A new model for General Relativity.

[ajb]

My rationing is, Couldnt Newton tell us everything we know about the physics of golf? Did GR effect those types of things?

For a standard golf ball moving at typical golf ball speeds standard classical mechanics will do a good job. Corrections due to relativistic effects are going to be so small you will not measure them.

[Mordred]

Lol why a BH spins is the same reason a planet does or a sun.

 

Same rules conservation of angular momentum.

 

The chances of having a non rotating BH is nearly nil. Possible but highly unlikely.

 

Any star that collapses into a BH will have a higher rate of spin just like the figure skater that pulls her arms into her body.

 

The article I posted on the accretion disk covers angular momentum extensively.

[elfmotat]

But im asking about the moment of impact...an event horizon...at that moment, all the physics it took to get there dont matter...we have an impact with direction and force....if we do this in a vacuum, are there any other forces effecting that reaction?

 

I know that I, along with at least one other person (Strange I believe), already stated in this thread that nothing special happens at the event horizon. There is no "impact." You would pass right through without noticing a thing. Passing through the event horizon just means that you would have to move faster than light to escape.

 

It's like a boater in a river approaching a waterfall -- the closer he gets to the edge, the faster the water flows. Eventually, when he gets close enough, the water flows faster than the boat's top speed -- he has passed a point of no return and will inevitably fall off the edge of the waterfall. Nothing special happens at this point, just like nothing special happens at the event horizon.

Edited January 13, 2015 by elfmotat

[JohnSSM]

Lol why a BH spins is the same reason a planet does or a sun.

 

Same rules conservation of angular momentum.

 

The chances of having a non rotating BH is nearly nil. Possible but highly unlikely.

 

Any star that collapses into a BH will have a higher rate of spin just like the figure skater that pulls her arms into her body.

 

The article I posted on the accretion disk covers angular momentum extensively.

So Mordred, you are referencing all that stuff we talked about and we no longer need golf or pool...You know im trying to learn about BHs...Im still looking for confirmation or otherwise on a couple subjects within the Schwartzchild radius discussion.

 

There was only 1 conclusion that I could draw from hearing that the theory needed a "non rotating, symmetrical sphere"...and the conclusion I drew was that an object without perfectly round symmetry would always spin while in space-time...even if acted upon by no other force...it made sense to me, with my understanding of GR, that the forces of an object itself can cause its own spin...and the only thing that could keep itself balanced in space-time without incurring its own spin, was a perfect sphere...and you may really have to reach to understand this, but, if an object were perfectly spherical and its Schwartzchild radius was figured for...then we just changed the shape of the object by a hair out of symmetry, it would incur spin and we would have to reduce the schwartzchild radius.

 

 

One other small thing and my current confusions about Schwartzchild will be clear...

 

Does "r", which is used in the equations, stand for the radius of the mass? Or the radius of the schwartzchild "effect"?

 

It seems there is an effect, that when the density of a mass is increased by lowering its volume to the schwartzchild radius, an EH is created, making a BH....BUT...does that EH occur at the radius of the mass? or somewhere else in space? and which one is then referred to as the schwartzchild radius....

 

even after a couple very compete diagrams, I never saw the representation of the mass/volume radius...

 

I know that I, along with at least one other person (Strange I believe), already stated in this thread that nothing special happens at the event horizon. There is no "impact." You would pass right through without noticing a thing. Passing through the event horizon just means that you would have to move faster than light to escape.

 

It's like a boater in a river approaching a waterfall -- the closer he gets to the edge, the faster the water flows. Eventually, when he gets close enough, the water flows faster than the boat's top speed -- he has passed a point of no return and will inevitably fall off the edge of the waterfall. Nothing special happens at this point, just like nothing special happens at the event horizon.

In the case of the golf ball, do you see the moment of impact when the club hits the ball as the EH?

In my theoretical BH, when one even approaches the EH the forces of gravity have allready smashed you down without impacting anything....

