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Same is true with your measurements in a 4D universe. You must incorporate the fourth dimension in your math or you are using Newtonian 3-dimensional math which is wrong.

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They are observing the simple orbiting of a planet and star and the physics working at these masses and velocities should work exactly the same for both observers. If Newtonian Physics will give a close approximation of orbits at the extremely slow speeds (relative to C) of the planets orbital velocities it should do so in either frame of reference. Is that not correct? If not, one of the observers is in a special state and special states cannot exist. The only difference between the two observers is the method of measurement between the planet and star.

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Same is true with your measurements in a 4D universe. You must incorporate the fourth dimension in your math or you are using Newtonian 3-dimensional math which is wrong.

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If the fourth dimension is time then how is it excluded in Newtonian mechanics? g=9.8m/s^2 cannot be expressed without reference to time. Perhaps time is what connects the Newtonian world with the view of Einstein?

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The original question was based on measurements of length being taken while one frame was at relativistic speed with respect to another.

As you fly by the system in your spacecraft you are holding your ruler against the window and measuring distances.

Just plugging in your reading off the ruler for the X, Y and Z planes will give you a 3D length. Plugging all the distances measured this way will result in answers that appear to not be possible.

In order to get the actual length (sun/earth orbital distance for example) you need to include a forth Cartesian point that includes time.

Nasic geometry: To measure the length of any line you use Pythagoras theorem where A squared plus B squared plus C squared equals the length squared of any 3D line.

In a 4D world you need to account for space/time dilation/ contraction to get the correct length of any measurement.


That extra Cartesian point reflects (time x c) squared and reduces to a length. It is the forth dimensional measurement necessary to give you the correct length.

People here are saying you need relativistic calculations and not Newtonian, I just gave an example of the simple geometric math that does this calculation for a given line measurement in the system.

Pesse (Basic high school geometry) Mist

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I just gave an example of the simple geometric math that does this calculation for a given line measurement in the system.

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There is another big difference between the two observers: one is at rest relative to the system being observed, and the other is moving at relativistic velocity.

If both observers attempt to use Newtonian physics, this difference is precisely what is being ignored by the equations. Special relativity takes this difference into account. In the case of the at-rest observer, Newtonian physics gives an excellent solution, but in the case of the relativistic observer, the Newtonian solution is ignoring a very significant factor.

There is no "special state" because the special-relativistic equations give the correct answer in both cases. But "no special state" doesn't mean that all conditions are absolutely identical -- it just means that the *physics* is identical despite certain well-defined differences between the states.

What it *doesn't* mean is that every possible approximation that ignores certain possibly-critical aspects of the situation must yield equally valid results.

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I think it's finally becoming clear and corresponds with intuitive logic.

In the scenario above, observer "A" has taken off from Earth and moves out in space. The ship reverses and accelerates to .8C passing Earth and then the Sun. He has a yardstick held up to his window (tks. Pess) and measures the distance of the passing. It is much less than the distance an "at rest relative to the system being observed" observer calculates.

Orbits are calculated on orbital body mass, velocity, distance and the gravitational factor etc. This is the "at rest" condition or (correct me if wrong here) what could be called the "real" or "baseline" state of this system once motion relative to the observed system ceases. No observer's observations will alter the steady state at rest values for the orbital parameters. The bodies mass will be the same, the distance between them (at rest) will be the same, the velocities around barycenter will be the same only the observer in motion's observations will "appear" different. To explain the questioned orbital anomaly of the reduced distance between the bodies calculations must be done with relativistic correction factors. In essence, adjusting the observations to "at rest" values.

Observer "A" can leave Earth do the flyby of the Earth and Sun in 10 minutes (8mins/.8C) and record the distance measured relative to his speed of transit. He then returns to Earth and shows observer "B" his results. They won't match until relativistic correction factors are calculated in. Observer "A" then finds his measured distance only applies while he is in motion, he didn't age as much, the distance stayed the same in steady state, and his ears got torn off from the turn, rapid acceleration and deceleration.

Is this over-simplification about right?

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Jerry
LX200ACF 14", Tak FS 152 & TOA 150
AP-1200 & Mach1

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