The Burn Mark Problem
The below experiment will avoid clocks and use light distance travel and frame distance travel. Since the SR clock synchronization method uses distance and light travel for its implementation, then distance and light travel are more fundamental than clocks.
Assume a stationary light source O a moving frame O’ moving at v in the direction of the negative x-axis.
When O and O’ are co-located, O emits a light pulse. O concludes when light moves a distance d, the observer O’ moves to the x coordinate –vd/c.
O decides to place a burn mark at that x location. Therefore, when O’ and the burn mark are co-located, O concludes light has traveled such that it is a distance vd/c + d from the burn mark.
O concludes O’ must measure this distance light traveled with a length contracted rod and hence, O’ will measure this distance light traveled as
(vd/c + d)/λ.
O’, on the other hand, draws different conclusions when taken as stationary. O’ sees the burn mark coming toward it from the left at v.
Also, when O and O’ are co-located at light emission, the burn mark is a distance (vd/c)/λ from O’. While light travels d/λ, the burn mark travels (vd/c)/λ toward O’. Hence, O’ concludes it is co-located with the burn mark when light travels d/λ from the light emission point O’ since O’ is taken as stationary for this set of conclusions. Hence, O’ concludes when it is co-located with the burn mark, light has traveled a distance d/λ from the burn mark. Also, O’ concludes O will measure this distance as d/λ2.
To summarize, when the burn mark and O’ are co-located.
O stationary
1) An O observer co-located with the burn mark concludes the one light beam is a distance vd/c + d from the burn mark.
2) O concludes O’ will measure this distance as (vd/c + d)/λ.
O’ stationary
1) An O observer co-located with the burn mark concludes the one light beam is a distance d/λ from the burn mark.
2) O’ concludes O will measure this distance as d/λ2.
Obviously, sans length contraction, frames cannot disagree on the length, from a co-located point, of a single light beam.
The below experiment will avoid clocks and use light distance travel and frame distance travel. Since the SR clock synchronization method uses distance and light travel for its implementation, then distance and light travel are more fundamental than clocks.
Assume a stationary light source O a moving frame O’ moving at v in the direction of the negative x-axis.
When O and O’ are co-located, O emits a light pulse. O concludes when light moves a distance d, the observer O’ moves to the x coordinate –vd/c.
O decides to place a burn mark at that x location. Therefore, when O’ and the burn mark are co-located, O concludes light has traveled such that it is a distance vd/c + d from the burn mark.
O concludes O’ must measure this distance light traveled with a length contracted rod and hence, O’ will measure this distance light traveled as
(vd/c + d)/λ.
O’, on the other hand, draws different conclusions when taken as stationary. O’ sees the burn mark coming toward it from the left at v.
Also, when O and O’ are co-located at light emission, the burn mark is a distance (vd/c)/λ from O’. While light travels d/λ, the burn mark travels (vd/c)/λ toward O’. Hence, O’ concludes it is co-located with the burn mark when light travels d/λ from the light emission point O’ since O’ is taken as stationary for this set of conclusions. Hence, O’ concludes when it is co-located with the burn mark, light has traveled a distance d/λ from the burn mark. Also, O’ concludes O will measure this distance as d/λ2.
To summarize, when the burn mark and O’ are co-located.
O stationary
1) An O observer co-located with the burn mark concludes the one light beam is a distance vd/c + d from the burn mark.
2) O concludes O’ will measure this distance as (vd/c + d)/λ.
O’ stationary
1) An O observer co-located with the burn mark concludes the one light beam is a distance d/λ from the burn mark.
2) O’ concludes O will measure this distance as d/λ2.
Obviously, sans length contraction, frames cannot disagree on the length, from a co-located point, of a single light beam.