# Thread: Would you like to help me interpret some equations I was pondering?

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## Would you like to help me interpret some equations I was pondering?

To start off, the gravitational parameter is given as

[1]

This is pretty standard, now I derived this form for the standard gravitational parameter

[2]

Seeing the energy in terms of quantum mechanics we can have

[3]

I don't think this has ever been written in this form and it occurred to me that simply solving for gives

[4]

The gravitational redshift is

[5]

where is the Schwarzschild radius. Plugging equation 4 into equation 5 yields

[6]

Interestingly, the quantity on the right hand side has yielded the gravitational fine structure, or also known as the gravitational coupling constant giving

[7]

Because

[8]

So how does someone interpret the gravitational time dilation formula with the gravitational coupling constant? Perhaps this is by no means a mistake it has appeared since the two undoubtedly have characteristics which play off each other. The Schwartzschild radius is sometimes set equal to the Compton wavelength, and loosely speaking the Compton wavelength describes when quantum effects take role in the presence of gravity... so as I speculated perhaps the way it appeared in the equation is not by a mistake.

If this is taking about quantum effects, since the use of the gravitational coupling constant has appeared in the equations and since the Schwarzschild radius is the radius of the gravitational field then perhaps the gravitational coupling constant is some kind of limit as well?

I have looked everywhere for a relation that is similar... and even equations that have some sort of Schwarzschild radius on one side and the constant on another but I cannot find anything in the literature anywhere. Also, there is very little literature to go on with the constant anyway in general, according to wiki.
Last edited by Aethelwulf; 2012-May-21 at 04:26 AM.

2. Originally Posted by Aethelwulf
To start off, the gravitational parameter is given as

[1]

This is pretty standard, now I derived this form for the standard gravitational parameter

[2]

Seeing the energy in terms of quantum mechanics we can have

[3]

I don't think this has ever been written in this form and it occurred to me that simply solving for gives

[4]

The gravitational redshift is

[5]

where is the Schwarzschild radius. Plugging equation 4 into equation 5 yields

[6]

Interestingly, the quantity on the right hand side has yielded the gravitational fine structure, or also known as the gravitational coupling constant giving

[7]

Because

[8]

So how does someone interpret the gravitational time dilation formula with the gravitational coupling constant? Perhaps this is by no means a mistake it has appeared since the two undoubtedly have characteristics which play off each other. The Schwartzschild radius is sometimes set equal to the Compton wavelength, and loosely speaking the Compton wavelength describes when quantum effects take role in the presence of gravity... so as I speculated perhaps the way it appeared in the equation is not by a mistake.

If this is taking about quantum effects, since the use of the gravitational coupling constant has appeared in the equations and since the Schwarzschild radius is the radius of the gravitational field then perhaps the gravitational coupling constant is some kind of limit as well?

I have looked everywhere for a relation that is similar... and even equations that have some sort of Schwarzschild radius on one side and the constant on another but I cannot find anything in the literature anywhere. Also, there is very little literature to go on with the constant anyway in general, according to wiki. A similar relationship can be derived:

[9]

Cancel out the on both sides gives

[10]

rearrange

[11]

substitute again for equation 4,

[12]

Multiply on both sides gives

[12]

And so we have retrieved the constant again. So any idea's how to interpret this? This one is a little different because it is not concerned with a gravitational red shift.
Offhand, I'd say there was an algebra error, going from 10 to 11?

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Hmmm let's see...

Yes... there is an error in that part. Thanks! I think the rest is fine, so ignore... the second part.

Cheers

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I've had to delete that part because I don't want to confuse anyone. That wasn't my intentions.

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I think I've got a new way to do that second part in my head, just gonna check it out first on paper.

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Cancel the R's

Showing this in a slightly different form

Now substituting with the same method before

this time we have only a slightly different derivation... do I have my units right... why does it look wrong?

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just checking the units on

the right hand side has dimensions of mass...

Does the Schwarzschild radius have dimensions of mass? That seems like a silly question because I would have believed it to have dimensions of length... so I do believe the derivation has to be wrong some where... I am clueless where I have messed up

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But,

doing the rearranging right this time,

That is definately right... so I am confused.com

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Originally Posted by Aethelwulf
But,

doing the rearranging right this time,

That is definately right... so I am confused.com
Two things. M should be squared, right? Which doesn't help you, because the Schwartzchild radius does have the dimension of length, and, IIRC, is dimensionless.

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Originally Posted by Tensor
Two things. M should be squared, right? Which doesn't help you, because the Schwartzchild radius does have the dimension of length, and, IIRC, is dimensionless.
No, the mass isn't squared there... and is the constant dimensionless? I didn't know that.

Thanks.

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Ahhh! I see. This is why you asked if the mass was squared... because if was dimensionless (which it is most obviously is now after checking the units), then

Doh! Totally missed that.
Last edited by Aethelwulf; 2012-May-21 at 06:09 AM.

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Originally Posted by Aethelwulf
No, the mass isn't squared there...
Oooops, I had looked at the wrong equation there for the squared M. But, as it helped you find your way, I guess it worked out.

Originally Posted by Aethelwulf
and is the constant dimensionless? I didn't know that.
Coupling constants for all the forces are dimensionless. Alpha for EM, as you probably know is ~1/137.

Originally Posted by Aethelwulf
Thanks.
Your welcome. Sorry for the confusion at the beginning.

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Yes, I probably should have cottoned onto the electromagnetic coupling constant since is the ratio .

14. Thread moved from the ATM forum, as it isn't (according to the OP) actually proposing an ATM claim. (Please do read the rules and advice threads (again)).

(The ATM fourm is not a place to simply discuss things that have an ATM slant. Nor is it the place to develop or discuss in general an ATM claim.)

If it turns out later the purpose of this thread was to push an ATM view, it'll be moved back.

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Originally Posted by Aethelwulf
[6]

Interestingly, the quantity on the right hand side has yielded the gravitational fine structure, or also known as the gravitational coupling constant giving

[7]
The right hand side is incorrect, it should be
giving

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In any case goes by mass and goes by mass squared, so there is definitely something wrong here.

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Originally Posted by caveman1917
In any case goes by mass and goes by mass squared, so there is definitely something wrong here.
The problem is because I am using dimensions that don't work - the fine gravitational constant is dimensionless. Well at least I think that is the problem Tensor established.

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