CONCEPT OF RELATIVE MOTION- How Can We Say That Planets revolve around Sun?

[OnlyMe]

ECEF is an inertial frame if you exclude GR effects, almost.

chinglu, It seems like you are confusing descriptions of orbiting objects and the coordinate system chosen to describe their motion. Even still any object in orbit is accelerating. Its path or velocity, is constantly changing in direction, even if not in speed.

ECEF is a rotating coordinate system. It does not mater whether that rotation is within the context of GR or SR, the rotation itself, when applied to an object, is a form of acceleration. That excludes it from being inertial in any sense. That said, it is an even larger error, to think of a coordinate system as if it were an object. Coordinate systems are abstractions, we use to describe the relative positions and/or dynamic relationships of objects, which can be either inertial or accelerating.

The following Wiki links describe both ECEF and ECI frames.

http://en.wikipedia.org/wiki/ECEF
http://en.wikipedia.org/wiki/Earth-centered_inertial​

Note that the ECI link, includes the following,

"ECI frames are called inertial in contrast to the Earth-centered, Earth-fixed (ECEF) frames which rotate in inertial space."​

The ECI frame is only considered inertial when compared to the ECEF frame. That is not the same as saying that it is inertial.

Earlier when I posted, (referring to both ECI and ECEF coordinate systems)

These are two different coordinate systems. Each could be considered as inertial from some frame of reference,...

I was making the same error and treating coordinate systems as objects.., and assuming that a coordinate location on the axis of rotation could be considered inertial. However, if we place an object anywhere on that axis, it would still be rotating.., a form of acceleration.

Pete corrected my error below.

The ECEF is not an inertial frame. No, you can't make it inertial.

I would not have caught my conceptual error, had it not been for Pete's comment, which caused me to look back at what I had previously posted.

 

[chinglu]

chinglu, It seems like you are confusing descriptions of orbiting objects and the coordinate system chosen to describe their motion. Even still any object in orbit is accelerating. Its path or velocity, is constantly changing in direction, even if not in speed.

ECEF is a rotating coordinate system. It does not mater whether that rotation is within the context of GR or SR, the rotation itself, when applied to an object, is a form of acceleration. That excludes it from being inertial in any sense. That said, it is an even larger error, to think of a coordinate system as if it were an object. Coordinate systems are abstractions, we use to describe the relative positions and/or dynamic relationships of objects, which can be either inertial or accelerating.

The following Wiki links describe both ECEF and ECI frames.

http://en.wikipedia.org/wiki/ECEF
http://en.wikipedia.org/wiki/Earth-centered_inertial​

Note that the ECI link, includes the following,

"ECI frames are called inertial in contrast to the Earth-centered, Earth-fixed (ECEF) frames which rotate in inertial space."​

The ECI frame is only considered inertial when compared to the ECEF frame. That is not the same as saying that it is inertial.

Earlier when I posted, (referring to both ECI and ECEF coordinate systems)



I was making the same error and treating coordinate systems as objects.., and assuming that a coordinate location on the axis of rotation could be considered inertial. However, if we place an object anywhere on that axis, it would still be rotating.., a form of acceleration.

Pete corrected my error below.



I would not have caught my conceptual error, had it not been for Pete's comment, which caused me to look back at what I had previously posted.

I can't disagree with any of your statements.

Yet, GPS and Neil Ashby are able to isolate GR effects and so they can be eliminated.

http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node1.html
See Chapter 3.

There are thus three distinct contributions to this effective potential: a simple contribution due to the earth’s mass; a more complicated contribution from the quadrupole potential, and a centripetal term due to the earth’s rotation. The main contribution to the gravitational potential arises from the mass of the earth; the centripetal potential correction is about 500 times smaller, and the quadrupole correction is about 2000 times smaller. These contributions have been divided by in the above equation since the time increment on an atomic clock at rest on the geoid can be easily expressed thereby. In recent resolutions of the International Astronomical Union [1], a “Terrestrial Time” scale (TT) has been defined by adopting the value . Eq. (18) agrees with this definition to within the accuracy needed for the GPS.

Therefore, GPS is able to isolate GR effects and hence eliminate them.

