Time travel

[waitedavid137]

I thought it might be of interest to derive the first order differential equation for time travel for geodesic motion through a charged nonrotating black hole. Though physically realistic black holes in nature will be of little if any charge, but of extreme spin, the result and math is far more messy but gives similar results to that of a charged nonrotating hole, and its worked out most simply the same way, so this will be the case of a charged but nonrotating hole. No black hole in nature will be Schwarzschild. They will be Kerr like and any radiative aspect will be Vaidya like. As such dump anything you ever worried about from Susskind and Hawking. Neither ever once ever mention Vaidya, because they didn't understand what he did, and because he utterly undermines their publications. Anyway, the nonrotating but charged hole, Reissner-Nordström, solution is

Now the metric elements read off the elements of the coordinate differentials here are all independent of time. Now I know no one here, and hardly any physicists, knows Noether's first name for the same reason that they don't know Vaidya's but do know Einstein and Hawking's first names, so look it up if you feel the need, but anyway in accordance with her theorem that means there is a timelike Killing vector

for that isometry in the metric yielding as a constant of the geodesic motion of

Here

is merely what I name that constant where this

is often called the conserved energy parameter of geodesic motion. In the case that it is far enough from the hole to neglect the mass and charge terms, it is equal to the

of special relativity. Since the metric is diagonal there is only one element corresponding to the nonzero element of that Killing vector that contributes to the sum

Which results in

simplified

QED

 

[Shadowprophet]

There is another relatively easy way to journey to the future utilizing general relativity. If you recall, we saw that the spacetime metric equation was dependent on the matter content in that spacetime region. The German physicist Karl Schwarzschild was the first to work out a solution for the spacetime surrounding a static spherical mass. This is the metric he derived, and it bears his name.

Would not Latex, For whatever reason. Could be something I'm missing ... IDK, Not perfect :/

Where G is the universal gravitational constant and M is the mass inside the spherical distribution. Notice that the metric is in spherical coordinates, t, r(radius from the origin), theta and phi. From this metric, a relation between proper time and coordinate time can be found in the same way as before. That relation is

The form of this time dilation formula is nearly the same as that for the special relativistic case. The critical parameter now is the radial distance, r, from the mass, M. A person very far from the surface of the mass will measure a different time than a person close to the mass. Indeed this effect has been measured on Earth. Atomic clocks placed in a basement of a very tall skyscraper ran slower than clocks on the top floor by billionths of a second. In order to get significant time travel effects from this, we need a stronger gravitational field. There is a critical radius in the Schwarzschild metric like the critical velocity of the previous example. It occurs at r = 2GM/c^2

 

[Thomas R. Morrison]

There is another relatively easy way to journey to the future utilizing general relativity. If you recall, we saw that the spacetime metric equation was dependent on the matter content in that spacetime region. The German physicist Karl Schwarzschild was the first to work out a solution for the spacetime surrounding a static spherical mass. This is the metric he derived, and it bears his name.

Would not Latex, For whatever reason. Could be something I'm missing ... IDK, Not perfect :/

Where G is the universal gravitational constant and M is the mass inside the spherical distribution. Notice that the metric is in spherical coordinates, t, r(radius from the origin), theta and phi. From this metric, a relation between proper time and coordinate time can be found in the same way as before. That relation is

The form of this time dilation formula is nearly the same as that for the special relativistic case. The critical parameter now is the radial distance, r, from the mass, M. A person very far from the surface of the mass will measure a different time than a person close to the mass. Indeed this effect has been measured on Earth. Atomic clocks placed in a basement of a very tall skyscraper ran slower than clocks on the top floor by billionths of a second. In order to get significant time travel effects from this, we need a stronger gravitational field. There is a critical radius in the Schwarzschild metric like the critical velocity of the previous example. It occurs at r = 2GM/c^2

Dude, you totally lifted that from this blog article by Dr. Bryan J. Méndez at Berkeley:
Time Travel

 

[waitedavid137]

There is another relatively easy way to journey to the future utilizing general relativity. If you recall, we saw that the spacetime metric equation was dependent on the matter content in that spacetime region. The German physicist Karl Schwarzschild was the first to work out a solution for the spacetime surrounding a static spherical mass. This is the metric he derived, and it bears his name.

Would not Latex, For whatever reason. Could be something I'm missing ... IDK, Not perfect :/

Where G is the universal gravitational constant and M is the mass inside the spherical distribution. Notice that the metric is in spherical coordinates, t, r(radius from the origin), theta and phi. From this metric, a relation between proper time and coordinate time can be found in the same way as before. That relation is

The form of this time dilation formula is nearly the same as that for the special relativistic case. The critical parameter now is the radial distance, r, from the mass, M. A person very far from the surface of the mass will measure a different time than a person close to the mass. Indeed this effect has been measured on Earth. Atomic clocks placed in a basement of a very tall skyscraper ran slower than clocks on the top floor by billionths of a second. In order to get significant time travel effects from this, we need a stronger gravitational field. There is a critical radius in the Schwarzschild metric like the critical velocity of the previous example. It occurs at r = 2GM/c^2

That time dilation formula from the blog from which you got it, relates time for a clock held stationary at constant r to that of one identical removed to a remote location for a Schwarzschild hole. The formula I gave is for geodesic motion, not stationary, and for a Reissner-Nordström hole.
If the clock near the hole is held stationary with respect to a Reissner-Nordström hole then the result would have been

I'm more interested in something falling through the spacetime, not held stationary in it, so its not that one which is interesting. What you want to do is look at something that falls through the multiply connected space time of either the RN hole or Kerr's.

