The real twin paradox.
in [Relativity]
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From: Sue... on 2 Dec 2007 01:35 On Dec 1, 3:14 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > "Sue..." <suzysewns...(a)yahoo.com.au> wrote innews:873636c4-2a93-4f87-88a4-19394f1d85f3(a)e6g2000prf.googlegroups.com: > > > SR *does* address clocks that are moving toward each other. > > "General results of the Theory" > > random citation by Sue, only relevance is that it mentions SR > > >http://www.bartleby.com/173/15.html > > [quote] > Sue says that ONLY light clocks obey Einstein-Lorentz time equation.http://en.wikipedia.org/wiki/Proper_time[which 'she' has cited recently as > a source of wisdom] > show the equations of SR and how they can be derived using GR. > > It also shows the so-called twin paradox, and how it can be worked. > > There is no hint that 'proper time' only applies to light clocks. > In fact, such a suggestion would seem to be highly 'improper', to me. Are you offering argument that the semantic operator should be acceptable in mathematics? I think you know that it isn't. When using *time* in an expression, it is meaningless without a process. Read the NIST definition of *second*. http://physics.nist.gov/cuu/Units/second.html I won't even defend my statement in the context you offer it because you failed to port relevant context with your quotes. I think you know better. (I am not sure Einstein did know better, at least in 1905) In this Hyperphysics page approprate context IS included: (pictures too) << A clock in a moving frame will be seen to be running slow, or "dilated" according to the Lorentz transformation. The time will always be shortest as measured in its rest frame. The time measured in the frame in which the clock is at rest is called the "proper time". >> http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html Is it clear to you that the light-path is the only element which can change to conform to the equations? Whether the clock moves away from the obserer or the observer moves away from the clock, the same equations should work. Eh ? That is not the case if we allow a balance clock to respond to an accelerating force. (The force is balanced on the wheel) That is not the case for the Fizeau light-clock moving in dielectric media. (the dielectric provides a preferred frame of reference) That would not be the case if light could move inertially. (many of Einstein's contemporaties and perhaps Einstein too thought that light did move inertially) The speed of light would be violated) Rather than play word games to *win* an argument or nurture a popular myth you can gain some insight to the paradox if you'll ask what role the light path plays with each scenario and each clock type. If a clock is supposed to slow whether moving to or from the observer, only the Fizeau light clock has the necessary elements. An observer *receeding* with it will see it as in-sync with a stayhome clock and therefor indicating the *proper-time* at home. You may recognise, a moving clock is not even required to derive the equation: http://www.eden.rutgers.edu/~mbarbato/Remote%20Sensing_files/page0003.htm ....but a light path IS required. What Einstein says about inertia in 1905 is not the same in 1920 and neither may be totally on-the-mark. <<One may define a quantity which is divergence free analogous to the energy-momentum density tensor of special relativity, but it is gauge dependent: i.e., it is not covariant under general coordinate transformations. Consequently the fact that it is divergence free does not yield a meaningful law of local energy conservation. Thus one has, as Hilbert saw it, in such theories `improper energy theorems.' >> http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html Sue... > > -- > bz
From: Sue... on 2 Dec 2007 01:59 On Dec 1, 9:12 pm, "papar...(a)gmail.com" <papar...(a)gmail.com> wrote: > On 1 dic, 22:23, colp <c...(a)solder.ath.cx> wrote: > > > > > > > On Dec 2, 6:10 am, Dono <sa...(a)comcast.net> wrote: > > > > On Nov 30, 11:03 pm, colp <c...(a)solder.ath.cx> wrote: > > > > > On Dec 1, 6:58 pm, Bryan Olson <fakeaddr...