The twin paradox is a very well-known example to present the theory of relativity. One of twins jumps into a space ship and the other one stays on Earth. Each of the twins moves in relation to each other. The traveler-twin, once back on Earth, is younger than the twin who stayed.
What I don't understand is what this aging really means. I DO understand that the watches each of them is wearing show a difference in time. But does the traveler really change BIOLOGICALLY? Does he "look younger" than the other twin? In practice, would the traveler-twin get gray hair later than the other twin? Or does aging in this context mean something else? So my question, shortly put, is: does aging in the context of theory of relativity mean 1)just impression that time is going faster on Earth than in space 2)real changes in biology, real physical aging? The twin who returns back from the space ship journey: does he look exactly as old as the other twin or has he really remained younger?|||Yes. It means that for the twin that stayed on Earth, the time really passed for him, and for the twin who traveled, less time passed.
The older twin doesnt just "look" older, he really is older. He really experience that time. And the younger twin really experienced less time passing.|||The twin paradox, sometimes called the "clock paradox", stems from Paul Langevin's 1911 thought experiment in special relativity: one of two twin brothers undertakes a long space journey with a high-speed rocket at almost the speed of light, while the other twin remains on Earth. When the traveler returns to Earth, he is younger than the twin who stayed put. Or, as first stated by Albert Einstein (1911):
If we placed a living organism in a box ... one could arrange that the organism, after any arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had already long since given way to new generations. For the moving organism the lengthy time of the journey was a mere instant, provided the motion took place with approximately the speed of light. (in Resnick and Halliday, 1992)
Like all paradoxes, this occurs because of faulty assumptions. This one happens because one twin undergoes acceleration while the other does not, something that isn't taken into account when this twin-paradox story was invented.
Contents [hide]
1 Specific Example
2 Origin of the Paradox
3 Resolution of the Paradox in Special Relativity
4 What it looks like: the relativistic Doppler shift
4.1 The asymmetry in the Doppler shifted images
5 Calculation of elapsed time from the Doppler diagram
5.1 The distinction between what they see and what they calculate
5.2 Simultaneity in the Doppler Shift calculation
6 Resolution of the Paradox in General Relativity
7 See also
8 References
9 External links
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Specific Example
Consider a space ship going from Earth to the nearest star system a distance d = 4.45 light years away, at speed v = 0.866c (i.e. 86.6% of the speed of light). The round trip will take t = 2d / v = 10.28 years in Earth time (i.e. everybody on earth will be 10.28 years older when the ship returns). Ignoring the effects of the earth's rotation on its axis and around the sun (at speeds negligible compared to the speed of light), those on Earth predict the aging of the travellers during their trip as reduced by the factor , the inverse of the Lorentz factor. In this case ε = 0.5 and they expect the travellers to be 0.5×10.28 = 5.14 years older when they return.
The ship's crew calculate how long the trip will take them. They realize that the distant star system and the earth are moving relative to the ship at speed v during the trip. Therefore, the distance between the earth and the star system will be shortened (by the length contraction) to εd = 0.5d = 2.23 light years, for both the outward and return journeys. Each half of the journey takes 2.23 / v = 2.57 years, and the round trip takes 2×2.57 = 5.14 years. The crew arrives home having aged 5.14 years, just as those on Earth expected.
If a pair of twins were born on the day the ship left, and one went on the journey while the other stayed on earth, the twins will meet again when the traveller is 5.14 years old and the stay-at-home twin is 10.28 years old. This outcome is predicted by Einstein's special theory of relativity. It is a consequence of the experimentally verified phenomenon of time dilation, in which a moving clock is found to experience a reduced amount of proper time as determined by clocks synchronized with a stationary clock. Examples of the experimental evidence can be found in the time dilation page.
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Origin of the Paradox
The strange result of twins of different physical age was not the central problem of the "twin paradox". As early as 1905, Einstein predicts that a clock which is moved away and brought back, will lag behind on stationary clocks. Einstein calls that result "peculiar", but the calculation is straightforward and the example is not presented as paradoxical, despite his suggestion in the introduction of the same paper that only relative motion between objects should matter.
In 1911, Langevin discusses the evolution of the concepts of space and time in physics and presents the principal aspects of special relativity. He suggests that special relativity implies the existence of a stationary ether and states: "Every change of speed, every acceleration, has an absolute sense". To stress this fact he provides several examples such as that accelerated electric charges emit electromagnetic radiation. He proceeds with a thought experiment similar to the specific example above. Langevin next explains the different aging of the twins: "Only the traveller has undergone an acceleration that changed the direction of his velocity." According to Langevin, acceleration is here "absolute", in the sense that it is the cause of the asymmetry (and not of the aging itself). Also in this discussion there seems nothing paradoxical about it.
