## What this shows us is that for any given path through space-time, a stationary one is always the longest one in terms of proper time.

Originally Posted by SpeedFreek Originally Posted by space at the centre We have seen that A and B are simultaneous, meet Einstein’s test for simultaneity, in two separate Frames and we can go on to prove that they will meet that test in any Frame, in each and every Frame. An observer in B will measure those properties as L/2 and 2T (Lorentz factor = 2).Add another body C moving at 0.6c and an observer on C will measure those properties as 0.8L and 1.25T (Lorentz factor = 1.25)So what are the physical Properties now? Are those properties really different in the two Frames? Yet still the original values in Frame A?And so on for very differently moving body in the whole of Spacetime?I don’t think so!How are those transformations determined?

By measurement? So the measurements differ according to the relative speed of the observer while in A they haven’t changed?Welcome to the Perspective of Relativity.Just as in optical perspective, only the apparent/measured dimensions are a function of the relative speed rather than their separation.And how can the speed of light still be c? (c = L/T = L/? .1/?T = L/?2T)It is because in length contraction we are contracting the unit size; whereas in time dilation we are dilating the unit quantity by the same Lorentz factor. Both observers agree as to the outcome – that the muon can reach the earth’s surface. To the laws of physics, no Gods-eye view is allowed.

The lights will flash at the same time, from the frame of the embankment.But from the frame of the train, the embankment is shorter than the train, due to length contraction! The embankment is in motion in relation to the train, after all. And vice versa. The right hand end of the train lining up with the right end of the embankment is one event.

AM = MB, M is physically midway between A & B. If we have all the signals involved propagating at c in relation to the embankment, then even though the signals propagate up and down the carriage and reach the ends at different times, due to the motion of the carriage, the return signals to the flare will reach it at the same time, due to the motion of the carriage. SR is just a subset of GR and GR simplifies to SR in the appropriate conditions. But in doing so, and as he clearly stated, he is basing the frame of the experiment in the embankment frame.To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example.Let’s look at this another way, using length contraction.Let’s say, from the frame of the embankment, the train is the same length as theembankment as it passes through.

Thank you for shewing us that description. If it is the same length as the embankment whilst in motion, this means it must be longer than the embankment when at rest.So, from the frame of the embankment, the ends of the train and the ends of the embankment line up simultaneously. Try it without flitting instantaneously between frames. Consider: three points in space A,M,B. That distance is not the same in both frames, due to relative motion.

The lights will flash at different times, from the frame of the train.Only from the frame of the embankment, when the train is motion, are the events simultaneous. Or, to put it differently, an observer travelling through space experiences less proper time than a stationary observer, and thus will have aged less when they are brought together back into the same frame of reference. I leave you to draw your own conclusions about the rigour of those muon experiments! The muon situation is very simple. The SR relation does not apply here, you need to use the full definition for proper time :wherein the metric tensor encapsulates the acceleration information.

Thank you Markus. The average lifetime of a muon is about 2.2ns, which is by far not enough for a cosmic ray muon to reach the earth’s surface. That is correct – from the point in time at which the twins are back in the same frame of reference onwards, they once again measure the same proper time for any given interval. The GPS system in your car would not work without it.

Markus’ equations come from General Relativity. The left hand end of the train lining up with the left hand end of the embankment is another event.Let’s say that a light flashes at that position when each end of the train lines up with each end of the embankment.So, if whilst the train is in motion, it is same length as the embankment, from the frame of the embankment, then those events must be simultaneous from the frame of the embankment. Originally Posted by sigurdV Well then what is simultanity?

In how many ways can it be defined? Simultaneity is the question as to whether two events separated by space occur at the same time, or not.The answer is frame dependant – it depends on the frame of reference of the observer. So the absolute dimensions of the said properties ie. unit size x unit quantity will remain constant.The Body’s property dimensions remain the same, while the measurements made by a moving

observer are transformed.This way it all makes plain and simple sense with out any of that ‘wibbly-wobbly timey-wimey stuff’ What matters is if the timing of those events, as measured by M, shows M that the events occurred at the same time after subtracting the light-travel time from the event to the observer, with the observer knowing the distance to those eventsin their own frame. Originally Posted by SpeedFreek Tell that to those famous identical twins, who end up having different ages at the end of the thought-experiment. However, muons move at relativistic speeds – from the point of view of a stationary observer on earth the muon experiences time dilation, thus extending its lifetime before it decays. But they are not simultaneous from the frame of the train.QED.By arguing against the time-dilation we have measured and confirmed in muon experiments, you are proposing a view that goes against the scientific consensus, which was obtained through experiment.

