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The Twin Paradox Made Simple

Special Relativity Twin Paradox

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#1 A-wal

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Posted 24 March 2018 - 01:14 PM

The twin paradox is a great way to show what special relativity models and it's something that most people who want to understand it get stuck on. First it's important to understand basic Galilean relativity, all motion is relative. That just means that there's no distinction between object A moving away from object B and object B moving away from object A. Adding more objects for comparison makes no difference because an object at rest relative to one would in motion relative to the other.

Special relativity is based on the speed of light being the same for all inertial (non accelerating) observers. Velocity is a measurement of distance over time so if observers that are in motion relative to each other measure light to be moving at the same velocity then they must measure different lengths for either space, time or both. SR is the description of how space contracts and time dilates (always by the same amount) to keep the speed of light constant in all inertial frames of reference.

Because there's only two dimensions involved (the spatial direction of motion and time), what's going on can be easily represented using diagrams. This represents two objects that are at rest relative to each other. The vertical axis is space and the horizontal axis is time. They aren't moving through space at all in relation to each other so the lines are parallel and they're moving through time at the same rate. Light moves along the vertical axis, at full speed through space and not all through time.

1.JPG

 

Now the red object accelerates to 0.6c (0.6 of the speed of light) at the point of the curve but we stay in the original frame of reference. Once it's moving in a straight line again it's no longer accelerating so I'm using instant acceleration. Now because Red moving at an angle (moving through space at 0.6c relative to Blue's frame) Red is moving through time at 80% the rate of Blue, both 'worldlines' are the same length. It's also shorter in length in its direction of motion in Blue's frame.

2.JPG

 

Now we switch to the frame of reference that Red accelerates into. In this frame it's Blue who's length contracted and moving through time at 80% the rate of Red after Red has accelerated. Light still moves along the vertical axis, moving at the full speed of light through space and not all through time. Both frames are equally valid and there's no contradiction, it's just that every frame of reference measures time and space differently to keep the speed of light constant across all frames.

3.JPG

 

Now we switch back to the original frame and see what happens when Red accelerates back into Blue's inertial reference frame (when the two lines are running parallel again). They're now separated in space because Red accelerated away but they're in the same reference frame as each other again and Red has traveled through less time than Blue. Red's motion through space in relation to this frame of reference has shortened it's motion through time because it's moved along a curved wordline.

4.JPG

 

Finally Red accelerates towards Blue and then decelerates (just means accelerates in the opposite direction) so the the twins are reunited and they find that Red is younger than Blue. They were both moving through spacetime at the speed of light (that's why their wordlines are the same length) but because Red's worldline wasn't a straight line because of the accelerations, Red took a more indirect route and therefore experienced less 'proper time' (the time that passes for an observer).

5.JPG

 

So although the twin that accelerates is the one that experiences less proper time, acceleration is not the direct cause of the difference in age when they reunite. The time intervals at the bottom of the graphs are arbitrary, the difference in their age is directly proportional to the length of the time intervals but the amount of acceleration doesn't change, it depends on how far the path of the accelerator's worldline deviated from the straight inertial worldline of the twin that doesn't accelerate.

This also means that mass is affected by relative velocity because it takes a greater amount of acceleration for a moving object to increase its velocity by the same amount the faster it's already moving in that frame of reference, so mass increases as relative velocity increases because it takes more energy to produce the same amount of acceleration. It would take an infinite amount of energy and acceleration for an object to reach a velocity of the speed of light relative to another object.


Edited by A-wal, 02 May 2018 - 03:53 PM.


#2 A-wal

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Posted 26 March 2018 - 05:16 AM

Updated.



#3 Moronium

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Posted 07 April 2018 - 09:01 PM

....all motion is relative. That just means that there's no distinction between object A moving away from object B and object B moving away from object B. 
 

 

 

1.  There is a difference between the earth revolving around the sun and the sun (and the entire universe, for that matter) revolving around the earth, wouldn't you agree?



