Which clock is slower?
Edward Schaefer
time in history allows people to go at relativistic speeds wrt each
other. As their first project, they have decided to test Relativity and
its prediction a clock which is moving wrt ones self goes slower. To do
this, they agree to set a line of clocks into motion at .866c (the speed
where gamma = 2) and have consecutive clocks be 1.732 light-seconds
apart. That way each clock will pass the other's clock once every 2
seconds.
So observer B, with the zamjet, heads out, and in a frame of reference
moving at 0.866c wrt observer A sets up his clocks, synchronizes them,
and sets them in motion. In the meantime, observer A has also set up
his own line of clocks in the same way, and also synchronizes them.
Finally, at the appointed time, clock 0 of observer B passes clock 0 of
observer A (You will see why I call the initial clocks "clock 0" in a
moment), and does so at the designated 0.866c. Then one second later,
clock 1 of observer B passes clock 0 of observer A; 2 seconds into the
experiment B's clock 2 passes A's clock 0; 3 seconds into the experiment
and here is yet another of B's clocks! So A shoots off a message to B
saying "Hey! The clocks are supposed to be 1.732 light seconds apart,
not .866 light seconds apart". But no sooner has he sent his message
off, then an identical message arrives from B!
So A looks at the times recorded as being on B's clock 0 as it passed
each of his clocks. As A's clock 1 was passed as it read t=2, B's clock
0 read t'=1. At A's clock 2 as it read t=4, B's clock 0 read t'=2. And
so on. So it seems that B's clock really is ticking slower, and that is
why he sees A's clocks coming at him more quickly than expected. Even
so, it is disturbing that from B's viewpoint, A's clocks really are
closer together. Then again, A is also seeing B's clocks being closer
together! "Oh my God!" says A "We are seeing the Lorentz Contraction!".
So now that A understands why he is seeing a clock every second, he then
decides to see the time on each of B's clocks as they pass his clock 0.
B's clock 1 passed it at A's t=1, and read t'=2. At t=2, B's clock 2
read t'=4. At t=3, B's clock 3 read t'=6! To make matters worse, A
finds that each of these clocks are ticking at half-time. When B's
clock 3 passed A's clock 1 at A's t=5, it read t'=7! Then he realizes
that at that same t=5, B's clock 5 is passing his clock 0 reading
t'=10. Then it hits him: B's clocks are not synchronized! Little
wonder they are making his clocks look slow!
So once again A sends a message to B, this time reading "Hey you
idiot!! You forgot to synchronize your clocks! At my t=5, your clock 3
read t'=7 and your clock 5 read t'=10! Get your act together! OK?"
and now having smugly sent it off receives a message from B saying
exactly the same thing to him! So A shoots off a reply to that: "You're
not getting away with that kind of thing this time! I used Einstein's
calibration procedure. What did you do?" Then, no sooner is his reply
sent out, then one comes in from B, once again saying the same thing!
Then he looks at the time results again: B's clock 1 passed his clock 3
at its t=7, and read t'=5; and his clock 5 at t=10 was passed by B's
clock 0 as it read t'=5! Finally, A remembers the Relativity of
Simultaneity: Since it takes the calibration signals chasing a moving
clock from a moving source longer to get to the clock than return, the
rule of setting the clock being calibrated to the midpoint time between
the sending and receiving of the light pulses by the source causes the
time coordinates in a moving frame to be offset as a function of
distance in the direction of motion. So his readings and B's all turn
out to be consistent after all. All that was needed was to use the full
Lorentz Transformations, and the observed results fall right out.
So which clock is slower? Each in the other's frame-of-reference! Does
this make Relativity self-contradictory? Not at all.
EMS
pmb
Edward Schaefer <em...@erols.com> wrote in message
news:38D84ACF...@erols.com...
> Observers A and B have just invented the zamjet, which for the first
> time in history allows people to go at relativistic speeds wrt each
> other. As their first project, they have decided to test Relativity and
> its prediction a clock which is moving wrt ones self goes slower. To do
> this, they agree to set a line of clocks into motion at .866c (the speed
> where gamma = 2) and have consecutive clocks be 1.732 light-seconds
> apart. That way each clock will pass the other's clock once every 2
Alot there to read. I think I got the gist of it but I may be wrong since I
skimmed over it. It seems that your concern is on the rates and
syunchronization of clocks. SR does not state that one clock runs slower
than another. Only that A reckons B's clock to be runnning slow and that B
reckons A's clock to run slow. As far as synchronization goes - clocks in
relative motion can't in general be synchronized. If two clocks pass by each
other then they can be set to zero and we call them "synchronized" in the
sense that they both read "0." However the synchroniation doesn't hold for
all clocks at rest in each of A's an B's frames.
Did I skim too much?
Pete
Edward Schaefer
>
> Edward Schaefer <em...@erols.com> wrote in message
> news:38D84ACF...@erols.com...
> > Observers A and B have just invented the zamjet, which for the first
> > time in history allows people to go at relativistic speeds wrt each
> > other. As their first project, they have decided to test Relativity and
> > its prediction a clock which is moving wrt ones self goes slower. To do
> > this, they agree to set a line of clocks into motion at .866c (the speed
> > where gamma = 2) and have consecutive clocks be 1.732 light-seconds
> > apart. That way each clock will pass the other's clock once every 2
> > seconds. [snip]
>
> Alot there to read. I think I got the gist of it but I may be wrong since I
> skimmed over it. It seems that your concern is on the rates and
> syunchronization of clocks. SR does not state that one clock runs slower
> than another. Only that A reckons B's clock to be runnning slow and that B
> reckons A's clock to run slow.
Very good.
> As far as synchronization goes - clocks in
> relative motion can't in general be synchronized. If two clocks pass by each
> other then they can be set to zero and we call them "synchronized" in the
> sense that they both read "0." However the synchroniation doesn't hold for
> all clocks at rest in each of A's an B's frames.
>
> Did I skim too much?
Yes, but you are very close to the point anyway. A and B, independently
of the other, can synchronize their at-rest clocks. Note the "at rest"
is wrt the observer doing the synchronization. The trouble is that said
synchronization cannot be extended into the moving frame: "At the same
time" in A cannot contain the same events as "at the same time" in B
when both are in relative motion. Hence B's clocks, when read at the
same time in A's frame, each contain a different t' (and vice versa
too).
EMS
and...@attglobal.net
>
> Observers A and B have just invented the zamjet, which for the first
> time in history allows people to go at relativistic speeds wrt each
> other. As their first project, they have decided to test Relativity and
> its prediction a clock which is moving wrt ones self goes slower. To do
> this, they agree to set a line of clocks into motion at .866c (the speed
> where gamma = 2) and have consecutive clocks be 1.732 light-seconds
> apart. That way each clock will pass the other's clock once every 2
> seconds.
>
> moving at 0.866c wrt observer A sets up his clocks, synchronizes them,
> and sets them in motion. In the meantime, observer A has also set up
> his own line of clocks in the same way, and also synchronizes them.
>
As opposed to having me read the rest of this overly long epistle,
could you tell me what the punch line is?
You should realize that when you synch the clocks and then accelerate
them to some new velocity with the same acceleration for
each clock in the original rest frame, they won't be synched
with frame clocks in their new rest frame. What you did
to these clocks is not the equivalent of a Lorentz transformation.
This definitely affects which clock appears to be slower
since relativity of simultaneity is an important part
of explaining this when you consider two inertial frames.
That is definitely what you don't have in your scenario.
John Anderson
Frank Wappler
> Observers A and B have just invented the zamjet, which for the
> first time in history allows people to go at relativistic speeds
> wrt each other. As their first project, they have decided
> to test Relativity and its prediction a clock which is
> moving wrt ones self goes slower.
Talk of "experimental tests of relativity" is about as sensible as talk
of "experiments without specific experimental/measurement procedures".
Unless you specify _how_ to compare various clocks, this so-called
"prediction" is obviously not experimentally falsifiable at all.
And if you _do_ select a specific measurement procedure for
how to make that comparison, e.g. the measurement procedures of SR,
then your result doesn't provide "a test of the measurement procedure"
(since you've applied it already anyways; it couldn't be found "false",
after the fact, based on the very results it obtained),
but a test and measurement of whether or to which extent the clocks
you compared were equal, in your trial.
> To do this, they agree to set a line of clocks into motion at .866c
To do that, they must measure values of pairwise "velocity".
(Your specification of a velocity value measured as a fraction of "c"
suggests that they'd be using the SR procedures already.)
> (the speed where gamma = 2) and have consecutive clocks be
> 1.732 light-seconds apart.
To do that, they must measure values of pairwise "distance".
(Your specification of distance values measured as "c * interval"
suggests that they'd be using the SR procedures already.
If so, note that observers who measure nonzero velocity wrt. each other
will necessarily fail to calibrate their individual proper intervals
(such as "one second") directly to each other; instead, they'd use
the Lorentz transforms for those comparisons.)
> [...] So observer B, with the zamjet, heads out, and in a frame
> of reference moving at 0.866c wrt observer A sets up his clocks,
(I suppose that those clocks constitute "a frame of reference" if they
succeed in measuring their velocities as zero, pairwise wrt. each other,
as well as wrt. B, throughout the experiment.)
> synchronizes them
By which procedure?
(Given that the indicated measurements of distances and velocities
are obtained through the SR procedures, they'd be required to
succeed conducting Einstein's calibration procedure already.)
> [...]
> So A shoots off a reply [...] I used Einstein's calibration procedure.
There you go.
> [...] So his readings and B's all turn out to be consistent after all.
> All that was needed was to use the full Lorentz Transformations,
> and the observed results fall right out. So which clock is slower?
> Each in the other's frame-of-reference! Does this make Relativity
> self-contradictory? Not at all.
Splendid.
Now just what did A and B's experiment test?
AFAIU, the prediction/assumption/expectation that the proper interval
that A calls "second" and the proper interval that B calls "second"
are (pretty much) equal, as measured through the SR procedures.
