Re: Question about light clock and derivation of time dilation


"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote in message
news:daol15011pu@xxxxxxxxxxxxxxxxxx
> Androcles says...
>
>>"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote
>
>>> Hmm. Usually, the time axis is chosen to be a timelike vector.
>>
>>I think your "timelike vector" lacks an identity.
>
> Look. An event (such as the landing on the moon, the
> signing of the Magna Carta) is specified by giving (1)
> a time, and (2) a spatial location. In Cartesian coordinates,
> this information is specified by 4 numbers: x,y,z, and t.

Look.
We can return to the moon, but not to Neil Armstrong planting a
footprint in 1979.
We cannot return to Runymede to see Magna Carta signed in 1215 either,
but we can return to Runymede.


>
> So when we are talking about events, we are talking a 4-dimensional
> vector space.
Let (x1,y1,z1,t1) be a 4-vector.
Let (x2,y2,z2,t2) be a 4-vector.

Add the vectors.
(x1-x2, y1-y2, z1-z2, t1-t2)

Put in numbers
x1 = y1 = z1 = t1 = 1
x2 = y2 = z2 = t2 = -1
(1-1,1-1,1-1, 1-1) = (0,0,0,0)

I've now moved from (1,1,1, 1pm)
to (0,0,0, midday) and gone backwards in time.
LOOK!


That's true whether you are talking about Galilean
> relativity or Special Relativity.

Time is not a vector.
Referring to an event is not the same as re-visiting it.



>>V is a commutative group under addition of vectors
>> 1.. There exists an additive identity element 0 in V, such that for
>>all elements v in V, v + 0 = v.
>> 2.. For all v in V, there exists an element w in V, such that v + w
>> =
>>0.
>> 3.. Vector addition is associative: u + (v + w) = (u + v) + w.
>> 4.. Vector addition is commutative: v + w = w + v.
>>http://en.wikipedia.org/wiki/Vector_space
>
> That's right. In Minkowsky spacetime, the coordinates of
> an event form a 4-D vector space, with a point in that
> space specified by the four numbers (t,x,y,z).
>
>>So where is your element w so that v+w = 0?
>
> If v is the vector with components (t,x,y,z), then
> its inverse is (-t,-x,-y,-z).

There is no -t in the real world, but there are -x, -y and -z.
Referring to an event is not the same as visiting it.
Boring, perhaps, but that's the way it is.
Of course I have no problem with you REFERRING to
Minkowski space-time or events in the past,
but it doesn't reflect physical phenomena today.
You can't change the past.




>
>>Or can you travel backward in time to when you were?
>
> Who said you could travel backwards in time?

I have no trouble moving back to where I was.
If time were a vector I could travel back to when I was as well.


Vectors
> are about *describing* the world.

Ok. So add vectors to give me a resultant force and describe
where the forces will take the object. Easy. I can predict what will
happen.
Now add vectors to describe how I move back in time.



> Just because I can
> write down a vector with a negative time component
> doesn't mean that I can *move* in that direction.

So you are not describing the world, then. Your vector with a negative
time component cannot be added to another vector that will take you back
to the origin. The other components, x,y and z can be negative, and
they WILL get you back to the origin.
I cannot predict a past event, it has already happened.

> If e1 is the event at which Jesus was born, and
> e2 is the event at which Aristotle was born, then
> the vector from e1 to e2 has time component -384 years.

Then go to when Aristotle was born. I have no trouble going to Greece,
I get on a plane and the pilot uses vectors to get there.
Androcles.





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