TrueHeart

There you go again using sloppy wording - tsk tsk! "Time slows down" is not a truism; time slows down relative to the clock of an observer higher up in the gravitational potential field, and time slows down relative to the clock of a presumed still observer, when you are falling ie. in motion. Time dilation attributable to relative motion is a purely mutual effect, ie. he sees your clock run slow and you see his clock run slow. Gravitational time dilation (as its called) has an unambiguous orientation: the one deeper down in the G-field perceives clocks of one higher up to run fast, while the higher up one perceives the deeper down one to run slow.

Many thanks! Of course we Americans have heard of Brunei --an extremely wealthy kingdom, free housing and medical care for all the citizens. As I stated in my post #27, the buoy clock reads 9 months earlier than Earth's clock at any given instant, from the astronaut's perspective. No matter where the astronaut is located, the buoy clock will read 9 months earlier than Earth. The astronaut twin can rightly claim himself to be stock still, all the time. So to him, the Earth-to-buoy "real estate" is a frame in relative motion. I don't see clearly where to go from here. Perhaps 15 is too young to fully grasp the concepts of relativity, but I refuse to believe that. Just realize that length contraction and time dilation are meaningless on their own -- you must cipher in the time dissynchronicity element as well, in order to arrive at any coherent analysis. The three distortions all conspire together to make relativity work, and be consistent. Remember: I said that the astronaut took a photograph of the buoy clock as he passed it, so there are no illusions or tricks. When later analyzing the data, the clock readings, photographs of clock readings, etcetera; the Earth twin will conclude that the journey took 1.0 of his years... the astronaut will conclude that the journey took 6 of his months while only 3 Earth months elapsed. Realize that this is not a round trip scenario, merely one-way; so the two twins will disagree on how much time elapsed. But, by applying the formulas of relativity, each will reason why the disagreement exists. There is no universal time, no universal space, no "bigger picture". Humans are always yearning to "play God" and see things from the top down, to see the bigger picture, the larger truth; but relativity taught us the lesson that such efforts will always be in vain. And the entire field of Physics is consequently somewhat vain: what is true here and now is something that can be ascertained, not what is true from some supposed "master viewpoint".

I know exactly why light speed has to be the same for all observers. Light (EM radiation) is the quintessential mediator of all that exists, so her unique speed is inviolable and expressly tantamount to an infinity. Note that infinity plus any number, minus any number, times any number or divided by any number, is still infinity. Hence, light speed will seem to be uniform among all observers. In the number line that is speed, c is infinity... Einstein said as much. Speeds in excess of c are 'undefined'. True, in the study of cosmology, as described by General Relativity, speeds in excess of c are defined -- but all that is a fudge... if you study the formulae of cosmology, there are a lot of expedient compromises employed to arrive at useful descriptors of the whole universe. It's a cheat so to speak; SR is the purist part of relativity. Furthermore, if light were not the same to each observer... if light moved relative to some master cosmic space/aether, then where would that leave all the poor hapless folks who live on all those zillions of galaxies that are ever speeding away from us in every which direction we look, hmmm?? It would leave them up the creek without a paddle; their worlds would be ever distorted and uninhabitable; their surroundings would be all hot and blue-shifted in one direction, yet pale and red-shifted in the other. Not only people (aliens) but physics itself would come to a crashing halt, I think, if that were the case. We would no longer live in a wide wonderful world. 'Not to mention, if light did not behave as relativity describes it, then we would live in a world where objects could OUTRUN being seen. And worse yet, we would live in a world where objects could smash into you with devastating impact, before you would even feasibly have the opportunity to see them coming. That just ain't right! edit: you were right, KennyC, it would be "blasphemy" indeed if light failed to behave in its known relativistic manner... good word!

That's fairly accurate. If the clocks are in sync to a native of the frame, then the clocks are out of sync to a non-native, meaning to someone who is in relative motion. The dissynchronicity of the clocks is a fact to such a non-native observer. Yes, I mentioned in an earlier post that you can't really trust what you see at such high speeds, at near light speeds, because of the Doppler shift and other thorny dynamics. That's why I prefer to use the term "reckoned". But the distortions of relativity are a fact, to the observer. Various different observers, moving at various differing speeds, will reckon various differing distortions... so those distortions are not an objective (absolute) fact, but they are nevertheless totally REAL to each observer. For example: a house is engulfed in flames. An observer 3 feet away will get scorched; an observer 30 feet away will feel intense heat; an observer 300 feet away will feel warm, and an observer 3000 feet away will feel nothing. All of those effects are totally real, yet they are not "universal"... they differ for each observer. I suppose I have to say "Happy Thanksgiving". Do I have to say that?? Maybe I have to say that.

