Faulty reasoning: You assume the 'years' difference is 16 for the traveller, and 20 years for the fixed earth resident. There is no reason to assume this without the actual experiment. Better to assume the speed of travel is 0.8 c and then calculate the resultant relative 'time' difference. If the calculation matches the actual measured time difference, you are correct.
Okay, so when he stops, he changes frames, and by his reckoning, when he does, the time on Earth goes from the year 2003 to 2010. In other words Earth ages more slowly than he does on the outbound trip, then advances to read ahead of his own clock when he comes to a stop at Twin Earth. You have to remember that there is no one reference frame for B in this scenario. There is the frame when he is traveling from A to B, and the frame where he is at rest with respect to them. So what happens according to B is a combination of what happens while he is traveling and what happens when he changes frames. I'll try and answer that with an analogy: Assume that you have a 3in x5in rectangle sitting on a table. You look at it and say that it is 3 in wide and 5 in tall. Someone else looking at it from a different position says that it is 5 in wide and 3 in tall. From this we see that the measurements of width and height are dependent on the direction you are looking from. In Relativity, time and space are "frame dependent" in much the way as width and height are "direction dependent" in the above example. For Twin A, Time runs slow for Twin B as he travels between Earth and Twin Earth. For Twin B, the distance between Earth and Twin Earth is only 4.8 ly. Asking which of these views represents what truly determines the time differential between the two is like asking whether the rectangle is really 3 in. wide or 5 in. wide.
A velocity of .8c means that you travel at a velocity of 239,833,966.4 m/s. 16 years is 16*(365.25*24*60*60 seconds per year), which is 504,921,600 seconds. A distance of 16 light years is 504,921,600*299,792,458=151,371,687,561,292,800 meters. 151,371,687,561,292,800/239,833,966.4=631,152,000 seconds of travel time. 631,152,000/(365.25*24*60*60)=20 years So it takes 20 years to travel a distance of 16 light years at the velocity of .8c.
The calculations are far easier like this, \({\frac{16}{0.8} = 20\). Edit: but this Has only a peripheral relationship to the time dilation issue of the thread.
This is a little off topic as well (and more to your point) but Dan Koks has an article on how clock rates only depend on velocity and are unaffected by acceleration. The internet article is entitled “Does a clock’s acceleration affect its timing rate (I am unable to post links yet) and I agree with most of what he says. I take issue, however, with his section on gravitational time dilation. In this section he uses an example of two astronauts who are at rest on the launch pad who believe they are accelerating in deep space at 1 g. If they are at opposite ends of rocket (one at the top ad one at the base) and exchange light signals the astronaut at the base sees the light blue shifted while the astronaut at the top sees the light redshifted (nothing here about actual clocks). I think what he is implying is that the reason for gravitational time dilation with a GPS satellite is because the signal on the way up is redshifted and the signal on the way down is blue shifted and this must be taken into account. I always thought a clock that was higher in a gravity well ran faster than one on the surface of the Earth. I am not sure I ever really understood the reason why but if it is because of the differential in the signaling that would explain it. I tend to think it is something different.
My earlier post on the issue was in response to this quote from your post #18, in this thread, I only raised the issue since it almost always confuses the underlying discussion. Even when the primary posters/debaters are well versed in both SR and GR, as they relate to the issues involved. The current GPS system accounts for time dilation associated with both satellite velocity and position in the Earth's gravitational field (SR and GR effects). As mentioned earlier the gravitational effect is far greater than the velocity dependent effect, still miscalculating either could send you into a neighbor's tree, instead of your driveway. There are also timing issues that involve the Doppler effect and time delays for transmission signals between the satellites and ground, but these are handled in a different manner. They are a separate issue, from the SR and GR time dilation effects. BTW the best hit from a quick search for "Dan Koks" and this issue was your post above... I could find nothing else relevant, to the issue.
Thank you for clarifying that for me. I guess gravitational time dilation could be the topic of its own thread.
Thank you for that analogy and I think I understand your point. I know, however, that this is what we say. I just do not think that anyone really believes that the distance that Twin B traversed was foreshortened to 4.8 light years. I think the concept of length contraction is a measurement problem and not an issue of perspective. The distance is really measured to have contracted - motion affects that measurement and hence reality. At the end of his journey to Twin Earth, all that we can demonstrate is that six years has passed for Twin B while on Earth (for Twin A) and Twin Earth 10 years have passed. The 3 in. by 6 in. rectangle is still 3 in. by 6 in. no matter what your perspective is. So yes I think we can ask what truly causes the time differential. In special relativity time is treated with a sense of perpendicularity to the space dimensions and in general relativity time is treated more formally as a fourth coordinate. Because of this we assume time has a dimensional quality and as such we also assume and the equations seem to indicate that this degree of freedom – motion though time – is in some fashion related to our motion in space. It is believed that at rest our motion through time is c. We assume that as our motion through space increases our motion through time slows and hence time dilation. David Bohm said: “In my opinion progress in science is usually made by dropping assumptions.” Maybe it is time to drop some of our assumptions and see what we are then left with.
There is a subtle issue involving length contraction that often comes up in these discussions, which is an assumption of a direct relationship between time dilation and distance traveled. The length of objects, becomes length contracted when the object is in motion. This only becomes apparent when relativistic velocities are involved. "Distances" are never length contracted, except when the distance in question is represented by the length of an object. The distance between two points or two planets, is defined from their mutual at rest frame of reference. There is no object in motion to become length contracted. When the traveling twin travels at a relativistic velocity, though his/her clock is affected by time dilation, the distance traveled is not. In this hypothetical the distance is defined by a rest frame of reference established by two planets. That distance does not change, even for someone traveling at the speed of light, while the time experienced during their trip is affected. If this were not the case, a light year would be a variable..., the speed of light is agreed to be a universal constant, with that one must also accept that the distance light travels in a given time is also constant. A light year is a light year to all observers... Even when an observer's experience of time is affected by their velocity.