Best regards, Frank W ~@) R
Edward Schaefer
>
> Edward Schaefer wrote:
> >
> > Observers A and B have just invented the zamjet, which for the first
> > time in history allows people to go at relativistic speeds wrt each
> > other. As their first project, they have decided to test Relativity and
> > this, they agree to set a line of clocks into motion at .866c (the speed
> > where gamma = 2) and have consecutive clocks be 1.732 light-seconds
> > seconds.
> >
> > and sets them in motion. In the meantime, observer A has also set up
> > his own line of clocks in the same way, and also synchronizes them.
> >
>
> As opposed to having me read the rest of this overly long epistle,
> could you tell me what the punch line is?
It is that which you wrote next!
> You should realize that when you synch the clocks and then accelerate
> them to some new velocity with the same acceleration for
> each clock in the original rest frame, they won't be synched
> with frame clocks in their new rest frame. What you did
> to these clocks is not the equivalent of a Lorentz transformation.
>
> This definitely affects which clock appears to be slower
> since relativity of simultaneity is an important part
> of explaining this when you consider two inertial frames.
> That is definitely what you don't have in your scenario.
You mean that you don't recognize Androcles' favorite question? Has it
not occurred to you that if Androcles learned of the discovery of the
zamjet first that he would have A and B set up the experiment like this?
Given that and an SR spacetime, what do you think would happen as a
result? That is what this posting is about.
EMS
Edward Schaefer
>
> Edward Schaefer wrote:
> >
> > [...] So his readings and B's all turn out to be consistent after all.
> > All that was needed was to use the full Lorentz Transformations,
> > and the observed results fall right out. So which clock is slower?
> > Each in the other's frame-of-reference! Does this make Relativity
> > self-contradictory? Not at all.
>
> Splendid.
> Now just what did A and B's experiment test?
SR itself. This gedanken (and I hope I spelled it correctly for once)
itself is to demonstrate the self-consistency of SR.
> AFAIU, the prediction/assumption/expectation that the proper interval
> that A calls "second" and the proper interval that B calls "second"
> are (pretty much) equal, as measured through the SR procedures.
Agreed, and that is a point that I should have made myself (instead of
taking it for granted). Thanks.
EMS
Androcles
> So which clock is slower? Each in the other's frame-of-reference! Does
> this make Relativity self-contradictory? Not at all.
Hmmm... So who is the younger, A or B?
Wait! I think I get it! They both are, right?
Androcles
Edward Schaefer
It depends on the world-line the each travelled before getting to the
experiment.
Suppose that A and B set it up so that they passed when they were both
exactly the same age. Now in A's frame, B is not aging as fast, while
in B's frame, A is not aging as fast. Each one's clock is good, and as
long as they stay the same state of relative motion there is no problem
and no contradiction (since the will never be side-by-side again in that
case).
Now suppose that one the experiment is over B uses the zamjet. He is
now in a different inertial frame, and his view of spacetime is modified
because of that that. So there is no symmetry between the observers
because acceleration is an absolute effect, and not a relative one like
velocity. (You *feel* an acceleration. You cannot feel a velocity.) So
B gets to see A age more than he as he rejoins A **after
accelerating**. There is symmetry here. If A had accelerated, he would
have wound up younger as he rejoins B **in B's inertial frame** for the
experiment. So the PoR applies here.
I trust that I have demonstrated the consistency of SR on its own terms
now. If you accept that you have three effects working together (time
dilation, Lorentz Contraction, and the Relativity of Simultaneity), then
the twin "paradox" will soon cease to be a problem. If you do not
accept the interconnectedness of the effects, then there is no use in
bothering with the "paradox" becuase you are discarding the machinery
needed to resolve it.
EMS
P.S. I can tell that you read it, and I can tell that is stymied you.
Go over it again. After all, if SR is not consistent, then there must
be problem **within the snipped text itself**.
Androcles
> P.S. I can tell that you read it, and I can tell that is stymied you.
> Go over it again. After all, if SR is not consistent, then there must
> be problem **within the snipped text itself**.
Aw... C'mon. I thought it was a good yarn. I just didn't quite get the
punchline, though.
Did you hear the one about how Santa delivers all the gifts to the little
kiddies on Xmas Eve? After all his time has run out in the early Xmas
morning, he flies around the world backwards, Superman style, until he is
back to 9:00 p.m. when all the little kiddies are tucked up in bed fast
asleep. Then he continues climbing down chimneys and eating cookies and
milk, delivering gifts as usual. As soon as it is Xmas morning again and the
kiddies are waking up, why, its "Hi, Ho!, Rudolph, away!" to fly around the
world backwards again for more deliveries at 9:00pm. In Santa's own frame of
reference this actually takes a year, so it really is a full-time
occupation.
We know this is true because all the little kiddies do get their prezzies,
and it is obvious that Santa couldn't deliver them all in just one night
without some very special relativistic physics to help him along.
You know what is wrong with this yarn?
It assumes the all the prezzies come from Santa, delivered in one night, so
it is circular.
Just like your yarn.
If we assume a = b, why, then of course we conclude a = b, don't we?
Where do you make the assumption?
Right in the first paragraph, of course.
"To do
this, they agree to set a line of clocks into motion at .866c (the speed
where gamma = 2) and have consecutive clocks be 1.732 light-seconds
apart. That way each clock will pass the other's clock once every 2
seconds."
The assumption having been made, naturally all that follows from it will be
as ridiculous as the original assumption. See Santa and the prezzies for an
example.
Androcles
Edward Schaefer
>
> Edward Schaefer <em...@erols.com> wrote:
>
> > P.S. I can tell that you read it, and I can tell that is stymied you.
> > Go over it again. After all, if SR is not consistent, then there must
> > be problem **within the snipped text itself**.
>
> The assumption [of SR spacetime] having been made, naturally all that
> follows from it will be as ridiculous as the original assumption.
That does not apply if a=b is somehow inconsistent with itself, which
you accuse SR of being.
Since you cannot find a problem with the original posting in this
thread, I trust that you now accept that SR is self-consistent. (That
does not refute c+v btw. It's observation that does that. :-) )
EMS
Frank Wappler
> Frank Wappler wrote:
> > Now just what did A and B's experiment test?
> SR itself.
> This gedanken (and I hope I spelled it correctly for once)
... not AFAIU. Perhaps you mean the german "Gedankenexperiment",
corresponding to the english translation "thought experiment" ...
> itself is to demonstrate the self-consistency of SR.
A demonstration, sure; but hardly an experimental test.
I'd call an experimental procedure (incl. preselected
measurement procedures) a test only wrt. results that are
_not_ explicitly assumed or predetermined, by those procedures.
For instance the test of whether
> > [...] the proper interval that A calls "second" and the proper
> > interval that B calls "second" are (pretty much) equal,
> > as measured through the SR procedures
or not.
The self-consistency of measurement procedures _can be_ evaluated
abstractly, as you just did, before and without referring to
any actual experimental results. And indeed, this _must be_ done,
in order to select self-consistent measurement procedures by which
to derive any experimental results in the first place.
Androcles
> Androcles wrote:
> >
> > Edward Schaefer <em...@erols.com> wrote:
> >
> > > P.S. I can tell that you read it, and I can tell that is stymied you.
> > > Go over it again. After all, if SR is not consistent, then there must
> > > be problem **within the snipped text itself**.
> >
> > If we assume a = b, why, then of course we conclude a = b, don't we?
> > ...
> > The assumption [of SR spacetime] having been made, naturally all that
> > follows from it will be as ridiculous as the original assumption.
>
> That does not apply if a=b is somehow inconsistent with itself, which
> you accuse SR of being.
Of course I do.
You wrote:
So which clock is slower? Each in the other's frame-of-reference! Does
this make Relativity self-contradictory? Not at all.
This was your punch-line, wasn't it? So a<b and b<a (or t'<t and t<t' if you
prefer).
That's a contradiction.
> Since you cannot find a problem with the original posting in this
> thread, I trust that you now accept that SR is self-consistent.
Of course I can. It's rather obvious, t'<t and t< t'.
If that is your idea of "consistent", then I'll agree that SR is
self-consistently self-contradictory.
> does not refute c+v btw. It's observation that does that. :-) )
Sure, just as the kiddies presents on Xmas day is observation of Santa's
visit.:-)
Androcles
Dan H. Lewis
>You wrote:
>>So which clock is slower? Each in the other's frame-of-reference!
>>Does this make Relativity self-contradictory? Not at all.
>
>This was your punch-line, wasn't it? So a<b and b<a
>(or t'<t and t<t' if you prefer). That's a contradiction.
I suppose you're just joke about this, but in case you honestly
don't understand, your mistake is failing to distinguish between
distinct things. Let the symbol (x|y) denote the rate of x's
clock with respect to y's inertial coordinate system. Then for
two relatively moving clocks a and b, we have (b|a) < (a|a)
and (a|b) < (b|b). This obviously doesn't imply a contradiction.
If you prefer to think pictorially, suppose you and I depart from
a point and travel at the same absolute speed v in straight lines
with an angle of theta between our directions. The rate at which
you are advancing in my direction of travel is cos(theta) v, and
likewise the rate at which I am advancing in your direction of
travel is cos(theta) v. So we are each going slower than the
other in our own directions! Is this a paradox? Of course not.
It's exactly the same when comparing clock rates in special
relativity, because each of us is evaluating the others speed
or rate projected onto our own axis. Obviously such projections
don't tell the whole story, but they aren't false or self-
contradictory.
Androcles
Dan H. Lewis <dhl...@circuitcircus.com> wrote in message
news:38dac506....@news.gte.net...
of a magnifying glass, and each sees the other as huge. The reality of the
situation is that they are both normal size, and the magnifying glass
produces illusion. The same applies to your idea about time, or your
directions.
When the two meet again, at rest, both wristwatches will be reading the
exact same hour, minute and second if they were previously synchronized
before they parted.
