Travelers L and R (a revised thought-experiment)
ghar...@comcast.net
= multiple clocks?", a number of contributors got involved in a
discussion of the acceleration of the two observers, which distracted
this discussion from the principal question that I had in mind. The
error was mine, in framing the experiment as I did. Accordingly, I'd
like to revise the question appropriately, as follows:
Let's suppose that there are only two things in the universe, two
persons whom we'll name Jack Left and Joe Right -- for short, "Left"
and "Right," or "L" "R," respectively. L and R are at a great distance
from one another, and have had no interactions with one another at
all, apart from the tiny gravitational force that, according to our
understanding of gravitation, each exerts upon the other. Let's assume
also that L and R have always existed. We may suppose that at one time
in the past they lived on planets, but now these planets have ceased
to exist. At the moment that each of these planets ceased to exist, L
and R each departed from that point -- the point where their
respective planets ceased to exist -- at nearly the speed of light and
in the direction of the other -- straight at one another, in other
words; or almost straight at one another; let their direction of
travel be shifted ever so slightly, so that they do not crash into one
another at this fabulous speed, thus short-circuiting this thought-
experiment in a hyper-relativistic burst of scattering body-parts.
(Sorry, couldn't resist adding a little color.) Note that no
acceleration has necessarily occurred anywhere in the universe as thus
described. The planets on which L and R were traveling might also have
been traveling in the same directions and at the same speeds at which
L and R are traveling now.
I have two questions about this situation:
First, at what speed are L and R closing upon one another, given that,
according to the theory of special relativity ("T-SR"), it is
impossible to travel faster than the speed of light? Each departed
from the point of his planet's demise at nearly the speed of light,
but, as they are traveling in opposite directions and thus directly
toward one another, they are now closing upon another, it would seem,
at nearly twice the speed of light.Yet according to T-SR, motion at
greater than the speed of light is impossible. Let's symbolize the
distance covered by any traveler as D, and the speed of light by C. As
I understand T-SR and its implications with respect to motion, the
huge distances covered by, let us say, traveler L would be recorded by
L's own wristwatch as taking almost no time, given his speed of
motion, while, by R's wristwatch, the time taken by L in covering any
distance will be recorded as having taken D/C.
Second, what, if anything, happens to the rates of their wristwatches
when they pass one another? (This is the heart of the situation that I
wanted to consider in asking the question of my first thread about
"though-experiments," the one involving Observers A and B.) When that
happens, the rate of their speed of motion with respect to one another
remains the same, but their directions of travel with respect to one
another reverses. As I understand T-SR, the wristwatch of each party,
as thitherto, continues to show almost no change, given his speed of
travel (relative to the point at which his originating planet last
existed) at nearly C. Nonetheless, each party is covering huge
distances, which are clocked as before by the other party at D/C. I
presume that the answer to this question is "nothing," and that this
second half of the situation does not differ in any important way from
the first. I ask it only to establish the link between the problem
posed in this thread and that posed in the other, for the benefit of
those who participated in the prior discussion.
Note, incidentally, that I have not called the two parties, L and R,
"observers." This is not a problem of observation. The peculiarities
of light and the problems posed by its speed of motion are
interesting, but not fundamental to the ontological problems raised by
T-SR.
My thanks.
G Harnett
Dirk Van de moortel
<ghar...@comcast.net> wrote in message news:8ef20244-364f-406f...@m34g2000hsf.googlegroups.com...
> In response to my question on the thread entitled "do multiple speeds
> = multiple clocks?", a number of contributors got involved in a
> discussion of the acceleration of the two observers, which distracted
> this discussion from the principal question that I had in mind. The
> error was mine, in framing the experiment as I did. Accordingly, I'd
> like to revise the question appropriately, as follows:
>
> Let's suppose that there are only two things in the universe, two
> persons whom we'll name Jack Left and Joe Right -- for short, "Left"
> and "Right," or "L" "R," respectively. L and R are at a great distance
> from one another, and have had no interactions with one another at
> all, apart from the tiny gravitational force that, according to our
> understanding of gravitation, each exerts upon the other. Let's assume
> also that L and R have always existed. We may suppose that at one time
> in the past they lived on planets, but now these planets have ceased
> to exist. At the moment that each of these planets ceased to exist, L
> and R each departed from that point -- the point where their
> respective planets ceased to exist -- at nearly the speed of light
So they both accelerate their brains inside out.
