Twins flying at the speed of light in opposite directions

[Janus]

I understand that asking "why two clocks on different curves show different time" is the same as asking "why two clocks on the same curve show the same time"... The "why" part of the question starts with an assumption that it should be otherwise.

In that case I am like a child asking a parent an indefinite tree of "but why" questions, expecting that there's some ultimate underlying mechanism at the end that explains Everything.

So, is it that modern physics simply does not explain underlying causes or mechanisms for variations observed in aging, clocks, or muon decay? There's just no value in researching/defining it for "ultimate clarity", because the model we have today for observing it is completely predictable and satisfactory already? ...Or it's just because it's the same nonsense for 21st century physics as asking "why is there something instead of nothing"?

The "why" for as far as we can take it, it that the measurement of time and space differs between inertial frames with relative motion with respect to each other. The best way I can think of for you to picture this is to imagine a "map" of time and space. Just like a normal map our space-time map has the equivalent of a North-South and East-West direction. We can think of North-South as time and East-West as "space" Now in this map we have limited space to one direction and it really has 3 dimensions, but we will limit it to one so we don't have to try and visualize four dimensional map and It simplifies the example without affecting the salient points.

So now that we have our map, we can place points on it and call them "events" with an event describing something at a particular place and time. (the corner of 5th and Elm at 5:00pm). If we have two events, we can tell how far apart they are in time and space by their locations on our map. So two events can be 4 miles and 3 hrs apart. Now imagine this map as really large with people standing on it, all of them facing different directions. Ask anyone of these people about these events and they will say that they are 4 miles apart and 3 hrs part (just like anyone looking at a typical road map would say that town A is 30 miles to the North and 40 miles to the East of town B.)

This was pretty much the way time and space were viewed before Relativity. What Relativity has revealed to us is that the North-South, East-West way of distinguishing between time and space doesn't work; That, in fact, we need to treat it more like front-back, left-right, and unlike North-South, East-West, front-back, left-right is not something that everyone agrees on. In our example above, two people facing different directions will give different answers for the relative position of the two events. One might still say that they are 4 miles and 3 hrs apart, but the other could say that they are 5 miles apart and happened at the same time.

Now to make this analogy a bit more complete, our people are not allowed to stand still. They all have to be walking at the same pace. And since for each person, time is in the direction he is facing, this means he is always moving forward in time. If two people are facing different directions, their paths will converge or diverge, so from either person's perspective, as time passes the other person gets closer or further. Put another way, they have a relative motion with respect to each other.

So considering the above, let's use the example of two men, walking side by side. They are facing the same direction, thus they measure time the same, they are not moving apart, so they have no relative motion with respect to each other. Since they both see each other as progressing through time at the same rate, they see each other as aging at the same rate.

Now one man, call him A. changes direction and is now walking in a different direction then B. Consider what happens to him as seen by B. B sees himself progressing forward through time at his normal rate unchanged. But when he considers A, he notes that he is no longer remaining a breast with him, he is falling further and further behind. Since by his measure, time progresses in the direction he is walking, then, by his measure, A is making less progress in time, or is aging slower.
If we consider things from A's perspective, he sees himself as progressing normally through time, while B is not, So A sees B as aging slower. This is time dilation. Note that this is not due to some outside influence effecting how fast either man walks (ages), but due to the fact that they measure "time" differently.

Now consider what happens if A changes direction again, so that he is once again walking in the same direction as B. From B's perspective, this means he stops losing ground as far as aging goes and he once again begins to age at the same rate. However he doesn't make up the ground he lost and remains younger.

What happens according to A? Well, as he turns, B's position with respect to him will change. Just like and object behind you can become in front of you by your turning towards it, B, according to A goes from being "behind" to "in front" when A changes direction. Since progress in time is still defined by A as the direction he is facing moving, A suddenly sees B progress ahead of him in time. Or put another way B ages quickly as A turns toward him, so that by the time A and B are walking in the same direction again B is older than A according to A, ( just as is true for B)

A can continue his turn until so that his new path cuts across B's path. As he turns B will move even further " ahead" in time. After the turn, he will note that B once again is progressing slower through time than he is. However, by the time he crosses B's path again, this slower aging will not be enough to make up for the gain made during the turn, and B will still be older. A can then turn to "follow" A. So A will have returned to the same point in space as B, but will had made less progress through time. Put another way, A traveled away from B, turned around and returned to B, having aged less during the trip. All without some outside influence acting on A or B.

