[ExI] QT and SR

[Lee Corbin]

Jeff writes

> On Fri, Aug 8, 2008 at 1:51 AM,
> 
> After Lee cCorbin wrote:

I never was a cat. And so far as I know, the Cordwainer
(Smith) never narrated my adventures. You may be thinking
of C'mell or of some of the other cat people, but none of
my ancestors were animals or underpeople any more
recently than were yours. (Unless you're really Jeff D'avis.)

>>> Your "line of simultaneity" shifts as your velocity increases.

It was my need for email conciseness that caused me to fail
to imply that this is a technical term in the special relativistic
theory.  The absolute *key* to both an intuitive and technical
understanding of Special Relativity is to thoroughly expunge
the intuition of simultaneity in one's thinking.

>"My" line, by which you mean the line of someone outside the
> ships/strings frame of reference.  But then you go back into the
> ships/strings frame of reference and cite the sleepy cabin officer's
> view of things.  Isn't there some inconsistency here?  I mean frame if
> reference -wise?

Sorry, I meant that your line of simultaneity, the x-axis on any
ordinary spacetime diagram you draw, is horizontal in that
diagram before you begin to move, but then it's at an angle.
But at the risk of being misunderstood, I mean this: if on an
ST diagram you plot your position as x=0, then you "move"
up the t-axis as time passes, while someone moving at c/2
to the right relative to you, has, on the same diagram his
t-axis tilted slightly to the right.

That part is easy to understand (and you probably already do).
Because to him, he's not moving, and so his own motion is
only into the future, and that's along his t-axis, which has to
be inclined at a small angle to yours.

But his "line of simultaneity" is also at a small angle to yours!
(Many apologies if you already understand all this, but at least
I console myself that there are readers who don't.)  It so 
happens, and can be figured out (I think) without recourse
to equations by carefully thinking it through, that his line
of simultaneity is rotated a bit counter-clockwise, (while
recall that his t-axis is rotated a bit clock-wise). 

Naturally, in his frame of reference, it's just opposite, and
your t-axis is tilted slightly to the left (according to his
diagram), and your x-axis line of simultaneity is garishly
rotated clockwise.

> Now Jeff Davis is writing: Whoops!  I misread Lee's line above.  He is
> indeed referring consistently to the view from inside the accelerating
> frame of reference.  To wit, "Your line,,,as your velocity increases."

Actually, I agreed with your criticism!  At very least, the way 
you at first misread it will happen to others too.

For about 20 years I kept being under the illusion, as I encountered
one more SR puzzle ("paradox") after another, whether it was the
"pole and barn", or or "twin paradox" or "the rotated cube", (and
conquered them) that I had reached mastery. Then around 1990
I saw this "Bell Spaceship Paradox" in his book "Speakable and
Unspeakable in Quantum Mechanics", and I realized that sooner
or later someone will present me with yet another paradox that
baffles me.

One of the more recent was this, and it's good! (I think so,
mainly because it was my own invention.)  You are in a 
spaceship approaching a solar system face on (not edge on).
You see the planets rather too quickly moving around their
sun (in conflict with the Federation's excellent Star System Atlas
and Catalog), but then, of course, you correct for the fact that you
are *approaching* and there is a Doppler shift. 

But now your new *measurements* (rather than mere observations,
as at least I like to say), yield motion that is too slow for the
planets!  "Of course", finally you exclaim, "due to time dilation, things
in my reference system (my reality) really are moving more slowly."
But then you have a horrid thought:  "Wait! The masses of all those
planets in my frame of reference---the masses as I would weigh
them if I pass close enough to bound balls off them---will be increased!
And then, because that sun and those planets are more massive, their
motion will speed up because of the excellent Newtonian formula
F = Gm1m2/r^2, and the greatly needed increase in centrifugal force
necessary to overcome the resulting force!  So how can that be?"

I credit Hal Finney, probably on this forum, for providing the answer.

But I do understand that there will always be yet one more
paradox, even in SR, of which I have not yet heard, that will
floor me.

