Re: Travelers L and R (a revised thought-experiment)
- From: xxein@xxxxxxxxxxx
- Date: Thu, 3 Jan 2008 22:33:42 -0800 (PST)
On Jan 3, 3:22 pm, "gharn...@xxxxxxxxxxx" <gharn...@xxxxxxxxxxx>
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. 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
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.
.
- References:
- Travelers L and R (a revised thought-experiment)
- From: gharnett@xxxxxxxxxxx
- Travelers L and R (a revised thought-experiment)
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