On 1/23/15 1/23/15 5:05 PM, Marjorie Delarosa wrote:
> Tom Roberts wrote:
>> On 1/22/15 1/22/15 12:18 PM, Marjorie Delarosa wrote:
>>> Tom Roberts wrote:
>>>> The twin paradox _IS_ a triangle in the space-time plane. But the
>>>> geometry is hyperbolic, not Euclidean, and the twin who traverses
>>>> two sides has a smaller elapsed proper time than the twin who
>>>> traverses one.
>>> Hmm, shouldn't more distance take more time? NY to NJ say 1h, NY to CA
>>> say 6h.
>> For distance, yes. But that distance is in a space-space plane. This is
>> in a space-time plane, and as I said, the geometry is hyperbolic, not
>> Euclidean.
>
> So just by changing some rules in the middle of the game one can prove
> anything.
Not at all! No rules "changed" -- this is SR and the geometry has always been
Minkowski; in a space-time plane that is hyperbolic.
Yes, this is different from Euclidean geometry. The "change" is from your naive
expectation of Euclidean geometry to the Minkowski geometry of SR. That's YOUR
problem, not mine.
>>> You just said "the twin who traverses two sides has a smaller elapsed
>>> proper time than the twin who traverses one". What is going on exactly?
>>
>> The geometry is not Euclidean. The time coordinate enters into the
>> metric with a minus sign (relative to the way spatial coordinates
>> enter). Speaking loosely, traveling a distance in space "subtracts" from
>> the elapsed time. But not very much for c<<c.
>
> Enters! However, can be an artefact and something completely else may
> exteriorize in the above ANOMALY.
I have no idea what you are trying to say.
By "The time coordinate enters into the metric with a minus sign" I meant that
the time-time component of the metric, g_tt, is negative. But you probably don't
know what that means, which is why I phrased it the way I did.
> Before that, let's stick consistent,
_I_ have been consistent, but YOU keep attempting to apply Euclidean notions to
Minkowski geometry, and that MISAPPLICATION is inconsistent.
> which is (i) Distances cannot become
> negative;
You are fixated on Euclidean geometry. In Minkowski geometry, the invariant
interval can indeed be negative. It is the closest analogy there is to distance
in Euclidean space, but it is not so very close.
> (ii) Time cannot become negative either (arrow).
Hmmm. A time coordinate can of course have negative values, it's just that no
timelike object can evolve to increasingly negative values.
>> This handwaving can be made rigorous and described mathematically --
>> learn how by studying SR and the Lorentz group.
>
> You first. Then save me the trouble, come back and show me what you did.
Hopeless. You clearly don't understand the nomenclature, and I'm not about to
type in a book on SR. You need a textbook, such as:
Taylor and Wheeler, _Spacetime_Physics_.
> (I need the source code, disregard languages and platform dependency)
This is not software at all. This is physics. And you need understanding -- you
can't get that from code.
You cannot hope to play a Beethoven piano sonata without a
serious study of both the piano and music in general. You
cannot hope to understand modern physics without a serious
study of both mathematics and physics.
Tom Roberts