I realize that it seems a bit 'unnatural' for time and space to behave this way. But that is just because through the vast majority of man's history on Earth we were only used to dealing with velocities that were so slow, that these effects were just too small to notice and had no effect on everyday life, so we didn't know they were there.

As to "why" time and space behaves like this, that delves into a lot deeper level of "why".( And the funny thing about "why" questions is that no matter how far you dig, you will always find another "why" underneath.)

 

[Herman Trivilino]

So, is it that modern physics simply does not explain underlying causes or mechanisms for variations observed in aging, clocks, or muon decay?

The underlying cause is that time itself has these "variations". Once you accept that, it explains the variations in aging, clocks, and muon decay.

You can go further and ask why. And the reason is that inertial reference frames are equivalent. The speed of light is the same in all of them.

You can go further and ask why those things are true, And maybe it goes that way forever or maybe it doesn't. Maybe there's some fundamental thing that can't be explained. This is not some issue arising in modern physics. It has always arisen in physics, and every other human quest for knowledge.

Physicists create models that explain the way nature behaves. The models are not tangible items like a fossil that lay hidden to be discovered. They are products of the human intellect. They are products of human imagination. Many people expect these models to be more than that. That they somehow are the things they model.

Time dilation is a difficult thing to teach to people. It confuses them when they first hear about. Anyone who isn't confused isn't engaged. This is often the way of it when we introduce new ideas into our worldview. We are always confused until we understand the new idea.

 

[Feeble Wonk]

They do each age normally in their own reference frame. They each age slowly in the other's reference frame.

Ouch! This seems to be logically problematic.

 

[Alan McIntire]

If two guys, each sitting on a different Earth-like habitable planet, fly in the opposite directions, each at the speed of light, which guy would age slower? And slower compared to what?

My own understanding is that they both age normally. Because Special Relativity doesn't describe physiological processes, but only hints at visual disparity of the spacetime (photons can't travel fast enough to observe the reality from any given reference frame).

If this is true then the whole twin paradox is a very unfortunate way of teaching kids, just creates confusion...

They would not see each other "NOW". They would each see the image of the other after light had traveled for minutes or hours. They would see each other slowed down due to the doppler shift, and would compute the other's time as traveling slowly. As long as they travel apart, they will never meet again, so there's no way to verify who is "really" aging slower.

Assume Alpha Centari is exactly 4 light years away, and one twin is
traveling
there at 4/5 speed of light. (Using a 3,4,5 triangle I avoid
irrational numbers in my computations.

Traveling at 4/5 the speed of light, from the point of view of the
stay at home twin, the trip will take 10 years, 5 years there, 5 years
back.

Time for the traveller T’ = T( sqrt( 1- (v^2/c^2))) = 3/5 T
Likewise, the distance for the traveler, D’ = 3/5 D

The traveler on the spaceship sees himself traveling a distance of
4*3/5 = 2 2/5 light years in a time of 3 years, and likewise the 2 2/5
light years back
in a time of 3 years, so the traveler will see the trip as lasting 6
years.

Say the twins have super telescopes and can see each other throughout
the trip.
As long as they are traveling apart, the twins will see each other as
aging at 1/3 speed. As long as they are traveling towards each other,
the twins will see each other as aging at triple speed.

The difference is, the traveling twin will see the stay at home twin
as aging at 1/3 speed for the 3 years to Alpha Centauri, for a total
of 1 year,
and at triple speed for the 3 year trip back to Earth = 3*3=9.
The traveling twin will see the stay at home age 1 year during the
trip out, and 9 years during the trip back, for a total of 10 years.

The stay at home twin will see the travel age at 1/3 speed for 9
years, the 5 years it takes the traveler to get to Alpha Centauri,
plus the 4 years it takes the light to get back to earth. Since the
total trip will take 10 years, the stay at home twin will see the
traveler age at triple speed during the one year he observes the
traveler coming back to earth. The Earth observer sees the traveler
age at 1/3 speed for 9 years, for a total of 3 years, and at triple
speed for 1 year, for another 3 years, giving 6 years for the round
trip.

Both observers see each other aging at the same slow rate while moving
apart, they see each other aging at the same fast rate while moving
together. The difference lies in one observer deliberately changes
the relative motion of his rocket from moving away from Earth to
moving towards earth, and the other observer remaining passive, and
not seeing the change until the light from the
traveler reaches earth. If the Earth could be accelerated like a
rocket ship, and the earthbound observer decided to change his frame
so the rocket appeared to be moving towards him at 4/5 lightspeed
rather that away at 4/5 lightspeed, while the rocket remained in
motion past Alpha Centauri, then it would have been the Earth twin who
appeared to age less.
Of course you could have some intermeditate situation where BOTH
observers decide to change their relative motion before they see the
other observer change his motion.

