In the standard formulation of the twin paradox an “accelerated” twin considers Hence, when formulating the twin paradox, one uses the general principle of. PDF | 25 minutes read | It is pointed out that a complete resolution of the twin paradox demands that the travelling twin takes into account the gravitational effect. PDF | Does time tick by at the same rate for everyone?.
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Resolution of the twin paradox. • The earthling did not experience any acceleration. Therefore, he can use special relativity to determine time. The astronaut. Abstract: The twin paradox is often misunderstood, both in textbook and science Keywords: Twin Paradox, Time Dilatation, Inertial Frame. In physics, the twin paradox is a thought experiment in special relativity involving identical twins Create a book · Download as PDF · Printable version.
The key points of the problem are: The ship carrying one of the twins goes straight to Alpha Centauri and back. Alpha Centauri is assumed to be in relativisticly static motion relative to the Earth with a proper distance of 4 light years. Each twin is equiped with a powerful transponder that pings with a source frequency of exactly once per second or 1Hz.
The Earth twin sees that Alpha Centauri is a static 4 lightyears away. The ships twin has a different perspective of the trip when moving at 0. Therefore from his point of view, the trip will only last 3 light years each way or 6 years total. The paradox is based on the fact that each twin should have symmetrical points of view of their brothers time which is true: When the ships twin is on the outbound leg moving away from Earth at 0.
These time shifts are due to the relativistic redshift which I didnt bother working out the math again, but the formulas are pretty simple and include time dialaion plus normal doppler effect due to lagtime, so that you can verify the results yourself or just refer to the Wikipedia example which uses the exact same problem. The logical resolution to this paradox is the fact that while their views of each others time is symetrical, their views of the distance traveled is asymetrical.
Another words while their point of view of time is symmetrical, their point of view of distance is asymtrical which accounts for their deviation in time experienced. In fact, the asymmetry normally used to justify the different ages of the twins is related with the inertia forces, and only the traveling twin will feel this effect.
A simple argument can reveal this question. In the second situation, the same travel twin travels strictly with the same accelerations and speeds as the previous one, but for only one year in the outward trip and another year in the return trip marked on his clock.
It is clear that in the second case the age difference will be lower, so we can conclude that it is not the acceleration itself that causes the discrepant aging but rather the time spent at constant speed.
In order to visualize the true role of acceleration in this problem, let us consider the figures from 1 to 6 below where are represented the time periods of the acceleration and deceleration of the trip of one of the twins to a distant planet in a spaceship with a velocity of the order of speed of light while the other twin remains on the Earth.
The events featured in them are simply indications of clocks on the spaceship, on the Earth and in the outer space at certain points of the trip. These clocks are physically identical.
Let us consider now that the Earth inertial reference frame is practically stationary with the target planet, because the speeds involved in the movements of the planets are despicable when compared with the speed of the spaceship that is of the order of the speed of light. Let us further consider that the acceleration time period, for example a few days, are not significant in comparison with the total travel period of time, for example 20 years, and so we can disregard it for simplification without changing the final result of the problem7.
So, just after the acceleration period, we can admit that the clocks of the Earth and the spaceship are still approximately zeroed. Note that, in this reference frame, the Earth is approximately stationary with the planets, since the speeds involved in the movements of them are negligible compared to the speed of the spaceship that is the order of the speed of light. Note that in this reference frame the Earth and the planets are moving together relative to the spaceship with speeds in the order of the speed of light, and so there is a loss of synchronization with the time of departure.
They are representing the events showed in the figures 1 and 2 above. Note that, after the acceleration, the events that are simultaneous for one reference frame will be successive for the other one and vice versa. From figure 1 we can see that in the Earth and the planet inertial reference frame represented in the figures by the planets, ruler and clocks , even after the acceleration, the clocks will still be all synchronized since, as we saw above, they are practically stationary in this reference frame.
Neither will there be any change in the distances between the planets and the return point of the trip in this reference frame. This loss of synchronism occurs progressively with increasing speed and distance considered shown in the figure as a delta parameter. When the spaceship arrives near the return point, begins the deceleration period that, like the example of the acceleration period, can also be disregarded in relation to the total journey period of time.
Here we can see that, at this place, the deceleration period will not cause any significant changes in time too, in a both reference frames. This loss of synchronism and contracted distances decrease progressively with the reduction of speed and, at the end of the deceleration period, the clocks come back to be synchronized and the distances between the Earth, the planets and the spaceship returned to be the same as the beginning of the journey.
We can see that near spaceship, the deceleration period will not cause any significant changes in time. We can see too that near spaceship, the deceleration period will not cause any significant changes in time too. However, in this reference frame, before the deceleration, there was a loss of synchronization between clocks and the distances between the Earth, the planets and the spaceship are all contracted.
After deceleration, the clocks back to synchronize and the distances between the Earth, the planets and the ship returned to be the same as the beginning of the trip. They are representing the events showed in the figures 4 and 5 above. During the trip, both twins will measure a proper time and this causes that, each of them, in their respective reference frame, will measure a longer time interval than their twin in the other frame, since each of them will be in motion relative to the other and vice versa.
For the latter are simultaneous the events D and F. In the other words, this clocks are in the same plane of simultaneity. For the latter are simultaneous the events C and E. They are representing the events showed in the figures 7 and 8 above.