You have symmertic situation now.
You'll get symmetric results.
So you should be able to answer your own questions.
> and
> in the direction of the other -- straight at one another, in other
> words; or almost straight at one another; let their direction of
> travel be shifted ever so slightly, so that they do not crash into one
> another at this fabulous speed, thus short-circuiting this thought-
> experiment in a hyper-relativistic burst of scattering body-parts.
> (Sorry, couldn't resist adding a little color.) Note that no
> acceleration has necessarily occurred anywhere in the universe as thus
> described. The planets on which L and R were traveling might also have
> been traveling in the same directions and at the same speeds at which
> L and R are traveling now.
>
> I have two questions about this situation:
>
> First, at what speed are L and R closing upon one another, given that,
> according to the theory of special relativity ("T-SR"), it is
> impossible to travel faster than the speed of light? Each departed
> from the point of his planet's demise at nearly the speed of light,
> but, as they are traveling in opposite directions and thus directly
> toward one another, they are now closing upon another, it would seem,
> at nearly twice the speed of light.Yet according to T-SR, motion at
> greater than the speed of light is impossible
No object can be measured to have a speed greater than
light speed with respect to himself.
The distance between two objects can increase (opening speed)
or decrease (closing speed) at a rate of max twice the speed of light
as measured by a third party observer.
>. Let's symbolize the
> distance covered by any traveler as D, and the speed of light by C. As
> I understand T-SR and its implications with respect to motion, the
> huge distances covered by, let us say, traveler L would be recorded by
> L's own wristwatch as taking almost no time, given his speed of
> motion, while, by R's wristwatch, the time taken by L in covering any
> distance will be recorded as having taken D/C.
>
> Second, what, if anything, happens to the rates of their wristwatches
> when they pass one another?
L will measuse R's clock to "run slower than his own".
R will measure L' clock to "run lower than his own".
When they pass each other the readings are the same.
You have created a symmertic situation.
You have symmetric results.
> (This is the heart of the situation that I
> wanted to consider in asking the question of my first thread about
> "though-experiments," the one involving Observers A and B.) When that
> happens, the rate of their speed of motion with respect to one another
> remains the same, but their directions of travel with respect to one
> another reverses. As I understand T-SR, the wristwatch of each party,
> as thitherto, continues to show almost no change, given his speed of
> travel (relative to the point at which his originating planet last
> existed) at nearly C. Nonetheless, each party is covering huge
> distances, which are clocked as before by the other party at D/C. I
> presume that the answer to this question is "nothing," and that this
> second half of the situation does not differ in any important way from
> the first. I ask it only to establish the link between the problem
> posed in this thread and that posed in the other, for the benefit of
> those who participated in the prior discussion.
>
> Note, incidentally, that I have not called the two parties, L and R,
> "observers." This is not a problem of observation.
Physics is about observation.
Different observers make measurements, write everything
down, and get together ten years later to compare the
results. Then it turns out that they noticed each other's
clock to run slower, yet showed the same time when they
passed each other.
> The peculiarities
> of light and the problems posed by its speed of motion are
> interesting, but not fundamental to the ontological problems raised by
> T-SR.
>
> My thanks.
>
> G Harnett
Dirk Vdm
PD
wrote:
Let's be concrete. Let's assume that in the frame of reference where
they are observed traveling at the same speed, that speed is (say)
0.995000c. Then in this reference frame, the closing speed between L
and R is 1.990000c. In the reference frame in which L is at rest, then
R's speed (which happens to be the closing speed between L and R) will
be 0.999987c. In the reference frame in which R is at rest, then L's
speed (which happens to be the closing speed between L and R) will be
0.999987c.
