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Time Dilation - mainly for you physics people.
Xano
Registered User regular
Registered User regular
Hey guys,
i need some help in understanding Special Relativity, mainly time dilation.
I'm having trouble in understanding how time can pass more slowly for someone approaching the speed of light ( c ), than for someone at a different reference frame at rest.
I'm thinking my difficulty is mainly coming from the fact that common sense is fooling me into thinking time is absolute. Hopefully you guys can explain it in simple terms for me, thanks!
i need some help in understanding Special Relativity, mainly time dilation.
I'm having trouble in understanding how time can pass more slowly for someone approaching the speed of light ( c ), than for someone at a different reference frame at rest.
I'm thinking my difficulty is mainly coming from the fact that common sense is fooling me into thinking time is absolute. Hopefully you guys can explain it in simple terms for me, thanks!
[SIGPIC][/SIGPIC]
Xano on
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Another way to consider it is to start with length contraction. You're compressing the space that holds objects. Since space and time are related dimensions, and you're processing more object-information in less space, time has to "expand" to accommodate for the shrinkage in space.
There's a bad joke somewhere in there. I just can't seem to find it between all these writhing manifolds.
Time dilation is bound up in the fact that there is a universal speed limit, c. I can't really tell you why it happens (maybe someone who's taken a modern physics course more recently than seven years ago can) but the effect is, you can attempt to accelerate to any speed you like to arrive at your destination in as short a time as you desire, and from your frame of reference you will succeed. The laws of the universe, however, prohibit anyone from moving faster than c. So from your perspective, the distance to your destination contracted, while from a stationary frame of reference it appears that time slowed down for you.
Light is only special inasmuch as it always travels at the maximum velocity. It's the properties of time and space which result in the universal speed limit, and light so happens to travel at that velocity.
Imagine a train. Now imagine that in that train, there's a light set up such that it bounces photons off of a mirror vertically, back to itself.
When the train is standing still, an observer in the train can measure the speed of the photons to be exactly C. Similarly, an observer outside the train also can measure those photons to be moving at exactly C. C is constant, and both observers see it that way.
Now, the train starts moving at a significant fraction of C. The observer on board the train can measure the velocity of the photons as being exactly C, right?
Now, take the observer who's outside the train. That observer sees the photon moving both vertically (bouncing between the light and the mirror) and horizontally (moving with the train). Since C is constant, the observer will see the photons still moving at C - but they're covering more distance. They can't go faster than C, since nothing can. But somehow, they're covering the vertical movement (bouncing between the light and the mirror) and the horizontal movement (movement of the train) in the same time for the external observer as they're covering for just the horizontal movement relative to the observer on board the train.
The only way to explain this (well, the easiest, at least) is that time is actually different on the train going near C than it is for a static external observer.
Assume, for simplicity's sake, that the photon's path can be described in a right triangle - a 3-4-5 will do nicely for explanation.
The observer on the train sees the photon travel 3 meters to the mirror, then 3 meters back to the light at C in x number of seconds. C is constant.
The static observer off the train sees the photon travel 5 meters to the mirror, then 5 meters back to the mirror at C in y number of seconds. C is constant.
Now, those photons can't be in two places at once. (Well, not for the purposes of this model.) So, the photon leaves the light at exactly 0 seconds. Both observers see the photon return back to the light at exactly the same time. Since the photon covered less distance relative to the observer on board the train, but C is constant, then less time must have gone by for that observer than for the external observer.
That's correct, no massive particle can travel at c. The equation you are looking for is E=mc^2 I think. There is another one with gammas and betas you use to do the calculation.
If the mirrors are on the floor and the ceiling of the carriage, and each "tick" is defined as the photon striking a mirror then you get different rates of ticking for the observer outside the train and inside the train by inspection (the photon moves at c in both cases but the distance travelled depends on where you stand).
Inside the train it just goes up and down, nice and simple.
