Talk:Twin paradox/Archive 2

message: Not using GR seems silly -- as I understand it, GR has no problem with special references frames; the "co-moving clocks" (in free fall from the moment of the Big Bang to the Big Crunch) will age the greatest (show the greatest age in the closed Universe) from creation to destruction. All other clocks, moving with respect to the co-moving clocks will experience a shorter life from bang to crunch. You could find (approximately) this reference frame in your locality by finding the frame in which the entire Universe appears the most symmetrical; or you could find the reference frame in which the Doppler shift of the cosmic micro-wave background radiation is isotropic (this has already been done?) 
: There is a possibility that these two references frames may be slighlty different since it has been claimed that the Universe is rotating with respect to the back-ground radiation (Birch, P. 1982 "Is the Universe Rotating", Nature 298, 451). It has also been claimed, on statistical grounds, that we should expect some tiny difference between the matter and radiation reference frames, even if it is not as large a difference as that apparently observed (Macrossan, M. N. 1987 "A thermodynamic origin of a universal mass-angular momentum relationship"Astrophys. Space Sci, 133(2), 403)
Would there be any philosophical objection to assuming this is a privileged reference frame? As long as length contraction and time dilation happened with respect to this frame, the Lorentz transformations will hold between any two inertial frames in which simultaneity is defined by assuming the speed of light is c in that frame. The situation is then identical to all we know about SR - the effects will appear symmetric to all inertial observers as long as they remain unaccelerated. And no one in the privledged reference frame could claim anything special about their inertial frame, except for the theoretical prediction of GR that clocks in their frame will show the greatest age of the universe at the big crunch.
It may seem a retrograde step to say one frame (in our locality) is privileged - so that the contractions and dilations are real with respect to this frame and "apparent" (i.e. arising from a combination of the real effect and the clock synchronisation procedure, relativity of simultaneity) with respect to all other inertial frame. Nevertheless, it might satisfy the "realists" and might even stop the endless discussion. Of course I could be wrong on this, or about the closed universe and co-moving clocks, and wait for enlightenment. E4mmacro 03:20, 17 December 2005 (UTC)
thread_title: Something like "absolute space": Privileged frames OK in GR?

message: The article says that the (false) paradox arises because some people think
"Relativity says that all observers are equivalent, and no particular frame of reference is privileged."
I am not so sure that that is the only reason. Some people thought that
"Relativity says that physical effects depend ONLY on the RELATIVE motion between bodies (or observers), i.e. kinematics". In fact, the introduction to the 1905 paper would indeed make you think that. Were some people wrong to think SR implied only relative motion mattered?  In this case, the relative motion seems symmetrical (it certainly is kinematically symmetrical in Newtonian mechanics). Einstein himself saw this as a flaw of SR and was prompted to develop GR. It is far too easy to say acceleration makes it obviously asymmetric and not a problem. Read the intoduction to Einstein's 1915 paper on GR, or Newton's discussion of the rotating bucket, and see if you can similarly dismiss the questions raised as non-problems because "the acceleration makes the situation non-symmetric" E4mmacro 14:03, 30 December 2005 (UTC)
replies: text: IMO the two reasons, as you sketch it, boil down to one and the same. I would thus go along with either way of formulating it. And indeed it was understood (and not denied) from the start that according to Einstein only relative motion mattered. But I can't fit your interest in Einstein's motivations and the apparent relevance that you adhere to it for this article with your claim below that others will consider it to be distractive or not of interest. If on the other hand you think that I did not phrase it well in the "origin" paragraph, then please go ahead and improve it, for here I think that you phrased it very well, and we apparently reached consensus on this topic. IMO, some of your sentences here and of Cleon on my personal page deserve a place in the article; just make sure that similar clarifications can be found in literature. Cheers, Harald88 13:32, 4 January 2006 (UTC)
thread_title:  Why it might be considered a paradox 

message: :*I have thought of splitting the article up in two distinct articles, the question is how to call them and how to link them. For sure Einstein's 1918 paradox is less "history" than the 1905 SRT text book exercise. Maybe the following is a good idea, in line with E4mmacro's suggestion: we can have an article called "Twin paradox", that starts with the two meanings, for example "as commonly discussed in textbooks" and "as originally discussed by Einstein", and then link to "Einstein's twin paradox" (Or "Einstein's clock paradox"). The "Twin paradox" page can then limit itself to the text book exercise. 
: Harald88 22:43, 9 January 2006 (UTC)
replies: text: PS I also found guidelines for splitting : Wikipedia:NPOV_tutorial#Article_splitting Harald88 21:21, 12 January 2006 (UTC)
thread_title:  split the article? 