 

[Janus]

Ouch! This seems to be logically problematic.

It is no more logically problematic than my analogy of two men walking in different directions from a single origin. Each man is walking normally as far as he is concerned, but he will also note that the other man is falling behind. (he will have to crane his neck more and more to look at him.). In other words, each sees the other man as making slower progress in the direction he himself is walking.

It may seem counter-intuitive to treat time this way, but this is simply due to the fact that in our everyday environment we are not exposed to the type of velocity differences that makes this type of behavior apparent. If we had evolved in an environment where relative velocities of a good fraction of c were common, we would take this as being perfectly natural.

 

[puf_the_majic_dragon]

I'm kind of amused at all of the overly technical explanations in this thread.

Here's the simplest explanation I can give:
The faster you move, the slower time moves. But slower implies comparison, time is moving slower for you compared to what? Anything moving slower than you are, really. But let's take the twin paradox.

If you send your twin off at (close to) the speed of light, time will pass more slowly for your twin than for you. But what does that mean? Your twin will see a clock on the wall on his spaceship move like an ordinary clock. For your twin, time appears to be moving normally. But if you had a time/space visualizer and tuned it into watch your twin on his spaceship, everything on your twin's spaceship would appear to be moving in extreme slow motion. This is what we refer to as reference frames: your reference frame is the universe around you, all moving "together". When your twin takes off in his ship, his ship becomes a separate reference frame. Everything inside the ship appears normal, but outside the ship looks very different because of the difference in speed.

So #1: Time is not a constant. The passage of time is not a constant.

To answer the original question, how fast you and your twin "age" (ostensibly, how faster or slower time appears to move) depends on who is observing and what their reference frame is. Some observer standing at the point of origin with a time/space visualizer would see you both age (time passing) at the same rate as each other (but much more slowly than for him), since you are both traveling at the same speed relative to the observer.

Hopefully this is a little more comprehensible to the layman than some of the more technical answers in this thread.

 

[jbriggs444]

If one tries to explain the twin paradox without invoking relativity of simultaneity then chances are near 100% that the explanation will be poor. If the explanation depends on an absolute frame of reference, the odds worsen.

Possibly the best advice about posting in a twin's paradox thread is to do so quietly and wash your hands after.

The faster you move, the slower time moves. But slower implies comparison, time is moving slower for you compared to what? Anything moving slower than you are, really. But let's take the twin paradox.

The notion of "moving slower than you" appears to implicitly assume the existence of an absolute reference frame.

But if you had a time/space visualizer and tuned it into watch your twin on his spaceship, everything on your twin's spaceship would appear to be moving in extreme slow motion. This is what we refer to as reference frames: your reference frame is the universe around you, all moving "together".

The mental image conjured by the phrase is of a piece of hardware that actually measures something. That is a misleading suggestion. This "time/space visualizer" is not a feature of the universe at all. It amounts to one's choice of coordinate system. A mere accounting gimmick. Any choice will do. It need not be anchored to the universe or to any particular object.

When your twin takes off in his ship, his ship becomes a separate reference frame. Everything inside the ship appears normal, but outside the ship looks very different because of the difference in speed.

The phrase "difference in speed" is questionable. It suggests the existence of an absolute reference frame in which velocities are subtracted.

When the twin takes off in his ship, his ship does not become a separate reference frame. It happens to be at rest in a new and different reference frame. The traveling twin can still directly observe his wristwatch ticking away at one second per second. If the traveling twin tunes his "time/space visualizer" to read zero speed for the outbound ship then it will agree that time is passing normally for the traveler and slowly for the stay-at-home twin.

When the traveling twin turns around and re-tunes his "time/space visualizer" to read zero speed for the return trip, there is a problem. How old was the stay at home twin before re-tuning the visualizer? How old was the stay at home twin after? That is the problem of relativity of simultaneity.

 

[Dale]

Ouch! This seems to be logically problematic.

Why?

Edit: it is easier to see that there is no logical problem if you write it down clearly. If $r_{clock,frame}$ is the rate of a given clock with respect to a given frame then "they each age normally in their own frame" means $r_{A,A}=1$ and $r_{B,B}=1$ while "they each age slowly in the others frame" means $r_{A,B}<1$ and $r_{B,A}<1$. There is no logical problem with that.

 

[puf_the_majic_dragon]

The mental image conjured by the phrase is of a piece of hardware that actually measures something. That is a misleading suggestion. This "time/space visualizer" is not a feature of the universe at all.

