## Why does a travelling twin age slower but not get shorter?

Special relativity tells us that twins age differently if after birth they part, follow different paths through spacetime and then reunite. The twin who follows the longest worldline ages least. At least this is how I imagine the twin paradox, which I thought I understood.

Here's a silly question. Why doesn't a difference in say, height, develop between the twins as they travel? What aspect of the time dimension makes it so different from the space dimensions, even in relativity where dimensions are treated democratically? Is it just the mysterious fact that "time flies" while space dimensions don't?
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 Ya, after 20th century,thanks to great scientists,we know that time and space are just concepts of human beings . Before we thought that they were natural laws,especially time. since now we describe physical laws using (ct,x,y,z) coordinates. time,before it is a natural law, can now be "used" to describe the outside world natural laws. growth of human is a natural law. so BY the well-known kinematic equation: NATURAL LAW(I)=TIME(T)-SPACE(S) I is SS T is (ct )(ct) S is XX+YY+ZZ if I is the natural law,we see that when "speed"(X/ct) increases ,that means XX increases or T decreases or some of their combination , we should not change I. therefore our "sense" of space should be decreased and "sense" of time should be increased. but the natural law(growth of the twins) should be just like as usual and is still there~. PROVIDED that they have delicious food and toys to play and air-conditioning too. just as our daily life~ in fact it is not too bizarre when we use the time concept after 20th century developed but if we get stuck in the middle ,we may think "WHY NATURAL LAW changes?", always in mind and mind

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 Quote by oldman Why doesn't a difference in say, height, develop between the twins as they travel? What aspect of the time dimension makes it so different from the space dimensions, even in relativity where dimensions are treated democratically?
My take is that a difference in 'height' (in the direction of travel, i.e., twins are traveling head-first) does develop as far as observations from one frame to the other is concerned, just like a difference in clock rates are observed. Then, just as observed differences in clock rates vanish when the two twins are brought to the same frame again, observed height differences vanish.

However, elapsed time is an integration of clock rates and will differ if the twins took different spacetime paths.

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## Why does a travelling twin age slower but not get shorter?

 Quote by oldman Special relativity tells us that twins age differently if after birth they part, follow different paths through spacetime and then reunite. The twin who follows the longest worldline ages least. At least this is how I imagine the twin paradox, which I thought I understood. Here's a silly question. Why doesn't a difference in say, height, develop between the twins as they travel? What aspect of the time dimension makes it so different from the space dimensions, even in relativity where dimensions are treated democratically? Is it just the mysterious fact that "time flies" while space dimensions don't?
"Height" (length in the direction perpendicular to relative motion) is not affected by SR effects. During the whole trip both twins agree that they are the same height.

"Width" (length in direction parallel to relative motion) would be a different thing. During the trip, in A frame the width of B is shorter and vice versa. At the end of the trip, when they reunite, it is still so. This means, certainly, a difference. As to time, one twin is younger than the other, whilst as to length both twins keep holding that the other is thinner. This, in my opinion, is due to the way one measures: ages or clock readings can be compared in one single spacetime point, while length measurement requires two distant synchronised clocks. To measure the length of a moving object you need either (i) two observers with synched clocks who see the back and the front of the object at the same time (and then you infer that the distance between them is the length of the object) or (ii) one single observer who measures the time it takes for the two ends of the object to pass by (and then length = vt, but in order to measure v beforehand you also needed two synched clocks). So, since simultaneity is relative in SR = synch operations give different results in different frames, the twins are doomed to get different measurements as to their respective widths, whether they are together or not

 Quote by oldman Special relativity tells us that twins age differently if after birth they part, follow different paths through spacetime and then reunite. The twin who follows the longest worldline ages least. At least this is how I imagine the twin paradox, which I thought I understood. Here's a silly question. Why doesn't a difference in say, height, develop between the twins as they travel? What aspect of the time dimension makes it so different from the space dimensions, even in relativity where dimensions are treated democratically? Is it just the mysterious fact that "time flies" while space dimensions don't?
It does on the face of it seem a bit odd. I think the answer is roughly along these lines.

When the twins reunite and compare the proper time as shown on their clocks, they are reading the number of ticks, which effectively represents the result of the clock's integration of time during their respective journeys. If each carried some sort of device which measured their distance travelled during their journeys, say one click per meter, these results, representing an integration of their distances journeyed, would also be different. Their clock rates and measuring stick lengths are the same as each other when they reunite and so any length measurements made after reuniting are the same, as are any clock measurements made after reuniting.

Perhaps it is easier to think of the proper time as a count of the number seconds laid along their time intervals between parting and reuniting. In the same way the distance travelled can be thought of as a count of the number of meter sticks laid end to end along the path length. Both cumulative effects.

I think there is confusion here between the height of a twin and the cumulative distance travelled. One is the same after reuniting, the other is not.

I am not entirely happy with this so I too would like to see a definitive answer.