 

[Shadowprophet]

Dude, you totally lifted that from this blog article by Dr. Bryan J. Méndez at Berkeley:
Time Travel

Oh yes I absolutely took that from a page I was reading Yes I'm studying this. in fact, if you read the first paragraph it even says it's Karl Swartzchilds original equation, The deal is, it's somewhat relevant, The thing is, People, can grab a news article, But for convenience sake they can't grab something along the lines of a time travel thesis? is there a difference?

 

[Shadowprophet]

It's like someone drives up in a car, and someone else says, Hey shadow you didn't build this car by hand. Well, That's not the point, is it? I wanted to illustrate that there were different methods of proposed time travel in strong gravitational fields. it was late and I took a shortcut. Bad Shadow, Bad lol Still though, I assumed you guys immediately knew this, I also assumed it wouldn't be an issue of any sort.

 

[wwkirk]

I'm not learned in science, but I just wanted to mention that any method of time travel will have to involve precise movement through space. This is because the earth and solar system don't stay in the same place over time. HG Wells style time travel misses this nuance. (Though he can be excused as he was a pioneer of the genre.) Legends of Tomorrow's Wave Rider gets it right.

Don't mind me; just piping in.

 

[Shadowprophet]

Fine, Fine fine fine, I want you guys to know, Latex is a huge pain in the ass, But I will use it to please you guys.

Okay, Now my functions and applications are probably off, But we will need to discuss Kerrs Metric and get into Ring singularities When it comes to Roy Kerr, Ring Singularities and his Metric are all I'm studied on so if this somehow does not apply,
Pft, Damn, I'm not God... In Kerr's Metric, You first need to get an idea of the Structure of Spacetime. You need to assign coordinates So the Metric uses X, Y, Z, And T You know, Height width depth and time, Pretty much standard calculus.

In this example

Then

Which resolves to

That's the family of ellipsoids While the principal curvature component is

The hyperboloids give

And boom Ring singularity.

The problems here, I don't think these compiled correctly in latex. Secondly, It's easier to talk about statutes than create them from scratch. Just saying though. upon inspection, I am certain they didn't compile correctly, oh well maybe it's still legible

 

[Shadowprophet]

some people are naturals at this, I am not, This shit is hard yo, It's stressful. I like a challenge that's why I'm here. But damn, I'm not going to pretend this is my second language, It's simply not lol it takes me time with this stuff, I can't just flow it out as you guys can.

I envy the people who can just process this without a vast amount of study time. for me though, This is like translating a language it takes me a few minutes So sorry if I come off stressful in this whole thing. The truth I can tell is, I have to push to grasp this shit. And I do grasp it, at the cost of stress headaches.

I don't know if you guys are aware, This is really high-level shit here. it takes me a few minutes.

 

[wwkirk]

some people are naturals at this, I am not, This shit is hard yo, It's stressful. I like a challenge that's why I'm here. But damn, I'm not going to pretend this is my second language, It's simply not lol it takes me time with this stuff, I can't just flow it out as you guys can.

I envy the people who can just process this without a vast amount of study time. for me though, This is like translating a language it takes me a few minutes So sorry if I come off stressful in this whole thing. The truth I can tell is, I have to push to grasp this shit. And I do grasp it, at the cost of stress headaches.

I don't know if you guys are aware, This is really high-level shit here. it takes me a few minutes.

Do you have a physics or higher mathematics background?

 

[Shadowprophet]

Do you have a physics or higher mathematics background?

Yes, I studied at Tennesee Tech for three years. You have to concede though These subjects with time travel and Kerr metrics, these are masters thesis material. It's a high level even in the high levels brother. one could go as far as to say, They are extravagant, To truly fully grasp some of these theories, It's beyond standard college-level education. in most cases.

Sometimes though, In some of David's math, He takes concepts I understand and applies in ways I fully do not understand. I need more context in some cases. it could be my refusal to accept Gr, But it's also in the applied mathematics category. He's applying in ways I've never seen it done before. It's not that it's incorrect, It's that I've not seen it applied in this way, It's like he knows a form of application That I just never learned.

 

[Shadowprophet]

He's apparently studied mathematicians and concepts I've literally never encountered. And that's fascinating, and stressful lol. Believe me, I'm not calling BS,

I'm just trying my best to keep up. Most people by far will back away when the equations begin flying around, That's no way to learn, the learning comes from the Math, It explains the function. So one is posed with this decision, Back away because it's getting difficult. Or grasp it.

