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Physics, Astronomy & Cosmology / moving in time
« on: 03/11/2014 17:27:49 »
Moving in time is a literal interpretation of the space and time merger proposed by Minkowski. It’s also another perspective of the moving light clock.
Light is emitted from a source in a direction p, perpendicular to x, the direction of motion, and reflects from a mirror a distance d=1, to a detector/counter. For the clock to function, the photon path must have an x and p component. The x component compensates for the motion of the clock at speed v. The p component becomes the active part of the clock. Since the photon speed is constant, its path in any direction generates a circular arc for the 90º between the p axis and x axis. This means the relative photon speed along p = c*sqrt(1-(v/c)^2) = c/γ, i.e. the clock ticks slower, the faster it moves past an observer.
With vt the x component and pt the p component, the relation can be rephrased as
1. (vt)^2 + (pt)^2 = (ct)^2, or
2. (light motion)^2 + (light motion)^2 = (light motion)^2, or
3. (object motion)^2 + (object time)^2 = (object motion)^2
Conclusion:
Line 3 being so similar to line 2, allows a metaphorical interpretation as popularized by Briane Green and others. The clock moves in a 1-dimensional space, while/(simultaneously) the photon moves in a 2-dimensional space. The clock is counting spatial increments of (2γd) which are labeled in the traditional manner as ‘time’.
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Light is emitted from a source in a direction p, perpendicular to x, the direction of motion, and reflects from a mirror a distance d=1, to a detector/counter. For the clock to function, the photon path must have an x and p component. The x component compensates for the motion of the clock at speed v. The p component becomes the active part of the clock. Since the photon speed is constant, its path in any direction generates a circular arc for the 90º between the p axis and x axis. This means the relative photon speed along p = c*sqrt(1-(v/c)^2) = c/γ, i.e. the clock ticks slower, the faster it moves past an observer.
With vt the x component and pt the p component, the relation can be rephrased as
1. (vt)^2 + (pt)^2 = (ct)^2, or
2. (light motion)^2 + (light motion)^2 = (light motion)^2, or
3. (object motion)^2 + (object time)^2 = (object motion)^2
Conclusion:
Line 3 being so similar to line 2, allows a metaphorical interpretation as popularized by Briane Green and others. The clock moves in a 1-dimensional space, while/(simultaneously) the photon moves in a 2-dimensional space. The clock is counting spatial increments of (2γd) which are labeled in the traditional manner as ‘time’.
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