It seems the Doctor Who reference was completely lost. The idea is of a magical "window" that peer into another reference frame and yet let's you observe it relative to your own. Of course no such feature of the universe exists. But neither does a cat in a box with a poison capsule and a radioactive isotope.

As I read over this thread, it seemed the OP was having difficulty understanding the idea that time is not a constant, and none of the responders seemed to be addressing that in a way that made sense to the OP. My illustration (hopefully) suffices to convey the idea that time is not constant, but you're absolutely right that it loses quite a bit of technical accuracy in the process of simplifying it down to that key concept. Kind of like the movie Interstellar.

If the inaccurate illustration serves the purpose of conveying the idea, then you can feel free to correct all of its inaccuracies once the OP understands the context of time not being a constant.

 

[Feeble Wonk]

Why?

Edit: it is easier to see that there is no logical problem if you write it down clearly. If $r_{clock,frame}$ is the rate of a given clock with respect to a given frame then "they each age normally in their own frame" means $r_{A,A}=1$ and $r_{B,B}=1$ while "they each age slowly in the others frame" means $r_{A,B}<1$ and $r_{B,A}<1$. There is no logical problem with that.

Sorry Dale. I wasn't questioning your math. And I'm certainly not disputing the validity of relativity. I was simply making the observation that the statement (each of the travelers aging slowly relative to the other within their own reference frame) APPEARS on its face to be a logical conflict. It would intuitively (while admittedly naively) seem impossible for both of those situations to be true "at the same time". I think that is the OP's primary confusion.

As I read over this thread, it seemed the OP was having difficulty understanding the idea that time is not a constant, and none of the responders seemed to be addressing that in a way that made sense to the OP.

Perhaps the OP's confusion is not so much that "time" isn't constant, but rather that the general experience of "now" is not constant.

If one tries to explain the twin paradox without invoking relativity of simultaneity then chances are near 100% that the explanation will be poor. If the explanation depends on an absolute frame of reference, the odds worsen.

...

The mental image conjured by the phrase is of a piece of hardware that actually measures something. That is a misleading suggestion. This "time/space visualizer" is not a feature of the universe at all. It amounts to one's choice of coordinate system. A mere accounting gimmick. Any choice will do. It need not be anchored to the universe or to any particular object.

...

When the twin takes off in his ship, his ship does not become a separate reference frame. It happens to be at rest in a new and different reference frame. The traveling twin can still directly observe his wristwatch ticking away at one second per second. If the traveling twin tunes his "time/space visualizer" to read zero speed for the outbound ship then it will agree that time is passing normally for the traveler and slowly for the stay-at-home twin.

When the traveling twin turns around and re-tunes his "time/space visualizer" to read zero speed for the return trip, there is a problem. How old was the stay at home twin before re-tuning the visualizer? How old was the stay at home twin after? That is the problem of relativity of simultaneity.

I think Briggs makes that point very well here. If the twins were traveling at their identical "near light speed" velocities in a circular path in opposite directions, they would be the same age when they met again at the starting point. The total time elapsed would be precisely the same for both twins. The only variation would be with regard to when "now" was for either of the twins at any given time... which would (again naively) appear to require an absolute time reference clock to compare the two.

 

[Feeble Wonk]

Having reviewed a portion of the thread I had previously overlooked, I find myself confused by the role of acceleration as it pertains to GR. I'm hoping someone can enlighten me.
If we consider a single spaceship launching from earth, obtaining near-light speed, and then returning to earth, the spaceship and occupants will have aged more slowly than Earth and it inhabitants. If it is not the boost/acceleration forces that alter the space ships inertial frame state, what determines the "object" in motion? If it's only the distance and velocity that matter, why can't we say that the Earth launched away from the spaceship and then returned. I've always had the layman's understanding that the acceleration and change in inertial state experienced by the spaceship is what determines relative time dilation. Can anyone explain my misconception without resorting to complicated mathematical formulation that will definitely be over my head.

 

[Herman Trivilino]

If it is not the boost/acceleration forces that alter the space ships inertial frame state, what determines the "object" in motion?

Nothing! That's the entire point of the Principle of Relativity. There is no way to determine which twin is in a state of motion and which isn't, as long as the motion is uniform.

It is the acceleration of the traveling twin, though, that distinguishes his experience from that of the stay-at-home twin.

If it's only the distance and velocity that matter, why can't we say that the Earth launched away from the spaceship and then returned. I've always had the layman's understanding that the acceleration and change in inertial state experienced by the spaceship is what determines relative time dilation. Can anyone explain my misconception without resorting to complicated mathematical formulation that will definitely be over my head.