More specifically, Ashby indicates this:

The Sagnac effect can be regarded as arising from the relativity of simultaneity in a Lorentz transformation to a sequence of local inertial frames co-moving with points on the rotating earth.

So, we have a sequence of local inertial frames co-moving with points on the rotating earth as indicated by Ashby.

Yet, this entire sequence can be eliminated by noting that a GPS receiver moves down only .4 cm during the satellite signal travel.

Thus, if we move the unit up uniformly .4 cm during the signal's travel, then we have an inertial frame as described by Ashby for the unit.

Then, we note in this adjusted ECEF, t =d/c does not hold true because of the sagnac effect in this adjusted inertial frame.

That is the whole point.

 

[chinglu]

The ECEF clocks are not synchronized in that inertial frame.


No, that's not correct. Using clocks that are synchronized in a given comoving frame gives a constant speed of light.

The issue is not to claim a constant speed of light.

Einstein said t = d/c holds true in any inertial frame.

Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body. Hence
c=d/t.
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Chapter 2.

So, you cannot declare a constant speed of light unless c=d/t is true as mandated by Einstein.

In these co-moving frames, none prove c=d/t is true because of the sagnac effect.

 

[rpenner]

Yet, GPS and Neil Ashby are able to isolate GR effects and so they can be eliminated.

The effects aren't "eliminated" -- they still affect all clocks and local conventions of time. Instead they are laboriously compensated for by the equation 18.

More specifically, Ashby indicates this:

The Sagnac effect can be regarded as arising from the relativity of simultaneity in a Lorentz transformation to a sequence of local inertial frames co-moving with points on the rotating earth.
So, we have a sequence of local inertial frames co-moving with points on the rotating earth as indicated by Ashby.

That is not what Ashby "indicate" for what you quote is not the thrust of his article but a digression. It is the third concept that is developed in Section 3, not the one you displayed.

Eqs. (7) and (11) can be reinterpreted as a means of realizing coordinate time t′ = t in the rotating frame, if after performing a synchronization process appropriate corrections of the form $$+ 2 \omega_{\textrm{E}} \int_{\textrm{path}} dA'_z /c^2$$ are applied. It is remarkable how many different ways this can be viewed. For example, from the inertial frame it appears that the reference clock from which the synchronization process starts is moving, requiring light to traverse a different path than it appears to traverse in the rotating frame. The Sagnac effect can be regarded as arising from the relativity of simultaneity in a Lorentz transformation to a sequence of local inertial frames co-moving with points on the rotating earth. It can also be regarded as the difference between proper times of a slowly moving portable clock and a Master reference clock fixed on earth’s surface.

This was recognized in the early 1980s by the Consultative Committee for the Definition of the Second and the International Radio Consultative Committee who formally adopted procedures incorporating such corrections for the comparison of time standards located far apart on earth’s surface. For the GPS it means that synchronization of the entire system of ground-based and orbiting atomic clocks is performed in the local inertial frame, or ECI coordinate system [6].

Chinglu, you have lost track of your thesis. Proving any or all of us wrong does not demonstrate that your claims are right. There are, after all, many more ways of being wrong than being right. Don't for get your burden of proof.

 

[chinglu]

The effects aren't "eliminated" -- they still affect all clocks and local conventions of time. Instead they are laboriously compensated for by the equation 18.

That is not what Ashby "indicate" for what you quote is not the thrust of his article but a digression. It is the third concept that is developed in Section 3, not the one you displayed.

​

Chinglu, you have lost track of your thesis. Proving any or all of us wrong does not demonstrate that your claims are right. There are, after all, many more ways of being wrong than being right. Don't for get your burden of proof.

I accept the burden or proof.

So, the equation demonstrates the isolation of the GR components. Now, if you think that is false, let it be known. If you are right and GR effects cannot be decided, then GPS does not work, so good luck with that.

But, also contained therein is the sagnac effect.

And, Ashby, gave his interpretation of the sagnac effect, which I already posted.

So, what exactly have you contributed here?

 

[chinglu]

I am going to reiterate for clarity, the ECEF frame, which can be SR'ized, does not satisfy ct = d as required by the SR light postulate.

So, SR cannot be true.

