Student understanding of time in special relativity: simultaneity and reference frames

Rachel E. Scherr, Peter S. Shaffer, and Stamatis Vokos
Department of Physics, University of Washington, Seattle, WA

This article reports on an investigation of student understanding
of the concept of time in special relativity. A series of research
tasks are discussed that illustrate, step-by-step, how student
reasoning of fundamental concepts of relativity was probed. The
results indicate that after standard instruction students at all
academic levels have serious difficulties with the relativity of
simultaneity and with the role of observers in inertial reference
frames. Evidence is presented that suggests many students construct
a conceptual framework in which the ideas of absolute simultaneity
and the relativity of simultaneity harmoniously co-exist.

See: http://arxiv.org/pdf/physics/0207109

VII. CONCLUSION

"This investigation has identified widespread difficulties that
students have with the definition of the time of an event and the
role of intelligent observers. After instruction, more than 2/3 of
physics undergraduates and 1/3 of graduate students in physics are
unable to apply the construct of a reference frame in determining
whether or not two events are simultaneous. Many students interpret
the phrase “relativity of simultaneity” as implying that the
simultaneity of events is determined by an observer on the basis of
the reception of light signals. They often attribute the relativity
of simultaneity to the difference in signal travel time for different
observers. In this way, they reconcile statements of the relativity
of simultaneity with a belief in absolute simultaneity and fail to
confront the startling ideas of special relativity".

Black holes violate time laws. They are not what is being seen.

Mitch Raemsch

I remember that one.. wasn't it published in the EJP? The authors were
good in identifying the problem, but weak in their suggested
improvements.

- The careless use of jargon ("in a reference frame", "observer",
etc.) is not helpful for students
- Many textbooks are less thoughtful and clear with definitions of
such things as simultaneity than Einstein was in his 1905 paper.

Harald

There is fastest time fundamental if there is a slowdown.
Time math is time flow slowing down from light speed for
matter by gravity and motion or the Two Times.

Mitch Raemsch

xxein: Go live in your wonderland and f**k yourself. You have no
idea how the physic manifests itself to observers.

Imagine what you want (Einstein's imagination included).

Go to mushrooms.com and be with people that will believe whatever you
say.

thus:
"one" is no special decimal case;
none of the "terminating decimals" actually ever finish
there "zero-endings."

> so a completed number ie 1 can not be the same as a number that never
> completes or never terminates

thus: yeah, Apollonius; no need
to not use four spheres as givens; eh?

thus: typically, OPsters supress the real meaning
of the real number, one, to use "1.", "period,
instead of 'dot,'" when, what they tend to mean is that
1.0000... is not equal to 0.9999...,
which is just the sole ambiguity of "decimals,"
per Stevin (15cce ?-)
many tlansrations!

--les ducs d'Enron!
http://tarpley.net

--Light, A History!
http://wlym.com

1. It can be very useful to image how the Lorentz transformations
function
2. It can mislead people into thinking that in SRT, "time" and "space"
must be conceptually mixed

Harald

e4cb9978-ecc3-4209...@u31g2000yqb.googlegroups.com

"harald" <hv...@swissonline.ch> wrote in message
news:4a88a871-42f5-43dd...@n3g2000yqb.googlegroups.com...

now, what about his *usefull* stuff?

For example ("googled", didn't check):
http://hubpages.com/hub/Using-the-Minkowski-Diagram-

Harald

Yes.

But they inherently _ARE_ mixed, in the following sense:

In inertial frame A, consider a timelike 4-vector parallel to the time
coordinate, so its spatial components are all zero in this frame. Now project it
onto some other inertial frame (moving wrt the first one) -- in this frame its
spatial components are not all zero. So what was "pure time" in the first
inertial frame is "mixed time and space" in the second inertial frame.

Tom Roberts

"Tom Roberts" <tjrobe...@sbcglobal.net> wrote in message
news:EKKdnWD0CtP...@giganews.com...

