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If for two data sets (e.g., hexadecimal encryptions) which maybe reduced (conserved) to two binary data sets, one located in the reference frame of the observer and the other data set in a unspecified frame, [This is just Emma Noether’s famous test for symmetry in the 4D spacetime of E =mc^2, thus validating our right to ask the question] how do we know which data set precedes the other?
Does it matter? We can attempt to “link” the two, either by a commonality of location with a third reference frame or a common reference frame, or just simply apply an arbitrary time stamp to each as agreed.
In most situations that humans find themselves here on Earth, this suffices.
In the singular work, GRAVITATION, Nobel Prize recipient Kip Thorne gives a basic definition of time at the outset in the practical sense of General Relativity, in terms of a “good clock,”
“Good clocks make spacetime trajectories of free particles look straight.” *
That is, good clocks make particles move simply, in straight paths, on their natural world-lines. Time is not definable outside of the other three space dimensions. They are linked by “c”, the proportionality constant between space dimensions and time. Sometimes confused with the speed of light, which has the same value.
Trying to understand a rich topic such as time, sometimes averting one’s attention and watching science-fantasy helps.
This is one of those…times. Why were the Time Lords so powerful in the Dr. Who series from BBC? As Dr. Who, herself embodied? Not because they could go backwards or forwards in time, which gained them very little, as they tried to stay on the same “time-line” (whatever THAT was) and “not change history.” It was, because they controlled time and made motion “look simple.”
Challenge Question: Who controls your time? In your frame-of-reference?
Someone or something does. Time-lords? (just kidding, I hope!) GPS, GNSS, or GLONASS constellation of satellites, Grandpa’s giant clock, an XY Oracle(tm) network? You really believe you are independent of them? Prove to yourself who controls time in your frame of reference.
An Issue of Causality
I bet you rely on GPS for your time control. So I will give this as my example, in words. What if I told you that without any fancy tricks and without spoofing, etc.; even in a state of complete ignorance on my part to what I was doing, I could initiate an event (t=0) using a legitimate GPS time sequence at the base of the Himalayas or any massive mountain range and it will appear to occur after an event occurring everywhere else on the surface of the Earth at (t=1).
That is called an issue of causality. Two locales on the surface of the Earth that “appear” to be in the exact same spacetime frame-of-reference, are in fact not.
Yet the GPS time-signal “assumes” that all receivers on the Earth’s surface are in the same spacetime frame-of-reference.
One reason for this occurring here, is that GPS corrections for special and general relativity are taken on the satellites before the signal is sent to Earth. It is built-in to the time sequence. All this is public knowledge. Everyone can and should know how GPS works.
‘Banks to the Moon. Bonds to Mars?’
The reason it might be “Banks” is that financial institutions, unhindered, could manipulate or by the same token, fall prey to, the mass difference between Earth and Moon to effect sudden, catastrophic financial event reversals. How?
We know GPS signals may reach the Moon. NASA has even navigated by them successfully in inter-Lunar space.
In the third in the series, “The Study of Spacetime and Gravity” I raised the issue of NASA proposing or being “conned” or a “spoof” on using Earth-based GPS to navigate to the lunar surface from orbit, as illustrated below in “Beyond Space Service Volume…
Is NASA Goddard for real or is the a spoof, or “Fake-News”?
I quantitatively demonstrated in one dimension this idea was not feasible…
I think I have a far better idea than relying on the GPS for position of space probes and The Gateway Space Station orbiting the Moon.
While in orbit around Earth, the GPS atomic cesium clocks are set-up to run +38,700 nanoseconds (nS) faster than similar ones on Earth.
Ge-Se = corrected time, where Ge is the general relativity correction of 45,900 nS and Se is the special relativity time correction of -7,200 nS slower for speeding around Earth.
The earth approximate mass is = 597.2 x 10^22 kg
It is from the proximity of this massive object, Earth, that general relativity can be thought to function for us in one frame-of-reference, as opposed to the frame-of-reference of the GPS satellites. However, there is subtlety here. On Earth.
Earth is 81.28 times more massive than the Moon (Mm = 7.348 x 10^22 kg).
In one-dimension, it is straight forward to see there will be different time-delays involved with Moon orbit.
For Earth and near-Earth orbit
Se = -7,200 nS
Ge= +45,900 nS
Delay T = +38,700 nS.
For the Moon and near-Lunar orbit…
Gm = 45,900/81.28 = +565 nS
The fixed Delay T of +38,700 nS from the GPS, or GNSS, or GLONASS, or any constellation of atomic clocks will not work accurately near the Moon,
Delay T = +565 nS – Sm
Sm = the special relativity correction for satellites orbiting the Earth as seen from Earth, and now seen in another frame of reference, the Moon.
Yep, not too simple is it?
Their is a sign change in time delay. This is a simple one-dimensional representation of the metric tensor, Guv, which holds all the information on spacetime, mass variation, and curvature. Guv separates for us, future from past. In four-dimensional calculations of the tensor, it may have both positive and negative reversals.
My better idea for NASA is to solve the 4D metric tensor numerically (bringing to mind Euler’s Method from Hidden Figures) taking into account all topology on the lunar surface, and any known assymmtries under the surface, BEFORE making any pronouncement on how we can use GPS all the way into Lunar orbit.
Or even more simply, just have a separate LPS (Lunar Positioning System) in orbit around the Moon, made up of two or three CubeSats, like JPL designed so eloquently for communications recently for the Mars InSight probe.
References hold their own copyrights
*[Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald. Gravitation (Page 26). Princeton University Press, Princeton, New Jersey, (1971).]
**[Huth, John Edward. The Lost Art of Finding Our Way (Page 25). Belknap Press of Harvard University Press, Cambridge, Massachusetts, (2013).]