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Seiryuu
2008-Oct-12, 01:04 AM
A small math question. Can anyone tell me if I'm allowed to do the following:

Starting from a formula from Wikipedia
http://upload.wikimedia.org/math/a/8/2/a82acb0200bb91d7dabec509a3c5f0d4.png

where

t is time as calibrated with a clock distant from and at inertial rest with respect to the Earth,
r is a radial coordinate (which is effectively the distance from the Earth's center),
θ is the latitudinal coordinate, being the angular separation from the north pole in radians.
phi is a longitudinal coordinate, analogous to the latitude on the Earth's surface but independent of the Earth's rotation. This is also given in radians.
m is the geometrized mass of a central massive object, being m = MG/c2,

M is the mass of the object,
G is the gravitational constant.

When standing on the north pole, we can assume dr = dtheta = dphi = 0 (meaning that we are neither moving up or down or along the surface of the Earth)

Giving the following formula
http://upload.wikimedia.org/math/2/1/7/217d81c5cd35bcf723bd60b769c21f4a.png

So we have

dτ = dt(1 - 2GM/rcē)^1/2
dτ/dt = (1 - 2GM/rcē)1/2

I use the variable Td for the left part. So

Td = dτ/dt

And we get

Tdē = 1 - 2GM/rcē
2GM/rcē = 1 - Tdē
G = (1 - Tdē)rcē / 2M

Inserting it in F = GMm/rē we get

F = (1-Tdē)rcēMm/2rēM
F = (1-Tdē)cēm/2r

Which leads to

F = mcē(1-Tdē)/2r

Is this allowed or am I making some stupid errors here?

Ken G
2008-Oct-12, 08:18 AM
Seems fine to me, though what is less clear is why you would want to do that.

Neverfly
2008-Oct-12, 08:29 AM
Seems fine to me, though what is less clear is why you would want to do that.

The cancellations and such are fine.
Over-all, it looks good but
The Td throws me for a loop.

As well as that the purpose seems undefined except for support of his idea that motion is the cause of gravity. I'm not dragging ATM into the thread- actually suggested this Q&A thread- But I admit I spent all day on this one looking things up too.

ETA: Let me clarify- It looks like misapplication to me. Sure, they cancel out- and he has corrected his variables. But...

Ken G
2008-Oct-12, 09:14 AM
Yes, one must be careful when intepreting equations. At one level, all they are is statements of mathematical necessities, not logical causalities. A random example of this is if I write Newton's law for a constant mass as M = F/A, I might imagine that I have figured out the logical origin of mass-- if I group a bunch of processes together that have the same acceleration, then the mass is basically given by the forces applied within each group. So mass comes from the force applied in that group. But logically, mass exists prior to and independently of the forces applied, it's just a weird way to group the information to make it sound like a certain conclusion is warranted when in fact it was all just a mathematical necessity being interpreted as having logical content.

Neverfly
2008-Oct-12, 09:41 AM
Yes, one must be careful when intepreting equations. At one level, all they are is statements of mathematical necessities, not logical causalities. A random example of this is if I write Newton's law for a constant mass as M = F/A, I might imagine that I have figured out the logical origin of mass-- if I group a bunch of processes together that have the same acceleration, then the mass is basically given by the forces applied within each group. So mass comes from the force applied in that group. But logically, mass exists prior to and independently of the forces applied, it's just a weird way to group the information to make it sound like a certain conclusion is warranted when in fact it was all just a mathematical necessity being interpreted as having logical content.

Ahh MUCH better wording than I could ever have come up with.

Seiryuu
2008-Oct-12, 09:48 AM
While that is true, writing M = F/A will not change the value of M if we assume that the first is constant. It's the value of F/A that will change. So, writing it like this does not result in any erroneous reasoning.

The reason I'm writing it like this, is because I think there's a relation between gravity and time dilation and yes, I am turning the assumption that time dilation is caused by gravity upside down, because it has important implications and I feel that it seems no one has ever considered this before as to what is the cause and what is the effect.

While we know that mass can exist independant of the forces applied, this has not been proven for gravity as well. It's part of what I'm proposing and I may be wrong of course, but one has to at least consider the possibility. IF gravity is caused by time dilation instead of the other way around, then things are getting a lot more interesting as this opens up options that are otherwise not available.

Neverfly
2008-Oct-12, 09:50 AM
While that is true, writing M = F/A will not change the value of M if we assume that the first is constant. It's the value of F/A that will change. So, writing it like this does not result in any erroneous reasoning.

The reason I'm writing it like this, is because I think there's a relation between gravity and time dilation and yes, I am turning the assumption that time dilation is caused by gravity upside down, because it has important implications and I feel that it seems no one has ever considered this before as to what is the cause and what is the effect.

