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On, Investigating a Planckian Redshift of Origin from Spacetime Uncertainty
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On, Investigating a Planckian Redshift of Origin from Spacetime Uncertainty
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Dubbelosix
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On, Investigating a Planckian Redshift of Origin from Spacetime Uncertainty
«
on:
18/08/2017 09:29:32 »
In a recent post (see ref after work), I investigated non-commutation in the Friedmann equation and the Einstein equations. In this post, the first equation is specifically derived by another author, Prof. Crowell and from it we will argue a derivation that leads to a relationship between the spacetime uncertainty and the red shift of the gravitational field which can be corrected to higher orders.
A spacetime uncertainty is suggested from L. prof. Crowell's own spacetime uncertainty investigations;
Rearranging and identifying the metric identity
we have
expanding the metric to first order we get
and by identifying
then
This was constructed from
ref
https://www.thenakedscientists.com/forum/index.php?topic=71199.msg520886#new
note
You can expand the gravitational field further
For higher corrections to the red shift.
«
Last Edit: 19/08/2017 00:39:45 by
Dubbelosix
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Dubbelosix
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Re: On, Investigating a Planckian Redshift of Origin from Spacetime Uncertainty
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Reply #1 on:
18/08/2017 09:58:08 »
sorry about those latex errors coming out, all fixed now.
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Dubbelosix
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Re: On, Investigating a Planckian Redshift of Origin from Spacetime Uncertainty
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19/08/2017 00:57:19 »
I was really tired yesterday when I wrote it, a missing square root was rectified. Let's discuss some of the implications and meanings of the equations.
This equation involves the dimensionless time-time component of the metric. A metric notation is also
and we will see use of it later.The Planck length is
so we clearly have a squared Plankian structure to the spacetime metric. The non-commutation is expressed on the LHS. A formally similar type of spacetime uncertainty is linked in string theory as well which predicts a spacetime uncertainty linked to the Planck scale.
A simple rearranging of the metric term, and a second order expansion leads to:
The expansion is analogous to gravitational corrections of the redshift value. In a way, this equation already suggests a link between some spacetime uncertainty relationship to the Planck structure and redshift of the system. The next form of the equation is solved for the uncertainty in a single length, but also makes use of
which is a metric term, like we discussed not long ago and is actually just relativity's way to discuss the square of a spacetime interval.
Basically we have some Planck structure weighted by a spacetime interval which depends on uncertainties in the metric. The result on the LHS may in a way, be interpreted to mean even intervals on the Planck length can jiggle due to uncertainty.
ref
https://www.thenakedscientists.com/forum/index.php?topic=71199.msg520886#new
note
You can expand the gravitational field further
For higher corrections to the red shift. [/size]
[/quote]
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