"TomGee" <lvlus@hotmail.com> wrote in message
news:1108743767.544269.163600@l41g2000cwc.googlegroups.com...

george@briar.demon.co.uk wrote:

TomGee wrote:

George Dishman wrote:

I'm not sure why you include the word "parallel". We
live in a 4D universe, three dimensions describing space
and one for time.

Yes, I know, so why would AE make up another one just like ours?

boggled my imagination to think that he ignored the fact you

pointed out, and so did all the scientists who have mentioned

claim. Dumb, isn't it? Or maybe you know why he made up

I just assumed his was a parallel one to ours since he ignored

universe.

If you are referring to GR then he didn't make up any
other universe, it describes _our_ universe. He didn't
deal with any "parallel" universes AFAIK, certainly he
didn't like QM and I doubt he would have liked the MWI.

Of course it's possible you are referring to some
comments he made that I haven't yet come across. If so
a pointer would be appreciated.

I appreciate your point. I ascribed the term "parallel" on my own

his explanation of curved space as printed in several publications
through the years. I never read where he said it was the same

as ours.

If you think of it the other way round, since he was
describing our universe why would he bother saying it.
Remember he was writing in 1905 and ideas like "parallel
universes" were far in the future.

I assumed it was another one since everyone already knew ours
is a 4d universe. What I read seemed to strongly infer a second
universe.

More recently, Stephen Hawking wrote in his book, "A Brief History

Time", page 24, that "It is often helpful to think of the four
coordinates of an event as specifying its position in a
four-dimensional space called space-time. It is impossible to

a four-dimensional space." Here, even Hawking refers to s-t as if

were a parallel U.

I can see how you might read it that way. It's always
difficult to throw off a false impression like that
when you have no doubt interpreted everything you
read since in that way. Oh well, all I can say is
rest assured he was talking of our universe, not a
parallel one.

The idea of "moving through space" implies some sort of
static condition of space which is the Newtonian view
that relativity discarded.

I see no such implication because objects move through space all

time in our everyday world, which seems will happen even though
everything in the universe is always moving through space.

OK, we can agree to differ on that, I only see it as
an implication. Language isn't always definitive.

However,
having said that, my model does claim that dark matter is

static in space. Waves move through space, and so does visible

but invisible matter stays in place in space.

Relativity says the concept of "static in space" is
meaningless.

In SR any inertial frame can arbitrarily
be called "static" and everything else is moving in
that frame. GR extends that to accelerated frames.
Hence the implication, if "moving through space" is
to mean anything, there should exist some special
condition which could be described as static against
which the motion is to be measured.

And once again I note that you refer to classical physics as being
"discarded", as in rejected, by Relativity, although many here

they do not act as if they still believe that.

In everyday life, speeds are so far below the speed
of light that the two views are indistinguishable.
The Newtonian world view is a pefectly adequate
approximation.

He means that if you view the
world as four-dimensional, each particle or object can
be considered as moving through it at a fixed rate.

But Hawking said that is impossible.

If you mean the quote above, he said it was impossible
to _imagine_ or perhaps visualise would be a better word.

But, if it wasn't, I assume you
mean above "at a fixed rate" IN TIME but not necessarily at a fixed
rate of speed, no?

It means at a fixed rate through spacetime. The rate
through time and through space are then related in a
manner similar to Pythagoras' Theorem. The combination
of the two rates always produces the speed of light.

The
spatial axes are orthogonal to the time axis as well as
each other so if you are at rest in your chosen inertial
frame then all the motion is along the time axis.

Yes, I know all that, but my contention is that it is only possible

do all that with the math construct which is space-time, and not,
according to Hawking, in reality.

See my next two paragraphs where I already addressed this:

<snip>

All of physics consists of mathematical models of the
world around us. Ohm's Law says voltage equals current
times resistance. Ohm's Law is a mathematical model of
a resistor, it isn't actually a resistor. Relativity is
no different in this respect.

So AE's 4d universe is imaginary?

No, like all others, his theories are descriptive and
to be quantitative (i.e. useful), they are mathematical.
What they attempt to describe is what is real.

