Relative Time Dilation Paradox

[ArthurDent]

I joined this forum because I have always had a problem understanding why a space traveller returning to earth will be younger than his twin brother. I get ( I hope) the reasoning behind time dilation generally but didn't know why it wasn't equally valid for the earthbound twin to be younger than the traveller since his speed relative to his brother is the same as his brother's to him. Thanks to a link supplied by Buffy on an earlier thread I now at least see that the traveller's experience is different from the "stationary" twin due to the accelerations undergone and that he passes through more than one inertial frame of reference so the scenario is not symmetrical. However, I still can't really grasp what is happening in physical terms; if any of you bright sparks can explain it simply for me or have an appropriate analogy it might stop my brain aching.

Also, am I correct in saying that if two clocks at the same point, A, in space flew in opposite directions, travelled the same distance and arrived back at A at the same time they would still be in synch' (both behind a third clock that remained at A) but if one travelled further or arrived back earlier it would be behind the other?

[Tormod]

This has been discussed several times now...maybe we need a Total Perspective Vortex function...

[ArthurDent]

That's a "no" then. I have spent all morning searching threads for a satisfactory explanation (honest!) and am very chuffed to find I wasn't the only one to think of this as a paradox and that it does have a genuine resolution. Perhaps, if you don't mind, you could point me in the direction of previous threads where this has been discussed.

 

As for a total perspective vortex...I have a wife that does a very similar job!

 

regards

A Dent

[Tormod]

Did you search for "time dilation"?

[geistkiesel]

That's a "no" then. I have spent all morning searching threads for a satisfactory explanation (honest!) and am very chuffed to find I wasn't the only one to think of this as a paradox and that it does have a genuine resolution. Perhaps, if you don't mind, you could point me in the direction of previous threads where this has been discussed.

 

As for a total perspective vortex...I have a wife that does a very similar job!

 

regards

A Dent

There is a serious problem with time dilationt hat is related to the twin paradox. It has been said many times that two observers moving relative to each other sees the other's clock moving slower than his own. This has been described as completely reasonable and not a contradiction in terms of contradiction in SRT.

 

The problem comes when one would like to prove the statement as having some realistic physical truth attached. It is to me as well as the rest of the world (including SRTists) that two measurements cannnot ever be smaller in value wrt the other. If the observers are moving away from each other at .433c each, the measured relative velocity would be .866c and therefore it becomes a bit sticky to consider the other's clock rate as slower than his own. The only explanation for this lack of physical reciprocity is that each observer can mentally consider anythng they choose to consider. In the twin paradox the resolution that you briefly offered is, as far as I am able to determine, the prevailing answer and solution to the paradox. However, this brings up another question of the equivalence of inertial frames. Are the two frames you described equivalent if only on one of them will time dilation occur wrt the other?

 

Consider the planet earth. The earth is never seen to accelerate such that earth motion is counted as intrinsic velocity measured in relatrive velocity of embankment and earth borne object. Of course earthquakes and nuclear explosions are treated differently, but in general the statement holds true. Trains then are always the object accelerated and it is the acomopanying train velocity that accounts for

all

the train/embankment relative velocity.

 

Now we are told that when only one of the inertial frames has undergone acceleration that the resultant is asymmetric inertial frames i.e. the frames are not inertially equivalent. Taking this line of argument to its natural conclusion, unless the acceleration history of inertial frames moving relative to each other are exactly alike, identical, the inertial frames are not equivalent for the purposes of SRT

 

Geistkiesel

[GreekTTC]

Not to veer too far off course, but what would one experience looking out the windsheild of a vehicle travelling at the speed of light? Theoretically?

[Qfwfq]

to find I wasn't the only one to think of this as a paradox

In fact, it has always been called the "Twin Paradox". Maybe you could search the net for that. Actually, unless you learn the calculus of relativity in detail, you can't say much more than the fact that the traveller doesn't stick to one inertial frame.

[Erasmus00]

If the observers are moving away from each other at .433c each, the measured relative velocity would be .866c and therefore it becomes a bit sticky to consider the other's clock rate as slower than his own.

 

Thats not quite true. You need to use the relativistic addition of velocities, you can't simply add them.

-Will

[UncleAl]

Special Relativity is a self-consistent geometry. It contains no paradoxes. Acceleration is irrelevant. The clock that passes through the most space is seen to have accumulated the least time. ds^2 is a constant. Simple as that. The universe is not Euclidean, Galilean, or Newtonian. Get over your prejudices.

 

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

The triplet Gedankenexperiment:

Google Groups Message-ID: <[email protected]>

[bumab]

Yup- Al's right. Sorry.

[geistkiesel]

Thats not quite true. You need to use the relativistic addition of velocities, you can't simply add them.

-Will

Erasamus00,You are correct in the context of SRT. I was making the point that the two travelers were moving at the same absolute speed and therefore, neither could physically have their clocks running slower than the the other.

