Einstein, Gravity, and the Twin Paradox (Einstein's 1918 Solution)

explanations to the twin paradox are as numerous as the various channels on youtube which purport to have them but what most people don't know is that in the eyes of the inventor of relativity himself almost all of these explanations are insufficient that is according to einstein there is only one solution that provides a completely consistent answer to the mystery that has fascinated so many adherents of relativity but what exactly is that solution and how conclusive is it really and does it actually require us to leave the framework of special relativity where the paradox was formulated this is dialect with einstein gravity and a twin paradox [Music] in 1905 einstein introduced his special theory of relativity in a paper titled on the electrodynamics of moving bodies there he noted a peculiar consequence of his new theory namely that if a clock traveling at constant velocity is returned to a starting point it will show less elapsed time than a clock which has remained stationary now oddly enough even though relativity is all about the equality of different frames of reference at the time einstein didn't seem to have considered the reverse perspective wherein the stationary clock could be considered traveling and therefore should also show less elapsed time rather this contradiction which would eventually become christened the twin paradox was not addressed by einstein until 1911 when he was giving a lecture in zurich there when posed a question about the clock example by a student he was inspired to assert that although a traveling clock runs slower if it is in uniform motion if it undergoes a change of direction as the result of a jolt then the theory of relativity does not tell us what happens by change in direction or jolt einstein means acceleration essentially he is saying that special relativity cannot handle acceleration so contradictions like the twin paradox are outside its scope this wasn't a spur of the moment defense rather it was a claim einstein truly believed and which he repeated multiple times over the years what's strange is that this claim is most definitely wrong special relativity has no issue handling accelerated frames of reference its postulates merely have to be covariantly extended in more complex forms it's not likely this distinction eluded someone as intelligent as einstein more probably something else about accelerated frames and special relativity bothered him but what was it exactly his take on the twin paradox during his later career gives us some insight in a 1918 lecture einstein gave an explanation to the twin paradox that in a private letter to his friend friedrich adler he indicated he found preferable to all other explanations this solution however appeared to require moving treatment of the problem from special relativity to general relativity and likely because of that fact it never gained wider acceptance as an explanation many physicists aren't aware of it and most textbooks don't even address it but without it einstein implied our picture of reality is incomplete so what is the explanation according to einstein there are two equally valid but distinct perspectives to the paradox the first perspective is that of the earthbound twin who sees her counterpart leave earth at constant velocity travel to the turnaround point briefly experience a force and then return to earth again at constant velocity because the space twin is in motion his clocks run slow and when he rejoins his twin on earth he has aged less than her this is the same as how the earth twins perspective is usually described in the paradox but now let's consider the space twins perspective according to einstein the space twin can claim that he is actually at rest during his entire journey indeed from his point of view it is the earth and the rest of the universe that are traveling away at constant velocity turning around and traveling back again and whose clocks are therefore running slow he can even say that it is his twin along with the rest of the universe that is accelerating at the turnaround point not him this is keenly distinct from the viewpoint of the solution in special relativity where the acceleration of the space twin is treated as absolute and moreover where it is considered to be the reason why the twins's situation cannot be regarded as symmetric but in einstein's view we can still preserve the cemetery we can say that both twins have equal right to claim that they are at rest the entire journey but how does this work how can two completely different accounts of motion remain consistent according to einstein the answer is through gravity [Music] let's take a closer look during the constant velocity portions of the trip the space twin will see his earthbound twins clocks running slow just as in the usual formulation of the paradox however something unique occurs to his perspective at the turnaround point rather than observe himself accelerate the space twin will instead claim to see a uniform gravitational field arise throughout all space one that accelerates the earth his twin and the rest of the fixed stars towards him at the same time he feels a force from his rockets which keeps him from moving along with the rest of the universe now because clocks run faster farther out in gravitational fields distant objects will appear to age very rapidly from his perspective and thus by the time he finishes turning around he will see that his earth twin has aged through more elapsed time than himself this rapid aging will be more than enough to compensate for the dilated passage of time he observed for his earthbound counterpart during the constant velocity portion of her trip this is why when the twins are reunited they both will agree that the earth twin is older alright so that's the explanation it definitely seems a little out there so the question we want to ask is what's really being said here now on youtube one of the few videos dealing with this subject is eugene kutoriansky's twin paradox in general relativity therefore adam will believe that the gravitational field is causing time on earth to flow much if you read his comment section you can see that there's almost more skepticism surrounding this solution than surrounding the conventional solution many viewers see something absurd in the idea of suddenly observing a gravitational field filling the entirety of the universe several commenters point out the fact that since there exists no source to produce such a gravitational field it has to be regarded as fictitious meaning the space twin cannot truly claim that he is at rest einstein actually had an answer for this latter objection he claimed that the source of the gravitational field could be attributed to the motion of the fixed stars that is he wrote just as an accelerated charge induces a changing electric field so should an accelerated mass induce a changing gravitational field in this way an observer's worldview will remain consistent with being at rest even if they are accelerating [Music] we can begin to understand now why einstein believed special relativity couldn't handle acceleration he thought that only by incorporating gravity into the picture could the relativity of all motion be accounted for and the twin paradox fully explained otherwise if you wish