Einstein's Relativity and Everyday Life -- Clifford M. Will

What book told you that GR is based on SR?

Uhhh...yes?

That doesn't mean it is bsed on SR. "Based on" implies something a lot
stronger than the actual relationship between SR and GR.

The derivation of the field equations does not invoke SR. The local
limit is an additional assumption.

It is like saying special relativity is based upon Newtonian mechanics
because at the low velocity limit, SR's kinematic equations reduce to
the Newtonian versions. Or, that GR is based upon Newton because with
some specific assumptions the Newtonian potential is recovered.

 

It must be easy to make all these asinine assertions about physics when
you have never studied physics.

 

see
http://relativity.livingreviews.org/Articles/lrr-2003-1/

 

For those interested in calculating the time dilation effects...

Relativistic Effects on Satellite Clocks
http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node5.html

 

So you have been claiming I don't understand GR and you DO,
and now you are saying all this is based on some peculiar understanding
you and Tom Roberts have of the English phrase "based on"?

If SR is a base (support) for GR, then GR would
be considered "based on" SR by most people.

Let me put it this way, if it turns out that SR doesn't hold and
spacetime is therefore NOT locally Minkowskian (thus
pulling out the base), what does that mean for GR?

 

[...]

It would have helped if you kept reading because I made my point
exceptionally clear in the part you snipped without marking.

The derivation of the field equations does not invoke SR. The local
limit is an additional assumption.

Saying GR is "based on" SR is like saying special relativity is based
upon Newtonian mechanics because at the low velocity limit, SR's
kinematic equations reduce to
the Newtonian versions. Or, that GR is based upon Newton because with
some specific assumptions the Newtonian potential is recovered.

So yes, I have been and continue to claim you do not understand GR
because you keep saying asinine shit and support it with loads of
nothing.

I ask again because you have yet to answer.

What education in mathematics and physics do you have? I will simply
assume you have none, as I have been doing, if you dodge the question
again.

 

In case you haven't noticed, it happens every time the drool
from the physics groups gets into the headers.

 

If so, then how it is that light emitted from moving sources is measured
to propagate at c? (certain idiots in this newsgroup notwithstanding)

Note, please, that if a speed could be ascribed to the em field, inside
the source it surely must be moving with the source, so you seem to be
claiming that light emitted from a moving source propagates with speed
c+v, where v is the speed of the source. This has been soundly refuted.
Many times.

I also think you have not really thought this through. For instance,
what is the em field generated by a neutral object? If there were two
neutral objects that pass near each other, what is the speed of light
near them at their nearest approach? What is the "speed of the em field"
in intergalactic space (where some of the tests of source independence
were carried out)? -- why should it "just happen" to be "at rest"
relative to earth? (which is what those observations imply for your claim)

Note also that for the common and normal meanings of these words, no
speed or rest frame can be ascribed to any field, including the em
field. So you really: a) need a better way of describing this, as your
statements above are nonsensical, and b) need to formulate a theory that
can be tested (rather than just blabbering around here).

That is a very different situation. The water has a clear and definite
rest frame; not so the em field.

Sure. See above for "enclosing the em field" in a source that is moving.
Your feeble analogies do not hold up -- electrodynamics is _different_.
<shrug>

[As a simple demonstration: for water waves, what is the
analogy to the electric field of a charged particle?]


Tom Roberts

 

For what?


Bob

 

Sam raises a good point!

Rumsfeld, Cheny and Tenet were asked by Bush
to determine if the intelligence,
used as the rationale for the war against Iraq,
was properly handled,
and it was.

In fact Tenet got the highest civilian medal
for handling the intelligence so properly.

Considering that Dan Bolef, who headed the Washington University Physics
department,
Arnie Rostel, the chief engineer in the physics department, and I,
formed a corporation back in the 1960's,
I know a little about how that university,
and many other universities operate.

Arnie Rostel made millions using his knowledge of
electronics and computers.

No doubt the General Relativity gurus,
like Clifford M. Will,
will make billions of dollars in the free market,
using their powerful, esoteric knowledge.

Charlatans and conmen in such fields as astrology,
fortune telling, and the like capitalize upon the gullibility
of people in order to achieve fame and fortune.

