Twin Paradox hypothesis

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Summary:

Why someone age faster and the other one doesn't if the fundamental unit of time is constant and it is one second. For example at one moving vessel the time experinced is less as compared to someone which is outside of that framework. For this to happen the unit of time experinced by the observer which is on the moving frame has to be stretched as compared to the one which is not moving.
And How is that possible...?

Main Question or Discussion Point

It is a long message indeed but there is one doubt I want to ask, As from the above video the time measured by the person which is outside the Frame of reference let's say t' depends on the position and time measured by the person within the Frame of reference. But how do we know that whose measurement is correct as everything I'm this universe is moving with respect to one another.

Let's consider a hypothesis in which one person went to a planet and when he comes back he is younger than his colleagues i.e who were of same age when he left earth. For this scenario to happen the time has to pass slowly on the planet and rocket as compared to earth. That means the fundamental unit of time which is one second stretches on the other planet than in the earth but how can this happen because one second can also be defined as the duration in which light travels 2.99 x 10^8 m.
As from the second postulate of Einstein special theory of relativity the speed of light is always constant.
That means one second is always constant so this rules out the possibility of one being younger than other.
I'm only asking if someone can explain this to me they are welcomed.😀
 

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  • #2
Ibix
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There are a great many explanations of the Twin Paradox. The simplest one is to realise that elapsed time is a measure of "length" of lines in spacetime. The two twins follow different paths through spacetime, and their paths are of different "lengths". This is very closely analogous to the fact that if two cars meet up twice their odometers do not necessarily show the same distance between the meetings.

The reason I'm putting "length" in quotes is that the actual quantity is called interval, and is equal to the speed of light times the elapsed time for someone following a given path through spacetime. It doesn't behave exactly like the Euclidean concept of length that you are familiar with, but it has the same logical place in Minkowski geometry as length has in Euclidean geometry. So my analogy with the cars' odometers measuring distance through space being analogous to the twins' clocks measuring "distance" through time is quite a precise one.
 
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There are a great many explanations of the Twin Paradox. The simplest one is to realise that elapsed time is a measure of "length" of lines in spacetime. The two twins follow different paths through spacetime, and their paths are of different "lengths". This is very closely analogous to the fact that if two cars meet up twice their odometers do not necessarily show the same distance between the meetings.

The reason I'm putting "length" in quotes is that the actual quantity is called interval, and is equal to the speed of light times the elapsed time for someone following a given path through spacetime. It doesn't behave exactly like the Euclidean concept of length that you are familiar with, but it has the same logical place in Minkowski geometry as length has in Euclidean geometry. So my analogy with the cars' odometers measuring distance through space being analogous to the twins' clocks measuring "distance" through time is quite a precise one.
Thanks, But still I didn't get the ans that why time is stretched at one place.
 
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PeroK
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It must be at least 15 minutes since we had a thread on the twin paradox!
 
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Ibix
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Thanks, But still I didn't get the ans that why time is stretched at one place.
It isn't stretched. Again, the analogy to length is helpful. If you lay two rulers crossing each other at a slight angle, the marks on one ruler mark off distances of 1cm in one direction, and the marks on the other ruler mark off 1cm in another direction - or alternatively, mark off distances of ##\cos\theta## centimeters in the direction of the first ruler, if ##\theta## is the angle between the rulers. Neither ruler is stretched. It's just that one isn't measuring in quite the same direction as the other.

Similarly, clocks measure "distance" through spacetime. If the clocks' paths make an "angle" ##\psi## between them then each clock sees the other tick once every ##\cosh\psi## seconds, just as each ruler sees the other's marks at ##\cos\theta## centimetres. Again, the "angle" ##\psi## isn't an ordinary angle. It's a hyperbolic angle, which is why the hyperbolic cosine is used. It's called rapidity, and is ##\sinh^{-1}(v/c)##, where ##v## is the velocity of the clock relative to us and ##c## is the speed of light.

So, in short, time is not stretched. Two clocks in relative motion measure "distance" in slightly different directions in spacetime. Hence the projection of the "length" between ticks of one clock onto the worldline of the other is slightly longer than one tick of that clock.
 
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It must be at least 15 minutes since we had a thread on the twin paradox!
15.000000000000002 minutes for me - I've been for a run.

Edit: D'oh! Messed up the punchline! That should be 14.999999999999998 minutes.
 
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It isn't stretched. Again, the analogy to length is helpful. If you lay two rulers crossing each other at a slight angle, the marks on one ruler mark off distances of 1cm in one direction, and the marks on the other ruler mark off 1cm in another direction - or alternatively, mark off distances of ##\cos\theta## centimeters in the direction of the first ruler, if ##\theta## is the angle between the rulers. Neither ruler is stretched. It's just that one isn't measuring in quite the same direction as the other.