 

If the theoretical spaceship go could through it and survive the forces, i guess nothing would happen...and nothing i can estimate with my ideas...When my "foam" is smashed down to nothing, all the forces change and would remain unknown to us...

 

Do remember though...I do not even know if my logic works even in my head...

[Strange]

There was only 1 conclusion that I could draw from hearing that the theory needed a "non rotating, symmetrical sphere".

 

The "theory" (in the general sense) doesn't require a non rotating, symmetrical sphere. Only the Schwarzschild solution to the equations of GR require that. There are other solutions that describe a rotating sphere, a charged sphere, a rotating charged sphere, a homogeneous distribution of mass, and so on.

 

..and the conclusion I drew was that an object without perfectly round symmetry would always spin while in space-time...even if acted upon by no other force...

 

You could have a non-spinning object as well. There is no theoretical reason why not.

 

Does "r", which is used in the equations, stand for the radius of the mass? Or the radius of the schwartzchild "effect"?

 

It is the distance from the center. The specific value r_s refers to the Schwarzschild radius.

 

It seems there is an effect, that when the density of a mass is increased by lowering its volume to the schwartzchild radius, an EH is created, making a BH....BUT...does that EH occur at the radius of the mass?

 

The event horizon occurs at a radius, the Schwarzschild radius, which is proportional to the mass: double the mass and you double the Schwarzschild radius.

 

If the mass is concentrated inside the Schwarzschild radius, then it will be a black hole. In this case, the mass will be inexorably crushed to a radius of zero.

 

In my theoretical BH, when one even approaches the EH the forces of gravity have allready smashed you down without impacting anything....

 

If you are describing the tidal forces, then these would tend to tear you apart rather than crush you. And would be greater for a small black hole.

 

When my "foam" is smashed down to nothing, all the forces change and would remain unknown to us...

 

This is certainly true within the black hole. Once matter gets inside it will, according to GR, be crushed to zero size. It is generally assumed that this may not be realistic and that there may be other (quantum?) effects that prevent this. But we have no idea what they might be.

 

For example, string theory describes black holes as "fuzzballs": https://en.wikipedia.org/wiki/Fuzzball_%28string_theory%29

 

And some recent work suggests that quantum effects may mean that the event horizon itself is not well defined.

 

[JohnSSM]

Thats all pretty clear...

Im still trying to figure out if spin and momentum have to share a total amount of force when an impact occurs...or, when effected by gravity...I know how smart you are...you would have to be to understand what you understand...I was pretty thorough in my example with a golf ball...and...I know how smart you are...

This is apparently where we go back to discussing the 2 blocks impacting each other to account for this impact with direction and force, transferring a total amount of spin and force to another object depending on the angle of impact....Which is what I set out to find out and yet again what has not been covered....

And you know when i find out the answer about this effect on a ball, i will apply to it my knowledge of gravity's effect on a ball...are we both on the same page now? Cmon man...you know more math than me..lets leave it there and become equals in all other senses...

Didnt we say we allready figured each other out?

I do appreciate the info you did hand over to my lazy ass

Sorry strange...i thought was replying to Mordred...yall just pop in and start talking whenever you feel inspired...I need to pay more attention to the little icons...sorry again...

Theres another good reason to pay someone...they are one...taking info form 3 different guys who probably dont agree on everything themselves is tough...ha

[Mordred]

Ok look at newtons three laws of motion

 

http://en.m.wikipedia.org/wiki/Newton's_laws_of_motion

 

These laws is what makes up the conservation of momentum.

 

F=ma.

 

Force and accleration is both vectors

Mass being scalar.

 

In the case gravity the acceleration is due to gravity.

 

What I recommend is to look for practice problems applying those three laws to first two bricks then to two balls like the pool table example.

 

Once you do that you will have understand how spin is induced due to gravity as it is completely explained by newtons laws of motion.

 

The vector calculus book I posted has numerous examples.

I'm heading back up North for field work for the week, so my online times will be limited to when I catch a connection.

[imatfaal]

...

I'm heading back up North for field work for the week, so my online times will be limited to when I catch a connection.

