Mutual dreaming or shared dreaming is the claim that two or more people can share the same dream environment. I have experienced a numerous lucid dreams but I've never met a known person in such dreams.
So, is this phenomenon possible and if it is what would be the explanation?
Yes, it is theoretically possible, in one narrow, specific sense:
Some people talk in their REM sleep.
Some dream content is influenced by auditory stimuli.
Take two people sleeping within earshot of each other: if one starts talking in their sleep about their dream content, while the other is dreaming, then that may influence the other's dream. (If they were then to start talking about their dream content too, that could influence the first person's dream content.)
However, that is only a "shared dream" in a very narrow sense: information is passed from one person's dream to another's by the ordinary medium of speech.
TL;DR: This site shows no evidence for the paranormal, and indeed is careful not to explicitly claim it exists. What is described could be largely explained by known psychological theories and coincidence.
If we examine the World of Lucid Dreaming web-site which is the source of the claims, we find that its claims have no strength. It doesn't assert that paranormal dreaming exists, but merely one may find it.
First there is a definition, claiming that sharing a dream environment is paranormal:
Mutual dreaming (also known as shared or group dreaming) is the paranormal claim that two or more people can share the same dream environment. The concept was popularized in the 2010 movie, Inception, where lucid dreamers could link up via a device and roam around the subconscious of a single dreamer.
Note the vaguaries of "share the same dream environment". If both dreams were identical, I would concede this would be evidence for the paramormal. But if all this means is both dreams involve a house, it can be explained by more prosaic reasons. They elaborate further on this point themselves, later.
They then introduce the concept (the main subject of the site) of "lucid dreamer" who can deliberately modify the outcome of their dreams.
That's why we are poised to prove the existence of mutual dreaming - if such a phenomenon truly exists.
Note the qualifier here - they aren't asserting a claim.
Then they define "meshing dream":
They happen when you share certain dream elements with someone else. For instance, you and your partner may both watch LOST on TV and then dream about being stranded on a deserted island. Understandably, your shared waking experience leads to similar dreams. Even Freudian dream analysis offers an explanation for this kind of coincidence.
So meshing dreams aren't paranormal. Note that Freudian dream analysis is not required to explain this. A psychological phenomena known as the Tetris Effect (which has been popularised by researcher Dr Robert Stickgold) explains common elements of dreams held by people who have had common experiences.
Finally, they get to the paranormal claim:
The less likely experiences are called meeting dreams. This is the true meaning of mutual dreaming, where two or more people meet up and communicate in the dream world. As yet there is no firm evidence for the existence of such shared dreams, although it is arguably a difficult concept to prove.
Note that they themselves admit there is no firm evidence for this claim. As for a difficult concept to prove, it strikes me that the experiment would be as simple as having one person fall asleep, while observed in a lab, after being given a large random number or a random image, and have another person in another lab wake up and report what the message was.
They delve into paranormal theories explanations for as yet non-existent phenomena. Without evidence, they have no merit. You don't need a scientific model to explain away non-existent unexpected data.
Next they describe two experiments.
The first, if it was to succeed, could be explained by the Tetris Effect and coincidence.
The second, if it succeeded, and the dream-conversation conveyed truly novel information (as opposed to being primed by experience or by prior agreement), would be challenging new evidence for telepathy.
However, there are no reports here that the experiment has been successful.
In fact the site warns people to remain skeptical:
When you're exploring a paranormal phenomenon such as group dreaming, remember to record as much data as you can and be objective. This means trying to rationalize events as much as you can before jumping to conclusions - and not getting carried away by things that could easily be due to coincidence. It's all too easy to trick ourselves into false beliefs that skew our entire outlook.
In conclusion, there is no claim here to address - just a description of some wishful thinking. On the other hand, it could be seen as good news for all the people who have studied their respective parts of all of the physics, psychology and biology knowledge that we have assembled over the past few hundred years of painstaking experiments. They can breathe a sigh of relief. No need to throw it all out and start again over this particular web-site.
I acknowledge I don't provide a lot of references here: My key reference is the original web-site itself. The Tetris Effect is just background for people who are skeptical about the validity of Freudian dream analysis; I could find published papers, but it seems overkill. I am looking for claim I make that needs more evidentiary support, but I can't see any. Have I missed anything?