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On Earth there is both Newtonian (non-relativistic) and relativistic kinematics, for reasons of history and practicality. For example

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versus

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On the neutron star world Dragon's Egg in the book of the same name by Robert L. Forward had something like non-relativistic kinematics ever been conceived or developed, or was everyday life so relativistic that the first theories of kinematics would have required a full relativistic treatment to be at all useful?



Kinematics:

As a refresher, kinematics is the study of how every day objects move, the stuff we study in school. Balls rolling up and down inclines, bouncing off of each other, etc. From The Physics Classroom:

enter image description here

enter image description here

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Since the cheela would not encounter relativistic velocities in their daily lives, they would use the obvious and intuitive Galilean transformation in the course of normal existence, just as we do. They probably would have to reach 3% of the speed of light before the size of the Lorentz contraction exceeds the error bars of normal experimental results. Much higher speeds would be required to produce effects that can be perceived by the normal senses. The rotation of Dragon's Egg only produces a tangential velocity of about 1% of light speed and that's relative to a fixed observer, not someone on Egg itself.

The development of physics on Egg would have been significantly altered by human interference. By receiving the ship's encyclopedia the cheela were handed many hard-won facts about the physical universe that are non-obvious, including the finite speed of light, which itself makes non-Galilean transformations necessary for accurate predictions at high relative velocities. So it is hard to predict how long they would have held on to the Newtonian view.

  • Update: It seems I had been drinking insufficiently strong coffee when I first read your answer, and completely missed your points in the second paragraph. I read the book when it first came out and so have forgotten just how early in their history the cheela encountered knowledge from the humans. What a great book - time to read it again! Hopefully in the future I will be able to detect insufficiently strong coffee. – uhoh Mar 19 '17 at 7:44
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I would like to add a little. It's some time since I read the book so I need to skip references.

@kyle-jones clearly answers for special relativity. It's effects would hardly be observable.
But there is also general relativity - which in short is all about non-flat space-time. Given the incredible gravitation on dragon's egg the effects of space-time distortion should have been notable to the cheela. Especially they should be able to see the light "bends" around the egg, and also that time flows differently in valleys and on mountain peaks. (I don't recall how high the highest mountain was, but I believe there was an chapter about this).

btw. I have never seen the equations you post as refresher outside a textbook. Professionals typically use canonical coordinates. They have the nice properties that equation of motions are the same in relativistic and non-relativistic case:

dx/dt = p/m
dp/dt = F

p and m just need to be replaced by relativistic or non-relativistic variants. And think vectors for x, p and F.

On another side not the equations of motion were mostly derived by study of planetary motion. So from that side the cheelas should come to similar equations as us.

update

I got also interested again. Seems my memory was wrong about the time dilation, probably mixed it up with some Interstellar alike. They did some calculations on the wikipedia talk page of the book.

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    Interesting. Greg Egan's novel Incandescence is built upon the idea that a pre-industrial civilization in the right environment could jump straight to GR, that environment being a planetesimal in the accretion disk of a collapsed star. I pondered this while thinking about Dragon's Egg but couldn't disentangle the cheela's development from the introduction of the encyclopedia. There's also Egg's trillion gauss magnetic field to contend with, which the cheela were unaware was distorting both their bodies and their instruments. – Kyle Jones Mar 27 '17 at 20:55
  • @KyleJones and bdecaf; now I really really want to read it again! I added the equations because there is a wide variety of people passionate about science fiction, and those who encounter relativity mostly from scifi will normally hear about space travel and time contraction. For them, I wanted to just mention that relativity might happen in a simple bench top kinematics experiment. Anyone not recognizing those equations must have either skipped grade school, or have forgotten about it completely. In my case I had that in 7th, but calculus didn't come until 9th, all quite long ago. – uhoh Mar 28 '17 at 0:55

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