Yet, the ECI frame does satisfy ct = d, making it a preferred frame.

 

[Lakon]

I am going to reiterate for clarity, the ECEF frame, which can be SR'ized, does not satisfy ct = d as required by the SR light postulate.

So, SR cannot be true.

Yet, the ECI frame does satisfy ct = d, making it a preferred frame.

I like it that you've reduced it to this. The (comprehensable) reply should be interesting.

 

[brucep]

I am going to reiterate for clarity, the ECEF frame, which can be SR'ized, does not satisfy ct = d as required by the SR light postulate.

So, SR cannot be true.

Yet, the ECI frame does satisfy ct = d, making it a preferred frame.

Clarify what a scientific illiterate troll you are? If you can't do any of the science you're complaining about then put a cork in it and leave it to folks who can.

 

[brucep]

I like it that you've reduced it to this. The (comprehensable) reply should be interesting.

Why would any reply to this bullshit nonsense be interesting?

 

[Lakon]

Why would any reply to this bullshit nonsense be interesting?

Replies can always be interesting.

 

[Pete]

I am going to reiterate for clarity, the ECEF frame, which can be SR'ized, does not satisfy ct = d as required by the SR light postulate.

So, SR cannot be true.

Chinglu, the adjustment you make to the ECEF frame does not result in an SR inertial frame, because the clocks in that adjusted frame are not SR synchronized.
That's why the speed of light is not constant according to measurements made with clocks and rulers in that frame.

 

[chinglu]

Chinglu, the adjustment you make to the ECEF frame does not result in an SR inertial frame, because the clocks in that adjusted frame are not SR synchronized.
That's why the speed of light is not constant according to measurements made with clocks and rulers in that frame.

You are correct that GR eliminated EFEF clocks cannot perform Einstein's clock sync method.

However, please why this is true.

Also explain why GR eliminated ECI clocks can perform Einstein's clock sync method.

Please exclude any GR effects since the equations of Ashby prove that can be done.

 

[Pete]

However, please why this is true.

Because the ECEF is defined using ECI time.
ECEF clocks are synchronized to ECI clocks

 

[chinglu]

Because the ECEF is defined using ECI time.
ECEF clocks are synchronized to ECI clocks

I agree.

However, where in special relativity can you make this statement and it be true?

 

[Pete]

Where does it say you can't?

 

[OnlyMe]

Because the ECEF is defined using ECI time.
ECEF clocks are synchronized to ECI clocks

Pete, this has been puzzelingly me.

Both ECI and ECEF frames are centered on the earth's center of mass. The ECI frame is fixed with the earth rotating within it and the ECEF frame rotates with the earth.

By convention we use UTC time as a standard, but UTC time is determined as an average of several clocks at several locations. Those clocks all rotate with the earth so they are synchronized in an ECEF frame, not an ECI frame. Though, again by convention we use the same time standard for both frames.

Things get even more complicated in that, even an atomic clock maintained at a uniform distance from the earth's center of mass and moved from equator to pole will record the passage of time at a different rate... Though the change may be outside of our current ability to measure, being due only to the SR effects of velocities less than 1000 MPH (give or take).

We synchronize our clocks in an ECEF frame. Clocks so synchronized remain accurate only within a localy defined inertial laboratory setting. In an ECEF frame the rate a clock runs at varies more by its distance from the earth's center of mass than its velocity of rotation... The GR affect is greater than the SR affect.

The problem it seems to me with chinglu's hypothetical is three fold. First he attempts to exclude the effects of gravity, which can as you mentioned be accounted for, but not excluded.., which means clocks on satellites run at different rates than the same clocks on the surface of the earth... And second when he makes changes to the satellite's orbit, in an attempt to create an inertial frame of reference, he confuses the satellite's frame, with both ECEF and ECI frames centered at the earth's center of mass... And thirdly, he does not account for the fact that the whole GPS system uses dynamic synchonization to the UTC standard.

In any case GPS satellite clocks are dynamically synchronized to UTC time. Only on the first GPS satellite(s?) were the clocks allowed to run at rates relative to their GR and SR conditions, which confirmed the time dilations predicted for the affects of GR and S.R All other GPS Satelites are preadjusted and dynamically synchronized to UTC time standard. Since those clocks are located on the rotating surface of the earth, they are synchronized in an ECEF frame.

