Noobish question on time dilation

[Übermensch]

Hm. I'll use the Twin Paradox to phrase me question. if you need a refresher, http://en.wikipedia.org/wiki/Twin_paradox

Everything I read about it seems to make a blatant claim that "the twin on Earth will be older". Are such texts missing the point, or am I?

Suppose I'm twin A (so I'm on Earth as the frame of reference). My brother, B, is orbiting the Earth near light speed. Of course, from my inertial frame, I'm stationary and he's moving. It seems to me as if time moves slower for him. So when he sends me a picture of himself each year, I'm surprised how young he looks. Great, so good so far.

But let's start from the beginning again. This time, I'm B. The Earth seems to be moving around me near the speed of light. Naturally, time seems to be going slow for them. So, when I receive a picture of my brother each year, I'm surprised to see that HE is the younger one.

Yet, I've generally read that the twin that leaves Earth is objectively younger-- which assumes that the Earth's frame of reference is the most important.

On a similar note, suppose I orbit near light speed with a clock. When I get back, I find that Earth's clocks are all behind mine, since the Earth was moving rapidly compared to my inertial frame. Yet, my boss who sent me up on the mission will look at my clock and tell me that it's behind, right? So if we put the clocks side by side and look at them, then what?

Sorry, just started with this branch of physics an hour ago or so. But, I wouldn't be able to get sleep tonight without asking.

 

[yenchin]

You should search the forum, there have been many threads on this. After reading those, if you still have question, you are welcome to ask again.

 

[Wallace]

There are many ways to view the resolution of this apparent paradox, as suggested do a search on 'Twin paradox' and there are some good links and explanations given.

One key thing to realize is that the classic 'twin paradox' is not a situation in which two observers move at a constant speed with respect to each other, one of the paths accelerates while the other does not, meaning that the experiences of the two observers are not the same.

If you had two people who simply move past each other very fast then they both see the others time running slower in the way you suggest, however this is not the classic twin paradox since in that case one of the observers turns around and comes back while the other does not. You could argue that in the rest frame of the twin who leaves the Earth the Earth 'turns around and comes back' however the twin on the rocket would feel the non-inertial force of the rocket firing whereas the twin on Earth does not experience such a force. Hence the paths are different. By the way the Wiki page pretty much explains all of this, but have a look at some of the links given previously as well.

 

[jcsd]

Bascically someone traveling at constant velocity has worldine in spacetime that is analgous to a straight line. Between any two staright lines there's always an axis of symmetry; for two observers traveling at constant velocity time dilation is symmetric.

An obserever that is accelrating has a worldline that is analagous to a curve (or more properly a curve that is not a straight line). For a straight line and a curve there is an axis of symmetry between the straight line and every line that is tangent to the curve, but there is no axis of symmetry between the curve and the straight line. Simlairly time dilation is not symmetric for an accelrating and non-accelerating observer.

 

[JesseM]

Suppose I'm twin A (so I'm on Earth as the frame of reference). My brother, B, is orbiting the Earth near light speed. Of course, from my inertial frame, I'm stationary and he's moving. It seems to me as if time moves slower for him. So when he sends me a picture of himself each year, I'm surprised how young he looks. Great, so good so far.

But let's start from the beginning again. This time, I'm B. The Earth seems to be moving around me near the speed of light.

But you're leaving out the part that if B is orbiting, B does not have a single inertial rest frame--only moving in a straight line at constant speed is "inertial" motion, anything else involves G-forces. The laws of SR are only symmetrical between inertial frames, there is no such symmetry between non-inertial ones.

 

[Übermensch]

I did a search, but it didn't clear up my issue, I might actually just be too dumb.

So, I understand know *what* happens, but I'm not completely sure why. Let's pretend I never said it was orbiting. I thought that would make it easier, as I haven't taken much of a look at gravity's role in GR yet.

If B was receiving a movie from Earth of A(ignore the physical problems of this). What would he see when he accelerated? Would A just suddenly become older while B instantly accelerates? Since time always seems normal for B, doesn't this mean that Earth would have to seem to speed up?

Perhaps answering another similar question would help. I'm traveling in a single inertial frame towards planet Z(near the speed of life). They've been watching me come for hundreds of years. To them, I've shown no sign of aging whatsoever.

However, to me, planet Z is moving towards me near the speed of light, and I'm perfectly still. They show no signs of aging. Yet, since I'm in my own inertial frame, I age normally. I can't "do more i my life" than anyone else. Thus, I die of old age long before I get to planet Z. Yet, according to the people on planet Z, I couldn't have aged (thus died), as no time seemed to pass, right?

