Physics/dilated space = dilated time?
QUESTION: hi Dr. Nelson,
consider a binary system of equal weight neutron stars. At the center node between the two bodies the gravity should be completely zero. this is what could be considered 'dilated space' a point where gravitational influence is very strong however it is completely balanced.
At this point of space, is time slowed relative to a distant observer who is experiencing no gravitational influence?
Also has any sort of experiment been performed to determine the time effects of gravitationally zero 'dilated space'?
ANSWER: I've never heard the term "dilated space" except in medical terminology before, but sure. This is a known quantity in general, since General Relativity has to account for multiple bodies of orbital satellites (Earth, Moon) when it works. Sometimes those forces are additive, sometimes not. Same concept, just not limited to one single point in the center. GR calculations work, or else GPS navigation would not (that was proven when GPS launched). As far as I know, no one is going to a Lagrange point or similar place to do any specific studies, though that will be important in the navigation of planned space telescopes which orbit at such points and need ultra-precise navigation like LISA. As far as a point in the exact center of two co-orbiting bodies of equal mass...there are none local, so that's out...and kind of overkill. If it works in general for multiple bodies in places where their gravitation adds as well as subtracts, then it will work in the center of your idealized system as well.
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QUESTION: thanks for the feedback. By sure do you mean, yes time flows at the same rate for both observers?
In my understanding of GR, the more gravity you experience the slower your time is relative to an observer not experiencing the gravity. A person in space watching a person on the ground would see the ground person as moving slightly slower. The person on the ground would see the space person as moving slightly faster. (Assume that there is no angular momentum or relative velocity involved).
It is also my understanding that this effect is subject to vector cancellation. In this way, according to my understanding, the point in the center of the binary system and the far off point would observe each other as being normal speed.
I am well aware that GR 'thinks' it knows what is going on and can calculate the time effect in such areas of space. I am not considering Lagrange points as they are points of balanced angular momentum in terms of orbital position, not absolute zero.
An absolute zero point would be found somewhere directly between the earth and the sun. in this point a small body would follow a purely straight trajectory with no angular acceleration exerted on the object by gravity. This point by definition could not be observed unless with a 'fly through' as using propulsion to follow the points orbit would add acceleration to the craft and exert a time effect, as per my understanding of GR.
For this reason I have used the ideal system to depict a stationary node in which an object could remain balanced and observed if perfectly central.
I have a notion about a scalar applied to the cosmological constant, inversely proportional to the amount of matter in the vicinity. The mass vicinity would be irrespective of vector cancellation. Applying this to GR would neatly explain dark matter.
This is the foundation of a deeper concept that ties dark matter, dark energy and GR.
By "sure" I meant that we'll go ahead and use that term. But no, it's not quite that simple. The person in the center of the point of cancellation would still be at a different gravitational potential relative to a distant observer. Time would still definitely move slower for them. Light moving between them would still eventually have to over come the net gravitation of two stars pulling on it as it went between one and another, leaving the "exact cancellation" point, and would lose energy (i.e. lower frequency). I asked a similar question of a theorist who studied this exact subject, and he affirmed that light is indeed the arbiter of time in such questions. What happens to light, happens to clocks. The spacecraft in your flythrough point would still experience time dilation from the Earth and Sun relative to an observer distant to our solar system, because of the net gravitational potential change between the two points. The forces can cancel, but the potential at two relative points involves all the forces at the points in between, so your concept of how near the masses are to the point of time dilation is already accounted for in GR formalism.