The Krsna who comes to the material world is not the original Kṛṣṇa from the spiritual world Prabhupada has explained to us.

The Kṛṣṇa who comes to the material world is a manifestation of the 4 armed Visnu form who plays the role of child Kṛṣṇa in the material world as painting below reveals.

As said above, this is because Krsna as His original form never leaves Goloka-Vṛndāvana in the spiritual world.

All forms of Krsna outside Goloka-Vrindavana are coming from Krsna's Visnu-tattva forms Prabhupada explains.

Srila Prabhupada - "The original Lord Kṛṣṇa never leaves Goloka Vṛndāvana. All the plenary expansions are one and the same Viṣṇu-tattva, and there is no difference in Their potency. (SB, Canto 3 Ch 1 Text 34 Purport)

As said above, when Krsna comes to this material world for His childhood pastimes, it is His 4 armed Visnu-tattva expansion who play's the role of two armed Krsna as the paintings below reveals.

Srila Prabhupada - "Because Kṛṣṇa never leaves Vṛndāvana, all the Forms of Kṛṣṇa that appear elsewhere are His expansions. Vāsudeva is Kṛṣṇa's immediate expansion, so Vāsudeva is not different from Kṛṣṇa. It is to be understood that the Vāsudeva referred to in this verse of Bhagavad-gītā is Baladeva, or Balarāma, because He is the original source of all incarnations and thus He is the sole source of Vāsudeva. The immediate expansions of the Lord are called svāṁśa (personal Visnu/Narayana expansions), and there are also expansions called vibhinnāṁśa - separated jiva-tattva (jiva-soul) expansions." (BG, Ch 7 Text 2 Purport)

Srila Prabhupada - "Because Mathurā and Vṛndāvana are intimately connected with Kṛṣṇa eternally, it is said that Lord Kṛṣṇa never leaves Vṛndāvana (vṛndāvanaṁ parityajya padam ekaṁ na gacchati)." (SB, Canto 3 Ch 1 Text 34 Purport)

Srimad Bhagavatam - "Since that time, the city of Mathurā had been the capital of all the kings of the Yadu dynasty. The city and district of Mathurā are very intimately connected with Kṛṣṇa, for Lord Kṛṣṇa lives there eternally." (SB, Canto 10 Ch 1 Text 28)

Srila Prabhupada - "There are many expansions, Lord Śrī Kṛṣṇa is the origin, as confirmed in the Brahma-saṁhitā. He is like the original candle, from which many thousands and millions of candles are lit. Although any number of candles can be lit, the original candle still retains its identity as the origin. In this way Kṛṣṇa expands Himself into so many forms, and all these expansions are called viṣṇu-tattva. Viṣṇu is a large light, and we are small lights, but all are expansions of Kṛṣṇa." (CC Introduction)

Srila Prabhupada - "The great authority Śukadeva Gosvāmī remarks that Kṛṣṇa almost always passed His time with Rukmiṇī, and Rukmiṇī was a bit proud to be so fortunate that Kṛṣṇa never left her even for a moment." (Krsna Book 60)

When Krsna enters the material creation for His Vrindavana pastimes, He does so as His Visnu expansion who plays the role of Krsna by acting the part of Krsna appearing like His original Form.

As said above, Krsna, as His original bodily Form never leaves Goloka-Vrindavana in the spiritual world, this means He never enters the decaying temporary material creation or even the perpetual Vaikuntha planets either as His original two-armed Form because child Krsna never leaves Goloka-Vrindavana in the spiritual world as explained above.

Srila Prabhupada - "Kṛṣṇa is the original Supreme Personality of Godhead, and Baladeva is Kṛṣṇa's immediate expansion. Both Lord Kṛṣṇa and Baladeva appeared as sons of Vasudeva, so both of Them may be called Vāsudeva. 

From another point of view, because Kṛṣṇa never leaves Vṛndāvana, all the forms of Kṛṣṇa that appear elsewhere are His expansions. 

Vāsudeva is Kṛṣṇa's immediate expansion, so Vāsudeva is not different from Kṛṣṇa. 