I'll tell you why. When they depart, a light signal is sent to a very
distant point in space where it reflects and returns to its point of
departure. This happens to coincide with the moment that A and B return.
Since the velocity of light is (supposedly) the same for them both and the
distance to the remote point in space is the same for them both, the time
for the light to go out and back is the same for them both. Now if you want
to, you can suppose that the distance point, (Pluto for example) jumped out
of its orbit for one of them so that they can record different times for the
light's journey while they went off jaunting in Ed's zamjets. Me, I don't
buy it. Pluto doesn't change its distance from Earth just because one of
them went for a ride, and if you think you can take me for a ride, think
again. Incidentally, their two watches will also synchronize with the clocks
on Earth, unless they are defective.
When Armstrong stood on the Moon, everybody recognized that it takes finite
time for light to travel the intervening distance, and nobody pretended that
Armstrong's watch was 1.285 seconds lagging Earth clocks (except
relativists), and Armstrong did not pretend that Earth's clocks lagged his
by 1.285 seconds either.
Androcles
Edward Schaefer
>
> Pluto doesn't change its distance from Earth just because one of
Yes and No. Its distance as perceived from the Earth does not change
becuase one of them went for a ride. That says nothing nothing about
that distance as perceived by the one who is riding.
Go back to my exercise. As far a A is concerned, B's clocks are only
seperated by .866 light seconds instead of the desired 1.732 light
seconds, and yet B has made sure that they are seperated by 1.732
light-seconds --- in *his* frame-of-reference. And since B's clocks are
time dilated (in A's frame), he is quite right to tell A "Hey! It's your
clocks that are too close together" even though A see's one of B's
clocks pass each of his at rate of 1 every 2 seconds. After all, B's
clocks get to tick only 1 second between clock passes.
And becuause of the Relativity of Simultaneity, you can exchange "A" and
"B" in the last paragraph without trouble.
So there are three "odd" effects in SR:
- Time Dilation.
- Lorentz Contraction.
- Relativity of Simultaneity.
It takes *all three* to make Relativity self-consistent. Declare any
one of them to be "obviously bogus" and refuse to consider it in an
analysis of SR, and voila! Contradiction! The trouble is that what is
self-contradictory is not SR, but instead your failure to use it.
It's something that every anti-relativist does, and you need to be aware
of that.
I wish you luck in finding the truth. Not Truth (which is what you now
have), but just plain truth.
EMS
Dan H. Lewis
>>So which clock is slower? Each in the other's frame-of-reference!
>(or t'<t and t<t' if you prefer). That's a contradiction.
I replied: No, it just means that (b|a) < (a|a) and (a|b) < (b|b).
On Fri, 24 Mar 2000 "Androcles" wrote:
>I don't think it is a paradox if two people look at each other
>on each side of a magnifying glass, and each sees the other as
>huge.
Okay, so you now agree that each clock running slow with respect
to the other clock's inertial coordinates is not logically
self-contradictory. Good.
Now you're in search of a NEW basis for claiming that special
relativity is inconsistent. Let's see what you come up with:
On Fri, 24 Mar 2000 "Androcles" wrote:
>When the two meet again, at rest, both wristwatches will be
>reading the exact same hour, minute and second if they were
>previously synchronized before they parted.
Hmm... well, this isn't a claim of logical inconsistency, it's
a claim that special relativity fails empirically. What has
happenned to your claim of inconsistency? Do you now conceed
that it isn't inconsistent? Let's see where you go with this:
On Fri, 24 Mar 2000 "Androcles" wrote:
>I'll tell you why. When they depart, a light signal is sent to a
>very distant point in space where it reflects and returns to its
>point of departure. This happens to coincide with the moment that
>A and B return.
Okay.
On Fri, 24 Mar 2000 "Androcles" wrote:
>Since the velocity of light is (supposedly) the same for them both
>and the distance to the remote point in space is the same for them
>both, the time for the light to go out and back is the same for
>them both.
Nope, the speed of light need not generally c with respect to
accelerating coordinate systems (according to special relativity).
Hence your argument fails.
Okay, so we've dispensed with your second objection. Let's see what
else you can come up with:
On Fri, 24 Mar 2000 "Androcles" wrote:
>Now if you want to, you can suppose that the distant point, (Pluto
>for example) jumped out of its orbit for one of them so that they
>can record different times for the light's journey while they went
>off jaunting in Ed's zamjets. Me, I don't buy it.
Who or what is asking you to "buy" Pluto jumping out of it's orbit?
We were talking about special relativity, and now you seem to be
critiquing some unnamed theory that says planets jump out of their
orbits. Suffice it to say that special relativity predicts no such
thing, so again your argument (really just an insane allegation) is
invalid.
Well, let's follow this through to the bitter end. What's your
next argument? This better be good.
On Fri, 24 Mar 2000 "Androcles" wrote:
>When Armstrong stood on the Moon, everybody recognized that it
>takes finite time for light to travel the intervening distance...
True enough.
>..and nobody pretended that Armstrong's watch was 1.285 seconds
>lagging Earth clocks...
True enough.
>(except relativists)
False. No relativist (if by that you mean someone who is acquainted
with relativity) pretended, claimed, implied, or asserted that clocks
on the Moon lag 1.285 seconds behind clocks on Earth. So again, this
argument (if that's what it was) is invalid.
>and Armstrong did not pretend that Earth's clocks lagged his
>by 1.285 seconds either.
I would say this is also true, but has no bearing on the predictions
of special relativity.
Well, that was your post, in all its glory. I'd have to say that
you were unsuccessful in articulating any cogent, or even coherent,
argument against either the logical consistency or the empirical
validity of special relativity. If that's your best shot, then
it's pretty sad.
Androcles
> On Fri, 24 Mar 2000 "Androcles" wrote:
> >>So which clock is slower? Each in the other's frame-of-reference!
> >This was your punch-line, wasn't it? So a<b and b<a
> >(or t'<t and t<t' if you prefer). That's a contradiction.
>
> I replied: No, it just means that (b|a) < (a|a) and (a|b) < (b|b).
>
> On Fri, 24 Mar 2000 "Androcles" wrote:
> >I don't think it is a paradox if two people look at each other
> >on each side of a magnifying glass, and each sees the other as
> >huge.
>
> Okay, so you now agree that each clock running slow with respect
> to the other clock's inertial coordinates is not logically
> self-contradictory. Good.
>
> Now you're in search of a NEW basis for claiming that special
> relativity is inconsistent. Let's see what you come up with:
>
> On Fri, 24 Mar 2000 "Androcles" wrote:
> >When the two meet again, at rest, both wristwatches will be
> >reading the exact same hour, minute and second if they were
> >previously synchronized before they parted.
>
> Hmm... well, this isn't a claim of logical inconsistency, it's
> a claim that special relativity fails empirically.
Well, ok. SR fails empirically.
What has
> happenned to your claim of inconsistency? Do you now conceed
> that it isn't inconsistent?
No, I do not concede.
Let's see where you go with this:
>
> On Fri, 24 Mar 2000 "Androcles" wrote:
> >I'll tell you why. When they depart, a light signal is sent to a
> >very distant point in space where it reflects and returns to its
> >point of departure. This happens to coincide with the moment that
> >A and B return.
>
> Okay.
>
> On Fri, 24 Mar 2000 "Androcles" wrote:
> >Since the velocity of light is (supposedly) the same for them both
> >and the distance to the remote point in space is the same for them
> >both, the time for the light to go out and back is the same for
> >them both.
>
> Nope, the speed of light need not generally c with respect to
> accelerating coordinate systems (according to special relativity).
> Hence your argument fails.
Okay, It fails. Given your statement plus the fact that there are NO
non-accelerating anywhere in the Universe, SR is about as pointless as a
discussion on the mating habits of bright green flying elephants.
And pointless as special relativity. There are no non-accelerating frames in
all of Nature.
However, there seems to be a bone of contention between relativists as to
what it's equations should be.
If as EMS states (and you agree with) each sees the other's clock as slower
than his own, then it should follow that
t' = gamma*(t - x*v/c^2)
t = gamma*(t' - x'*v/c^2)
Having made this point myself, it was strongly disputed by EMS and Paul
Andersen, both of whom insisted that the equations should be
t' = gamma*(t - x*v/c^2)
t = gamma*(t' + x'*v/c^2)
As far as I can tell, special relativity and its proponents are pretty sad
(and inconsistent).
Still, perhaps you can resolve the dispute between them. Obviously I cannot,
for I'm not a relativist and will not be listened to.
Androcles
Androcles
> Androcles wrote:
> >
> > Pluto doesn't change its distance from Earth just because one of
> > them went for a ride.
>
> Yes and No. Its distance as perceived from the Earth does not change
> becuase one of them went for a ride. That says nothing nothing about
> that distance as perceived by the one who is riding.
>
> Go back to my exercise. As far a A is concerned, B's clocks are only
> seperated by .866 light seconds instead of the desired 1.732 light
> seconds, and yet B has made sure that they are seperated by 1.732
> light-seconds --- in *his* frame-of-reference. And since B's clocks are
> time dilated (in A's frame), he is quite right to tell A "Hey! It's your
> clocks that are too close together" even though A see's one of B's
> clocks pass each of his at rate of 1 every 2 seconds. After all, B's
> clocks get to tick only 1 second between clock passes.
>
> And becuause of the Relativity of Simultaneity, you can exchange "A" and
> "B" in the last paragraph without trouble.
So why does Paul insist that
t' = gamma*(t - x*v/c^2)
t = gamma*(t' + x'*v/c^2)
?
After all, I'm exchanging A and B and is seems to be causing a great deal of
trouble.
> So there are three "odd" effects in SR:
> - Time Dilation.
> - Lorentz Contraction.
> - Relativity of Simultaneity.
>
> It takes *all three* to make Relativity self-consistent. Declare any
> one of them to be "obviously bogus" and refuse to consider it in an
> analysis of SR, and voila! Contradiction! The trouble is that what is
> self-contradictory is not SR, but instead your failure to use it.
