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# Time Dilation - mainly for you physics people.

Registered User regular
edited December 2008
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!

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Xano on
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Registered User regular
edited December 2008
I just took a class on this and I'm still not 100% on it, but what I think is essential to grasp is that time is a dimension. Not in the sense that it is the mystical plane where you fight demons, but in the sense of measurement, and since all measurements are relative to one another, as you approach the speed of light, which IS absolute, time slows to accommodate length contraction and relative simultaneity.

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.

The Cow on
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Columbia, SCRegistered User regular
edited December 2008
The key to understanding relativity is to accept the fact that there's no such thing as an omniscient, omnipresent observer. If you try to sort things out from every frame of reference at once you will give yourself a headache. The idea is to pick one frame of reference at a time and sort out what an observer there is experiencing.

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.

FunkyWaltDogg on
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Registered User regular
edited December 2008
why must time and space accommodate light? Why is light so special?

Xano on
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Columbia, SCRegistered User regular
edited December 2008
Xano wrote: »
why must time and space accommodate light? Why is light so special?

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.

FunkyWaltDogg on
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Registered User regular
edited December 2008
I'll try this out - see how well I can remember my HS physics teacher's explanation, which spelled it out nicely for me. Of course, that's 15 or so years ago, so I might fail horribly.

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.

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Registered User regular
edited December 2008
Also, I think the speed of light is a limit...but mathematically. As in you can approach it...but never reach there. It has to do with this equation that says as speed approaches light ( c ), mass approaches infinity. However, an infinite force is required for this mass...and obviously an infinite force is impossible.

Xano on
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Columbia, SCRegistered User regular
edited December 2008
Xano wrote: »
Also, I think the speed of light is a limit...but mathematically. As in you can approach it...but never reach there. It has to do with this equation that says as speed approaches light ( c ), mass approaches infinity. However, an infinite force is required for this mass...and obviously an infinite force is impossible.

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.

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We are only now beginning to understand the full power and ramifications of sexual intercourse Registered User regular
edited December 2008
The best way to think about it is to consider a clock made from a photon bouncing between mirrors on a train.

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.

Mojo_Jojo on
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Registered User regular
edited December 2008
So if two people start out at opposite ends of the universe, and move to intercept at light speed, they would be closing at 2x lightspeed? And rather than let that happen the universe just....throws up on them and you get a freaky time effect?

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Registered User regular
edited December 2008
mathematical physicist here!

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)

Fuzzywhale on
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Registered User regular
edited December 2008
is light really the "Universal Speed limit" ? What about smaller particles than light - I know they haven't been proven. I mean, light has a dual property of both particle/wave right? Doesn't the dual property mean there has to be something even smaller?

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We are only now beginning to understand the full power and ramifications of sexual intercourse Registered User regular
edited December 2008
The first chapters of The Elegant Universe were indeed a very good read. The problem was that once he gets onto String Theory he loses the thread and can't find the balance between saying something useful and something accurate.

Mojo_Jojo on
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We are only now beginning to understand the full power and ramifications of sexual intercourse Registered User regular
edited December 2008
Xano wrote: »
is light really the "Universal Speed limit" ? What about smaller particles than light - I know they haven't been proven. I mean, light has a dual property of both particle/wave right? Doesn't the dual property mean there has to be something even smaller?
Why would "smaller" mean faster?

Mojo_Jojo on
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Registered User regular
edited December 2008
I think i phrased my question wrong, I just got lost in thought i guess.

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

Xano on
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Registered User regular
edited December 2008
The physics community most universally agrees that light is the 'universal speed limit'.

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.

Fuzzywhale on
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Columbia, SCRegistered User regular
edited December 2008
Xano wrote: »
I think i phrased my question wrong, I just got lost in thought i guess.

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

Particle/wave duality doesn't just apply to light, it also affects massive particles.

FunkyWaltDogg on
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Registered User regular
edited December 2008
Fuzzywhale wrote: »
mathematical physicist here!

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)

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?

VThornheart on
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Registered User regular
edited December 2008
Man, i just had like 50 epiphanies from reading these explanations. They are really starting to sink in.

Xano on
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Columbia, SCRegistered User regular
edited December 2008
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.