Harald does seem to have a stumbling block regarding SR that is so great he
can't even comprehend that he has one .. its not that he's stupid or
dishonest, of course, like some here .. but its just a conceptual leap he's
apparently not been able to make.

Lets see what he thinks of this ...

In a world as modeled by classical / Euclidean / Galilean / Newtonian space
and time, a unit length is a unit length and a second is a second,
regardless of motion. Something that happens at a particular point in time
for you happens at that same point in time for every object, regardless of
motion. Space and time are disjoint and orthogonal. But in a world as
modeled by SR space-time, this is not the case. Lets look at that sort of
world .. a world where SR applies.

Lets say there is a rod (or spaceship or train or whatever) moving past you
from your left to your right (from your -x to your +x). Lets take the usual
meanings of front and rear of the rod as its leading edge and trailing edge
respectively.

Consider the moment that the centre of that rod is directly adjacent to you.

At the moment in (your) time, the past of the front of the rod exists in
your frame, and the future of the rear of the rod exists in your frame
{where past present and future are for the rod itself). That is the past,
present, and future of that rod exist simultaneously in your frame. The
present of the front of the rod does not yet exist for you, and the present
of the end of the rod no longer exists.

Indeed .. SR tells us that the further to the right you go, the further into
the rod's past that exist now for you. And the further to the left you go,
the further into the rod's future exists now for you.

As it is the past of the front of the rod that exists now for you, and the
rod is moving relative to you, the location of that endpoint is going to be
a bit to the left of where we would otherwise expect (because in its past it
was more to the left).

Similarly, as it is the future of the rear of the rod that exists now for
you, and the rod is moving relative to you, the location of that endpoint is
going to be a bit to the right of where we would otherwise expect. (because
in its future it moves more to the right).

So if the rear is more to the right, and the front more to the left, that
means if you take the distance between between front and end of the rod now
(in your time), you are taking the distance between where the rear of the
rod will be in the future and where the front of the rod was in the past,
and this will obviously be less than the rods proper length.

[ This gets more interesting when you do the same analysis from the point of
view of the rod, and when you start plugging in numbers ]

I wonder if Harald can grasp that notion? I wonder if he can see the the
future of the rear, present of the middle, and past of the front of the rod
existing simultaneously now for the observer (and how it depends on position
relative to the observer) is a rotation in space-time ?

Again .. my little song (to the tune of "There's a Hole in the Bucket")
might help ...

Your ruler is contracted, dear Liza, dear Liza,
Your ruler is contracted, dear Liza, contracted
But you measured is wrongly, dear Henry, dear Henry,
But you measured it wrongly, dear Henry, wrongly
But how was it wrong, dear Liza, dear Liza,
But how was it wrong, dear Liza, but how?
You looked at the ends at different times, dear Henry,
You located the ends at different times you see?
So how can I fix it, dear Liza, dear Liza,
So how can I fix it, dear Liza, so how?
I'll light up the ends at the same time, dear Henry,
I'll light up the ends at the same time, like this
Now they're are too far apart, dear Liza, dear Liza
Now they're are too far apart, dear Liza, apart
Of course that's what *you* think, dear Henry, dear Henry
Of course that's what *you* think, dear Henry, of course
But I measured it with my ruler, dear Liza, dear Liza
But I measured it with my ruler, dear Liza, my ruler
But your ruler is contracted, dear Henry, dear Henry,
Your ruler is contracted, dear Henry, contracted

AND THE ANSWER IS...

xi = (x-vt)/sqrt(1 - v^2/c^2) -- Einstein.

In agreement with experience we further assume the deranged babbling
incompetent cretin couldn't answer his own inquiry, he was too stupid to
realise xi is greater than L when he wrote 'for v=c all moving
objects--viewed from the "stationary'' system--shrivel up into plane
figures', whereas the equation shows they stretch to infinity...
sqrt(1-c^2/c^2) = 0.

"Inertial" <relat...@rest.com> wrote in message
news:4ca9723c$0$11120$c3e...@news.astraweb.com...

