Re: Inflationary Theory ; I'm confused

From: George Dishman (george_at_briar.demon.co.uk)
Date: 02/18/05 

Date: Fri, 18 Feb 2005 21:18:27 -0000

"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? It
>> > boggled my imagination to think that he ignored the fact you just
>> > pointed out, and so did all the scientists who have mentioned his
>> > claim. Dumb, isn't it? Or maybe you know why he made up another one?
>> > I just assumed his was a parallel one to ours since he ignored our 4d
>> > 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 to
> his explanation of curved space as printed in several publications
> through the years. I never read where he said it was the same universe
> 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 Of
> 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 imagine
> a four-dimensional space." Here, even Hawking refers to s-t as if it
> 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 the
> 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 essentially
> static in space. Waves move through space, and so does visible matter,
> 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 claim
> 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 to
> 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 moving
>> > 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 is a
> 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 curved
> space of the earth, is it? Everyone knows that while it sits on Earth,
> it then is also moving through time, as is the planet and all of us on
> 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 on us?
> Or was it just another one of those theories that don't work but are so
> complicated few if any can understand it much less explain it (like his
> 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 curved
> surfaces.

See my comments on Ohm's Law again. Geodesics are
like the gently curving Cartesian grid lines you
see faintly on maps of space when a TV program
wants to illustrate a black hole. There are no
glowing lines in space, but it really bends and
if the TV could represent a 4D grid, that would
be more accurate.

George

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