Is special relativity incomplete?

[flexible_time]

I feel a difficulty in understanding SP at fundamental level which is somewhat related with twin paradox.

Let me take a thought scenario: in empty space or vacuum two boxes(A and B) with their own light sources attached are separated from each other at a far distance r initially. If they are approaching to each other in different inertial reference of frame (they know this by receiving light signal sent from other), they would say ( assuming they can think and talk) that I am at rest and you are moving so what A think is $v_A=0, v_B=-v$ and what B think is $v_A=-v, v_B=0$. My understanding is that under SR two views are equally valid because SR only talks about the relative motion by comparing states between two inertial reference of frames.

In such cases, if my logic is right, then it generates a fundamental problem. Just single global event( two approaching to each other) can yield two different views which are valid under SR view. The first postulate of SR says that "1. The Principle of Relativity The laws of physics are the same in all inertial frames of reference" and it conflicts with the result of two boxes approaching. Can a single event create two different result? Where am I wrong?

 

[DrClaude]

If they are approaching to each other in different inertial reference of frame

The wording here is incorrect. You can't say that they are in "different inertial reference frames." You can have an inertial reference frame in which $v_A=0$, one in which $v_B=0$, one in which the center of mass of A and B is not moving, etc. But one an inertial frame is selected, all objects are in that frame.

In such cases, if my logic is right, then it generates a fundamental problem. Just single global event( two approaching to each other) can yield two different views which are valid under SR view. The first postulate of SR says that "1. The Principle of Relativity The laws of physics are the same in all inertial frames of reference" and it conflicts with the result of two boxes approaching. Can a single event create two different result? Where am I wrong?

How are the laws of physics different in the different reference frames?

By the way, you problem has nothing special to do with SR. You would get the same thing considering Galilean relativity. You should make sure that you understand the latter before embarking on SR.

 

[flexible_time]

The wording here is incorrect. You can't say that they are in "different inertial reference frames." You can have an inertial reference frame in which vA=0vA=0v_A=0, one in which vB=0vB=0v_B=0, one in which the center of mass of A and B is not moving, etc. But one an inertial frame is selected, all objects are in that frame.

Let me ask differently. if A is selected as the one inertial reference frame, then what is correct interpretation about who is moving? A or B? Whose time flow slower? I guess SR cannot determine which view is correct.

 

[DrClaude]

Let me ask differently. if A is selected as the one inertial reference frame, then what is correct interpretation about who is moving? A or B? Whose time flow slower? I guess SR cannot determine which view is correct.

There is no "correct" view. They are both right. They will not agree on the simultaneity of events, but the laws of physics are going to be the same for both.

 

[flexible_time]

There is no "correct" view. They are both right. They will not agree on the simultaneity of events, but the laws of physics are going to be the same for both.

My concern is that how a single event can create two different physical result. Taking one side view of moving A means that A will age slowly and the other view will show different physical result. If both are right then we need to accept two paradoxical views at the same time. A's time flow slowly than B and B's time flow slowly than A.

 

[Ibix]

My concern is that how a single event can create two different physical result. Taking one side view of moving A means that A will age slowly and the other view will show different physical result. If both are right then we need to accept two paradoxical views at the same time. A's time flow slowly than B and B's time flow slowly than A.

This isn't paradoxical. Imagine two cars traveling at 30mph along straight roads that diverge at 10°. Each car will observe that the other car is falling behind because its forward velocity is only 30 cos 10. The point here is that the two cars disagree on what "forward" means. They are using different frames of reference.

Much the same thing is happening in the relativistic case. Time is a dimension - a direction. The twins disagree on which direction is "time" so they disagree about whose clocks are ticking slowly.

 

[flexible_time]

Much the same thing is happening in the relativistic case. Time is a dimension - a direction. The twins disagree on which direction is "time" so they disagree about whose clocks are ticking slowly.

I cannot get what you say "they disagree about whose clocks are ticking slowly".

