- #1
Austin0
- 1,160
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Hi
The setup for this conundrum is like the light sphere illustration.
Two frames F and F' ------- F' moving ---->+x at v=.8c
At the point of colocation of the origens: x=0 and x'=0 t=0,, t'=0 a light burst is emitted .
Looking at two points at opposite sides of the expanding sphere
P+ and P-
P+ at x=10. t=10 , x'=3.334, t'=3.334
P- at x=-10,t=10, x'=-30,t'=30
As these locations in both frames are large photosentive panels. Lensless photodiode
arrays directed at the origens and orthogonal to the motion so it can be assumed they are the same actual sizes. These measure the number of photons intersecting them over the whole area and output a luminosity value ( L)
The question is: What would the respective relative values be?
Assumptions :
Any photon in the sphere at a point in its worldline is actually simultaneous with all other photons at that time and all are absolutely equidistant from the origen.
Because of this the sphere can be viewed for convenience as having a single worldline.
The spheres luminosity will diminish along the worldline. Any local segment will have an absolute luminosity at any given point.
A point on the worldline may intersect relative frames at different points on their worldlines but it would be assumed that colocated observers at those points would be measuring the same point of the sphere.
1) Based on this,, it would seem that at any colocated point, the measurements would have to be equal.
Both frames at P+ would measure equal values:
P+ L+=L'+
P- L-=L'-
2) Based on the 1st Postulate and the fact that luminosity must diminish as a function of distance D ,,,dec reasing exponentially with increasing distance
it would mean that L+ with D=10 must equal L- with D=10
L'+ [D=3.334] must be greater than L'- [ D=30]
________________________________________________________________________
A) If we assume ----#1)
that the measurments must agree between both frames colocated at a point then the L values cannot be a function of distance in both frames because the distances are equal in one frame [F] but greatly unequal in the other [F']
B) If we assume -----# 2)
that the values must be a function of D then the frames cannot agree on colocated measurements.
The measurements must be equal in F but cannot be equal in F'
If A) then there is a violation of the 1st Postulate.
If B) then it has to be explained how two colocated measurements of the same point on the light cone could possibly be different?
Or alternately how two observers measuring two different points on the cone [with different luminosities ] could possibly be colocated ?.
As far as I can see:
---------- [Both A and B must be true]---- AND[---- Both A and B cannot be true.]------------
So any solutions or insights would be great.
Thanks
The setup for this conundrum is like the light sphere illustration.
Two frames F and F' ------- F' moving ---->+x at v=.8c
At the point of colocation of the origens: x=0 and x'=0 t=0,, t'=0 a light burst is emitted .
Looking at two points at opposite sides of the expanding sphere
P+ and P-
P+ at x=10. t=10 , x'=3.334, t'=3.334
P- at x=-10,t=10, x'=-30,t'=30
As these locations in both frames are large photosentive panels. Lensless photodiode
arrays directed at the origens and orthogonal to the motion so it can be assumed they are the same actual sizes. These measure the number of photons intersecting them over the whole area and output a luminosity value ( L)
The question is: What would the respective relative values be?
Assumptions :
Any photon in the sphere at a point in its worldline is actually simultaneous with all other photons at that time and all are absolutely equidistant from the origen.
Because of this the sphere can be viewed for convenience as having a single worldline.
The spheres luminosity will diminish along the worldline. Any local segment will have an absolute luminosity at any given point.
A point on the worldline may intersect relative frames at different points on their worldlines but it would be assumed that colocated observers at those points would be measuring the same point of the sphere.
1) Based on this,, it would seem that at any colocated point, the measurements would have to be equal.
Both frames at P+ would measure equal values:
P+ L+=L'+
P- L-=L'-
2) Based on the 1st Postulate and the fact that luminosity must diminish as a function of distance D ,,,dec reasing exponentially with increasing distance
it would mean that L+ with D=10 must equal L- with D=10
L'+ [D=3.334] must be greater than L'- [ D=30]
________________________________________________________________________
A) If we assume ----#1)
that the measurments must agree between both frames colocated at a point then the L values cannot be a function of distance in both frames because the distances are equal in one frame [F] but greatly unequal in the other [F']
B) If we assume -----# 2)
that the values must be a function of D then the frames cannot agree on colocated measurements.
The measurements must be equal in F but cannot be equal in F'
If A) then there is a violation of the 1st Postulate.
If B) then it has to be explained how two colocated measurements of the same point on the light cone could possibly be different?
Or alternately how two observers measuring two different points on the cone [with different luminosities ] could possibly be colocated ?.
As far as I can see:
---------- [Both A and B must be true]---- AND[---- Both A and B cannot be true.]------------
So any solutions or insights would be great.
Thanks