Lee

----- Original Message ----- 
From: "Lee Corbin" <lcorbin at rawbw.com>
To: "Jeff Davis" <jrd1415 at gmail.com>
Sent: Saturday, August 09, 2008 12:26 PM
Subject: Re: [ExI] QT and SR


> Jeff writes
> 
>> On Fri, Aug 8, 2008 at 1:51 AM,
>> 
>> After Lee cCorbin wrote:
> 
> I never was a cat. And so far as I know, the Cordwainer
> (Smith) never narrated my adventures. You may be thinking
> of C'mell or of some of the other cat people, but none of
> my ancestors were animals or underpeople any more
> recently than were yours. (Unless you're really Jeff D'avis.)
> 
>>>> Your "line of simultaneity" shifts as your velocity increases.
> 
> It was my need for email conciseness that caused me to fail
> to imply that this is a technical term in the special relativistic
> theory.  The absolute *key* to both an intuitive and technical
> understanding of Special Relativity is to thoroughly expunge
> the intuition of simultaneity in one's thinking.
> 
>>"My" line, by which you mean the line of someone outside the
>> ships/strings frame of reference.  But then you go back into the
>> ships/strings frame of reference and cite the sleepy cabin officer's
>> view of things.  Isn't there some inconsistency here?  I mean frame if
>> reference -wise?
> 
> Sorry, I meant that your line of simultaneity, the x-axis on any
> ordinary spacetime diagram you draw, is horizontal in that
> diagram before you begin to move, but then it's at an angle.
> But at the risk of being misunderstood, I mean this: if on an
> ST diagram you plot your position as x=0, then you "move"
> up the t-axis as time passes, while someone moving at c/2
> to the right relative to you, has, on the same diagram his
> t-axis tilted slightly to the right.
> 
> That part is easy to understand (and you probably already do).
> Because to him, he's not moving, and so his own motion is
> only into the future, and that's along his t-axis, which has to
> be inclined at a small angle to yours.
> 
> But his "line of simultaneity" is also at a small angle to yours!
> (Many apologies if you already understand all this, but at least
> I console myself that there are readers who don't.)  It so 
> happens, and can be figured out (I think) without recourse
> to equations by carefully thinking it through, that his line
> of simultaneity is rotated a bit counter-clockwise, (while
> recall that his t-axis is rotated a bit clock-wise). 
> 
> Naturally, in his frame of reference, it's just opposite, and
> your t-axis is tilted slightly to the left (according to his
> diagram), and your x-axis line of simultaneity is garishly
> rotated clockwise.
> 
>> Now Jeff Davis is writing: Whoops!  I misread Lee's line above.  He is
>> indeed referring consistently to the view from inside the accelerating
>> frame of reference.  To wit, "Your line,,,as your velocity increases."
> 
> Actually, I agreed with your criticism!  At very least, the way 
> you at first misread it will happen to others too.
> 
> For about 20 years I kept being under the illusion, as I encountered
> one more SR puzzle ("paradox") after another, whether it was the
> "pole and barn", or or "twin paradox" or "the rotated cube", (and
> conquered them) that I had reached mastery. Then around 1990
> I saw this "Bell Spaceship Paradox" in his book "Speakable and
> Unspeakable in Quantum Mechanics", and I realized that sooner
> or later someone will present me with yet another paradox that
> baffles me.
> 
> One of the more recent was this, and it's good! (I think so,
> mainly because it was my own invention.)  You are in a 
> spaceship approaching a solar system face on (not edge on).
> You see the planets rather too quickly moving around their
> sun (in conflict with the Federation's excellent Star System Atlas
> and Catalog), but then, of course, you correct for the fact that you
> are *approaching* and there is a Doppler shift. 
> 
> But now your new *measurements* (rather than mere observations,
> as at least I like to say), yield motion that is too slow for the
> planets!  "Of course", finally you exclaim, "due to time dilation, things
> in my reference system (my reality) really are moving more slowly."
> But then you have a horrid thought:  "Wait! The masses of all those
> planets in my frame of reference---the masses as I would weigh
> them if I pass close enough to bound balls off them---will be increased!
> And then, because that sun and those planets are more massive, their
> motion will speed up because of the excellent Newtonian formula
> F = Gm1m2/r^2, and the greatly needed increase in centrifugal force
> necessary to overcome the resulting force!  So how can that be?"
> 
> I credit Hal Finney, probably on this forum, for providing the answer.
> 
> But I do understand that there will always be yet one more
> paradox, even in SR, of which I have not yet heard, that will
> floor me.
> 
> Lee
>