Lets replace two boxes with twin babies and the initial distance is long enough to make a big difference in their growth when they join. As they are approaching, my belief is that they will see only one physical result either baby A growing faster than B or B growing faster than A but not both of them regardless they disagree or not.

 

[PeroK]

In such cases, if my logic is right, then it generates a fundamental problem. Just single global event( two approaching to each other) can yield two different views which are valid under SR view. The first postulate of SR says that "1. The Principle of Relativity The laws of physics are the same in all inertial frames of reference" and it conflicts with the result of two boxes approaching. Can a single event create two different result? Where am I wrong?

And how is that any different from classical physics? Where velocity, momentum and kinetic energy are all frame dependent?

 

[Ibix]

I cannot get what you say "they disagree about whose clocks are ticking slowly".

Lets replace two boxes with twin babies and the initial distance is long enough to make a big difference in their growth when they join. As they are approaching, my belief is that they will see only one physical result either baby A growing faster than B or B growing faster than A but not both of them regardless they disagree or not.

How are you going to get twin babies a long distance apart?

You have two possible answers. One is that they aren't actually twins, just born on the same day. The problem with that is that they are in motion relative to each other, and the relativity of simultaneity means that they won't agree on what "the same day" means. Only one of the two (A for the sake of argument) will say that the other was born on the same day. A will be older when they meet up. B will say that A was born much earlier than him so, although A's clock ticks slowly, he is unsurprised that A is older when they finally meet up.

The other answer is a proper twin paradox where the twins move apart and return. In that case the resolution is that the twin who travels changes his definition of "now back on Earth" when he turns around. The result is the same as one of the cars in my analogy above turning back towards the other - the car that was falling behind suddenly jumps ahead.

I strongly recommend looking up Minkowski diagrams. They are far and away the easiest way to understand what's happening in the twin paradox.

 

[flexible_time]

And how is that any different from classical physics? Where velocity, momentum and kinetic energy are all frame dependent?

What I understand is that SR is better than classical view in understanding time and space at the fundamental level. I just want to know whether SR is complete and more specifically there is a way to know there a inertial reference frame of single system is standing still or moving.

 

[Ibix]

SR does not cover situations where gravity is important. For that you need General Relativity. Otherwise it is complete, self-consistent and well tested.

There is no answer to the question "is something moving or not" unless it is accelerating. While it is accelerating it is undeniably moving. However there is no detectable difference between unaccelerated motion and no motion, so there you are always free to pick any object not under acceleration and declare it to be at rest.

 

[PeroK]

What I understand is that SR is better than classical view in understanding time and space at the fundamental level. I just want to know whether SR is complete and more specifically there is a way to know there a inertial reference frame of single system is standing still or moving.

You seem to think that "object A has a velocity of v" is a law of physics. And, that if another observer concludes that, in his/her reference frame, object A has velocity 0, then a law of physics has been broken.

But, the specific velocity of a specific object is not a law of physics and there is no confict if two observers disagree about that. Although, as an aside, they do not really disagree about anything. Since both observers know the relationship between their reference frames, they would agree on the velocity of object A in both reference frames: it's simply that they choose to use different reference frames to measure things.

One of the reasons you don't understand SR is that you don't understand reference frames - even in the simpler case of classical physics, where time and space are absolute. Although, even in classical physics there is no such thing as absolute motion: every inertial reference frame has equal status and the laws of phyics must hold in them all. Until you grasp that, then understanding SR is going to be problematic for you.

 

[russ_watters]

What I understand is that SR is better than classical view in understanding time and space at the fundamental level. I just want to know whether SR is complete...

The way you talk about the paradox you think you see implies you want to know if SR is correct. Yes, it is.

...and more specifically there is a way to know there a inertial reference frame of single system is standing still or moving.

There is not. As said above, just as in Galilean relativity, you can arbitrarily declare one or the other to be "moving" and the other "stationary".

 

[flexible_time]

SR does not cover situations where gravity is important. For that you need General Relativity. Otherwise it is complete, self-consistent and well tested.