#4 Moronium

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Posted 07 April 2018 - 09:31 PM

Likewise, there is a difference (distinction) between loading a rocket up with fuel, igniting it and:

 

1.  The rocket beginning to move away from the earth and toward the moon, versus

 

2.  The rocket remaining absolutely motionless while the earth begins moving away from the ship, and the moon toward it.


Edited by Moronium, 07 April 2018 - 09:33 PM.


#5 A-wal

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Posted 08 April 2018 - 02:33 PM

1.  There is a difference between the earth revolving around the sun and the sun (and the entire universe, for that matter) revolving around the earth, wouldn't you agree?

If you mean a difference between the universe moving around an observer and the observer spinning that's actually a very interesting question (look up Newton's bucket) but it's nothing to do with anything described here. That's angular motion and this deals purly with linear motion.

 

Likewise, there is a difference (distinction) between loading a rocket up with fuel, igniting it and:

 

1.  The rocket beginning to move away from the earth and toward the moon, versus

 

2.  The rocket remaining absolutely motionless while the earth begins moving away from the ship, and the moon toward it.

No! Absolutely no distinction whatsoever between the two. Motion is a meaningless concept unless it's relative to something else. If two objects are in motion relative to each other then there's no distinction between object A being in motion relative to object B and object B being in motion relative to object A because it makes no difference at all.



#6 Moronium

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Posted 08 April 2018 - 04:46 PM

If you mean a difference between the universe moving around an observer and the observer spinning that's actually a very interesting question (look up Newton's bucket) but it's nothing to do with anything described here. That's angular motion and this deals purly with linear motion.

 

No! Absolutely no distinction whatsoever between the two. Motion is a meaningless concept unless it's relative to something else. If two objects are in motion relative to each other then there's no distinction between object A being in motion relative to object B and object B being in motion relative to object A because it makes no difference at all.

 

 

So you say, and you can say it 1,000 times if it helps you convince yourself, but modern physycists still won't agree with you.

 

Given the known laws of physics, it would be impossible for the entire universe to revolve around the earth, and no one thinks it does.  Similarly, it is accepted theory that the solar system revolves around the center of mass of the MIlky Way; that the galaxy itself is travelling at a speed of about 1 million mph toward the Great Attractor; etc.

 

The great attractor is not coming toward us any more than a rubber ball 100 feet in the air above the earth's surface remains motionless while it's "gravitational pull" causes the earth to come meet it before they collide.

 

Why argue otherwise? I don't get it.


Edited by Moronium, 08 April 2018 - 04:51 PM.


#7 Moronium

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Posted 08 April 2018 - 05:10 PM

 If two objects are in motion relative to each other then there's no distinction between object A being in motion relative to object B and object B being in motion relative to object A because it makes no difference at all.

 

I disagree.  It makes a huge difference, especially with respect to the formulation of any coherent physical laws.  If I throw a baseball over the 15 feet high left field fence, that is quite different than the ball remaining motionless when I release it, while I instantly start travelling away from it the second I let go of it, and while the bleachers (and everything else attached to the earth in that direction) come rushing toward the baseball, with the earth simultaneously "dipping down" so the ball can clear the fence.

 

It strikes me as absurd to claim otherwise, sorry.


Edited by Moronium, 08 April 2018 - 05:18 PM.


#8 A-wal

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Posted 08 April 2018 - 05:51 PM

So you say, and you can say it 1,000 times if it helps you convince yourself, but modern physycists still won't agree with you.

Actually modern physicists do agree with me, this is just how relative motion works. It's well established and not in any way in doubt with the physics community.

 

Given the known laws of physics, it would be impossible for the entire universe to revolve around the earth, and no one thinks it does.  Similarly, it is accepted theory that the solar system revolves around the center of mass of the MIlky Way; that the galaxy itself is travelling at a speed of about 1 million mph toward the Great Attractor; etc.

 

The great attractor is not coming toward us any more than a rubber ball 100 feet in the air above the earth's surface remains motionless while it's "gravitational pull" causes the earth to come meet it before they collide.

 

Why argue otherwise? I don't get it.

