All horizons are "apparent", subjective, not objective. 

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You ( Tom Roberts ) replied to me:
You (Tom) are wrong about conditions at:

· The cosmological horizon ( i.e. the start of the big bang ).

· The event horizon of a supermassive black hole.

All horizons are "apparent", subjective, not objective.
The horizon depends on where/when you are.

This is just plain not true.
Some types of horizons are so dependent,
but most types are not.

For concreteness, I'll discuss
the Schwarzschild manifold of GR.

According to Wikipedia, the Schwarzschild metric assumes
"a stationary clock located infinitely far from the massive body".
https://en.wikipedia.org/wiki/Schwar...zschild_metric

In other words, it does ·not· describe
what local obserers see, beyond our horizon.

[ ..... ]
the locations of the horizons do NOT depend on
where you are located or what coordinates you use.

They are objective properties of the manifold:
on one side it is possible to reach spatial infinity,
and on the other side it is not.

Yes, but ·only· for:
"a stationary clock located infinitely far from the massive body".

The start of the "big bang",
indeed the ·apparent· start of space and time ( the timescape ),
depends on where/when you are.

[ ..... ]
The "cosmological horizon" of a given observer in these models does depend on
the observer's location. This is the locus beyond which the observer can never
observe any portion of a non-spacelike geodesic path, and that obviously depends
on where/when the observer is located. Perhaps this is what you are thinking of
-- but it is NOT a general property of horizons.

Yes, the start of the timescape ( i.e. the cosmological horizon )
depends on where/when you are.

Local observers see a ·much· lower energy density there/then,
beyond our horizon.

A local observer, at what appears (to us) to be a horizon,
would see no such horizon ( i.e. no redshift ).

Not true for the event horizon of a black hole, or for the big bang.
But it is true for an observer's cosmological horizon.

What ? ! Per General Relativity,
the redshift depends on when/where the observer is.

Locally, the energy density within these horizons is quite low.

Hmmm. The entire visible universe is within the cosmological horizon
of an observer on earth ( that's what these words mean ).

No, I'm saying:

Local observers, outside of our horizon, measure
a ·much· lower energy density ( vs. what we see ).

[ ..... ]
in the limit as one approaches the limit point of a
past-directed non-spacelike geodesic
(i.e. approaching the big bang from the future),
the energy density increases without bound.
[ ..... ]

Yes, but ONLY for:
"a stationary clock located infinitely far from the massive body".

On 9/16/14 9/16/14 10:08 PM, Jeff-Relf.Me wrote:
You ( Tom Roberts ) replied to me:
Some types of horizons are [coordinate/observer] dependent,
but most types are not.
For concreteness, I'll discuss
the Schwarzschild manifold of GR.

According to Wikipedia, the Schwarzschild metric assumes
"a stationary clock located infinitely far from the massive body".
https://en.wikipedia.org/wiki/Schwar...zschild_metric

Either you are quoting them incorrectly, or they are flat-out wrong. Most likely
the former.

The usual Schwarzschild COORDINATES are indeed based on an observer at spatial
infinity. The manifold itself is completely independent of coordinates, and has
no such dependence or assumption.


In other words, it does ·not· describe
what local obserers see, beyond our horizon.

This is just flat-out wrong. Such a manifold represents the modeled world at
each and every location at each and every time. From that one can deduce what an
observer located anywhere/anywhen would observe.

The only horizon in the Schw. manifold is a geometrical property common to all
observers; it is not "ours".

Of course the Schw. manifold does not model the world we inhabit at all.


[ ..... ]
the locations of the horizons do NOT depend on
where you are located or what coordinates you use.

They are objective properties of the manifold:
on one side it is possible to reach spatial infinity,
and on the other side it is not.

Yes, but ·only· for:
"a stationary clock located infinitely far from the massive body".

No. You misread or misinterpreted a Wikipedia article. And Wikipedia is not a
completely reliable source of such things.


The "cosmological horizon" of a given observer in these models does depend on
the observer's location. This is the locus beyond which the observer can never
observe any portion of a non-spacelike geodesic path, and that obviously depends
on where/when the observer is located. Perhaps this is what you are thinking of
-- but it is NOT a general property of horizons.

Yes, the start of the timescape ( i.e. the cosmological horizon )
depends on where/when you are.

No. I said "cosmological horizon", not "big bang" -- the latter is a geometrical
property of the manifold, common to all observers. The big bang is the "start of
the timescape", not the cosmological horizon of any observer.

For PRECISELY the reason that the cosmological horizon depends
on the observer, but the big bang does not.


Local observers see a ·much· lower energy density there/then,
beyond our horizon.

Observers cannot see ANYTHING beyond their cosmological horizon -- that's what
the words mean.

AT the horizon, there is no constraint on energy density at all; it might HAPPEN
to be much lower, but not necessarily.


[... no point in continuing, as you confuse too many incommensurate notions]

Like so many others around here, you need to improve the accuracy of your
reading. You have repeatedly made trivial mistakes.


Tom Roberts

"Tom Roberts" wrote:
snip crap
===== Of course the Schwartzschild manifold
===== does not model the world we inhabit at all.

hanson wrote:
Bravo! Tom, for posting that 2-liner. As long as
you and other Einstein Dingleberries do make
that exclusionary prelude to express their own
brain farts a in any "non-shop" environment such
as the Usenet sci-groups, go right ahead with
joy and wanton, ... the wilder, the better.

You might also include that already 60+ years
ago, for the very same reasons, Einstein fessed
up & 2 years before AE folded his SR/GR tent,
closed his umbrella, kicked the bucket, bit the
grass, and puffed,...
Einstein himself became a RELATIVITY DENIER

http://tinyurl.com/Einstein-denied-his-SR-and-GR
in which he concluded that:
____ SR is short for STUPID RANT _____ and
.. ____ GR stands for GULLIBLE RECITAL _____.
on grounds of:
|||AE:||| "as far as the laws of mathematics refer to
|||AE:||| reality, they are not certain; and as far as they
|||AE:||| are certain, they do not refer to reality."