# Time Contraction

This is my first time posting on this site. I am a computer programmer that stumbled across a physics text book and have a question on special relativity. So firstly, I understand that there is no preferential inertial frame of reference. Secondly, as a A body travels faster relative to another body B at rest, body A experiences time dilation, effectively resulting in a forward jump in time. Thirdly, the speed at which a body in relative motion can travel is limited by the speed of light (c).

Due to the the first premise (that there is no preferential frame), could we not also argue that the body at rest is actually travelling at a negative velocity relative to the other body? Thus, if we consider the situation in from this reversed perspective, a time contraction is then experienced to the body moving at relative negative velocity. For instance, if we consider a person on Earth as being at rest (0 km/h), then could we think of a person standing on Pluto (which has an orbital velocity of 0.159 relative to Earch) as having a negative velocity relative to that of the person stationary on the surface of Earth, thus experiencing time contraction relative to the time experienced on Earth?

This can be confirmed by substituting a negative value in the standard time dilation equation for u^2. This results in a value greater than 1 occurring as the divisor, causing the numerator to 'shrink' in value, thus resulting in a 'time contraction' rather than time dilation.

With some searching, I have come across a number of examples of time dilation. However, all of them seem to assume that a body on rest is traveling at 0 km/h. Rather, I argue that such a body would be 'relatively' at rest, as from a greater perspective, this body is subject to the turning of the Earth about its axis, the movement of the Earth along its orbit around the Sun, the Sun around the Milky Way, and finally the Milky Way away from other galaxies due to the expansion of the universe.

If my above reasoning is correct, then it seems that if there was a body moving at 0 km/h relative to the expansion of the universe, then the Earth would be travelling faster than that body, which means that the Earth would experience time dilation relative to this body, and that body would experience time contraction relative to the Earth. If time dilation equates to a forward jump in time, then it stands to reason that time contraction would likewise equate to a backwards jump in time. Although, it occurs to me that perhaps it is more useful to not think of the body moving backwards in time, but rather to think of it as being stationary relative to the expansion of space-time, thus time is moving forward past the body experiencing time contraction.

I know I am not a physicist, but I was wondering if anyone could tell me if my above speculations are correct, or that I'm an idiot, or if all of this is already well documented somewhere (which I have yet to discover).

Any clarification would be greatly appreciated.

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You need to use -(v^2) instead of (-v)^2. The reason for this is that practically, you can't have time dilation occurring from both inertial frame perspectives, otherwise you would never have the twin paradox. – ralfe Nov 24 '12 at 22:37

## 1 Answer

Any clarification would be greatly appreciated.

So firstly, I understand that, firstly, there is no preferential inertial frame of reference. Secondly, as a body travels faster relative to another body at rest, the body in relative motion experiences time dilation, effectively resulting in a forward jump in time. Thirdly, the speed at which a body in relative motion can travel is at the speed of light (c).

It's true that there is no preferred inertial frame of reference (IRF). However, your second point is, at best, confused.

Since there is no preferred IRF, there isn't a body in relative motion. To have relative motion, you need at least two bodies.

Relative motion means that the distance between the two bodies changes with time. While body A can claim that it is body B that is moving, body B has an equally valid claim that it is body A that is moving.

Thus, when it comes to time dilation, you must understand that one body doesn't "experience" it while the other doesn't.

This is important: According to A, B's clocks run slow; according to B, A's clock run slow. Neither A or B "experience" time dilation. They simply observe that the other's clocks run at slower rate then their own. (They also note that the other's clocks are not synchronized but, while ultimately important, it's not needed now).

Likewise, according to A, B's rulers are contracted; according to B, A's rulers are contracted. Neither A or B "experience" length contraction. They simply observe that the other's rulers are shorter than theirs.

So, your speculations reveal a fundamental misunderstanding of Special Relativity. Time dilation and length contraction are perfectly symmetrical.

(As more a less an side and to your third point, no material object can be observed travelling at the speed of $c$. The speed can be arbitrarily close but it must be less than $c$.)

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Thank you for the clarification. As I said, I'm no physicist, I just came across this stuff the other day and had some thoughts. The text book I was looking at said that in the twin paradox the younger twin jumped forward in time. Would this not be relative to the older twin? If so, could you not state that the older twin jumped backwards in time relative to the younger twin? – ralfe Nov 25 '12 at 1:03
Properly understanding the twin "paradox" involves only recognizing that the stay at home twin never changes reference frames while the space travelling twin changes from an outgoing to an ingoing reference frame halfway through his journey.  The world lines of the two twins are then not congruent and thus, the lapse of proper time along the world lines are different.  See:  en.wikipedia.org/wiki/… – Alfred Centauri Nov 25 '12 at 1:16
Thank you once again. That does make a lot of sense. My next question is then what if the space travelling twin were to change reference frames to an inertial frame slower than than that of the stay at home twin? – ralfe Nov 25 '12 at 1:38
A slower frame of reference according to... what? – Alfred Centauri Nov 25 '12 at 1:50
So, if the surface of Earth where the stay-at-home twin lives is moving at a certain speed, then I am asking how would the time dilation equation be interpreted if the space travelling twin were to remain stationary in the space ship relative to the Sun, thus in a 'slower' frame of reference relative to the stay-at-home twin? The Earth would continue rotating and travelling around the Sun, thus travelling at a velocity greater than that of the spaceship. – ralfe Nov 25 '12 at 1:59
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