According to General Relativity, the time dilation is given very simply as

t' = t / [1 - 2 G M / (c^2 r)], where

G = gravitational constant
c = speed of light
M = mass of a star (or a planet...)
r = distance for the center of M
t = time observed at r
t' = time observed at infinite distance from M

r = 2 G M / c^2, of course

If r 2 G M / c^2, then t' = t [1 + 2 G M / (c^2 r)]

Granted it is an approximation of something utterly complex, but does it
conflict with the Principle of Relativity?

Let's examine the time dilation strictly from the Principle of Relativity.

Start with F = dp(t)/dt = m d/dt[v(t) (1 - v(t)^2 / c^2)^-1/2], where

F = any force applied to the test object
p(t) = momentum of test object
v(t) = speed of test object
m = rest mass of object, then

g = F / m = d/dt[v(t) (1 - v(t)^2 / c^2)^-1/2], or

g t = v(t) (1 - v(t)^2 / c^2)^-1/2, or

v(t) = g t / [1 + (g t / c)^2], or

(1 - v(t)^2 / c^2)^-1/2 = [1 + (g t / c)]^-1/2, where

t = time observed by the test object

Then, apply Lorentz Transform,

dt' = (1 - v(t)^2 / c^2)^-1/2 dt = [1 + (g t / c)^2]^1/2 dt, where


t' = time observed by some one other than the test object, or

t' = (c / 2g) {arcsinh(g t / c) + (g t / c) [1 + (g t / c)^2]^1/2}, where

g = G M / r^2

This equation does not reduce to anything similar to the General Relativity
one. You have this test object in a gravitational field generating virtual
speed as time goes on. The Principle of Equivalence tells us that you can
do this. Now, does General Relativity even agree with the Principle of
Equivalence since it does not even agree with the Principle of Relativity?

When physicists turn their backs on the Aether almost 100 years ago without
even disproving its existence, they have been running into walls after
walls. Oh, despite they can imagine something up to climb each of these
walls, there seem to be one ahead of them --- endless. Maybe the
professional physicists need to back-track to 1,905. In modern day
educational systems, professionals tend to get their professions scrutinized
by some ones of other professions entirely different.

\(formerly\)" dlzc1.cox@net wrote in message news:cSGYa.7469$2g.2751@fed1read05...
Dear Australopithecus Afarensis:

"Australopithecus Afarensis" wrote in message
news:JcGYa.64500$zy.12630@fed1read06...
...
When physicists turn their backs on the Aether almost 100 years ago
without
even disproving its existence,

Disprove the existence of flying saucers.
Disprove that your Aunt Fanny cannot fly by flapping her arms fast enough.

The aether is not discernable by any theory that has survived 100 years of
experimentation. Just accept the fact that all surviving theories say it
cannot be detected. Crying about the facts doesn't change them.

Define discernable...

Once we have that definition, then we can talk about facts.

I'll start,

Discern(able)

adjective: perceptible by the senses or intellect...

Main Entry: dis·cern
Pronunciation: di-'s&rn, -'z&rn
Function: verb
Etymology: Middle English, from Middle French discerner, from Latin discernere
to separate, distinguish between, from dis- apart + cernere to sift
-- more at DIS-, CERTAIN
Date: 14th century
transitive senses
1 a : to detect with the eyes b : to detect with senses other than vision
2 : to recognize or identify as separate and distinct : DISCRIMINATE
3 : to come to know or recognize mentally

intransitive senses : to see or understand the difference - dis·cern·er noun

Paul Stowe

Dear Paul Stowe:

"Paul Stowe" wrote in message
om...
\(formerly\)" dlzc1.cox@net wrote in message
news:cSGYa.7469$2g.2751@fed1read05...
....
Disprove the existence of flying saucers.
Disprove that your Aunt Fanny cannot fly by flapping her arms fast
enough.

The aether is not discernable by any theory that has survived 100 years
of
experimentation. Just accept the fact that all surviving theories say
it
cannot be detected. Crying about the facts doesn't change them.

Define discernable...

Once we have that definition, then we can talk about facts.

I'll start,

Discern(able)

adjective: perceptible by the senses or intellect...

Main Entry: dis·cern
Pronunciation: di-'s&rn, -'z&rn
Function: verb
Etymology: Middle English, from Middle French discerner, from Latin
discernere
to separate, distinguish between, from dis- apart + cernere
to sift
-- more at DIS-, CERTAIN
Date: 14th century
transitive senses
1 a : to detect with the eyes b : to detect with senses other than
vision

Since the physical bodies of which we are composed are supposed to be
maintained by forces that propagate through the aether, this will not be
possible. Ever.

2 : to recognize or identify as separate and distinct : DISCRIMINATE

By the same supposition, "separation" or "different" are not possible.

3 : to come to know or recognize mentally

So it will become arguments over things that cannot be separated from
physical reality. A thankless task for sure...