Outside the train when you have to consider the carriage's motion. So when a photon strikes the bottom mirror it then moves upwards at speed c, but the top mirror is moving (in your frame of reference) so the photon has to travel further increasing the time between ticks.
Voilà, time dilation. If you don't get it then draw the systems, it'll be a line for inside the carriage and a triangle for outside.
Edit: Beaten with the train example.
I think brian greene put it best in "the elegant Universe".
Here's my paraphrase: Motion is equipartioned between all dimensions. I think this is a result of thermodynamics, but its been a while since ive looked at that. Think about just walking around your room. You you have a velocity as you walk about, and you are moving equally through an x dimension, a y dimension, and a z dimension(ie space appears 3d).
However special relativity tells us there is at least a 4th dimension(im a string theorist lol) that acts like time. You've got to therefore extend your equipartion principle to this time dimension. So, If i start Running around very quickly through space, more of my motion is being put into the physical dimensions, and time motion slightly slows down. This is why atomic clocks slow down every so slightly aboard jets. they are flying fast enough to move enough of their motion into physical dimensions; their motion through time decreases ever so slightly as a result.
So the crux of it is: You've a motion allowance that you have to expend between moving through physical dimensions and the time dimension: You move quicker through physical space your motion through the time dimension slows as a result.
Make sense? (I hope so)
What gives Light its wavelike property? Could it just be traveling through an even smaller medium? I'm not talking about the aether.
Shit, i'm not even making sense here lol
ocassionally smart guys think about what would happen if the speed of light is variable. I think at least Dirac investigated it. Currently I think there's some dudes at imperial college researching that.
photons are an elementary kind of particle, which means they aren't made of anything else. they're just photons.
wave-particle duality is "just" a statement that old timey definitions of particles and waves weren't good enough. you can have a bit of both.
edit: your questions are getting kind of spacey :P. I would say its just fundamental that light has wavelike properties. it also has particle properties. hence 'wave particle duality'. Depending on what sort of experiment you do, you can coerce light to behave like one or the other.
if i do a double slight experiment, ill get an interference pattern like normal waves.
if i try to mess around with the photoelectric effect, thats mostly a particle result.
these are both tied up into each other. If i set up my light source in the double slit experiment to just spit out a single photon at a time, you still get an interference pattern. the photoelectric effect depends on the frequency of the photon, a wavelike property.
Particle/wave duality doesn't just apply to light, it also affects massive particles.
Does that mean that if you're completely immobile, time is faster for you as well? Or does this only apply when put to tremendous speeds (approaching C), and doesn't really apply at slower speeds?
I'm curious now... and underprepared from a physics standpoint. I apologize if these are dumb questions.
And does this account for our motion due to us being on a moving planet that's revolving around a star that's in a moving solar system that's moving away from a possible central big bang point? For example, if we could determine the direction that's exactly parallel to the direction that we're moving away from the big bang, and shone a flashlight TOWARDS the big bang, would the speed of the light be C - (speed of our movement away from the big bang) to us, or would it still just be C?
It doesn't work like that; you can't point to the direction of the Big Bang. It's not an explosion but an expansion. Galaxies and such aren't traveling away from a central point; space itself is getting larger. Picture a balloon with galaxies drawn on it, then pretend you exist in 2d on the surface of the balloon. As you inflate the balloon, each galaxy moves away from the others, yet there isn't a central point of expansion on the surface. Something like this is happening in our universe, with an extra dimension.
Like if I had a string attached between two far away star systems, if the string was stretched over time that stretch would not be due to motion but rather a change in the definition of distance itself? Or would the string itself actually expand in size as well to compensate?