Then
why does almost everyone believe it is a real place, and that

through time is the same as moving through space?

That is a philosophical point of view regarding our
universe which is fairly easy to conclude from the
mathematical model.

Yes, quite so. Thank you.

It is less easy but more accurate
to visualise the whole 4D manifold with eveything in
it as a single structure. In this view I am a spiral
line (round the Sun once a year) with some thickness
hopefully about 70 years long and "now" is a point
along that line.

Hmmm.... How is that more accurate than s-t?

I think there is some confusion here, what I said
isn't an alternative to spacetime, it is a way of
thinking about spacetime as was the previous
paragraph. We live in a 4D manifold which we is
called spacetime. My life in that is a 4D shape,
about 174cm by 35cm by 20cm by 70 years.

<aside>
I'm mixing my units a bit, 70 years = 2.1Gm ;-)
</aside>

The concept of me moving through spacetime implies
I am a 3D creature living in a 4D universe. Note
that the idea of "now" is also somewhat misleading,
it may not really exist. Every instant of my life
was/is/will be "now" at that instant.

To put it in lay terms, if you stand still you will
still get older - you are moving forward in time. Look
up "four-velocity" for better explanations than I can
offer.

George, we move forward in time whether we're still or moving,

everyone

knows that.

Exactly. It also follows that different paths from
one event (point in spacetime) to another may have
different lengths, hence it is easy to understand
the Twins Paradox. Clocks flown around the world
(and many other experiments) have demonstrated this
effect is quite real.

But here again you are mixing math with reality.

Again, see above what I said about this. The math
is a description of the reality.

We know that
different paths from an event may have different lengths, but that
knowledge is based on the Principle of Equivalence and not on s-t.

http://aether.lbl.gov/www/science/equiv.html

I don't see the relevance. Are you perhaps thinking
of the invariant interval?

math. If it was based on math, we would have to believe that s-t

real place.

It is. We live in it.

How does the rocketship on the surface of Earth move
through the curved space of Earth, as AE said?

This is the way I think of it though it's a personal
view. If, like me, you have trouble thinking in 4D,
you'll need to use a little imagination ;-)

First think of a slice through the Earth at the equator.
The Earth is a 2D circle which is red in the centre
and has a thin blue and brown edge. Now think of that
extended in time as a cylinder which is red in the
centre and blue/brown on the surface. An object free-
falling from space would form a curved line approaching
the cylinder until it hits the surface, say on a brown
bit (land, not sea).

At that point the surface forces
it off the path it would have taken had it been able to
continue falling to the centre. Thereafter the path of
the object is continually being pushed off these curved
lines

Which curved lines, George?

The lines described by a family of free-falling
objects, geodesics I believe, as I said later.

and it is forced to lie along the surface of the
cylinder.

As the cylinder moves through time,

The axis of cylinder _is_ time.

yes, but the cylinder is imaginary,

It is in our imagination but it is a visualisation
of reality. As you said, most people know we live
in a 4D universe. All I have done is ignore the
north-south direction so that you can more easily
visualise the remaining three. As Hawking said in
your quote above, "It is impossible to imagine a
four-dimensional space." I have seen a few people
say they can do it but it's certainly very hard.

George, and so the rocketship is not really moving through the

space of the earth, is it? Everyone knows that while it sits on

it then is also moving through time, as is the planet and all of us

it, but that does not mean it is moving through the curved space of
Earth.

It is moving through spacetime which is curved by
the gravity of the Earth (and Sun etc.).

Was not this then another one of the Great Scientist's Great Jokes

Or was it just another one of those theories that don't work but

complicated few if any can understand it much less explain it (like

complex math of his static universe theory)?

With the possible exception of a few post-Newtonian
variants that are observationally indistinguishable,
it is the only model of the universe we live in that
accurately describes gravity. It is a model that
reflects the currently accepted view of reality.

These curved lines are a family of geodesics
if I understand the term correctly (which is in doubt!).

And geodesics is a math construct relating to the geometry of

surfaces.

See my comments on Ohm's Law again. Geodesics are
like the gently curvin