So my DM and I are fighting over the use and physics of the astral arms. TCoE clearly states that they are spectral, and that they are force type damage. They are an extension of my chi, and I currently have them in the form that hover over my shoulders.

In our current scenario, a giant spider has me pinned in the snow by the shoulders. Another spider has an ally pinned ten feet away, within range of the arms. When I went to attack the spider 10 ft away, my DM asked "How are you maneuvering to attack it? Your shoulders are pinned. They are not free floating arms."

Is there a ruling anywhere on if the monk is physically restrained, the arms are stuck too? Because if you can restrain someone's manifestation of chi physical this way, what is the point of playing the subclass ?

Quote from Talerask>>

In our current scenario, a giant spider has me pinned in the snow by the shoulders. Another spider has an ally pinned ten feet away, within range of the arms. When I went to attack the spider 10 ft away, my DM asked "How are you maneuvering to attack it? Your shoulders are pinned. They are not free floating arms."

I'd turn the question around and ask why and how they've incapacitated your character. Being restrained does not prevent you from attacking; it only imposes disadvantage on your attack rolls. If the spider was withing 10 feet of you, should should've been able to attack it.

Is there a ruling anywhere on if the monk is physically restrained, the arms are stuck too?

Not that I know of. What you see in the feature is what you get. I'm not going to assume there's malicious intent behind their decision but your DM is playing dirty. If the arms hover near your shoulders, that strongly implies you can manipulate them independently of your real shoulders and arms, and creatures shouldn't be able to disable specific limbs mid-combat without very, VERY good reason.

I would agree, the Restrained condition doesn't prevent you from making attacks and it sounds like the DM here wasn't intending even that, just for you to be physically restrained (small r) which may have been better represented with a Grapple check if that was what he wanted. Astral Self specifies that you can choose how they manifest. I would argue that even had you chosen to have them surround your arms they wouldn't necessarily be restrained if your physical arms were, they are astral manifestations after all. 

Yep, I think it’s a bad call on the DM’s part, but it is their call to make and you need to abide by their ruling. I don’t believe anywhere in the rules (unless it’s an optional one in the DMG) that specific body parts can be targeted. So being “pinned by the shoulders” should really only be narrative flavor and not mechanics. So you should have been able to attack with the arms. And with your physical arms, knees, feet, etc on the one pinning you as well as the astral arms of you so choose. 

But again it’s all within the DM’s discretion. 

From what I know, your arms should be perfectly free to attack.