# Re: Does GR tell us why anything moves?

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On Sunday, March 11, 2018 at 10:30:46 AM UTC-4, agrays...@gmail.com wrote:
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> On Saturday, March 10, 2018 at 10:54:50 PM UTC-5, Brent wrote:
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>> On 3/10/2018 7:32 PM, agrays...@gmail.com wrote:
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>> On Saturday, March 10, 2018 at 10:09:45 PM UTC-5, Brent wrote:
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>>> On 3/10/2018 5:04 PM, agrays...@gmail.com wrote:
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>>> On Sunday, March 4, 2018 at 11:35:24 PM UTC-5, agrays...@gmail.com
>>> wrote:
>>>>
>>>> I don't think so. I think its equations of motion mix time and space,
>>>> so if time increases, spatial position must change. That is, the
>>>> assumption
>>>> that time increases, produces changes in spatial position. CMIIAW. AG
>>>>
>>>
>>> Here's a related question; if you assume a 4d spacetime manifold, how
>>> does one imagine the shortest path between two points, aka a geodesic path,
>>> using the Lorentzian metric? AG
>>>
>>>
>>> In the Lorentz metric a geodesic is the longest path between two
>>> time-like events.
>>>
>>> Brent
>>>
>>
>> Right; we've discussed this in the past. But if that's true, why choose
>> motion along a geodesic in spacetime for a model of gravity
>>
>>
>> He didn't "choose" it, it's implicit in the motion being force-free.  As
>> Russell pointed out it's implied by conservation of energy-momentum.
>>
>> Brent
>>
>
> Where exactly is it argued that conservation of energy-momentum implies
> motion along a geodesic in the absence of external forces? TIA, AG
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I suppose, for say a Lorentzian metric, one could define a geodesic as the
path where the length between two points is maximal, that it's unique, and
all other paths do not conserve energy-momentum.  Offhand, the proof
doesn't seem obvious. Does Epstein do it? AG

> if it's the LONGEST path between two time-like events. Wasn't Einstein
>> motivated by the fact that a geodesic along a sphere using the Euclidean
>> metric for path length, is the SHORTEST distance between two points on a
>> sphere? AG
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