When I created this thread, I tried to pull the gravity what GR cares about by mentioning that "in empty space or vacuum" to minimize the effect of gravity and my main focus was the relation between the velocity and the time tick rate of a single system.

Since both observers know the relationship between their reference frames, they would agree on the velocity of object A in both reference frames: it's simply that they choose to use different reference frames to measure things.

One of the reasons you don't understand SR is that you don't understand reference frames - even in the simpler case of classical physics, where time and space are absolute. Although, even in classical physics there is no such thing as absolute motion: every inertial reference frame has equal status and the laws of phyics must hold in them all. Until you grasp that, then understanding SR is going to be problematic for you.

I think I understand pretty well what you say. My question begins based on your statements. As russ mentioned, I understand that I can arbitrarily declare one or the other be "moving" and the other "stationary" and the law of physics is always same in both reference frame. But what I don't understand in this thought experiment is that what SR can predict about whose time tick rate is slower than the other. Having in mind that the time dilation described within SR is the function of velocity of a system(http://scienceworld.wolfram.com/physics/TimeDilation.html), arbitrarily declaring the velocity of A either $v_a=0$ or $v_a=v$ seems to lead to the different world in future. In A reference view with the declaration $v_a=0$, the time flow of B will flow slower than A and in A reference view with the declaration $v_a=v$, the time flow of B will flow faster than A. It is hard to accept that the arbitrary choice on the declaration of the velocity lead to different future. Is the time dilation a illusion?

Let's make it simple. Let me know what SR can say about whose time tick rate flow slower than the other, A or B.

 

[Ibix]

Let's make it simple. Let me know what SR can say about whose time tick rate flow slower than the other, A or B.

Whichever one you have declared to be moving ticks slower. Since the two clocks are moving, you cannot unambiguously compare them at two times without accelerating one of them so that they meet again. This means that there are no physical consequences to the arbitrary choice of frame - you just get different descriptions of the same scenario.

I think you are confusing different descriptions of one thing with descriptions of two different things.

 

[russ_watters]

By the way, this apparent paradox is resolved when the two objects are brought together to become stationary together. The simplest case would have one fire a rocket to join up with the other, and you would typically (though you don't have to) declare that one was moving and now it isn't.

 

[PeroK]

Let's make it simple. Let me know what SR can say about whose time tick rate flow slower than the other, A or B.

The simple answer to that is:

1) Each clock ticks at the same rate in a frame of reference where it is at rest. Compared to a third clock, say.

2) Each clock ticks slower than the third clock if it is moving in a frame of reference at rest with respect to the third clock.

3) Each clock tick slower than the other in the other's frame of reference.

Neither clock has absolute velocity; neither clock has absolute time dilation; neither clock ticks faster or slower absolutely.

Everything is relative to a frame of reference: velocity, momentum, energy (as classical physics), length of an object, tick rate of a clock, rate at which physical processes take place (additionally in SR).

 

[flexible_time]

I think you are confusing different descriptions of one thing with descriptions of two different things.

I hope to find where I confused at.

I think one possible way to determine who is moving or rest in the journey would be storing some same amount of radioactive decaying materials and informing the remaining quantity to each other. If the time rate of a moving object flow 2x slower that the one at rest, radioactive decaying rate of the material in moving box will be halved so whenever they compare the remaining quantity, they will know who is moving unambiguously. It seems to me that the existence of the decaying material does not change the time flow rate of boxes. It is confusing me.

 

[ZapperZ]

I hope to find where I confused at.

I think one possible way to determine who is moving or rest in the journey would be storing some same amount of radioactive decaying materials and informing the remaining quantity to each other. If the time rate of a moving object flow 2x slower that the one at rest, radioactive decaying rate of the material in moving box will be halved so whenever they compare the remaining quantity, they will know who is moving unambiguously. It seems to me that the existence of the decaying material does not change the time flow rate of boxes. It is confusing me.

This is wrong.

