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In turiya, is it possible to travel (teleport like narada) to different Lokas, such as Vishnu, deva loka? Like how devas went to Vaikunta, begged Vishnu to reincarnate to get rid of Ravana and other rakshasas on the Earth. Also are all Ashta siddhis achieved automatically when one reaches turiya?

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Presuming knowing self is to experience Turiya, one can indeed wander about in various worlds. From Chandogya Upanishad,

अथात आत्मादेश एवात्मैवाधस्तादात्मोपरिष्टादात्मा पश्चादात्मा पुरस्तादात्मा दक्षिणत आत्मोत्तरत आत्मैवेदं सर्वमिति स वा एष एवं पश्यन्नेवं मन्वान एवं विजानन्नात्मरतिरात्मक्रीड आत्ममिथुन आत्मानन्दः स स्वराड्भवति तस्य सर्वेषु लोकेषु कामचारो भवति अथ येऽन्यथातो विदुरन्यराजानस्ते क्षय्यलोका भवन्ति तेषां सर्वेषु लोकेष्वकामचारो भवति ॥ ७.२५.२ ॥ ॥ इति पञ्चविंशः खण्डः ॥

athāta ātmādeśa evātmaivādhastādātmopariṣṭādātmā paścādātmā purastādātmā dakṣiṇata ātmottarata ātmaivedaṃ sarvamiti sa vā eṣa evaṃ paśyannevaṃ manvāna evaṃ vijānannātmaratirātmakrīḍa ātmamithuna ātmānandaḥ sa svarāḍbhavati tasya sarveṣu lokeṣu kāmacāro bhavati atha ye'nyathāto viduranyarājānaste kṣayyalokā bhavanti teṣāṃ sarveṣu lokeṣvakāmacāro bhavati || 7.25.2 || || iti pañcaviṃśaḥ khaṇḍaḥ ||

Next is the instruction on the Self: The Self is below; the Self is above; the Self is behind; the Self is in front; the Self is to the right; the Self is to the left. The Self is all this. He who sees in this way, thinks in this way, and knows in this way, has love for the Self, sports with the Self, enjoys the company of the Self, and has joy in the Self, he is supreme and can go about as he likes in all the worlds. But those who think otherwise are under the control of others. They cannot remain in the worlds they live in, nor can they move about in the worlds as they like [i.e., they are under many limitations].

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In Turiya, one attains Jeevanmukta state and after Gyani's death it is called Videha mukti(without a body, also called Nirvana in Buddhism), also called Turiyateet(beyond Turiya). One who is in Turiya or Jeevanmukta state need not travel to lokas as Gyani becomes one with Omnipresent consciousness. But, Turiya and Turiyateet are same eventually, as one who is already liberated neither worries whether he is in a body or without a body as he is self-realized.

Avadhut Geeta

1.31 When the pot is broken, the space within it is absorbed in the infinite space and becomes undifferentiated. When the mind becomes pure, I do not perceive any difference between the self and the supreme Being.

1.32 There is no pot; there is no pot's interior space. Neither is there an individual soul nor the form of an individual soul. Know the absolute Brahman, devoid of knowable and knower.

1.36 Some seek nonduality, others duality. They do not know the Truth, which is the same at all times and everywhere, which is devoid of both duality and nonduality.

Desires are all born from the tricky mind and the main cause of ignorance and miseries. Siddhis are the last temptation of a yogi in the path of spiritual realization as they mislead a person in thinking that a body can be made all powerful and immortal and worshipped like God just like Ravana and Hiranyakashyap tried but failed. Even if you get all the 8 main Siddhis, but still the giver of those Siddhis that is infinite formless Brahman consciousness will be more powerful than you and wont tolerate anyone trying to misuse those powers for personal gains.

The_Complete_Works_of_Swami_Vivekananda/Volume_6/Notes_Of_Class_Talks_And_Lectures/Lessons_On_Raja-Yoga

This is why the human being is greater than others, because all planes, all experiences, are possible to the spirit in the human body. We do not need another; for man can, if he likes, finish in his body his probation and can after that become pure spirit.

The great danger of psychic powers is that man stumbles, as it were, into them, and knows not how to use them rightly. He is without training and without knowledge of what has happened to him. The danger is that in using these psychic powers, the sexual feelings are abnormally roused as these powers are in fact manufactured out of the sexual centre. The best and safest way is to avoid psychic manifestations, for they play the most horrible pranks on their ignorant and untrained owners.

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