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I was reading the wiki page on special relativity postulates. And wiki says,

The two-postulate basis for special relativity is the one historically used by Einstein, and it remains the starting point today. As Einstein himself later acknowledged, the derivation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness.

I understand homogeneity is necessary to be able choose the origin anywhere and isotropy is necessary to be able to choose directions of axis of the coordinate system randomly.

What does memorylessness mean?

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what does memorylessness mean?

Essentially, it means that the length of a rod and the rate of a clock depend on their current state only.

The alternative would require that, e.g., two otherwise identical clocks at rest with respect to each other may run at different rates if their histories differed.

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  • $\begingroup$ So is it possible to come up with a mathematical model that respects the two postulates but where clock rates do depend on their past histories in this way? $\endgroup$ – Hypnosifl Jan 29 '15 at 5:11
  • $\begingroup$ @Hypnosifl :Check the other answer. $\endgroup$ – Paul Jan 29 '15 at 11:16
  • $\begingroup$ @Paul - The other answer says "If this may respect the other two postulates is another story", so it doesn't really answer my question. $\endgroup$ – Hypnosifl Jan 29 '15 at 13:56
  • $\begingroup$ @Hypnosifl, why not make that a separate question? $\endgroup$ – Alfred Centauri Jan 29 '15 at 15:28
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So is it possible to come up with a mathematical model that respects the two postulates but where clock rates do depend on their past histories in this way? – Hypnosifl

Of course you COULD make up a mathematical model where the clock rate depends not on the moment but on the history, then the Gammafactor would for example not depend on the velocity at a given time t, but on the integral of the velocity over the history of the particle from t1 to t2. If this may respect the other two postulates is another story.

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