 

How many hours of sun do you get at this time of year? Leaves a lot of time for contemplating the eternal mysteries of cosmology...

[Mordred]

Roughly three. Good thing I bring textbooks to read.

Not as far north as my last trip lol

[JohnSSM]

Ok look at newtons three laws of motion

 

http://en.m.wikipedia.org/wiki/Newton's_laws_of_motion

 

These laws is what makes up the conservation of momentum.

 

F=ma.

 

Force and accleration is both vectors

Mass being scalar.

 

In the case gravity the acceleration is due to gravity.

 

What I recommend is to look for practice problems applying those three laws to first two bricks then to two balls like the pool table example.

 

Once you do that you will have understand how spin is induced due to gravity as it is completely explained by newtons laws of motion.

 

The vector calculus book I posted has numerous examples.

I'm heading back up North for field work for the week, so my online times will be limited to when I catch a connection.

Nice...A little review of those laws was good...

 

Field work? farming? Do you have a job in physics? Freelance scientist? coooool

[JohnSSM]

The little review of Newton turned into a massive five hour reading session...I had to read each sentence slowly, over and over...and often had to interrupt one concept, to go read about another that was being referenced.

Im a bit blown away with how much info I didnt have...and I wonder if things are actually as they appear to me with this new info...The vision hasnt so much changed as it has evolved...

I dont have much confidence in the things im about to say, but since they really address the original topic of this thread, I thought I would post them here...

It seems that Newton thought of space as just something that was being filled with varying moving masses. His space was essentially unmoldable. His inertial reference frames all "moved" together, and I did have to research what rectilinear meant...Space, in those terms truly does reside on a grid of equal coordinates which do not move.

The main shift that my perspective took, and I may be wrong in my description of it, is that Einstein no longer viewed space as a strict coordinate system. Which is to say, the coordinates of space are now dictated by the "things" within it and even perspective is a thing.

And the vision has changed...I dont see a square grid which is "waiting" for mass to enter it and change its nature. I see a round, or polarized grid emerging from every mass. There is no perfectly uniform grid with nothing or no mass within it. So, in theory, if the universe had only one mass within it and that mass was perfectly spherical, it would have no spin and space-time would radiate out from it in a "sunburst" pattern. Space-time is not a "thing" that has been "compressed", within a grid that already existed. If you remove our one mass, there is no grid and no relative positioning within it.

So Newton, it seems, did use a coordinate system for space that was always "square"...And you could view things as "god" seeing it all happen within the grid without reference or bother in creating a position to view it from, but then how could you know anything about the grid? And when you do stop being god and enter,space-time, it changes simply in accordance with your position in it. And it makes me think, Schroedinger's cat would have no mystery if you were also in the box.

Edited January 14, 2015 by JohnSSM

[ajb]

The biggest difference between Newtonian physics and Einsteinian physics is that in Newton's world space is not absolute, but time is, as where in Einstein's world neither space nor time is absolute.

 

Your comment on the coordinates is not quite right. In Newtonian physics space-time decomposes globally as [math]\mathbb{R}^{3} \times \mathbb{R}[/math]. You can then pick Cartesian coordinates (x,y,z,;t). These define for us inertial observers, and we can think of Newtonian physics as giving us a preferred class of coordinates on space. Though you can pick other coordinate systems say polar (r, theta, phi; t), but you have to be careful with effects such as fictitious forces when dealing with these other coordinates.

 

In Newtonian physics we have the Galilean transformations. With no details here these are the transformations that allow you to translate measurements from one inertial observer to another. But note that these transformations act on space only, time remains the same.

 

In special relativity, we do not have this God given decomposition into space and time. Space-time is [math]\mathbb{R}^{4}[/math]. Again I can pick Cartesian coordinates here and these define for me the inertial frames; (x,y,z,t). However, the Poincare transformations, which relate one inertial observer to another, now mix space and time. There just is not global splitting that everyone will agree on. Moreover, you are free to use other coordinate systems, but what special relativity says is that within all possible coordinate systems the inertial ones are a special class.