None of what you said has any baring on the actual point. Whether or not there's any real distinction between an object spinning and all other objects in the universe orbiting around it (I never claimed there wasn't), it in no way has any baring on the orbital motions of bodies around massive objects.

 

I disagree.  It makes a huge difference, especially with respect to the formulation of any coherent physical laws.  If I throw a baseball over the 15 feet high left field fence, that is quite different than the ball remaining motionless when I release it, while I instantly start travelling away from it the second I let go of it, and while the bleachers (and everything else attached to the earth in that direction) come rushing toward the baseball, with the earth simultaneously "dipping down" so the ball can clear the fence.

 

It strikes me as absurd to claim otherwise, sorry.

No it doesn't make any difference to the formation of any coherent laws because the laws of physics don't distinguish between an object at rest and an object in constant inertial motion.

 

What's absurd is to try claiming that there's a distinction when the only sense in which an object can be said to be in motion is if it's in motion relative to another object. Which objects are in motion and which are at rest is entirely arbitrary, the laws of physics are the same in all inertial frames of reference.



#9 Moronium

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Posted 09 April 2018 - 11:12 AM

Actually modern physicists do agree with me, this is just how relative motion works. It's well established and not in any way in doubt with the physics community.

 

None of what you said has any baring on the actual point. Whether or not there's any real distinction between an object spinning and all other objects in the universe orbiting around it (I never claimed there wasn't), it in no way has any baring on the orbital motions of bodies around massive objects.

 

No it doesn't make any difference to the formation of any coherent laws because the laws of physics don't distinguish between an object at rest and an object in constant inertial motion.

 

What's absurd is to try claiming that there's a distinction when the only sense in which an object can be said to be in motion is if it's in motion relative to another object. Which objects are in motion and which are at rest is entirely arbitrary, the laws of physics are the same in all inertial frames of reference.

1.  How about laws such as the inverse square law of gravitation, F=MA, etc.?  Which object is moving is crucial to those laws.

 

2. All inertial frames are preferred frames, where the laws of physics take the simplest form.  The "laws of physics" are different in accelerating frame, so why make that an issue or pretend like it settles something?  Furthermore,  who's to say that there is actually an inertial frame anywhere in the universe it motion can't even be detected?

 

3.  You use the word "relative" in an equivocal and trivial way.  "Relative motion," is this context, does not mean "moving with respect to something else."  It means motion that is frame-dependent (relative) versus frame-independent, iike acceleration (absolute).  The distinction to be made is between relative and absolute motion, and this is totally ignored if all you do is merely observe that all motion is "relative" to something else (which is simply an uninformative, tautological truism).

 

4.  Did we send men to the moon, or did the moon simply come to them?  If you can't answer that question, then all physics must be completely meaningless to you.


Edited by Moronium, 09 April 2018 - 12:38 PM.


#10 Moronium

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Posted 09 April 2018 - 11:49 AM

The thread topic here is the "twin paradox."  A few things worth noting about that, I think;

 

1.  Even though the space traveller (because he assumes he is motionless while travelling at a uniform speed) "thinks" the earth's clock is moving slower than his, he is wrong.  It isn't.  Both twins do NOT end up being younger than the other.  He, and only he, is younger.

 

2.  The "resolution" to the twin paradox simply ends up treating the earth as a preferred frame.  This is supposedly prohibited by SR, but you can't get any type of "absolute" answer, such as the twin paradox gives, without adopting a preferred frame.

 

3. Data from the GPS, and tons of other data, empirically prove that time dilation is not "reciprocal" as a matter of fact.  You can adopt that premise, for theoretical purposes, if you want, but it still won't be true in the real world.  No empirical test is even required though.  The concept of "reciprocal time dilation" can be rejected a priori because it is logically impossible.

 

4.  In SR (and in fact) it is the "moving clock" which slows down when applying the Lorentz transformations.  So, given the resolution to the paradox, it is clear that the space traveller was the one moving, relative to the earth.  The earth was NOT moving relative to him while he remained motionless.   Your repeated proclamations that there is no distinction doesn't seem to very well thought out, if you ask me.


Edited by Moronium, 09 April 2018 - 12:00 PM.


