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the gravity effect of the mass of an object is depends on the location of the object and it mass ,but the problem is that the mass also depends on the speed of the object (relativistic mass). since we cant tell the speed of a particle and the it location in short scale, then mass measurement is always inaccuracy because if we tell where the particle is then we won't be able to tell it speed which effect it mass and if we know it speed then we don't know it location so it effect also would be difference depends on the distance form the particle to the sensor

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    $\begingroup$ You can read here about "relativistic mass". $\endgroup$ – Charlie Feb 14 at 16:43
  • $\begingroup$ @Charlie to sum up isn't it saying that when the velocity is change so the mass a little bit $\endgroup$ – daniel Feb 14 at 16:48
  • $\begingroup$ @Charlie as I see in the last line of the answer "m increases with v" $\endgroup$ – daniel Feb 14 at 16:49
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    $\begingroup$ The reason I linked that is because the idea that mass increases with velocity is generally considered outdated. However, you seems to be asking about quantum effects (the uncertainty principle) in general relativity, even thought general relativity is not a quantum theory and doesn't have anything to say about the uncertainty principle (i.e. there is no inherent uncertainty in measurement in GR). If you are asking what theories of quantum gravity have to say about this you might want to make that clearer. $\endgroup$ – Charlie Feb 14 at 17:51
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    $\begingroup$ That's an interesting question and pertains to whether or not you can treat mass as an observable in quantum mechanics. The answer is yes, you could read here for an interesting (but maybe not particularly layman friendly) discussion. $\endgroup$ – Charlie Feb 14 at 19:52
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In general relativity, which is the consistent picture relativistic gravity, the gravitating source is not "mass", but rather the stress-energy tensor. This is a two dimensional matrix $T_{ab}$, whose components are:

$T_{tt} = $ density of matter

$T_{ti} = $ ith component of the 3-momentum density of the matter

$T_{ii} = $ pressure felt by matter in the i-direction

$T_{ij} = $ "sheer" or "strain" force associated with the i,j direction

Since this tensor already contains information about the motion of a particle, there is already a consistent way to account for any relativistic motion effects of gravitating sources, which can produce "new" effects not seen in Newtonian gravity, like Gravetomagnetism.

In particular, if you have a stationary point mass, then $T_{tt}$ will be the only non-zero component, but a lorentz transformation to a moving frame will transform the stress-energy tensor according to the rules of the transformation, and since Einstein's equation is covaraiant, you will get the same forces, but they will be described in a different way.

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  • $\begingroup$ this is very interesting effect but still the mass effect it depends the location of object and it speed and if we cant tell both of them then the effect of the mass is inaccurate $\endgroup$ – daniel Feb 14 at 17:24
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Your implicit assumption is that if A and B are both uncertain, then A+B is uncertain. This is not true. The ground state of an atom is not a state of a definite kinetic energy or a state of a definite potential energy, but it is a state of good energy. Relativistically, it's a state with a definite mass-energy.

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  • $\begingroup$ not both of them it just that one of them always uncertain $\endgroup$ – daniel Feb 15 at 17:56

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