(a)nowhere.org> wrote: > > > > > > colp wrote: > > Describing the experiment from the point of view of one of the twins > > does show the paradox; the twin observes the time dilation of the > > other twin during both the outbound and return inertial frames, and > > this effect must be compensated for somehow if a paradox is to be > > avoided at the end of the experiment when the twin's clocks are > > observed to tell the same time in a common inertial frame. > > > What is required to solve the paradox is a description of how a twin > > sees the other twin's clock jump forward. > > None of the twins can (realistically) see anything from the other twin > but the signals he receives. This is a really problem of communication > of information. That is the reason why a geometric view helps to see > what is going on. That is the reason why using a third twin, who stays > at Earth, eases the drawings and understanding of the problem (any > frame of reference can be used with the same results but using the > Earth frame helps). From the graphic representation, one can see that > each travelling twin experiences time dilation, with respect to the > Earth frame, both in the outward and inward legs of the trip, the > effect being caused by them moving at relativistic speeds. Information > received by one of the twins from the other two, is clearly dependent > on whether his ship is going outward (and so the signals take a longer > time to reach him) or coming inward (where signals take less time to > reach him). Final result: both travelling twins arrive back to Earth > having experienced the same length of time (according to their local > clocks), but during the trip they "saw" the signals coming from the > other twin doing strange changes of rates (very slow in the first part > of the trip, then quite normal in the middle part and, finally, quite > fast in the last part. Those observations say nothing with respect to > the time dilation experienced (as it has been pointed out they will > notice nothing peculiar in their voyages), which finally manifest > itself when both twins compare their clocks with the third twin who > remained at Earth, observing that they are indeed younger. This is a violation of the Principle of Relativity. > Acceleration is not really relevant in this problem, as long as the > acceleration period is small with respect to the inertial period (just > a little bit over a couple of years of acceleration at 1 g will take > the ship to near 0.99c, or shorter if larger g's are used). If the Twins agree on the number of orbits made by Jupiter's moons, you have quite an argument in the field of biology if you want to say the twins hair length should differ because of their relative motion. Arrange for your twins measure and record hair length at the beginning, middle and end of the experiment. If the records are not in reasonable agreement, then the principle of relativity has been violated. << it is impossible to perform a physical experiment which differentiates in any fundamental sense between different inertial frames. >> http://farside.ph.utexas.edu/teaching/jk1/lectures/node7.html Sue... > > Miguel Rios- Hide quoted text - > > - Show quoted text -
From: colp on 2 Dec 2007 02:15 On Dec 2, 6:10 pm, Dono <sa...(a)comcast.net> wrote: > On Dec 1, 5:23 pm, colp <c...(a)solder.ath.cx> wrote: > > > On Dec 2, 6:10 am, Dono <sa...(a)comcast.net> wrote: > > > > On Nov 30, 11:03 pm, colp <c...(a)solder.ath.cx> wrote: > > > > > On Dec 1, 6:58 pm, Bryan Olson <fakeaddr...(a)nowhere.org> wrote: > > > > > > colp wrote: > > > > > > Bryan Olson wrote: > > > > > >> colp wrote: > > > > > >>> What am I making up? > > > > > [...] > > > > > >>> For their clocks to be the same time, A must have observed that B's > > > > > >>> time was compressed at some stage. > > > > > >>> SR does not describe time compression. > > > > > >> That you made up. According to SR, A's change it frames will > > > > > >> result in A seeing B's age jump forward. > > > > > > > Wrong. SR has nothing to say about non-inertial frames. > > > > > > > Special relativity (SR) (aka the special theory of relativity) is the > > > > > > physical theory of measurement in inertial frames of reference > > > > > > proposed in 1905 by Albert Einstein in his article "On the > > > > > > Electrodynamics of Moving Bodies". > > > > > > >http://en.wikipedia.org/wiki/Special_relativity > > > > > > Reading the page you cite, we find: > > > > > > Special relativity does not account for gravity, but > > > > > it can deal with accelerations. > > > > > How does special relativity deal with accelerations? > > > > > Cyclotron experiments have shown that, even at accelerations of 10^19 > > > > g (g = acceleration of gravity at the Earth's surface), clock rates > > > > are unaffected. Only speed affects clock rates, but not acceleration > > > > per se. > > > > >http://metaresearch.org/cosmology/gps-relativity.asp > > > >http://physics.nmt.edu/~raymond/classes/ph13xbook/node59.html > > > The physics.nmt.edu page describes accelerations in SR. However the > > page does not describe what time dilation effects occur in an > > accelerated frame. Such a description is necessary to solve the > > paradox described in the OP for SR. > > http://en.wikipedia.org/wiki/Twin_paradox#Accelerated_rocket_calculation Those calculations are just more complex forms of the standard SR gamma equations. The extra complexity is that calculus is used to determine the integral time dilation for varying velocity. Thus gamma will still be greater than one, just as it is for interial frames.
