# Re: Block Universes

This is why time has a minus sign in SR. (I believe the usual way this
informally is put is that the space-traveller "trades space for time".)

On 8 March 2014 13:26, Jesse Mazer <laserma...@gmail.com> wrote:

>
> On Fri, Mar 7, 2014 at 7:20 PM, Edgar L. Owen <edgaro...@att.net> wrote:
>
>> Jesse,
>>
>> Do you understand why the world line that is depicted as LONGER in the
>> typical world line diagram is ACTUALLY SHORTER?
>>
>> E.g. in your diagram do you understand why even though A's world line
>> looks longer than C's world line, it is ACTUALLY SHORTER?
>>
>> Edgar
>>
>
> Are you actually reading my posts carefully all the way through, or just
> skimming them or something? I spent a whole extended section of my post
> discussing just this point, read it again:
>
> 'It is true that if you just look at the spatial lengths of each path on
> the diagram, the ratio between the spatial lengths doesn't actually match
> up with the ratio between the proper times that would be calculated using
> relativity. If you use any Cartesian spatial coordinate system to draw x-y
> axes on the diagram, then you can use this coordinate system to assign x
> and y coordinates to the endpoints of any straight blue segment, x1 and y1
> for one endpoint and x2 and y2 for the other, and then calculate the
> spatial length of that segment using the Pythagorean theorem:
> squareroot[(y2 - y1)^2 + (x2 - x1)^2]. Note that you ADD the squares of the
> two terms in parentheses when calculating spatial length, but my earlier
> equation showed that you SUBTRACT the square of the two terms in
> parentheses when calculating proper time, which explains why this sort of
> spatial path length on a spacetime diagram can be misleading. For example,
> in spatial terms a straight line is the SHORTEST path between two points,
> but in spacetime a straight (constant-velocity) worldline is the one with
> the LARGEST proper time between points.
>
> Nevertheless, the math for calculating the invariant spatial path length
> using a Cartesian coordinate system is closely analogous to the math for
> calculating the invariant proper time using an inertial frame. The diagrams
> show the spatial length of the paths being different despite identical red
> acceleration segments, and this remains true if you actually calculate
> proper time, even though in terms of proper times C > B > A which is the
> opposite of how it works with spatial lengths.'
>
>
>
>
>>
>>
>>
>>
>>
>> On Friday, March 7, 2014 5:15:57 PM UTC-5, jessem wrote:
>>>
>>>
>>>
>>>
>>> On Fri, Mar 7, 2014 at 4:02 PM, Edgar L. Owen <edga...@att.net> wrote:
>>>
>>> Jesse,
>>>
>>> Finally hopefully getting a minute to respond to at least some of your
>>> posts.
>>>
>>> I'm looking at the two 2 world line diagram on your website and I would
>>> argue that the world lines of A and B are exactly the SAME LENGTH due to
>>> the identical accelerations of A and B rather than different lengths as you
>>> claim.
>>>
>>> The length of a world line is the PROPER TIME along that world line.
>>> Thus the length of a world line is INVARIANT. It is the length of the world
>>> line according to its proper clock and NOT the length according to C's
>>> clock which is what this diagram shows.
>>>
>>>
>>> I don't understand what you mean by "the length according to C's
>>> clock"--are you just talking about the numbers on the vertical time axis,
>>> 2000-2020? That axis represents the coordinate time in C's rest frame, and
>>> obviously the coordinate time between "2000" at the bottom of the diagram
>>> and "2020" at the top is 20 years regardless of what path you're talking
>>> about, so I don't see how it makes sense to call this the "length" of any
>>> particular path. But you can also use C's
>>> ...
>>
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>
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