From: Daryl McCullough on
harald says...
>
>On Jul 5, 3:00=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote:

>> What do you consider to be the *real* twin paradox?

>The one that Einstein was confronted with - the first "twin" or
>"clock" paradox that we know of.

I meant: what do you consider paradoxical about it? Can you say that
in your own words? I don't want you to quote Einstein. I want you to
describe the paradox and why in the world you consider it paradoxical.

You complain that I miss your point, but it seems to me that you have
scrupulously avoided making one with any clarity. If you want to make
a point, lay it out in detail and give your arguments in your own words.

--
Daryl McCullough
Ithaca, NY

From: Daryl McCullough on
harald says...

>Acceleration effects are not identified as gravitational fields in
>Newtonian physics (which, as you now know, you didn't know); and
>neither is that the case in SRT. In those theories acceleration is
>"absolute", and no gravitational fields are caused by acceleration.

This is a topic for another discussion, but I'm talking about
"pseudo-gravitational" fields, which crop up in both SR and Newtonian
physics if you use accelerated coordinates.

>> I think it is because you have not made it very well. I still
>> have no idea what your point is.
>
>Just study Einstein's paper carefully,

I want to know what *YOUR* point is. State it in your own words.

>In this thread, you pretend no less than that:
>
>- Newton was mistaken with his Space postulate (while you evidently
>didn't even bother to read his arguments)
>- you know better than Einstein what his own theory is about (Cranky)

That isn't cranky. 100 years of relativity development does give
one a more complete perspective. I would say that a typical physics
graduate student understands Newtonian physics better than Newton,
and understands relativity better than Einstein. That doesn't mean
that they are smarter than Newton or Einstein---it's a lot harder
to invent a new theory than it is to understand or expand on an
existing theory.

Anyway, I don't care to argue with Newton or with Einstein.
They are not around to argue with.

If you have a point to make, make it yourself. Don't
hide behind Newton or Einstein.

--
Daryl McCullough
Ithaca, NY

From: Daryl McCullough on
Daryl McCullough says...

>harald says...
>
>>Acceleration effects are not identified as gravitational fields in
>>Newtonian physics (which, as you now know, you didn't know); and
>>neither is that the case in SRT. In those theories acceleration is
>>"absolute", and no gravitational fields are caused by acceleration.

The idea that "gravitational fields are caused by acceleration" is, as I have
pointed out many times, a very misleading way to describe the equivalence
principle. It's not that acceleration effects are a kind of gravitational field,
it's that gravitational fields are a kind of acceleration effect (they are an
indication that you are accelerating relative to the local inertial frame).

You don't need a theory of gravity in order to know what things "look like" in
an accelerated coordinate system. You just take the description in inertial
coordinates, and apply a coordinate transformation. It's just calculus.

But if you do this for SR, you find some interesting things:

1. All objects accelerate downward (unless acted upon by a force) at a rate that
is independent of the composition of the object. A thrown object will follow,
not a straight line, but a parabola (roughly speaking).
2. Clocks that are "higher up" run faster than clocks that are "lower down".

These are effects of acceleration that are derivable without any mention of any
theory of gravity. The key observation behind the equivalence principle is that
fact (1) is true (or approximately true) for objects in a uniform gravitational
field. So perhaps it is possible to interpret *gravitational* fields as a kind
of acceleration field due to the use of noninertial coordinates. If so, this
identification makes a definite prediction, namely (2) that clocks that are
higher up in the gravitational field should run faster.

So the real insight in General Relativity is not that acceleration effects
are gravitational fields, it's that gravitational fields are a kind of
acceleration effect. To make this work, it is necessary to have curved
spacetime, so that the notion of being unaccelerated can vary from place to
place (to allow for nonuniform gravitational fields). The same insight could
have been done with Newtonian physics, but historically it wasn't. Newtonian
gravity can likewise be described in terms of curved spacetime, and under this
description, the "force of gravity" becomes just an acceleration effect.

