Exploring Time Relativity with Identical Twins: Sam & Pam

[SpY]]

First check that I am formulating it correctly:
Sam and Pam are identical twins.
In 2000, Sam departs on a 20-light year journey at the speed of light (hypothetically). When she returns (travelling a total of 40-light years) she finds Pam in 2040, being 40 years older than she is (physically, ie. wrinkles).

My first question is how much time passed for Sam? For Pam, the observer, it's 40 years. Would Pam have experienced 40 years (in her frame of reference) while traveling at the speed of light? If so, then her organs should also have aged 40 years... just as Pam.

Another way of saying this: as a person approaches the speed of light, does time slow down for them relative to the frame of reference they are traveling in, but time within their own frame remains unchanged?

If you saw that silly movie 'clockstoppers', the guy who moves at the speed of light (equivalent to Sam) appears older when he returns to proper time (so he would be older than his identical twin). Did they get Special relativity wrong?

 

[mathman]

If Sam goes on this journey at the speed of light (or close to it), then essentially no time passes in his frame. He is experiencing time and length dilation, so the 20 light year distance gets shrunk to almost 0 in his frame, and the time elapsed shrinks accordingly.

 

[harrylin]

Hi did you search the forum for "twin paradox"?
Anyway, the short answer is that if you travel at the speed of light (which you cannot reach!), your biological clock stops running.

Note that accelerating frames are not valid reference frames in SR, and distance clocks in an accelerating frame must continuously be re-synchronised - it's even a way that you could measure your acceleration.

I did not see that movie, but the way you tell it, it does sound wrong.

 

[JesseM]

First check that I am formulating it correctly:
Sam and Pam are identical twins.
In 2000, Sam departs on a 20-light year journey at the speed of light (hypothetically). When she returns (travelling a total of 40-light years) she finds Pam in 2040, being 40 years older than she is (physically, ie. wrinkles).

You can't accelerate a massive object to the speed of light, it would take an infinite amount of energy. But if, relative to some inertial frame you have a speed of v which is some significant fraction of light speed, then relative to the time coordinate of that frame your aging is slowed down by a factor of $$\sqrt{1 - v^2/c^2}$$ (c is the speed of light). For example, if you travel at 0.6c relative to Earth then your aging is slowed down by a factor of sqrt(1 - 0.6^2) = 0.8 relative to the Earth, so if you travel at that speed for 40 years in the Earth frame, when you return you will only have aged 32 years.
[QUOTE='SpY]Another way of saying this: as a person approaches the speed of light, does time slow down for them relative to the frame of reference they are traveling in, but time within their own frame remains unchanged?[/quote]
Yes, in fact the very notion of "approaching the speed of light" can only be defined relative to a particular inertial frame, if a ship is moving away from the Earth inertially at 0.99c in the Earth's frame, it's just as valid to adopt the perspective of a frame where the ship is at rest and it's the Earth that's moving at 0.99c. If either of them accelerates and changes velocities (which would be necessary in order for them to reunite and compare ages at the same spot), then all inertial frames agree which one accelerated, and no matter which frame you use to do the calculation you always find that the one that accelerated aged less when they reunite than the one that moved inertially between both meetings.
[QUOTE='SpY]If you saw that silly movie 'clockstoppers', the guy who moves at the speed of light (equivalent to Sam) appears older when he returns to proper time (so he would be older than his identical twin). Did they get Special relativity wrong?[/QUOTE]
I only saw bits of that movie on TV (didn't Riker from Star Trek direct it? Oh Riker...), didn't know they ever "explained" the clocks in terms of relativity, but from what you say it does sound like they got it wrong.

 

[SpY]]

Strange thing about SR is I understand it one second, then confuse it another :/
I know it's impossible to reach the speed of light, but hypothetically if one did, then they could 'freeze time' of the frame with respect to which they are moving.

Hi did you search the forum for "twin paradox"?
Anyway, the short answer is that if you travel at the speed of light (which you cannot reach!), your biological clock stops running.