--
Tom Potter
http://home.earthlink.net/~tdp/
http://tdp1001.googlepages.com/home
http://no-turtles.com
http://www.frappr.com/tompotter
http://photos.yahoo.com/tdp1001
http://spaces.msn.com/tdp1001
http://www.flickr.com/photos/tom-potter/
http://tom-potter.blogspot.com

 

You are being disingenuous.

The local limit is a fundamental assumption of GR, not an
additional assumption -- as it defines the metric on
which the field equations operate.

What exactly is the relevance here? Why do you keep harping
on ME instead of the subject matter?

 

This is very basic -- any wave velocity is source independent,
and medium dependent.

Consider a supersonic plane. Any sound it makes, when
it moves through the surrounding air, cannot propagate
faster than the speed of sound. The speed of the source
is not relevant here.

But the sounds inside the supersonic plane will also
move at the speed of sound, wrt the _medium_.

 

PS: The entire disturbance is not typically source independent.
However, the "wave propagation" part is the part that is
independent of source velocity. Near the source, there
is a very small disturbance that does depend upon source
velocity. That part would be studied as "turbulence", however,
not as "wave motion."

A simple experiment is to drag a stick in a lake.
No matter how fast you drag the stick, the waves
you create will move at the same velocity. But
near the stick, the turbulence you create will
be dependent upon the stick velocity.

Note that the waves are moving WITH the lake.
So whether a giant bulldozer were moving the entire
lake steadily north at 20mph or not, the waves would
still have the same velocity wrt the lake.

wave propagates as disturbance of successive
segments of the medium, therefore the speed
of propagation depends upon the properties of
that medium and not upon the speed
of the source.

 

Uhh...no.

The field equations are what determine the metric.

Why am I even bothering? You are an idiot with no education in the
subject.

 

I don't know why you are bothering, but for any reader who
cares (and is not conversant with the terminology), I think a
quote from Clifform M. Will (conveniently, given the subject
line here) may show the relationship between GR and SR better,
without your attempt to confuse the subject and without
your response _based_ (!) upon personal attacks:

http://relativity.livingreviews.org/Articles/lrr-2006-3/articlesu1.html#x6-30002.1

Specifically: In any "metric theory of gravity" (of which GR is one),
"In local freely falling reference frames, the non-gravitational laws
of physics are those written in the language of special relativity."

In GR, The local laws of physics MUST conform to SR. It
is not optional, additional, or otherwise irrelevant.

 

Some more simple English references:

http://nuclear.ucdavis.edu/~cherney/dvd/gr.html

Recall that the invariant interval between neighboring events in
special relativity
(with rectangular coordinates) is ds2=dx2+dy2+dz2-(cdt)2 so there
g=1,1,1,-c2
across the diagonal, 0 off diagonal. A space likethis is called
Minkowskian (as
opposed to Euclidian which has 1s all across the diagonal, 0s off.)
This is a
direct result of the postulate that the speed of light is the same in
all reference
frames. The same assumption is made in general relativity, and thus
all g
are similar to (there exists a similarity transformation between) the
special
relativity g above.

Using this approach, I suppose one could claim that GR doesn't "depend"
upon SR, but arrives at SR very independently! Which is just another
way
of saying the same thing. In GR, c must be the same in all reference
frames,
hence all of SR must hold, period.

Or
http://www.superstringtheory.com/forum/geomboard/messages3/163.html
which is more straightforward:
"LOcally GR spacetime is Minkowskian (special relativity)"...

There are many more references on the web that could be used
to verify that GR requires that spacetime is locally
Minkowskian, and from that assumption it derives a basic
metric [1 1 1 -c^2] to operate upon.

"Locally Minkowskian" is simply another way of saying
SR holds, as can also be verified by various references
on the Web.

 

In GTR the rigid spacetime structure of SR is generalized. A. Einstein
arrived at this generalization on the basis of his "principle of
equivalence"--gravitation can be "locally" transformed away in a
freely falling, non-rotating system. This means that on the
infinitesimal scale, relative to a locally inertial system, that SR
remains valid. Special Relativity is a subset of General Relativity.

Can Special Relativity handle accelerations?
Ref: http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

The only sense in which special relativity is an approximation when
there are accelerating bodies is that gravitational effects such as
generation of gravitational waves are being ignored. But of course
there are larger gravitational effects being neglected even when
massive bodies are not accelerating and they are small for many
applications so this is not strictly relevant. Special relativity gives
a completely self consistent description of the mechanics of
accelerating bodies neglecting gravitation, just as Newtonian mechanics
did.