#11 A-wal

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Posted 13 April 2018 - 04:09 PM

1.  How about laws such as the inverse square law of gravitation, F=MA, etc.?  Which object is moving is crucial to those laws.

This only applies to inertial frames of reference. The frame of reference of an accelerating observer is outside of the frame work of what this model describes. That's why I used instantaneous acceleration, as well as just keeping it simple it means there's no point when one of the observers is acceleration because they instantaneously jump from one frame of reference to another. It doesn't invalidate the example, you could just assume that the times in which an observer is accelerating are removed.

 

2. All inertial frames are preferred frames, where the laws of physics take the simplest form.  The "laws of physics" are different in accelerating frame, so why make that an issue or pretend like it settles something?

Because the laws are the same in all inertial frames of reference, that's the point. The speed of light isn't constant in accelerating frames, it's always slower.

 

In fact the rate that light slows as acceleration increases at a constant rate is identical to the rate that the relative velocity difference between two observers decreases (at a constant rate of acceleration). The actual rates depend on the rate of acceleration increase with the speed of light and the rate of constant acceleration with two inertial observers obviously but the curve is the same. It does';t matter if you don't know what I'm taking about here, it's not really got anything to do with what you said, it's just that I've never seen it mentioned anywhere and it's really important.

 

Furthermore,  who's to say that there is actually an inertial frame anywhere in the universe it motion can't even be detected?

There is an inertial frame everywhere in the universe because motion can't be detected. Every inertial observer is in an inertial frame of reference and objects that are at rest relative to that observer are in the same inertial frame, because there's no length contraction and time dilation needed for them to measure the same speed of light if they're not in motion relative to each other.

 

3.  You use the word "relative" in an equivocal and trivial way.  "Relative motion," is this context, does not mean "moving with respect to something else."  It means motion that is frame-dependent (relative) versus frame-independent, iike acceleration (absolute).  The distinction to be made is between relative and absolute motion, and this is totally ignored if all you do is merely observe that all motion is "relative" to something else (which is simply an uninformative, tautological truism).

Again, all inertial motion is relative. If you want to think of acceleration as absolute motion that's something else entirely. I actually believe that all motion including accelerating is relative, I think that's what Mach's principle is basically saying but that's a different discussion.

 

4.  Did we send men to the moon, or did the moon simply come to them?  If you can't answer that question, then all physics must be completely meaningless to you.

That's the same thing. The astronauts didn't leave their bodies so they themselves didn't go anywhere, from their perspective Earth moved away from and the moon moved towards them. Of course they accelerated to leave the Earth and the had to overpower the gravitational acceleration of the planet to do that but during the journey when they weren't accelerating, the moon was moving towards them every bit as much as they were moving towards it because there's no distinction between the two.

 

1.  Even though the space traveller (because he assumes he is motionless while travelling at a uniform speed) "thinks" the earth's clock is moving slower than his, he is wrong.  It isn't.  Both twins do NOT end up being younger than the other.  He, and only he, is younger.

That's only because the one that stays on Earth doesn't change reference frames and the other twin does, I explained this in the example. If one twin were to leave Earth and accelerate just the once so they were moving away at a constant velocity and the other twin left Earth later on to catch up and then accelerate into the frame of reference first twin to leave once the second twin catches up then it would be the second twin that left Earth who would be younger.

 

2.  The "resolution" to the twin paradox simply ends up treating the earth as a preferred frame.  This is supposedly prohibited by SR, but you can't get any type of "absolute" answer, such as the twin paradox gives, without adopting a preferred frame.

It has nothing to do with a preferred frame of reference, the younger twin is always the one who's world line deviated further from the frame of reference they end up in because every object moves through space-time at the speed of light. The one who deviated further from that frame of reference traveled through more space from that frame's reference and therefore traveled through less time to keep it's overall velocity through space-time constant.

 

3. Data from the GPS, and tons of other data, empirically prove that time dilation is not "reciprocal" as a matter of fact.  You can adopt that premise, for theoretical purposes, if you want, but it still won't be true in the real world.  No empirical test is even required though.  The concept of "reciprocal time dilation" can be rejected a priori because it is logically impossible.

