Good question. Although this statement does not replace the postulate of the special theory of relativity:

1. The existing quasistationary motion obviously has the nesting of cyclic orbits, respectively, there is no complete equivalence of states of observers tied to arbitrary cycles. They are not invariant.

2. By virtue of 1 (and the fact that the attractor of the entire open dynamical system is divergent, this requires a separate discussion) at every point, that is, for an arbitrary cyclical orbit, there is an uncompensated components (of gravity and not only).

3. By virtue of 2 the positions of any observer in reality do not correspond to the definition of an inertial frame of reference, which is an abstract concept that makes sense only in a truly equilibrium (symmetrical) case (which also applies only to abstract ideal situation, in which, at least, there is no gravity).

It should be noted that in a sufficiently correct theory (which tends to the ToE), indeed, infinite-stable (or asyptotically-stable) cyclical orbits (not only regards to gravity) should not be obtained (possible only in models that take into account no more than locally-equilibrium region or, in other words, a quasi-equilibrium one), this concerns open dynamical systems and Gödel's theorem.

Not all gravitational objects are in stable orbits. I guess you intend to exclude the obviously unstable orbits and apply your question to those that appear to be long time stable. Not all stabilities are equal or long lasting. In study of exo planets the simulations are done for millions or billions of years.

All stable gravitational objects are not stationary, since it is the motion that counter acts gravity to create stability. Dark energy might be applied to this question, but I don't find a need for dark energy to account for gravitational objects in stable orbits.

If you are intending to remedy some deficiency in Newton or Einstein, then it needs a better definition. Hafele and Keating experiments agree with Einstein relativity SR and GR. Arguments against are published, but not well received.

https://www.researchgate.net/post/Is_the_Hafele-keating_experiment_credible

@ Vasily

All good points. But an acerbic critique is necessary.

I would like  to know what major objections you have.

I agree with Jerry Decker

@Jerry 

Stable orbits mean just that-  binary pulsars orbiting each other, or black holes doing the same - not stable -huge gravitational waves.

Hafele and Keating - defy Einstein's reciprocity. Rule No 1 does not work. All observers are far from equal

Challenge the obvious

@ Saeed

Well acerbic- not quite 

@Vasily

The corollary to your 3rd comment is there are no non inertial systems

If I could describe inertial systems, this thread would definitely count.

Where's Stam and Kare, when you need an in depth critique

Objects on their Motion do not describe an Orbit: it is no closed curve while they fly arround and the centre itself moves (for instance a black hole moves with the whole galaxy)

AW: Can we treat this as a new postulate, instead of all observers are equal in STR,

The special theory is not applicable in the presence of gravity (other than locally) so it is entirely irrelevant.

The Schwarzschild solution for a single object is stationary but the field of any binary system (such as a planet orbiting a star) is certainly not, all binary systems radiate orbital energy as gravitational waves so cannot be stable.

@ George

Ah thankyou, good point

Putting the question another way, there are no inertial systems in the Universe by definition as gravity is everywhere.. So the inertial system concept becomes irrelevant.

I like you single entity concept- but again there are no single entities in the universe.

So we have to rid ourselves of the inertial concept.

That leaves us with the non inertial frame. You might well say there are approximate inertial frames, but that is unsatisfactory.

Having said that planets, like the Earth can be stationary relative to Dark energy -new postulate 1.

This explains why we appear completely stationary, when stationary with regards the Earth's surface. With regards the Moon's surface, the very fine dust there does not move even though it is in a non-inertial frame going at 2,288 mph. Further, Hafele and Keating's experiments prove the point.

"So we have to rid ourselves of the inertial concept." 

I agree. I think the concept of inertia is grossly misunderstood by the physics community. At its very core, inertia can be simply defined as resistance to change. Loss of inertia is change. So, yes, if our frame of reference is continuously changing, then it cannot be considered an inertial frame. Inertial frames cannot experience change. 

