going the speed of light, there is some frame of reference in which they happen at the same time in different locations. These are mutually exclusive: No matter where you are, non-correlatable events will be non-correlatable and vice versa.
^--- I took this image from
http://en.wikipedia.org/wiki/Lorentz_transformation. It was one of the featured Wikipedia images. I made rest of these animations myself.
Thinking about this you start to realize just why traveling faster than light is impossible, and why if you did it would be equivalent to time travel.
Here's an interesting thought experiment that I haven't specifically seen anywhere else (possibly because it's not entirely correct.) Try to imagine the situation of the reflecting mirrors, but combine the two situations together and see what it looks like from all angles.
Imagine you have a really tiny object that emits light inside of a circle made of reflective material. From the perspective of the center, the circle on the outside is not moving. The light flashes for an instant, and a sphere of light is emitted in all directions. A moment later, it reflects off the edge, and imagine that it's a perfectly smooth mirror so the light all reflects off in exactly the opposite direction.
First thing to realize: Since the speed of light is the same in all reference frames, this sphere will look like a sphere no matter who is observing it. If you're moving relative to the original flash, the location of the object in the middle won't match up with the center of the sphere, but it will still remain the same sphere growing at the speed of light, even in a different frame.
Second thing to realize: Since the reflective sphere is now a moving length-contracted object, the light will not reflect off of all of it at the same time. If you're moving close to the speed of light and looking at it, you'd see the flash go off, and then immediately you'd see the flash hit the wall behind it, since not only is the light moving backwards but the sphere is moving forwards to catch it.
From there the light hitting the edge would spread out to the sides, then reach the other side. Everything would reflect back, and it would meet back up with the original center point.
Now remember, the light is always coming off as a sphere. So when it gets to the halfway point, all the light coming from the light source would still be in a spherical shape from this perspective, centered around where the light flash originally appeared. Since this light reflection is a totally symmetrical event, this means that the light reflecting back is also a perfect circle, and when it reflects back it will all reach the center point at the same time.
You can think of the situation relative to the center point as a way of measuring a simultaneous moment. Everything reflects off the sphere at the exact same time, so you can define that as a single instant where everything happens at once. But because you see the light reflecting at different times from other perspectives, it means the instant of time itself is "moving" from one side to the other from some vantage point. Each plane of existence then represents a slightly different moment, with the past in one direction and the future in another direction. This is what resolves the ladder paradox. The "planes of simultaneity" defining the moment where the light reflects off will always move faster than the speed of light.
Here's something else that trips me out about relativity: Try to imagine what the world would look like from the point of view of a single photon traveling at the speed of light. I don't think that's actually scientifically meaningful, but if you were to put yourself in that vantage point you would see that it doesn't experience any passage of time. This has something to do with the fact that it is massless. From our point of view, a beam of light that travels to Earth from the Andromeda galaxy travels 4 million light years and doesn't seem to experience time passing. From the photon's point of view, it would start and finish its journey in the same moment, and the two galaxies would be length contracted until everything was on the same plane, perpendicular to how the photon was moving. It took no time at all because it was traveling a distance of 0.
When I was kid I heard that nothing could go faster than the speed of light, and I came up with an interesting thought experiment that would seem to contradict that. What if you built a track that went along the entire equator of the earth, and then connected wires along evenly spaced intervals that ran from the track to one of the poles? At the pole, you send out electrical signals that spin around at a rate faster than 8 times per second, and then once they reach the track it activates something like a lightbulb or an electrical motor. At the equator, the wave of incoming signals would appear to be moving faster than the speed of light.
I guess in retrospect it wouldn't need to be this big, but I came up with the idea for a sci-fi story or something.