Similarly, clocks measure "distance" through spacetime. If the clocks' paths make an "angle" ##\psi## between them then each clock sees the other tick once every ##\cosh\psi## seconds, just as each ruler sees the other's marks at ##\cos\theta## centimetres. Again, the "angle" ##\psi## isn't an ordinary angle. It's a hyperbolic angle, which is why the hyperbolic cosine is used. It's called rapidity, and is ##\sinh^{-1}(v/c)##, where ##v## is the velocity of the clock relative to us and ##c## is the speed of light.

So, in short, time is not stretched. Two clocks in relative motion measure "distance" in slightly different directions in spacetime. Hence the projection of the "length" between ticks of one clock onto the worldline of the other is slightly longer than one tick of that clock.
Thanks again but how would you measure the projection of their distance or length, It is multiplying the time with their velcity or s= vt.
Or More technically we can use the Lorentz transform for position.
But again we will use the time and velocity observed by us.

As from the above stated hypothesis for twin paradox the twin which come backs on earth after space travel is said to be younger than other followed by the condition that earth has to be stationary.
But Earth is not stationary as it revolves around the sun so when the twin comes back to earth , the earth must have moved to a different position as compared to the position when he left the earth. Hence when he comes back he have to travel more So how could we agree that he is younger.?? Because earth is not stationary..
 
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  • #8
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But Earth is not stationary as it revolves around the sun so when the twin comes back to earth , the earth must have moved to a different position as compared to the position when he left the earth.
The earth is not stationary, but it turns out that the effects of its motion are small enough that they don’t change the answer enough to matter. If this bothers you, you can change the thought experiment: substitute “hypothetical planet that is floating in otherwise empty space” for “earth” everywhere. The analysis will be the same.
 
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But Earth is not stationary as it revolves around the sun so when the twin comes back to earth , the earth must have moved to a different position as compared to the position when he left the earth. Hence when he comes back he have to travel more So how could we agree that he is younger.?? Because earth is not stationary..
The twin paradox assumes that a space-flight at high relativistic speed (relative to the Earth) is undertaken. This leads to large relativistic effects on the age of the returning astronauts. There are small relativistic effects associated with the motion of the Earth around the Sun, but these are small or negligible compared to the effects associated with high-speed interstellar space travel.
 
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Thanks again but how would you measure the projection of their distance or length
Mathematically it is literally just the standard projection of a vector, i.e. the dot product with a unit vector. Experimentally you use synchronized clocks. The purpose of the synchronization is to give the projection onto the time axis at each event in spacetime. That is how coordinate systems work.
 
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As a guy who doesn't understand or follow the maths, It took me a while to understand this also. It was only from reading lots of posts on this forum together with watching many popular science videos from youtube channels such as "PBS Spacetime" and The Science Asylum," which show a bunch of spacetime diagrams that the concept finally sank in. Also looking at videos on terms which keep coming up again and again helped me enormously such as "what is a tensor" and "what is a 4-velocity."

Don't expect to "get it" straight away, it will take time and research of the appropriate material to get your head around it.
 
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15.000000000000002 minutes for me - I've been for a run.

Edit: D'oh! Messed up the punchline! That should be 14.999999999999998 minutes.
As a guy who doesn't understand or follow the maths, It took me a while to understand this also. It was only from reading lots of posts on this forum together with watching many popular science videos from youtube channels such as "PBS Spacetime" and The Science Asylum," which show a bunch of spacetime diagrams that the concept finally sank in. Also looking at videos on terms which keep coming up again and again helped me enormously such as "what is a tensor" and "what is a 4-velocity."

Don't expect to "get it" straight away, it will take time and research of the appropriate material to get your head around it.
Thanks for your advice but I have studied relativity in one of my subject while doing my graduation. I have also done it's numericals So I have no problem with it's math. But I want to grab th concept from which the equations come from that's why I'm here 😀
 
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Thanks for your advice but I have studied relativity in one of my subject while doing my graduation. I have also done it's numericals So I have no problem with it's math. But I want to grab th concept from which the equations come from that's why I'm here 😀
Then I suggest you start approaching relativity geometrically. Are you familiar with spacetime diagrams? If so, then draw the spacetime diagram for the scenario and simply calculate the “length” of each path using ##\Delta s^2 = c^2 \Delta t^2 - \Delta x^2##
 
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15.000000000000002 minutes for me - I've been for a run.

Edit: D'oh! Messed up the punchline! That should be 14.999999999999998 minutes.
The earth is not stationary, but it turns out that the effects of its motion are small enough that they don’t change the answer enough to matter. If this bothers you, you can change the thought experiment: substitute “hypothetical planet that is floating in otherwise empty space” for “earth” everywhere. The analysis will be the same.
Sir In one of the Einstein's thought experiment where he observes two lightning bolts behind a fast moving train while standing at some other location and they appear to be simultaneous. But when he observes this scenario while being on the moving train he observes two lightning bolts differently.
So why does he concluded that time is not absolute
Because as train moves towards one far from other by the time the flashes will reach observer he will be closer to one flash lightning bolt and away from the other so this conclusion is inevitable. Then why does he said that time is not absolute....?
 