That's the theory of relativity... that clocks and rulers have to be attributed some certain variances in order to allow the perception of lightspeed to be the same from all viewpoints. Complications! Give it a rest, will you please.

Let's say that point B is a space buoy (unmoving with respect to Earth) that has a clock on it which is perfectly synchronized with Earth's clock. When the astronaut was at point B, the clock on the buoy read zero, and he takes a snapshot to prove it. When the astronaut gets to Earth, the clock there reads 1 year, and both twins can bear witness to that reading. Now according to the Earth twin, the buoy clock is in perfect sync with his own, so the data indicates that one year elapsed. But according to the astronaut twin, the buoy clock reads 9 months earlier than what Earth's does (at any given instant), so the data indicates that only 3 months elapsed on the Earth-to-buoy frame. The foregoing assumes that accelerations are not an issue because the astronaut was already in relative motion when he passed the buoy, and he keeps moving as he passes his twin on Earth.

Both clocks are not out of sync. And both earth and the astronaut do not agree that the earth twin has aged more. There are actually three clocks at issue so let's get it straight. First, let's clarify that in the scenario you describe, point B is some "space buoy" or something that is unmoving with respect to Earth. That makes it easier to get a handle on things. And you're calling Earth point A. You've allowed for only a one-way segment of travel in the scenario you've drawn up. So... according to the earth twin, the astronaut aged only half as much as he himself did. According to the astronaut twin, the earth twin aged only half as much as he himself did. Reviewing; the earth twin knows that he ages 1 year and the astronaut aged only 6 months. The astronaut knows that he ages 6 months and the earth twin aged only 3 months. The discrepancy is attributable to the two parties disagreeing on exactly when the journey began.

The resolution to that apparent contradiction lies in the fact that clocks separated along an elongated moving frame are not in sync -- as reckoned by the presumed still observer of course. The astronaut twin is just such a presumed still observer, and the "real estate" consisting of A-to-B is just such an elongated moving frame. Because of the length contraction of that frame, only 6 months of the astronaut's time is required for it to pass by him, at the stated .866c speed. Only 3 months are witnessed to elapse on Earth's clock during that period, but the Earth frame time at point B was 0.75 years (9 months) earlier than Earth's time, when the astronaut twin was at point B. So according to the Earthbound twin, the astronaut journeyed from a clock reading -9 months to a clock reading 3 months... hence one whole year elapsed (as the A & B clocks are perfectly synchronized to Earth natives). It's tough to fathom alright; and I am sorry if my wording leaves yet an iota of doubt. Maybe someone else can word it better.

You don't need a whole web site because it's pretty simple stuff. Use the formula 1/sqrt(1-v^2) to arrive at what's known as the gamma. [NOTE WELL that in the formula I just gave, v is the velocity of the observed entity/frame expressed as a fraction of lightspeed.] The observed (reckoned) length of the moving frame is equal to its native length divided by gamma. Of course you know that length contraction is only along the direction of motion. Observed time spans of the moving clocks are their native amount divided by gamma. And -- don't forget this one! -- the amount by which separated clocks are out of sync (does not involve gamma) is equal to the time it would take light to travel their uncontracted distance apart, multiplied by the frame's velocity expressed as a fraction of lightspeed. A trailing clock reads a later time than a forward located clock (of course, only if their separation is along the direction of motion). That's a complete summation of the basic SR Lorentz Transform. More to follow.

Yeah, it's a morass alright, trying, flailing, fumbling to come up with the right words. Me personally, I will accept that "space" is nothing.. nothing but a construct of the human intellect. Space is no thing and in fact it is defined as the absence of any "thing". What yourdadonapogos said about space can be stretched or compressed -- I'm not buying it for a minute. Ok, so this thread is all about gravitational fields. In Special Relativity we came to accept that motion only pertains relative to physical objects, and not to "space", proper. Now we add gravitation, and it's still the same enchilada: you can know your motion relative to a gravity tensor, but that itself derives from a physical object. The bottom line is that motion is still relative to the physical object and not to 'space' (in my humble opinion). I think it's all word play. The real truth is deeply buried in the math.

