Thanks to RogerRabbitt, Agar and Anno for their posts in the cultivation forum that made this document possible.

Compilation and additions by Nibin.

SHORT ANSWER

NO

LONG ANSWER

You can see that perlite is crystalline and impervious to water, but with a large surface area to hold and evaporate it off from.

Vermiculite is soft and resembles a mineral sponge, able to soak up water and hold it. Vermiculite also has lots of passageways the mycelium can colonize while absorbing the moisture within.

Hopefully, these pictures will put to rest the idea of substituting one for the other. They're not even remotely similar.

PERLITE

VERMICULITE

BOTH TOGETHER COMPARED

Anno and Agar determined the ability to absorb water of both Perlite and Vermiculite. Agar soaked each 1 cup of medium grade perlite and vermiculite in water for 5 minutes, then drained for 5 minutes. They weighed both of the materials before and after the process.

It turns out that perlite absorbs 1.14 times its weight in water, whereas vermiculite absorbs 3.54 times its weight in water.

This means that vermiculite absorbs ~3 times as much water per weight as perlite.
Taking volume as basis, vermiculite absorbs ~2.2 times as much water per volume as perlite.

CONCLUSION

We use vermiculite in a cake because it provides enough water for the mycelia to grow and a structure for it to grow into. As we have proven above, perlite neither has the same water retention abilities or the right kind of structure for the mycelium to grow on. Ergo, they are not interchangeable.

For more information and to read the original threads this info came from, visit:

https://www.shroomery.org/forums/showflat.php/Number/6610766#Post6610766

https://www.shroomery.org/forums/showflat.php/Number/5097253#Post5097253