Relationship of Time vs Gravity.

[CraigD]

So I guess my next question would be what happens when gravity of two celestial bodies are fighting...what would be the affects of that?

I think you asking about gravitational time dilation at a point between two bodies where the gravitational force on a small test body due to one is equal and opposite to the force due to the other, so that the test body isn’t accelerated toward either body.

 

You might guess that the gravitational time dilation factor [math]\frac{t_1}{t_0} = 1[/math], that is, that there’s no time dilation relative to a far away observer’s clock [imath]t_0[/imath], but this guess is wrong.

 

In post #14, I gave the usual formula for gravitational time dilation, [math]\frac{t_1}{t_0} = \sqrt{1-\frac{2Gm}{c^2 r}}[/math]

 

This formula assumes we’re calculating for a point distance [imath]r[/imath] from a body with mass [imath]m[/imath]. If we wanted to make it more general, so it could be used to calculate for a point between 2 bodies – or any other situation we can describe mathematically – we replace the factor [math]\frac{-Gm}{r}[/math] with one we’ll write [math]u[/math], rewriting it

[math]\frac{t_1}{t_0} = \sqrt{1+\frac{2u}{c^2}}[/math]

 

If you’ve studied some basic physics and are paying attention, you’ve likely noticed that

[math]u = \frac{-Gm}{r}[/math]

is the usual formula for gravitational potential energy for a single body. The formula for GPE for a point between 2 bodies is

[math]u = -\frac{Gm_1}{r_1}-\frac{Gm_2}{r_2}[/math]

 

To keep things simple (though it’s easy to find [math]r_1[/math] and [math]r_2[/math] for any [math]m_1[/math], [math]m_2[/math], separated by distance [math]D[/math]), assume [math]m = m_1 = m_2[/math] and [math]r = r_1 = r_2 = \frac{D}2[/math] We can now compare

[math]\left( \frac{t_1}{t_0} \right)_{\mbox{1 body}} = \sqrt{1-\frac{2Gm}{c^2 r}}[/math]

to

[math]\left( \frac{t_1}{t_0} \right)_{\mbox{2 bodies}} = \sqrt{1 -\left(\frac{Gm_1}{r_1}+\frac{Gm_2}{r_2}\right)\frac2{c^2 }}[/math]

 

Doing the math (which you can likely do by just looking at the two equations), you’ll find that the time dilation effect of adding the second body is exactly the same as doubling the mass of the first.

 

The key point to take away from this is that gravitational time dilation is a function of gravitational potential energy, not the local net acceleration of gravity. You can be weightless – not accelerated in any direction – by two or more massive bodies – yet still have your clock slowed down by the effect of their masses.

Is gravity a wave or a particle..is it both and retains a duality structure? and if so then can we observe and better understand how it would effect the rate of time?

The best answer I can give to this is nobody really knows. Unlike the other 4 fundamental forces – electromagnetism, and the 3 forces that dominate the protons and neutrons in atomic nuclei – there’s not yet a definitive theoretical explanation of what causes gravity, but rather a wild and complicated zoo of speculative ones. The theory that explains the 4 forces we do understand well – the Standard Model of particle physics – is intentionally built based on the geometry that gives rise to Relativity, so agrees with the predictions of Relativity (since these predictions agree with actual experiments, the SM must agree with them, or it wouldn’t be correct, or as physicists put it “physically realistic”)

 

If I may guess, I have a sense of what you’re trying to get at, Taer: some sort of mechanical explanation for time dilation. Without having a long, complicated discussion essentially equivalent to an intro class in modern physics, the best I can do is note that nearly every good student of physics has had this thought and explored this approach, and hint that it’s not the right one. Instead, you need to look at geometry, from which Relativity is derived. Keep in mind that you could replace all the particles and math in the SM with completely different ones (though, for it to remain “realistic”, you’d have to move to a different universe ;)), and if the underlying geometry of the universe is the same, Relativity would still apply. In short, Relativity is a consequence of the nature of space, not the particles in it.

