I think here Einstein here wants us especially to think of a shell-less mollusc, of which the sea slugs and nudibranchs from the Gastropoda as well as the octopus from the Cephalopoda are the only examples i can think of[1].

He’s being a bit fancy and “polymathematic” in using this word but basically he means something that is “sqidgy” and sqishy, like a ball of Play-Doh. And his main point is that in relativity (special as well as general) there is no such thing as a rigid body that undergoes rigid Euclidean transformations in its motion in response to any force. Simplest example: we try to imagine a “rigid” bar reaching from here to Mars, at least twenty light minutes away. We hit it with a hammer, its end is shoved a few millimeters axially. It’s meant to be rigid and thus undergo a Euclidean translation. But that would mean our stroke would be immediately detectable at the other end on Mars, twenty light minutes away! Our shove is transmitted faster than $c$, which violates the assumption in relativity that there can be no faster that light signaling (we make this postulate to protect causality and avoid such weirdness as the Tachyonic Antitelephone Scenario). So we conclude that the bar can’t be rigid and indeed must have an acoustic wave speed less than $c$.

His statement is also illustrated by the famous Ehrenfest “Paradox”. See my description here. Euclidean Rigidity in relativity can be partially salvaged as a concept known as Born Rigidity, but this is a “squidgy” Rigidity designed to avoid faster than light signaling that is not very intuitive in terms of everyday experiences of “stiffness” and “hardness”.

[1] I’m not a marine biologist but i am a diver of 35 years‘ experience with a particular love of cephalopods. My fave is Sepia Apama of my homeland halfway across the world, which does have a stiff shell (cuttlebone) within, and which I think is just sublimely beautiful, especially with its gorgeous „peplum fin“ that girds its whole lower body and whose wave motion gives this gorgeous creature an astonishingly deft control of its attitude and bearing in its 3D world.

I think here Einstein here wants us especially to think of a shell-less mollusc, of which the sea slugs and nudibranchs from the Gastropoda as well as the octopus from the Cephalopoda are the only examples I can think of[1].

He’s being a bit fancy and “polymathematic” in using this word but basically he means something that is “sqidgy” and sqishy, like a ball of Play-Doh. And his main point is that in relativity (special as well as general) there is no such thing as a rigid body that undergoes rigid Euclidean transformations in its motion in response to any force. Simplest example: we try to imagine a “rigid” bar reaching from here to Mars, at least twenty light minutes away. We hit it with a hammer, its end is shoved a few millimeters axially. It’s meant to be rigid and thus undergo a Euclidean translation. But that would mean our stroke would be immediately detectable at the other end on Mars, twenty light minutes away! Our shove is transmitted faster than $c$, which violates the assumption in relativity that there can be no faster that light signaling (we make this postulate to protect causality and avoid such weirdness as the Tachyonic Antitelephone Scenario). So we conclude that the bar can’t be rigid and indeed must have an acoustic wave speed less than $c$.

His statement is also illustrated by the famous Ehrenfest “Paradox”. See my description here. Euclidean Rigidity in relativity can be partially salvaged as a concept known as Born Rigidity, but this is a “squidgy” Rigidity designed to avoid faster than light signaling that is not very intuitive in terms of everyday experiences of “stiffness” and “hardness”.

[1] I’m not a marine biologist but I am a diver of 35 years‘ experience with a particular love of cephalopods. My fave is Sepia Apama of my homeland halfway across the world, which does have a stiff shell (cuttlebone) within, and which I think is just sublimely beautiful, especially with its gorgeous „peplum fin“ that girds its whole lower body and whose wave motion gives this gorgeous creature an astonishingly deft control of its attitude and bearing in its 3D world.