Okay, I'll use it.
t' = gamma*(t - x*v/c^2)
t = gamma*(t' - x'*v/c^2)
Each sees the other's clock as slower than his own. Happy?
> It's something that every anti-relativist does, and you need to be aware
> of that.
Okay, I used it. Happy?
>
> I wish you luck in finding the truth. Not Truth (which is what you now
> have), but just plain truth.
Sure. Each sees the other's clock as slower than his own. Got it.
When Armstong was standing on the Moon, we saw his watch was lagging clocks
on Earth and he saw clocks on Earth were lagging his clock. When Armstrong
was on his way to the Moon, he saw clocks on Earth gradually losing time,
and we saw his watch gradually losing time.
You know what is really odd about this? When he was on his way home he saw
clocks on Earth gaining, not losing. And strange as may seem to a
relativist, we saw his watch gaining, not losing. When he arrived, lo and
behold his watch was synchronized with Earth clocks.
And guess what? It really doesn't matter what the value of v is for this to
happen.
There is another way that we can tell this is so. As Armstrong approaches
the Earth, the Earth itself is eclipsing background stars. Light from those
stars takes a finite time to reach Armstrong.
The position of the Earth against the cosmic background is the hand of a
clock that displays the universal time. Armstrong agrees with that time. We
also can note that Armstrong's craft, tiny though it may be, eclipsed
starlight reaching us. If Armstrong finds by his watch that the Earth is not
where it ought to be, then you may safely conclude that time, for Armstrong,
has in some way become different to time on Earth.
So it is with your array of clocks. Each planet is always in exactly the
correct position throughout any journey at any velocity you care to make,
and the only factors that will make it appear otherwise is the finite speed
of light and the distance. You can predict with full accuracy when you will
arrive at Pluto from Newtonian calculations, at any velocity you care to
use. If you imagine for one moment that when you get there Pluto will not
have arrived because "its clock is running slow", then I can only say that
is sad indeed.
Androcles
Dan H. Lewis
>> Dan wrote: Nope, the speed of light need not generally c with
> relativity). Hence your argument fails.
>Okay, It fails.
Good. We saw last time that your argument for logical inconsistency
failed, and you declined to defend it any further, and now you agree
that your argument for empirical falsification also fails. We're
making great strides!
Androcles wrote:
>Given your statement plus the fact that there are NO non-
>accelerating anywhere in the Universe, SR is ... pointless...
There are quite a few interesting things about your statement.
Most noticeable, of course, is the fascinating evidence of
cognitive dissonance, when you said there are NO non-acceling
[blank] anywhere in the Universe, the [blank] is rather
conspicuous. One imagines that you got to that point and
your subconscious realized that you couldn't say there are
no non-accelerating coordinate systems, so you just left
it blank. Another interesting point is how common it is among
crackpots like yourself to resort to this particular sophism,
i.e., that it is impossible for two clocks to have quantifiably
different accelerations, and for the accelerations of one to be
negligibly small in comparison with those of the other. More
seriously, we should point out that the special theory of
relativity is well known to be just the idealized limiting
case of the more comprehensive general theory, which enables
us to quantify the effects of slight deviations from flatness,
confirming that SR is applicable in a very wide range of
circumstances.
In addition, I have to point out that you began by proclaiming
SR to be logically inconsistent, but when the fallacy of your
claim was exposed, you immediately switched to the claim that
it was empirically false, but you have agreed above that this
claim was also invalid, whereupon you immediately switched to
still ANOTHER complaint, this time saying that special relativity
is inapplicable. Now we have shown that this charge, too, is
totally specious. What's fascinating about this is not just
your obvious desperation to find some flaw, but your facility
for flowing so effortlessly from one charge to another. My
expectation now would be for you to cycle back around to your
first charge, and begin proclaiming logical inconsistency again,
and so it goes, round and round, endlessly. You say A, someone
points out that A is false, you switch to B, which is immediately
shown to be indefensible, you switch to C, which is also shown
to be unfounded, and then you switch back to A. And so it goes.
Is this really how you wish to spend the remainder of your days?
Androcles wrote:
>However, there seems to be a bone of contention between relativists
>as to what it's equations should be. If as EMS states (and you agree
>with) each sees the other's clock as slower than his own...
Sees?? It's true that if two people are receding from each other,
they will both see each other red-shifted, i.e., but this is primarily
due to the classical component of the Doppler effect. Nothing
mysterious about that at all, right? I think what you object to
is not classical Doppler, but the relativistic "transverse" term,
which is only significant at quite high speeds. But you should
be careful not to mix up the garden variety Doppler effect, and
transport delays (e.g., the lag in Neil Armstrong's radio) with
relativistic effects. I fear this is what you're doing, but since
you seem to avoid ever expressing yourself clearly and directly,
it's hard to know for sure.
Androcles wrote:
> then it should follow that
>t' = gamma*(t - x*v/c^2)
>t = gamma*(t' - x'*v/c^2)
It should? Let v denote the velocity of the t' frame with respect
to the t frame, and let v' denote the velocity of t with respect
to t'. Obviously we have v = -v', and with c=1 the transformation
equations would be
t' = g(t - vx) t = g(t' - v'x')
x' = g(x - vt) x = g(x' - v't')
where g = 1/sqrt(1-v^2) = 1/sqrt(1-v'^2). So, what you forgot to
do is use the "primed" velocity v' in your second time transformation
equation. Kind of a dumb mistake, no? The classical Galilean
transformations are
t' = t t = t'
x' = x - vt x = x' - v't'
where, again, v = -v'. If we made the same mistake with these
equations that you made with the Lorentz equations, we would
have
x' = x - vt and x = x' - vt'
which would imply x' = (x' - vt') - vt, and so 2vt = 0. Hence,
motion is impossible or else time must stand still! But of
course this mistake of yours is just demented gibberish.
Androcles wrote:
>Having made this point myself, it was strongly disputed by EMS
>and Paul Andersen, both of whom insisted that the equations should
>be
>t' = gamma*(t - x*v/c^2)
>t = gamma*(t' + x'*v/c^2)
>
>Still, perhaps you can resolve the dispute between them. Obviously
>I cannot...
Ummm... what is the dispute between them? Didn't you just say that
"EMS and Paul Anderson" both insist on the same thing? As it happens,
the equations they insist on are correct, and in agreement with
special relativity. The only disagreement and error I can see here
is in all the things YOU have written.
By the way, I notice you're back to logical inconsistency now.
That didn't take long. ABCABCABC... So it goes...
Androcles
> Androcles wrote:
> > then it should follow that
> >t' = gamma*(t - x*v/c^2)
> >t = gamma*(t' - x'*v/c^2)
>
> It should? Let v denote the velocity of the t' frame with respect
> to the t frame, and let v' denote the velocity of t with respect
> to t'.
t doesn't have a velocity, but never mind, I get the idea.
Obviously we have v = -v',
So?
t = gamma*(t' + x'*(-v')/c^2)
That's what I said.
The magnitude of v' is the same as the magnitude of v, obviously.
Since v = -v',
t = gamma*(t' - x'*v/c^2)
as above.
Paul Andersen (being a crackpot relativist) has persistently claimed
(quote)
Of course you know that the transformations are:
t' = (t - x*v/c^2)/sqrt(1 - v^2/c^2)
and the inverse:
t = (t' + x'*v/c^2)/sqrt(1 - v^2/c^2)
(unquote)
Naturally I said
"Prove it, for I do not know".
Why anyone would argue with that is beyond my understanding, unless it is
mere trolling.
And to quote EMS
(quote)
In each frame, the moving clock is slower. A contradiction? **As
presented**, of course it is. There is alot more to Relativity than
just clocks. You are acting like the transformations are:
t' = t/sqrt(1 - v^2/c^2) and
t = t'/sqrt(1 - v^2/c^2).
They are not, as you know.
(quote)
I have never said this, or "acted" like this.
But EMS is correct in one respect.
"In each frame, the moving clock is slower. A contradiction?
**As presented**, of course it is. "
As should be obvious to anyone reading these quotes, relativists do not have
a clue.
Androcles
Androcles
Stephen <stephe...@deathtospam.hotmail.com> wrote in message
news:stephenwells-2...@mac014.joh.cam.ac.uk...
where Virgil has made the same ridiculous statement.
Androcles
Edward Schaefer
>
> Edward Schaefer wrote:
> >
> > And becuause of the Relativity of Simultaneity, you can exchange "A" and
> > "B" in the last paragraph without trouble.
>
> t' = gamma*(t - x*v/c^2)
> ?
> After all, I'm exchanging A and B and is seems to be causing a great deal of
> trouble.
What trouble? The coordinate axes stay parallel, so that v(A|B) = -
v(B|A) where v(A|B) is the velocity of B in A's frame and v(B|A) is the
velocity of A in B's frame. Note that who's velocity is being measured
has changed. So we can rewrite Paul's equations as:
t' = gamma * (t - x * v(A|B) / c^2)
t = gamma * (t' - x' * v(B|A) / c^2)
Now just substitute v(A|B) -> v and v(B|A) -> -v, and out come Paul's
equations.
> When Armstong was standing on the Moon, we saw his watch was lagging clocks
> on Earth and he saw clocks on Earth were lagging his clock. When Armstrong
> was on his way to the Moon, he saw clocks on Earth gradually losing time,
> and we saw his watch gradually losing time.
> You know what is really odd about this? When he was on his way home he saw
> clocks on Earth gaining, not losing. And strange as may seem to a
> relativist, we saw his watch gaining, not losing.
So far so good, but you are only considering propagation delay in this,
and not relativistic effects.
> When he arrived, lo and
> behold his watch was synchronized with Earth clocks.
Actually, it was not. It was a few microseconds *ahead* of the Earth
clocks. You see, he was in inertial motion (which free-fall is) while
we were being pushed by the surface of the Earth from one frame to
another continuously. It was sort of like a twin paradox situation,
except that *we* are the "travelers".
The GPS with its atomic clocks were found to unsynchonizable unless this
effect was considered.