The difference between general and special relativity is that in the
general theory all frames of reference including spinning and
accelerating frames are treated on an equal footing. In special
relativity accelerating frames are different from inertial frames.
Velocities are relative but acceleration is treated as absolute. In
general relativity all motion is relative. To accommodate this change
general relativity has to use curved space-time. In special relativity
space-time is always flat.

See: http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

The following quote doesn't necessarily suppport your argument that
"GTR is based upon SR".


_____________________________________________


The Einstein equivalence principle

The principle of equivalence has historically played an important role
in the development of gravitation theory. Newton regarded this
principle as such a cornerstone of mechanics that he devoted the
opening paragraph of the Principia to it. In 1907, Einstein used the
principle as a basic element of general relativity. We now regard the
principle of equivalence as the foundation, not of Newtonian gravity or
of GR, but of the broader idea that spacetime is curved.

One elementary equivalence principle is the kind Newton had in mind
when he stated that the property of a body called ``mass'' is
proportional to the ``weight'', and is known as the weak equivalence
principle (WEP). An alternative statement of WEP is that the trajectory
of a freely falling body (one not acted upon by such forces as
electromagnetism and too small to be affected by tidal gravitational
forces) is independent of its internal structure and composition. In
the simplest case of dropping two different bodies in a gravitational
field, WEP states that the bodies fall with the same acceleration (this
is often termed the Universality of Free Fall, or UFF).

A more powerful and far-reaching equivalence principle is known as the
Einstein equivalence principle (EEP). It states that:

1. WEP is valid.

2. The outcome of any local non-gravitational experiment is
independent of the velocity of the freely-falling reference frame in
which it is performed.

3. The outcome of any local non-gravitational experiment is
independent of where and when in the universe it is performed.

The second piece of EEP is called local Lorentz invariance (LLI), and
the third piece is called local position invariance (LPI).

For example, a measurement of the electric force between two charged
bodies is a local non-gravitational experiment; a measurement of the
gravitational force between two bodies (Cavendish experiment) is not.

The Einstein equivalence principle is the heart and soul of
gravitational theory, for it is possible to argue convincingly that if
EEP is valid, then gravitation must be a ``curved spacetime''
phenomenon, in other words, the effects of gravity must be equivalent
to the effects of living in a curved spacetime. As a consequence of
this argument, the only theories of gravity that can embody EEP are
those that satisfy the postulates of ``metric theories of gravity'',
which are:

1. Spacetime is endowed with a symmetric metric.

2. The trajectories of freely falling bodies are geodesics of that
metric.

3. In local freely falling reference frames, the non-gravitational
laws of physics are those written in the language of special
relativity.

The argument that leads to this conclusion simply notes that, if EEP is
valid, then in local freely falling frames, the laws governing
experiments must be independent of the velocity of the frame (local
Lorentz invariance), with constant values for the various atomic
constants (in order to be independent of location). The only laws we
know of that fulfill this are those that are compatible with special
relativity, such as Maxwell's equations of electromagnetism.
Furthermore, in local freely falling frames, test bodies appear to be
unaccelerated, in other words they move on straight lines; but such
``locally straight'' lines simply correspond to ``geodesics'' in a
curved spacetime

 

If you write it that way, I can provide (or rather, have provided) an
interpretation where this has nothing particular to do with C.

Except that C-glass, C-vacuum, C-water should have the
same values everywhere. But so should the specific
gravity of coconut oil.

However, in the original formulation of GR, this meant SR,
(even if using other math/terminology.) C was specially written-in
as being invariant, and by that was meant a very special
kind of invariant. And that's why the choice of time-conversion
unit conveniently used c, thereby making SR a law of nature
(hence my claim that it's based on SR being a law of nature.)

By contrast, notice that the specific gravity of coconut oil
doesn't make a significant appearance in GTR.

 

Light simply does not behave that way.

Light is not sound, and sound is not a good analogy for the behavior of
light. <shrug>


Tom Roberts

 

<rest snipped as being too cretinoid>

No , cretin. This does not apply to light. Plenty of experiments prove
it, shithead.