message: is linked to in this article, but the image doesn't exist.  Bowlhover 02:12, 20 January 2006 (UTC)
thread_title:  Image:Rstd4.gif 

message: I copy and paste from above:
:I'm not sure what you mean by 'distance travelled'. They both travel the same distance relative each other, as they do in the regular paradox. Neurodivergent 16:52, 23 January 2006 (UTC)
thread_title:  Mapping motion in a coordinate system 

message: To explain my point, I need to introduce one word of more abstract terminology. The expression manifold is a more abstract word for 'space'. Minkowski space-time is referred to as a manifold. A manifold is analogous to a space, but one or more of the dimensions of the manifold does not have to be a spatial dimension. In the case of the Minkowski manifold, one of the dimensions is time.
Newton's three laws of motion are all three about inertia. All three describe properties of inertia, and thus the three laws serve as three axioms that are sufficient to generate all theorems of newtonian mechanics. The two operative factors in Newton's terrestrial and celestial mechanics are the force of gravity and inertia. 
Special relativity is, like the three laws of motion of Newton, a theory of motion. In other words: special relativity is a theory of the properties of inertia, how the properties of inertia are embedded in the structure of space-time.
In newtonian dynamics, the absolute space serves the purpose of codifying the properties of inertia. First law: absolute space has a structure, and objects in inertial motion follow that structure. It is assumed that Euclidean geometry models the geometric structure of absolute space perfectly, and it is assumed that that is why objects in inertial motion are seen to follow paths that correspond to the straight lines of Euclidean geometry. Second law describing a property of inertia: change of velocity with respect the geometric structure of space is proportional to the applied force. This means that inertia is linked to asserting absolute time. Third law: the geometric structure of space is uniform. If two objects exert a force on each other, changing each others momentum, then their common center of mass remains moving in a straight line with uniform velocity.
Likewise, in special relativity Minkowski space-time serves the purpose of codifying the properties of inertia. Special relativity asserts the existence of the absolute Minkowski manifold. The Minkowski manifold is absolute in the sense that it is immutable, and not being acted upon. Special relativity assumes that all of space-time has a structure and the purpose of using the Minkowski manifold is to model the geometric structure of space-time.
The transition from newtonian dynamics to special relativity was a transition from one concept of an absolute manifold (Euclidean 3-space plus absolute time) to another absolute manifold: the Minkowski manifold.
In special relativity, the concept of velocity with respect to the structure of space-time does not enter the theory. This is in parallel to Newtons three laws, velocity with respect to Newtonian absolute space does not enter Newton's three laws. 
On the other hand, acceleration with respect to the absolute Minkowski manifold is an essential operative factor in special relativity.
: Your explanation about how special relativity can't help to keep something "absolute" about it is nice, I like it. 
: However, you overlook that different mathematical formalisms are possible to describe SRT. The above one is most popular under mathematicians and "geometers", as Oliver Lodge called them. Another mathematical formalism that was very popular among physicists, is the Lorentz-Poincare formalism as also used by Einstein, in which length contraction, time dilation and mass increase are combined with the Newtonian concepts of separate time and space. That approach to relativistic physics had become standard in the time of Feynman. See also special relativity. Harald88 20:05, 25 January 2006 (UTC)
replies: text: The space-time diagram is from the perspective of the 'stationary' twin, Terance, judging from the simultaneity dots. That is, Stella's time is dilated in relation to Terance's. What would a diagram done from Stella's perspective look like? Neurodivergent 18:13, 25 January 2006 (UTC)
thread_title:  The structure of space-time as a theory of inertia 

