> Does speed slow down time or is it acceleration that does it?
Both are involved. If you take a long voyage at near-lightspeed, you leep losing time as long as you continue at that speed. Time doesn't just 'look like' it's slowing down -- it really is. If you check your watch against standard time every time whenever you pass a planet, you find your watch IS losing time. There's experimental evidence for that. Atomic clocks aboard moving satellites do lose time. Particles which would normally decay quickly reach Earth from space undecayed, because high velocity slows down their decay. The same thing happens in particle accelerators.
HOWEVER, acceleration does play a role. Consider the Twins' Paradox. One twin travels to a distant star at near-lightspeed. The other twin stays home. How does relativity 'know' which twin is supposed to age? The answer is that one twin accelerates; the other twin doesn't.
Most explanations of the Twins' Paradox leave out the acceleration, because that's the hard part to calculate. There's a simplified Special Theory of Relativity, covering the special case of coasting objects. When an object coasts, it has its own "inertial frame of reference". For the more general case where an object accelerates / decelerates, there's the General Theory of Relativity, which has been experimentally tested in particle accelerators.
For coasting objects, there's a simple way to derive the slowdown of time. You start with the remarkable fact that the speed of a given light beam is the same passing any observer -- including you. Imagine a thought experiment in which you're traveling at near-lightspeed, being observed by someone who isn't. Instead of a watch, you carry a meter stick with a perfect mirror on each end. Light bounces continuously between the two mirrors -- one bounce, one tick. The distance between mirrors is exactly one meter, so the clock has to be accurate.
However to a stationary observer, your meter stick isn't stationary -- it's moving through space. The light bouncing back and forth between the two mirrors isn't stationary either -- it's zig-zagging through the stationary observer's frame of reference. Because you're traveling at near-lightspeed, the zig-zag path of the light is highly elongated. Yet the stationary observer clocks the zig-zagging light at C. Hence, since the light must cover extra distance on each zig-zag, the stationary observer sees the light taking longer to bounce between the 2 mirrors. Neither observation is an illusion -- you can plot what happens on a piece of graph paper, including the light's actual zig-zag path through space. That's how it's explained in _Feynmann's Lectures on Physics_
http://en.wikipedia.org/wiki/Feinmann.
Most of Special Relativity can be derived from the single fact that light always passes an observer at the same speed, no matter how fast the observer is moving. It doesn't matter whether the observer is on a moving planet, or whether the source of the light is a receding galaxy, or a receding space probe.
The speed of light is always OBSERVED to be constant
That means, said Einstein, that space and time really aren't the "absolutes" we imagine them to be. Simultineity is also an illusion, said Einstein -- there's no such thing as universal 'now', because time passes at different rates depending on where you are in, say, a galactic gravity well, and how fast you're going. Two events can only be simultaneous if they happen at the exact same place and time. That's why you reset your watch when you pass a planet -- you can only be sure it's the same time if you're right there.
There is however an "invariant spacetime INTERVAL" between any two events. Suppose you place two firecrackers in space a certain distance apart, set to go off ten seconds apart. To a stationary observer in the same frame, the interval between flashes is 10 seconds -- simple. In a moving observer's frame of reference, the time interval between flashes is distorted, plus the firecrackers have moved. Yet all observers, moving or not, get the same answer for the "invariant spacetime interval" between the two flashes -- square_root ( distance-squared minus time-difference-squared ), or sqrt ( x^2 + y^2 + z^2 - t^2 ). Yhat's just the Pythagorean formula for distance, but with a timelike component. In other words spacetime is real, but space and time separately are not. Space and time only SEEM separate if you're not moving -- if you are moving, space and time shift in a coordinated way, but invariant intervals remain constant. That's why you can use intervals as a measuring tool, such as the events generated by a bouncing beam of light hitting 2 mirrors.
Invariant intervals between EVENTS are like the gold standard of special relativity -- they always work. The trick is to forget about the firecrackers themselves and just look at EVENTS that you know actually happened at a particular point in spacetime. Different observations of the same EVENTS can then be reconciled using the invariant interval. The only catch is that observers can't necessarily reconstruct a SEQUENCE of events, because in some frames of reference the 'wrong' firecracker goes off first.