It is to be understood that the Vāsudeva referred to in this verse of Bhagavad-gītā is Baladeva, or Balarāma, because He is the original source of all incarnations and thus He is the sole source of Vāsudeva. 

The immediate expansions of the Lord are called svāṁśa (personal expansions), and there are also expansions called vibhinnāṁśa (separated expansions).

Amongst the sons of Pāṇḍu, Arjuna is famous as Dhanañjaya. He is the best of men and therefore represents Kṛṣṇa. 

Among the munis, or learned men conversant in Vedic knowledge, Vyāsa is the greatest because he explained Vedic knowledge in many different ways for the understanding of the common mass of people in this Age of Kali. 

And Vyāsa is also known as an incarnation of Kṛṣṇa; therefore Vyāsa also represents Kṛṣṇa. 

Kavis are those who are capable of thinking thoroughly on any subject matter. Among the kavis, Uśanā, Śukrācārya, was the spiritual master of the demons; he was an extremely intelligent and far-seeing politician. 

Thus Śukrācārya is another representative of the opulence of Kṛṣṇa." (BG, Ch 10 text 37, Purport)

Srila Prabhupada - "Ādi-caturbhuja, the original expansions from Baladeva, are 

Vāsudeva, 

Saṅkarṣaṇa, 

Pradyumna,

Aniruddha. 

All of Them are viṣṇu-tattvas, or nondifferent Personalities of Godhead. 

In the incarnation of Śrī Rāma, all these different expansions appeared for particular pastimes. Lord Rāma is the original Vāsudeva, and His brothers were 

Saṅkarṣaṇa, 

Pradyumna,

Aniruddha. 

Aniruddha is also the cause of Mahā-Viṣṇu, from whose breathing the Ṛg Veda appeared. All this is nicely explained in the Mārkaṇḍeya Purāṇa. 

In the incarnation of Lord Kṛṣṇa, Aniruddha appeared as the son of the Lord. 

Lord Kṛṣṇa in Dvārakā is the Vāsudeva expansion of the original group. 

The original Lord Kṛṣṇa never leaves Goloka Vṛndāvana. All the plenary expansions are one and the same viṣṇu-tattva, and there is no difference in Their potency." (SB, Canto 3 Ch 1 text 34, Purport)

Srila Prabhupada - "It is understood that Mathurā City is the transcendental abode of Lord Kṛṣṇa; it is not an ordinary material city, for it is eternally connected with the Supreme Personality of Godhead. 

Vṛndāvana is within the jurisdiction of Mathurā, and it still continues to exist. 

Because Mathurā and Vṛndāvana are intimately connected with Kṛṣṇa eternally, it is said that Lord Kṛṣṇa never leaves Vṛndāvana (vṛndāvanaṁ parityajya padam ekaṁ na gacchati). 

At present, the place known as Vṛndāvana, in the district of Mathurā, continues its position as a transcendental place, and certainly anyone who goes there becomes transcendentally purified. 

Navadvīpa-dhāma (West Bengal) is also intimately connected with Vrajabhūmi." (SB, Canto 10 Ch 1 text 28, Purport)

Srila Prabhupada - Lord Krsna said, "As I have already explained, I am not very much interested in family life or love between husband and wife. By nature, I am not very fond of family life, wife, children, home and opulences. As My devotees are always neglectful of all these worldly possessions, I am also like that. Actually, I am interested in self-realization; that gives Me pleasure, and not this family life." 

After submitting His statement, Lord Kṛṣṇa suddenly stopped. The great authority Śukadeva Gosvāmī remarks that Kṛṣṇa almost always passed His time with Rukmiṇī, and Rukmiṇī was a bit proud to be so fortunate that Kṛṣṇa never left her even for a moment. 

Kṛṣṇa, however, does not like any of His devotees to be proud. As soon as a devotee becomes so, by some tactic He cuts down that pride. 

In this case also, Kṛṣṇa said many things which were hard for Rukmiṇī to hear. She could only conclude that although she was proud of her position, Kṛṣṇa could be separated from her at any moment. 

Rukmiṇī was conscious that her husband was not an ordinary human being. He was the Supreme Personality of Godhead, the master of the three worlds. 