Or have I utterly confused myself? This is why I could never get beyond the applied physics classes. =(
a big result from the relativity theories is that there is no possible way to do this. you are always moving relative to something else.
if you could you do that sort of measurement(find out where the big bang is, and you cant), that transformation is still kind of off. That's called i think a galilean transformation, which is how you move through reference frames when you dont care about relativity. since we do care about relativity, you've got to use what's called lorentz transformations.
i love the questions i think id like to be a teacher when im out of grad school(reading papers is so boring).
edit: funkywaltdog's got the idea. thats basically general relativity. that spacetime is dynamcial. its kind of spooky. if you want more mathy definitions im down.
So can you figure out the time given space or any other unknowns?
This is correct, as far as I know. If you'd like a simpler example, go to about 5:45 on this clip of the Bill Nye show. He gives a simplistic example. It also continues on the next part, too.
you can do this for old person classical motion. Those rules are only good when you don't care about relativity, which means basically for slow stuff v<<c.
if you want to talk about fast moving business, v getting close to c, you have to use the ideas of proper length and proper time, which give the distance between to "frames' and time differences, respectively. if you use the formulas that go with those, then you can solve for whatever you like.
example!: the proper time equation looks like this t'=(1/gamma)t. gamma looks like this :=(1-v^2/c^2)^(.5). v is the speed two guys or whatever are moving wrt to each other. so with some funny algebra you can figure out whatever you like given other stuff.
im pretty sure the proper length equation looks the same.
See, that's what I was wondering about. Interesting... so if a theoretical object was moving at the speed of light (not that it's possible), a light shining from it wouldn't actually be shining at all, because it wouldn't be projecting forward from the object! Fascinating. Thanks for the clip!
Actually, I think that's the other way around. Because the speed of light will never change, even something moving at the speed of light will still shine light out as though it were standing still. That clip cuts out in the middle, so you need to go to the next one to finish it up.
lol, so you could never ever 'catch up' with light, even at speeds of 1(c).
i love magic.
But if it projected forward at the speed of (c) as you were moving at (c), wouldn't an observer on the ground then perceive the light as moving at 2(c) if that were true? And is that okay?
I'm going to stop asking questions here, I think I'm unintentionally derailing the H/A post. =(
Okay, so the observer would see light moving at exactly C (therefore, he would see the light moving WITH my theoretical vehicle, as opposed to zooming out in front of it)
Would I, as a passenger of said vehicle, see the light projecting out in front of me?
Say they were like car headlights.
Would I see the headlights projecting as normal, while people on the ground, or even people I pass, not see the headlights projecting at all (since they'd be moving at the same rate as the vehicle itself, and therefore never projecting beyond the actual bulb they are being emitted from, except to my eye because I'm in a vehicle moving at C along with it)?
It's not light that's special, it's that anything moving at c or a large fraction of it is subject to different rules.
Okay. I'm going to stew on that a while. Thanks for your patience, despite the fact that it wasn't my OP. I hate to do that, but I didn't want to make a new post on exactly the same subject while this one was still going.
a=(v1+v2)/(1+(v1v2)/c^2)). let me explain all the things.
v1 and v2 are the velocities of two participants as measured by some 3rd guy watching. a is going to be the correct relativistic velocity that each sees the other.
so if im watching you ride on your speed of light moving spaceship, v2=c. relative to the 3rd guy watching, i am not moving so v1 is zero.
plug all this stuff in a=(0+c)/(1+(0*v2)/c^2). so a=c, regardless of reference frame.
The crux of the matter is: relativity changed the old newtonian way of thinking about motion. This is consistent as well! lets say v1 and v2 are really small. Small number*small number=really small number. divide that by c^2 and you can ignore it. so in the low speed limit your transformation rules is a=v1+v2, the old everyday velocity rule, which is called a galilean transformation.
Ok. lets pretend that both VT and I have a stop watch.
I stay on earth while VT gets in his super cool Speed of Light Machine.
we both start our stop watches at the same time. VT takes his ship for a joy ride say... 1 Million KM away. and then comes back.
Now that we're both back on earth. what will each of our stopwatches say?
ie, we need more information