While we know that mass can exist independant of the forces applied, this has not been proven for gravity as well. It's part of what I'm proposing and I may be wrong of course, but one has to at least consider the possibility. IF gravity is caused by time dilation instead of the other way around, then things are getting a lot more interesting as this opens up options.

How do you know that no one has thought of it?

Seiryuu
2008-Oct-12, 09:53 AM
I don't. I wrote "I feel that it seems"... :p

All I know is that gravity cannot exist without time dilation, but time dilation can exist without gravity, due to motion.

On a side note, I just want to express my appreciation for the effort you are willing to put up on my behalf, Neverfly.

WaxRubiks
2008-Oct-12, 10:01 AM
perhaps one does not cause the other, but they are just connected.

Neverfly
2008-Oct-12, 10:02 AM
On a side note, I just want to express my appreciation for the effort you are willing to put up on my behalf, Neverfly.

Oh, it's no problem.
You know how mothers are...
Cuz, she called me up and you know... said, "I know my baby is strange.. but give him a chance.. he's a good boy..."
......

Ok actually, nevermind. Maybe you don't need to know all that - uhhh...
:doh:

anyway yeah- glad to help in whatever way I can...

Seiryuu
2008-Oct-12, 10:04 AM
Agreed, any connection would make the question as to what is the cause and what is the effect rather obsolete. But if there's a connection, I reckon it should be no problem to write a gravitional pull in terms of a parameter Td instead of the constant G.


You know how mothers are...

I should have known. She can be quite persuasive you know! :p

Neverfly
2008-Oct-12, 10:08 AM
I should have known. She can be quite persuasive you know! :p

Actually, Ben Franklin was but hey... Not one to deny credit for efforts...

Seiryuu
2008-Oct-12, 10:09 AM
Think he could help me out with this math question?:lol:

*cough* we're getting off topic!

Neverfly
2008-Oct-12, 10:10 AM
Think he could help me out with this math question?:lol:

*cough* we're getting off topic!

Maybe. Could cover one book.

Or he can make it possible for you to totally forget the question too if taken to the right place...

Seiryuu
2008-Oct-12, 10:11 AM
What question?

...

Oh this one (http://www.bautforum.com/questions-answers/79931-math-question.html#post1341506)!

Now back in the cage so we can study the math!

Ken G
2008-Oct-12, 12:51 PM
IF gravity is caused by time dilation instead of the other way around, then things are getting a lot more interesting as this opens up options that are otherwise not available.Actually, the idea that gravity can be thought of as a form of spatially varying time dilation is not new. I've seen Feynman use it, for example. Now, having an idea in common with Feynman is nothing to feel unhappy about, but Feynman didn't point it out to say that time dilation "comes first" and gravity "second", as all this means is that the two come together. The real issue is that Feynman was offering a different way to picture gravity than spacetime curvature-- he offered the completely equivalent picture that gravity comes with a spatially varying time dilation.

You see, the point is we have two ways to picture gravity, curvature or time dilation, where the first is very geometric and the second is more mechanistic, but the issue is never which is right or whether gravity causes them or they cause gravity, because there is no way to test any of this independently. They all come together, in one big basket-- the value of thinking about them is simply to grasp all of the connected ramifications, because it lets you decide how you favor thinking about the phenomenon.

Seiryuu
2008-Oct-12, 01:24 PM
I have no problem with that explanation that they come together. In fact, I can pretty much agree to it.

Maybe I should explain further. The purpose of this equation was to show a connection between gravity and time dilation and the fact that they cannot exist without eachother, since you can always replace G in the equation for gravity with the parameter Td from the equation of gravitational time dilation. This means that if you know G, you can calculate Td, but also the other way around: if you can measure the time dilation, it should be possible to calculate G from it.

This leads me to believe that either time dilation or whatever is responsible for time dilation is responsible for gravity and hence gravity is not the cause but rather the effect. You are right though, I cannot conclude that this is true from the math alone, but I can conclude that it is a possibility. It depends on how you want to look at it.

I cannot discuss my theory here, as it's probably ATM, but what I'm proposing is very similar to what you describe. I offer two ways of picturing gravity and try to relate them together. However, I don't make a distinction between time dilation and spacetime curvature. For me, they're one and the same thing and part of the same "combined picture" so to speak. I do try to relate spacetime curvature to something else though, but I need the phenomenon of time dilation to do it, as it plays a crucial role. Without time dilation, I cannot relate it. :)

mugaliens
2008-Oct-12, 09:56 PM
Seems fine to me, though what is less clear is why you would want to do that.

Perhaps he knows an elf at Santa's North Pole workshop who's on unemployment due to the economic slowdown...

Seiryuu
2008-Oct-12, 10:07 PM
Why, as a matter of fact, I do! :p