By the way He was speaking, she was afraid of being separated from the Lord, for she had never heard such harsh words from Kṛṣṇa before. Thus she became perplexed with fear of separation, and her heart began to palpitate. 

Without replying to a word of Kṛṣṇa's statement, she simply cried in great anxiety, as if drowning in an ocean of grief. She silently scratched the floor with her toenails, which reflected reddish light on the floor. 

The tears from her eyes mixed with the black cosmetic ointment from her eyelids and dropped down, washing the kuṅkuma and saffron from her breasts. Choked up on account of great anxiety, unable to speak even a word, she kept her head downward and remained standing just like a stick. 

Due to extremely painful fear and lamentation, she lost all her powers of reason and became weak, her body losing so much weight that the bangles on her wrists became slack. 

The cāmara with which she was serving Kṛṣṇa immediately fell from her hand. Her brain and memory became puzzled, and she lost consciousness. The nicely combed hair on her head scattered here and there, and she fell down straight, like a banana tree cut down by a whirlwind." (Krsna Book 60)

Srila Prabhupada - "Śrī Īśopaniṣad points out that one who worships the demigods and attains to their material planets still remains in the darkest region of the universe. 

The whole universe is covered by the gigantic material elements; it is just like a coconut covered by a shell and half-filled with water. 

Since its covering is airtight, the darkness within is dense, and therefore the sun and the moon are required for illumination. Outside the universe is the vast and unlimited brahmajyoti expansion, which is filled with Vaikuṇṭhalokas. The biggest and highest planet in the brahmajyoti is Kṛṣṇaloka, or Goloka Vṛndāvana, where the Supreme Personality of Godhead, Śrī Kṛṣṇa Himself, resides. 

Lord Śrī Kṛṣṇa never leaves Kṛṣṇaloka. Although He dwells there with His eternal associates, He is omnipresent throughout the complete material and spiritual cosmic manifestations. 

This fact has already been explained in Mantra Four. The Lord is present everywhere, just like the sun, yet He is situated in one place, just as the sun is situated in its own undeviating orbit.

The problems of life cannot be solved simply by going to the moon planet or to some other planet above or below it. Therefore Śrī Īśopaniṣad advises us not to bother with any destination within this dark material universe, but to try to get out of it and reach the effulgent kingdom of God. 

There are many pseudo worshipers who become religionists only for the sake of name and fame. Such pseudo religionists do not wish to get out of this material universe and reach the spiritual sky. They only want to maintain the status quo in the material world under the garb of worshiping the Lord. 

The atheists and impersonalists lead such foolish pseudo religionists into the darkest regions by preaching the cult of atheism. The atheist directly denies the existence of the Supreme Personality of Godhead, and the impersonalists support the atheists by stressing the impersonal aspect of the Supreme Lord." (Sri Isopanisad 12, Purport)

Srila Prabhupada - "Thus the Lord is always engaged in transcendental loving activities with His spiritual associates in the various relationships of śānta (neutrality), dāsya (servitorship), sakhya (friendship), vātsalya (parental affection) and mādhurya (conjugal love).

Since it is said that Lord Kṛṣṇa never leaves Vṛndāvana-dhāma, one may ask how He manages the affairs of the creation?

This is answered in the Bhagavad-gītā (Ch 13 text 14-18): 

The Lord pervades the entire material creation by His plenary part known as the Paramātmā, or Supersoul. Although the Lord personally has nothing to do with material creation, maintenance and destruction, He causes all these things to be done by His plenary expansion, the Paramātmā. Every living entity is known as ātmā, soul, and the principal ātmā who controls them all is Paramātmā, the Supersoul.

This system of God realization is a great science. The materialistic sāṅkhya-yogīs can only analyze and meditate on the twenty-four factors of the material creation, for they have very little information of the puruṣa, the Lord. 

And the impersonal transcendentalists are simply bewildered by the glaring effulgence of the brahmajyoti. 

If one wants to see the Absolute Truth in full, one has to penetrate beyond the twenty-four material elements and the glaring effulgence as well. Śrī Īśopaniṣad points toward this direction, praying for the removal of the hiraṇmaya-pātra, the dazzling covering of the Lord. 