to resolve the paradox and special relativity you'd have to begin by asserting that acceleration is somehow a privileged absolute form of motion absolute motion was an idea that einstein strongly disliked and which he claimed kinematically made no sense anyway einstein's answer seems to wrap everything up in a nice bow so is there any reason to remain skeptical of his solution well it turns out yes einstein makes two crucial flaws in his reasoning in his 1918 lecture the first is with his electric charge analogy while it's true an accelerated charge will induce a changing electric field there's a distinct causal order to this process that plays an important role we can break down this order as follows one a force is applied to the charge two as a consequence of one the charge accelerates three as a consequence of two a changing electric field is induced attempting to construct an analogous order for the gravitational field however leads to a contradiction since from the space twins perspective we only have the following two occurrences one a uniform gravitational field arises two earth and the fixed stars accelerate einstein muddles the cause-and-effect relationship of these two occurrences in the first half of his lecture he asserts that as seen from the space twins perspective two is a consequence of one that is that the gravitational field is responsible for accelerating the earth and the rest of the stars but then in the second half of his lecture he claims that the acceleration of the stars is what actually induces the gravitational field to appear in the first place meaning that one would therefore have to be a consequence of two this circular relationship is obviously somewhat problematic the arising of the gravitational field is even more problematic however because from the space twins perspective it appears in a non-local instantaneous fashion throughout all of space this strongly suggests that the space twin can't assert the reality of the gravitational field in fact the whole formulation seems pretty ad-hoc since obviously any intelligent human observer would be able to correlate the firing of his rockets to the acceleration of everything around him and thereby deduce that the force fields he sees are fictitious like the ones observed from inside the frame of an accelerating car this leads to an important point about gravity in general relativity if an observer sees a gravitational field that can be transformed away by a change of coordinates then the curvature of that corresponding space-time region is flat and there exists no real gravity if the observer is unable to find a transformation such that the gravitational field can be made to vanish just as we observers on earth are unable to do with our own gravitational field then this indicates the presence of curved space-time or real gravity this means that the gravitational field formulation of the twin paradox never actually leaves the domain of special relativity because the twins's space-time always remains flat [Music] it's clear einstein conflates some of these issues in his 1918 lecture in hopes of preserving the symmetry of the twins motion but this brings us to the second flaw in his reasoning the fact that he muddles what it actually means to assert the relativity of all motion certainly an observer inside an accelerating vehicle could choose to assert that he is at rest but then the laws of physics he would have to develop to describe the behavior of his system would be different than the laws of physics an inertial observer would use this is exactly because of the force fields he would have to invent in order to explain the motion of everything around him this ability that is to extend the laws of physics to non-uniform frames of motion by modifying their form is called the principle of general covariance now as quoted from the beginning of the video einstein believed in what's called the general principle of relativity or the idea that the laws of physics should take the same form regardless of one's frame of reference for a while he mistakenly thought he had achieved this principle through the theory of general relativity but it was eventually pointed out to him by a physicist named eric kretschman that general relativity only upholds the principle of general covariance not the general principle of relativity in fact one can construct a generally covariant coordinateless framework for newtonian mechanics a fact which surprisingly indicates that we're no closer to truly relativizing motion than we wore three centuries ago this means that explanations such as eugenes which imply that general relativity upholds the quality of all frames in motion are in fact strongly misleading acceleration in general relativity is still an absolute phenomenon and can according to the theory be objectively agreed upon by all observers ultimately this means that the twins do not have equal right to claim that they are at rest the entire journey so where does that leave einstein's twin paradox explanation then well essentially his explanation is just an application of the equivalence principle which asserts the equivalence of accelerated frames of reference and homogeneous gravitational fields the key word here is accelerated the equivalence principle can't even be applied in the first place unless we can objectively agree that a given frame is accelerating alternatively you can say that being in the presence of a gravitational field indicates that your frame is accelerating but either way what you mean by acceleration in these cases is something that will be objectively agreed upon by all inertial observers [Music] now if you ask what in einstein's explanation is responsible for causing the difference in the twins experiences you'll find that the answer is still the force the space twin feels when he fires his rockets which is the same answer you'd get from the special relativity solution in fact if you stack the two explanations side by side the primary difference between them is that in einstein's explanation the rapid aging of the earth twin is attributed to the gravitational field whereas in special relativity that aging is attributed to the rotation of the space twins planes simultaneity this brings us finally to what is actually being said by this explanation which is that the equivalence principle essentially implies the equality of these two phenomena [Music] so ironically it's not gravity that tells us something about the twin paradox but rather the twin paradox that tells us something about gravity [Music] so our final verdict gravity does not resolve the paradox incorporating it into the picture gives us some insight into the equivalence principle and points us in the direction of general relativity but the paradox itself never leaves the framework of special relativity and so those questions that continue to plague us namely what it actually means to say that force is the agent of asymmetry and whether that's ultimately even correct we will continue to explore in future videos this has been dialect thanks for watching [Music] you

Channel: Dialect

Views: 63,136

Keywords: Einstein, Gravity, Twin Paradox, Explanation, General Relativity, Special Relativity, Relativity, Solution, Physics, learning, philosophy

Id: cccuzND_LoQ

Length: 16min 20sec (980 seconds)

Published: Sat Jan 09 2021