[Time_Travel]

So Gravity controls the time according to gravitational time dilation.

 

Black holes are such powerful beasts that not even light escapes from it.

It means that black holes have gravity that exceeds the speed of light.

If anything that has the energy to exceed speed of light time reverses(travel into past).

Since Black holes have Gravity that exceeds speed of light time reverses in it.

It is sad that no instrument can measure the reverse of time in a black hole as it will be crushed even before it enters the core of Black Hole.

[CraigD]

So Gravity controls the time according to gravitational time dilation.

A fair summary statement, IMHO :thumbs_up

Black holes are such powerful beasts that not even light escapes from it.

Another fair summary statement, IMHO :thumbs_up

It means that black holes have gravity that exceeds the speed of light.

An unsupported assertion :thumbs_do

 

A more mainstream view is that the propagation of gravitational force, unlike that of massive bodies and light (“light” here meant to include all EM radiation), is not affected by gravitational fields.

 

The consensus theoretical speculation of physicists is that gravitational force propagates at exactly the speed of light, and some experimental results that appear to at least confirm that the speed of gravity is within 0.8 to 1.2 c. See the preceding link for additional summary and some links, but be warned, this is a technically complicated subject.

If anything that has the energy to exceed speed of light time reverses(travel into past).

Since Black holes have Gravity that exceeds speed of light time reverses in it.

This isn’t what general relativity predicts at all! :thumbs_do

 

Looking back to the equation in post #14, [math]\frac{t_1}{t_0} = \sqrt{1-\frac{2Gm}{c^2 r}}[/math]

and again rearranging it slightly, to [math]\frac{t_1}{t_0} = \sqrt{1-\frac{r_s}{r}}[/math]

where [math]r_s=\frac{2Gm}{c^2}[/math]

 

A black hole is simply a body compact enough that it can fit within a sphere or radius [imath]r_s[/imath] (famously known as the Schwarzschild radius, and the sphere described by it, the event horizon of a black hole).

 

we find that when a clock outside of a nonrotating spherical body reaches a critical distance from the center of the body [imath]r_s[/imath], it stops (“freezes”) as seen by a far-away watcher.

 

When it approaches more closely, [math]\frac{t_1}{t_0}[/math] becomes the square root of an negative number (which is conventionally written [imath]i a[/imath], where [imath]i=\sqrt{-1}[/imath]), a number know mathematically as imaginary. It does not become a simple negative number, which it what it would have to be to find that time reverses (travels into the past).

 

Most texts and people with whom I’ve discussed it interpret an imaginary [math]\frac{t_1}{t_0}[/math] as not finding anything physically meaningful – that is, the GR’s time dilation formula is not usable (“breaks down”) when [imath]r[/imath] is less than [imath]r_s[/imath]. Though many people have at some point heard or independently speculated that it means pastward time travel, nobody I’ve ever read or known who’ve studied and understood GR clung to this interpretation.

It is sad that no instrument can measure the reverse of time in a black hole as it will be crushed even before it enters the core of Black Hole.

That anything crossing the event horizon of every possible black hole will be crushed or torn apart (“spaghettified” by “tidal force” is a common description) is unambiguously false according to GR and the simple classical mechanics in which GR is written.

 

A sufficiently massive black hole can have very slight tidal forces at its event horizon. For a [imath]4 \times 10^{34} \,\mbox{kg}[/imath] black hole, the tidal force on a human is about the same as experienced when hanging from an bar.

 

I present this and some example values for various objects in Some numbers about very big black holes.

[Taer]

"If I may guess, I have a sense of what you’re trying to get at, Taer: some sort of mechanical explanation for time dilation. Without having a long, complicated discussion essentially equivalent to an intro class in modern physics"

 

I was simply attempting to gain a basic understanding of

A) how gravity exist as we understand it

B) How gravity affects Time relative to earth.

C)What happens to Time trapped in between 2 large gravitational "fields"

D)What Makes up gravity particle, wave or both.

 

I think this thread has satisfied my curiosity to a point that I can comprehend and I thank you.