 

In general relativity we lose this special class of coordinate systems, apart from locally. In general we have no preferred coordinate systems and have to treat them all equally.

[JohnSSM]

The biggest difference between Newtonian physics and Einsteinian physics is that in Newton's world space is not absolute, but time is, as where in Einstein's world neither space nor time is absolute.

 

Your comment on the coordinates is not quite right. In Newtonian physics space-time decomposes globally as [math]\mathbb{R}^{3} \times \mathbb{R}[/math]. You can then pick Cartesian coordinates (x,y,z,;t). These define for us inertial observers, and we can think of Newtonian physics as giving us a preferred class of coordinates on space. Though you can pick other coordinate systems say polar (r, theta, phi; t), but you have to be careful with effects such as fictitious forces when dealing with these other coordinates.

 

In Newtonian physics we have the Galilean transformations. With no details here these are the transformations that allow you to translate measurements from one inertial observer to another. But note that these transformations act on space only, time remains the same.

 

In special relativity, we do not have this God given decomposition into space and time. Space-time is [math]\mathbb{R}^{4}[/math]. Again I can pick Cartesian coordinates here and these define for me the inertial frames; (x,y,z,t). However, the Poincare transformations, which relate one inertial observer to another, now mix space and time. There just is not global splitting that everyone will agree on. Moreover, you are free to use other coordinate systems, but what special relativity says is that within all possible coordinate systems the inertial ones are a special class.

 

In general relativity we lose this special class of coordinate systems, apart from locally. In general we have no preferred coordinate systems and have to treat them all equally.

"space-time decomposes globally as "

decomposes as in, fades away? no longer needed? and What is big R? ha

 

I must investigate transformations...I had just finished with Minkowski and Lorentz.

 

You can use different coordinate models and GR works for them all the same? Didnt see that coming...

If you have a pond that's totally still, and gravity works as other forces, mass or some property of mass, would seem to be perturbing the pond, to create gravity (gravity being the waves in the pond). If the field of space-time is only a product of mass's perturbations, then a "still" pond would represent no space-time (to me)...Since space-time has no defined field, the water in the pond, would not even exist. Its just a theoretical surface as space-time seems to be. The stone drops in the still pond...now there IS a field of space-time...the waves create the only field that exists since there is no water...i wanted foam, yall said no...for the same reason....it isnt there...it doesnt need to be...the pond needs no water and has none...but perturbations still create a field that we consider to be "space-time", with "gravity" seeming to be an added or after effect of space-time, when they really go hand in hand like forrest and jenny...peas and carrots...as soon as an object hits that pond it creates both the surface and the waves...cuz remember...no water...

Is it scientifically sound to say "the properties of mass and motion contribute fully to the effects of GR?"

[ajb]

"space-time decomposes globally as "

decomposes as in, fades away? no longer needed? and What is big R? ha

As in it is topologically given as a product; you can split it into space and time. By [math]\mathbb{R}^{n}[/math] I mean the standard coordinate space. Every point can be understood as a an n-tuple of real numbers (x1, x2, ..., xn).

 

 

You can use different coordinate models and GR works for them all the same?

All of physics has this property, but the situation maybe harder to understand in different coordinates.

 

If you have a pond that's totally still, and gravity works as other forces, mass or some property of mass, would seem to be perturbing the pond, to create gravity (gravity being the waves in the pond). If the field of space-time is only a product of mass's perturbations, then a "still" pond would represent no space-time (to me)...Since space-time has no defined field, the water in the pond, would not even exist.

A better analogy would be that the flat surface of the pond is more like space-time when the gravitational field is zero. Remember, it is not space-time that is the gravitational field, but its local geometry.

 

 

 

Is it scientifically sound to say "the properties of mass and motion contribute fully to the effects of GR?"

I suppose so, the energy-momentum tensor is the important thing here.

[JohnSSM]

As in it is topologically given as a product; you can split it into space and time. By [math]\mathbb{R}^{n}[/math] I mean the standard coordinate space. Every point can be understood as a an n-tuple of real numbers (x1, x2, ..., xn).