> If you imagine for one moment that when you get there Pluto will not
> have arrived because "its clock is running slow", then I can only say that
> is sad indeed.
LOL! All that this means is that you have not properly computed the
orbit! Actually, that is not a problem for Pluto because it goes so
slow and is so far from the Sun that the relativistic effects don't
matter for more than an inch or two. However, you could miss Mercury if
you used old position data and a Newtonian model to predicts its orbit.
:-) The trouble with this is that we are now talking GR, and that is
most useless if you don't accept SR.
EMS
P.S. I wish that you would stop hating SR so much. You are on the
verge of understanding it, and will be so much happier if you would.
You are a smart, astute person whose intransigence is making him look
(and act) like a fool.
Dan H. Lewis
>>Dan: Obviously we have v = -v'.
>So? t = gamma*(t' + x'*(-v')/c^2) That's what I said. The
What? The first equations you've written there is
t = gamma*(t' + x'*(-v')/c^2)
= gamma*(t' - x'*v'/c^2)
and then you agree that v=-v', so making this substitution
we get
t = gamma*(t' + x'*v/c^2)
i.e., with the opposite sign from what you have written as
your conclusion. That's a pretty careless mistake. Also,
I didn't notice any response to the fact that this same mistake
makes gibberish of the Galilean transformations too. How do
you account for this? Do you also reject the intelligibility
of Galilean kinematics?
On Sat, 25 Mar 2000 "Androcles" wrote:
>Paul Andersen (being a crackpot relativist) has persistently
>claimed...that the transformations are:
> t' = (t - x*v/c^2)/sqrt(1 - v^2/c^2)
> t = (t' + x'*v/c^2)/sqrt(1 - v^2/c^2)
>Naturally I said "Prove it, for I do not know". Why anyone would
>argue with that is beyond my understanding...
I don't follow you. Are you disputing those equations, or are
you saying you don't understand why anyone would dispute them?
Androcles
> Androcles wrote:
> >
> > Edward Schaefer wrote:
> > >
> > > And becuause of the Relativity of Simultaneity, you can exchange "A"
and
> > > "B" in the last paragraph without trouble.
> >
> > So why does Paul insist that
> > t' = gamma*(t - x*v/c^2)
> > After all, I'm exchanging A and B and is seems to be causing a great
deal of
> > trouble.
>
> What trouble? The coordinate axes stay parallel, so that v(A|B) = -
> v(B|A) where v(A|B) is the velocity of B in A's frame and v(B|A) is the
> velocity of A in B's frame. Note that who's velocity is being measured
> has changed. So we can rewrite Paul's equations as:
>
> t' = gamma * (t - x * v(A|B) / c^2)
> t = gamma * (t' - x' * v(B|A) / c^2)
v = -v'.
Then
t' = gamma * (t - x * v) / c^2)
t = gamma * (t' + x' *(-v') / c^2)
Note that the second equation is NOT Paul's equation
t = gamma * (t' + x'*v) / c^2)
and Paul's equation is totally incorrect.
BTW, your equation is incorrect also.
It should read:
t = gamma * (t' (PLUS) x' * v(B|A) / c^2)
if you want positive x aligned with positive x'.
> Now just substitute v(A|B) -> v and v(B|A) -> -v, and out come Paul's
> equations.
Nope.
Paul's equation is
t = gamma * (t' + x'*v) / c^2)
and the correct equation is
t = gamma * (t' + x' * v(B|A) / c^2)
which is the same as
t = gamma * (t' - x' * v(A|B) / c^2)
or
t = gamma * (t' - x' * v / c^2)
as I have insisted throughout. I see now that Stephen Wells (who signs off
as "Virgil") has also made the same error.
You do understand that, I trust?
>
> > When Armstong was standing on the Moon, we saw his watch was lagging
clocks
> > on Earth and he saw clocks on Earth were lagging his clock. When
Armstrong
> > was on his way to the Moon, he saw clocks on Earth gradually losing
time,
> > and we saw his watch gradually losing time.
> > You know what is really odd about this? When he was on his way home he
saw
> > clocks on Earth gaining, not losing. And strange as may seem to a
> > relativist, we saw his watch gaining, not losing.
>
> So far so good, but you are only considering propagation delay in this,
> and not relativistic effects.
That's right. There are no relativistic effects.
>
> > When he arrived, lo and
> > behold his watch was synchronized with Earth clocks.
>
> Actually, it was not. It was a few microseconds *ahead* of the Earth
> clocks. You see, he was in inertial motion (which free-fall is) while
> we were being pushed by the surface of the Earth from one frame to
> another continuously. It was sort of like a twin paradox situation,
> except that *we* are the "travelers".
vmax~ 25,000 mph. Distance to moon ~ 239,000 miles.
239/25 = 9.5 hours. Actually it took about 3 days, but the ship was slowing
all the way until the moon's pull became dominant.
Let's err on the side of the higher velocity.
gamma = sqrt(1-v^2/c^2)
Thats about one minus 7 miles/second squared divided by 186,000 miles per
second squared.
gamma = 0.999999998583651
So for every second that passes on Armstrong's watch, 0.999999998583651
seconds pass on Earth.
Therefore his watch will gain 1- 0.999999998583651 = 0.000000001416349
seconds. This lasts for 9.5 hours, so the total time lost on Earth is about
50 microseconds.
But as I said, the ship actually took three days, not 9.5 hours. Armstrong
was in a constant state of acceleration although he doesn't realize it
because his ship was also. Had there been sufficient fuel to maintain
thrust, he could have accelerated to the moon at a constant velocity instead
of slowing down, right? And that would mean he was NOT in an inertial frame,
right? So since my calculation above is for a non-acclerated frame, then
Armstrong loses 50 microseconds compared with Earth, as per
t' = gamma*t
t = gamma*t'
Hence his watch remains in perfect synch with Earth clocks and gamma = 1.
>
> The GPS with its atomic clocks were found to unsynchonizable unless this
> effect was considered.
Nonsense. GPS clocks remain in perfect synch with Earth clocks. They
wouldn't work otherwise. The relativistic fudge that was added to them is
corrected by regular updates from signals from Earth, under the guise that
their orbits are perturbed, which is in fact true. The orbits are perturbed.
>
> > If you imagine for one moment that when you get there Pluto will not
> > have arrived because "its clock is running slow", then I can only say
that
> > is sad indeed.
>
> LOL! All that this means is that you have not properly computed the
> orbit! Actually, that is not a problem for Pluto because it goes so
> slow and is so far from the Sun that the relativistic effects don't
> matter for more than an inch or two. However, you could miss Mercury if
> you used old position data and a Newtonian model to predicts its orbit.
> :-) The trouble with this is that we are now talking GR, and that is
> most useless if you don't accept SR.
>
> EMS
>
> P.S. I wish that you would stop hating SR so much.
It isn't emotional. I don't "hate" SR at all.
It is a pity that you love it so much, being enarmored of the exotic idea
that time is relative.
> You are on the
> verge of understanding it, and will be so much happier if you would.
Happiness is an emotional state, and quite irrelevant to my understanding of
SR.
SR is logically unsound, based as it is on assumptions which do not reflect
Nature.
> You are a smart, astute person whose intransigence is making him look
> (and act) like a fool.
On the contrary, both you and Paul have made yourselves look like
intransigent fools by persistently insisting that
t = gamma * (t' + x'*v) / c^2)
instead of
t = gamma * (t' + x'*(-v')) / c^2)
or
t = gamma * (t' + x'*(-v(B|A)) / c^2)
if you prefer.
When you and Paul admit your error, then perhaps we can move on to more
interesting ideas, but until you can understand how to get a sign right,
that is going to be difficult.
Androcles
Androcles
> On Sat, 25 Mar 2000 "Androcles" wrote:
> >>Dan: Obviously we have v = -v'.
> >So? t = gamma*(t' + x'*(-v')/c^2) That's what I said. The
> >magnitude of v' is the same as the magnitude of v, obviously.
> >Since v = -v', t = gamma*(t' - x'*v/c^2) as above.
>
> What? The first equations you've written there is
>
> t = gamma*(t' + x'*(-v')/c^2)
>
> = gamma*(t' - x'*v'/c^2)
>
> and then you agree that v=-v', so making this substitution
> we get
>
> your conclusion. That's a pretty careless mistake.
Time runs backwards.
Androcles
Edward Schaefer
>
> Edward Schaefer wrote:
> >
>
> vmax~ 25,000 mph. Distance to moon ~ 239,000 miles.
> 239/25 = 9.5 hours. Actually it took about 3 days, but the ship was slowing
> all the way until the moon's pull became dominant.
> Let's err on the side of the higher velocity.
>
> But ... Armstrong
> was in a constant state of acceleration although he doesn't realize it
> because his ship was also.
Under the equivalence principle, that circumstance means that he and the
ship were in inertial motion.
> Had there been sufficient fuel to maintain
> thrust, he could have accelerated to the moon at a constant velocity instead
> of slowing down, right?
Yes, but that is constant velocity wrt us in our accelerated frame. To
maintain that, you need to be in an accelerated frame yourself. Keep in
mind this business of frames of reference that you are actually getting
fairly good at.
> ... So since my calculation above is for a non-acclerated frame, then
> Armstrong loses 50 microseconds compared with Earth, as per
> t' = gamma*t
> t = gamma*t'
> Hence his watch remains in perfect synch with Earth clocks and gamma = 1.
All that you did was to recompute the same effect in a different frame.
That does not make it go away.
> On the contrary, both you and Paul have made yourselves look like
> intransigent fools ...
If so, that is becuase we think that the truth may actually win you
over. Maybe it is foolish to hope that you can convert an
anti-relativist, but it is sure fun to try. :-)
EMS
Dan H. Lewis
>[an obvious and careless algebra mistake, which I corrected]
>
>Well, alright. Have it your way.