The radioactive decay rate remains THE SAME in its rest frame. If you have Ba137, you'll measure its half life as 2.55 minutes. Another person in another moving frame, having the same identical Ba137 will ALSO measure its half life as 2.55 minutes. So how can you tell that that person is moving and you're not?

It is when you measure the time of decay of THAT person's Ba137 is when you measure something different. But that person also measures the same difference when he/she looks at your Ba137! By simply comparing both of your observations, there is a perfect symmetry. You cannot tell who is actually "moving".

Zz.

 

[stevendaryl]

I hope to find where I confused at.

I think one possible way to determine who is moving or rest in the journey would be storing some same amount of radioactive decaying materials and informing the remaining quantity to each other. If the time rate of a moving object flow 2x slower that the one at rest, radioactive decaying rate of the material in moving box will be halved so whenever they compare the remaining quantity, they will know who is moving unambiguously. It seems to me that the existence of the decaying material does not change the time flow rate of boxes. It is confusing me.

The problem is that if you have two hunks of uranium, in order to compare them to see which one has decayed more, you have to bring them back together. The details of how you do that determine which one has "aged more".

Here's an analogy: Suppose you have two roads, Highway A and Highway B, that meet at an angle of, say, 30 degrees. On each road, there are distance markers, one every 100 meters. Now suppose that Highway A runs East-West, and Highway B runs Southwest-Northeast. As you move along Highway A, when you pass a distance marker, you can look to your left (straight north) to see the corresponding distance marker on Highway B. What you will find is that the distance along Highway B will show a longer total distance than for Highway A. The ratio will be: $\frac{\delta D'}{\delta D} = \frac{1}{cos(30)} \approx 1.155$ where $\delta D'$ is the change in the distance along Highway B, and $\delta D$ is the change in the distance along Highway A. You can reason as follows: "If this ratio keeps up, then when the two roads get back together, the total distance along Highway B will be longer than the total distance along Highway A." But surely the reasoning should work just as well for someone traveling on Highway B! That seems to be a paradox. But the paradox is resolved by the fact that, in order for the two highways to meet to compare distance markers, either one or the other highway must bend (or both). Which distance is longer when they get back together depends on how each bends.

 

[Ibix]

We don't keep talking about cars on roads just for the fun of it, by the way. Paths through space have a lot (although not everything) in common with paths through spacetime. In particular, bodies in motion in space have their notions of forward in time rotated through a (hyperbolic) angle with respect to each other. That's why the analogy with cars moving along roads at an angle to one another is relevant.

 

[bahamagreen]

Motion can be confusing... in fact I might be confused, myself. :)

Imagine two objects in relative motion.

If you are thinking from the standpoint that there is such a thing as absolute motion (and absolute rest), then you may believe:

1] Perhaps both objects are in absolute motion

2] At least one of the objects must be in absolute motion

3] Both objects cannot be in absolute rest

4] Although you don't know how it is allocated between the two objects, you know for certain that there is some motion.

The tricky thing is that last one, number four. The certainty of motion seems to be the certainty of absolute motion in spite of absolute rest being undetectable... this certain motion when the allocation of it between the objects is unknown comprises relative motion which may be allocated freely and variously between the two objects pending the choice of inertial frame from which to observe and measure.

Ibix wrote in post #5, "There is no answer to the question "is something moving or not" unless it is accelerating."

That may seem to be strictly true when a single object is in question; and still but not quite as strongly true when multiple objects with relative motions are in question... in the sense that the allocation of an absolute motion is not possible for an individual object, but it certainly is possible to say that there is actual true absolute motion without regard to an absolute rest when multiple objects have relative motion.

This does not seem any more peculiar than absolute acceleration without the need for an absolute rest from which to base it.

However, the present standpoint is that there is no detectable or theoretically useful absolute rest. It is from that standpoint that motion must be considered... carefully.

Using accelerations as suggested above can also be a bit confusing because co-moving objects within the universal expansion do not experience accelerations, yet their mutual distance magnitudes accelerate, so now the four ideas listed above are all messed up and not even the "certain" forth one is held to be true.