Completely wrong on both counts. All the data empirically proves that the speed of light is constant and therefore that time dilation and length contraction are a fact because it's logically impossible for them not to be.

 

4.  In SR (and in fact) it is the "moving clock" which slows down when applying the Lorentz transformations.  So, given the resolution to the paradox, it is clear that the space traveller was the one moving, relative to the earth.  The earth was NOT moving relative to him while he remained motionless.   Your repeated proclamations that there is no distinction doesn't seem to very well thought out, if you ask me.

Both clocks are moving relative to the other's frame of reference, therefore both are time dilated and length contracted from the perspective of the other. It's true that when the twin the left Earth returns it's that twin that was in motion and therefore younger, but in motion relative to that frame of reference. You can start from any arbitrary frame, it makes no difference. Once they end up back in the same frame it's the one who left that frame and returned that experiences less proper time and will be younger.


Edited by A-wal, 13 April 2018 - 04:13 PM.


#12 Moronium

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Posted 14 April 2018 - 03:02 AM

A-wal said:  "The astronauts didn't leave their bodies so they themselves didn't go anywhere, from their perspective Earth moved away from and the moon moved towards them. Of course they accelerated to leave the Earth and the had to overpower the gravitational acceleration of the planet to do that but during the journey when they weren't accelerating, the moon was moving towards them every bit as much as they were moving towards it because there's no distinction between the two."

 

-------

 

You seem to find it impossible to distinguish fictitious theoretical mathematical/philosopical claims from practical reality, A-wal.  You say "from their perspective," but that's absurd.  What you really mean is "from MY perspective, which I impute to them and demand that they adopt and adhere to."

 

No astronaut who went into outer space EVER, from "their perspective," thought they were motionless while the earth moved away from and the moon moved toward them.  EVER!  They know better, as a practical matter, and would (properly) reject and resist your attempt to impute a different "perspective" to them just so you can claim the math model of SR is true as a matter of empirical fact (which it aint).

 

They wouldn't deny all other physical principles to maintain this philosophical fiction.  You concede that "of course they accelerated to leave the Earth and the had to overpower the gravitational acceleration of the planet."  And what does Newton's law of inertia (which SR accepts) say about that?  That a body in motion will stay in motion unless acted upon by an external force, right?

 

Yet YOU want to say that the instant they stop accelerating and settle into maintaining a uniform speed, then they INSTANTLY STOP ON A DIME and become motionless.  At that moment THEY are suddenly motionless without any explanation of how that is possible (which it aint).  Normal people don't ignore the known laws of physics like that--at least not to the point of claiming that's what's actually happening as opposed to saying it just a complete, yet presumably useful, theoretical fiction to pretend that it's true.

 

No astronaut has ever taken the "perspective" you impute to them, and none ever will.  You couldn't ever even become an astronaut if you were that oblivious to physics.  Astronauts aint stupid.


Edited by Moronium, 14 April 2018 - 10:30 AM.


#13 Moronium

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Posted 14 April 2018 - 03:18 AM

A-wal said:  "This only applies to inertial frames of reference.  The frame of reference of an accelerating observer is outside of the frame work of what this model describes...The speed of light isn't constant in accelerating frames, it's always slower."

 

Exactly, which is just one of many reasons why a theory of relative motion which incorporates absolute simultaneity (such as the RMS model) is vastly superior to SR and is used in the GPS while SR is rejected (because it would give inaccurate and contradictory predictions).

 

With accelerating objects, there is no pretense to "reciprocal time dilation," etc.  It is explicitly acknowledged that the clock of an accelerating object runs slower and that the clocks of (relatively) inertial objects run FASTER, NOT SLOWER.  This is an ABSOLUTE phenomenon, not a relative one, as even all SR adherents admit.

 

An AST (absolute simultaneity theory) makes perfectly accurate predictions for ALL moving objects, not just the that extreme minority of objects (if there really are any at all) that are not accelerating.


