md65536

That's accounted for in the example. Both the inertial twin and traveler see 365,000 pulses. If that's all there were, and then it blew up, that's all anyone would see. Inertial twin saw 365,000 pulses while aging 1 year, and the traveler saw 365,000 pulses while aging 0.5 years. After a cursory glance at that topic, one way to see that Janus is right is to consider the perspective of the traveler in its rest frame. In this frame, the pulsar has a relative velocity pointing "backward" of the direction the traveler is facing. If the pulsar is far away, and light from it comes in "now" at 90 degrees, then the pulsar was directly to the side when that light *left* it, so the pulsar must have traveled a great distance "backward" while the light was incoming. However if we establish that the pulsar really is directly to the side "now", but that light from it has still taken a long time to reach us---just shift what we observe of the pulsar forward---it must appear to be coming from a forward direction. The animation here shows what I mean: https://en.wikipedia.org/wiki/Aberration_of_light#Relationship_to_Light-Time_Correction_and_Relativistic_Beaming

That's an interesting twist I usually avoid thinking about! Edit: And after reading the preceding post by Janus, I realize the following is in error: Moving 90 degrees relative to something is transverse motion and the transverse Doppler effect applies again. Based on a reply in another thread (http://www.scienceforums.net/topic/75019-gravitational-redshift-and-length-contraction-factors/#entry744881), I think that the relativistic Doppler effect is time dilation combined with (multiplied by) a pseudo-classical Doppler shift of light. With transverse motion, there's no classical Doppler shift, so you get only the effect of time dilation, which is why the transverse Doppler effect is 1/gamma -- perhaps this is false due to aberration?? So you'd see the pulsar's clock tick at its actual rate of 1/gamma compared to yours, redshifted due to time dilation but not due to any change in delay of light. In a way, this would give you a sense of what time dilation "really looks like." Edit: or... quite the opposite! Now I'm not sure now if the transverse Doppler effect applies, but if it does and is applied correctly it predicts what Janus said...

Are the length contraction and redshift factors the same in GR? Say there are 2 observers A and B, with A on the surface of a planet and B hovering high above. If A sends a signal to B it loses energy climbing out of the gravitational well, and appears red-shifted to B. Also, B's meter stick appears longer than a meter to A, and A's appears shorter than a meter to B. Suppose A sends a signal with a wavelength of 1 m, and B receives it with a wavelength of 1.1 m, does that mean that A sees B's meter stick measuring 1.1 m long, and B sees A's measuring 0.909 m long? I think I must have this wrong just because the factors aren't the same in SR. I guess time dilation must also affect the redshift, but not the length contraction??? Would the difference in redshift and length contraction factors be fully accounted for with time dilation? Are there any examples online that calculate the two factors in a simple case?

Another way to put it is that a reversed movie reverses causality. You see effects happen before their causes. You see ET leaving before it leaves. The movement of photons is reversed with everything else. Having ET pass us by and recede is not the same as reversing all of time. Perhaps that, rather than simple understanding, is what you're looking for?

No, if you reverse a movie it will take the same length as the movie! It's a 1 day movie of incoming ship and incoming photons. Reversed it would be a 1 day movie of outgoing ship and outgoing photons. So for example, if you watch the ship leaving you over 730001 days, and you sent a signal after 1 day, ET would get your signal at the same time that it arrives at its destination (after it travels for 365000 additional days by your watch). The difference in time that it takes a ship at v=365000/365001 to travel 365000 light-days, vs light, is 1 day, whether it's incoming or outgoing. Edit: Or if you mean that a movie of reverse action will not appear the same as a reversed movie, then yes that's true. A movie of either forward or reversed action will still require incoming photons, so appearance is not time-symmetric reversal of observations are not the same as observations of reversed phenomena. Or something.

So you see that it all works out. If it comes in very near the speed of light, there is little difference between the timing of it and light (according to the astronomer). If it goes out near the speed of light, it takes about twice the time of light, because the object has to get out there and the light has to come back in. The object starts and ends at the same distance from Earth; the two events have the same delay of light. So the change in delay averages to 0 and on average it appears to travel at velocity v: (365000+365000) light-days traveled / (1 + 730001) days watched = 0.99999726 light days per day. This is true in SR. As long as we're using only one observer and clock, it's also true in classical physics, where the speed of light is c (eg. unaffected by ship's velocity, or signals are sent from markers at rest, or Earth is at rest in an aether).

