# Length contraction and time dilation

• I
• rasp
In summary, the conversation discusses different approaches to understanding special relativity, particularly the concepts of time dilation, length contraction, and the relativity of simultaneity. One approach involves using the Pythagorean theorem to demonstrate the effects of motion on the speed of light, while another involves drawing and interpreting space-time diagrams. The conversation also mentions the importance of understanding the relativity of simultaneity in order to fully grasp special relativity.
Jim Fern said:
I guess the crux of it is this: according to the scientific method, if something can't be observed, then how can it be tested? (I do hope that yet another rule that I may not have noticed or yet committed to memory arises here.)
I think you may need to start to think of SR differently. In the 19th century, mathematicians discovered many different geometries, not just Euclidian Geometry, all equally as logically consistent. What applies to our world is an experimental matter. As they delved further into the issue, something called the 'Erlangen Program' emerged:
https://en.wikipedia.org/wiki/Erlangen_program

Now group theory is the mathematical language of symmetry. So scientists can look at geometries as what results if we have certain symmetries. A fundamental concept, not often emphasised in the physics literature (Landau - Mechanics is a notable exception), is a precise definition, in terms of symmetry, of what an inertial frame is. The definition is as far as the laws of physics is concerned; all points, directions and instants of time are equivalent. Note an inertial frame is a conceptualisation - they do not exist in nature. But do exist to very high accuracy in interstellar space. For many practical purposes, the Earth can be considered an inertial frame even though it is easily demonstrated it isn't. But it is useful for theoretical work. A law of physics (well, a meta law, to be precise), called The Principle of Relativity, states the laws of nature are the same in any inertial reference frame or frame moving as constant velocity to an inertial frame. This is a symmetry condition, and our knowledge of math should allow us to work out the geometry of an inertial frame.: http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf.

This determines the geometry up to a constant c. Both theoretical considerations and direct experiment show c is the speed of light. These are the Lorentz transformations. It predicts length contraction, time dilation and all the other strange stuff. It depends on the POR, of course, which has been tested in many experiments - in fact, it is really is Newton's first law in disguise - but that is another story. It is about as rock-solid as any theory in physics can be.

Thanks
Bill

vanhees71 and PeroK
Thank you all for this information and answering my questions, regardless of how idiotic some of them seemed, to be sure. You've certainly given me a great deal of things to look into. :)

vanhees71 and PeroK

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