Here's some links I found last time I was researching this question.

https://en.wikipedia.org/wiki/GPS_signals#Almanac

My impression from this was that the individual satellites reset and rescynchronize their times according to UTC on a regular basis, and have an additional technique that speeds up and slows down their clock, depending on where they are in orbit

I never was quite sure, though.

http://www.cv.nrao.edu/~rfisher/Ephemerides/times.html

Coordinated Universal Time (UTC) is the time broadcast by WWV and other services. By definition, UTC and TAI have the same rate, but UTC stays close to Mean Solar Time by adding integer numbers of seconds, called leap seconds, from time to time. This keeps solar noon at the same UTC (averaged over the year), even though the rotation of the earth is slowing down. The offset is changed as needed to keep UTC within about 0.9 seconds of earth rotation time, UT1. Leap seconds are typically added once per year at the end of December or June, but they can be added (or subtracted) at other designated times throughout the year. The offset between TAI and UTC is currently 30 seconds, e.g., 20:00:00 UTC = 20:00:30 TAI.

UTC = TAI - (number of leap seconds)

Before UTC, the time broadcast by WWV and other services was a close approximation to Greewich Mean Time (GMT) [ref 2]. GMT is an earth rotation time and is now called UT1 or simply UT.

http://www.stjarnhimlen.se/comp/time.html

UT = Universal time. Defined by the Earth's rotation, formerly determined by astronomical observations but today GPS satellites are used instead. This time scale is slightly irregular. There are several different definitions of UT, but the difference between them is always less than about 0.03 s.

http://tycho.usno.navy.mil/systime.html

Universal Time (UT) is counted from 0 hours at midnight, with unit of duration the mean solar day, defined to be as uniform as possible despite variations in the rotation of the Earth.

AW:  After all we do not alter Earth's clock we alter the satellite clock, there is no reciprocity

Okay, the fact that we can alter the satellite clocks SO THAT their signals are synchronized when they reach the UTC.. (Somewhere in Greenwich, I guess?).  Does that support the existence of a Universal reference frame?  I don't think so.  But opinions may differ.

AW: Putting the question another way, there are no inertial systems in the Universe by definition as gravity is everywhere

Inertial motion is defined as that which occurs when there is no force applied to an object. Gravity is not considered to be a force in that definition so free-fall motion in a gravitational field is considered inertial. For a satellite for example, it would be the orbit excluding effects of atmospheric drag and Solar radiation pressure.

@George

Thank you for that, interesting  that gravity is not considered to be a force - so are you saying that Earth's rotation on its axis and  motion around the Sun is inertial. And is that standard mainstream because some would disagree.

Hi Lori,

Quite right, even a free falling object is subject to a coriolis force, i.e it does not fall in a straight line because the Earth is rotating, as every gravitational object is in some form of rotation I would be careful of the concept of inertial motion. 

Andrew, the orbital path round the Sun is considered to be inertial motion other than the pressures I mentioned but rotation is not, a rotating frame is not inertial but you can describe a rotating object in an inertial frame. The surface of the Earth is supported against gravity by electrostatic forces in the material so is not inertial but for most experiments it is a good approximation.

@ George,

I am agreeing with you on the one hand the surface of the Earth is non inertial.

But neither is anything else in the Universe; the Earth rotates on its axis and around the sun. The sun rotates in the galaxy, the galaxy as a whole rotates and we have galaxy clusters which rotate and collide and then we have the possible axis of evil where the whole Universe rotates.

Where are the other cogniscenti on this thread?

@Andrew, You`re right! I think Gods were/are drunk while everything rotates

Andrew, be careful not to confuse an inertial object with an inertial frame.

@ George,

Just answer this  question. Why are the clocks on the Equator going at the same rate as those on the North pole. There is clearly a velocity difference at the equator, and the clocks should slow there.

If you try to pile up a mound of water, you will fail of course, the water flows until the surface is "level", but what does "level" mean for the surface on a planet. If you try to pile up water on a non-rotating planet, it will flow until the surface is equidistant from the centre. The sea finds a level where surface is everywhere at the same gravitational potential. Because the planet rotates, there is "centrifugal force" which alters the potential near the equator be leaves it unaffected at the poles. The effect of potential still causes water to flow so "mean sea level" remains a surface of uniform potential, also known as the geoid. The SR effect of the speed at the equator therefore contributes to the radius of the geoid and consequently mean sea level is a surface of uniform clock rate. The slowing of clocks due to speed is equal and opposite to the increase due to the fact that they are farther from the centre of the Earth, remember the Pound-Rebka experiment.

