# SR's Length Contraction and Time Dilation

## Main Question or Discussion Point

If an observer rotates a four dimensional object, the lengths of the object would change to the observer. If that same observer walks backwards, the lengths of the object will also appear to change from his frame. In fact, if either the observer or the object rotates or moves in any way, it will also appear to the observer that the object's lengths have changed. This is very similar to the effects of special relativity in our world.

Here's the question, is length contraction, time dilation, etc, actually just consequences of a fourth spatial dimension?

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I don't follow your logic, but we can only detect 3 spatial dimensions in any case. If there are others they must be microscopic and/or cyclic or we would could move around in them.

However Euclidean relativity introduces a fifth dimension, and all four dimensional things in the 5-space move at c, while all us 3d beings suffer the laws of SR.

Yes, we can only detect three dimensions, the fourth is brought to us through contortions of our detected three, i.e. length contraction.

I wish you would read beyond the first two sentences I wrote. They are merely cautionary because there is no evidence for extra dimensions.

Euclidean relativity theory, does exactly what you want, boosts become rotations into an extra spatial dimension, thus creating length contraction in the normal 3-space slice.

So the answer to your question is - yes it is possible to make a theory where this happens.

DrGreg
Gold Member
The fourth dimension isn't space, it's time.

A change of speed is the 4D-equivalent of a rotation in 4D spacetime. Length contraction and time dilation can be viewed as consequences of the rotation.

A rotation in 2D Euclidean space through angle $\theta$ can be written as

$$x' = x \cos \theta - y \sin \theta = \Gamma (x \, - \, V \, y)$$
$$y' = y \cos \theta + x \sin \theta = \Gamma (y \, + \, V \, x)$$​

where $\Gamma = \cos \theta$ and $V = \tan \theta$. Compare this with the Lorentz transform

$$x' = \gamma ( x \, - \, (v/c) \, ct )$$
$$ct' = \gamma ( ct \, - \, (v/c) \, x )$$​

(I wouldn't get involved in "Euclidean relativity", as that is a somewhat contentious, non-mainstream topic.)