Reflecting on the physics of Gravitational metric

Trapped is talking about \(1 + z = \sqrt{\frac{g_{tt}(receiver)}{g_{tt}(source)}}\)

Trapped is right, brucep (and you are wrong)
\(1 + z = \sqrt{\frac{g_{tt}(receiver)}{g_{tt}(source)}}\) is indeed gravitational redshift, it falls out straight from the metric.

 

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Hi Bruce,

How's it going? Well, I hope. Just a simple/trivial note; 1 + z is not cosmological redshift, z is. It's a waste of time trying to convince him of this fact. Let them believe what they want to. They've proven to have a high capacity for ignore facts in front of them.

It’s good to see that you’re still posting online. We’ve had our differences in the past but those are fading. You’re increase in knowledge since I first met you is impressive. Well done.

 

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No, z can be different types of shift. The context is established by the RHS of the expression. See here. In the case of \(1 + z = \sqrt{\frac{g_{tt}(receiver)}{g_{tt}(source)}}\) , z clearly represents gravitational redshift. Trapped is right (in this instance).

 

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Now you are not even using your own arguments, someone else said this the other day and it was terribly wrong.

Someone said (1+z) is the cosmological shift and not the gravitational redshift. I corrected them as I corrected you:

(1+z) is also the expression for the gravitational resfhift where z takes on different shift roles.

cosmological shift

\(1+z = \frac{a_{now}}{a_{then}}\) 1.

gravitational redshift

\(1+z = \sqrt{\frac{g_{tt}(r)}{g_{tt}(s)}}\) 2.

The RHS of eq. 2 is a ratio of lengths \(\frac{\lambda}{\lambda_0}\) and so is equation 1. on the RHS which describes the proper lengths of the scale factor.

 

Glad someone appears to know what they are talking about.

 

Just a quick summary.

We established that Motz is indeed talking about the \(g_{tt}\) of the metric;the author of the modified work has written it for a metric charge and also for the ratio of the \(g_{tt}\) components which gives rise to the redshift.

Now that we have allayed the misconception of Brucep which was on repeat-mode anyway, we can see there is nothing wrong with the algebra either as was claimed by Origin.

 

But the ratio of the \(g_{tt}\) values is not physically relevant to every pair of locations even in the Schwarzschild geometry.
Motz correctly uses part of the metric because he knew something about the space-time vectors he was evaluating.
While you, Trapped, present the appearance of quote-mining good sources on a topic on which you know nothing. You called one frame-dependant component of the Schwarzschild metric "the metric" and even now you don't use the correct terminology for a component of a tensor field when understanding General Relativity requires understanding tensors. You also didn't acknowledge that you characterized that component as "the strength of the gravitational field" which was disputed. Your claim fails because your term shrinks the closer you get to a gravitational source. That's not even tensor analysis -- that's simple algebra.

You need to quit the bloviating and quit your reliance on authority (and purported authority) for matters you don't understand. Otherwise you will be "Trapped" in ignorance and uselessness and have the reputation to match.

 

For lo these many years Trapped in his various personas has remained constant in his mining of topics he does not understand and puking out random equations to cobble together using high school algebra while employing a complete disregard for logic or physical realities in the mistaken thought that he is dazzling us all with his intellect. Go figure...:shrug:

 

Yet the author also found the relationship

\(j* = \frac{ \epsilon(\lambda) \sigma T^4}{(\frac{\sqrt{1 - 2\frac{Gm}{\Delta E_{rec}} \frac{M}{r} + \frac{GQ^2}{c^4 R^2}}}{\sqrt{1 - 2\frac{Gm}{\Delta E_{sou}} \frac{M}{r} + \frac{GQ^2}{c^4 R^2}}})^2}\)

simply from the luminosity and the bolometrix flux

\(f = \frac{L}{4\pi R^2 (1+z)^2}\)

Which suggests this kind of set-up isn't totally out of bounds. We are also using the same arguments as Motz - the same argument is the equivalence principle.

 

That's right pmb. Thanks for pointing that out. Really, we shouldn't have any disagreements beyond some intellectual difference of opinion while having a discussion. I've been reading the thread on the uncertainty relationships.

 

Thanks for pointing that out?

Willing to forget your own mistake, you do realize this is a mistake of it's own? pmb has been corrected a few times concerning the idea that there is only one z (shift) and that it isn't cosmological.

I don't need to explain yet again, that the cosmological shift and the gravitational shift are 1+z with different z as the shifts. This is what means to be scientific, as close to the truth as possible brucep. Just liking posts because they seem at conflict with this post won't make you look better either. No amount of kissing Rpenners behind or liking pmb's posts will rectify the fact that a lot of people here have actually said a lot of bad science.

 

I can't recall now why I said that. Perhaps because I've never seem it used in any other context than cosmological redshift. I suspect Bruce said it for the same reason. Just to keep an open mind I e-mailed an authority I know on the subject and will wait until I hear back from him before I do anything. Until then if you can prove your claim then I'm all ears. However I don't accept Wiki as a valid reference. I use them quite often and respect it but in this case I find it suspect.

 

Bruce – I’ve never seen z used to refer to gravitational redshift before, only cosmological redshift. That’s why I took the position I did. However I was reviewing all of this when I looked at the Wiki reference given by Tach. It indicates that z is also used to refer to gravitational redshift too. I’ve never seen this before. Given Trapped’s poor reputation it almost seemed natural to disagree with him. After all, how can anybody who claims that g[sub]tt[/sub] is the metric be taken seriously? Lol!! When rpenner wrote While you, Trapped, present the appearance of quote-mining good sources on a topic on which you know nothing. he sure hit the nail flat on the head, didn’t he?

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But that’s no reason to ignore Wiki. So I e-mailed a friend who knows GR and cosmology very well. He’s been published the much esteemed journal American Journal of Physics and has published three beautiful GR texts. If he says it’s not true then I personall would reject it. At least, that is, until I see published proof. I.e. from a reference to a scientific journal or textbook or two.

re - Uncertainty thread - I came across a new twist to it last night. Somone e-mailed me a reference to some interesting background on the two interpretations. Check it out if and when you have the chance

 

Then don't join a clique and there is a lesson learned.

I have just about as many posts as yourself here, just a little over a hundred posts and the only posts I have posted in was in this thread and one other. I haven't even got into any dog fights apart from those pretty much forced me into by other posters.

If you are just going to assume I am wrong, then I don't think forums is the place for you because quite frankly, you will from time to time find yourself corrected whether you like it or not.

 

Did he? If that was the case you better take a page out of my book, since all this time all it took you was a google search by Tach to prove you wrong.

 

Regarding my promise above, i.e.

Here is his response

I e-mailed him back showing him http://en.wikipedia.org/wiki/Redshift to ask him about it. It's difficult to believe Wiki regarding things like this because nobody knows who the authors are.

 

It would have to be that way since it's the only redshift associated with the path of light over cosmological distance. Thanks for asking your friend. Tach probably authored the wiki page. LOL. wiki works as a first reference when you can recognize the physics is correct. If you can't it's an untrustworthy source at any time.

 

Yes, that is what he did.



*rolls eyes*

 

Here is a relevant paper which talks about the cosmological shift



http://arxiv.org/pdf/1112.1328v1.pdf

Here is a very nice relevant online discussion which even talks about the general expression the original author used for the equivalence principle

http://www.physicsforums.com/showthread.php?t=399155

 

Here is a link how his terms relate to each other (which I found earlier)

http://scienceworld.wolfram.com/physics/GravitationalRedshift.html