Unless this covering is removed so one can perceive the real face of the Personality of Godhead, factual realization of the Absolute Truth can never be achieved." (Sri Isopanisad 15, Purport)

Srila Prabhupada - "There is no second book in the whole world which contains so full of knowledge. So jñāna. And vairāgya also. In spite of all the property of Kṛṣṇa, Kṛṣṇa doesn't care for this material world. He is busy in the spiritual world. 

Rādhā-mādhava kuñja-bihārī. He's busy in Vṛndāvana. He has many servants. Just as big man has got many secretaries, servants, they look after, similarly, in this material world His representatives—

Brahmā, Viṣṇu, Maheśvara—they are managing the affairs of this whole universe. But He's enjoying in Vṛndāvana. 

Jaya rādhā-mādhava kuñja-bihārī. 

He has no concern, He doesn't care what is happening here. But that does not mean He doesn't care and has no anxiety how things are being managed. 

When it is mismanaged, then sometimes Kṛṣṇa comes in His Vāsudeva form. Not the original Kṛṣṇa form. Original Kṛṣṇa never leaves Vṛndāvana. Padam ekaṁ na gacchati. He's always in His abode. 

cintāmaṇi-prakara-sadmasu kalpa-vṛkṣa-

lakṣāvṛteṣu surabhīr abhipālayantam

lakṣmī-sahasra-śata-sambhrama-sevyamānaṁ

govindam ādi-puruṣaṁ tam ahaṁ bhajāmi

(Bs. 5.29)

He is very much adhered to His cows. Surabhīr abhipālayantam. And He's surrounded by hundreds and thousands of goddesses of fortune, these gopīs. He is surrounded.

 Lakṣmī-sahasra-śata-sambhrama-sevyamānam (Bs. 5.29). We are, we are praying goddess of fortune to have some favor, but in the spiritual world, Kṛṣṇa is served by hundreds and thousands of goddess of fortune. This is Kṛṣṇa's position." (Lecture BG, Ch 2 text 1 Ahmedabad, Dec 7, 1972)

Srila Prabhupada - "So Nārāyaṇa's place is there, sa dhāmani. That is His own abode. This is also Nārāyaṇa's abode, this material world. Just like a king. 

King's kingdom is very widespread, but still, he has got a palace. That is sa dhāmani. Everywhere his property, government property, but still there is a government house, particular. 

Similarly, everything belongs to God, īśāvāsyam idaṁ sarvam (ISO 1), everything. Everything, God's property. Bhoktāraṁ yajña-tapasāṁ sarva-loka-maheśvaram (BG 5.29). 

He is the proprietor. But still He has got His own abode. That is Goloka Vṛndāvana. Goloka eva nivasaty akhilātma-bhūto (Bs. 5.37). That is God. He's always there. He hasn't got to go out for some business. No. He hasn't got to work for maintaining His establishment. No. He is complete, and He's staying there. 

Just like Kṛṣṇa... It is said in the śāstra: vṛndāvanaṁ parityaja na padam ekaṁ gacchati. Kṛṣṇa never leaves Vṛndāvana. He doesn't go anywhere. He's always existing there. But still, He's everywhere. That is His inconceivable potency. Goloka eva nivasaty akhilātma-bhūto. 

We are limited. I am sitting here; I'm not in my apartment. But Kṛṣṇa is not like that. Kṛṣṇa is in His abode, Goloka Vṛndāvana—He doesn't leave that place any moment—but you'll find Kṛṣṇa everywhere. Goloka eva nivasaty akhilātma-bhūto (Bs. 5.37). 

Don't think that "Kṛṣṇa is not here." Kṛṣṇa is here also. You see, personally, Kṛṣṇa is present here. 

Don't think that it is not Kṛṣṇa, it is some stone statue. No. He's Kṛṣṇa. But because you cannot see Kṛṣṇa, He's appearing just that you may see. Because you cannot see without stone and wood. Therefore it is called arca-vigraha, arca-avatāra. Arca-avatāra." (Lecture SB, Canto 6 Ch 1 text 41 Los Angeles, June 7, 1976)**.