However, it was Einstein's objective to show that all motion is "relative", and he thought to have reached that objective with General relativity. Thus he stated in 1916, in his introduction to that theory: "The laws of physics must be of such a nature that they apply to reference systems in any kind of motion" (including accelerated motion). And he concluded about two relatively accelerated systems K and K': "From the physical standpoint, the assumption readily suggests itself that the systems K and K' may both with equal right be looked upon as "stationary", that is to say, they have an equal title as systems of reference for the physical description of phenomena." In other words, all observers are equivalent, and no particular frame of reference is privileged.
The perception of paradox is rooted in a misunderstanding of the meaning of equivalent frames in relativity and therefore arises in both SR and GR. The Principle of Relativity states that the mathematical forms of the laws of physics – say, mechanics and electrodynamics — are identical in all frames of reference independent of their relative motion; i.e., all frames are equivalent in this restricted but important sense that the laws of physics are invariant from one frame to another, whether the frames are accelerating or not. In the twin problem, although the respective frames are equivalent in this sense, they are not dynamically symmetric since only the traveling twin experiences acceleration. However, if one assumes that the frames of the traveling and stay-at-home twin are dynamically symmetric and confuses dynamic symmetry with equivalence (and perhaps, additionally, falsely infers equivalence to mean identical calculations in all frames), one erroneously concludes the same result for each twin's time dilation as calculated by the other twin; i.e., one expects the traveler upon return, to have aged more and less than his twin – which is clearly impossible. In this connection, it is important to understand that relativity does not claim that all observers make identical measurements when observing the same phenomena; generally they do not. Nor does relativity claim that a time dilation calculation that each observer performs for his twin is a "law of physics" that must remain invariant from one observer or frame to another. However, these calculations would be expected to be identical for dynamically symmetric frames!
It is to be noted, however, that time dilatation has no relationship whatsoever to the amount, direction, or duration of acceleration. Even the time dilatation of particles in the Fermilab ring is determined only by their speed, in spite of the huge accelerations they undergo. In the usual resolution of the twin paradox, it is only the bare fact of acceleration which is invoked, and not any measured quantity. Some might object that, while the travelling twin experiences acceleration, so does the stay-at-home twin, both by ordinary motion and by being in a gravity field. Why one has the "better" acceleration which controls the direction of time dilataion is not apparent. Also, the journey can be arranged so that the stay-at-home twin experiences exactly the same accelerations as the traveller (by moving around on a stationary gravitating planet to exactly match the accelerations of the traveller whose rocket ship always accelerates at one planet gravity).
The erroneous belief that the twins are in dynamically symmetric frames is likely rooted in Einstein's attempt to formulate a theory in which physical phenomena could be fully explained in terms of relative motion. In his landmark 1905 paper, “On the Electrodynamics of Moving Bodies”, when offering a motivating example for his Principle of Relativity, Einstein states that it is immaterial whether one considers the coil or the magnet as moving, and that only relative motion matters since the resultant induced current is the same. Thus, part of the misconception of what the Principle of Relativity means — which is essentially responsible for the perception of "paradox" — probably stems from these comments. That is, Einstein’s casually–stated claim that all motion is relative (as well as his original objective for relativity theory), can easily mislead in its suggestion that equivalent frames (with respect to invariance of the laws of physics) are necessarily symmetric with respect to motion.
Although the paradox is necessarily implied if one assumes dynamic frame symmetry, showing that it is non-existent due to the acceleration of one twin is just a necessary condition for resolution of the paradox, but not by itself sufficient. For sufficiency, one must perform the calculations to demonstrate that from the point of view of each twin, the traveler returns younger. Moreover, this must be done independently in both SR and GR, since the problem appears in both theories.
In 1918, Einstein reacts to objections to his relativity theory and issues arising in connection with the twin paradox. In that paper he reconfirms the differential aging prediction of special relativity, and points out that the equations of special relativity are only valid for inertial frames, that one twin is in an accelerating frame (if modeled in one frame throughout), and that the twins are not in symmetric frames for the reasons explained above. Next, after affirming the general principle of relativity, he sets out to show in a detailed example with clocks, that general relativity yields the same answer as special relativity and he claims that he thus "fully explained the paradox".
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Resolution of the Paradox in Special Relativity
The usual resolution of the paradox as presented in physics text books ignores its origin (it only surfaced with general relativity, see above) and regards it as a problem due to misunderstanding of special relativity. Here the Earth and the ship are not in a symmetrical relationship: the ship has a "turnaround" in which it feels inertial forces, while the Earth has no such turnaround. Since there is no symmetry, it is not paradoxical if one twin is younger than the other. Nevertheless it is still useful to show that special relativity is self-consistent, and how the calculation is done from the standpoint of the traveling twin.