Edited by Moronium, 14 April 2018 - 04:12 AM.


#14 Moronium

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Posted 14 April 2018 - 03:28 AM

A-wal:  "There is an inertial frame everywhere in the universe because motion can't be detected."

 

-----

 

Yes, I agree that SR does make this claim, but it's absolutely absurd, nonetheless.

 

SR merely mimics an AST by postulating a preferred, absolutely motionless, frame for every calculation it makes.  According to SR, the preferred frame is always the one YOU are in (if you are inertial).  Any and every thing in the entire universe which is moving with respect to YOU is moving.  YOU are absolutely motionless.  Every observer is a motionless luminous ether unto himself, per the mandates of SR, and there are an infinite number of motionless frames.   Problem is,  as a practical and possible matter, only one frame can be motionless, never more than one when there is relative motion between them.  As I said, the whole notion is ridiculous.


Edited by Moronium, 14 April 2018 - 04:14 AM.


#15 Moronium

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Posted 14 April 2018 - 03:46 AM

Awal said:  "If one twin were to leave Earth and accelerate just the once so they were moving away at a constant velocity and the other twin left Earth later on to catch up and then accelerate into the frame of reference first twin to leave once the second twin catches up then it would be the second twin that left Earth who would be younger."

 

----

 

Yes, of course.  But this is not caused by a change is some fictitious "frame of reference," which exists only as a mental construct.  It is because the accelerated twin is the one ACTUALLY MOVING and it is the moving clock which ALWAYS runs slow.  For whatever reasons, increased speed actually causes clocks (and all physical precesses) to slow down

 

The circumstances are NOT symmetrical, needless to say.  Relative to each other, one is moving (faster), one is not.


Edited by Moronium, 14 April 2018 - 09:51 AM.


#16 Moronium

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Posted 14 April 2018 - 03:51 AM

A-wal said:  "Completely wrong on both counts. All the data empirically proves that the speed of light is constant and therefore that time dilation and length contraction are a fact because it's logically impossible for them not to be."

 

-----

 

Wrong.  As I have noted in another thread, the speed of light is NOT constant in every frame, and logically in can't be.  It is, however, always MEASURED to be the same.  But that's not because it IS the same.  It's because speed distorts the measuring instruments which are used to calculate and determine the speed of light (time and distance).  That distortion is exactly what the LT "correct for.'


Edited by Moronium, 14 April 2018 - 02:08 PM.


#17 Moronium

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Posted 14 April 2018 - 10:03 AM

If it is claimed that one object is "moving faster" than another, then it is legitimate and natural to ask:  "Compared to what?"  AST theories give accurate predictions ONLY when ALL motion is calculated by reference to the center of the dominant gravitational field of the locality where the prediction is made.  As Einstein said: "All physics are local."

 

For calculations involving the speeds of various objects in motion on or near earth, this would be the ECI, as used in the GPS.  For measurements on a solar scale, it is the barycenter, which even the Sun revolves around. Compared to anything else in the solar system, the barycenter is indeed the only point which is not "moving."  Newton, Keppler, Copernicus, et al, used this point to calculate the speed and direction of planetary orbits--using the background of the "fixed stars" as a "close approximation" to another "motionless" frame.

 

For the Milky Way, the black hole at the center of the galaxy's mass is used.  For "universal" measurements, the CMB has been used by astrophysicists as the preferred frame of reference for many decades now.  For practical purposes, all such local frames of reference can be treated as "motionless" for local experiments in order to achieve accurate predictions, even if they are not "truly motionless" in the overall scheme of things..   Reference to the CMB tells us, for example, that the entire MIlky Way is moving at a high rate of speed toward the "great attractor."  But since that motion is common to every object in the Milky Way, it can be ignored when making intra-galactical calculations of relative motion.

 

Of course all such calculations are prohibited by SR, which (purportedly, at least) forbids the use of a preferred frame.  But that does not make their use less accurate--it merely exposes how inaccurate predictions based on the strictly relative motion relied on by SR can be.
 


Edited by Moronium, 14 April 2018 - 02:09 PM.




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