There are several useful things to learn from this exercise:
1. The closing speed between two moving objects in a given reference
frame is not limited to c. Only the measured speed of any given object
is limited to c.
2. The closing speed between two objects is not the same from
reference frame to reference frame. And no, the principle of
relativity does NOT demand that they should be the same.
3. To move from one reference frame to another does not mean simply
adding or subtracting speeds. Speeds don't combine that way, despite
what you might have read in chapter 2 of a physics book.
I'm curious what preconceptions you have about these useful things
learned.
>
> Second, what, if anything, happens to the rates of their wristwatches
> when they pass one another? (This is the heart of the situation that I
> wanted to consider in asking the question of my first thread about
> "though-experiments," the one involving Observers A and B.) When that
> happens, the rate of their speed of motion with respect to one another
> remains the same, but their directions of travel with respect to one
> another reverses. As I understand T-SR, the wristwatch of each party,
> as thitherto, continues to show almost no change, given his speed of
> travel (relative to the point at which his originating planet last
> existed) at nearly C. Nonetheless, each party is covering huge
> distances, which are clocked as before by the other party at D/C. I
> presume that the answer to this question is "nothing," and that this
> second half of the situation does not differ in any important way from
> the first. I ask it only to establish the link between the problem
> posed in this thread and that posed in the other, for the benefit of
> those who participated in the prior discussion.
They will show the same time on the watches as they pass by each
other. However, if they were to observe each other's watches for a
short period of time surrounding that moment, L would say that R's
watch is running slow, and R would say that L's watch is running slow.
There are also a number of interesting lessons from this exercise as
well, but I think I'll let you splutter about the first exercise
first.
Androcles
dx/dt for L in the frame of R.
d(xi)/d(tau) for R in the frame of L. (Sorry, no can do real Greek
characters.)
xi = (x-(dx/dt)t)/sqrt(1- (dx/dt) ^2/c^2)
tau = t * sqrt(1- (dx/dt)^2/c^2)
xi/tau = (x-(dx/dt)t)/ (t * (1- (dx/dt)^2/c^2))
BTW, you need not worry about the crash, L meets R at
a different time to R meeting L.
: Each departed
: from the point of his planet's demise at nearly the speed of light,
: but, as they are traveling in opposite directions and thus directly
: toward one another, they are now closing upon another, it would seem,
: at nearly twice the speed of light.Yet according to T-SR, motion at
: greater than the speed of light is impossible. Let's symbolize the
: distance covered by any traveler as D, and the speed of light by C. As
: I understand T-SR and its implications with respect to motion, the
: huge distances covered by, let us say, traveler L would be recorded by
: L's own wristwatch as taking almost no time, given his speed of
: motion, while, by R's wristwatch, the time taken by L in covering any
: distance will be recorded as having taken D/C.
:
: Second, what, if anything, happens to the rates of their wristwatches
: when they pass one another?
Sorry, we are not permitted to discuss that. See footnote 3.
"We shall not here discuss the inexactitude which lurks in the concept of
simultaneity of two events at approximately the same place, which can only
be removed by an abstraction."
Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/
[illegal discussion removed]
Sue...
wrote:
[...]
>
> Let's suppose that there are only two things in the universe,
Not really the sort of place you'd visit to study inertia.
<< Already Newton recognized that the
law of inertia is unsatisfactory
in a context so far unmentioned in this
exposition, namely that it gives no
real cause for the special physical
position of the states of motion of the
inertial frames relative to all other
states of motion. It makes the observable
material bodies responsible for the
gravitational behaviour of a material
point, yet indicates no material cause
for the inertial behaviour of the material
point but devises the cause for it
(absolute space or inertial ether). This
is not logically inadmissible although
it is unsatisfactory. For this reason
E. Mach demanded a modification of the
law of inertia in the sense that the
inertia should be interpreted as an
acceleration resistance of the bodies
against one another and not against "space".
This interpretation governs the expectation
that accelerated bodies have concordant
accelerating action in the same
sense on other bodies (acceleration induction).
