We know that the scariest attack "meltdown", cannot be reproduced on AMD or ARM chips at all[1]. The second attack "Spectre" is also greatly mitigated due the neural network predicting pathways for the application. Thus it's unlikely/less-likely that you'll be able to access other locations in memory[2]. However, it's definitely possible.
Intel(R) Xeon(R) CPU E5-1650 v3 @ 3.50GHz (called "Intel Haswell Xeon CPU" in the rest of this document)
AMD FX(tm)-8320 Eight-Core Processor (called "AMD FX CPU" in the rest of this document)
AMD PRO A8-9600 R7, 10 COMPUTE CORES 4C+6G (called "AMD PRO CPU" in the rest of this document)
An ARM Cortex A57 core of a Google Nexus 5x phone [6] (called "ARM Cortex A57" in the rest of this document)
https://googleprojectzero.blogspot.com/2018/01/reading-privi...