--
Daryl McCullough
Ithaca, NY

From: Edward Green on
On Jul 4, 9:14 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote:
> Edward Green says...
>
>
>
>
>
>
>
> >On Jun 30, 10:11=A0pm, stevendaryl3...(a)yahoo.com (Daryl McCullough)
> >wrote:
>
> ><...>
>
> >> Actually, with the correct statement of time dilation, time
> >> dilation is all you need to solve most of the problems involving
> >> clocks, twins, etc.
>
> >> The correct statement is this: As measured in any standard INERTIAL
> >> coordinate system, the elapsed time T on a moving clock satisfies
>
> >> dT/dt =3D square-root(1-(v/c)^2)
>
> ><...>
>
> >From which may be deduced an amusing fact. Say that v is grows quickly
> >enough towards c to force the r.h.s. to decay quickly enough to make
> >the integral of dT bounded.  Then we have a material particle which
> >travels to infinity in bounded proper time.
>
> Yes, that is interesting. But it's kind of like the fact that in
> Newtonian physics, it's possible for a material object to travel
> infinite distance in finite coordinate time. There is actually
> even an arrangement of point-masses that realizes this, using
> no forces other than gravity.

That indeed is also interesting. I guess you know that I bring this up
from time to time to argue that while in some cases reaching a horizon
in finite proper time indeed shows that nothing particularly
interesting is going on (Rindler horizon), in other cases it shows
nothing of the sort. I suspend judgement on whether the infalling
particle in the Schwarzschild geometry is more like case one or case
two, but I think the argument should give us pause, and kind of brings
the usual argument that finite proper time shows that things really
happen to a null.

Geez. I seem to becoming a crank -- or at least a bore: I've run out
of original ideas.
From: harald on
On Jul 5, 2:46 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote:
> harald says...
>
> >Acceleration effects are not identified as gravitational fields in
> >Newtonian physics (which, as you now know, you didn't know); and
> >neither is that the case in SRT. In those theories acceleration is
> >"absolute", and no gravitational fields are caused by acceleration.
>
> This is a topic for another discussion, but I'm talking about
> "pseudo-gravitational" fields, which crop up in both SR and Newtonian
> physics if you use accelerated coordinates.

We agree on "pseudo", while Einstein rejected that.

> >> I think it is because you have not made it very well. I still
> >> have no idea what your point is.
>
> >Just study Einstein's paper carefully,
>
> I want to know what *YOUR* point is. State it in your own words.

I did, also in the part of my sentence that you exactly here snipped:

*you'll know what theory the paradox challenges*.

THAT (and only that) was my point: the clock paradox challenges the
General PoR.

You certainly are aware that, despite Einstein's *suggestion* to that
effect in the introduction of his 1905 paper, SRT is *not* based on
the General PoR.

> >In this thread, you pretend no less than that:
>
> >- Newton was mistaken with his Space postulate (while you evidently
> >didn't even bother to read his arguments)
> >- you know better than Einstein what his own theory is about (Cranky)
>
> That isn't cranky. 100 years of relativity development does give
> one a more complete perspective. I would say that a typical physics
> graduate student understands Newtonian physics better than Newton,

?! You have just become aware (except if it hasn't sunk in yet) that a
typical physics student is clueless about Newtonian mechanics, since
he/she is taught something else instead. I find it a very illogical
statement that such a student would know Newton's physics better than
himself, after having been misinformed about it!

> and understands relativity better than Einstein.

That could very well be so (the word "relativity" isn't specifically
Einstein's theory).
Perhaps this is just about words? Do you call a plastic cup a "glass",
while I insist that it is a plastic cup, after which you insist that
plastic cups are much better glasses?!

> That doesn't mean
> that they are smarter than Newton or Einstein---it's a lot harder
> to invent a new theory than it is to understand or expand on an
> existing theory.

Yes.

> Anyway, I don't care to argue with Newton or with Einstein.
> They are not around to argue with.
>
> If you have a point to make, make it yourself. Don't
> hide behind Newton or Einstein.

I made my point at the start (a factual statement) - and you jumped on
it. ;-)

Harald