Eise

But why don't you say it the simplest way? The speed of T is 0.8c in the FOR of earth and planet X. There is no length contraction of the distance in the FOR of earth and X. Yes, in the FOR of Earth and X. What an observer from Earth sees is time dilation: the clock of T seems to run slow by a factor of 0.6. So the Earth's observer, using T's clock, T needs only 0.6 x 60 minutes = 36.66 minutes. According T however, the distance between Earth and X is length contracted 0.6 x 1Lh, and his own clock runs normally, so he does that distance in ... 0.6 x 1Lh x 60 minutes = 36.66 minutes. So both Earth's observer and T see the same: T's clock shows that the trip took 36.66 minutes*. But according to Earth's own clock it took 1 hour/(0.8c) = 1 hour and 15 minutes. * That it takes another hour before he actually sees T arrive a X plays no role. He can see T arrive at X, and that his clock shows 36.66 minutes 'trip time'.

Which makes no sense at all. From the FOR of the earth, you just see T traveling with 0.8c. A ruler attached to T will be length contracted with a factor of 0.6, but the distance between Earth and planet X will still be 1 Lh because they are still in the same FOR. So after one hour, T has simply traveled 0.8Lh in the FOR of Earth and X.

Right. So why do you say then something like this?

So how much does the clock travel? 1LH or 0.6 x 1LH?

No, you are not, and the syndrome that Swanson, Markus, md65536, Janus, Bufofrog, and I have, is that we have a more than superficial knowledge of relativity. Let's assume, as you do, that Earth and planet X are in the same inertial frame. Two spaceships, T1 and T2 (Traveler) make up for planet X, 1 light hour away. T1 travels with 0.8c, and T2 with 0.6c. What is the distance from Earth to Planet X? When T1 arrives at Planet X how far did T1 travel from the view of Earth's and planet X's FOR? When T1 arrives at Planet X how far did T2 travel from the view of Earth's and planet X's FOR? So how far is planet X from Earth?

... length contracted. But not the length traveled.

Of course not, as md65536 explained. The earth sees the travelling clock running slower by a factor of 0.6. Further your diagrams 5 and 6 do not make sense. Spacetime diagrams should always be drawn from one single inertial frame. But the travelling clock changes its inertial frame. And the gap is an artifact of the physically not realisable instantaneous change of inertial frame. In reality it would be something like this: From here. You do not need to invoke General Relativity (we do not have curved spacetime), SR can handle this.

No. You should know if you had read my posting: the distance to X is not the same for A and B. For A the distance to X is contracted. And now stop with this 'observing'. The changing signal delay only makes the example more complicated. Just assume that A and B are intelligent enough to account for the signal delay, OK?

😄 Yes, maybe. You recognised what was in the back of my head when I wrote that...

AFAIK, the real problem he wanted to solve is that Newtonian gravity does not fit to Special Relativity, especially that nothing can go faster than light. In Newtonian gravity, gravity is instantaneous. To say it a bit more technically: Newtonian gravity is not Lorentz invariant. @DEFinning: Just to tell you: on the day that somebody joins the forum, he can only post 5 times. So you reached the limit for today. From tomorrow on you can post again, and as much as you want.

That is true. That objects with different mass accelerate exactly the same in a gravity field was already discovered by Galileo, and mathematically underpinned by Newton. Where Einstein went further is to wonder why mass has such totally different effects (inertia against forces, and the same attraction in a gravitational field). He realised (at least) two things (which are in fact just mirror phenomena, but it helps to spell them out): In a windowless laboratory, it is impossible to experimentally find out if you are put in a (homogeneous) gravitational field or suddenly accelerating if the same laboratory is in free fall in a (homogeneous) gravitational field, you can do no single experiment that shows you are accelerating From this he concluded that 'inertial mass' and 'gravitational mass' are exactly the same thing, and so are gravitation and acceleration. However, normally homogeneous gravity fields do not exist (only on small scales gravity fields can be approximated by homogeneous fields). To get the mathematics sound, Einstein had to use (difficult, even for him) techniques from differential geometry. And so he came to the conclusion that gravity can be described as spacetime curvature. In this way Einstein could explain the orbit of Mercury, which showed deviations from Newtonian gravity, and the bending of light in gravitational fields. And there followed many more discoveries and predictions which only make sense when using General Relativity. Phenomena that would not exist at all is Newtons theory would be correct.