Okay suppose his speed is just 0.9999c, so then his biological clock wouldn't "freeze" it would "slow down tremendously" right? This slow factor would only be between him and an external observer: he wouldn't notice any change in his frame of reference. To him, him heartbeat would be say 60bpm, but an observer would see 71x60bpm - from the time dilation formula, γ=71. His twin (observer) would have a heartbeat 71x greater than him, which is why the twin ages faster. (Am I right up to here? Or did you mean that even to him, his biological clock would almost stop?)

If he was traveling at that speed and he could still observe his twin, he would see her age 71 years in 1 year of his time. To him, events seem to be happening faster than if he was in that frame... this doesn't seem right ;(

 

[JesseM]

Okay suppose his speed is just 0.9999c, so then his biological clock wouldn't "freeze" it would "slow down tremendously" right? This slow factor would only be between her and an external observer: he wouldn't notice any change in his frame of reference. To him, him heartbeat would be say 60bpm, but an observer would see 71x60bpm - from the time dilation formula, γ=71.

The time between beats would increase by a factor of 71 as measured by the observer, but this means the number of beats per minute would shrink by a factor of 71, so the observer would only measure his heart to beat 60/71 = 0.845 beats per minute.

His twin (observer) would have a heartbeat 71x greater than him, which is why the twin ages faster. (Am I right up to here?)

In the observer's frame, the observer's own heart would beat 71x faster than the slowed-down rate of the traveler, but this wouldn't be true in other frames (for example in the traveler's own frame it's the observer's heart that's slowed by a factor of 71)

If he was traveling at that speed and he could still observe his twin, he would see her age 71 years in 1 year of his time. To him, events seem to be happening faster than if he was in that frame... this doesn't seem right ;(

No, as long as both are moving inertially (not accelerating) all effects are completely reciprocal, if A sees B's heart slowed down then B also sees A's heart slowed down. You do have to distinguish between what's measured in a frame and what's actually seen visually though--visual rates of heart beats/clock ticks are also influenced by the Doppler effect.

 

[SpY]]

The time between beats would increase by a factor of 71 as measured by the observer, but this means the number of beats per minute would shrink by a factor of 71, so the observer would only measure his heart to beat 60/71 = 0.845 beats per minute.

Is it only the measurements that are relative, or the actual events? If t is the time for the traveller (proper time) and t' is for the observer, t' =71t . Then is it correct to say that for every heartbeat of the traveller, the observer's experiences 71 heartbeats (or is it other way ><). This explains how the observer will end up being older, but it seems like the traveller will be moving in slow motion (1 heartbeat in 71 heartbeats of the observer)? I really get confused back and forth with this

I also came across another paradox within the twin paradox: relative motion. Going back to my first example, Sam travels near the speed of light and comes back to find her twin Pam to have aged more than Sam has. But suppose we look at Sam's frame of reference as stationary. To her, it may seem that Pam is the one accelerating away. Applying the same logic, it would end up that when Pam 'comes back', she will see that Sam has aged more! So we end up with two different situations depending which was our inertial frame of reference. I don't see how the time dilation/aging depends on who was accelerating or travelling, since it could be either depending on the reference.

They can't both have aged more than the other - the paradox. I've heard that this can be resolved using General relativity.

 

[Mike_Fontenot]

[...]
They can't both have aged more than the other - the paradox. I've heard that this can be resolved using General relativity.

General relativity isn't needed at all, as long as there are no large masses anywhere nearby. It is a common misconception that special relativity can't handle accelerating observers.

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7

https://www.physicsforums.com/showpost.php?p=2923277&postcount=1

Mike Fontenot

 

[JesseM]

Is it only the measurements that are relative, or the actual events?

In relativity an "event" refers only to some fact localized to a single point in spacetime, like what my clock reads at the moment a certain light beam reaches me, or what two people's clocks read at the moment they pass next to each other (idealizing them as points so that their separation is zero at the moment they pass). Statements about whether two events at different locations in space happened at the same time (see below) are not "events" for example.