message: In the twin scenario in Minkowski space-time the structure of space-time is acting upon any object when it goes through a stage where it is accelerating with respect to the structure of space-time. When an object accelerates with respect to the structure of the Minkowski manifold, (which requires a force), its space-like and time-like relations to the rest of the manifold change. See the animation :Image:Lorentz_transform_of_world_line.gif (also featured in the special relativity article, for a spectacular depiction of that. 
The change in relation to the rest of the manifold is represented in the diagram as a shift of the orientation of the plane of simultaneity.
:The space-time diagram is from the perspective of the 'stationary' twin, Terance, judging from the simultaneity dots. That is, Stella's time is dilated in relation to Terance's. What would a diagram done from Stella's perspective look like? Neurodivergent 18:13, 25 January 2006 (UTC)
thread_title:  How this applies to the twin scenario 

message: I would like to emphasize that I'm not introducing anything novel here. I am presenting a synthesis of established knowledge. Because I am presenting existing knowledge, existing diagrams illustrate my 
point. --Cleonis | Talk 12:34, 25 January 2006 (UTC)
thread_title:  Synthesis of existing knowledge 

message: Can anyone make diagrams similar to :Image:Twin_paradox_Minkowski_diagram.png (right), showing the world as seen in the rest frames of the outgoing twin and the returning twin? Having all three side by side might be useful. —wwoods 16:17, 25 January 2006 (UTC)
thread_title:  Spacetime diagrams 

message: In the following paragraph, I have changed "acceleration" to "motion". Please verify. 
"It is hardly surprising that this led to a paradox: If motion is relative, then the traveller may pretend to be stationary. From the traveller's perspective, the Earth is moving away and eventually comes close again. Thus the traveller claims that he can expect everything on Earth to experience time dilation, by the same factor. There is a paradox to be resolved: the traveller can't on return have both aged more and less than people on earth. The issue was about consistency between special relativity's prediction and Einstein's concept of relative motion."  green228 65.88.65.217 05:17, 26 January 2006 (UTC)
replies: text: That's fine; I had put "acceleration" once, because some people misread "motion" to mean "inertial motion" only. But in fact it's clear from the next sentence. Harald88 08:02, 26 January 2006 (UTC)

text: Which earlier 1911 quote? According to literature, the Twin paradox stems from Langevin's article which we have. We don't have Einstein 1911 yet, only this week we heard of it (quotes are unreliable compared to the source itself). If you have it, please send it to me, thanks! Harald88 20:50, 27 January 2006 (UTC)
replies: text:  I didn't mean a quote by Einstein prior to 1911, but the quote below first paragraph in the article, allegedly by Einstein in 1911 (about the organism in a box). green228 65.88.65.217 04:50, 30 January 2006 (UTC)
thread_title:  Origin of the "Paradox" 

message: The first sentence of this section is totally misleading imo. As written, it suggests that the Twin Paradox is not originally a problem of SR -- but of course it must be if it first surfaced in 1911! 
WAS: The usual resolution of the paradox as presented in physics text books ignores its origin and regards it as a problem in special relativity. 
IS:  The usual resolution of the paradox as presented in physics text books regards it as a problem in special relativity, where it first surfaced, although the same paradox exists in general relativity. 
green228 65.88.65.217 07:18, 27 January 2006 (UTC)
replies: text: So far we have no citation of anyone calling the twin scenario paradoxical in 1911, nor even suggesting so. I will clarify it more, apparently we should point out what paradox means... Harald88 12:11, 28 January 2006 (UTC)
thread_title:  The resolution of the Paradox in special relativity 

message: Shouldn't the 'Specific example' section also mention that the travellers could in turn calculate how many years the people of Earth have aged, using Lorentz, as moving clocks run slow. That would be 5.14 * 0.5, or 2.57 years. (This is what the paradox is). Of course, acceleration is not taken into account here, and much of the obfuscation would go away if all the numbers were layed out. Shall we do this with an acceleration of 10g let's say? Neurodivergent 15:29, 28 January 2006 (UTC)
replies: text: Here are the numbers. It's possible for such a ship to reach 0.866c in 30 days. So the trip can be divided in 5 legs: (1) 30 days at 10g acceleration, (2) 5 years at 0.866c velocity, (3) 60 days at 10g acceleration, (4) 5 years at 0.866c velocity, and (5) 30 days at 10g acceleration. Only the travellers 'feel' the 10g acceleration and that's where the asymmetry is. Clocks run slow in gravitational fields, and this is not relative, which helps. However, it's not necessary to be an Einstein to realize that a 10g field does not result in any significant time dilation. Observers in different gravitational fields are not equivalent, but if the gravitational fields are low, they are pretty much equivalent. The effects of time dilation due to velocity don't disappear once the travellers start to experience 10g forces. In other words, the asymmetry is not significant enough to resolve the paradox. I further propose that all 'resolutions' of the paradox are simply alternative ways to calculate time dilation from the perspective of ground control. They don't address the paradox at all or simply respond in general terms without giving further details (e.g. 'the u-turn accounts for it'). It appears to me that time dilation due to relative velocity cannot exist. (Time dilation due to velocity in relation to an absolute aether is still possible, as is time dilation due to gravitational forces.) Neurodivergent 14:57, 30 January 2006 (UTC)
thread_title:  Specific example 