Plus 365001 days measured on Earth for ET to get there equals...

No, you're forgetting that light from the receding object is also delayed.

Sorry if I'm straying off-topic here: Ignore this post if you're only concerned with the twin paradox. But there's a curiosity here... At the closest that the object comes, I think that light seen from this event will already be redshifted (http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Transverse_Doppler_effect). So the change from blue to red appears to occur sometime earlier, when the object still appears to be approaching (transversely). I think? This effect, and the time that the object appears to significantly change from blue to red, is negligible if it passes close enough.

Interesting. So here, A and B have identical periods of acceleration, with the same experience of proper acceleration, but with different periods of inertial motion before and after the accelerations. And still the twin paradox effect occurs here. This is probably a much better example than mine. Acceleration is still important here, in order to get the twins to follow different paths and return to a common path. However this is done here with twins while I relied on swapping one of the twins with a surrogate. The point is slightly different but I think this more clearly shows that it is time or distance traveled at particular velocities that produces the entirety of the difference in aging in SR, and not the acceleration.

What's funny, tho frustrating, is that the same diagram can be used to describe a classical version, where the traveler ages the same amount as the inertial twin. Or to be more precise: The diagram doesn't even specify the traveler's measure of time. Ignoring time dilation, the prediction of events according to only the inertial twin's clock can be made using only classical physics, and it still works out the same! Velocity = 0.5c, duration of trip = 4 units of time, Turn is seen at t=3, distance to turn is 1 unit of distance. Delay of observation of Turn, shown clearly on the diagram, is 1 unit of time. Relativity isn't even needed to understand this diagram! It probably requires a grade-school level of understanding of math and physics to understand it??? (And highschool or likely greater to see it work in SR though.) michel123456, this whole problem could be understood in terms of classical physics first, if that would make it easier!

Draw a horizontal line from Turn to the t-axis, and say "Light 'should' arrive instantaneously." Why do you have light at a 45-degree angle, traveling at a velocity of c, if the astronomer really should observe T4-T2? The astronomer does observe what the math says, including the observation of Turn being delayed by 1 unit of time due to the velocity of light. The astronomer observes what the math says, what the graph says, what her eye says. The astronomer does not instantly observe the entire universe. I've never known anyone to have so much trouble with the concept of delayed observation due to speed of light. I mean, how are you accounting for light in your diagram or description? You drew a line representing light... you realize that what the astronomer observes of Turn arrives at the astronomer in the form of light??? So what sort of calculation or reasoning could possibly convince you that the astronomer "should" observe Turn instantaneously?

0.99999726 c IS very (very very) very extremely fast... the calculations reflect that. I was curious if it would be enough energy to destroy the entire Earth if ET crashed at that speed. Just using the google, I plugged the number into http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html, using the mass of Enterprise D, and got an answer of 1.524x10^28 joules. http://io9.com/5876473/how-much-energy-would-the-death-star-require-to-destroy-earth claims it would require 2.25x10^32 J to destroy the Earth using the Death Star's laser... almost 15000 times more. So no, ET on the Enterprise at this speed would only destroy 1/15000th of the Earth. So that's like an area close to the size of Australia to a depth of 10km. Or vaporize 140m off the entire surface of the Earth. Another way to put it, it's about 363 times the estimated energy of the asteroid that killed the dinosaurs. These are just google-based calculations so I might be off by some orders of magnitude, but anyway: I assure you that the astronomer does not tell you this near-c impact will be gentle!!! Edit: If it was just ET without any ship, it'd only be like 1/690th the impact of the Chicxulub impact... so probably nothing for most of us to worry about.