 

[JesseM]

I did a search, but it didn't clear up my issue, I might actually just be too dumb.

So, I understand know *what* happens, but I'm not completely sure why. Let's pretend I never said it was orbiting. I thought that would make it easier, as I haven't taken much of a look at gravity's role in GR yet.

If B was receiving a movie from Earth of A(ignore the physical problems of this). What would he see when he accelerated? Would A just suddenly become older while B instantly accelerates? Since time always seems normal for B, doesn't this mean that Earth would have to seem to speed up?

In SR the rate you see a moving clock ticking using light-signals is different from the rate it actually is ticking in your frame, since signals from successive ticks of the clock have a different distance to travel to reach your eyes because of the object's movement. For example, if a clock is moving at 0.6c away from me, then in my frame it's ticking at $$\sqrt{1 - 0.6c^2/c^2}$$ = 0.8 the rate of my own clock, so it only ticks once every 1/0.8 = 1.25 seconds. But in 1.25 seconds, it will have moved a distance of (1.25 s)*(0.6c) = 0.75 light-seconds, so if it's moving away from me the light from a given tick takes 0.75 s longer to reach me than the light from the previous tick, meaning I only see the ticks every 1.25 + 0.75 = 2 seconds, while if it's moving towrds me the light from a given tick takes 0.75 s less time to reach me than the light from the previous tick, meaning I see the ticks every 1.25 - 0.75 = 0.5 seconds. So if the clock is moving away from me I see it ticking twice as slow as my own, and if it's moving towards me I see it ticking twice as fast as my own, but in both cases if I factor out the signal delays I'll calculate that it's really ticking 1.25 times as slow as my own. This visual change is known as the "Doppler shift", you can see here that in general the frequency I observe is $$\sqrt{\frac{1 + v/c}{1 - v/c}}$$ times the frequency of the signal in the emitter's frame, so if a clock is sending out signals at 1 tick per second in its frame and it's moving at +0.6c (positive meaning it's moving towards me), this equation tells me I'll see it ticking at $$\sqrt{\frac{1 + 0.6}{1 - 0.6}}$$ = $$\sqrt{4}$$ = 2 ticks per second, or twice as fast as my own clock, the same result I got above.

So, in the twin paradox, each twin will see the other twin's clock ticking slow before the turnaround when they're moving apart, and fast after the turnaround when they're moving towards each other. John Baez's page on The Twin Paradox has a subsection devoted to The Doppler Shift Explanation which shows what each twin actually sees throughout the process, and there's a nice spacetime diagram of when each twin's light-signals reach the other in fig. 2 of the Too Many Explanations section, I recommend taking a look at them.

Perhaps answering another similar question would help. I'm traveling in a single inertial frame towards planet Z(near the speed of life). They've been watching me come for hundreds of years. To them, I've shown no sign of aging whatsoever.

However, to me, planet Z is moving towards me near the speed of light, and I'm perfectly still. They show no signs of aging. Yet, since I'm in my own inertial frame, I age normally. I can't "do more i my life" than anyone else. Thus, I die of old age long before I get to planet Z. Yet, according to the people on planet Z, I couldn't have aged (thus died), as no time seemed to pass, right?

In this case, since you didn't start at a common location, you have to worry about the issue of "simultaneity", meaning that different frames disagree about whether two events at distant locations happened at the "same time" or "different times". Say you're moving towards Z at 0.6c again, and say that in your frame, when you turn 30 you're 15 light years away from them, and that "Zed" on the planet is turning 30 "at the same time" in your frame. 25 years later according to your clock, you've traveled (25 years)*(0.6c) = 15 light years, so you're finally arriving at the planet, aged 30+25 = 55 years old, and you find that Zed has only aged 0.8*25 = 20 years, so he's only 50 years old. However in the Z frame the event of Zed turning 30 and your turning 30 were not simultaneous, instead the event of his turning 30 was simultaneous with the event of your turning 39, so in 20 years according to his clock, you've only aged 0.8*20 = 16 years, explaing why you're 39+16 = 55 years old when you arrive.