AND THE ANSWER IS...

news:4ca97597$0$11102$c3e...@news.astraweb.com...

Thanks for the illustration! Such explanations easily confuse people
into thinking that in SRT the concepts of "time" and "length" as used
in an inertial reference system are "mixed" in the sense that in SRT
time is the same as space.

Harald

e4cb9978-ecc3-4209...@u31g2000yqb.googlegroups.com

news:f83dc6c0-1000-460c...@j24g2000yqa.googlegroups.com...

On Oct 4, 8:20 am, "Inertial" <relativ...@rest.com> wrote:
> "Tom Roberts" <tjroberts...@sbcglobal.net> wrote in message

I have issues with how SRT apparently is *taught* at a number of
schools; the findings that Sam here cites confirm my concerns. As a
reminder, I commented:

- Many textbooks are less thoughtful and clear with definitions of

And when asked about the effect of Minkowski geometry on students, I
commented:

must be conceptually mixed.

Warning: the above account is potentially misleading, but for sure
"Inertial" doesn't know that.

I will suppose that with "of the rod" Inertial actually meant "of an
inertial reference system in which the rod is in rest". A more precise
SRT description of the above thought experiment would be:

"Suppose that you set up an inertial orthogonal coordinate system S
according to the rules of SRT, in which you are in rest; we'll call
the time of S "your time".

respectively. And let's define an inertial reference system S' in
which the rod is centered and in rest, and which we call "its system".

Pay attention to the definition of simultaneity in S', as measured
with S. Make sure to understand the instruction material of section 2
of http://www.fourmilab.ch/etexts/einstein/specrel/www/ .
Thus as a result from your assumption that the speed of light is c
relative to S, you find that as measured by S ("you"), a clock of S'
at the rear of the rod will be advanced relative to a clock of S' at
the front.

Now, consider the moment that the centre of that rod is directly
adjacent to you.

At that moment in your time, the front of the rod is still in the past
according to
its system S', while a clock of S' at the rear of the rod already
indicates the future. Thus the past,
present, and future as determined with that system appear
simultaneously as function of position in your system. To be clear,
you measure the whole rod - from front to end - as now in the present;
measurements of S' merely assign different coordinates and times to
events; they relate to your measurements but cannot affect your
measurements.

This can be illustrated with a Minkowski space-time diagram, as for
example elaborated in fig.7 of http://hubpages.com/hub/Using-the-Minkowski-Diagram-
.

Moreover, fig.2 illustrates how the relativity of simultaneity is
important for the symmetry of observation of length contraction."

Note that where Inertial writes "At the moment in (your) time, the
past of the front of the rod exists in your frame", I write "At that
moment according to your time, the rod's system S' measures the front
of the rod as still in the past".

Further, I fully agree with Bell's take on "how to teach special
relativity". It would be interesting if we could set up a test with
fresh students, to see which group achieves better results as function
of the way SRT is taught to them.

I'll also reproduce here Bell's comments in his article "How to teach
special relativity":

"I have for long thought that if I had the opportunity to teach this
subject, I would emphasize the continuity with earlier ideas. Usually
it is the discontinuity which is stressed, the radical break with more
primitive notions of space and time. Often the result is to destroy
completely the confidence of the student in perfectly sound and useful
concepts already acquired. [..]
This old problem [of the spaceships] came up for discussion once in
the CERN canteen. A distinguished experimental physicist refused to
accept that the thread would break, and regarded my assertion, that
indeed it would, as a personal misinterpretation of special
relativity. We decided to appeal to the CERN Theory Division for
arbitration, and made a (not very systematic) canvas of opinion in it.
There emerged a clear consensus that the thread would not break! [..]
It is my impression that those with a more classical education,
knowing something of the reasoning of Larmor, Lorentz, and Poincare,
as well as that of Einstein, have stronger and sounder instincts."

Harald

--

news:bed3452d-88c6-41f3...@30g2000yqm.googlegroups.com...