 

[Mister T]

Let's make it simple. Let me know what SR can say about whose time tick rate flow slower than the other, A or B.

Each must see the other's clock running at a slower rate. Symmetry requires it because otherwise you'd have a way to distinguish between a state of rest and a state of uniform motion.

There is a way to resolve what is, in your mind, an apparent paradox. That is, it's possible for each to see the other's clock as running slow in a logically consistent way. You first have to open your mind to the possibility. I suggest you look at this Insight article:

https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/

 

[flexible_time]

Each must see the other's clock running at a slower rate. Symmetry requires it because otherwise you'd have a way to distinguish between a state of rest and a state of uniform motion.

It is the prediction based on SR, but seems to be inconsistent with the result. I can see it as an analogy with the famous so called "Unstoppable Force paradox". Bear with me to explain more for those who are not familiar with it.

From https://en.wikipedia.org/wiki/Irresistible_force_paradox,

"This term originates from a story (see the Kanbun example) in the 3rd century BC philosophical book Han Feizi.[2] In the story, a man was trying to sell a spear and a shield. When asked how good his spear was, he said that his spear could pierce any shield. Then, when asked how good his shield was, he said that it could defend from all spear attacks. Then one person asked him what would happen if he were to take his spear to strike his shield; the seller could not answer. This led to the idiom of "zìxīang máodùn" (自相矛盾), or "self-contradictory". "

SR says, borrowing your view point, that in view of A, A must see B's clock running at a slower rate and in view of B, B must see A's clock running at a slower rate. Here I think what SR says about A and B is similar to what the Chinese sales man who is trying to sell spear and shield. I am really curious about the answer when we ask "what would happen if A meet B?". Will each other see younger than himself/herself if they are twin? Or will see same aged twin? It is our common belief that unstoppable forces and immovable objects cannot both be true at the same time. Similarly, it seems to me that younger than B and younger than A cannot both be true at the same time.

From now, it is just my opinion which may be wrong. Where the paradox comes from? What is common in both paradoxical cases? I think it comes from the fact that there is only relativistic difference. Let's assume that the unstoppable force means a force with infinite amplitude and the immovable object means a mass with infinite mass. Then can we say the infinite force stronger than infinite mass so that unstoppable force win against immovable object or vice versa? Is there any such thing a number bigger than infinity? It is my view point that if we are allowed to use only the relative difference by comparing two with no absolutely measurable/comparable property, then we are not able to escape from seeing a sort of paradox like this case. If we accept it is true that "There is no answer to the question "is something moving or not" unless it is accelerating.", then the paradox is unavoidable. I could not find a way to resolve this paradox yet and am still searching for. Would be appreciable if you correct me.

There is a way to resolve what is, in your mind, an apparent paradox. That is, it's possible for each to see the other's clock as running slow in a logically consistent way. You first have to open your mind to the possibility. I suggest you look at this Insight article:

I just wanted to know my observation on this issue will make sense to others. What I have in mind is just a crazy private idea which is close to science fiction, not matured yet and quit long to write down so hesitant to write such a crazy personal view here. Anyhow I would like to keep learning and sharing more about the most fundamental level of understanding about time, space, mass and the universe.

 

[stevendaryl]

SR says, borrowing your view point, that in view of A, A must see B's clock running at a slower rate and in view of B, B must see A's clock running at a slower rate. Here I think what SR says about A and B is similar to what the Chinese sales man who is trying to sell spear and shield. I am really curious about the answer when we ask "what would happen if A meet B?". Will each other see younger than himself/herself if they are twin? Or will see same aged twin? It is our common belief that unstoppable forces and immovable objects cannot both be true at the same time. Similarly, it seems to me that younger than B and younger than A cannot both be true at the same time.

Of course not "at the same time". A and B have different notions of what "at the same time" means.