This is incorrect, distances are contracted the same exact way as lengths are. Think about the "muon" experiment, in the frame of the muon, the distance traveled is contracted , thus explaining the outcome of the experiment. Same error as above. ...from the perspective of the traveler, the above is incorrect. At the root of your confusion is your belief that only lengths attached to material objects "contract" , while distances, do not. There is no rational reason for this belief, the distance between two points is observer dependent, just as the way length is.
Tach, we have had this same debate in the past. Your position is tired and without merit. While you can argue that there is time dilation in the muon's frame, the distance it travels remains unchanged by its motion. Distance itself is not moving. Your argument is like saying if I drive fast the road gets shorter. The length of the road and the distance any object travels in space are NOT length contracted by the motion of a spaceship, muon or even with your foot on the floor board. The twin paradox is a SR thought experiement in flat spacetime and abscent any forces apart from those expressly mentioned. To your last point..., so as soon as the traveling twin finds that his clock was running slow relative to the fixed distance between the two planets, you content that they suddenly jump back to their original distance? What in the world have you been smoking?
Don't get trapped into thinking that the Distqnce as measured by A is somehow more "real" than the distance measured by B. The distance according to A is just as much a "measurement" as the distance according to B.
This is as incorrect now as it was before. A basic rebuttal of your misconceptions can be found here. Read carefully the explanation "Relativistic, Muon-Frame Observer ". In relativity, distance measurement is observer dependent, you can find this in any elementary book on SR. Somehow, you got in your head that while (object) length contracts, distance doesn't. It is very simple really, if observer A measures a distance as \(D\), any other observer A' moving with speed \(v\) with respect to A, will measure the distance as being \(D'=D \sqrt{1-(v/c)^2}\). Mainstream science says you are wrong.
I hear a lot of comments saying Tach is right and no proof of that statement. The two planet thought experiment begins with two planets and a defined distance between them. One twin stays at home on one planet the other travels. The traveling twin experiences time dilation as a function of his/her velocity during a trip between the two planets. What is being suggested is that because the traveling twin's clock measures time at a different rate than clocks at rest on both planets, the distance between the planets is different for the traveling twin than it is for the stay at home twin or any observer on either planet. The difficulty with this argument is that, when the traveling twin returns home, and compares his clock with the stay at home twin's clock, the affect of time dilation is discovered and properly determined to have affected the traveling twins clock.., not the stay at home twin's clock or any clock on either planet. Second, while the traveling twin is traveling, without any knowledge apart from observation of each other neither twin knows who is actually traveling, they both see the other as if they were the one moving, this is at least in part a portion of the paradox resolved when the traveling twin returns home and lies at the heart of SR, WITHOUT special knowledge or an outside outside frame of reference what each twin measure appears to be the same, until they are reunited. Remember, this is a flat space(time). There is no curvature of space or gravitational interactions. The only thing that supports any conclusion that a "distance" is an attempt to define the distance traveled using the traveling twin's clock, which is time dilated relative to the two planets and the distance between them. The muon link does present the time dilation issue well, and while one can argue there is some length contraction of a distance, that can only be accomplished should you also set aside knowledge of affect that velocity has on clocks. Length contraction of a distance has never been proven where the distance is defined in a flat space(time). We cannot even reproduct the time dilation paradox using lengths, since while clocks do retain a record of time dilation, lengths do not. As long as the traveling twin and you are unaware of the time dilation affect on the twin's clock the length contraction argument has some logical place. As soon as SR and the time dilation of the traveling twin's clock is known, something I assume you all are aware of, the elapsed time as defined by the traveling twin's clock can only be used to define the distance traveled where the time dilation is incorporated into the calculations, at which point the "distance" between the planets remains fixed and unaffected by any illusion of length contraction resulting from ignorance and illusion. A distance is defined in the at rest frame of the "distance" and is not changed by the time dilation affects that velocity has on a traveler's clock. And once more remember the thought experiment is limited to the conditions of SR and a FLAT space(time). All other forces and effects cannot be applied to resolution of the paradox.
It also occurs to me that this is actually a faulty application of the Lorentz factor. Distance is a measurement between two points or locations. The Lorentz factor is a relativistic modifier for velocity. Distance by itself is only related to velocity and visa versa, as a function of time. And this assumes you are using a clock which is measuring time in the same frame of reference in which the distance is defined. Tach, you have a far better working knowledge of the math than I do. If you want to present something like the above go through the trouble of connecting the dots. While one's perception of distance may be affected by velocity, velocity does not in and of itself define distance.
Simple question: do the twins measure the distance between the two planets to be the same? Yes or No? This is not what "is being suggested". Make the effort to understand the links provided to you. Nope, this is not what has been pointed out to you. Make up your mind, is there contraction of the distance in the muon experiment or there isn't? There is no such thing as "there is some ....". Yes or No? Ahh, here come the denial of length contraction in all its glory. You realize that the interpretation of the muon experiment as viewed from the muon frame fully contradicts your fringe denial of length contraction, don't you? No one claimed that, you simply do not understand (and deny) the length contraction effect. First you denied it applies to "distances" (you claimed it only applies to the length of material objects), now you deny it wholesale. So? What does this have to do with your inability to accept length contraction as a standard effect in SR?