No?

 

[Pete]

Pete, this has been puzzelingly me.

Both ECI and ECEF frames are centered on the earth's center of mass. The ECI frame is fixed with the earth rotating within it and the ECEF frame rotates with the earth.

By convention we use UTC time as a standard, but UTC time is determined as an average of several clocks at several locations. Those clocks all rotate with the earth so they are synchronized in an ECEF frame, not an ECI frame.

Hi OnlyMe,
I don't know the details of how actual UTC standard clocks are synchronized with each other in practice, so this post is purely theory-based.
There is a theoretical problem with synchronizing clocks in a rotating reference frame.

Imagine a set of clocks spread around the equator. Starting from a master clock, each clock is synchronized with its neighbor using Einstein synchronization or equivalent. When we get back to the last clock, it will be out of synch with the master clock (its neighbor) by about 200 nanoseconds.

So, if we are to have ECEF clocks meaningfully synchronized to high precision without a discontinuity at some longitude, then whenever two ECEF clocks at different longitudes are synchronized, the synchronization has to be artificially adjusted so that they are synchronized in the ECI frame.

The problem it seems to me with chinglu's hypothetical is three fold. First he attempts to exclude the effects of gravity, which can as you mentioned be accounted for, but not excluded.., which means clocks on satellites run at different rates than the same clocks on the surface of the earth... And second when he makes changes to the satellite's orbit, in an attempt to create an inertial frame of reference, he confuses the satellite's frame, with both ECEF and ECI frames centered at the earth's center of mass... And thirdly, he does not account for the fact that the whole GPS system uses dynamic synchonization to the UTC standard.

Chinglu's argument is essentially that:
1 - We should be able to use two close-together ECEF clocks to make measurements in their momentary comoving inertial reference frame
2 - Doing so would result in different speeds for East to West light and West to East light (by about 900m/s)

If these two points were correct, then this would obviously mean a violation of SR.

The second point is correct, but the first point is not. The side-by-side ECEF clocks are not synchronized in the comoving inertial reference frame, but in the ECI.

 

[Aqueous Id]

By convention we use UTC time as a standard, but UTC time is determined as an average of several clocks at several locations.

Unfortunately due to the shutdown the NIST site is closed, so I have to wing it here. Last I checked UTC was referenced to the NIST time standard in Boulder.

Those clocks all rotate with the earth so they are synchronized in an ECEF frame, not an ECI frame. Though, again by convention we use the same time standard for both frames.

It's true, local time may deviate by some small amount from UTC.

Things get even more complicated in that, even an atomic clock maintained at a uniform distance from the earth's center of mass and moved from equator to pole will record the passage of time at a different rate... Though the change may be outside of our current ability to measure, being due only to the SR effects of velocities less than 1000 MPH (give or take).

On top of that, the Earth's rotation is not uniform, it is slowing due to losses from tides, and the local gravitational field varies from the clock in Boulder.

We synchronize our clocks in an ECEF frame. Clocks so synchronized remain accurate only within a localy defined inertial laboratory setting. In an ECEF frame the rate a clock runs at varies more by its distance from the earth's center of mass than its velocity of rotation... The GR affect is greater than the SR affect.

And SR would not even come into play unless the local clock were mobile.

The problem it seems to me with chinglu's hypothetical is three fold. First he attempts to exclude the effects of gravity, which can as you mentioned be accounted for, but not excluded.., which means clocks on satellites run at different rates than the same clocks on the surface of the earth...

They indeed were confirmed to show time contraction at altitude. This was demonstrated at finer resolution at NIST with its aluminum clocks. chinglu may not understand relativity, but the empirical data speaks for itself.

And second when he makes changes to the satellite's orbit, in an attempt to create an inertial frame of reference, he confuses the satellite's frame, with both ECEF and ECI frames centered at the earth's center of mass...

I've noticed that too. And here again we have empirical evidence of SR which demonstrates time dilation as predicted.

And thirdly, he does not account for the fact that the whole GPS system uses dynamic synchonization to the UTC standard.

