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Twins paradox and ageing 
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#19
Dec2109, 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. 


#20
Dec2109, 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).



#21
Dec2109, 11:24 PM

P: 15,319




#22
Dec2209, 12:06 AM

P: 3,967




#23
Dec2209, 01:23 AM

P: 801

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. 


#24
Dec2209, 02:06 AM

P: 801

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. 


#25
Dec2409, 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". 


#26
Dec2409, 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????



#27
Dec2409, 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....



#28
Dec2509, 09:49 AM

P: 127




#29
Dec2609, 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. 


#30
Dec2609, 02:09 PM

P: 1,414




#31
Dec2609, 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.



#32
Dec2609, 02:27 PM

P: 801




#33
Dec2609, 02:29 PM

P: 451




#34
Dec2609, 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.) 


#35
Dec2609, 04:12 PM

P: 801




#36
Dec2609, 05:04 PM

P: 127

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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