If t is the time for the traveller (proper time) and t' is for the observer, t' =71t . Then is it correct to say that for every heartbeat of the traveller, the observer's experiences 71 heartbeats (or is it other way ><).

It depends what you mean by "experiences". If the observer considers the time coordinate t'0 assigned to one traveler heartbeat in the observer's frame, and the time coordinate t'1 assigned to the traveler's next heartbeat, and also considers the time coordinates assigned to her own heartbeats, she will find that her heart beat 71 times between t'0 and t'1. But because of the relativity of simultaneity other frames would disagree; if the traveller and observer departed from a common location at the moment their hearts were each beating, and then counted heartbeats after departure, it might be true in the observer's frame that the observer's 71st heartbeat since departure was simultaneous with the traveler's 1st heartbeat after departure (these events are assigned the same time-coordinate in the observer's frame), but in the traveler's frame it would be reversed, with the observer's 1st heartbeat since departure being simultaneous with the traveler's 71st heartbeat after departure.

This explains how the observer will end up being older, but it seems like the traveller will be moving in slow motion (1 heartbeat in 71 heartbeats of the observer)? I really get confused back and forth with this

As long as they are both moving inertially (no change in speed or direction), the perspectives of each one's frame are totally symmetrical, so each one defines the other one to be aging slower than themselves, as measured in their own rest frame.

I also came across another paradox within the twin paradox: relative motion. Going back to my first example, Sam travels near the speed of light and comes back to find her twin Pam to have aged more than Sam has. But suppose we look at Sam's frame of reference as stationary. To her, it may seem that Pam is the one accelerating away. Applying the same logic, it would end up that when Pam 'comes back', she will see that Sam has aged more! So we end up with two different situations depending which was our inertial frame of reference.

That argument from symmetry is exactly what is meant by the term "twin paradox"! But the argument doesn't work because in special relativity there is an objective truth about whether an object moves inertially or whether it accelerates--any object that accelerates will feel G-forces that can be measured by an onboard accelerometer, and more generally if they try to construct a coordinate system where they are at rest they will see that the same equations of physics (say, the laws of electromagnetism) that apply in inertial frames no longer apply in their new coordinate system. So we can always define in an objective sense what an "inertial frame" is, and relative to any inertial frame, one twin has a constant velocity (is moving inertially) while the other changes velocity at some point to turn around. You can calculate their total aging using any inertial frame you like, but you'll always end up with the conclusion that the one that has a constant velocity ages more in total than the one that accelerated.

For more, this is a good page on the twin paradox:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[ZealScience]

The Lorentz transformation of time, is a time dilation, NOT a antiaging machine. Actually speed of light is impossible to reach. Using the t'=tγ, you would find that time simply "stops flowing" by that I mean on Earth the 40 years passes at an instant, like watching movie with a interlude, 40 years later.

If you you use a case where Sam is reaching 99.999% of c, he still won't feel any difference, just seeing Earth going arround very fast, maybe 40 times in 0.01 sec. Then it's like watching a movie at 100 times speed.

 

[JesseM]

If you you use a case where Sam is reaching 99.999% of c, he still won't feel any difference, just seeing Earth going arround very fast, maybe 40 times in 0.01 sec. Then it's like watching a movie at 100 times speed.

Not if he is moving at constant speed! In that case the situation is symmetrical, if Earth sees his clock moving slowly, then he also sees Earth clocks moving slowly, and the Earth rotating slowly as well. But there is some ambiguity in the word "see", the answer may be different depending on whether we are talking about each observer's inertial rest frame and how fast the other one's clocks are ticking relative to coordinate time in this frame, or whether we are talking about what they actually see visually using light signals (in this case, because of the Doppler effect, if they are moving apart they both see each other's clocks moving slowly, even more slowly than what's predicted by the time dilation equation in fact, whereas if they are moving towards one another they both see the other one's clock ticking faster than their own). The twin paradox FAQ page has a section on the Doppler effect if you want to know more.