David A. Smith

(formerly)" dlzc1.cox@net wrote in message
news:7jeZa.7815$2g.6701@fed1read05...
| Dear Paul Stowe:
|
| "Paul Stowe" wrote in message
| om...
| \(formerly\)" dlzc1.cox@net wrote in message
| news:cSGYa.7469$2g.2751@fed1read05...
| ...
| Disprove the existence of flying saucers.
| Disprove that your Aunt Fanny cannot fly by flapping her arms fast
| enough.
|
| The aether is not discernable by any theory that has survived 100
years
| of
| experimentation. Just accept the fact that all surviving theories
say
| it
| cannot be detected. Crying about the facts doesn't change them.
|
| Define discernable...
|
| Once we have that definition, then we can talk about facts.
|
| I'll start,
|
| Discern(able)
|
| adjective: perceptible by the senses or intellect...
|
| Main Entry: dis·cern
| Pronunciation: di-'s&rn, -'z&rn
| Function: verb
| Etymology: Middle English, from Middle French discerner, from Latin
| discernere
| to separate, distinguish between, from dis- apart +
cernere
| to sift
| -- more at DIS-, CERTAIN
| Date: 14th century
| transitive senses
| 1 a : to detect with the eyes b : to detect with senses other than
| vision
|
| Since the physical bodies of which we are composed are supposed to be
| maintained by forces that propagate through the aether, this will not be
| possible. Ever.
|
| 2 : to recognize or identify as separate and distinct : DISCRIMINATE
|
| By the same supposition, "separation" or "different" are not possible.
|
| 3 : to come to know or recognize mentally
|
| So it will become arguments over things that cannot be separated from
| physical reality. A thankless task for sure...

Hmmm. I swear if I rub a ballon on my head, it will stick to the wall.
Hmmm. That magnet I stuck to the refrig didn't fall off either. These
sure seem like physical reality to me. Now what makes them do that?
Fields you say? What are these fields made from?

FrediFizzx

Dear FrediFizzx:

"FrediFizzx" wrote in message
...
(formerly)" dlzc1.cox@net wrote in message
news:7jeZa.7815$2g.6701@fed1read05...
....
| So it will become arguments over things that cannot be separated from
| physical reality. A thankless task for sure...

Hmmm. I swear if I rub a ballon on my head, it will stick to the wall.
Hmmm. That magnet I stuck to the refrig didn't fall off either. These
sure seem like physical reality to me. Now what makes them do that?
Fields you say? What are these fields made from?

You can stick your head to the wall, just by rubbing a balloon against it?
English is pretty squirmy...

Lorentz's aether (as opposed to some other "flavour") would have the rod
physically change length, ostensibly because the c-moderated forces that
control its size can't do their thing any other way. So if:
1) length and time are relative, so you measure the rod as being
contracted, OR
2) the rod is contracted by its motion, so it will be measured as being
contracted.

Can you discern which definition is correct by making a length measurement?

I cannot discern what you are trying to point out with your "fields"
comment. Perhaps you are trying to remind me that magnetic fields
"decompose" into length contraction and electrostatic attraction. Or maybe
that your hair is standing up because you just rubbed a balloon on it. ;}

David A. Smith

Australopithecus Afarensis wrote:
According to General Relativity, the time dilation is given very simply as
t' = t / [1 - 2 G M / (c^2 r)], where [...]

That is NOT General Relativity (in general). That is a particular
solution to the equations of GR known as the Schwarzschild geometry. And
you forgot a sqrt[] on your angle brackets.


Granted it is an approximation of something utterly complex, but does it
conflict with the Principle of Relativity?

First, you should learn what the Principle of Relativity and the
Principle of Equivalence actually are.


Let's examine the time dilation strictly from the Principle of Relativity.
[sloppy derivation of a uniformly-accelerated object]

This equation does not reduce to anything similar to the General Relativity
one.

Of course not! They represent DIFFERENT physical situations. duh!


The Principle of Equivalence tells us that you can
do this.

No, it does not. You need to learn what the PoE actually says.


Now, does General Relativity even agree with the Principle of
Equivalence since it does not even agree with the Principle of Relativity?

You are confused about what these Principles actually mean. GR is
consistent with the PoE and the PoR, but they must be applied LOCALLY.


When physicists turn their backs on the Aether almost 100 years ago without
even disproving its existence, they have been running into walls after
walls.

Not really. Of course it is imposible to "disprove" the existence of
most things. But physics isn't about "proof" or "disproof" anyway --
physics is about modeling the world we inhabit.


In modern day
educational systems, professionals tend to get their professions scrutinized
by some ones of other professions entirely different.

SR and GR have been "scrutinized" by engineers in many varied ways. They
have never been found wanting. No knowledgeable person can dispute that
SR and GR provide excellent models for the world we inhabit, in their
respective domains of applicability. The interesting thing is to
consider their implications and potential application outside those
domains, and occasionally to explore the boundaries....


Tom Roberts

Dear Paul Stowe:

"Paul Stowe" wrote in message
...
(formerly) wrote:
....
You can stick your head to the wall, just by rubbing a balloon against
it?
English is pretty squirmy...

Are you that obtuse or just being sarcastic? My guess, the latter...

Good guess.

Lorentz's aether (as opposed to some other "flavour") would have the rod
physically change length, ostensibly because the c-moderated forces that
control its size can't do their thing any other way. So if:

1) length and time are relative, so you measure the rod as being
contracted, OR
2) the rod is contracted by its motion, so it will be measured as being
contracted.

