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robphy
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Assuming absolute time (so that the heights of the diamonds are equal),
Alice (red) receives Bob's signal at 3.2, whereas Bob (blue) receives itAlice's at 5.
Bob's ticks need to be scaled up from this size. This hints that there is time-dilation... but by how much?
robphy-RRGP-absoluteTime

Assuming absolute space (so the lengths of the cross-sections of the light-clocks are equal),
Alice (red) receives Bob's signal at 5, whereas Bob (blue) receives itAlice's at 3.2.
Bob's ticks need to be scaled down from this size. This hints that there is length-contraction... but by how much?
robphy-RRGP-absoluteSpace

Assuming absolute time (so that the heights of the diamonds are equal),
Alice (red) receives Bob's signal at 3.2, whereas Bob (blue) receives it at 5.
Bob's ticks need to be scaled up from this size. This hints that there is time-dilation... but by how much?
robphy-RRGP-absoluteTime

Assuming absolute space (so the lengths of the light-clocks are equal),
Alice (red) receives Bob's signal at 5, whereas Bob (blue) receives it at 3.
Bob's ticks need to be scaled down from this size. This hints that there is length-contraction... but by how much?
robphy-RRGP-absoluteSpace

Assuming absolute time (so that the heights of the diamonds are equal),
Alice (red) receives Bob's signal at 3.2, whereas Bob (blue) receives Alice's at 5.
Bob's ticks need to be scaled up from this size. This hints that there is time-dilation... but by how much?
robphy-RRGP-absoluteTime

Assuming absolute space (so the lengths of the cross-sections of the light-clocks are equal),
Alice (red) receives Bob's signal at 5, whereas Bob (blue) receives Alice's at 3.2.
Bob's ticks need to be scaled down from this size. This hints that there is length-contraction... but by how much?
robphy-RRGP-absoluteSpace

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robphy
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Once the light-clock diamond size is established (using the Bondi k-calculus in the above), the spacelike-diagonal of the light-clock diamond determines the reflection events on the mirror worldlines of the longitudinal light-clock. So, draw through those events parallels to the timelike diagonal (the observer's worldline). This shows length-contraction as viewed in the lab frame. (The construction can be shown to be symmetric between the observers.)

Once the light-clock diamond size is established (using the Bondi k-calculus in the above), the spacelike-diagonal of the light-clock diamond determines the reflection events on the longitudinal light-clock. So, draw through those events parallels to the timelike diagonal. This shows length-contraction as viewed in the lab frame. (The construction can be shown to be symmetric between the observers.)

Once the light-clock diamond size is established (using the Bondi k-calculus in the above), the spacelike-diagonal of the light-clock diamond determines the reflection events on the mirror worldlines of the longitudinal light-clock. So, draw through those events parallels to the timelike diagonal (the observer's worldline). This shows length-contraction as viewed in the lab frame. (The construction can be shown to be symmetric between the observers.)

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robphy
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  • The Bondi k-calculus (an algebra-based method) develops the basic ideas of special-relativity in the $tx$-plane (without using the transverse direction). This approach is presented in his book “Relativity and Common Sense” (1962, 1964). In addition, Bondi presented “E=mc2: Thinking Relativity Through”, a series of ten lectures on BBC TV running from Oct 5 to Dec 7, 1963. (Read more at my contributed article to a blog at https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/ )

Using $v=(3/5)c$... and assuming the Speed of Light Principle.. we have the shape of Bob's diamonds... but what is the correct size?

Assuming absolute time (so that the elapsed timesheights of the diamonds are equal),
Alice (red) receives Bob's signal at 3.2, whereas Bob (blue) receives it at 5.
Bob's ticks need to be scaled up from this size. This hints that there is time-dilation... but by how much?
robphy-RRGP-absoluteTime

Assuming absolute space (so the lengthlengths of the light-clock is the sameclocks are equal),
Alice (red) receives Bob's signal at 5, whereas Bob (blue) receives it at 3.
Bob's ticks need to be scaled down from this size. This hints that there is length-contraction... but by how much?
robphy-RRGP-absoluteSpace

  • The Bondi k-calculus (an algebra-based method) develops the basic ideas of special-relativity in $tx$-plane (without using the transverse direction). This approach is presented in his book “Relativity and Common Sense” (1962, 1964). In addition, Bondi presented “E=mc2: Thinking Relativity Through”, a series of ten lectures on BBC TV running from Oct 5 to Dec 7, 1963. (Read more at my contributed article to a blog at https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/ )

Using $v=(3/5)c$...

Assuming absolute time (so the elapsed times are equal),
Alice (red) receives Bob's signal at 3.2, whereas Bob (blue) receives it at 5.
Bob's ticks need to be scaled up from this size. This hints that there is time-dilation... but by how much?
robphy-RRGP-absoluteTime

Assuming absolute space (so the length of the light-clock is the same),
Alice (red) receives Bob's signal at 5, whereas Bob (blue) receives it at 3.
Bob's ticks need to be scaled down from this size. This hints that there is length-contraction... but by how much?
robphy-RRGP-absoluteSpace

  • The Bondi k-calculus (an algebra-based method) develops the basic ideas of special-relativity in the $tx$-plane (without using the transverse direction). This approach is presented in his book “Relativity and Common Sense” (1962, 1964). In addition, Bondi presented “E=mc2: Thinking Relativity Through”, a series of ten lectures on BBC TV running from Oct 5 to Dec 7, 1963. (Read more at my contributed article to a blog at https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/ )

Using $v=(3/5)c$... and assuming the Speed of Light Principle.. we have the shape of Bob's diamonds... but what is the correct size?

Assuming absolute time (so that the heights of the diamonds are equal),
Alice (red) receives Bob's signal at 3.2, whereas Bob (blue) receives it at 5.
Bob's ticks need to be scaled up from this size. This hints that there is time-dilation... but by how much?
robphy-RRGP-absoluteTime

Assuming absolute space (so the lengths of the light-clocks are equal),
Alice (red) receives Bob's signal at 5, whereas Bob (blue) receives it at 3.
Bob's ticks need to be scaled down from this size. This hints that there is length-contraction... but by how much?
robphy-RRGP-absoluteSpace

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