Yes, and since the errors he's claiming would accumulate, it means that GPS would have lost its ability to geolocate any receiver shortly after deployment, with ever increasing errors since. That error would accmulate as ca. 1 ft / ns in the raw measurement. That works out to something like 7200 ft of error (well over a mile) per day which would have rendered GPS useless long before it became available for public use.

In any case GPS satellite clocks are dynamically synchronized to UTC time. Only on the first GPS satellite(s?) were the clocks allowed to run at rates relative to their GR and SR conditions, which confirmed the time dilations predicted for the affects of GR and S.R All other GPS Satelites are preadjusted and dynamically synchronized to UTC time standard. Since those clocks are located on the rotating surface of the earth, they are synchronized in an ECEF frame.

In fact, if you think about it, the geolocation algorithm actually runs in the receiver. It's simply using the satellite messages to ascertain the position of each satellite in the constellation, and to measure the range (cΔt) to each. Obviously they all have to be synchronized in order to get a reasonably accurate measurement of each Δt. But since they are moving quickly there is SR dilation, and since they are at altitude there is GR contraction, and without the corrections for both each Δt would drift ever higher since the moment of deployment, which would have rendered them useless within the first day, much less the error that would have accumulated since.

 

[OnlyMe]

Hi OnlyMe,
I don't know the details of how actual UTC standard clocks are synchronized with each other in practice, so this post is purely theory-based.
There is a theoretical problem with synchronizing clocks in a rotating reference frame.

UTC time is just the time standard agreed upon, as a global standard. How the individual clocks are synchronized is not really important. It does show that the individual clock rates, does vary by location, thus an average is used as the standard.

The point I was attempting to make is that even though we tend to think of our frame as an ECI frame, we are actually standing on a rotating ball, the earth, which travels through an ECI frame. (See correction below) The frame of reference associated with fixed coordinates on the earth's surface, is an ECEF rotating frame. That means that our time standard is based, by convention, on the UTC time standard, which is the ECEF frame of the earth's rotation. If the earth did not rotate and was, both a true sphere and of a uniform mass density, our clocks would be synchronized in an ECI frame and would all keep time at the same rate.., theoretically... The earth does rotate.

So, if we are to have ECEF clocks meaningfully synchronized to high precision without a discontinuity at some longitude, then whenever two ECEF clocks at different longitudes are synchronized, the synchronization has to be artificially adjusted so that they are synchronized in the ECI frame.

For most day to day purposes once even a wrist watch is initially synchronized (set), it keeps time accurately enough for day to day purposes. However, even many consumer clocks and watches today, re-synchronize to the UTC standard once to several times a day. For sensitive scientific or GPS purposes synchronization often becomes more dynamic.

BTW all clocks that are not dynamically synchronized do have to be adjusted to location, or reset on a routine basis.

Chinglu's argument is essentially that:
1 - We should be able to use two close-together ECEF clocks to make measurements in their momentary comoving inertial reference frame
2 - Doing so would result in different speeds for East to West light and West to East light (by about 900m/s)

If these two points were correct, then this would obviously mean a violation of SR.

The second point is correct, but the first point is not. The side-by-side ECEF clocks are not synchronized in the comoving inertial reference frame, but in the ECI.

This is correct. In the first he is or was, either not aware that location alone affects the rate clocks in an ECEF frame record time. This would be true with or without the affect of gravity, though the GR affect due to gravity is far more significant than the SR affect due to velocity. I still think the second issue re the speed of light is complicated by confusing frames of reference. What the speed of light is for a satellite has nothing to do with either the ECEF or ECI frame it moves through. It is only subject to the satellite's own frame of reference and would require the satellite's clock be initially synchronized in the satellite's frame... GPS satellite clocks are not synchronized to the satellite's frame, as mentioned before they are dynamically synchronized to an ECEF frame.., the UCT time standard, which almost all earth based clocks are set or synchronized to.