Now suppose there is another fellow Zeke on the planet who is turning 30 at the same time you turn 30 in the Z frame. He will actually be 11.25 years older than Zed, at an age of 61.25 when you finally arrive; he's aged 31.25 years, while you've only aged (31.25)*(0.8) = 25 years in the Z frame. In your frame you and Zeke did not turn 30 at the same time, instead you turned 30 when Zeke was already 41.25 years old (remember that you and Zed both turned 30 at the same time in your frame, and Zeke is always 11.25 years older than Zed), so in the 25 years it took you to reach the planet, Zeke only aged 25*0.8 = 20 years, bringing his age up to 61.25.

So, we see that in all these cases everyone agrees about how old each person is when they meet at a common location--there can be no disagreements about events which happen in the same local region of spacetime in relativity--but they disagree about who was aging slower during the trip, and this is connected to the fact that they disagree about the simultaneity of distant events.

 

[yogi]

I did a search, but it didn't clear up my issue, I might actually just be too dumb.

Perhaps answering another similar question would help. I'm traveling in a single inertial frame towards planet Z(near the speed of life). They've been watching me come for hundreds of years. To them, I've shown no sign of aging whatsoever.

However, to me, planet Z is moving towards me near the speed of light, and I'm perfectly still. They show no signs of aging. Yet, since I'm in my own inertial frame, I age normally. I can't "do more i my life" than anyone else. Thus, I die of old age long before I get to planet Z. Yet, according to the people on planet Z, I couldn't have aged (thus died), as no time seemed to pass, right?

You are not going to get a satisfying answer to this question because there is a mix of observational times and actual aging that is going on - Einstein first treated the problem of two separated clocks synchronized in one frame and then predicted the time difference between the two clocks when one was put in motion toward the other and they were compared when they came together (Part IV of his 1905 paper). The clock put in motion will read less. Different authors explain the phenomena in different ways - some using SR only, others insisting that the fact of putting one clock in motion requires General Relativity.

 

[pervect]

I did a search, but it didn't clear up my issue, I might actually just be too dumb.

So, I understand know *what* happens, but I'm not completely sure why. Let's pretend I never said it was orbiting. I thought that would make it easier, as I haven't taken much of a look at gravity's role in GR yet.

If B was receiving a movie from Earth of A(ignore the physical problems of this). What would he see when he accelerated? Would A just suddenly become older while B instantly accelerates? Since time always seems normal for B, doesn't this mean that Earth would have to seem to speed up?

Perhaps answering another similar question would help. I'm traveling in a single inertial frame towards planet Z(near the speed of life). They've been watching me come for hundreds of years. To them, I've shown no sign of aging whatsoever.

However, to me, planet Z is moving towards me near the speed of light, and I'm perfectly still. They show no signs of aging. Yet, since I'm in my own inertial frame, I age normally. I can't "do more i my life" than anyone else. Thus, I die of old age long before I get to planet Z. Yet, according to the people on planet Z, I couldn't have aged (thus died), as no time seemed to pass, right?

It might help you to focus on what you observe, before you start interpreting it.

If someone had a giant clock, and you moved towards them at a high velocity, if you looked through a telescope you would see the clock hands spin around rapidly. Similarly, if they transmitted a video signal, it would when watched in real time appear to be moving rapidly.

If you move away from someone, the clock appears to run slowly - the video also appears to run slowly.

In fact, the speedup / slowdown factor, k, depends only on your relative velocity. This is the basis for Bondi K-calculus, which I'm not going to explain here, but you might want to look up sometime. (If you want a specific book title, try "relativity and common sense" by Bondi. It's a cheap dover paperback, you might also find it at your local library).

The accelerating case is also fairly simple - as you left, you would be moving away, and hence see everything in slow-motion. When you started to turn around, there would never be any discontinuity in what you saw, but you'd see it gradually speed up, reaching normal speed when you reach zero velocity, and going up to a high rate as you start to move towards the planet.

The idea of "time dilation" occurs when you interpret what you actually see in terms of a coordinate system, by subtracting the estimated "trip time" of the signals to come up with a time coordinate for events.

So, for instance, if you are approaching a planet at a very high speed, you will seem them moving very quickly, but you will estimate that almost all of this quickness is due to the fact that the distance between you and the planet is decreasing rapidly. When you correct for this by imposing your own ideas of simultaneity, you find that the rate of aging on the planet after corrections is slowed down.

 

[Übermensch]

Aha, sorry for disappearing. I ended up having surgery, and after the weeks in bed, I just forgot about this.

On a brighter note, I'm feeling I understand this much better now. The Zeke and Zedd story was quite a nice way to explain it. Thanks. :)