Is it possible to remotely engage in a side project with a postdoc in order to gain experience? I'm a PhD student in theoretical Physics. Recently I was watching a lecture and the professor told a story that as a PhD student he used to engage in side projects with postdocs in order to get more experience, learn something and try to publish as well, all of which worked very nicely for him. This would work for both sides because he would help and at the same time learn and gain experience.
Now, there is one particular topic I'm very interested for a long time. This topic is being activelly investigated by some of the most renowed researchers around the world and they say that there is a lot to be done, what makes me consider it very worthwhile to be able to work in this field. To be honest, that is the topic I want to work with after I finish my PhD! I have studied some of the main papers on the subject but still didn't have any idea of something to do that could end up in a publication. My guess is that this happens because I lack experience.
In that case the story my professor told inspired me in doing the same. The issue is that in my department (and as far as I know in my country, unfortunatelly) I can't find people working on the subject. In particular there is no postdoc working on it in my department.
That said, I know about one postdoc from another country which actively works on the field and already published very relevant papers on the subject. I've watched some of his recorded seminars on YouTube and he seems quite engaged in really getting people to understand the subject.
In that case would it be possible to do what my professor did remotely? Could I send a message to this guy and ask if I could participate and help with something in his work in order for me to get started in the field? Or would this be frowned upon and considered unacceptable? If the answer is yes, how should I approach this?
You end your post with multiple questions. It is usually better to try to write one focussed post per question on these sites. However, I will focus on two questions that I feel are key here:

Would it be possible to do this project remotely?
How should you contact the postdoc?



Would it be possible to do this project remotely?


You can always ask to do a side project, research is about collaboration. Remote collaboration should be fine, given that that is how a lot of companies and universities are functioning now due to the pandemic. Zoom/Teams/Slack or something similar should work fine, use whatever the postdoc is using. Do go to your advisor first and see if they agree that this fits in your PhD or if you should do this on your own time.


How should you contact the postdoc?


An unprompted message might go unnoticed. Ask your professor if they by any chance know the postdoc you want to collaborate with. If they do, ask if they can introduce you and already vouch for your work. If they don't, look for another possible connection to do this. This will give you the highest probability of success. If you end up not being able to find somebody to help you, send them a message directly. Keep your message brief, direct and describe your background and how you'd like to help (depending on the topic you could help with for example data cleaning, analysis or visualization, literature reviews, etc.) and ask them if they have something for you, now or in the future.