Geistkiesel

[Erasmus00]

Erasamus00,You are correct in the context of SRT. I was making the point that the two travelers were moving at the same absolute speed and therefore, neither could physically have their clocks running slower than the the other.

Geistkiesel

 

There is no such thing as absolute speed! All motion is relative. The thing with SR is that time measurements don't have to agree. So observer A sees observer B's clock running slow,and B sees A's clock running slow.

-Will

[geistkiesel]

There is no such thing as absolute speed! All motion is relative. The thing with SR is that time measurements don't have to agree. So observer A sees observer B's clock running slow,and B sees A's clock running slow.

-Will

In the context of SRT you are correct, but within that context they both cannot be physically correct. The observer on A can assume his frame is at rest wrt the B frame and vice versus. Like you said the clocks don't have to agree unless they are infact moving at the same "absolute" veocity (meaning as measured). Assume A and B frames both accelerated from the earth's surface and both were moving uniformly .4c as measured wrt earth. Neither observer on the two frames need have any information regarding these velocity measurements.

 

When the two observers detect the relative motion, I'll use the crude .8c number (corrected by SRT measurement requirements if necessary) each observers clocks will be the same, exactly the same. It seems to me in this situation where one observer assumes the other at rest wrt his relative motion of .8c that any calulations must be approximate (in error) as both clocks will definitely have the same tick rate will they not? Roughly speaking wouldn't it be more accurate for the observers to take an average of the realtive velocity instead of assume one or the other is moving and the other at rest? In generla the re will always be intrinsic velocity of both reference frames so it seems to me more accurate to use the average relative ve;ocity instead of the extreme at rest and total relative velocity distributed between the two ships .

 

I have no problem of understanding and even accepting that within the context of SRT each observer may "see" the other;s clock as ticking at a dofferent rate, but this "seeing" cannot possibly be a mutual observation provable by an instantaneous measurment as when the two ships pass each other in opposite directions each moving .4c wrt the earth.

 

In this sense the theoretical justification of the observers "seeing" the other's clock rate different than his own has no physical reality attached, but as confined within SRT the "seeing" of both observers is justified.

Geistkiesel

[Erasmus00]

In this sense the theoretical justification of the observers "seeing" the other's clock rate different than his own has no physical reality attached, but as confined within SRT the "seeing" of both observers is justified.

 

What you fail to understand is that time is a relative quantity, not an absolute quantity. You say it has no physical reality, but I disagree. Just because its not absolute doesn't mean it isn't physical.

-Will

[adnaan]

Lets say one of two twins goes to Mars and back at the speed of light. The one who went to Mars at the speed of light will be younger than the other one who choose to stay on Earth.

 

My question is why is that? I dont understand why this happens, I would appreciate some sources or just explained help.

[geistkiesel]

What you fail to understand is that time is a relative quantity, not an absolute quantity. You say it has no physical reality, but I disagree. Just because its not absolute doesn't mean it isn't physical.

-Will

Will,

To break this down two ships accelerating from earth in opposite directions with identical measured velocity wrt the earth and with synchrionized clocks make wide gentle turns in space until they are moving uniformly toward each other. As seen from the earth the ships have identical motion and time histories. At one hour before the noses of the ships pass they each automatically begin emitting a series of pulses that are one second apart as measured from their own frame of reference. The instant the noses pass each other each ship emits the indicated accumulated time on their respective clocks. I say that whatever the observers consider as "seeing" the other's tick rate wrt their own, the measured accumulated time and tick rates will be measured the same on each ship.

 

For the tick rate lets assume each ship receives the other ships series of tick rates and compares those rates with their own tick rate as they are received from the other.

 

I say the accumulated time and tick rate as

measured

from the earth frame will show the ships emitting identical tick rates and accumulated time when passing nose to nose, though the tick rates and accumulated time measured from the earth may be different than measured from the respective ships.

 

I also see the observers on each ship as

measuring

the same tick rate of the other and the same accumulated time on their clocks. I say this as the time and motion history of each is identical (though the mutual histories is unknown to observers on board the respective ships.).

 

Should the observers be surprised later when learning that the measurments of each are identical? Why?

Geistkiesel

[Erasmus00]

Will,

To break this down two ships accelerating from earth in opposite directions with identical measured velocity wrt the earth and with synchrionized clocks make wide gentle turns in space until they are moving uniformly toward each other. As seen from the earth the ships have identical motion and time histories. At one hour before the noses of the ships pass they each automatically begin emitting a series of pulses that are one second apart as measured from their own frame of reference. The instant the noses pass each other each ship emits the indicated accumulated time on their respective clocks. I say that whatever the observers consider as "seeing" the other's tick rate wrt their own, the measured accumulated time and tick rates will be measured the same on each ship.

 

In your example, both ships broadcast their accumulated proper time. The proper time of each ship is, in fact, an invariant. As such, your statement is true. All observers should note the proper time elapsed in the two symmetrical ships is identical. This doesn't make time dilation any less physical, and doesn't pose a problem with time dilation.

-Will