Let's name some events:
$e_1$: Alice and Bob depart at some relative speed of $v$ (let's pick $v=0.866 c$, which means a time dilation factor of two). Assume that they are both 20 years old.
$e_2$: Alice turns 25.
$e_3$: Bob turns 25.
$e_4$: Alice turns 30.
$e_5$: Bob turns 30.

In Bob's frame, $e_2$ and $e_5$ are simultaneous. So Bob concludes that he is 5 years older than Alice.
In Alice's frame, $e_3$ and $e_4$ are simultaneous. So Alice concludes that she is 5 years older than Bob.

There is no contradiction between these views. The two just have a different notion of which events are simultaneous with which other events.

 

[A.T.]

It is the prediction based on SR, but seems to be inconsistent with the result.

Which result?

 

[flexible_time]

In Bob's frame, e2e2e_2 and e5e5e_5 are simultaneous. So Bob concludes that he is 5 years older than Alice.
In Alice's frame, e3e3e_3 and e4e4e_4 are simultaneous. So Alice concludes that she is 5 years older than Bob.

This seems to be weird to me. Do you mean that when Bob and Alice meet together at the same place and the same time, Bob will see 5 years older than Alice and Alice will see 5 years older than Bob? It is so much confusing me.

Let me label two sentences as follows.

S1: Bob will see himself 5 years older than Alice.
S2: Alice will see herself 5 years older than Bob.

Your statement is forcing me to believe that both S1, S2 are true at the same time and same space when they meet. So from S1, I, from the view point of 3rd person, conclude that Bob(S1)=30 Alice(S1)=25 and with this condition, S2 must be true so that Alice(S2) = Bob(S1) + 5 = 30 + 5= 35 which is not equal to Alice(S1)=25. If you dislike the engagement of 3rd person, I can make an additional rule such that at ever year, they will add a star shaped sticker on their face so if he is 30, then he will get 30 start stickers on his face. In this way, they can compare their actual age with the other without the engagement of 3rd person. Using the scheme that put additional sticker on the face at every year, I wonder what the number of stickers Bob and Alice will see on their faces when they meet at the same place and the same time. My argument is that only one among S1 and S2 must be true and both cannot be true when they meet together. I think it is contradiction if Alice(S1), which is determined by considering S1 only, is not the same with Alice(S2), which is derived from considering S1 and S2 both.

If S1 and S2 both cannot be true at the same place/time, then it is so confusing what is the true meaning of "both view are valid under SR".So what will you say about the number of stickers on their faces when they are at the same place?

 

[flexible_time]

Which result?

I mean that there should be both of prediction and verification for theory to be true but it seems we do not have any result for the verification of this issue.

 

[DrClaude]

Others here are more knowledgeable than me on the subject, but I think they have missed the main source of the misunderstanding.

Answers such as stevendaryl's are based on the assumption that Alice and Bob will never be reunited, and will only know about the other through speed-of-light communications. This is the only case where both can always be in inertial reference frames. Everything is symmetric: both see the other as aging slower.

You have in mind a scenario where they get reunited. This falls back to the twin paradox, which is resolved by the fact that symmetry is broken: one of the twins must turn around to be reunited with the other. Acceleration is necessary for this to happen, hence you can't say that they are both associated with an inertial reference for the duration of the trip.

 

[Ibix]

To expand slightly on DrClaude's comment, the symmetry you, OP, are talking about holds between inertial frames of reference. But for two people to start at one point and meet up again, at least one of them must change frames; otherwise they just drift further apart. If they do choose to meet up then the details of how and when they accelerate will lead to a unique answer for who will be the older when they meet. One may be oldrr than the other, or they may be the same age - and while both will have different reasons for predicting which it will be, they will agree.

If they never meet up again they can never compare their clocks again without making assumptions. Since the natural set of assumptions for two people in relative motion are different they have different impressions of whose clock is ticking faster.

 

[stevendaryl]

This seems to be weird to me. Do you mean that when Bob and Alice meet together at the same place and the same time, Bob will see 5 years older than Alice and Alice will see 5 years older than Bob? It is so much confusing me.

