Let's consider a scenario in which we have two clocks. Clock A is placed stationary with respect to the Earth's surface. Clock B is placed on a hypothetical spaceship moving at constant speed (close to the speed of light).

As I understand it, if I am an observer in the same frame of reference as clock A, clock B will appear to tick more slowly than clock A. Conversely, if I am an observer in the same frame of reference as clock B, clock A will appear to be tick more slowly than clock B. This is so because, in either case, the observer can view their frame of reference as the stationary one and the other as moving. My question concerns the actual rates of the clocks while the experiment is in progress.

From what I understand, if we rejoin the clocks on Earth, clock A and clock B will disagree. More specifically, I expect clock A to be ahead of clock B, due to the effects of special relativity on fast-moving clocks. You might say that clock A has aged more than B?

But I am a bit confused. This problem is very similar to the scenario of the twin's paradox. In justifying how the twin's paradox is not a violation of relativity many people will refer to the asymmetry of the two twins' journeys. While one could equally argue that either twin is stationary and the other is moving, the twin in the spaceship switches from being at rest in an inertial frame moving away from the Earth to being at rest in an inertial frame moving towards the Earth. In doing so, the spaceship twin must undergo a period of acceleration. In other answers I have seen people seem to attribute the aging of the Earth twin to the acceleration period experienced by the spaceship twin. Is this to imply that the aging of the Earth twin is somehow brought about by the acceleration of the spaceship twin or has the Earth twin already aged more rapidly and the information is just "catching up" to the spaceship twin?

In other words, if we consider our clock scenario again... obviously we know both observers will report the other's clock to be moving more slowly than their own, but is one actually moving slower than the other (regardless if whether we can tell which)? To rephrase, when the experiment is underway, is the spaceship's clock actually ticking more slowly than the Earth clock or is this disparity between the clocks, like the twin's experiment, somehow created when the spaceship's clock is accelerated back towards the Earth? I understand that both observers will see one another's clocks ticking more slowly than their own, but I get confused how the realities merge when the clocks are brought back together. When did the disparity between the clocks start? Many people say that both perspectives are equally valid, what is meant exactly by this; how can both perspectives be equally valid but when the clocks are rejoined there is only one reality?

Also, is it valid to say that the Earth twin and spaceship twin ultimately arrive at the same coordinates in space-time, but that they took different paths to get there? In other words, is it valid to say that the Earth twin took a "shorter" path through space-time than the spaceship twin which presents in the Earth twin having aged more rapidly.

Really appreciate any help with this question! I guess I am just looking for clarification, it's all a bit tricky to conceptualize what exactly is going on. People often speak of clocks ticking more slowly relative to your frame of reference but then also say stuff like "fast-moving clocks tick more slowly". Sorry if these questions are a bit ignorant, just trying to get a better grasp on the interpretation aspect.

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    $\begingroup$ I think your use of the word actually and the phrase "when does the disparity actually start" is where you go wrong. In whose frame? In the Earth's frame (forever inertial), its clock ticks at a normal speed and the twin's clock is always running slowly. In the ship's first inertial frame (where the ship sits at the origin for a bit, then boosts away all of a sudden to head back to earth), its clock is running normally for a bit, and then super slowly as it heads towards earth. In any one inertial frame, all of the time dilation measurements add up to say the earth aged more! $\endgroup$ – user12029 Feb 24 '17 at 9:48
  • $\begingroup$ Very true, I guess I can't really ask when the disparity starts, because that would depend on which frame of reference you are in. I think what confuses me is the concept of multiple realities. Is this a case of multiple realities? Are both frames of reference correct or is one correct the whole time and we just can't tell which until we observe the clocks side-by-side afterwards. $\endgroup$ – dwhite5914 Feb 24 '17 at 10:03
  • $\begingroup$ For instance, you say: "In the Earth's frame (forever inertial), its clock ticks at a normal speed and the twin's clock is always running slowly", but isn't this only true from the Earth frame of reference. Won't the space twin think the Earth's clock is slow also? And if both are right, how do the clocks end up verifying that the spaceship clock ran slower, was it going slower the whole time and each twin just has a different perspective? Sorry for being so wordy, having a hard time putting my thoughts into words. $\endgroup$ – dwhite5914 Feb 24 '17 at 10:03

Disparity starts as soon as twins change frame. It is often said that single clock dilates relatively to a set of spatially separated clocks. Set of synchronized clocks will appear running faster, is single clock compares its own readings with synchronized clocks successively. It makes no sense to speak about motion, if there is no reference frame. It is not possible to compare ticking rate of single clock to single clock. You must to introduce a reference frame by means of putting two synchronized clocks at least. Then single clock moves from clock to clock and compares readings. Single clock dilates from point of view of the set of two clock. Set of two clocks is reference frame. In special relativity observers do not come to agreement, which frame is "mutual". We, people a bit cleverer, since we have Greenwich meridian. Imagine what would happen if there was no Greenwich meridian. Relativity of simultaneity! Then moving twin does the same. He introduces his own frame and places another additional clock at certain distance from himself. Then single clock moves in this frame from clock to clock of that frame. Moving clock shows 12 and clock at rest Nr.1 shows 12. Then single clock moves further and approaches clock at rest Nr. 2. Single moving clock shows 3 and clock at rest Nr. 2 shows 5 for example. If twin turns back at clock Nr.2 and moves back towards clock Nr.1 and we think in terms of that same frame, it dilates further and when it comes back, it will obviously show less time. If we don't change frames that describe relative motion, there is no paradox. As soon as we jump from one frame to another frame paradox appears.


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