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Because as train moves towards one far from other by the time the flashes will reach observer he will be closer to one flash lightning bolt and away from the other
Not in his frame. In his frame he is always at rest in the middle.
 
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  • #16
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Sir In one of the Einstein's thought experiment where he observes two lightning bolts behind a fast moving train while standing at some other location and they appear to be simultaneous. But when he observes this scenario while being on the moving train he observes two lightning bolts differently.
So why does he concluded that time is not absolute
Because as train moves towards one far from other by the time the flashes will reach observer he will be closer to one flash lightning bolt and away from the other so this conclusion is inevitable. Then why does he said that time is not absolute....?
Because for the observer in the midpoint of the train, the lightning bolts struck the ends of the train, which are both an equal distance from him. The speed of light is invariant, which means that he must measure the light coming from those strikes as traveling at c relative to the train.
In order for two light beams traveling at the same speed, and leaving points an equal distance from him to arrive at different moments, they had to have left at different times.
 
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The flash lightning bolts are events, that means points in 4D-spacetime. They cannot be at rest in the one or the other reference system, because they have no world-line.

Here is the explanation of Einstein:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity
Thanks for the link.
But I'm not saying they are at rest this misunderstanding has happened because you have read a line not the full post. I'm saying as the train is travelling the flash created by the first lightning will reach it earlier because the time taken by the observer to witness this event is less as compared to the other one as the distance travelled by the light will be less because train is also moving simultaneously.
 
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Thanks for the link.
But I'm not saying they are at rest this misunderstanding has happened because you have read a line not the full post. I'm saying as the train is travelling the flash created by the first lightning will reach it earlier because the time taken by the observer to witness this event is less as compared to the other one as the distance travelled by the light will be less because train is also moving simultaneously.
SR is not about the delay in light signals reaching an observer. This lightning strike example can be misleading in that respect.
 
  • #20
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...one second can also be defined as the duration in which light travels 2.99 x 10^8 m.
As from the second postulate of Einstein special theory of relativity the speed of light is always constant.
That means one second is always constant so this rules out the possibility of one being younger than other.
Well, no: distance = speed x time. So if we know the speed is the same and the time isn't, what else did we just break? :nb)
 
  • #21
Thanks for the link.
But I'm not saying they are at rest
I think, you said it indirectly by:
Satyam said:
he will be closer to one flash lightning bolt and away from the other
A correct formulation would be:
"he will be closer to the x-coordinate, where one flash lightning bolt happened and away from the x-coordinate, where the other happened"

Also correct would be (in the train system):
"he will have the same distance to the x'-coordinate, where one flash lightning bolt happened as to the x'-coordinate, where the other happend"

Imagine, according to the principle of relativity, the train would be at rest and the embankment would move in the opposite direction ...
 
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  • #22
Mister T
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Why someone age faster and the other one doesn't if the fundamental unit of time is constant and it is one second.
This is called proper time, or in other words, "my time". Each twin can conduct experiments that confirm that indeed, according to each of them, their own measurements of time fit the definition you refer to. In other words, they each age one year for every year of time that passes on their own clocks. But when they compare the passage of time on their clock to the passage of time on the other's clock, that is when they find discrepancies.

As from the above video [...]
What video?
 
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Thanks for the link.
But I'm not saying they are at rest this misunderstanding has happened because you have read a line not the full post. I'm saying as the train is travelling the flash created by the first lightning will reach it earlier because the time taken by the observer to witness this event is less as compared to the other one as the distance travelled by the light will be less because train is also moving simultaneously.
The light from the strike hitting the front of the train only travels a shorter distance than the light from the rear as measured from the embankment. As measured from the train, the light from both strikes travel an equal distance.
 
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Not in his frame. In his frame he is always at rest in the middle.
Let's say there are two frame of reference in this condition
1. Frame of reference in embankment
2. Frame of reference in moving train
As the events of lightning bolts happens For frame of reference for embankment and they appear to be simultaneous while for the observer in moving train they will not.
Does it mean that time dilation occurs because the observer in moving train consider himself at rest while he is not.

So we can say that we use time dilation to understand how the other observer will experience time.
So why are we concluding that time is not absolute for the observer in moving train while the reality is he does not know that he is moving w.r.t the events that has been occurred.
 
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  • #25
As the events of lightning bolts happens in the frame of reference for embankment
...
an event which is happening not in his frame of reference.
These statements are wrong.
 
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