There is something that has been puzzling me about the way that light cones are drawn, when we consider causality diagrams.(adsbygoogle = window.adsbygoogle || []).push({});

Lines representing a substantial point (as Minkowski referred to them) that is travelling as close to the speed of light, that is virtually at the speed of light, is drawn at an angle of 45°, that is that it will have travelled one light second along the x axis in a time of one second, that is measured as 1 light second on the ct axis. All very simple and logical, and correct using Newtonian mechanics.

Yet it seems to me that in Special Relativity this cannot be supported as drawn this way the speed of that substantial point would be 1.414 light seconds per second. Which is of course the problem with Newtonian Mechanics.

Complying with the Postulates of Relativity, however, we have a very different diagram where we measure from the known speed of the particle. For we know how far the particle will have travelled in the time measured along the rotated time axis of the moving particle measured from the stationary Frame.

We see this in the following Figure using two light clocks with clock B moving at 0.6c relative to clock A; where the time in the moving clock, measured from the stationary clock, is measured along the rotated time axis of that moving clock.

In the first diagram we see Newtonian mechanics, where clock A is stationary and clock B is moving and its time axis is rotated through angle α (where tan α = v/c). it is easy to see here that when clock B has travelled at 0.6c for 1 second, as measured from A, the speed has to be 1.16 c.

Whereas, in the second diagram obeying the postulates of relativity, we see that clock A, seen as moving from the stationary clock B, has travelled 0.6 light seconds in the time that the light has travelled 1 light second - in one second at the speed of c.

This also is in accordance with the time from the clocks passing event being an expanding circle (as light would travel in every direction from a flash of light at that event, the movement of light being the best clock there is).

In this case the time axis for the moving clock A is rotated through angle β (where sin β = v/c) and the time measured in Frame B is 0.8 seconds.

It is also worth noting that when 1 second has passed in frame B, the time in the moving clock A, measured from Clock B is 1.25 seconds, and a body moving at 0.6c would have a Lorentz factor of 1.25 and its time dilation after 1 second would be 1.25 seconds.

It seems to me, therefore that applying the special relativity postulates to the drawing of the light cone would, rather than a cone result in a hemisphere and that the cone of causality would include all within that hemisphere as for a body moving at hear the speed of light the time dilation would be approaching ∞.

https://ac0077b2-a-62cb3a1a-s-sites.googlegroups.com/site/specialrelativitysimplified/home-1/minkowski-diagrams/Mechanics%20compared.png?attachauth=ANoY7crGxhWFd0ch06oJfptUpnkbzusP2f5ViLUigLEnjsR7_HCrWyZPBAkoi07gtycp2uDeWilO-KLM7phtStO5N_nZlwR2PjvkzMxgFgzZjyW4rs7u-3d7SVo17lm8gQpiGxSzDCruxMj4LLGHeKxQCwk_v1deozl9zuPDQWB5-lkMcw4pcroQT_1t8HIaaJwsOquR0N8mzwnojA622xtpHaKtyhvUFzy6ec7Bf5kW2dKwMikuokNo13wAbWblANn88dAaErIrfyyqvsOJqqVOqK-mt-Sc6A%3D%3D&attredirects=0 [Broken]

Can someone explain why this is not the case?

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# B Light cones

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