Do the enchanted locations in the Harry Potter books occupy another dimension?

Question

I've finally watched more than the first 2 films, and am curious as to any explanation about the magical areas shown. In the Sorcerer's Stone, Harry goes to Diagon Alley. He sees a wall that is tapped in different points and opens up to reveal another city. The train station was similar; run at a wall, end up on the other side. The tents in Goblet Of Fire, once you went inside they were the size of a large apartment.

I'm curious if these places would be considered different dimensions? Meaning, the insides of the tents would be temporary dimensions. The walls for King's Cross and Diagon Alley lead to the same dimension in which Hogwarts and all those mythical creatures are found. But you can also fly there - do you cross an inter-dimensional barrier at some point?

Are the magical places like Hogwarts in a separate dimension or are they in the same world, just hidden from the naked eye?

Answer 1

No

Most of these locations are described as invisible to Muggles. With the exception of Platform 9 3/4 this seems reasonable as it is a magical world

Tent

These spells not only increase the interior dimensions of objects, while leaving the outer ones unchanged, they also render the contents lighter.
_{Extension charms - Pottermore}

This seems to suggest that it somehow magically warps the space around the object so that the people outside are unaware of the space within. However they are still in the same universe and dimension

Grimmauld Place

MAGICAL PROPERTIES
Invisible to Muggles
_{Number Twelve Grimmauld Place - Pottermore}

Number Twelves appearance seems to be there, although hidden from muggle view.

Harry thought, and no sooner had he reached the part about number twelve, Grimmauld Place, than a battered door emerged out of nowhere between numbers eleven and thirteen, followed swiftly by dirty walls and grimy windows. It was as though an extra house had inflated, pushing those on either side out of its way. Harry gaped at it. The stereo in number eleven thudded on. Apparently the Muggles inside hadn’t felt anything.
_{Harry Potter and the Order of the Phoenix, Chapter Four - Number Twelve, Grimmauld Place}

The above seems to describe that Number Twelve imply sits between Eleven and Thirteen, and can be accessed when required.

The Muggles who lived in Grimmauld Place had long since accepted the amusing mistake in the numbering that had caused number eleven to sit beside number thirteen.
_{Harry Potter and the Deathly Hallows, Chapter Twelve - Magic is Might}

Muggles don't question the numbering of the street as they have accepted it.

Furthermore the house is described as "Unplottable":

We do not know whether the enchantments we ourselves have placed upon it, for example, making it Unplottable, will hold now that ownership has passed from Sirius’s hands.
_{Harry Potter and the Half-Blood Prince, Chapter Three - Will and Won't}

“My father put every security measure known to Wizard-kind on it when he lived here. It’s Unplottable, so Muggles could never come and call — as if they’d have wanted to — and now Dumbledore’s added his protection, you’d be hard put to find a safer house anywhere.
_{Harry Potter and the Order of the Phoenix, Chapter Six - The Noble and Most Ancient House of Black}

The chapter goes on to describe the ability to see out of Number Twelve, even if it couldn't be seen from outside

Barely a day passed without one or two people arriving in Grimmauld Place with no other purpose, or so it seemed, than to lean against the railings facing numbers eleven and thirteen
[...]
Occasionally one of them started forward excitedly, as if they had seen something interesting at last, only to fall back looking disappointed.
_{Harry Potter and the Deathly Hallows, Chapter Twelve - Magic is Might}

Platform 9 3/4

Platform 9 3/4 is described as being part of Kings Cross Station. It's merely "well hidden" from muggle eyes. The description in the book (as below) seems to suggest that it was hidden in a similar way to how Grimmauld Place was hidden.

A scarlet steam engine was waiting next to a platform packed with people. A sign overhead said Hogwarts Express, eleven o’clock. Harry looked behind him and saw a wrought-iron archway where the barrier had been, with the words Platform Nine and Three-Quarters on it. He had done it.
_{Harry Potter and the Philosopher's Stone, Chapter Six - The Journey from Platform Nine and Three-Quarters}

J.K. Rowling decided to have multiple magic trains leave from in between Muggle platforms, and Platform 9 3/4 was chosen because of the ring in it's name.

In choosing the number of the concealed platform that would take young witches and wizards to boarding school, I decided that it would have to be a number between those of the Muggle platforms - therefore, it was clearly a fraction. This raised the interesting question of how many other fractional platforms lay between the whole-numbered platforms at King's Cross, and I concluded that were probably quite a few. Although these are never mentioned in the book, I like to think that it is possible to take a version of the Orient Express off to wizard-only villages in continental Europe (try platform seven and a half)
[...]
The number nine and three-quarters presented itself without much conscious thought, and I liked it so much that I took it at once. It is the 'three-quarters' that makes it, of course. _{Platform Nine and Three-Quarters: Pottermore}

Rowling suggests further that the platform was in the same "dimension" but simply concealed from Muggles.

The ticket officer controlled how you came through the gate, suggesting that it must be in the same location, otherwise he would not be able to see both platforms.

It took quite a while for them all to get off the platform. A wizened old guard was up by the ticket barrier, letting them go through the gate in twos and threes so they didn’t attract attention by all bursting out of a solid wall at once and alarming the Muggles.
_{(Harry Potter and the Philosopher's Stone - Chapter 17 - 'The Man with Two Faces')}

Hogwarts

"But Hogwarts is hidden,” said Hermione, in surprise. “Everyone knows that … well, everyone who’s read Hogwarts, A History, anyway.” “Just you, then,” said Ron. “So go on — how d’you hide a place like Hogwarts?” “It’s bewitched,” said Hermione. “If a Muggle looks at it, all they see is a moldering old ruin with a sign over the entrance saying DANGER, DO NOT ENTER, UNSAFE."
_{Harry Potter and the Goblet of Fire, Chapter Eleven - Aboard the Hogwarts Express}

Answer 2

These places are not in another dimension, they are simply hidden from the muggle world: that way there seems to be "nothing" when in reality a complete town is hidden from their eyes. When Harry and Ron follow the Hogwarts Express in the flying Anglia, they do not "cross" any dimensional border, they just start from "normal" London and follow the train. It is mentioned some times in that Szenes, that during their chase they try to hide their flying car in the clouds to not confuse muggels seeing them.

Another example of such a place is Grimaults Place 12, that is even hidden from other wizards that do not know about it: there simple seems to be no space between 11 and 13...

A totally different issue are the tents: There is no explicit explanation for the tents or e.g. Hermiones bag in the 7th part, just that they are "magically enlarged". How this magic is achieved is never mentioned. It is speculated that it indeed leads to another space in another dimension, but there is nothing in canon to support this thesis.