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Registered User regular
edited December 2008
Oh, I see... so that expanding motion isn't really "motion" (as in, it's not acceleration or velocity), it's the actual... notion of distance itself expanding? Or is that taking the notion of expansion too far?

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. =(

VThornheart on
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Registered User regular
edited December 2008
if you could be absolutely immobile, then you could screw with your motion through the time dimension.

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.

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Registered User regular
edited December 2008
space/time = c right? So time = space/ c ?

So can you figure out the time given space or any other unknowns?

Xano on
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Registered User regular
edited December 2008
any given observer will measure the speed of light from his point of reference to be c. Things do indeed get all kinds of confusing, "common sense" doesn't work so well for relativity.

Dman on
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Decorative Monocle Registered User regular
edited December 2008
I'll try this out - see how well I can remember my HS physics teacher's explanation, which spelled it out nicely for me. Of course, that's 15 or so years ago, so I might fail horribly.

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.

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.

Terrendos on
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Registered User regular
edited December 2008
Xano wrote: »
space/time = c right? So time = space/ c ?

So can you figure out the time given space or any other unknowns?

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.

Fuzzywhale on
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edited December 2008
AH! I love Bill Nye!

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! It's hard to envision, but I can sort of picture it.

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Decorative Monocle Registered User regular
edited December 2008
AH! I love Bill Nye!

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! It's hard to envision, but I can sort of picture it.

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.

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edited December 2008
Oh... hmm, let me see if I can find the next part of it. If that's how it goes, I definitely had it wrong.

VThornheart on
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edited December 2008
Terrendos is right, c is constant remember. Light would be projecting forward from you at the same speed.

lol, so you could never ever 'catch up' with light, even at speeds of 1(c).

i love magic.

Xano on
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Decorative Monocle Registered User regular
edited December 2008
Yeah, I try to be wary about talking about that kind of thing, because it really takes a doctorate in the subject to know exactly what's going on there, and I've only taken a year's worth of college physics myself so I'm barely qualified.

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Registered User regular
edited December 2008
Xano wrote: »
Terrendos is right, c is constant remember. Light would be projecting forward from you at the same speed.

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. =(

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Decorative Monocle Registered User regular
edited December 2008
No, see that's why light is so special. It is exempt from the additive properties of normal velocities. The observer in your example would see the light moving at exactly C. That is why time cannot remain constant.

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edited December 2008
Ack... I hope this is okay for me to respond. I know it wasn't my OP, but it's a really fascinating subject... and I seem to be getting deeper into it rather than figuring it out.

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)?

VThornheart on
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Decorative Monocle Registered User regular
edited December 2008
Theoretically speaking (obviously we can't know for sure) you would see the headlights project out ahead of you, just as though they were moving at 2C. But for the person who was watching the light come at him, it would be moving at 1C. Since v = d/t and the distance we absolutely know to be the same, the best explanation for the discrepancy is that time is a non-constant.

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Columbia, SCRegistered User regular
edited December 2008
Terrendos wrote: »
No, see that's why light is so special. It is exempt from the additive properties of normal velocities. The observer in your example would see the light moving at exactly C. That is why time cannot remain constant.

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.

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edited December 2008
Ahhh, which brings us back to it. Now I see where part 3 fits in with that.

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.

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edited December 2008
einstein answered this question: he came up with the proper relativistic rule for velocities. Looks like this!

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.

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edited December 2008
Terrendos wrote: »
No, see that's why light is so special. It is exempt from the additive properties of normal velocities. The observer in your example would see the light moving at exactly C. That is why time cannot remain constant.
Thinking of it as exempt from the additive properties is misleading - it isn't at all, but light isn't like a ball you throw, it's a waveform. Think of ripples caused by a boat - they're created by the boat's motion, but the speed they travel at is constant relative to the water - that's why you get wakes, that's when the boat travels faster than the waves so they end up on top of each other. Waves travel at a fixed speed relative to their medium, regardless of the speed of their source.

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edited December 2008
@ Fuzzywhale

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?

"we're just doing what smalllady told us to do" - @Heels
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edited December 2008
@ Fuzzywhale

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?
For this, you need general relativity and non-inertial frames of reference, because here the differences depend on the accelerations each individual underwent.