From: paparios on 2 Dec 2007 08:20 On 2 dic, 01:31, colp <c...(a)solder.ath.cx> wrote: > On Dec 2, 3:12 pm, "papar...(a)gmail.com" <papar...(a)gmail.com> wrote: > > > > > On 1 dic, 22:23, colp <c...(a)solder.ath.cx> wrote: > > > > On Dec 2, 6:10 am, Dono <sa...(a)comcast.net> wrote: > > > > > On Nov 30, 11:03 pm, colp <c...(a)solder.ath.cx> wrote: > > > > > > On Dec 1, 6:58 pm, Bryan Olson <fakeaddr...(a)nowhere.org> wrote: > > > > > > > colp wrote: > > > Describing the experiment from the point of view of one of the twins > > > does show the paradox; the twin observes the time dilation of the > > > other twin during both the outbound and return inertial frames, and > > > this effect must be compensated for somehow if a paradox is to be > > > avoided at the end of the experiment when the twin's clocks are > > > observed to tell the same time in a common inertial frame. > > > > What is required to solve the paradox is a description of how a twin > > > sees the other twin's clock jump forward. > > > None of the twins can (realistically) see anything from the other twin > > but the signals he receives. > > These signals can be described as clock ticks. According to SR, while > the twins are in inertial frames the ticks that are sent by the other > twin will be sent at a slower rate than the ticks that are sent from > the twin's local clock. > > It doesn't matter how long it takes for the tick signals to get from > one twin to another. All that matters is that the rate that the ticks > are generated by the other twin is slower becuase of the time dilation > while they are in inertial frames. Every signal than is sent must be > received by the other twin in the experiment. > Of course all of the signals sent are received, but the signals have to cover a lot of space to get into the other twins, and that takes time (years in this experiment) and so conditions, both at the sending and at the receiving twin, do change causing those signals to be received sometimes much slower than the time dilation, sometimes at the time dilation rate and sometimes much faster than the time dilation. The graphical view of the experiment shows these changes quite clearly. > > This is a really problem of communication > > of information. That is the reason why a geometric view helps to see > > what is going on. > > You're talking about Minkowski diagrams, right? > > > That is the reason why using a third twin, who stays > > at Earth, eases the drawings and understanding of the problem (any > > frame of reference can be used with the same results but using the > > Earth frame helps). > > The paradox isn't apparent when the events are viewed from a single > inertial frame. Minkowski diagrams represent events according to such > a frame. > In the page I mentioned some days ago, there are two graphics: the first represents the story line of the Earth twin. The second represents the story line of the travelling twin, so the same experiment is viewed from the two frames involved. Of course, the travelling twin diagram is more complex and I can tell you that the diagram for the two travelling twins is also more complex (it looks like a butterfly). > > > > From the graphic representation, one can see that > > each travelling twin experiences time dilation, with respect to the > > Earth frame, both in the outward and inward legs of the trip, the > > effect being caused by them moving at relativistic speeds. Information > > received by one of the twins from the other two, is clearly dependent > > on whether his ship is going outward (and so the signals take a longer > > time to reach him) or coming inward (where signals take less time to > > reach him). Final result: both travelling twins arrive back to Earth > > having experienced the same length of time (according to their local > > clocks), but during the trip they "saw" the signals coming from the > > other twin doing strange changes of rates (very slow in the first part > > of the trip, then quite normal in the middle part and, finally, quite > > fast in the last part. Those observations say nothing with respect to > > the time dilation experienced (as it has been pointed out they will > > notice nothing peculiar in their voyages), which finally manifest > > itself when both twins compare their clocks with the third twin who > > remained at Earth, observing that they are indeed younger. > > The fact that the twins are younger than a third twin at the end isn't > the paradoxical aspect of the experiment. > > > Acceleration is not really relevant in this problem, as long as the > > acceleration period is small with respect to the inertial period (just > > a little bit over a couple of years of acceleration at 1 g will take > > the ship to near 0.99c, or shorter if larger g's are used). > > The importance of acceleration is that it is the only situation where > a twin might be able to experience an effect which compensates for > the time dilation of the other twin. > > The consideration of acceleration is necessary because it must have an > effect if the explanation of the classic paradox is true. > In the classic paradox, acceleration is used as an argument against > symmetry, in which either twin could have been considered to be the > travelling twin. Paradoxically, <grin>, acceleration is not used to > quantify time dilation in the classic case, only velocity. (According > to the argument presented athttp://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_i...) > Well for me the explanation is more simpler than that, having to do with the obvious event of each travelling twin having to use two inertial frames, while the Earth twin just uses one. The travelling twins, in each one of their two used inertial frames, are experiencing time dilation, as viewed by the third twin. Miguel Rios
From: paparios on 2 Dec 2007 08:44
On 2 dic, 03:59, "Sue..." <suzysewns...(a)yahoo.com.au> wrote: > On Dec 1, 9:12 pm, "papar...(a)gmail.com" <papar...(a)gmail.com> wrote: > > > > > None of the twins can (realistically) see anything from the other twin > > but the signals he receives. This is a really problem of communication > > of information. That is the reason why a geometric view helps to see > > what is going on. That is the reason why using a third twin, who stays > > at Earth, eases the drawings and understanding of the problem (any > > frame of reference can be used with the same results but using the > > Earth frame helps). From the graphic representation, one can see that > > each travelling twin experiences time dilation, with respect to the > > Earth frame, both in the outward and inward legs of the trip, the > > effect being caused by them moving at relativistic speeds. Information > > received by one of the twins from the other two, is clearly dependent > > on whether his ship is going outward (and so the signals take a longer > > time to reach him) or coming inward (where signals take less time to > > reach him). Final result: both travelling twins arrive back to Earth > > having experienced the same length of time (according to their local > > clocks), but during the trip they "saw" the signals coming from the > > other twin doing strange changes of rates (very slow in the first part > > of the trip, then quite normal in the middle part and, finally, quite > > fast in the last part. Those observations say nothing with respect to > > the time dilation experienced (as it has been pointed out they will > > notice nothing peculiar in their voyages), which finally manifest > > itself when both twins compare their clocks with the third twin who > > remained at Earth, observing that they are indeed younger. > > This is a violation of the Principle of Relativity. > > > Acceleration is not really relevant in this problem, as long as the > > acceleration period is small with respect to the inertial period (just > > a little bit over a couple of years of acceleration at 1 g will take > > the ship to near 0.99c, or shorter if larger g's are used). > > If the Twins agree on the number of orbits made by Jupiter's > moons, you have quite an argument in the field of biology > if you want to say the twins hair length should differ > because of their relative motion. > > > > Sue... > > > Because the orbits made by Jupiter's moons are also by all means "information", and that information firstly, can be considered to be sent from an inertial system (like Earth) and, secondly, takes a long time to arrive to the travelling twins (if they can received it at all), then it is obvious that the rate of changing of that information will be observed sometimes slow, sometimes equal and sometimes faster than the actual number (or ticks), as the graphical representation puts in evidence if you take the time to do it. It is also evident that, at the end of the voyage, the number of orbits as counted by all the twins will be the same. However, the travelling twins will notice that (using numbers from my example) while to the Earth twin there were N orbits in 20 years (measured by his local clock), for the travelling twins there were N orbits in 16 years (measured by their local clocks). Miguel Rios |