 

 

 

All of physics has this property, but the situation maybe harder to understand in different coordinates.

 

 

A better analogy would be that the flat surface of the pond is more like space-time when the gravitational field is zero. Remember, it is not space-time that is the gravitational field, but its local geometry.

 

 

 

 

I suppose so, the energy-momentum tensor is the important thing here.

Yes..I meant that the flat pond is like space-time with no gravitational field...And precisely because space-time is only local geometry that I claim there is no surface of water when it is still...the only surface we ever see is rippled,,,it doesnt even exist as flat...which is why I claim or view that space-time is only induced by the effects of gravity...

 

I should have been calling it the energy-momentum tensor all along...in my descriptive I only say things like "energy has a vector"...I was referring to the energy momentum tensor...In my amateur mind, it is vectors that come together to define tensors...

Edited January 15, 2015 by JohnSSM

[ajb]

Yes..I meant that the flat pond is like space-time with no gravitational field...And precisely because space-time is only local geometry that I claim there is no surface of water when it is still...the only surface we ever see is rippled,,,it doesnt even exist as flat...which is why I claim or view that space-time is only induced by the effects of gravity...

I would say that it would be better to think of the surface of the water as always being there. Gravity is not this surface, but rather the local shape of this surface. One could also think of the flow or movement of space with respect time also. This leads to nice analogies...

 

You could think of a pond skater (Gerridae) as a test particle, he can still skate along the surface of your pond when there is no ripples. He can just glide along as he pleases. On a river he can have problems unless he sticks to the calm eddies. Once out in the main flow he will be pulled down stream, unless he can overcome this flow. There are points on the river for which he can match the flow and stay stationary and other for which he can freely move up stream.

 

The flow of a river changes, and let us imagine that the pond skater lives in a calm steady flow and that he can without too much effort move up and down how little area. Now let us suppose that the flow gradually increases as he heads up stream. At some point no matter how hard he tries he cannot get any further up stream. The flow matches his top speed. He cannot pass this line in the river. He can see things flowing down to him from up stream, but he cannot reach where they have come from.

 

For example there may be another calm area up stream and another pond skater there that decides to skate down. This is no problem, the skater can just use the flow of the river to carry them down. So, let us suppose our second skater reaches the first skater. After some time our second skater wants to go home... now there is a problem.

 

The second skater, like the first one cannot pass this line in the river where they just cannot swim fast enough to get further up stream. The second skater can never return home. The second skater did not notice that some was special about this point in the river, he just sat back and drifted down.

 

You see we have a kind of 'black hole' in the river. Pond skaters can pass this special line in the river but only one way. Moreover, nothing special happens to the skater as they pass this line.

 

The warning is that this is an analogy and that to really see what happens to test particles in general relativity you need to do some mathematics.

[JohnSSM]

I dunno about that...even a test particle will ripple the surface...i think!

With EMFs, it seems that they are only present when something with magnetic properties exists...

With the Gluon field, it seems it is always there even when nothing is pertubing it...they say it has "vacuum energy"...

This is a chicken/egg question, in a way...does spacetime exist before there is mass to influence it? To me, the answer seems to be no...if space-time is defined by the energy-momentum tensor...without it being present, there would be no curved lines...but i also say there would be no lines...no reason to create lines in empty-space...

Earlier in this topic, I believe Mordred or Strange gave me examples of GR in empty space...But even if GR can be used to predict what empty space might be like, we can never encounter empty space...a truly empty universe simply doesnt exist...with no mass, there is no spacetime...or so my login says at this point...

I am putting off knowing questions and answers like this because there is way too much stuff with actuality and grit to be studied for me...but my current reason keeps pulling me in this direction...

[ajb]

I dunno about that...even a test particle will ripple the surface...i think!

But so little that it can safely be ignored. The pond skater does not exactly set the pond rippling like a constant gust of wind would.

 

With EMFs, it seems that they are only present when something with magnetic properties exists...