___________
As a side issue, I have always wondered why there has been no attempt to run a laboratory type speed of light experiment performed in the free fall environment of one or another satellite or the space station. Even though the experimental equipment would be non-inertial relative to the earth, the experiment itself could be conducted in an essentially flat inertial frame of reference. Right now we have theoretical proof, based on predicted time dilations, but not physical experiment (that I have heard of) that actually tests the predictions. However, it may be largely due to the size and weight of clocks accurate enough to detect or exclude any variation.

Edit-correction: The earth does not move through an ECI frame. ECI frames at best move with the earth as it orbits the sun. The earth rotating within the ECI frame.

 

[brucep]

Unfortunately due to the shutdown the NIST site is closed, so I have to wing it here. Last I checked UTC was referenced to the NIST time standard in Boulder.


It's true, local time may deviate by some small amount from UTC.

On top of that, the Earth's rotation is not uniform, it is slowing due to losses from tides, and the local gravitational field varies from the clock in Boulder.


And SR would not even come into play unless the local clock were mobile.


They indeed were confirmed to show time contraction at altitude. This was demonstrated at finer resolution at NIST with its aluminum clocks. chinglu may not understand relativity, but the empirical data speaks for itself.


I've noticed that too. And here again we have empirical evidence of SR which demonstrates time dilation as predicted.


Yes, and since the errors he's claiming would accumulate, it means that GPS would have lost its ability to geolocate any receiver shortly after deployment, with ever increasing errors since. That error would accmulate as ca. 1 ft / ns in the raw measurement. That works out to something like 7200 ft of error (well over a mile) per day which would have rendered GPS useless long before it became available for public use.


In fact, if you think about it, the geolocation algorithm actually runs in the receiver. It's simply using the satellite messages to ascertain the position of each satellite in the constellation, and to measure the range (cΔt) to each. Obviously they all have to be synchronized in order to get a reasonably accurate measurement of each Δt. But since they are moving quickly there is SR dilation, and since they are at altitude there is GR contraction, and without the corrections for both each Δt would drift ever higher since the moment of deployment, which would have rendered them useless within the first day, much less the error that would have accumulated since.

This is an interesting way to find the required 'correction'. Model the GPS spacetime using the Schwarzschild metric of GR. Set the Earth as approximately spherically symmetric and non rotating. Set theta in the metric at 0.

Project A Global Positioning System
http://www.eftaylor.com/pub/projecta.pdf

This is the formula for predicting the 'correction'. There's a section on 'justifying approximations'.

dt_satellite/dt_earth = 1 - M_earth/r_satellite - v^2_satellite/2 + M_earth/r_earth + v^2_earth/2

We could substitute this equation dTau/dt = (1 - 3M/r)^1/2 for "M_earth/r_satellite - v^2_satellite/2". It accounts for both corrections, GR and SR, for r_satellite. The 'correction' is + 4.4453E-10 s per s. Or + 38,407392 ns/earth day. + .000038407392s/earth day. It would take 71 1/3 earth years to equal 1 second. So one, of many, amazing things associated with the GPS experiment is the success of the experiment requires such measurement accuracy. The experiment itself is a work of 'functional' art. It's a good reason why folks like chinglu should figure out what they're talking about before making claims that ECI and ECEF don't render the same science asserting relativity is falsified. The idea that the frames being discussed would change the science is nonsense from the mouth of a scientific illiterate crank. This type of posting [troll] is the MO of chinglu.

The derivation for dTau/dt = (1 - 3M/r)^1/2

Set the derivative of the effective potential term (from the equation of motion) into quadratic form (to find critical values)

r*^2 - L*^2r + 3L*^2 = 0

Where

r* = r/M, and L* = L/mM

Then divide through by L*^2 and manipulate to get

r*^2/L*^2 = r* - 3 [saving this for a later
substitution]

Setting dr = 0 in the Schwarzchild metric and
substituting dphi = (L*/r*^2)dTau the metric becomes

dTau^2 = (1 - 2/r*)dt^2 - (L*^2/r*^2)dTau^2

To find the ratio dTau^2/dt^2 divide through by the
bookkeeper time dt^2 and simplify to

(dTau/dt)^2 = (1 - 2/r*) / (1 + L*^2/r*^2)

Now substitute 1/(r*-3) for L*^2/r*^2 and simplify to

dTau/dt = (1 - 3M/r)^1/2