Because it's not only the distance and velocity that matter in the full analysis. There's more to the analysis than just that. The difference in aging of the twins is due not only to time dilation but to a combination of time dilation and the traveling twin's acceleration.

Now, if you want to understand this on a conceptual level, delving into the math only when necessary, you have two options.

The first is to understand things only from the perspective of the stay-at-home twin. His situation is different than his brothers because of the reason mentioned above. And because of that reason, his situation is easier to understand. You can use time dilation alone to understand things from his point of view. With a bit of easy arithmetic you can calculate the time dilation factor knowing only the speed. For example at a speed of 0.87 c the factor is about 2. So if the traveling twin ages 10 years, the stay at home twin ages 20.

To complete this first way of understanding you need a reason to not be able to use this same approach to analyze things from the traveling twin's perspective. And that reason is because the traveling twin's motion is not inertial, for the reason previously discussed.

The second way of understanding involves all of the above, plus an analysis of the situation from the traveling twin's perspective. That analysis includes not only the time dilation as discussed for the stay-at-home twin, but also the effect due to the relativity of simultaneity that occurs when the traveling twin changes direction. If you want to explore this let us know. The math involves only arithmetic, but the level of detail of the analysis is deeper and requires greater mental effort.

 

[Feeble Wonk]

So... The acceleration, and related shift in inertial state, of the traveling twin IS the factor that causes the time dilation experienced by the stay at home twin relative to the traveling twin? Orodruin's post here confused me.

While this is true, it gives the impression that acceleration plays a central role, which it does not. Any effects from the accelerating parts of the journey can be made completely negligible simply by extending the constant velocity parts. The twin "paradox" comes about simply from missing out on the relativity of simultaneity and blindly applying the time dilation formula.

Regarding the acceleration, it is relatively simple to show that the straight, unaccelerated path in Minkowski space between two events will maximise the proper time between them. This is no stranger than a straight line minimising the length of a curve between two points in Euclidean geometry.

 

[Herman Trivilino]

So... The acceleration, and related shift in inertial state, of the traveling twin IS the factor that causes the time dilation?

No, it's not. For the reasons I stated.

Orodruin's post here confused me.

Everything he said is not only correct, it's vital to an understanding.

 

[Feeble Wonk]

To complete this first way of understanding you need a reason to not be able to use this same approach to analyze things from the traveling twin's perspective. And that reason is because the traveling twin's motion is not inertial, for the reason previously discussed.

The second way of understanding involves all of the above, plus an analysis of the situation from the traveling twin's perspective. That analysis includes not only the time dilation as discussed for the stay-at-home twin, but also the effect due to the relativity of simultaneity that occurs when the traveling twin changes direction. If you want to explore this let us know. The math involves only arithmetic, but the level of detail of the analysis is deeper and requires greater mental effort.

Thanks. Let me think about this some before I waste your time. I had a general understanding that it was the change of directions and shift in inertial states that caused the relative time dilation, but now I don't think I properly understood the reason WHY that occurs. I'll have to ponder that.

 

[Herman Trivilino]

Note that the analysis of the situation from the stay-at-home twin's viewpoint involves only time dilation. His brother's acceleration has nothing whatever to do with his analysis.

It's when you try to understand or explain why the same analysis doesn't apply to the traveling twin that the acceleration comes into it. Or if you go deeper and try to explain things from the traveling twin's perspective.

 

[Feeble Wonk]

It's when you try to understand or explain why the same analysis doesn't apply to the traveling twin that the acceleration comes into it.

Yes. That's what I meant. My previous GENERAL understanding was that the "relative" time dilation (resulting in the traveling twin aging less than the stay-at-home twin) was due to the change in direction and shift in inertial states... and that was why the same analysis doesn't apply to the traveling twin. But there is obviously more to it than that. As I suggested in regard to the OP, the relativity of simultaneity is also difficult for me to wrap my head around. I think that's the issue I've got to understand better.

 

[Orodruin]

the relativity of simultaneity is also difficult for me to wrap my head around

Try reading this: https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/
It really is nothing but an effect of using different coordinate systems.

 

[Ibix]

The elapsed time for any observer is the length of their path through 4d spacetime. The rate at which someone else's clock is ticking depends on the angle between their path and yours.

The two twins took different length paths through spacetime, which is why they end up different ages. But (for any agreed definition of an instant) the angle between the two paths is the same measured from either path at the same instant, which is why both twins see the other's clock ticking slow.

As Mr T says, relativity of simultaneity is a big part of making all of this add up, but the above is basically "why".