Note that, after the deceleration, the events come back to be simultaneous for both reference frame. The reasoning above was applied for the outward journey. Then, we can conclude that there is no paradox.
A round trip to a distant place 6. Let us now consider a trip to a distant place from Earth 6. This speed corresponds to a Lorentz factor of 1.
In the Earth, the spaceship and at the return point there are physically identical clocks. The event A indicates the end of the spaceship's acceleration period relative to the Earth and vice and versa, i.
In the Earth reference frame the events A and B are simultaneous and the distance between them is 6. In this latter reference frame, the event A is simultaneous to the event C that will be 3. When the spaceship arrives near the return point, take a place the event F that corresponds to the beginning of the deceleration period and the spaceship will be 6. However, as we have seen previously, the loss of synchronism according to equation 24 will be equal to 6.
If we add up the above values, we will have 6. The Doppler effect is a phenomenon in which the frequencies of the electromagnetic waves change due to the relative movement between the source and the observer.
The relativistic Doppler effect is this frequency shift for objects moving at relativistic speeds. Taking into account the relativistic characteristics, it is possible to demonstrate that the period measured by an observer Tr and the period from the source Tp called the proper period are related by the following expressions. Let's start from the example seen in the previous section. In this example the space ship's twin sees his clock to mark eight years in the outward and in the return trip totaling sixteen years and his brother on the planet sees respectively ten years in the outward and in the return trip totaling 20 years.
The explanation given by the Doppler effect is based on the comparison that each twin makes of the time marked by his own clock and the another twin's clock during the trip. Let's assume that each twin has a very powerful transmitter that emits an electromagnetic pulse every year of the trip. The method in question seeks to explain the paradox by considering the time that the pulse takes to propagate between the two twins.
The spaceship's twin, in the outward trip, emits eight pulses, a pulse each year of your clock, and when he reaches the point of return, your clock strikes eight years. Then after receiving eight pulses your clock will have marked sixteen years. On the return trip, the spaceship's twin emits more eight pulses a pulse each year of your clock, and when he returns to Earth, his watch marks sixteen years.
Then, after eight pulses your clock will have marked four years. Adding the round trips, we will have twenty years marked on Earth's twin clock and sixteen years on the spaceship's twin clock.
So, he will receive four pulses before starting the return movement. On the return trip, the spaceship's twin begins to receive each pulse at half-year intervals as per calculated by equation 30 because now it is the approaching movement. So, he will receive, on the return trip, sixteen pulses. Over again, adding the round trips, we will have twenty years marked on Earth's twin clock and sixteen years on the spaceship's twin clock.
We can see that, although the final result is correct, this method does not explain the paradox, it only confirms the correct ages.
In other words, the rhythm of time would not depend on the direction of movement. By the method of the Doppler effect each observer would see its proper time dilated in the receding movement and contracted in the approaching one, in other words, the rhythm of time would depend on the direction of movement.
Analyzing the example as seen in section 6, using the relativity of simultaneity, we will see that in the outward trip after the deceleration, the period of time elapsed in the spaceship is eight years and on Earth is ten years because the clocks come back to synchronize again after the deceleration.
On the return trip occurs the same. By the method of the Doppler effect however, in the outward trip, it has spent a period of eight years on the spaceship and sixteen years on Earth. In the return leg, while the relativity of simultaneity the time is completely symmetrical in a both paths, by the Doppler effect it is not, having passed on the spaceship eight years and on the Earth only four years.
This distortion occurs due to the propagation characteristics of the electromagnetic waves. Thus, we can conclude that the equations 29 and 30 only transmit information about the total time elapsed and do not indicate how the time actually passes in each reference frame. Conclusion In the special theory of relativity STR , the simultaneity of events is not more absolute between moving inertial reference frames like it was in Newton's mechanics.
Therefore, when we are comparing the elapsed time for both twins we need to take into account the loss of synchronism between the moving inertial reference frames. As we have seen in this work, due to the relativity of simultaneity each twin can state that time runs more slowly for his brother in his reference frame when measured in the reference frame of the first twin and vice versa without violating the laws of physics. However, the comparison of the twins' ages has to take into account the loss of time synchronism between their inertial reference frames while they are in motion.
We discussed too the commonly explanation used for the solution this problem, namely the acceleration, and we remind that the acceleration occurs in both reference frames since the velocity varies in both of them and the acceleration is nothing more than the velocity variation with time. Some authors argue that only one twin changes from inertial reference frame to non- inertial one. However, this statement is not very simple because the characterization of these reference frames is not very clear.
For example, imagine two stones falling down in a uniform gravitational field. If we consider one stone relative to another one, we will have a perfect pair of inertial reference frames. But if we consider each of them with respect to the source of the gravity a planet for example these will be accelerated but the fictitious forces are not will exist.
In this case these references frames are inertial or non-inertial? However, this problem would still be solved by the relativity of simultaneity since it works perfectly in a totally flat space-time like Minkowiski space-time. I am also grateful to my wife and daughter who supported me in carrying out this work. References  Shuler Jr.
Journal of Modern Physics, 5, Barros et. Zur Elektrodynamik bewegter Korper. Annalen der Physik, 17, O manuscrito de Einstein de como pista para o desenvolvimento da teoria da relatividade restrita.