You're confused still

If you prefer .. I'm being deliberately informal here to avoid the jargon
you find so confusing

If you prefer .. its the same thing

I understand just fine

Time is advanced .. the clock is simply showing the time. Its not just an
arbitrary clock mal-adjustment going on there.

Yeup

The rear is in the future .. yes

That's what i said

In your system .. you are measuring where the rear is in the future and the
front in the past (it the rod's system).

> measurements of S' merely

Not merely

If that's how you want to illustrate it .

The differences in simultaneity mean length measurements differ, because
simultaneity is part of the operational definition of length.

It is still in the past, in the rod's frame, as much as it is in the present
in yours

[snip Harald changing topic]

Nope. Just can't be bothered with your copy/paste stalking. If you want to
learn relativity, I'm happy to help you .. but you're not.

That's the only topic you're interested in .. you only post about relativity
(which you do not understand) so that those who understand it will respond
to you. Pathetic.

news:4ca9cb02$0$28673$c3e...@news.astraweb.com...

They are mixed, by definition: The meter, or length, is defined as a
time measurement procedure.
You cannot theoretically measure length w/o a clock. That makes length
dependent on time. They are not independent; they are mixed.

In principle, distances in SRT are compared with rulers ("rods") and
the progress of natural processes with clocks. The modern definition
of the meter came AFTER SRT; that length standard now *depends* on the
time standard for practical (not principal) purposes. It is not
directly relevant for this topic.

Harald

"hanson" <han...@quick.net> wrote in message
news:i8d7kl$b48$1...@news.eternal-september.org...

Hahaha Hanson, I thought you were joking - but that Ether page
actually exists!
Thanks for the laughs. :))))
Harald

e4cb9978-ecc3-4209...@u31g2000yqb.googlegroups.com

news:0691ccfe-2365-47e8...@a36g2000yqc.googlegroups.com...

Not quite. Even in the 1905 SR, the lengths were described as a time
measurement.
But yes, most of those lengths were usually done by comparing with a
ruler.

As SR evolved, the ruler was dropped and the length measurement
procedure by clocks (also as described by Poincare before 1905 !) was
adopted: the current definition of the meter and distance. From this
standard (1983), distance has become dependent on time.

IOW,
In the 1905 SR, space and time were one according to the theory.
Today's SR, with the modern definition of meter, space and time are
one due to the *definition* of meter.

There is two time rate at every point in space. Space-time can be
empty.

BUT only by comparing locations of endpoints at the same time, which
requires synchronized clocks. its only the special degenerate case where
you are measuring the length of something at rest that you can do without
the clocks. Clock sync (RoS) has a very major influence on length
measurement of moving objects.

--
Predictions of relativity.

--
Clock A reads 6:00 am at dawn, its a perfect clock.
Clock B reads 12:00 pm at noon, its a perfect clock.
Clock A remains in synch with Earth wherever it goes because
"In accordance with definition the two clocks synchronize if
tB-tA = t'A-tB",clock A can see the Earth and Earth can see
clock A, "the ``time'' required by light to travel from A to B
equals the ``time'' it requires to travel from B to A."-- Einstein.

"the velocity of light in our theory plays the part, physically, of an
infinitely great velocity" -- Einstein.

Because of time dilation, "if one of two synchronous clocks
at A is moved in a closed curve with constant velocity until
it returns to A, the journey lasting t seconds, then by the clock
which has remained at rest the travelled clock on its arrival at
A will be 1/2 tv^2/c^2 second slow." -- Einstein.

Clock A meets clock B at A and is 6 hours slow. Both clocks
synchronize with Earth, because "in accordance with definition
the two clocks synchronize if tB-tA = t'A-tB."-- Einstein.

Therefore clock A meets clock B at dawn and clock B sees
clock A arrive at noon.

Inertbrain plays the part, physically, of a deranged lying cretin.

Prove it. How could you measure it if every clock is in "error"?