message: Historians of science have documented that Einstein wasn't particularly happy with the name 'theory of relativity'. Einstein liked the name 'invariance theory', because what he did was to focus on the invariants. Arguably the most important invariant of invariance theory is the invariant space-time interval, and the invariance of the space-time interval logically implies the twin scenario. 
Calculation of any twin scenario involves calculating a path integral. The outcome of that path integral is the proper time as counted  by a clock travelling along that path.
The invariance class of special relativity is the class of coordinate systems that are related in the form of Lorentz transformations. Einstein wanted to find out whether he could possible extend the theory to cover a much wider invariance class.
So Einstein was looking for a way to formulate the laws of physics in such a form that for each point in space-time the laws have the same mathematical form, and at the same time a path integral calculation of any physics taking place should reproduce special relativity predictions, which includes the wherabouts of the twins in the twin scenario.
In 1916 Einstein judged that he had met his requirements: extension to a much wider invariance class, and reproducing special relativity path integral predictions for situations with no space-time curvature. The scientific community quickly doubted whether his extension to a wider equivalence class was physically meaningful, but the mathematical soundness of the GR theory of gravitation and motion was not an issue. --Cleonis | Talk 10:28, 29 January 2006 (UTC)
thread_title:  Invariance theory instead of special relativity 

message: Recapitulating: there is the concept of spatial distance, there is the concept of velocity, (which is a ratio of distance and elapsed time), and there is acceleration, (which is a ratio of distance and time squared). Algebraïcally (and acceleration notated as a derivative):
: \Delta s \quad v = \frac{\Delta s}{\Delta t} \quad a = \frac{\delta^2 s}{\delta t^2} 
There are two operative factors in special relativity: difference in spatial distance travelled is one, and acceleration with respect to the structure of space-time is the other operative factor. Many authors have pointed this out, maybe Langevin was the first to do so.
The remarkable thing is that relativistic physics skips the level of velocity. Velocity with respect to any background does not enter relativistic physics. On the other hand, acceleration with respect to the structure of space-time is hugely important in relativistic physics.
How this can be is unexplained. All we know is that pragmatically the theory is working fine, it must be doing something right. 
I am inclined to the following speculation: Minkowski space-time, when interpreted as a manifold, seems to be intrinsically a velocity-space. The physical counterpart of a coordinate rotation of the spatial dimensions of Euclidean space is a re-orientation in space. If you take the Minkowski manifold, and you look at a coordinate rotation that involves the time dimension, then the physical counterpart is a change of velocity. Probably that is not a coincidence. My inclination is to guess that relativistic physics skipping the level of velocity is inderconnected with the properties of the Minkowski manifold. --Cleonis | Talk 17:12, 29 January 2006 (UTC)
thread_title:  Spatial distance, velocity, and acceleration 

message: By now a number of weblinks have been added that may be considered as WP:OR.
Is there an exception policy that I ignore concerning web links? If not, we should clean it up. Harald88 22:48, 16 March 2006 (UTC)
thread_title:  OR links 

message: It is above my editing knowledge, but can anyone nominate this article for a Wikipedia Featured Article?  I think with small corrections, this page has real potential! [21:38, 22 March 2006 72.146.142.73]
: I agree that it has potential, but IMO it's far too early. It needs some more work and - arguably - some elaboration at the end. Harald88 11:10, 23 March 2006 (UTC)
thread_title:  Featured Article