That's the big deal about Feynmann diagrams, which show only the EVENTS where, say, 3 particles collide like billiard balls. Those events are the only things the experimenters can be sure of, because they measured the angles of the flying particles from cloud-chamber tracks, point-of-detection and so on. reconstructing 2 or 3 spacetime EVENTS is a lot easier than trying to figure out how time and space looked from the standpoint of each particle in the act of bouncing off others, which is relativistically hairy.
A similar thing happens in quantum mechanics -- good experimental readings can be gotten on key EVENTS, but in between the events is a superposition of states -- useful, but hard to follow.
In both relativity and quantum mechanics, you have to 'stalk' the observation you want and set it up. That's why Einstein devised simple thought-experiments. He said in essence "OK look, since light is ALWAYS observed to overtake an observer at the same speed, how would that work if you're aboard a really fast train with a signal-flashlight and a stop-watch?" He gor some really strange answers, but they were CONSISTENT answers. When Einstein was asked if he thought other physicists would accept it, he said "They'll have no choice but to accept it" [because the constancy of the speed of light DICTATED how relative space and time had to come out -- there was no wiggle room].
Thought experiments are enormously powerful, when you find the right one to 'nai' a point. Einstein said in essence "start with what you know and have incontrovertible proof of, that light always overtakes at the same speed." That grabs the bull by the horns. Imagine if no matter how fast you were driving, you always blow past a traffic cop at 55, even if the cop is doing 54.
"Relativity defense yeroner -- my client didn't break the speed limit because nature doesn't let you break the speed limit." The cops wouldn't stand for that -- they'd paint stripes on the highway, they'd watch mile markers from chase helicopters, they'd collect evidence -- and Einstein would always get off. That's essentially what happened after Einstein published. There was no way to break special relativity without breaking the constancy of the speed of light in vacuum, which refuses to bend. If you put enormous energy into the tiniest of particles trying to break the light barrier, all you get is more relatibity -- which 'conspures' to keep the speed of light invariant in any frame of reference, almost all of which are experimentally reachable in particle physics.
More generally, it's always a good idea to "start with what you know" experimentally, and reason from there. That narrows down the problem. In mathematical physics, provable experimental facts are called boundary conditions -- they shape the problem for you [and in the case of special relativity, nail down the outcome]. If you don't start by collecting everything you know, you get lost in an infinity of possible mathematical universes, all of which describe SOME universe -- but not the one we live in.
This is an important point -- pure math can come up with solutions that don't apply to THIS reality, if you don't input all the conditions. Say for instance you're studying quadratic equations in school, and trying to solve an area problem. The math says you need either five yards by 4 yards of carpet, OR you need minus five by minus four yards. If you have a mathematical mind, you maybe go down to the carpet place and say "I need a negative yardage of carpet, sso the store has to pay me. The clerk, who also has a mathematical mind, says "No, minus four yards times minus five yards is still plus 20 square yards, so you have to pay us."
Yhe same thing happens in physics. Amateurs often seize on some particular ASPECT of an observed phenomenon, and try to "interpret" that into an 'alternative theory' -- which only works for selling books to amateurs. A professional says "Look, nature works a certain way, it consistently follows certain equations, which we can't break no matter how much energy we throw into a particle accelerator or find in a cosmic ray. We just have to find which equations nature is using, and see if there are any loopholes we can exploit. If no loopholes show up, we can still try to break conventional limits by pushing the extremes of physics -- looking at the very large / very small / very cold / very dense or very tenuous / exotic matter / whatever -- but our starting point has to be what nature unfailingly does, what quantities it preservs ( mass-energy, momentum, invariant interval etc. ) and so on. An Einstein-caliber mind then says "What ELSE is nature hiding in plain view. This speed-of-light constancy thing, how thoroughly has that been nailed down experimentally, has anyone worked out the implications, does that leave us with any wiggle room. OK, so there's maybe some wiggle room left along the boundary between relativity and quantum mechanics, because the same particle can be in 2 places at once (double slit experiment), the same particle can interfere with itself (UV lasers), and particles can be entangled at a distance. If we go there we have to grab the bull by the horns because there might be an inconsistency in our presumption of either causality or locality, if a particle can be its own causality or do stuff at a distance. Last time we grabbed the bull by the horns we had to give up the absoluteness of space and time, and then quantum mechanics came along and trashed determinism, but we came out ahead because the quantum weirdness made solid-state electronics work, so now we've got fast enough computers to sort out more weird experiments."
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"You can't get there from here." -- Snuffy Smith.