IS General Relativity necessary to explain the Twin paradox of Special Relativity?

Question

IS General Relativity necessary to explain the Twin paradox of Special Relativity?

Answer 1

ok, so... popular Relativity is the final case (acceleration and substantial mass is fantastic), and particular Relativity is for non-accelerating frames of reference (so substantial mass isn't in contact). The Lorentz transforms are derived for relative inertial action between 2 frames of reference, and describe length contraction and time dilation (a 2 headed coin). evaluate photograph voltaic muons. interior the laboratory, muons have a definite lifetime, and then decay. they're charged, and so are difficulty-free to locate. In our ecosystem, we see their lifespan dilated, they "decay slower" (time dilation). To the muons, in the event that they have been wakeful and conscious, their lifespan may be unchanged, yet they see our ecosystem decreased in length alongside their direction (length contraction). comparable coin, 2 distinctive aspects. popular Relativity honestly includes particular Relativity interior of it. in case you tension acceleration to 0, and occasional fee mass as trivial, you get particular Relativity. For that remember in case you're taking popular Relativity, and permit the fee of light bypass to infinity, you get Newtonian gravitation, and gravitation as a tension. "and would we are saying redshifts are linked to time dilation?" A guarded definite. If a deliver is passing by way of us, we see their finished "time dilation result" as redshift. in the event that they're coming in direction of us, the blue classical Doppler shift would be lots larger than the time dilation element. Likewise in the event that they're shifting remote from us (Doppler result's "additive" there). Then once you get to popular Relativity, if the "deliver" led to a supernova because it exceeded a particular length megastar, the size for the deliver's occupants may be the comparable, however the longer in the past it befell for us, the slower we see it take place now. there are a number of factors which would be in contact in "crimson shift"...

Answer 2

First, there is no paradox. SR holds that there is no "preferred" frame of reference and that all observers see the same thing. BUT, one twin experiences acceleration and the other does not ===> The frames of reference can be differentiated and assuming both twins started from the same frame of reference (and they must to be twins) the twin in the accelerating Frame of Reference is in the frame where Space-Time dilation occurs

Answer 3

Captain Mephisto is absolutely right. Special relativity says that the laws of physics are the same in different inertial frames, but changes in non-inertial frames. Special Relativity can perfectly well describe the physics in non-inertial frames, but it does not tell you the cause of the non-inertial frame. Acceleration is one way to create a non-inertial frame. General relativity says that another way to create a non-inertial frame is to be motionless (or in steady motion) relative to a nearby massive body. General relativity then tells you the relationship between the massive body and the non-inertial frame you find yourself in. Einstein developed this because he realized that if all you know is that you are in a non-inertial frame, then you still won't know whether it was caused by acceleration or gravity, or both. You have to "look outside" your frame to know that.

Answer 4

Yes it is, because Special Relativity applies only to inertial frames of reference, with no acceleration (or gravitational force). The twin paradox inherently involves one of the twins accelerating, because one of them must leave the other and come back.

Answer 5

You can't do a round trip without accelerating, so special relativity is not applicable. Einstein intended this story as a joke and a test to see if anybody had been paying attention during a lecture on special relativity in 1905. It should have brought the house down with laughter. He hadn't yet developed general relativity.



EDIT: In response to Cpt. Mephisto:



The disagreement is merely semantic. Einstein has a defacto copyright on the term "General Relativity". In the generic sense, general relativity (without capital leters) is any mathematical solution to problems involving gravity or acceleration. Yes, it is possible to solve general relativity problems without applying the equations of Einstein's General Relativity.



One numerical solution is to apply the equations of special relativity successively to a large number of small time increments. You accelerate for an hour, then coast for an instant and recalculate all the parameters; then accelerate again, and again, until you get where you're going. Repeat the process using 1/2 hour intervals, then 1/4 hour, etc., until you start getting the same result every time. If Einstein's General Relativity is correct, it should yield the same result.



Any form of general relativity that yields a different result is either wrong, or else it uses the same words with different meanings. Einstein's General Relativity tacitly redefined all the old words, like distance, time, velocity, mass, etc. This results from the fact that light following straight 4D lines is part of the definition of Minkowski space-time.