Great. So we've dispensed with ALL of your arguments, and
you now recognize that you have no rational basis whatsoever
for making the claims that you have repeatedly made here
about logical inconsistency, empirical falsehood, or total
inapplicability regarding special relativity. One wonders
how long your new-found rationality will last...
On Sat, 25 Mar 2000 "Androcles" wrote:
>Time runs backwards.
Well, that answers that.
Androcles
> Androcles wrote:
> >
> > Edward Schaefer wrote:
> > >
> >
> > vmax~ 25,000 mph. Distance to moon ~ 239,000 miles.
> > 239/25 = 9.5 hours. Actually it took about 3 days, but the ship was
slowing
> > all the way until the moon's pull became dominant.
> > Let's err on the side of the higher velocity.
> >
> > But ... Armstrong
> > was in a constant state of acceleration although he doesn't realize it
> > because his ship was also.
>
> ship were in inertial motion.
>
> > thrust, he could have accelerated to the moon at a constant velocity
instead
> > of slowing down, right?
>
> maintain that, you need to be in an accelerated frame yourself. Keep in
> mind this business of frames of reference that you are actually getting
> fairly good at.
>
> > Armstrong loses 50 microseconds compared with Earth, as per
> > t' = gamma*t
> > t = gamma*t'
> > Hence his watch remains in perfect synch with Earth clocks and gamma =
1.
>
> That does not make it go away.
much like it went away.
>
> > On the contrary, both you and Paul have made yourselves look like
> > intransigent fools ...
>
> If so, that is becuase we think that the truth may actually win you
> over. Maybe it is foolish to hope that you can convert an
> anti-relativist, but it is sure fun to try. :-)
Well, at least we both recognize that :-)
Of course what you refer to as "truth" is in fact supposition.
It is kinda neat, I suppose.
I really do like that bit about "in agreement with experience we further
ASSUME the quantity
2AB/(t'A = tA) = c.
Fascinating how many people are taken in by it.
Androcles
Edward Schaefer
>
> Edward Schaefer wrote:
> >
> > Androcles wrote:
> > >
> > > Edward Schaefer wrote:
> > > >
> > >
> > > vmax~ 25,000 mph. Distance to moon ~ 239,000 miles.
> > > 239/25 = 9.5 hours. Actually it took about 3 days, but
> > > the ship was slowing
> > > all the way until the moon's pull became dominant.
> > > Let's err on the side of the higher velocity.
> > >
> > > But ... Armstrong
> > > was in a constant state of acceleration although he doesn't realize it
> > > because his ship was also.
> >
> > ship were in inertial motion.
> >
> > > thrust, he could have accelerated to the moon at a constant
> > > velocity instead of slowing down, right?
> >
> > maintain that, you need to be in an accelerated frame yourself. Keep in
> > mind this business of frames of reference that you are actually getting
> > fairly good at.
> >
> > > then Armstrong loses 50 microseconds compared with Earth, as per
> > > t' = gamma*t
> > > t = gamma*t'
> > > Hence his watch remains in perfect synch with Earth clocks and
> > > gamma = 1.
> >
> > That does not make it go away.
>
> What? That Armstrong gained the 50 microseconds he lost? That looks very
> much like it went away.
>
If you really want to see the full derivation of the effect, I can find
it. IIRC it turns out that if you do this in the Earth's frame then SR
caused Armstrong to lose ~20 usec and GR caused him to gain ~30 usec,
resulting in a net gain of ~10 usec. (You get down to 20 usec after
allowing for the slowing down.) Do note that the GR effect is related
to potential instead of speed.
> > > On the contrary, both you and Paul have made yourselves look like
> > > intransigent fools ...
> >
> > If so, that is becuase we think that the truth may actually win you
> > over. Maybe it is foolish to hope that you can convert an
> > anti-relativist, but it is sure fun to try. :-)
>
> Well, at least we both recognize that :-)
> Of course what you refer to as "truth" is in fact supposition.
That's fair.
> It is kinda neat, I suppose.
> I really do like that bit about "in agreement with experience
> we further ASSUME the quantity 2AB/(t'A = tA) = c."
> Fascinating how many people are taken in by it.
Note the word "assume". Einstein himself was noting that if there is a
flaw here, that is where it will be. The assumption is in perfect
accord with the postulates of the paper, and so there is little to argue
with.
You don't realize what I did to you with this thread: It was a trap and
you walked straight into it and still don't know what got you. You have
conceeded the consistency of Relativity here more times than I can
count, even if you have no idea that you have done so. You could have
argued that what I wrote was inconsistent with SR of that it was somehow
inconsistent with itself or with the symmetry that you call for between
frames. You could do none of them, and really never tried. To top it
off, we are now arguing whether a GR effect canceled out an SR one.
That is hardly a debate that has Relativity in the ropes. :-)
EMS
Androcles
> If you really want to see the full derivation of the effect, I can find
> it. IIRC it turns out that if you do this in the Earth's frame then SR
> caused Armstrong to lose ~20 usec and GR caused him to gain ~30 usec,
> resulting in a net gain of ~10 usec. (You get down to 20 usec after
> allowing for the slowing down.) Do note that the GR effect is related
> to potential instead of speed.
I'm quite sure that if you make all the necessary assumptions you can
produce any result you like.
> > > > On the contrary, both you and Paul have made yourselves look like
> > > > intransigent fools ...
> > >
> > > If so, that is becuase we think that the truth may actually win you
> > > over. Maybe it is foolish to hope that you can convert an
> > > anti-relativist, but it is sure fun to try. :-)
> >
> > Well, at least we both recognize that :-)
> > Of course what you refer to as "truth" is in fact supposition.
>
> That's fair.
>
> > It is kinda neat, I suppose.
> > I really do like that bit about "in agreement with experience
> > we further ASSUME the quantity 2AB/(t'A = tA) = c."
> > Fascinating how many people are taken in by it.
>
> Note the word "assume". Einstein himself was noting that if there is a
> flaw here, that is where it will be. The assumption is in perfect
> accord with the postulates of the paper, and so there is little to argue
> with.
The second postulate is an assumption also. Two wrongs do not make a right,
and there is a lot to argue with.
As you yourself have pointed out, the symmetry of your zamjet gedanken
indicates each finds the other's clock runs slow.
Cars travel on the right. Cars have rear-view mirrors. Light from the
backseat of the car reflects in one of those mirrors and returns to the back
seat. A roadside observer can select an arbitrary coordinate frame with
himself at the origin and the road as the X-axis. He can assume that the
light from the back seat of the car is c in his frame of reference, and
conclude that clocks in cars run a little slower that his does. He can walk
out to a traffic island in a divided highway and find this result for cars
moving right. He can turn around and face the other direction (rotating his
X-axis as he does so) and find the same result for cars moving "right". He
can sit in a parked car which is on the right side of the road and get the
same result. He can refuse to rotate the frame, and that doesn't change the
result.
All of this is in agreement with special relativity.
Until.
A car breaks down and is hauled by a tow-truck, the car moving backwards.
Light is still reflected to the back seat, as before, but in this case
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))]= tau(x',0,0,t+x'/(c+v))
and all the beautiful theory collapses with the sign change.
The [time for the light to go from the back seat of the car to the mirror]
doesn't equal the [time to go from the back seat of the car to the mirror]
if the car is moving backwards, or indeed if I place a vanity mirror on the
back shelf that reflects the image of the back of the driver's head.
In equations,
tau(x',0,0,t+x'/(c+v)) =/= tau(x',0,0,t+x'/(c-v))
>
> You don't realize what I did to you with this thread: It was a trap and
> you walked straight into it and still don't know what got you. You have
> conceeded the consistency of Relativity here more times than I can
> count, even if you have no idea that you have done so.
No I didn't walk into any trap. I told you it was a yarn up front.
> You could have
> argued that what I wrote was inconsistent with SR of that it was somehow
> inconsistent with itself or with the symmetry that you call for between
> frames. You could do none of them, and really never tried.
That's right. I never really tried. You began by making an assumption
(Relativity is correct) and then proceeded to prove your assumption.
Circularity is most uninteresting.
> To top it
> off, we are now arguing whether a GR effect canceled out an SR one.
> That is hardly a debate that has Relativity in the ropes. :-)
It was your debate, your fun. You can prove what you assume as often as you
want to, it still doesn't impress.
tau(x',0,0,t+x'/(c+v)) does NOT equal tau(x',0,0,t+x'/(c-v))
You can argue that until the cows come home, it doesn't change v becasue the
car is still going in the same direction, it doesn't change t which is
arbitrary, it doesn't change x' because x' is still x-vt, it doesn't change
c because you insist c cannot be changed. All it does is change the value of
tau, very simply. As simple as moving the mirror to the back seat of the
car.
SR is inconsistent. Period.
Androcles
Edward Schaefer
>
> Edward Schaefer wrote:
> >
> > flaw here, that is where it will be. The assumption is in perfect
> > accord with the postulates of the paper, and so there is little to argue
> > with.
>
True. All physics starts with a set of assumptions. Even Newtonian
physics.
> As you yourself have pointed out, the symmetry of your zamjet gedanken
> indicates each finds the other's clock runs slow.
> Cars travel on the right. Cars have rear-view mirrors. Light from the
> backseat of the car reflects in one of those mirrors and returns to the back
> seat. A roadside observer can select an arbitrary coordinate frame with
> himself at the origin and the road as the X-axis. He can assume that the
> light from the back seat of the car is c in his frame of reference, and
> conclude that clocks in cars run a little slower that his does.
There you go. That's SR!
> He can walk
> out to a traffic island in a divided highway and find this result for cars
> moving right. He can turn around and face the other direction (rotating his
> X-axis as he does so) and find the same result for cars moving "right". He
> can sit in a parked car which is on the right side of the road and get the
> same result.
> He can refuse to rotate the frame, and that doesn't change the
> result.
Very good! Of course what that means in the some of the cars are moving
to the *left*. Therefore ...
> All of this is in agreement with special relativity.
> Until.
> A car breaks down and is hauled by a tow-truck, the car moving backwards.