Of course the traveling twin comes home younger. Special relativity does not claim that all observers are equivalent, only that all observers in inertial reference frames are equivalent. But the space ship jumps frames (accelerates) when it does a U-turn. The twin on Earth rests in the same inertial frame for the whole duration of the flight (no accelerating or decelerating forces apply to him) and he is therefore able to distinguish himself as "privileged" compared with the space ship twin. The accepted resolution of the paradox is that the crew must make a different calculation from that above, a calculation which explicitly recognizes the change of reference frame, and the change in simultaneity which occurs at the turnaround.
There are indeed not two but three relevant inertial frames: the one in which the stay-at-home twin remains at rest, the one in which the traveling twin is at rest on his outward trip, and the one in which he is at rest on his way home. It is during the acceleration at the U-turn that the traveling twin switches frames. That's when he must adjust the calculated age of the twin at rest. Here's why.
In special relativity there is no concept of absolute present. A present is defined as a set of events that are simultaneous from the point of view of a given observer. The notion of simultaneity depends on the frame of reference (see relativity of simultaneity), so switching between frames requires an adjustment in the definition of the present. If one imagines a present as a (three-dimensional) simultaneity plane in Minkowski space, then switching frames results in changing the inclination of the plane.
Twins paradox Minkowski diagramIn the spacetime diagram on the right, the first twin's lifeline coincides with the vertical axis (his position is constant in space, moving only in time). On the first leg of the trip, the second twin moves to the right (black sloped line); and on the second leg, back to the left. Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg. Just before turnover, the traveling twin calculates the age of the resting twin by measuring the interval along the vertical axis from the origin to the upper blue line. Just after turnover, if he recalculates, he'll measure the interval from the origin to the lower red line. In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the lifeline of the resting twin. The resting twin has suddenly "aged" very fast, in the reckoning of the traveling twin.
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What it looks like: the relativistic Doppler shift
Now, how would each twin observe the other during the trip? Or if each twin|||Yes. It would be biological. Because our biology and the aging process is based on time. The heart of the twin paradox is that time would move differently for each of the two twins.
The bodies and actual cells would be a different age. The cellular processes that are associated with aging would progress at a normal rate in the relative time frame for _each_ twin.|||Tut, tut, tut, Justin. Be very careful about any observer seeing events go "many times" faster. If two observers are moving at CONSTANT, unaccelerated velocity relative to one another, EACH sees the clocks of the other running slowly. This was the source of the twin paradox, with acceleration ignored.
The only time an observer can see other clocks running faster is during acceleration or when in a very strong gravitational field, as on the surface of a star.
The resolution of the twin paradox lies in one of the twins being accelerated and the other not.|||YES|||You got me thinking. Aging is merely the disintegration of the atoms due to oxygen. Without air, there'd be no life and no aging. Oxygen causes us to age from the day we're born.|||Yes. The aging is biological. Biological aging is just the reaction of the body to the passage of time. That's why the twin's paradox is used to illustrate the concept. Biological bodies are clocks! Irreversible clocks. So yes, the passage of time is faster on earth, so the earth-bound twin will have gray hair, etc.|||Well, aging is ALWAYS a biological process. I mean you age and get gray hair and wrinkled skin and eventually die BECAUSE of the passage of time.
But there is nothing biological at all about the twin paradox. The twin paradox is really a TIME paradox, but the example usually used to explain it involves either two twins or two people carrying clocks. The clock or aging person is just a familiar way to measure the passage of time. It is time itself that is acting weird in relativity.|||Yes he would look and be biologically younger, less time has passed for him. The watch is not broken in the example, it is telling true time and less time really did pass for the traveler. Humans tend to age at fairly steady rates so the traveler would have literally aged less.|||You are not understanding the theory of relativity.
The theory uses this analogy to explain that the closer you get to the speed of light (in other words the faster you go), the more time changes for you versus how fast time was moving at the slower (normal) speed.
If you have two twins and one goes out to space and travels to near the speed of light (the speed is the key factor, not the fact he is in space), and comes back, to him only a few hours may have past, but to his twin a whole lifetime may have.
This is because, as Einstein explained, when you approach the speed of light, time slows down for you. Of course you can't notice this yourself because to you everything is going normally. However if it were capable for you to look out the window and watch earth's events as you are travelling near the speed of light, you would see events moving many times faster than it should be, because of the time difference.
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