'George

Good answer,

But with SR if an object lets say, an electron, is going at 0.9999999999c relative to Earth then we view its clock as slowed as do (almost) all other observers. Reciprocity means that it, the electron. sees our clock as being slowed. But that is illogical because (almost) all other observers do not.

Moreover for this amount of slowing to be "true slowing" we would need to be going at the ridiculously high speed of 0.9999999999999c - and that is simply not possible.

Relativity and reciprocity is a conjuring trick

AW: Reciprocity means that it, the electron. sees our clock as being slowed. But that is illogical because (almost) all other observers do not.

The electron sees all clocks of observers that (almost) share our state of motion as slowed by (almost) the same amount.

If you think of all the electrons in a CRT beam, they all see all of our clocks slowed but the clocks of the other electrons are not.

Lay two rulers on your desk with a 40 degree angle between them. Then project the cm marks on one ruler by lines perpendicular to it until they meet the other ruler, they will hit it more with than cm spacing. Repeat that exercise starting from the second ruler and projecting perpendicular to it and you find the same thing when those lines reach the first ruler. It is simple geometry and of course it has to be symmetrical.

I don't think that could be described as anything like a "conjuring trick".

@ George

We are not just talking measuring we are talking "real" time differences. For instance muon decay is slowed. We don't know what the muon sees, but I doubt whether it sees us ageing slower.

The satellite clock has to be slowed on Earth before it is launched into orbit relative to the Earth's- not visa versa. GPS is a billion times a day test -and it disproves reciprocity..

STR is a conjuring trick as are you rulers. Special relativity needs to be redifined

P.S.

By the way, you seem to have skillfully avoided the second part of the question. How  realistically can Earth and its observers be going at 0.9999999999c? It is  impossible.

AW: The satellite clock has to be slowed on Earth before it is launched into orbit relative to the Earth's- not visa versa. GPS is a billion times a day test -and it disproves reciprocity.

Have you ever watched an Earth clock from a satellite? The symmetry has been confirmed to better than one part in 1018 recently (see the link), that's good enough for me.

AW: By the way, you seem to have skillfully avoided the second part of the question. How realistically can Earth and its observers be going at 0.9999999999c?

I tend to ignore silly questions but since you insist, it is trivial, just measure your position using a ruler that is moving past you at 0.9999999999c.

http://www.nature.com/articles/ncomms9174

Its not a trivial question.

We are not talking about solely measurements here we are talking real effects.

I can accept that the mass of the electron has actually gone up by a millionfold or so.

I cannot accpet that the mass of the Earth has actually gone up by a millionfold or so- otherwise it would in reality be heavier than the Sun.

I have studied psychology and it's amazing what peer pressure  and mass delusion can do to an apparently logical and intelligent person, There are experiments which show it time and time again.

AW: We are not talking about solely measurements here we are talking real effects.

In science, all real effects are known to us through measurement so there is no difference.

AW: I can accept that the mass of the electron has actually gone up by a millionfold or so.

I can't, and mass in SR is an invariant. Don't be confused by the archaic concept of "relativistic mass" which was a crutch for people brought up on Newtonian mechanics to migrate to the relativistic versions. Variable mass is only a real effect in aether theory.

By the way I  looked at you paper- The methods had nothing to do with satellites, it was a terrestrial experiment.

This is another classical sign of someone trying to bolster an untenable argument.

And by the way rest mass in STR is invariant, but relativistic mass which is measured as real is not - another conjurer's trick to get round this illogicality.

This is begiining to look like a classical psychological experiment. One memorable one, most people who were experimented on, were prepared to adminster supra-lethal shocks to people.knowing that it may kill, because of the presence of only a single instructor. What do you think they would do in the presence of many such instructors.