This interpretation is even more
plausible according to general relativity
which eliminates the distinction between
inertial and gravitational effects.
It amounts to stipulating that, apart
from the arbitrariness governed by the
free choice of coordinates, the
gm v -field shall be completely determined
by the matter. Mach's stipulation is favoured
in general relativity by the circumstance
that acceleration induction in accordance
with the gravitational field equations really
exists, although of such slight intensity
that direct detection by mechanical experiments
is out of the question. >>
http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.html
Sue...
>
> G Harnett
Jeckyl
news:ad4e3cfe-a527-454c...@s19g2000prg.googlegroups.com...
> On Jan 3, 3:22 pm, "gharn...@comcast.net" <gharn...@comcast.net>
> wrote:
> [...]
>
>
>
>>
>> Let's suppose that there are only two things in the universe,
>
> Not really the sort of place you'd visit to study inertia.
Same old copy-paste links that Sue pastes, regardless of the topic. She
doesn't acutally know wanything other than copyand paste
xx...@comcast.net
xxein: Troubled? At least you have the honesty to admit it. Almost
all others will latch onto the math of SR. Those not troubled are
idiots.
I want to give you a way to understand this but it cannot be short.
Maybe you can answer your own question by thinking that if L and R are
not observers, what is the basis for any velocity and wrt what. This
is a key element for an understanding of how velocity addition works
both within and without SR. Don't think in terms of Einstein, Mach or
Lorentz.
Then, can you come up with something that is physically logical that
differs from present existing theory candidates?
For now, I am way past a bedtime.
Don't let your belief be dictated by the devil with the most money.
Dirk Van de moortel
"Androcles" <Engi...@hogwarts.physics_c> wrote in message news:JZefj.74576$036....@fe1.news.blueyonder.co.uk...
That's what you get when you have no idea what the
variables, let alone the equations, are supposed to
represent. How amusingly painful.
Dirk Vdm
bryanjuggler...@yahoo.com
> In response to my question on the thread entitled "do multiple speeds
> = multiple clocks?", a number of contributors got involved in a
> discussion of the acceleration of the two observers, which distracted
> this discussion from the principal question that I had in mind.
A number of others pointed out that you need to specify the
frame in which you compare the watches. You incorrectly
dismissed the critical issue based on your misconceptions.
> The error was mine, in framing the experiment as I did.
Actually the discussion of acceleration showed that you had
it so wrong as to think accelerating one body means both
will experience symmetric acceleration. Even after you
looked it up, you had acceleration in units of mass over
the square of time.
> Accordingly, I'd
> like to revise the question appropriately, as follows:
The first two responses you got, from Dirk and PD, are
good. Do not dismiss them. If you only have time to write
one response, I suggest following up PD's, because of the
specifics he offered. Please do not continue your poor
Usenet behavior of wring off-strand dismissals,
disrespectful of the very explanations you had requested.
--
--Bryan
Dirk Van de moortel
<bryanjuggler...@yahoo.com> wrote in message news:745e12f0-eb15-4963...@j20g2000hsi.googlegroups.com...
> gharn...@comcast.net wrote:
>> In response to my question on the thread entitled "do multiple speeds
>> = multiple clocks?", a number of contributors got involved in a
>> discussion of the acceleration of the two observers, which distracted
>> this discussion from the principal question that I had in mind.
>
> A number of others pointed out that you need to specify the
> frame in which you compare the watches. You incorrectly
> dismissed the critical issue based on your misconceptions.
>
>> The error was mine, in framing the experiment as I did.
>
> Actually the discussion of acceleration showed that you had
> it so wrong as to think accelerating one body means both
> will experience symmetric acceleration. Even after you
> looked it up, you had acceleration in units of mass over
> the square of time.
>
>> Accordingly, I'd
>> like to revise the question appropriately, as follows:
>
> The first two responses you got, from Dirk and PD, are
> good. Do not dismiss them. If you only have time to write
> one response, I suggest following up PD's, because of the
> specifics he offered.
Yes, I second that.
Dirk Vdm