If Alice and Bob continue away from each other at constant velocity, then they can never meet. In order for them to meet, one or the other (or both) must change direction or speed of their motion. To figure out which one is older when they get back together, you must look at how they move to get back together.

The picture below shows an analogy to the "paradox" of mutual time dilation that occurs in good old 2-dimensional Euclidean geometry. Alice and Bob are traveling in their cars, and they come to a fork in the road, represented by the lower left vertex of the triangle. Bob decides to take the road that goes to the northeast, while Alice decides to travel straight east. Assume that their two roads make a 45 degree angle. When they get back together, who will have traveled the farthest?

Here's Alice's reasoning:

There are markers on each road that tells how far we've traveled (in miles). When I get to road marker #5 on my road, I look straight to my left, and I see that it corresponds to marker #7 of Bob's road. Similarly, when I get to road marker #10 on my road, I look straight to my left, and see road marker #14 of Bob's road. Bob's markers are increasing faster than mine, so when we get back together, Bob will have traveled farther. (In the picture, the red lines indicate Alice's view of which of her markers correspond to which markers of Bob.)​

Here's Bob's reasoning:

When I get to marker #5, I look straight to my right, and see that it corresponds to marker #7 of Alice's road. Similarly, when I get to marker #10, it corresponds to Alice's marker #14. So Alice's markers are increasing faster than mine. So when we get back together, Alice will have traveled farther (In the picture, the blue--or maybe they're purple--lines show Bob's view of which of his markers correspond to which of Alice's)​

So who is right? Well, Alice is. When they get back together, at the lower right vertex of the triangle, Bob will have traveled farther. Does that mean that there is an absolute answer to the question of which road markers are increasing faster? No. The difference between Alice and Bob is that Bob makes a right-angle turn half-way along his trip. When he turns, he completely changes his view of which of Alice's markers correspond to which of Bob's. Immediately before Bob's turn, at the top of the triangle, if he looks to his right, he will see Alice's marker #20. Immediately after he turns, when he looks to the right, he will see Alice's marker #0. So when he makes the turn, the correspondence between his marker and the corresponding marker for Alice changes. Because of this, Bob's accounting of how long each of their trips is will be wrong.

A similar thing happens in the twin paradox. For the two twins to get back together, Bob must change his velocity (assume it's Bob). During this change, his notion of which of his birthdays correspond to which of Alice's birthdays must change abruptly. Because of this change, Bob's accounting of their relative ages will be wrong when they get back together.

 

[MikeLizzi]

Hi All,
Here is a URL to an exercise I did for myself a while ago. It addresses cases where skeptics don't want to consider a back and forth sceneario like the traditional twins. I hope it can contribute some clarity, not add more confusion.

http://www.relativitysimulation.com/Documents/LookingForContradictionsWhenMovingClocksRunSlow.htm

 

[flexible_time]

This is just a clarification to fix some confusions. I assumed in my original post that there is neither acceleration nor change in the direction in the thought experiment and they are separated from each other at a distance r and are approaching each other in a uniform motion. Someone may have some critiques about technical issues such as how to separate twin at a far distance but that is not the main point I would like to know. Maybe such technical issues could be the real cause for my confusion.

 

[A.T.]

... I assumed in my original post that there is neither acceleration nor change in the direction... they are separated from each other at a distance r and are approaching each other in a uniform motion...

If they are twins and are now separated and approaching each other, there must have been some change in the direction since the separation.

 

[jbriggs444]

This is just a clarification to fix some confusions. I assumed in my original post that there is neither acceleration nor change in the direction in the thought experiment and they are separated from each other at a distance r and are approaching each other in a uniform motion.

It does change anything essential if the subjects are initially separated and are approaching or if they are initially together and are receding. If they are approaching, you have the problem agreeing on a simultaneity convention for starting the respective clocks. If they are receding you have the problem agreeing on a simultaneity convention for reading the respective clocks.

If they are together twice then, as has already been discussed, at least one must have accelerated in the interim.