Yeah, it's a morass alright, trying, flailing, fumbling to come up with the right words. Me personally, I will accept that "space" is nothing.. nothing but a construct of the human intellect. Space is no thing and in fact it is defined as the absence of any "thing". What yourdadonapogos said about space can be stretched or compressed -- I'm not buying it for a minute. Ok, so this thread is all about gravitational fields. In Special Relativity we came to accept that motion only pertains relative to physical objects, and not to "space", proper. Now we add gravitation, and it's still the same enchilada: you can know your motion relative to a gravity tensor, but that itself derives from a physical object. The bottom line is that motion is still relative to the physical object and not to 'space' (in my humble opinion). I think it's all word play. The real truth is deeply buried in the math.

I see the point of the original question, and it's a good one. SR demonstrated that "space" is not an entity and hence there is no such thing as a body's unequivocal motion "through space". But then along comes GR and all of a sudden space has properties, and a texture, and a layout. Does that now mean that there IS such a thing as a body's unequivocal motion "through space"?? I HONESTLY don't know a correct answer to that inquiry, but can only guess. First off, talk of "curved space" may be merely expeditious terminology, I'm not sure. I'll say, perhaps GR didn't really change anything of invalidating space as a "thing"... because all it did was add gravitational fields that are associated with massive bodies. Those celestial bodies still move about, and the gravitational biases move with them. I'm sure this is outmoded verbiage, but c'est la vie. So in conclusion, nothing is fundamentally changed from SR's negation of "space" as an entity: it is still only the presence of physical bodies that have any causal bearing... take away those landmarks and you're still left with nothing. So space is still a concoction of the human mind, and has no bearing on Physics. Matter has essential bearing and "curved space" is a convenient way of describing the gravitational fields, or tensors, that pervade. 'Not sure.

I see the point of the original question, and it's a good one. SR demonstrated that "space" is not an entity and hence there is no such thing as a body's unequivocal motion "through space". But then along comes GR and all of a sudden space has properties, and a texture, and a layout. Does that now mean that there IS such a thing as a body's unequivocal motion "through space"?? I HONESTLY don't know a correct answer to that inquiry, but can only guess. First off, talk of "curved space" may be merely expeditious terminology, I'm not sure. I'll say, perhaps GR didn't really change anything of invalidating space as a "thing"... because all it did was add gravitational fields that are associated with massive bodies. Those celestial bodies still move about, and the gravitational biases move with them. I'm sure this is outmoded verbiage, but c'est la vie. So in conclusion, nothing is fundamentally changed from SR's negation of "space" as an entity: it is still only the presence of physical bodies that have any causal bearing... take away those landmarks and you're still left with nothing. So space is still a concoction of the human mind, and has no bearing on Physics. Matter has essential bearing and "curved space" is a convenient way of describing the gravitational fields, or tensors, that pervade. 'Not sure.

Of course, you might wonder what assumptions had to be made in order to arrive at those simple whole numbers, the 18, the 3 the 12... I mean, acceleration is always a gradual event, and this means gradually changing speed, and consequences for the earthbound twin's reckoning of the astronaut's time dilation. What acceleration strength did I choose? or did I somehow compute an instantaneous turnaround? In other words, how does one eliminate any slop factor?? Answer: I allowed for instantaneous turnaround by using only the basic Lorentz transform. Read my brief explanation here and replace my numbers with yours: .866c speed, which makes the gamma=2; and make the earth-synchronous buoy be 10.4 light-years away, which makes for a 12-year outbound leg per earth reckoning.

Of course, you might wonder what assumptions had to be made in order to arrive at those simple whole numbers, the 18, the 3 the 12... I mean, acceleration is always a gradual event, and this means gradually changing speed, and consequences for the earthbound twin's reckoning of the astronaut's time dilation. What acceleration strength did I choose? or did I somehow compute an instantaneous turnaround? In other words, how does one eliminate any slop factor?? Answer: I allowed for instantaneous turnaround by using only the basic Lorentz transform. Read my brief explanation here and replace my numbers with yours: .866c speed, which makes the gamma=2; and make the earth-synchronous buoy be 10.4 light-years away, which makes for a 12-year outbound leg per earth reckoning.

Right! The space-travelling twin computes that during his/her turnaround, Earth and its residents age 18 years. Earth ages 3 years during the first leg, then 18 at turnaround, then 3 more, totalling 24 years for the round trip. This agrees with the reckoning of the earthbound twin: 24 years will elapse, but the astronaut twin ages only 12... 6 on the outbound leg and the same again for the return.