Matheinste.
 Recognitions: Science Advisor The ideal twins are points to illustrate proper time and the clock hypothesis. If they are not points, then you have to specify their rigidity, details of acceleration, etc which as we all know, are messy. In a baroque scenario where both twins accelerate, can you have one end of one twin age more than the other, and the other end age less?

 Quote by atyy The ideal twins are points to illustrate proper time and the clock hypothesis. If they are not points, then you have to specify their rigidity, details of acceleration, etc which as we all know, are messy. In a baroque scenario where both twins accelerate, can you have one end of one twin age more than the other, and the other end age less?
I thought it wouldn't be simple.

Matheinste.

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 Quote by matheinste I thought it wouldn't be simple. Matheinste.
Let's make each twin a bell spaceship string. One accelerates, and one doesn't. The one that snaps will be shorter?

 Quote by atyy Let's make each twin a bell spaceship string. One accelerates, and one doesn't. The one that snaps will be shorter?
I must have dozed off for a moment, For some reason I had a dream about a hornet's nest.

Matheinste.

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 Quote by matheinste I must have dozed off for a moment, For some reason I had a dream about a hornet's nest. Matheinste.

 Quote by oldman What aspect of the time dimension makes it so different from the space dimensions, even in relativity where dimensions are treated democratically? Is it just the mysterious fact that "time flies" while space dimensions don't?
I'm not sure what 'time and space are treated democratically' amounts to here. But somehow, because of it, you're expecting a symmetry?

I don't think distinctions between time and space do completely disappear in SR. There are time-like and space-like lines in SR - and these are distinguished by having a positive or negative Minkowski separation. Spatial and temporal coordinates make different contributions to the invariant 4-d Minkowski metric: in x^2 + y^2 + z^2 - c^2 t^2 (or, as some textbooks prefer, the negative of this) - the time coordinate has a different sign from the spatial ones.

If the separation between two events is + (or (-)) in one frame it will be + (or -) in all. Clocks are understood as moving along time-like lines whereas an extended body has a separation which is space-like in any frame. No amount of frame changing, or accelerating will take a clock on a time-like curve to one on a space-like curve.

This may not be enough to answer your feeling that, somehow, the distinction between time and space needs to be *explained*. However, such demands always for further explanation need to be treated with care - for every theory, explanations must eventually give out and we can only say this is how it is. And hopefully the above may be enough to see that there isn't a straightforward argument from Relativity's treatment of space and time, to the thought that there should be shape dilation analogous to time dilation.

 Quote by oldman What aspect of the time dimension makes it so different from the space dimensions, even in relativity where dimensions are treated democratically? Is it just the mysterious fact that "time flies" while space dimensions don't?
The "space" dimension in the direction of travel is shorter for the traveling twin, in the exact same proportion as the elapsed time.

Time elapsed is shorter, distance traveled is shorter. Sounds like they're more same than different to me.
 Age is 'accumulated' proper time. This is why the difference in age does not dissapear when twins meet again.

 Quote by Dmitry67 Age is 'accumulated' proper time. This is why the difference in age does not dissapear when twins meet again.
Exactly. If each twin had a clock and an "odometer", they would show both less time and distance for the traveling twin.
 Mentor IMO, this has more to do with the difference between "age" and "height" than the difference between time and space. When you ask for someone's height you are asking for their total spatial extent from head to foot. When you ask for age you are not asking for their total temporal extent in the birth to death direction, but just the extent between birth and "now". A comparable measure for space would be the vertical distance from "here" (e.g. my kitchen table top) to the top of a person's head. If one twin were standing bent over at the waist that measure would be different, not because the bent twin was "really" shorter but simply because the measurement itself captures a different piece of information. For time, the measurement comparable to height would be lifespan.

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 Quote by Saw "Height" (length in the direction perpendicular to relative motion) is not affected by SR effects. During the whole trip both twins agree that they are the same height.
So, if either person lays down (parallel to the direction of relative motion), they appear shorter to the other?

 Quote by DaleSpam IMO, this has more to do with the difference between "age" and "height" than the difference between time and space. When you ask for someone's height you are asking for their total spatial extent from head to foot. When you ask for age you are not asking for their total temporal extent in the birth to death direction, but just the extent between birth and "now". A comparable measure for space would be the vertical distance from "here" (e.g. my kitchen table top) to the top of a person's head. If one twin were standing bent over at the waist that measure would be different, not because the bent twin was "really" shorter but simply because the measurement itself captures a different piece of information. For time, the measurement comparable to height would be lifespan.
Along those lines, in someones own rest frame, while living, their age is increasing, while their meter stick remains the same length. However at the end of their life, neither is inceasing.

So in the case of the twins, let us assume that their non separated lifespans would have been equal. Then, after separating and reuniting they would have the same lifespan as measured by their own clocks at their respective deaths. But their actual deaths would not be simultaneous in their reunited rest frame inasmuch that the stay at home would die first.

So, same proper times at respective deaths and same meter stick lengths.

Does that seem reasonable.

Matheinste.

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