The Vedas explain the 4th dimension

Our physical world is composed of three dimensions, width, depth, and height. Apart from the three coordinates, there is also time. The Vedas however describe an extra dimension, the 4th.

An important concept given in the Vedas is the idea of a subtle vertical dimension. More than just a change in geographical location, to visit higher planets or to gain access to the spiritual sky one has to also change his consciousness, which can be done only by practicing a spiritual process of self-realization.

The main teaching of the Māṇḍūkya Upaniṣad, for example, is a description of Turīya, the transcendental stage, beyond the stages of external consciousness, dream, and deep sleep. Another definition is Turīya as the fourth dimension, as mentioned in the Caitanya Caritāmṛta (Adi 2.53):

"In the material world the Lord is designated as virāṭ, hiraṇyagarbha and kāraṇa. But beyond these three designations, the Lord is ultimately in the fourth dimension."

Our physical world is composed of three dimensions, width, depth, and height. Apart from the three coordinates, there is also time. To meet a friend in his apartment, three pieces of information are necessary: the address of the building in the two-dimensional space, the number of the apartment inside the building, including the floor (the location in the three-dimensional space), and the time of the meeting. Without knowing the correct time, we will not be able to find our friend, even if we know the address. The same building could be a junkyard a few years ago and may become something else a few years later. In some models, like the Minkowski space framework, time is accepted as a 4th dimension, and coordinates are composed of X, Y, Z, and T, but the Vedas refer to time as just an additional feature of our tridimensional world, and not as a separate dimension.

Apart from that, the Vedas describe another dimension that goes from gross to subtle, in the sense of refined. The demigods in Svargaloka also have bodies composed of material elements, but the elements that compose their bodies and the different objects that compose their world are more refined than the elements that compose our bodies and our physical reality. Because their bodies are refined, or subtle, we can't perceive them, unless they assume forms that are visible to us. Similarly, inhabitants of the still higher planetary systems of Maharloka, Janaloka, Tapoloka, and Satyaloka have bodies still more refined than the bodies of the demigods. Beings living in higher dimensions can see everything happening in lower dimensions and freely interact with the inhabitants there, but inhabitants of lower dimensions can see these higher beings only when they make themselves visible to them. Understanding the existence of this fourth dimension is the great secret to understanding the cosmological model of the universe described in the Purāṇas.

However, this fourth dimension doesn't stop at the higher planets. It continues into the spiritual realm, beyond all association with matter.

See for example how the Māṇḍūkya Upanisad (text 7) describes the fourth dimension (translation mine):

"In the fourth state, the individual soul recovers his original state of consciousness. This consciousness is not connected with a material body in any way. It is not turned to the outside, nor the inside, it is not materially conscious or unconscious. It is also not a state of unconscious contact with the Lord. This original state of consciousness is beyond the perception of the senses, beyond the comprehension of the mind, beyond the speculations of intelligence, and the perception of material consciousness. This ultimate state consists of the spiritual awareness of the soul, beyond the material manifestation. In this state, which is beyond material duality and fully auspicious, the soul attains the association of the Supreme Lord. This Supreme Lord, called Turīya (the fourth), who is invisible, transcendental, inconceivable by reasoning, full of eternity, knowledge and bliss, who is the destroyer of bodily bounds and false knowledge, should be realized as the ultimate knowledge (vijñeyaḥ)."

At one extreme is the gross dimension where we live, where everything is made of gross material elements and we need to work very hard to live. On the other extreme is the Lord Himself, surrounded by His eternal abode and His eternal associates.

In his purport to the same CC Adi 2.53, Srila Prabhupada explains:

"The three puruṣas — Kāraṇodakaśāyī Viṣṇu, Garbhodakaśāyī Viṣṇu and Kṣīrodakaśāyī Viṣṇu — all have a relationship with the material energy, called māyā, because through māyā They create the material cosmos. These three puruṣas, who lie on the Kāraṇa, Garbha and Kṣīra oceans respectively, are the Supersoul of everything that be: Kāraṇodakaśāyī Viṣṇu is the Supersoul of the collective universes, Garbhodakaśāyī Viṣṇu is the Supersoul of the collective living beings, and Kṣīrodakaśāyī Viṣṇu is the Supersoul of all individual living entities. Because all of Them are somehow attracted to the affairs of the material energy, They can be said to have some affection for māyā. But the transcendental position of Śrī Kṛṣṇa Himself is not even slightly tinged by māyā. His transcendental state is called turīya, or the fourth-dimensional stage."

Similarly, in his purport to CC Adi 2.18, he mentions:

"The Supreme Personality of Godhead is by nature joyful. His enjoyments, or pastimes, are completely transcendental. He is in the fourth dimension of existence, for although the material world is measured by the limitations of length, breadth and height, the Supreme Lord is completely unlimited in His body, form and existence. He is not personally attached to any of the affairs within the material cosmos. The material world is created by the expansion of His puruṣa-avatāras, who direct the aggregate material energy and all the conditioned souls. By understanding the three expansions of the puruṣa, a living entity can transcend the position of knowing only the twenty-four elements of the material world."

The Lord is called Turīya because he is Vāsudeva, the fourth member of the quadruple expansion of Godhead called the Catur-vyūha, because he is beyond the three dimensions of this material world, as well as time and physical laws, and because he manifests turīya, the fourth state of consciousness.

People living on earth are mainly associated with gross sense gratification, working to secure physical objects they desire to enjoy. In the celestial planets, demigods and others enjoy subtle sense gratification, while great sages in the higher planets renounce sense gratification but keep affinity with the false ego. Brahma is so pure that he practically doesn't have a physical body, but still, he is involved with matter in his service of creating the universe. As Prabhupada explains, even the three Puruṣa avatāras, Kāraṇodakaśāyī Viṣṇu, Garbhodakaśāyī Viṣṇu, and Kṣīrodakaśāyī Viṣṇu, have some affection for the material energy, although untouched by Maya. Krsna however is situated in the highest transcendental stage, not tinged by māyā even slightly. This fully spiritual and uncontaminated state is shared by the pure devotees who eternally serve Him as His eternal associates. This is the ultimate perfection for all of us, who although parts and parcels of the Lord are eternally striving to increase our natural love to Him. Turīya is thus, ultimately, the state of pure love of Godhead, the diametric opposite of the selfish search for sense gratification we observe in our plane. This pure love of Godhead is directed to the transcendental Lord and cultivated in the transcendental abode by the transcendental soul. All three exist in Turīya.