Sigh... First, I expect from you that you really explain to us how it is possible that muons reach the earth's surface. The (didactic) importance of that is either you see that you can't, in which case you know that your intuitions are wrong; or you think you can explain it, we see how you do it, and pinpoint precisely to the point where you make an error. Secondly, already said many times, you should start with the explanation why the twins did not age equally, and they agree on this difference. What observers see during the traveler's trip unnecessarily complicates the situation. But I know that for many people this is some kind of show stopper, so, look here in Wikipedia. Ask us questions if you do not understand it. And 'not understanding' is not the same as 'it is wrong'. Thirdly, just another try in the hope you will see the light: Say the traveler flies with 0.8c to the planet Solaris, 10 light years away, and to keep it simple, earth and Solaris are in the same frame of reference. Now for the traveler the distance, due to length contraction, is only 6 light years. Because the home stayer and the traveler agree on the speed of the traveler, that means that the traveler does the trip in 0.6 the time compared to the view from the earth. Moving back home of course the same. So the traveler grew 15 years older, the home stayer grew 25 years older. The asymmetry lies in the fact that the twins do not agree on the distance traveled. But because the twins agree on their different ages now, it means also that they do not agree on their time measurements. Taking that into account, the twins can be sure they live in the same reality: they agree on their age difference. And now, PLEASE, instead of throwing another conflicting intuition of yours at my post, work as carefully as you can through these points. If you get stuck with the muons, tell us where you are stuck. If you get stuck on the Wikipedia article, tell us exactly where, and why (no, not simply a conflict with your intuition, but where you cannot follow the logic of the explanations given). And tell us why you do not understand that the situation of the twins is not symmetric. Or simply refuse to understand relativity, but then say so honestly. In that case I would suggest to close the thread. So what it wanna be boy, trying to understand, or refusing to understand, yes or no?

As others also notice: you are consistently avoiding to explain from your view why muons make it to the surface of the earth. It is time you take the challenge. Another remark (which might help you with the 'muon-challenge'): you assert that in the so called 'twin paradox', there is an asymmetry, because the effect of the time dilation stays (the traveler has not grown older so much as the home-stayer), but the length contraction has gone (the twins are still equally sized). Truth is that you comparison is wrong. After arriving back home the twin's clocks tick at the same rate, so the time dilation itself is gone, just as the length contraction. However this is not true during the travelling: the length contraction of the length of the trip for the traveler is real, and its 'mirror' for the home-stayer is the real time dilation. As space and time are relative, but spacetime is not, this is no problem at all. Important is that the twins agree on their observations when they are in the same FOR again: they agree that the traveling twin has not aged so much as the home-stayer twin. So they live in the same reality.

Oh my... Our traveler sees the same light arriving from earth as the man in the bar. So they see the same. So according to you the man in the bar sees the earth suddenly bigger, because the traveler entered the bar??? Or maybe, maybe, when the traveler stops at the bar, he sees exactly what the man already sitting in the bar sees? Just the usual angular size as everybody else on 1 LH distance? Still waiting. Or do you start to see the problem with your interpretation?

As long he is moving away from earth, yes, he sees earth clocks go slow, but as soon as he stops at the bar, his clock and earth clocks go in the same pace. But, yes, the earth clocks seem to be one hour behind. That is the delay due to the distance. Right. At least a first step... Yes, and I want your interpretation of why muons reach the surface.

The delay is in what any observer in the bar sees happening on earth. So the traveler and the person living there see exactly the same: what happens on earth one hour ago. That is your delay. On his outbound trip the traveler notices an increasing delay. This increase stops when he stops traveling. If you are moving you see your starting point moving away. But the moment you stop, this moving away stops immediately. Otherwise you get the contradiction that Bufofrog and Janus pointed you to. Even Zapatos understands that! And when do I get your explanation that we can see muons reaching the surface of the earth? What does it look like for an observer on earth, and what does it look like from the FOR of the muon? I assume you cannot answer it, if I don't get an answer.

Galilean relativity yes., but not Relativity (because of SOL). What? Of course the out- and inbound trips take the same time in Galilean and Einsteinian relativity. Same speed, same distance, and therefore same time. The 'only' discrepancy is between both relativity principles. Take the example of flying to a star that has a fixed position seen from the earth, i.e. the star and the earth are in the same reference frame. In Galilean relativity: Traveler's view: travels the distance to the star with its speed and back with the same speed. His speed he can correctly derive from the distance traveled and the time on its own clock. But of course on the outbound trip, he sees a clock on earth running slow. But he knows this is just because the increasing delay. On the inbound trip, he sees exactly the opposite, the earth's clock is running fast. When he ends his journey back on earth his clock, and the earth's clock show the same time again. Earth's view: more or less the same as the view from the traveler. On the outbound trip the traveler's clock seems to run slow, on the inbound fast, and at the end of the trip the clocks show the same time again. Both agree on: the distance traveled and on the time it took. In Einsteinian relativity: Traveler's view: the distance between the star and earth has become smaller, however the speed is the same. So the traveler sees he arrives at the star faster, because the distance is smaller. Returning with the same speed (but opposite direction!, i.e. the traveler changed his reference frame), of course the distance will be shortened by the same amount as the outbound trip. Looking at the clock on earth on his outbound trip he sees it slowed down because on one side the delay, but on the other side the time dilation. Flying back he still sees the time dilation, but also the effect of nearing the earth's clock. So depending on the speed, he sees the earth's clock, ticking faster, but not as fast as in Galilean relativity. Earth's view: the trip takes just as long on earth's clock as in Galilean relativity, but from the earth the traveler's clock is running slow to time dilation. So from the earth, using the clock of the traveler, the trip takes the same time, but not according earth's own clock. On the inbound trip the same happens. So the traveler's clock runs slower than in Galilean relativity. For short: the traveler did fly a shorter distance than seen from earth, therefore he has not grown older as fast as the earth. for the earth the clock of the traveler ran slow, therefore the traveler has not grown older as fast as the earth. So they both agree about reality. Just as the example of the muons: they reach the earth's surface. @michel123456: When do you explain to us why muons can arrive the earth's surface, even if, using Galilean relativity, they live too short to reach the earth's surface? You never seem to answer any of the challenging questions we ask, or show us where our arguments are wrong. You only show us where the results of our arguments conflict with your picture of reality.