The way to salvage understanding here is to use calculations that everyone can agree on (it seems to have been done, using the numbers Janus gave in post #145), and contemplate the meaning or the visuals around that. The 1-day figure is a real observation of various events that occurred over a thousand years + a day for the astronomer, and the image of those events are just delayed different amounts. If ET lands "gently" then it has somehow decelerated extremely quickly. This works fine if it has negligible mass, but... Consider that at race speeds, a car hitting a wall can disintegrate. At relativistic speeds there's no "gentle" landing here. There are other relativistic effects that you'll see, too. If you can continuously watch the "hilarious fast motion" then there is light coming from ET for its 854.4 days, which you get all in one day, so it will appear brighter to you, also blue-shifted. To consider the hilarious motion, imagine it walking at relativistic speeds: Imagine that a light day is one step (of a giant)... the 1000 LY distance is 365000 steps for you, but the length-contracted distance is 854.4 steps for ET. That means that for every step you see it take, it covers 427.2 (=gamma) of your "rest" steps. In other words ET looks hilariously stretched, incoming (and hilariously squished if outgoing). The reason: Even though ET's lengths are actually length contracted according to you, the image of one step takes longer to reach you than the next step does (each step covers 472.2 of your light days so each next step is delayed 472.2 days less than the previous one). That is, it covered 1/854.4 of your rest distance in one step, taking 472.2 of your days to do it, but each step is seen over 101 observer seconds. It's not moving hilariously quickly (the opposite actually), it just appears so due to reduction in the delay of light as it approaches, and it's not stretched but it appears so (what you call "false", but is perhaps just an "illusion" or simply its "appearance"). This is getting complicated now, but suffice to say: The hilarious image of ET will appear distorted in several ways. It's probably hard to image because we don't experience it in every day life, and so it would probably be weird to see. (Note, they reduce c, while I scaled sizes way up with the giant ET, the result is the same.)

No problem... the original scenario presented by michel123456 (post #137, #143?) used 1 day for both the (proper) time that the traveler ages, AND the time that passes on Earth while the traveler is seen traveling, which doesn't work out. You presented the scenario where 1 day is the traveler's time, and Janus present the different scenario where 1 day is the Earth time while the traveler is watched, and the differences are now clear. If that confuses anyone they could simply choose one scenario and ignore the other...

So let me get this straight: ET traveled 365000 light-days in 365001 days (ignoring leap years) according to our measurements, equalling a velocity of 0.999997260281479c, and was measured by us as taking 365001 days by our clocks, but appeared to take only 1 day because the image of it leaving is delayed by 365000 days due to light's finite speed and that ET aged 854.4 days = 2.34 years during its trip according to its own clock, and appears to us to have aged 2.34 years during its trip according to its clock and this all works out simply and consistently even if the theory behind the calculations might be unintuitive?

I hope that I don't confuse michel123456, who seems to be struggling with even a classical notion of the notion of delay of light, but... If gamma is ~365,000 then ET's clock *appears* to tick at such a high rate that its one day of travel is seen over about 0.1 seconds for the observer (relativistic Doppler). The observer measures the trip taking about 1000 years, but sees it in 0.1 seconds, leading to michel123456's intentional confusion (intentional because the mistake has been pointed out MANY TIMES NOW by many people but it is ignored). The reduction in the delay of light is a first-order effect of v, and the slowing of its clock is a second-order effect... is that the right way to say it? So the observed frequency of ET's clock is faster than the astronomer's. I would call that appearing to live in fast motion, yet still not appearing to travel "at a fast velocity" as michel123456 might, because time has an inverse relationship to velocity (not to mention the proportional effect on distance here). And michel123456, things appear to do what they're doing. If it travels at .99c then that's what it appears to do. You're saying "If something is really doing *this*, then it appears to do *that* (something different)" but then turning it around and saying "And if it appears to do *that*, then it's really doing *that*." Be consistent! Either speak of reality (and delayed observations), or acknowledge the difference between reality and appearance when converting from reality to appearance AND vice versa. You're also considering only what is real for light (v=c) and only what is apparent for ET (v=some made-up measure).

The answer's straightforward. The question's nonsense. What does it even mean for something to appear to travel faster than the speed of light, if you're not using the real definition of speed but instead a made up one? If something arrives when or after it appears to leave, then it does not appear to travel faster than light. If it arrives before it is seen leaving, and yet is never out of sight, do you continuously see it appearing to move backward? If you see something approach very fast, it appears to move faster but its time also appears to tick fast; it appears to cover greater distances but appears to take longer to do so. Why use one measure for the speed of light (c, and the real definition of speed) and compare it to a different measure of an object (your mixed-frames measures). Why are you wilfully ignoring any delay of light, yet comparing "apparent" speeds to c, now suddenly acknowledging a travel time of the same light? Try working through your example in your imagination. A traveler sends a letter by fast plane, and leaves simultaneously by slightly slower plane. The letter arrives, and the traveler shortly after (let's say 1 minute for example). Do you honestly not understand "how the hell" that is possible? Honestly?! Did the traveler really appear to come at you thousands of times faster than the plane by any reasonable measure, even a made up one?

I don't see a cross at all. It actually looks more like a symbol from my religion.

