Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Replies: 25   Last Post: Jan 8, 2013 1:51 AM

 Messages: [ Previous | Next ]
 Paul B. Andersen Posts: 33 Registered: 8/5/10
Posted: Jan 6, 2013 8:47 AM

On 06.01.2013 07:23, Sylvia Else wrote:
> On 6/01/2013 3:59 PM, Koobee Wublee wrote:
>> On Jan 5, 5:57 pm, Sylvia Else wrote:
>>> On 5/01/2013 5:59 AM, Koobee Wublee wrote:
>>
>>>> Instead of v, let?s say (B = v / c) for simplicity. The earth is
>>>> Point #0, outbound spacecraft is Point #1, and inbound spacecraft is
>>>> Point #2.

>>>
>>>> According to the Lorentz transform, relative speeds are:
>>>
>>>> ** B_00^2 = 0, speed of #0 as observed by #0
>>>> ** B_01^2 = B^2, speed of #1 as observed by #0
>>>> ** B_02^2 = B^2, speed of #2 as observed by #0

>>>
>>>> ** B_10^2 = B^2, speed of #0 as observed by #1
>>>> ** B_11^2 = 0, speed of #1 as observed by #1
>>>> ** B_12^2 = 4 B^2 / (1 ? B^2), speed of #2 as observed by #1

>>>
>>>> ** B_20^2 = B^2, speed of #0 as observed by #2
>>>> ** B_21^2 = 4 B^2 / (1 ? B^2), speed of #1 as observed by #2
>>>> ** B_22^2 = 0, speed of #2 as observed by #2

>>>
>>>> When Point #0 is observed by all, the Minkowski spacetime (divided by
>>>> c^2) is:

>>>
>>>> ** dt_00^2 (1 ? B_00^2) = dt_10^2 (1 ? B_10^2) = dt_20^2 (1 ? B_20^2)
>>>
>>>> When Point #1 is observed by all, the Minkowski spacetime (divided by
>>>> c^2) is:

>>>
>>>> ** dt_01^2 (1 ? B_01^2) = dt_11^2 (1 ? B_11^2) = dt_21^2 (1 ? B_21^2)
>>>
>>>> When Point #2 is observed by all, the Minkowski spacetime (divided by
>>>> c^2) is:

>>>
>>>> ** dt_02^2 (1 ? B_02^2) = dt_12^2 (1 ? B_12^2) = dt_22^2 (1 ? B_22^2)
>>>
>>>> Where
>>>
>>>> ** dt_00 = Local rate of time flow at Point #0
>>>> ** dt_01 = Rate of time flow at #1 as observed by #0
>>>> ** dt_02 = Rate of time flow at #2 as observed by #0

>>>
>>>> ** dt_10 = Rate of time flow at #0 as observed by #1
>>>> ** dt_11 = Local rate of time flow at Point #1
>>>> ** dt_12 = Rate of time flow at #2 as observed by #1

>>>
>>>> ** dt_20 = Rate of time flow at #0 as observed by #2
>>>> ** dt_21 = Rate of time flow at #1 as observed by #2
>>>> ** dt_22 = Local rate of time flow at Point #2

>>>
>>>> So, with all the pertinent variables identified, the contradiction of
>>>> the twins? paradox is glaring right at anyone with a thinking brain.
>>>> <shrug>

>>>
>>
>>> You assert that there are a paradox. I take it you mean in the sense
>>> that the theory gives two results for one situation, such that they are
>>> impossible to reconcile.
>>>
>>> I challenge you to show that mathematically, rather than just asserting
>>> it. Do not just point at the maths above and claim that it's obvious.

>>
>> PD, are you turning into a troll now? For the n?th time, the
>> following is one such presentation of mathematics that show the
>>
>> - - -
>>
>> From the Lorentz transformations, you can write down the following
>> equation per Minkowski spacetime. Points #1, #2, and #3 are
>> observers. They are observing the same target.
>>
>> ** c^2 dt1^2 ? ds1^2 = c^2 dt2^2 ? ds2^2 = c^2 dt3^2 ? ds3^2
>>
>> Where
>>
>> ** dt1 = Time flow at Point #1
>> ** dt2 = Time flow at Point #2
>> ** dt3 = Time flow at Point #3
>>
>> ** ds1 = Observed target displacement segment by #1
>> ** ds2 = Observed target displacement segment by #2
>> ** ds3 = Observed target displacement segment by #3
>>
>> The above spacetime equation can also be written as follows.
>>
>> ** dt1^2 (1 ? B1^2) = dt2^2 (1 ? B2^2) = dt3^2 (1 ? B3^2)
>>
>> Where
>>
>> ** B^2 = (ds/dt)^2 / c^2
>>
>> When #1 is observing #2, the following equation can be deduced from
>> the equation above.
>>
>> ** dt1^2 (1 ? B1^2) = dt2^2 . . . (1)
>>
>> Where
>>
>> ** B2^2 = 0, #2 is observing itself
>>
>> Similarly, when #2 is observing #1, the following equation can be
>> deduced.
>>
>> ** dt1^2 = dt2^2 (1 ? B2^2) . . . (2)
>>
>> Where
>>
>> ** B1^2 = 0, #1 is observing itself
>>
>> According to relativity, the following must be true.
>>
>> ** B1^2 = B2^2
>>
>> Thus, equations (1) and (2) become the following equations
>> respectively.
>>
>> ** dt1^2 (1 ? B^2) = dt2^2 . . . (3)
>> ** dt2^2 = dt1^2 (1 ? B^2) . . . (4)
>>
>> Where
>>
>> ** B^2 = B1^2 = B2^2
>>
>> The only time the equations (3) and (4) can co-exist is...

>
>
> ... never
>
> In deriving [1] and [2] you prefaced them with caveats about who is
> observing whom. So they relate to different measurement situations. You
> cannot combine them in any meaningful way.
>
> Sylvia.
>

It's a variant of the old Dingle argument,
@t1/@t2 = @t2/@t1 is a contradiction.
(@ = partial derivative)

See:
http://tinyurl.com/ah3ctmm

Koobee's response:
http://tinyurl.com/a9jkwxp
<<
What Koobee Wublee wrote that you have quoted was an application of
the Lorentz transform in a specific scenario. You don?t understand
all that, and apparently, you don?t know what you are talking about as
usual. It is laughable that a college professor from the University
of Trondheim would attempt to swindle his way out using irrelevant,
bullshit claims. <shrug>

You are cornered. Why don?t you stay in the topic of discussion?
<shrug>
>>

His arguments were as lethal and to the point as always. :-)

--
Paul

http://www.gethome.no/paulba/