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Twins paradox and ageing

by adw73uk
Tags: ageing, paradox, twins
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edpell
#19
Dec21-09, 08:48 PM
P: 451
In space/time every thing is always traveling at the speed of light. That is

[tex]
(vt)^2 + (ct)^2 = c^2
[/tex]

It is only a question of how much of the traveling is done in the spacial direction and how much is done in the time direction.
edpell
#20
Dec21-09, 09:06 PM
P: 451
Kev, this all seems very Machian to me. There seems to be something special about the stay behind folks they age the most. How? Given that velocity is "relative". How do account for the asymmetry? The folks left behind are moving at exactly the same speed as the folks in the ship (when seen from the ship) (I say speed not velocity, the velocities are equal and opposite).
DaveC426913
#21
Dec21-09, 11:24 PM
DaveC426913's Avatar
P: 15,319
Quote Quote by edpell View Post
Kev, this all seems very Machian to me. There seems to be something special about the stay behind folks they age the most. How? Given that velocity is "relative". How do account for the asymmetry? The folks left behind are moving at exactly the same speed as the folks in the ship (when seen from the ship) (I say speed not velocity, the velocities are equal and opposite).
Special Relativity applies in inertial frames of reference; it does not apply to non-inertial frames of reference. The Earth and its inhabitants stay in an inertial frame of reference (by not accelerating), whereas the occupants of the spaceship change to an accelerating frame of reference. Thus it is no longer "all relative".
yuiop
#22
Dec22-09, 12:06 AM
P: 3,967
Quote Quote by edpell View Post
Kev, this all seems very Machian to me. There seems to be something special about the stay behind folks they age the most. How? Given that velocity is "relative". How do account for the asymmetry? The folks left behind are moving at exactly the same speed as the folks in the ship (when seen from the ship) (I say speed not velocity, the velocities are equal and opposite).
It is easy to account for the asymmetry. Have a look at the attached space time diagrams. The first is the point of view of an observer that stays in the Earth frame. (The stay at home twin that remains on the Earth only goes forward in time as represented by the red line A,C.) The second is the point of view of an observer that is at rest with the frame that represents the outward journey of the travelling twin (The green line labelled A,B). The third is the point of view of an observer that remains at rest in the frame that represents the travelling twin's return journey (The green line labelled B,C). In every case every observer measures the travelling twin's path through spacetime (path A,B,C) to be longer than the stay at home twins path through spacetime (path A,C). When looked at from the spacetime path point of view there is no symmetry.
Attached Thumbnails
twin2.GIF  
Al68
#23
Dec22-09, 01:23 AM
P: 801
Quote Quote by croghan27 View Post
So I understand, kev, but thank you. My question is what mechanism governs which biological process is the one to be affected.
The assumption in the twins paradox is that biological processes are completely unaffected. The reason the traveling twin ages less is simply because less time elapsed for him than the earth twin, not because some mechanism caused a change in some biological process.

The differential aging predicted is a result of assuming that a person will age less in 10 years than in 20 years, for example. The point of the twins paradox is that less time elapses for the ship twin, not that some mechanism slowed his aging process.
Al68
#24
Dec22-09, 02:06 AM
P: 801
Quote Quote by edpell View Post
The folks left behind are moving at exactly the same speed as the folks in the ship (when seen from the ship) (I say speed not velocity, the velocities are equal and opposite).
This is simply not true. The coordinate velocity of earth in the ship's frame doesn't match the velocity of the ship in earth's frame for the entire trip.

In the ship's frame(s), earth's coordinate distance from the ship increases at a constant rate, then during the turnaround goes from the length contracted distance to the proper distance and back again in a very short time, then decreases at a constant rate back to zero.

This is very different from the ship's coordinate distance from earth in earth's frame, which just increases at a constant rate then decreases at a constant rate.

Maybe someone could graph the coordinate distance between the earth and ship against each twin's clock reading to show how different they are.
edpell
#25
Dec24-09, 01:36 PM
P: 451
Kev, your diagram is very helpful. In others words a straight line is the shortest path between two points. The clock/observer who never alters their path direction in spacetime will have the shortest path length. The clock/observer who takes a turn in their spacetime path will have a longer path. I think this is the whole story of the twins.

But I still think we need better wording (maybe more careful wording) to talk about "time".
edpell
#26
Dec24-09, 01:49 PM
P: 451
Kev, in your first diagram you show time in the earth frame only. That is at the start before takeoff when they are both in the same inertial frame they both see 0 years on the earth clock. And when the ship returns from its round trip and stops they both see 20 years on the earth clock. And they both see 2 years (assuming gamma of 10) on the ship clock. To say that the ship board observer went only 2 years in time but ended up at the 20 year mark by the earth clock needs some careful wording. It gives the appearance that things went slower on the ship????
edpell
#27
Dec24-09, 02:12 PM
P: 451
It is almost like the traveler has a complex time vector with a "real" part and an "imaginary" part. Where the total time vector length is 20 in the earth frame (and all real) but the real component is 2 in the ship frame and the orthogonal part (imaginary) is 19.899 in the ship frame. and physical aging only takes place with movement along real time axis. I guess I would have to say the real time axis in the moving frame does not point in the same direction as the real time axis in the earth frame. I have no idea what that statement means "the real time in frame1 points in a different direction than real time in frame2".(?) Is there always a local (frame) time and when you transform the local (frame) time to another frame you get a real and imaginary part in the other frames point of view? That is earth sees 20 years of time vector for itself and 2 years of traveler time vector that projects on the real time in the earth frame and 19.899 that projects on the imaginary time axis. Help I am lost....
croghan27
#28
Dec25-09, 09:49 AM
P: 127
Quote Quote by edpell View Post
major snip action here .....
Help I am lost....
Thanks for that edpell - methinks that herein we are not only 'touching the face of God' (and physics) - we are also dancing about the limits of the language. English tenses were never meant to be treated so. "I am" works fine in my own temporal plane, - but "you are" is something temporally different for thee and for me. I shudder to consider "s/he is".
MikeLizzi
#29
Dec26-09, 12:21 PM
P: 191
With regard to the comment by kev by response is:

Obfuscation. Make the problem so complex that you can find your own mistake anymore.
It is the same mistake that evey other solution includes which does not take acceleration into account.
ThomasT
#30
Dec26-09, 02:09 PM
P: 1,414
Quote Quote by Al68 View Post
The assumption in the twins paradox is that biological processes are completely unaffected. The reason the traveling twin ages less is simply because less time elapsed for him than the earth twin, not because some mechanism caused a change in some biological process.

The differential aging predicted is a result of assuming that a person will age less in 10 years than in 20 years, for example. The point of the twins paradox is that less time elapses for the ship twin, not that some mechanism slowed his aging process.
I disagree with this. Acceleration affects the periods of oscillators. If the twins refer to a common third clock (say, revolutions of the earth around the sun), then they will both note the same elapsed time for the travelling twin's trip. But, the traveller will have aged less, and the traveller's clock will have counted fewer oscillations than his earthbound twin's clock.
edpell
#31
Dec26-09, 02:24 PM
P: 451
croghan27, yes I agree the English language is based on Newtonian time and has no direct words to deal with my time versus your time versus their time. In Newtonian English when we say the earth observer goes 20 years in time and the ship observer goes 2 years in time and they both meet at 2030 (say it starts in the year 2010 and gamma is 10). This does not make any sense in Newtonian English. I have no disagreement with SR or the results I just think we have to come up with a better vocabulary for SR time.
Al68
#32
Dec26-09, 02:27 PM
P: 801
Quote Quote by ThomasT View Post
I disagree with this. Acceleration affects the periods of oscillators.
If a clock is affected by acceleration, then it is simply not a valid clock in SR. This is the "clock hypothesis", that a clock's rate is unaffected by acceleration. Of course a real clock may be affected by acceleration, but the predictions of SR are not valid for such a clock.
If the twins refer to a common third clock (say, revolutions of the earth around the sun), then they will both note the same elapsed time for the travelling twin's trip. But, the traveller will have aged less, and the traveller's clock will have counted fewer oscillations than his earthbound twin's clock.
I think you must have misread my post. My point was that the traveler's clock is predicted to show a lower reading and the ship twin is predicted to age less for a common underlying reason: Less elapsed time passes.
edpell
#33
Dec26-09, 02:29 PM
P: 451
Quote Quote by ThomasT View Post
If the twins refer to a common third clock
What velocity does the third clock have with respect to the earth clock? What velocity with respect to the ship clock?
croghan27
#34
Dec26-09, 03:29 PM
P: 127
Somewhere between:

"Acceleration affects the periods of oscillators."
and
"What velocity does the third clock have with respect to the earth clock? What velocity with respect to the ship clock?"

I have become lost again. While velocity and acceleration are connected, they are not, in my philosophy, Horatio, the same thing. One involves achieving and is a change of velocity; while the other is a constant.

One must accelerate to achieve a certain velocity, or conversely decelerate, but the latter is the result of the former. What is the connection here and which results in the ageing or less ageing of the twins?

(At the risk of being a drag, there is another question in the background of this.)
Al68
#35
Dec26-09, 04:12 PM
P: 801
Quote Quote by croghan27 View Post
Somewhere between:

"Acceleration affects the periods of oscillators."
and
"What velocity does the third clock have with respect to the earth clock? What velocity with respect to the ship clock?"

I have become lost again. While velocity and acceleration are connected, they are not, in my philosophy, Horatio, the same thing. One involves achieving and is a change of velocity; while the other is a constant.

One must accelerate to achieve a certain velocity, or conversely decelerate, but the latter is the result of the former. What is the connection here and which results in the ageing or less ageing of the twins?

(At the risk of being a drag, there is another question in the background of this.)
The differential aging is the result of less elapsed time for the ship's twin, which is a function of velocity. Acceleration is relevant as the time derivative of velocity.
croghan27
#36
Dec26-09, 05:04 PM
P: 127
Quote Quote by Al68 View Post
The differential aging is the result of less elapsed time for the ship's twin, which is a function of velocity. Acceleration is relevant as the time derivative of velocity.
Thanks for that ... both terms seemed to be used interchangeably and I was being led astray.

The other question I have may be somewhat off the wall .... but as we sit on earth we are busy whurrling about in the motion that makes days, on top of that we are circulating about the sun, in the circuit that defines years. The sun is just one of the stars in a very mobile galaxy grandly twisting in 'space'. So we are moving in all direction at once when compared to just about any reference point.

What effect does all this motion have upon us relative to ...er....er.. relativity?


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