Does Time Dilation Vary Between Supermassive Black Holes and Solar System Gravity Fields?

Question

I would like to share an idea regarding the potential relationship between the time dilation experienced around supermassive black holes and within specific solar system gravity fields. I believe this correlation could shed new light on the nature of time dilation in these extreme gravitational environments.

According to the theory of general relativity, gravity is not simply a force exerted by massive objects but rather a distortion of spacetime caused by these objects. It suggests that mass and energy curve the fabric of space, resulting in a change in the passage of time. This phenomenon is known as time dilation.

Building on these principles, my hypothesis puts forth the idea that space and time are not an inseparable pair. Instead, space itself is influenced by gravity and provides the foundation for temporal experience. Heavier objects create deeper "gravity wells" wherein both space and time are more profoundly affected. Hence, the warping of space by gravity induces the perceptible effects of time.

Expanding upon this idea, my perspective posits that spacetime is not a singular entity but instead comprises separate components influenced by gravity. In this context, the larger effects of gravity, such as those exerted by supermassive black holes, play a crucial role in shaping spacetime for bodies in motion at specific regions of space.

At the heart of my thought process lies the influence of supermassive black holes. These astronomical entities possess immense masses, resulting in extraordinarily strong gravitational fields surrounding them. As such, the effects of gravity on the surrounding space are magnified. therefore, proposing that it is these pronounced distortions caused by supermassive black holes that induce the perceptible effects of time for bodies in motion within their gravitational fields.

Considering the effect of the supermassive black holes gravity , we can conclude that the experience of time varies due to the changing gravitational fields to which bodies are subjected. Time, being a compound effect, is influenced by various gravitational forces, such as those exerted by supermassive black holes, massive stars in a body's solar system (in this examples The sun as in our solar system ), and even the body's own gravitational field.

These combined gravitational influences contribute to the observed variations in the flow of time within different regions of space.

As postulated above, the effect of time is experienced differently due to changes in the gravitational field. It should be noted that time is a compound effect influenced by gravitational forces acting on a body. To further illustrate this, let's consider the following calculation: Let Tb represent the perceived time on a body, and T0 represent the "reference time" in the absence of any significant gravitational influence.

Tb = T0 * √(1 - (2GM)/(c^2r))

In this equation, G represents the gravitational constant, M denotes the mass of the supermassive black hole, c symbolizes the speed of light, and r represents the distance from the body to the center of the gravitational field.

By incorporating this calculation, we can better understand how the intricate interplay of different gravitational forces, including those exerted by supermassive black holes, massive stars in the body's solar system, and the body's own gravitational field, contribute to the observed variations in the perception and measurement of time.

To calculate the relative time dilation between the gravity field of a supermassive black hole and that of a specific solar system, we can use the following equation:

Δt_solar_system = Δt_black_hole * √(1 + (2GM_bh)/(c^2r_bh ) - (2GM_s)/(c^2r_s ))

In this equation, Δt_solar_system represents the perceived time in the solar system, Δt_black_hole represents the perceived time near the supermassive black hole, G is the gravitational constant, M_bh is the mass of the supermassive black hole, M_s is the mass of the sun in the solar system, c is the speed of light, r_bh is the distance from the body to the supermassive black hole, and r_s is the distance from the body to the sun in the solar system.

This equation takes into account the gravitational effects of both the supermassive black hole and the sun on the perception of time. It demonstrates the complex interplay of different gravitational forces and how they contribute to the observed variations in time dilation between different gravity fields.

Please note that these equations are a simplified representation and does not cover all possible factors influencing time dilation. Additionally, the actual effects on time may vary depending on the specific conditions and relativistic considerations.

Adding on : If we can theoretically find a way to escape the influence of gravity completely, it follows that the experience of time would be altered or potentially eradicated altogether. By removing part or whole of the combined compound gravitational forces influence, an individual could exist in a state of timelessness, detached from the unfolding of events experienced by those in gravitational fields. This could open up new realms of exploration and challenge our current understanding of the human relationship with time.

I am eager to receive your valuable input, suggestions, and critiques regarding this proposal.

Thank you.

Answer 1

Your summary of general relativity

"According to the theory of general relativity, gravity is ... a distortion of spacetime ... . It suggests that mass and energy curve the fabric of space, resulting in a change in the passage of time. "

contains the probably unintentional error that the "fabric of space" is curved. What probably was intended here is that the fabric of spacetime is curved, as you subsequently contrast it with your ideas.

Your idea of considering space and time as separate is not viable, in my opinion. 

Even without gravitational effects, i.e., in Minkowski space, two events, which for an observer A occur simultaneously at different locations in space, occur at a temporal distance for an observer B moving at constant speed relative to A. Therefore, separating space (for which there are only spatial distances) from time (for which there are only temporal distances) is not feasible.

If you consider space and time separate, you would also have to explain how, as you put it, the warping of space (only) by gravity induces the perceptible effects of time.

Furthermore, a clear distinction has to be made between spacetime, coordinate systems for spacetime, space-like, time-like and light-like directions in spacetime on the one hand, and the proper time experienced by an observer on the other hand.  The latter is determined via the metric of spacetime and the observer's trajectory therein:

$$\tau_2-\tau_1={1\over c}\int_{\lambda_1}^{\lambda_2}\sqrt{g(\gamma(\lambda))_{mn}{\dot\gamma}^m{\dot\gamma}^n}{\rm d}\lambda$$

where $\gamma$ is the observer's trajectory parametrised by $\lambda$, $g$ the metric tensor, and $\dot\gamma={{\rm d}\gamma/{\rm d}\lambda}$. In this context note that for the Schwarzschild metric

$$c^2{\rm d}\tau^2=\left(1-{a\over r}\right)c^2{\rm d}t^2-\left(1-{a\over r}\right)^{-1}{\rm d}r^2-r^2\left({\rm d}\theta^2+(\sin\theta)^2{\rm d}\phi^2\right)$$

for an observer at rest (${\rm d}r={\rm d}\theta={\rm d}\phi=0$) it is only the prefactor of $c^2{\rm d}t^2$ which affects ${\rm d}\tau$, i.e., only the purely temporal term, with no influence from the spatial terms. Hence, your statement that "the warping of space by gravity induces the perceptible effects of time" does not apply here.

Concerning the escaping from the influence of gravity completely:

A non-rotating observer in free-fall is in a local inertial system and does, in some sense, not experience gravitation. Nonetheless, this observer experiences time (i.e., proper time is passing for this observer). However, free-fall is determined by the geometry of spacetime and thus, in some sense, by gravitation.