Even that you know that special relativity is tested to the bone, and forms the basics of nearly all of physics? Quantum Field Theory would be wrong if relativity is wrong! The relationship between electrical and magnetic fields could not be understood if SR was wrong, etc etc. Instead of protesting against the arguments given in this (and other...) threads, you should point to the places where you do not follow the argument; but your only reaction is taking your wrong mental pictures and say that the argument's conclusion does not fit them.

Again, that is fair. But this is not: That is just logically wrong. Should I suppose that everything I do not understand is wrong, and therefore I should not accept it?

That is (nearly) fair. If you do not understand it, that's fine. You are surely not the only one. But as others already said, loads of people here try to explain it to you, but you keep sticking to your own, wrong, mental pictures. And really, you not understanding a counter-intuitive theory, does not mean in any way that the theory is wrong. All the experimental confirmations of special relativity should show you that the problem is your understanding, not the theory. Special relativity is the reconciliation! So everything should shrink, independent of the direction? And do not forget that space and time do not play the same role in spacetime. Where one second on a spaceship passing me is 10 seconds for me, 10 meters (yes, in the direction of flight) becomes one meter. Time 'expands', but length contracts. The time dimension in spacetime has the opposite sign as the space dimensions in the 'spacetime-distance' formula. Another confusion of yours. In SR nobody is wrong. It is just that you must take the velocity between 2 flying systems into account (and this is not about signal delay!). For a muon produced in earth's higher atmosphere the distance it travels to the surface is shorter than for us, therefore it can reach us. From our view it travels the 'longer distance' but its time is slower, and therefore it can reach us. That makes one consistent reality: muons detected in our detectors at the earth's surface. There is no symmetry. The travelling twin changes direction, i.e. it changes its reference frame, in order to return to earth. The home-staying twin doesn't. No symmetry, no paradox. And the 'twin paradox' is empirically confirmed, not with twins of course, but with travelling atomic clocks. 'Acceptability' by one person is not really an argument. Your logic is wrong, and as long as you stick to your, again wrong, mental pictures, you will never understand. This makes no sense. Special relativity is about how observers in different frames of reference see distance and time measurements in each other's frames. The symmetry is that of constant velocity, and therefore not existing preferred frame of reference. No, it is your stubbornness.

Where did Pascal got the time to write such things down? According to most other philosophers, philosophy only exists in cultures where people have spare time. E.g. the Greeks had slaves, which gave their masters time to reflect on nature, society and themselves. People who have no time could be: full in the struggle of life: all their time is used to get food, shelter, and stay safe for any danger totally unaware that their world could be different as it is, i.e. accept the culture or society in which they live as a 'naturally given' and conform to to it without reflecting (My disclaimer could be extended from science to more or less all of life ("There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination.")). Ideologically shaped societal dogmas are seen as 'natural', or 'obviously the best principles to live by'.

Yes.(1) (1) IIRC this effect is not taken into consideration in the twins paradox. Of course it is! I think if you google a little, you will find descriptions what A and B observe. That what they see is a combination of time dilation and delay because of the increasing distance. You are just saying something without being informed. However, only the time dilation is really responsible for the different age of the twins. No, of course not. You argument is based on non-physical assumptions. Assuming SOL is not invariant, without giving a premise what is the case then, you cannot know. I see 2 possibilities: light behaves as material objects, i.e. its velocity depends on the movement of the source only. If B moves away faster than SOL, you see nothing anymore because the light is also receding from you or there is a fixed medium, like sound in the air, in which case you continuously see B's clock ticking slower than A's clock. Now the frequency of the ticks depends on the velocities of A and B in relation to the medium. However, nothing of this gives you the time dilation of SR, which you should see now: if B moves to A, in 'your universe', you get a time contraction.

And now turn the direction. B travels back to A. Now the B's clock ticks faster than A's, from A's viewpoint. So what?

@20ny: You are confusing 'time' with 'measurement scales of time'. Time zones have nothing to do with relativity theory.

But aren't you taking general relativity for granted here? My point is only that even if we would live in a Newtonian universe, it would be dynamic because of gravity. Even if the universe would be infinite. If we would start with a 'magically created' homogeneous distribution of static mass, the universe would 'collapse', i.e in a Newtonian framework, all masses would be moving to each other. The only other option would be that all masses would have gotten an initial velocity large enough to move away from each other. Now this would look like a kind of explosion in space (not of space) I think many lay people still imagine the big bang like that.