As for the twins paradox, yes; there truly is a paradox if you apply special relativity to a round trip in the way that Einstein, himself, did in the 1905 lecture where he introduced the twins paradox. He said that each twin's clock runs slower from the other twin's point of view during both the going and coming phases of the trip; he failed to address the question of what happens during the acceleration phases. Therefor, Einstein concluded, with tongue in cheek, each twin perceives that the other twin has aged less than he. Then he waited for the audience to die laughing; instead they are scratching their head to this day. He explained what really happens when he published his general theory ten years later.

Answer 6

I dont know.... but im thinking not because i read that it can be described that the "traveling" twin only ages because he has undergone acceleration and deceleration while the "stationary" twin has not

Answer 7

Later note. There is no paradox, see quote at end of answer.



No it is not. The explanation involves accelerations it is true but special relativity is perfectly capable of handling accelerations. Read the book Special Relativity by AP French, part of some MIT series on physics. I borrow from the book since it is summed up much better than I can say it.



it has been argued by some writers that an explanation of the twin paradox must involve the use of general relativity. The basis of this view is that the phenomena in an accelerated reference frame (including the behavior of a clock attached to such a frame) are regarded in general relativity as being indistinguishable, over a limited region of space, from the phenomena in a frame immersed in a gravitational field. This has been interpreted as meaning that it is impossible to talk about the behavior of accelerated clocks without using general relativity. Certainly the initial formulation of special relativity, although it leads to explicit statements about the rates of clocks moving at constant velocities, does not contain any obvious generalizations about accelerated clocks...... Nevertheless, for any clock that is not damaged by the acceleration, the effects of a trip can be calculated without bringing in the notions of equivalent gravitational fields. Special relativity is quite adequate to the job of predicting the time lost. It had better be, for (as Bondi has facetiously put it) "it is obvious that no theory denying the observability of accelerations could survive a car trip on a bumpy road." And special relativity has amply proved itself to be a more durable theory than this.



And one more on accelerations within special relativity.



Because Einstein developed a whole new theory (his general theory of relativity, published in 1916) based upon the dynamical equivalence of an accelerated laboratory and a laboratory in a gravitational field, it is sometimes stated or implied that special relativity is not competent to deal with accelerated motions. This is a misconception. We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations.



EXTRA. Funny I am using quotes from books - I don't do that normally - but I happen to have a few of those things lying around and I feel that a published work is much better than some web site. So as to special relativity not being competent to handle the "paradox" ot whether or not there even is a paradox I quote from A First Course In General Relativity by Schutz (taken, incidentally, from the preliminary discussion about special relativity).



Elementary introductions to SR often try to illustrate the physical differences between Galilean relativity and and SR by posing certain problems called "paradoxes". The commonest ones include the 'twins paradox', the 'pole in the barn paradox' ......The idea is to pose these problems in language that makes predictions of SR seem inconsistent or paradoxical, and then to resolve them by showing that a careful application of the fundamental principles of SR leads to no inconsistencies at all: the paradoxes are apparent, not real, and result invariably from mixing Galilean concepts with modern ones. Unfortunately, the careless student (or the attentive student of a careless teacher) often comes away with the idea that SR does in fact lead to paradoxes. THIS IS PURE NONSENSE. Students should realize that all 'paradoxes' are really mathematically ill-posed problems, that SR is a perfectly consistent picture of spacetime which has been experimentally verified in countless situations in which gravitational effects can be neglected, and that SR forms the framework in which every modern physicist must construct his theories.



I did the caps stuff back there, not the author. He then gives a very detailed discription of the 'paradox' paying particular attention to the coordinate systems involved. It is too long to quote here since I do not have an electronic copy of the book but I suggest you go and get one and flip forward about 30 pages and do some reading. This applies to some of the other people giving answers. Do some reading. it can be very instructive.



Further note to philip. As Schutz analyzes the "paradox" you do not even need to consider accelerations hence the mention of coordinate systems above. He lays out three coordinate systems: one is on the earth, the other is moving away from the earth at some near light speed and the third is moving towards the earth at the same speed. He then has his space traveler merely jump from one to the other and then shows how the differences in age are realized. I suggest you look up the book since there is a diagram and I do not feel like drawing and posting it,