Sorry space at the centre, but you just aren’t getting it.It doesn’t matter if M is equidistant between the events or not. Maps created with different origins and orientations. When at rest, the train is already longer than the embankment, but when the embankment is in motion it is even shorter still! So, from the frame of the train, the ends of the train cannot possibly line upwith the ends of the embankment simultaneously. From the point of view of the muon, the thickness of the earth’s atmosphere is reduced due to length contraction along the trajectory of motion.

A simple scenario. Whilst the light reaches the back of the carriage first, due to the back of the carriage moving towards the light, the return signal to the flare takes longer, due to the carriage moving away from the signal. As the train is in motion, this means it is length contracted from the frame of the embankment. Time dilation – and length contraction – are effects of measuring one frame from another, moving frame, when the frames are not in relative motion their measurements will be the same.

The internal clocks in GPS satellites were set to run at a different rate to clocks on the ground before take off, to ensure they remained synchronised with clocks on the ground once in orbit, due to both the relative motions of the GPS satellites in orbit and the difference in gravitational potential, in relation to the surface of the Earth. Oh, and so will the events E1,E2,E3.For any Frame of Reference may be considered at rest in Spacetime, where movement is only relative.Therefore we can conclude that in ANY, that is in each and every, Frame of Reference there will be a point in space, M, midway in space between points A and B where the lights will arrive simultaneously.Note that because an Event is a specific point in Time at a specific point in Space, ie at a particular Spacetime Location it cannot moving.Therefore points A & B are proven, by Einstein’s test to be simultaneous in all Frames of Reference.But how can that be?Well the Spacetime point M maps to different coordinates in each Frame of reference: in Einstein’s Embankment Frame it is point M on the embankment, while in his Train’s Frame of Reference it is the point M’.Einstein’s M and M’ meet at E3 when the lights arrive there, but follow different Spacetime paths therefrom.Spacetime exists, while Frames of Referenceare only vies of it. On the traveller’s arrival back at base, their ages, measured by each other, will each be transformed by the Lorentz factor for their relative velocity, While they are travelling.t’ = gamma.tBut once the twins are once again at rest with one another, what are those transformed ages – gamma is now = 1?they are the same!

Time dilation – and length contraction – are effects of measuring one frame from another, moving frame, when the frames are not in relative motion their measurements will be the same.It is like looking through a microscope – it doesn’t matter how long you look, when you take the slide out the object is still the same size as it was before you magnified it!I leave you to draw your own conclusions about the rigour of those muon experiments! Markus is showing you the most rigorous proof possible.We have confirmed the “wibbly-wobbly timey-wimey stuff” in many experiments. Add two events, E1 and E2: Flashes light propagated at A and B, the light from these events arrive at M simultaneously.

Originally Posted by space at the centre On the traveller’s arrival back at base, their ages, measured by each other, will each be transformed by the Lorentz factor for their relative velocity, While they are travelling.t’ = gamma.tBut once the twins are once again at rest with one another, what are those transformed ages – gamma is now = 1?they are the same! The twin experiment is about proper time, and the crucial difference here is that one of the twins undergoes acceleration. Not at all. If they had not adjusted those clocks, your GPS would lose accuracy at around 10km per day.

After all, the laws of physics, and causality, have to apply in that frame. Not in any one Frame but in all Frames. Just stick to finding one frame from which the events are simultaneous in all other frames.

Now, the stationary twin moves only in time but not in space, thus his measured proper time is simplyThetravelling twin on the other hand moves through time and space along a different curve, so his proper time is measured aswhich is obviously less than the stationary twin. You will never find a frame of reference from which events are simultaneous in all other frames. and Originally Posted by SpeedFreek Originally Posted by sigurdV Well then what is simultanity? In how many ways can it be defined? Simultaneity is the question as to whether two events separated by space occur at the same time, or not.The answer is frame dependant – it depends on the frame of reference of the observer. What this shows us is that for any given path through space-time, a stationary one is always the longest one in terms of proper time.

Einstein only set up his scenario to be equidistant to simplify the calculation so that light-travel time did not need to be calculated. Originally Posted by SpeedFreek To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example. This event E3.E1 and E2 are therefore simultaneous.

Oh, but sorry, this is taking the God view; so let us take a Frame of Reference – any Frame of Reference, and the Points in space A,M B will exist in that Frame. What has it to do with Einstien’s theory of Relativity?His theory does not mention Proper time!The very idea of time dilation and length contraction being real Physical changes is logically confusing if not downright impossible!Consider: Body A is at rest in Spacetime and has properties – length L and duration TThen add Body B moving at 0.8667c. However, for the period when one of the twins was in accelerated motion, their proper times differ.

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