You are better off thinking of the field strength as being zero rather than there being no fields present at all. This is teh same as you should think in GR.

 

With the Gluon field, it seems it is always there even when nothing is pertubing it...they say it has "vacuum energy"...

You should think of all fields as always being there, well as much as you should think of fields as being real anyway.

 

This is a chicken/egg question, in a way...does spacetime exist before there is mass to influence it? To me, the answer seems to be no...if space-time is defined by the energy-momentum tensor...without it being present, there would be no curved lines...but i also say there would be no lines...no reason to create lines in empty-space...

It is impossible to answer this as one cannot in reality have a volume in space truly free of fields. Even of you classically minimise these fields you still have quantum fluctuations to take care of. Thus I cannot see a real meaningful answer here.

 

All I can say is that the formalism of relativity allow you to think of empty space-time, which is a good approximation in many physical situations.

 

Earlier in this topic, I believe Mordred or Strange gave me examples of GR in empty space...But even if GR can be used to predict what empty space might be like, we can never encounter empty space...a truly empty universe simply doesnt exist...with no mass, there is no spacetime...or so my login says at this point...

Lots of the exact solution to the field equations of GR are vacuum solutions. You are right, as I have said above that we can never really consider space as being empty of matter or fields, but for a lot of situations we get a good approximation to nature.

[JohnSSM]

I use an equals sign...is this not math?

IF spacetime is empty then mass value = 0
if mass value=0 then spacetime value=0
So, Empty spacetime = 0

Edited January 17, 2015 by JohnSSM

[ajb]

I use an equals sign...is this not math?

 

IF spacetime is empty then mass value = 0

if mass value=0 then spacetime value=0

So, Empty spacetime = 0

You need to define the left hand side carefully.

 

The mass of a space-time is in general not well defined, but under some conditions you have various notions here.

 

1. If the space-time is stationary, that is the metric does not depend on time, then you have the Komar mass. As the system has time translation symmetry, then Noether's theorem allows us to define an energy. Then using E = mc^2 we have a mass.

 

If the space-time is asymptotically flat then we have

 

2. The ADM mass

 

3. The Bondi mass

 

Both of these are similar, but the difference is how you define the 'infinity' that you use.

[JohnSSM]

Ill put those on the front of my reading list...

When I suggested earlier in this topic that spacetime did have it's "own" energy, i was arm-twisted into seeing it as "nothing" or at least as nothing that might influence GR beyond just being geometrically defined only by the properties of mass...and thats where i felt I took a real turn in understanding GR...

one step backwards, two steps backwards? ha! Ill get some forward motion soon

[ajb]

So space-time can have its own energy, just usually this is hard or impossible to define globally. Moreover, gravitational waves carry energy.

[swansont]

I use an equals sign...is this not math?

 

IF spacetime is empty then mass value = 0

if mass value=0 then spacetime value=0

So, Empty spacetime = 0

 

In the same sense that a Fisher-Price car dash having a steering wheel makes it a car. That is to say, no.

[JohnSSM]

 

In the same sense that a Fisher-Price car dash having a steering wheel makes it a car. That is to say, no.

I have no idea how that applies to this conversation...Im just trying to find the logic of giving something which is empty, a value which is based on whats inside it...

 

Like, an empty can of beans is said to have no beans...you dont claim to give it bean values because the can is made of something...and in the point of spacetime, there is no can as far as I know...there are only beans which create the shape of the can...no beans? no shape? no value, no can...

 

So space-time can have its own energy, just usually this is hard or impossible to define globally. Moreover, gravitational waves carry energy.

I get that...but gravitational waves are created by the properties of mass...IF we have empty space, where would gravitational waves come from?

 

space-time having its own energy blows my understanding of GR away...

[Strange]

I have no idea how that applies to this conversation...

 

It was a reply to this: "I use an equals sign...is this not math?"

 

 

Like, an empty can of beans is said to have no beans...

 

I'm not quite sure what the error/fallacy here is, but saying that the can (or spacetime) equals zero because it is empty is just meaningless. (Even if it contains an equals sign.)