Anyway, this almost works except for a few things:
1) If you tried to move an object using this method (say, by squeezing it or activating a magnet when the signal reached the track) it would require too much energy to actually move it to the speed of light
2) While you could get two things to activate at different times so that it looked like something was going faster than light, in reality you'd never be able to actually send information from one point to another that fast. If you were witnessing this scene from a fast-moving reference frame, the order of activation would get out of whack, so that parts of the wave on the track would appear to be moving backwards, due to the difference in the amount of time it takes for the signal to get from the pole to the equator. In this situation it's obvious that you can't send any information that fast, because one receiver would get the response before the other sent it.
The philosophical aspects of relativity become mind-boggling after you dwell on them enough. It's heavily connected with the big bang and the origin of the universe (an expanding or contracting universe is actually one of the conclusions of relativity.) The sphere of light that is emitted in a light flash is the thing I can't get my mind off of. It amazes me that everyone sees it as the same spherical shape. If you look into the sky with a powerful enough telescope, you can see objects as they were in the past, because the light takes so long to reach you. The further you look, the further back in the past you see. Eventually you get to a point where you're seeing the first light emitted in the universe, a few hundred thousand years after the big bang. The light from this flash started off with very high energy, and it has been slowly losing energy and increasing in wavelength over time, from gamma rays through all the different colors of visible light to microwaves. This is a red-shifting effect caused by the expansion of space.
If length contraction and time dilation applies to everything, that would seem to mean that at the "edge of the universe," all of the matter that is moving away from you would get more and more compressed the closer you got to light speed, and time would move more and more slowly.
So what's at the edge of the sphere? Could you ever actually reach that event horizon? In real life you can't, but imagine if there were something there, or imagine what happens as you approach that limit. Time moves more and more slowly the faster you go, so the light-sphere of the big bang itself would have to be experiencing no time passage whatsoever. So it's the same now as it was at the moment the univese started.
If it's in the same state now as it was when the universe started, then what determines its scale? The further you look outward, the more matter you can see, so it has to be "big" enough to encompass all that matter. So when the universe is 100 times older than it is now, the outer edge of this event horizon will be 100 times bigger and there will be more space in between, so it exists on that scale, and yet it also exists at the microscopic scale that it was at the beginning of time.
So...if it's in the same state now as it was when it was microscopic, then that state will be just as valid when it is 1000 times bigger and physics would seem to operate on a different scale. I guess everything would be expanded and there would be more space between the galaxies in future scales, but their trajectories would still be consistent with what happens at lower scales when the physical constants of the universe had different effects. I imagine it as an infinite fractal shape with no smallest unit of measurement.
This is the part that seems to take on religious significance, because it would mean that the moment of creation of the universe is frozen in time, the same now as it will be in a trillion years, and yet within the finite space you have an infinite universe with an eternal history playing out.
The "recombination" event, the earliest light we can see in the universe, happened about 300,000 years after the big bang. That would've essentially happened in the same moment everywhere, but just like the light reflecting off the sphere in my thought experiment, that moment is constantly moving away from us. So the further into the future you go, the bigger the sphere would be that determines a specific moment in the universe's history, and the more young galaxies you would be able to see. The older the universe gets, the more information you have about what the beginning was like for a bigger area, and yet reaching back to the very beginning would still be impossible. It may be fundamentally unknowable.
But does this event horizon I'm imagining actually exist? Without being an expert in the math, it seems possible that there could be an infinite amount of matter within a finite shell, as long as it got more and more contracted as you got closer to light speed at the right rate. Light speed would be the limit of the function, and you could get closer & closer but not actually get there.
On the other hand, from what I understand space itself can expand so that two points are moving away from each other faster than light, but the objects within that space still can't travel any faster. In this case, it would be possible for there to be some parts of the universe moving away so fast that there is no way for it to have any effect on us. If this is the case, then there is only a finite amount of matter than can interact with any given point in spacetime, even if "the whole universe" is infinite.
Whooooah, did I just blow your mind?
I could go on, but I'm starting to ramble more and more about stuff that I clearly don't know much about. Stop me before I start sounding like the TimeCube guy. It's fun to think about though.
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