> Only clocks show error.

If all clocks (ie all processes) at rest in some frame show the same "error"
.. and clocks in different motion show different times/rates .. then in what
sense is 'time' the same everywhere?

What causes/explains the differences in clock readings/rates that we see in
experiment to be just as SR/GR predicts?

Are you actually an LET aetherist who thinks difference motion through the
absolute 'ether' cause clocks to speed up or slow down. If not .. then what
is the explanation? Do you have one? Or do you just assert statements with
no proof or logical argument to support it.?

Sure, that's easy.
In agreement with experience we further assume clock A meets
clock B when clock B meets clock A.
We will raise this conjecture (the purport of which will hereafter be
called the "Principle of Simultaneity'') to the status of a postulate.
We assume that this definition of simultaneity is free from contradictions,
and possible for any number of clocks; and that the following relations

are universally valid:--

1.. If the clock at B meets with the clock at A, the clock at A meets with
the clock at B.
2.. If the clock at A meets with the clock at B and also with the clock at
C, the clocks at B and C also meet with each other.
If time were not the same everywhere then A would meet B at a
different time to B meeting A, and that has never been observed.

That violates the Principle of Simultaneity, therefore time is
same everywhere. QED.

No .. its not . .experience shows the correct clocks show different times
when they meet .. that time does indeed dilate.

Of course they meet each other at a single event .. that does not mean A and
B show the same time reading when they meet. And that is what we find in
relevant experiments .. when clocks reunite they show different times.

Bad choice of name

Trivially true

That does not follow unless A meets B *and& A meets C *both* at the same
time .. you didn't specify that. So 2 is not correct.

The clocks DO meet at one event (ie at the same time) .. that is consistent
with time being different depending on motion. But the clock reading on the
clocks when they meet is different.

The reading on clock A when it meets B is different to the reading on B when
it meets A then that is correct .. and that we DO see happen. And that is
also consistent with time NOT being the same regardless of motion (but not
with your claim)

But you seem to be wording it as though that means that they meet at two
different occasions. That is wrong.

[snip rest that follows from invalid conclusion]

You fail. Try again.

thus; quoth:
You fail.  Try again.- Hide quoted text -

thus: you are your very own Dingleberry d'Einstein, because
you can't do "special" relativity with cuternions (that is,
"the original vectors & language thereof") but,
mayhaps you can resolve the alleged problem,
with your approach, belowsville.

thus quoth:
Despite the denial of the self-styled physicists, that geodesic
equation dealing with the temporal dimension does lead to some
interesting results that supports the Newtonian law of gravity under
weak curvature in spacetime. <Frug>
In a diagonal metric such as the one indicated by the common
spherically symmetric polar coordinate system, the geodesic equation
dealing with the temporal dimension is the same between the least
actions of traversed time and accumulated spacetime. Notice these two
model of geodesic actions are very different. Under the action of
least spacetime, no photons are capable of coherent motions since
every single path available to a propagating photon would accumulate a
net spacetime of exactly ZERO, and thus violate the least action in
accumulated spacetime. Anyhow, despite the fatal error in this model,
it is how the self-styled physicists decide to take shelter under that
fatally flawed, mathematical model dealing with geodesic motions.
Given the example of the Schwarzschild metric, the geodesic equation
dealing with the temporal dimension can be derived as follows.

Constant = (1 - 2 U) / (1 - B^2), where
** U = G M / c^2 / r
** B^2 c^2 = (dr/dt)^2 / (1 - 2 U)^2 + r^2 (dO/dt)^2 / (1 - 2 U)
and ** dO^2 = dLongitude^2 cos^2(Latitude) + dLatitude^2
** Schwarzschild metric = c^2 (1 - 2 U) dt^2 - dr^2 / (1 - 2 U) - r^2
dO^2