It's his equations. They aren't someone else's, He's not ripped them from anywhere. You can see Roy Kerr's influence. But those are his. It's kind of amazing actually.

There are people who can do the Math, Like me, I can do the math. Then there are people who can formulate the math. I'm here to learn from these guys, I can only benefit from this.

 

[Shadowprophet]

Hey, David? I was looking up Multiply connected space as you suggested, And I found this,

Multiply Connected -- from Wolfram MathWorld Are you this same Whitehead guy?

 

[Shadowprophet]

I'm reading up on a guy called Hermann Minkawski who is speaking about the four-dimensional manifold with a flat metric signature of (+----) in which in the vacuum of space Light signals with Null curves as

<--- sorry the image latex output was that size,, anyway, I'm really not God, So can one of you please explain this Time manifold thing to me? I mean I understand the dimensional theory, But Theories for Time Manifolds, Yeah, I may be able to conceive something, But How many theories for time manifolds are there and where Can I read more on them.

By the way, This whole thing was dated into the early 1900s to it may be Irrelevant. I was just curious about the time manifolds thing.

 

[Shadowprophet]

I just had some gripes with LateX I had to work out. stress resolved

Gibberish? I think not, lol

 

[waitedavid137]

... we will need to discuss Kerrs Metric ...

Ok, but I'll warn you its much more complicated mess in the math that yields essentially the same answer, that something travels back in time if it is in geodesic motion between the two horizons.
So consider Boyer-Lindquist coordinates and I'll define the following terms

The spacetime is

To be continued...

 

[Shadowprophet]

Ok, but I'll warn you its much more complicated mess in the math that yields essentially the same answer, that something travels back in time if it is in geodesic motion between the two horizons.
So consider Boyer-Lindquist coordinates and I'll define the following terms

The spacetime is
View attachment 9544
To be continued...

Thank you, I may not immediately grasp this, I admit, This kind of math isn't something I can just immediately glance over and read, I have to study it But I promise I'm the kind of guy that will study this vigorously until I have a grasp of it bro

 

[waitedavid137]

Hey, David? I was looking up Multiply connected space as you suggested, And I found this,

Multiply Connected -- from Wolfram MathWorld Are you this same Whitehead guy?

Actually I was rerferring to the Penrose extension for a charged/rotating hole. So consider the diagram

Consider region I our universe external to a charged rotating hole. The line separating I from III is the outer horizon of the hole. Motion for an infalling test mass must lay between vertical and 45 degrees from vertical. The line separating region III from IV is the inner horizon. The line separating region IV from region VI is another inner horizon, and the line separating region VI from VIII is another outer horizon. Region VIII is external to the hole. Given the only constraint on the motion I mentioned, there is nothing stopping something falling from going from region I external to the hole to region VIII external to the hole, or even VII external to it for that matter. But while it is in region III and VI according to the time travel equation for the spacetime, it is traveling back in time.

 

[waitedavid137]

I'm reading up on a guy called Hermann Minkawski who is speaking about the four-dimensional manifold with a flat metric signature of (+----) in which in the vacuum of space Light signals with Null curves as

<--- sorry the image latex output was that size,, anyway, I'm really not God, So can one of you please explain this Time manifold thing to me? I mean I understand the dimensional theory, But Theories for Time Manifolds, Yeah, I may be able to conceive something, But How many theories for time manifolds are there and where Can I read more on them.

By the way, This whole thing was dated into the early 1900s to it may be Irrelevant. I was just curious about the time manifolds thing.

So imagine that the surface of a chair is a curved 2d surface imbedded in our 3d space. A 2d creature constrained to its surface may come up with 2d coordinates for his region on the surface. The coordinates may or may not be designed to cover the entire surface as he can not conceive of the 3rd dimension in which his chair's surface is imbedded. The entire surface of his experiencable universe is the entire surface of the chair, his universe's manifold, but his coordinates that he comes up with to describe a region around him may or may not cover the entire manifold. For us we live in a curved spacetime of 1 time and 3 normally conceivable dimensions of space. Our spacetime can in an analogy be described as a manifold of some shape imbedded in some higher dimensional hyperspace. Our coordinates describing the spacetime around us may or may not be designed in such a manner as to cover that entire manifold. That is the only thing important to know about what our manifold is about and beyond that those physicists that use the term manifold to often tend to not understand relativity at all, but rather think of an absolute space which is something that does not describe our spacetime at all.

 

[waitedavid137]

Ok, but I'll warn you its much more complicated mess in the math that yields essentially the same answer, that something travels back in time if it is in geodesic motion between the two horizons.
So consider Boyer-Lindquist coordinates and I'll define the following terms

The spacetime is

To be continued...

Defining three more functions of the coordinates,

The solution can now be expressed

The metric tensor elements can be read off as the coefficients and the elements that we will need are

To be continued...