 

[ZealScience]

Not if he is moving at constant speed! In that case the situation is symmetrical, if Earth sees his clock moving slowly, then he also sees Earth clocks moving slowly, and the Earth rotating slowly as well. But there is some ambiguity in the word "see", the answer may be different depending on whether we are talking about each observer's inertial rest frame and how fast the other one's clocks are ticking relative to coordinate time in this frame, or whether we are talking about what they actually see visually using light signals (in this case, because of the Doppler effect, if they are moving apart they both see each other's clocks moving slowly, even more slowly than what's predicted by the time dilation equation in fact, whereas if they are moving towards one another they both see the other one's clock ticking faster than their own). The twin paradox FAQ page has a section on the Doppler effect if you want to know more.

Yes, it is a problem in special relativity. But if Sam returns to Earth how can he have constant speed?? Relative to Earth there is curvature which makes the two frames different! During the acceleration back to earth, time is definitely goingto change, because of difference in space time. Also, a displacement in space causes the PROPER TIME to change, how do you explain that?

 

[ghwellsjr]

Yes, it is a problem in special relativity. But if Sam returns to Earth how can he have constant speed?? Relative to Earth there is curvature which makes the two frames different! During the acceleration back to earth, time is definitely goingto change, because of difference in space time. Also, a displacement in space causes the PROPER TIME to change, how do you explain that?

I cannot understand your post. Are you saying that the Twin Paradox cannot be explained in SR and that is the problem you refer to in the first sentence?

In the second sentence, are you saying that even if Sam always travels at the same speed, her direction has changed and so she has experience acceleration?

In the third sentence, are you referring to the curvature of the Earth or the curvature of spacetime as a result of the gravity of the earth?

In the fourth sentence, are you implying that time doesn't change except for the very brief interval during acceleration?

In your last sentence, are you suggesting that it is not Sam's speed that causes a change in proper time but rather the brief period of time during her acceleration?

 

[Quinzio]

If you you use a case where Sam is reaching 99.999% of c, he still won't feel any difference, just seeing Earth going arround very fast, maybe 40 times in 0.01 sec. Then it's like watching a movie at 100 times speed.

As JesseM already pointed out, this is not correct. I don't mean any critics to you, we're all falling into erroneous conclusion based on our perception when we deal with SR.
Point is: SR is simmetrical so I say, in my RF (reference frame), your clock is running slower, you, in you RF say my clock is running slower.
So who's running slower ? Someone must be wrong. No, not in SR.
In SR every RF has its own time, its one metric.
Comparing my time with your time has no meaning.

But imagine the Earth is like a pulsar, every turn it emits a signal that Sam can receive.
So, Sam can measure the Earth clock ?
Will the day still be 24h ?
Until Sam is traveling at a constant velocity, yes. The Earth is turning at, let's say 30h each turn.

So, wait a moment, Sam travels from the earth, the day is 30h, Sam is traveling back to the Earth the Earth day is still 30h, so, when does Pam, gets older ?

Pam, must find an interval of time to get older, while Sam actually doesn't get older.
As someone correctly said, traveling isn't an antiaging machine, so Pam must find a moment to get older while Sam doesn't.
This time cannot be other that the interval of time while Sam decelerates to reverse its speed from +v to -v.
During this time the relativity of simultaneity rules that Pam gets older.
Something very odd happens(for who does never make relativistic travels) during acceleration.
During this interval the Earth day is measured as really fast and the day is let's say 1h.
During this odd interval, Pam gets older. There's no other way to explain it.

Edit: simultaneity changes when an object accelerates: eg. when Sam accelerates from 0 to +v, then to +v to -v, then to -v to 0, back to state his twin is older.

 

[Quinzio]

In your last sentence, are you suggesting that it is not Sam's speed that causes a change in proper time but rather the brief period of time during her acceleration?

I am convinced of that. In Sam RF.

 

[Mike_Fontenot]

I am convinced of that. In Sam RF.

You are very perceptive, Quinzio.