> Light is still reflected to the back seat, as before, but in this case
> 1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))]= tau(x',0,0,t+x'/(c+v))
> and all the beautiful theory collapses with the sign change.
... that is just plain hogwash.
> The [time for the light to go from the back seat of the car to the mirror]
> doesn't equal the [time to go from the back seat of the car to the mirror]
> if the car is moving backwards, or indeed if I place a vanity mirror on the
> back shelf that reflects the image of the back of the driver's head.
Kindly specify the frame of reference. Is this in the frame of the
car? In that case it is false. Is it in the frame of the observer
sitting on the side of the road? Is it both (one time from one frame
and one from another)? In that case it is true and not contradictory.
> > You could have
> > argued that what I wrote was inconsistent with SR of that it was somehow
> > inconsistent with itself or with the symmetry that you call for between
> > frames. You could do none of them, and really never tried.
>
> That's right. I never really tried. You began by making an assumption
> (Relativity is correct) and then proceeded to prove your assumption.
> Circularity is most uninteresting.
You still don't understand the rules of logic and deduction. Logic has
nothing to do with postulates. You can input any set that you like into
the machinery of logic and mathematics. However, once done you can use
those rule to for instance prove consistency of a lack thereof.
If SR is truly self-contradictory as you say, then there is a flaw in my
description, without which I could not have made the case that I did.
So the circularity that you so dislike is a proof of self-consistency.
(Actually the rigorous proof is in "Space and Time" by Minkowski. You
have that article. It is in the same book as "On the Electrodynamics of
Moving Bodies".)
> SR is inconsistent. Period.
Man! You're close! You almost understand it all. It's reached the
point that you are saying this because you expect it to be true. In
fact, you are describing why that is not the case in the parts above the
I called good.
I'll be on vacation the rest of the week, but I hope this gives you
something to think about until I get back. Enjoy!
EMS
Paul B. Andersen
>
> Dan H. Lewis <dhl...@circuitcircus.com> wrote in message
> news:38dd006c...@news.gte.net...
> > >So? t = gamma*(t' + x'*(-v')/c^2) That's what I said. The
> > >magnitude of v' is the same as the magnitude of v, obviously.
> > >Since v = -v', t = gamma*(t' - x'*v/c^2) as above.
> >
> > What? The first equations you've written there is
> >
> > t = gamma*(t' + x'*(-v')/c^2)
> >
> > = gamma*(t' - x'*v'/c^2)
> >
> > and then you agree that v=-v', so making this substitution
> > we get
> >
> > your conclusion. That's a pretty careless mistake.
> Androcles
Would you please show us how you arrive at the very
interesting conclution that the equation:
t = gamma*(t' + x'*v/c^2)
implies that "time run backwards"? :-)
What? You will not?
Thought so.
Paul
Paul B. Andersen
>
> A car breaks down and is hauled by a tow-truck, the car moving backwards.
You sure don't describe you thought experiments very precisely, Androcles.
I will assume you mean that the greek k-car-frame moves "backwards" relative
the latin K-road-frame, e.g. the "v" is in the opposite direction of Einstein's.
> Light is still reflected to the back seat, as before, but in this case
> 1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))]= tau(x',0,0,t+x'/(c+v))
Right.
> and all the beautiful theory collapses with the sign change.
Does it? Why do you say that?
With your choice of direction of motion, we have x' = x + vt,
(as opposed to Einstein's x' = x - vt)
and if you carry through the calculation, you will find:
xi = gamma*(x + vt)
tau = gamma*(t + v*x/c^2)
The change of sign is no "collapse", it is an inevitability.
Different choice of co-ordinate systems - different transform equation.
Obviously.
> The [time for the light to go from the back seat of the car to the mirror]
> doesn't equal the [time to go from the back seat of the car to the mirror]
> if the car is moving backwards, or indeed if I place a vanity mirror on the
> back shelf that reflects the image of the back of the driver's head.
Does it not? Why not?
> In equations,
> tau(x',0,0,t+x'/(c+v)) =/= tau(x',0,0,t+x'/(c-v))
Androcles, Androcles :-)
Your math proofs are really something. :-)
(If anyone else had written this, I would have assumed it
to be a joke. Well, it _is_ a joke.
But it was not meant to be, was it?)
You see, Androcles, if we assume that there is but one k-frame
and one set of events, then indeed:
tau(x',0,0,t+x'/(c+v)) = tau(x',0,0,t+x'/(c-v))
which only states that there is but one tau for
the single event "light hit mirror".
Why is this not self contradictory?
Because the t and x' in the paranthesis on the left are not
the same as the t and the x' on the right.
They belong to two different frames of rererences!
We have one frame - Einstein's, let's call it K" - the origo
of which is moving in the negative direction of xi,
and another frame - Androcles', the origo of which is moving
in the positive direction of the xi-axis.
The single event "light hit mirror" has the co-ordinates:
t1" = t" + x"'/(c-v), x1"' = x"', where x"' = x" - vt"
in the former,
and it has the co-ordinates:
t1 = t + x'/(c+v), x1' = x', where x' = x + vt
in the latter.
Thus:
tau(x',0,0,t+x'/(c+v)) = tau(x"',0,0,t"+x"'/(c-v))
Nothing contradictory about that, is it?
I am looking forward to your next variant of
"refutation of SR by ridiculous application of math".
This is fun. :-)
Paul
and...@attglobal.net
>
> and...@attglobal.net wrote:
> >
> > Edward Schaefer wrote:
> > >
> > > Observers A and B have just invented the zamjet, which for the first
> > > time in history allows people to go at relativistic speeds wrt each
> > > other. As their first project, they have decided to test Relativity and
> > > its prediction a clock which is moving wrt ones self goes slower. To do
> > > this, they agree to set a line of clocks into motion at .866c (the speed
> > > where gamma = 2) and have consecutive clocks be 1.732 light-seconds
> > > apart. That way each clock will pass the other's clock once every 2
> > > seconds.
> > >
> > > moving at 0.866c wrt observer A sets up his clocks, synchronizes them,
> > > and sets them in motion. In the meantime, observer A has also set up
> > > his own line of clocks in the same way, and also synchronizes them.
> > >
> >
> > As opposed to having me read the rest of this overly long epistle,
> > could you tell me what the punch line is?
>
> It is that which you wrote next!
>
> > You should realize that when you synch the clocks and then accelerate
> > them to some new velocity with the same acceleration for
> > each clock in the original rest frame, they won't be synched
> > with frame clocks in their new rest frame. What you did
> > to these clocks is not the equivalent of a Lorentz transformation.
> >
> > This definitely affects which clock appears to be slower
> > since relativity of simultaneity is an important part
> > of explaining this when you consider two inertial frames.
> > That is definitely what you don't have in your scenario.
>
> You mean that you don't recognize Androcles' favorite question? Has it
> not occurred to you that if Androcles learned of the discovery of the
> zamjet first that he would have A and B set up the experiment like this?
>
> Given that and an SR spacetime, what do you think would happen as a
> result? That is what this posting is about.
>
Okay, no problem. I read the rest of it. I have an aversion
to long postings with complicated scenarios in them. I tend
to jump on them when see an incorrect or potentially sophist
argument. Your posting started by using Androcles' sophist AND
incorrect
argument and showing how to make it go away if you include
all of SR. My apologies.
As to recognizing Androcles' favorite question, I have never
seen him ask a valid question to answer.
John Anderson
Androcles
Paul B. Andersen <paul.b....@hia.no> wrote in message
news:38E07E23...@hia.no...
> Would you please show us how you arrive at the very
> interesting conclution that the equation:
>
> What? You will not?
> Thought so.
Run a movie backwards and you can simulated it.
The smoke goes back into the window, the billiard balls leap out of the
table pockets and form a triangle, etc. etc.
v-positive runs "forward" along the x'-positive axis with a "speed" that is
positive, but v' is negative.
so v'-negative runs "forward" along the x'-positive axis and time runs
backward.
If that's what Lewis want to conclude, so be it.
I'm bored with it.
Androcles
Androcles
> Androcles wrote:
> >
> > Edward Schaefer wrote:
> > >
a
> > > flaw here, that is where it will be. The assumption is in perfect
> > > accord with the postulates of the paper, and so there is little to
argue
> > > with.
> >
> > The second postulate is an assumption also. ...
>
> True. All physics starts with a set of assumptions. Even Newtonian
> physics.
Einstein's second postulate is, to quote the FAQ, "counter-intuitive". This
is all too evident by the many posts that have been sent to this NG.
Having decided that "intuition" isn't "common sense", we need to determine
what "intuition:" and "common sense" are all about. In doing that, we rely
upon mathematics. (Or we should - sometimes out "intuition" gets in the
way.)
>
> > As you yourself have pointed out, the symmetry of your zamjet gedanken
> > indicates each finds the other's clock runs slow.
> > Cars travel on the right. Cars have rear-view mirrors. Light from the
> > backseat of the car reflects in one of those mirrors and returns to the
back
> > seat. A roadside observer can select an arbitrary coordinate frame with
> > himself at the origin and the road as the X-axis. He can assume that the
> > light from the back seat of the car is c in his frame of reference, and
> > conclude that clocks in cars run a little slower that his does.
>
> There you go. That's SR!
Yep. SR is consistently absurd. What else is there to say about it?.
>
> > He can walk
> > out to a traffic island in a divided highway and find this result for
cars
> > moving right. He can turn around and face the other direction (rotating
his
> > X-axis as he does so) and find the same result for cars moving "right".
He
> > can sit in a parked car which is on the right side of the road and get
the
> > same result.
> > He can refuse to rotate the frame, and that doesn't change the
> > result.
>
> Very good! Of course what that means in the some of the cars are moving
> to the *left*. Therefore ...
Yes, do go on? Were you about to produce a statistical conclusion?
> > All of this is in agreement with special relativity.
> > Until.
> > A car breaks down and is hauled by a tow-truck, the car moving
backwards.