AW: By the way I  looked at you paper- The methods had nothing to do with satellites, it was a terrestrial experiment.

Correct but it confirms Lorentz Invariance which then applies to everything.

AW: And by the way rest mass in STR is invariant, but relativistic mass which is measured as real is not

As I said, that is an archaic concept, "relativistic mass" is actually the sum of the mass which doesn't change plus what you learned as "kinetic energy" in school and that does depend on speed.

AW: This is begiining to look like a classical psychological experiment.

Physics is always moving on and what you learned many years ago may have been superseded. Mass in SR is defined as the magnitude of the energy-momentum 4-vector which is a Lorentz invariant. Your responses are the equivalent of trying to prove that a nuclear reactor wont work using Phlogiston theory.

I am intruiged.

It does not confirm lorentz invariance on a satellite - this is wrong - not proper science,  Do the test first and then see what it shows not assume you know the results from what you expect to be the right answer. What about the space station that does not show lorentz invariance they see our clock as going faster! QED

I don' t know of any scientific theory which has not been superceded STR is over 100 years old- so why stick to it without question, and even confabulate the results to support you ideas................ 

AW: I am intruiged.

I'm not saying anything new, it's all been known for a century, only the evidence is from modern technology.

AW: It does not confirm lorentz invariance on a satellite - this is wrong - not proper science,

It confirms that nature is Lorentz Invariant to the limit of our ability to measure it, that is good science.

AW: Do the test first and then see what it shows not assume you know the results from what you expect to be the right answer. What about the space station that does not show lorentz invariance they see our clock as going faster!

The ISS doesn't have easily comparable clocks but GPS does. Comparing a GPS clock to one on the ground it goes 45us per day faster due to its higher altitude and 7us per day slower due to its speed, total 38us per day faster.

If you could be on the satellite and monitor a ground clock on the equator, it would be 45us per day slower because it is at the lower gravitational potential and 0.1 us per day slower due to the speed of the Earth's surface (465m/s).

AW: I don' t know of any scientific theory which has not been superceded STR is over 100 years old- so why stick to it without question, and even confabulate the results to support you ideas................ 

Because the results exactly match the theory. Many people are looking for a deviation because many of the newer string theories predict it and you can guarantee a Nobel prize for anyone who can find a repeatable discrepancy but to date, even at one part in 1018, the theory has always turned out to be exact. Any deviation must be even smaller.

There you go again, if you could be on the satellite  and look down at the Earth's clock - not science- do the tests. The ISS clocks have to be slowed to keep time with Earth's clock.

What does that tell you - Earth's clock is going faster

AW: The ISS clocks have to be slowed to keep time with Earth's clock. What does that tell you - Earth's clock is going faster.

No, if the ISS clocks have to be slowed, they would otherwise be ticking faster. Many experiments have been done and all confirm both GR and SR, that's why it is still accepted.

Why accept dogma, when it does not make sense 

We need to conduct an experiment to prove this.

Meaning a giant clock face needs to be erected on Earth, using a cesium clock whose  clock face can be seen from ISS. Then you have to take into account the speed of light triangulated (timed exactly) for the motion of the Earth because it is rotating (Sagnac effect) so the light path is longer, timed through the atmosphere, turbulence etc etc etc.

Then only can we accept reciprocity.

Not some experiment on Earth which proves nothing about reciprocity. Otherwise we might have to admit,  that reciprocity is lost.

the slower the clocks, the faster men`s minds :) 

@ george

GR has been superceded

There are a lot of problems with GTR, not least is presents with infinite singularities, does not explain dark matter, it cannot fully explain dark energy and gives us infinite time dilation at the event horizon, which means that matter cannot enter the black hole in the lifetime of the Universe

Herein some peer reviewed international publications that resolve this.

1).First to obviate the infinite density singularities.

1a)https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the galaxy.

2a)https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the galactic halo.

3a)https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter.

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation damping ) and is corroborated by black hole studies.

5a)https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

7). It does not offer infinite time dilation at the event horizon,

https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg

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