The constant can be interpreted as follows:
** constant = E^2 / m^2 / c^4
In which under weak curvature of spacetime, the 1st equation
simplifies into the following:
another constant ~ v^2 / 2 - U c^2, where
** 1 >> 2 U, ** 1 >> B^2, ** B^2 c^2 ~ v^2.
The immediate equation above is the Newtonian law of gravity in while
the overall energy equals the kinetic energy plus/minus the potential
energy (depending on what your definition of the potential energy is).
<Frug>

--les ducs d'Enron!
http://tarpley.net

--Light, A history!
http://wlym.com

. http://hubpages.com/hub/Using-the-Minkowski-Diagram-
> wherein it says:
<http://hubpages.com/hub/Relativity-indicates-the-possible-existence-of-the-Ether>

<http://hubpages.com/hub/Relativity-indicates-the-possible-existence-of-the-Ether>

> hanson wrote:
> The other profound insight JP Andro has expressed was:

Addressing Lintel Harald, hanson wrote:
... ahahaha... Harald listen, hanson never jokes. The jokes
are made by others to entertain hanson. The chief Joke is
JP Analdorcles himself who gets hilariously irate, when
one laughs at him or even because of him... ahahahaha...
JPA gets so aroused because of me that he runs after me,
begins to stutter and then he can only plagiarize, cut-n-paste
MY lines...as is seen in his post that wasn't even addressed
to him. Watch him now doing it again!... AHAHAHAHA..
>
Now Lintel, here's a little background on JP Analdorcles for ya.
Let me try the residuals of my Schytzerdütsch, so dass er sich
nid schäme mues. Vor zwo yohre händs im i sim grind drin öpis
ume gschneflet. Diä Sach isch irgendwiä abverreckt und siit
dänn ish sihs Hirni ebe a-tätchd und dä guete arme Sühche-
Vogel isch jetz halt hoch-ober-voll & total a-kafled & a-gfresse...
It's a shame, isn't it, Harald... but I thoroughly enjoy JPA's
company.... Thanks for the laughs to you too, Harald...
ahahahaha... ahahahahanson
>
BTW, Harald did you ever go and check out this
historic vignette about your idol Einstein?:
>
<http://tinyurl.com/Einstein-Vordergasse-pt-1>
>
<http://tinyurl.com/Einstein-Vordergasse-pt-2>
>
Notice how, in classic Talmudic fashion, poster kike
Klein / Stein aka "xxein" came immediately to
the rescue of his Yiddisher landsman Einstein,
with cusses and curses... ahahaha... Too much!
Hilarious... ahahahaha... AHAHAHAHA...

No .. its not . .experience shows the correct clocks show the correct time
whenever and wherever they are.. that time does indeed not dilate.

In agreement with experience we further assume clock A does NOT
meet clock B when clock B meets clock A, Inert cunt said so.

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

1) In agreement with experience we further assume clock A meets

2) In agreement with experience we further assume clock A does
NOT meet clock B when clock B meets clock A.

Which is it, you knee-jerking ignorant cunt?

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

You knee-jerk disagreed. I've said nothing about any reading yet.
You are dumb cunt who couldn't prove he has a hole in his arse.

In agreement with experience we further assume clock A meets

We will raise this conjecture (the purport of which will hereafter be

are universally valid:--

Yes indeed!

Harald

So now you agree ? Gees .. Can't you make up your mind?

Of course you did . And it got worse the more you said

And you failed

Don't care what jargon you used .. you still failed

What is not?

They show their proper time. Whether of not it is 'correct' depend upon who
you ask.

Experience shows time is different for different paths. You asserting the
opposite is meaningless .. seeing experiment proves otherwise.

Wrong.

> Inert cunt said so.

I said nothing of the sort, liar.

> You knee-jerk disagreed.

Where?

Neither did I.

But you're a lying shit .. already proved.

I already said 1) A meets B when B meets A, you moron. See above when I
said "of course". That doesn't mean they both show the same time.

[ snip Androcles' copy and paste misfiring .. he can't even do that right ]

Well .. you've proved yourself a liar and a moron once more. Thanks for
playing.. You lose