So he travels at the speed of light? Or is this photon "slow"? Imagine you're watching the ET through your telescope and you see it flip a switch on a laser. Do you expect to receive the signal from the laser a year later?

It was a huge step forward in analysis that I saw, but I figured you gave up. Well may I make a suggestion? Don't worry about all of those extra details and philosophical questions. Most of your questions would change as you learn anyway. Pretend you believe the predictions of SR are real, and work through the simplest twin experiment example from this thread or the web. First see what SR says is so, THEN begin questioning from there, or adding in all the details of reality vs. appearances etc, to see how everything fits. I think it would be a torturous task to try to intuitively understand the predictions of SR without first knowing what the predictions actually are. Certainly. That would be a Doppler analysis. I preferred figuring out the twin paradox using Doppler equations because they seemed so much more intuitive, describing it in terms of what observers actually see, however there are still a lot of complicated details of timing and frames etc and it's easy to make errors or get hopelessly lost. Knowing a Lorentz analysis of the same experiment lets you calculate and double-check any details you need, and makes a Doppler analysis easier.

You keep asserting that things you don't understand are wrong. And if Earth at year 3 sees Tom sending a light signal, and Earth at year 3 receives that signal, how fast has that signal traveled? Infinite speed? Could the observation of Tom sending the signal, or leaving the planet, not be delayed by the travel time of light? Edit: Oops, I see Iggy has already covered this...

As soon as you introduce specific events on the world-lines of the two reciprocal observers, you can have asymmetry. You may have 2 events that are simultaneous for one observer and not the other---that is asymmetry. In the experiment in post #1, observer A ages 4 years between AB and AC, and B ages 1 year between AB and BC, and everyone agrees. There's no way to change that with arguments about symmetry. Yes, according to A, A ages 4 years while B ages 2, and according to B, B ages 4 years while A ages 2, and that's reciprocal and doesn't demonstrate any twin paradox effect, but that has little bearing on the proper times between the events that are defined, it only affects the relative simultaneity of any events in question. Alright, I can agree with that. The wording of the title is misleading and poorly chosen, and I've taken back the claim in the title. I meant that acceleration is not important in certain respects, but stated it's not important in any respect, which is wrong. Agreed they're not physically equivalent. However they use the same theory and the same equations, meaning that in theory (assuming the clock postulate), the difference in the scenarios, ie. any effect attributed to the acceleration, has no effect on the predicted calculated timing discrepancies. The different scenarios I've presented are equivalent with respect to calculation of proper times between any pair of events, not with respect to all measurable phenomena (most notably any measurable effects of acceleration). I've been referring only to the difference in proper times ie. aging, when speaking of the "twin paradox effect". I agree the classical experiment's twins experience a difference in aging and also a difference in experience of the experiment, and I've only considered the former here. The measurable effects of acceleration besides determination of velocity, do not affect the relative timing of the twins within the domain of SR. I doubt I will. "In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses." http://en.wikipedia.org/wiki/Time_dilation So your statement is nonsense. Sorry I take that back, you can still make a distinction between proper time and coordinate time in yours and my respective statements. However the difference in proper times is still an effect of time dilation. (and other things) Anyway, I have learned some things over the course of this debate, and I realize there's still so much I don't know and I'm far from being able to express everything perfectly.

In about 9000 threads on these forums, there are people struggling to understand (or debunk???) the twin paradox effect using the same arguments over and over, including trying to explain the effect in terms of acceleration, while neglecting time dilation. I was trying to help steer people away from that futile line of reasoning, because the effect is present without the acceleration. However, I COMPLETELY underestimated the role of "belief" in people's understanding of the paradox, so this thread, like every reply in every thread that uses math and reasoning and goes completely ignored because it doesn't fit the reader's beliefs, has no point for those readers.

You're mixing what is measured (Lorentz analysis) and what is seen (Doppler analysis). Account for the delay of light, and you get a consistent answer. The Earth measures Tom has reached that point after 2 years. It is 1 LY away in Earth's rest frame, so the observation reaches Earth one year later. My mistake about your analysis. I thought you were so close to getting it, but I think you may have only presented the math because it (incorrectly) confirmed your belief that it shouldn't work out. When you accidentally got the right answer (by dividing by gamma) you reasoned out why the answer should be dismissed. Tom reaches the turnaround point when he does, when he thinks he does, when everyone thinks he does, only---as Janus has pointed out---the distance to that point, which is a rest length in Earth's frame, is length-contracted in Tom's frame, all according to plan.