Can you discern which definition is correct by making a length
measurement?


They're two different interpretations, #1 is philosophically based the
second
physically based. Both can lead to the same observation.

They both *always* lead to the same observation. Lorentz's aether is
physically undetectable.

I cannot discern what you are trying to point out with your "fields"
comment. Perhaps you are trying to remind me that magnetic fields
"decompose" into length contraction and electrostatic attraction. Or
maybe that your hair is standing up because you just rubbed a balloon
on it. ;}


His 'point' dear David was that every observation made is consistent
with the aether concept. The observational facts support the theory
and the very observing of the physicality of fields discerns
(by definition) the aether!

If you can read that in his comment about E&M fields, then you are quite a
stud.

P.S. this posting is using Netscape 7.0 and I don't know how it will
format & look to readers yet...

It looks fine.

David A. Smith

Dear FrediFizzx:

"FrediFizzx" wrote in message
...
(formerly)" dlzc1.cox@net wrote in message
news:B0fZa.7828$2g.489@fed1read05...
....
| I cannot discern what you are trying to point out with your "fields"
| comment. Perhaps you are trying to remind me that magnetic fields
| "decompose" into length contraction and electrostatic attraction.

Fields are physical reality. What are they composed of? Do you think
they exist by some kind of magic?

Fields are imaginary constructs relating to photons, mass, space and time.
They make calculations for a bulk property like "charge" less onerous than
trying to describe "trajectories" for each particle. You can create
"potential energy" and store energy in a volume... all sorts of oddities.
Oddities that you end up eliminating to move on to GR.

A "field" is just a measure of how much two or more particles with charge
interfere with one another. It is no justification for an aether, in and
of itself.

David A. Smith

(formerly)" dlzc1.cox@net wrote in message
newsFjZa.7861$2g.1647@fed1read05...
| Dear FrediFizzx:
|
| "FrediFizzx" wrote in message
| ...
| (formerly)" dlzc1.cox@net wrote in message
| news:B0fZa.7828$2g.489@fed1read05...
| ...
| | I cannot discern what you are trying to point out with your "fields"
| | comment. Perhaps you are trying to remind me that magnetic fields
| | "decompose" into length contraction and electrostatic attraction.
|
| Fields are physical reality. What are they composed of? Do you think
| they exist by some kind of magic?
|
| Fields are imaginary constructs relating to photons, mass, space and
time.
| They make calculations for a bulk property like "charge" less onerous
than
| trying to describe "trajectories" for each particle. You can create
| "potential energy" and store energy in a volume... all sorts of
oddities.
| Oddities that you end up eliminating to move on to GR.

A field is *not* an imaginary construct. I can certainly feel the
electric field around the balloon when it stands my hair on end. Did you
ever play with a magnet and some iron filings? Sprinkle some on paper
with the magnet underneath. You can see the field emanating from the
magnet. Fields are as real as can be. What are they made of?

| A "field" is just a measure of how much two or more particles with
charge
| interfere with one another. It is no justification for an aether, in
and
| of itself.

I say that a field has to be made of something. What are they made of? I
swear it must be something in the vacuum that they are made of.

FrediFizzx

(formerly)" dlzc1.cox@net wrote in message
news:4qjZa.7859$2g.2826@fed1read05...
| Dear Paul Stowe:
|
| "Paul Stowe" wrote in message
| ...
| (formerly) wrote:
| ...
| You can stick your head to the wall, just by rubbing a balloon
against
| it?
| English is pretty squirmy...
|
| Are you that obtuse or just being sarcastic? My guess, the latter...
|
| Good guess.
|
| Lorentz's aether (as opposed to some other "flavour") would have the
rod
| physically change length, ostensibly because the c-moderated forces
that
| control its size can't do their thing any other way. So if:
|
| 1) length and time are relative, so you measure the rod as being
| contracted, OR
| 2) the rod is contracted by its motion, so it will be measured as
being
| contracted.
|
| Can you discern which definition is correct by making a length
| measurement?
|
|
| They're two different interpretations, #1 is philosophically based
the
| second
| physically based. Both can lead to the same observation.
|
| They both *always* lead to the same observation. Lorentz's aether is
| physically undetectable.
|
| I cannot discern what you are trying to point out with your "fields"
| comment. Perhaps you are trying to remind me that magnetic fields
| "decompose" into length contraction and electrostatic attraction. Or
| maybe that your hair is standing up because you just rubbed a balloon
| on it. ;}
|
|
| His 'point' dear David was that every observation made is consistent
| with the aether concept. The observational facts support the theory
| and the very observing of the physicality of fields discerns
| (by definition) the aether!
|
| If you can read that in his comment about E&M fields, then you are quite
a
| stud.

I never said anything about E&M. I was talking about a pure electrostatic
field and a pure magnetostatic field. A pure electrostatic field would
require virtual photons of zero frequency. Seems a bit of a stretch to
me. Can anyone tell me exactly what a zero frequency virtual photon
really is? Is there an exact mathematical description?

FrediFizzx