Right! The space-travelling twin computes that during his/her turnaround, Earth and its residents age 18 years. Earth ages 3 years during the first leg, then 18 at turnaround, then 3 more, totalling 24 years for the round trip. This agrees with the reckoning of the earthbound twin: 24 years will elapse, but the astronaut twin ages only 12... 6 on the outbound leg and the same again for the return.

Case1=case2=no difference whatsoever in the gravitational force between observed speeding masses. Think about it: either they attract more or they don't -- and that's an absolute; and relativity isn't about absolutes!

YT2095: Okay, okay. I guess there's more to your point than just that c+4000. How can he do it?? Everything that facilitates his acceleration is found onboard, and everything onboard is in the native observatory (frame) and hence cannot be said to be in motion. The *other* guy is the one doing any moving -- that's quintessential relativity.

Thank you! I now get that you agree with the two paragraphs in effect, but not in terminology. Very good! The (charged) particle moving at relative speed .99c DOES make disproportionately more impact in a collision, and IS disproportionately harder to divert with EM fields... 'that right? One just shouldn't go about ascribing those two effects to "relativistic mass", which is -- yeah I knew -- outmoded terminology. A property of the body shouldn't change with reference frame, aye.

YT2085: Where do you get your (c+4000) figure?? (c-1000mph) + 5000mph does not equal c+4000mph .. that was my whole essential point.

Severian: Then it sounds as if you cannot agree with my subsequent paragraphs describing instances where relativistic mass increase IS pertinent. I'm all ears.

The worst myth ever about relativity is that a spaceship can never accelerate to light speed because it is steadily getting heavier, making it ever harder to accelerate. That is rubbish, and I'll convince you right here and now. Under relativity, the speeding space craft can rightfully consider itself to be stock still in space, and so cannot attribute causal distortions of any kind to itself... it's other folks who are in motion, duh. However, in a collision, then there is relativistic mass increase ascribed to the speeding projectile, and it becomes a factor in how much of an impact will result. In that case, it is the collidee's perspective that what impacts it is extra heavy. Similarly, if you were using a stationary force field to control a relatively speeding entity, then relativistic mass increase becomes pertinent. While using an electromagnetic field to alter the course of a speeding charged particle, it will become ever harder to divert the particle's momentum as its relativistic mass increases nearing light speed... because this all happens according to the perspective of the lab frame, whereon the EM field producer is mounted. So that begs the question then, "What is the real reason why a spaceship can't accelerate to light speed?" The reason is because of the limitations imposed by relativity's Addition of Velocities formula. Let's say that you, a stationary observer, see the craft going 1000 MPH slower than lightspeed, and then it accelerates. The pilot of the craft might discern that his recent engine thrust boosted his speed by 5000 MPH (confirmed by his observation of something he left behind, eg. a sister ship). But to you, when the speed 5000 is added to the speed (c-1000), the sum does not surpass c. You have to use the velocity addition formula, (u+v)/(1+(uv/c^2)).

To best understand the subject, perhaps you might have to temporarily forsake trying to figure what either observer actually sees with their eyes. The dynamics at high speeds are so complex, compounded by other-than relativistic effects -- like the Doppler effect and like simple transmission delay times -- that it may not be truly helpful (to you) to imagine what is seen. Instead, imagine what is reckoned by each party, assuming that both observers do understand Relativity.

gib65: You are 100% correct about your second paragraph! Bravo, very astute! The time hastening factor is proportional to the distance away. But you've got something else in your post horribly wrong: You must watch how you speak and phrase things when talking about Relativity! Nothing is absolutely true, nothing of the supposed "big picture" should be cited.. tsk tsk. You can only deal with observer and observed and with what is true of each of their viewpoints. No distortion inarguably affects any entity, it's all about each observer's reckoning of alien clockworks and alien measures. Please, carefully reread my post before yours and you'll understand what pains one must go to to make oneself clear, in describing relativistic situations. But even so, YES! Congratulations !! Your description is perfectly right about how the clock rate speeding-up works out mathematically, it needs to be more than enough to compensate, like you cited, because the rudimentary time dilation attributable to speeding entities must also be continually applied to the brother, per either twin's reckoning. I just read your 3rd paragraph and it is correct. I just read your 4th paragraph and it is correct.