> > Light is still reflected to the back seat, as before, but in this case
> > 1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))]= tau(x',0,0,t+x'/(c+v))
> > and all the beautiful theory collapses with the sign change.
>
> ... that is just plain hogwash.
Ah... A true believer, I see.
Well, so be it.
>
> > The [time for the light to go from the back seat of the car to the
mirror]
> > doesn't equal the [time to go from the back seat of the car to the
mirror]
> > if the car is moving backwards, or indeed if I place a vanity mirror on
the
> > back shelf that reflects the image of the back of the driver's head.
>
> Kindly specify the frame of reference.
LOL! The "stationary" frame of reference is the "hogwash" frame, and the
"moving" frame is the "wash-hog" frame.
> Is this in the frame of the
> car?
LOL! Relativity works just fine if the car moves in the expected direction
with its nicely centered rear view mirror mounted on the windshield. Move
the mirror to the rear shelf and now it's called "hogwash".
So we have to demand "Kindly specify the frame of reference." along with the
usual relativistic bullshit!
Look. Work it out for yourself. I moved the mirror to the back shelf of the
car. That's all. YOU explain relativity. YOU decide the frame. YOU are its
supporter, you describe what happens.
> In that case it is false. Is it in the frame of the observer
> sitting on the side of the road?
The car passes the observer. That's all. Most of the time, the car passes
the observer going forward. Now and again a tow-truck hauls a car going
backward.
> Is it both (one time from one frame
> and one from another)? In that case it is true and not contradictory.
Figure it out. Forget all that "frame" crap, and figure out the light ray
from the rear of the car to the mirror and back again, when the car is towed
backward.
Y'know, Ed, you are smart enough to understand relativity. Why aren't you
smart enough to understand what is wrong with it?
> > > You could have
> > > argued that what I wrote was inconsistent with SR of that it was
somehow
> > > inconsistent with itself or with the symmetry that you call for
between
> > > frames. You could do none of them, and really never tried.
> >
> > That's right. I never really tried. You began by making an assumption
> > (Relativity is correct) and then proceeded to prove your assumption.
> > Circularity is most uninteresting.
>
> You still don't understand the rules of logic and deduction.
Yes I do.
> Logic has nothing to do with postulates.
True.
> You can input any set that you like into the machinery of logic and
mathematics.
Yes you can. Mathematics is an Art, not a Science. We can discuss the
tooth-fairy, Santa Claus, leprechauns, anything you like in Mathematics.
All that it requires is consistency. If you want to put "light is always
propagated in empty space with a definite velocity c which is independent of
the state of motion of the emitting body" into it, you can do that too. Just
don't try to mix it with the PoR, or you have inconsistency.
> However, once done you can use
> those rule to for instance prove consistency of a lack thereof.
Yep. SR has a lack thereof.
>
> If SR is truly self-contradictory as you say, then there is a flaw in my
> description, without which I could not have made the case that I did.
Sure there's a flaw. "Each sees the other's clock as slower than his own"
contradicts
t' = sqrt(t-... da-dee-da
and
t = sqrt(t'+.... da-dee-da.
> So the circularity that you so dislike is a proof of self-consistency.
What?
> (Actually the rigorous proof is in "Space and Time" by Minkowski. You
> have that article. It is in the same book as "On the Electrodynamics of
> Moving Bodies".)
Minkowski is a known prankster. Anyone with a sense of humor would spot it
immediately.
Just read his words!
"I will now show by our figure that the Lorentzian hypothesis is completely
equivalent the the new conception..."
"In mechanics as reformed in accordance with the world-postulate, the
disturbing lack of harmony between Newtonian mechanics and modern
electrodynamics disappears of its own accord".
The hell it does!
>
> > SR is inconsistent. Period.
> Man! You're close! You almost understand it all. It's reached the
> point that you are saying this because you expect it to be true. In
> fact, you are describing why that is not the case in the parts above the
> I called good.
> I'll be on vacation the rest of the week, but I hope this gives you
> something to think about until I get back. Enjoy!
Yeah -right. Have fun, anyway!
Androcles
Paul B. Andersen
>
> Paul B. Andersen <paul.b....@hia.no> wrote in message
> news:38E07E23...@hia.no...
> > Would you please show us how you arrive at the very
> > interesting conclution that the equation:
> >
> > What? You will not?
> > Thought so.
> Hey, its not my idea. It's Lewis's.
> Run a movie backwards and you can simulated it.
> The smoke goes back into the window, the billiard balls leap out of the
> table pockets and form a triangle, etc. etc.
> v-positive runs "forward" along the x'-positive axis with a "speed" that is
> positive, but v' is negative.
> so v'-negative runs "forward" along the x'-positive axis and time runs
> backward.
> If that's what Lewis want to conclude, so be it.
> I'm bored with it.
> Androcles
Utter nonsense.
No one but you have insisted that the equation:
t = gamma*(t' + x'*v/c^2)
implies that "time run backwards".
I must say that I find it very hard to understand your difficulties
with understanding this. It should not be hard to understand at all.
But you seem to have an extremely closed mind, seemingly completely
unable to even consider that you may have misiterpreted something.
So the following is probably futile, but here goes anyway.
If we choose our two frames of references in such a way that
the origo of the K' frame moves in the positive direction
along the x-axis of K with the speed v, then the LT is:
x' = gamma*(x - v*t)
t' = gamma*(t - x*v/c^2)
This is a set of co-ordinate transformation equations.
That means that you can use it to transform the co-ordinaes
of an event from one frame to the other.
For example, if an event E1 has the co-ordinates x=2, t=1 in
the K-frame, we can find the co-ordinates of the same event
in the K' frame thus:
x' = gamma*(2 - v*1)
t' = gamma*(1 - 2*v/c^2)
But this is a one to one transform which works both ways.
For example, if an event E2 has the co-ordinates x' = 1, t' = 2
in the K' frame, we can use it to find the co-ordinates of
the same event in the K frame thus:
1 = gamma*(x - v*t)
2 = gamma*(t - x*v/c^2)
solving these with respect to x and t, give the co-ordinates:
x = gamma*(1 + 2*v)
t = gamma*(2 + 1*v/c^2)
The "inverse" transformation:
x = gamma*(x' + v*t')
t = gamma*(t' + x'*v/c^2)
is the _very same_ transformation written in an alternative form.
They are mathematically identical.
And this is a _fact_, Androcles, no "assertion".
If you don't believe it, then solve the transformation
above with respect to x and t, and see what you get.
Now, if we interchange the frames of references above
in such a way that the orgo of K moves in the positive
direction of the x'-axis of K' (and the origo of K'
moves in the negative direction of the x-axis of K),
then the symmetry makes it obvious that we can find
the co-ordinate transformation simply by interchanging
the marked and unmarked variables in the equations above.
Thus the LT is:
x = gamma*(x' - v*t')
t = gamma*(t' - x'*v/c^2)
and _the very same_ written in the inverse form:
x' = gamma*(x + v*t)
t' = gamma*(t + x*v/c^2)
There is a very strange misconception that the sign
has anything to do with "in which direction time flow".
Paul
Androcles
> Androcles wrote:
> >
> > A car breaks down and is hauled by a tow-truck, the car moving
backwards.
>
> I will assume you mean that the greek k-car-frame moves "backwards"
relative
> the latin K-road-frame, e.g. the "v" is in the opposite direction of
Einstein's.
Start over, without your false assumptions.
Remainder snipped.
Androcles
Paul B. Andersen
>
> Paul B. Andersen <paul.b....@hia.no> wrote in message
> news:38E0B307...@hia.no...
> > Androcles wrote:
> > >
> > > A car breaks down and is hauled by a tow-truck, the car moving
> backwards.
> >
> > You sure don't describe you thought experiments very precisely, Androcles.
> Yes I do. The car is being towed backwards. That's as simply as it gets.
No it is not.
You describe a verbal formulated thought experiment,
and then present an equation with no explanation whatsoever
of what the symbols in the equation stands for.
That's not simple. It is ridiculously imprecise!
> > I will assume you mean that the greek k-car-frame moves "backwards"
> relative
> > the latin K-road-frame, e.g. the "v" is in the opposite direction of
> Einstein's.
> Nope. You assume incorrectly, as usual. v is still the same.
So let me put it this way:
If I didn't assume correctly, then the equation you wrote
is wrong.
> Start over, without your false assumptions.
And how many times do you want me to guess at what your
imprecise formulated though experiment is meant to be?
> Remainder snipped.
As always.
Snipp the explanations of why you are wrong, and call
the conclusion of the correct derivations:
"Assertion, assertion, assertion.
Assertion, assertion, assertion.
Assertion, assertion, assertion.
Assertion, assertion, assertion."
Paul
Edward Schaefer
>
> Edward Schaefer wrote:
> >
> > So the circularity that you so dislike is a proof of self-consistency.
>
> What?
If you can use Relativity to "prove" Relativity, then you have
self-consistency. It's that simple. If you can't then you don't have a
viable theory. You keep tryig to disprove Relativity, but you keep
**changing the rules** to do it.
Note that Einstein "changed the rules" himself, but that left everyone
with a theory in need of validation or refuation due to observation. It
has been confirmed, as you would see if you looked at the totality of
data out there instead of at just a few highly specific exmaples.
> > (Actually the rigorous proof is in "Space and Time" by Minkowski. You
> > have that article. It is in the same book as "On the Electrodynamics of
> > Moving Bodies".)
>
> Minkowski is a known prankster. ... Just read his words!
>
> "In mechanics as reformed in accordance with the world-postulate, the
> disturbing lack of harmony between Newtonian mechanics and modern
> electrodynamics disappears of its own accord".
>
> The hell it does!
That is what Einstein showed in the Electrodynamical Part of "On the
Electrodynamics of Moving Bodies" and what Lorentz also showed in the
preceeding article in that book ("Electromagneitc phenomena ...").
I advise getting ahold of "Spacetime Physics" by Taylor and Wheeler.
It's time thast you learned this stuff instead of being angry that
reality fails to agree with you.
EMS