全像原理 kah 3D 茶鈷

探索宇宙¹！逐工會揀一幅無仝款 ê 影像抑是相片，𤆬你熟似咱這个迷人 ê 宇宙，閣有專業天文學者²為你解說³。

• 原始文章：The Holographic Principle and a Teapot
• 影像來源：Caltech
• 台文翻譯：An-Li Tsai (NCU)

[漢羅] 全像原理 kah 3D 茶鈷

無毋著！你會當看著 2D ê 四角形色彩。 毋閣你敢會當看較深 leh？ 咱若是來算 這幅圖 內底有偌濟塊色斑，你可能會估計講， 這个 2D 數位影像內底應該差不多有 60 塊（橫 ê）x 50 塊（直 ê）x 256个（可能 ê 色），攏總是 768,000 个位元。 毋閣，kah 直覺無仝，用猶未證明 ê 全像原理 來看，2D 圖內底可能會當 kā 3D 空間 ê 訊息攏包 tī 內底。 這个原理 是 ùi Planck 長度 衍生來 ê。 來到 Planck 長度 ê 尺度，會 ùi 本底 古典引力 主導 ê 世界 行入去 量子力學 主導 ê 世界。 這个長度是 kan-na 會當儉 差不多 1 位元訊息 ê 面積 ê 一維長度。 這个極限是物理學家 Gerard 't Hooft tī 1993 年 頭一擺提出 ê。 伊 ùi 可能 差傷遠 ê 推測 歸納產生 ê 結果講， 烏洞 紮 ê 訊息毋是按伊包 tī 內底 ê 體積決定 ê，是按 事件視界 ê 表面積決定 ê。 這个詞「全像」是 ùi 「全像 投影類比」來 ê。 是 kā 光線投影 tī 平面創造出來 ê 3D 影像。 毋閣愛注意！ 有一寡人 看 這張圖 可能會想講內底毋若 kan-na 768,000 个位元，嘛毋是 2,563,000 位元 ê 排列。 In 可能會講 內底有 一个 3D ê 茶鈷。

[POJ] Choân-siōng-goân-lí kah Saⁿ-D Tê-kó͘

Bô m̄-tio̍h! Lí ē-tàng khòaⁿ-tio̍h jī-D ê sì-kak-hêng sek-chhái. M̄-koh lí kám ē-tàng khòaⁿ khah-chhim leh? Lán nā-sī lâi sǹg chit-pak-tô͘ lāi-té ū gōa-chōe-tè se̍k-pan, lí khó-lêng ē kó͘-kè kóng, chit-ê 2D só͘-ūi iáⁿ-siōng lāi-té eng-kai chha-put-to ū la̍k-cha̍p tè (hoâiⁿ--ê) sêng gō͘-cha̍p tè (ti̍t--ê) sêng nn̄g-pah-gō͘-cha̍p-la̍k ê (khó-lêng ê se̍k), lóng-chóng chhit-cha̍p-la̍k bān poeh-chheng ê ūi-goân. M̄-koh, kah ti̍t-kak bô-kâng, iōng iáu-bōe chèng-bêng ê Choân-siōng-goân-lí lâi khòaⁿ, jī-D tô͘ lāi-té khó-lêng ē-tàng kā saⁿ-D khong-kan ê sìn-sit lóng pau tī lāi-té. Chit-ê goân-lí sī ùi Planck tn̂g-tō͘ ián-seng--chhut-lâi-ê. Lâi-kàu Planck tn̂g-tō͘ ê chhioh-tō͘, ē ùi pún-té kó͘-tián-ín-le̍k chú-tō ê sè-kài kiâⁿ--ji̍p-khì liông-chú-le̍k-ha̍k chú-tō ê sè-kài. Chit-ê tn̂g-tō͘ sī kan-na ē-tàng khiām chha-put-to chi̍t ūi-goân sìn-sit ê bīn-chek ê it-ûi tn̂g-tō͘. Chit-ê ke̍k-hān sī bu̍t-lí-ha̍k-ka Gerard 't Hooft tī i̍t-kiú-kiú-sam nî thâu-chi̍t-pái the̍h-chhut ê. I ùi khó-lêng chha siūⁿ hn̄g ê thui-chhek kui-la̍p sán-seng ê kiat-kó kóng, o͘-tōng chah ê sìn-sit m̄-sī àn i pau tī lāi-té ê thé-chek koat-tēng ê, sī àn sū-kiāⁿ-sī-kài ê piáu-bīn-chek koat-tēng ê. Chit-ê-sù "Choân-siōng" sī ùi "Choân-siōng tâu-iáⁿ lūi-pí" lâi ê. Sī kā kng-sòaⁿ tâu-iáⁿ tī pêⁿ-bīn chhòng-chok chhut-lâi ê saⁿ-D iáⁿ-siōng. M̄-koh ài chù-ì! Ū chi̍t-kóa lâng khòaⁿ chit-tiuⁿ-tô͘ khó-lêng ē siūⁿ kóng lāi-té m̄-nā kan-na chhit-cha̍p-la̍k bān poeh-chheng ê ūi-goân, mā m̄-sī nn̄g-pah-gō͘-cha̍p-la̍k-bān saⁿ-chheng ūi-goân ê pâi-lia̍t. In khó-lêng ē kóng lāi-té ū chi̍t-ê saⁿ-D ê tê-kó͘.

[KIP] Tsuân-siōng-guân-lí kah Sann-D Tê-kóo

Bô m̄-tio̍h! Lí ē-tàng khuànn-tio̍h jī-D ê sì-kak-hîng sik-tshái. M̄-koh lí kám ē-tàng khuànn khah-tshim leh? Lán nā-sī lâi sǹg tsit-pak-tôo lāi-té ū guā-tsuē-tè si̍k-pan, lí khó-lîng ē kóo-kè kóng, tsit-ê 2D sóo-uī iánn-siōng lāi-té ing-kai tsha-put-to ū la̍k-tsa̍p tè (huâinn--ê) sîng gōo-tsa̍p tè (ti̍t--ê) sîng nn̄g-pah-gōo-tsa̍p-la̍k ê (khó-lîng ê si̍k), lóng-tsóng tshit-tsa̍p-la̍k bān pueh-tshing ê uī-guân. M̄-koh, kah ti̍t-kak bô-kâng, iōng iáu-buē tsìng-bîng ê Tsuân-siōng-guân-lí lâi khuànn, jī-D tôo lāi-té khó-lîng ē-tàng kā sann-D khong-kan ê sìn-sit lóng pau tī lāi-té. Tsit-ê guân-lí sī uì Planck tn̂g-tōo ián-sing--tshut-lâi-ê. Lâi-kàu Planck tn̂g-tōo ê tshioh-tōo, ē uì pún-té kóo-tián-ín-li̍k tsú-tō ê sè-kài kiânn--ji̍p-khì liông-tsú-li̍k-ha̍k tsú-tō ê sè-kài. Tsit-ê tn̂g-tōo sī kan-na ē-tàng khiām tsha-put-to tsi̍t uī-guân sìn-sit ê bīn-tsik ê it-uî tn̂g-tōo. Tsit-ê ki̍k-hān sī bu̍t-lí-ha̍k-ka Gerard 't Hooft tī i̍t-kiú-kiú-sam nî thâu-tsi̍t-pái the̍h-tshut ê. I uì khó-lîng tsha siūnn hn̄g ê thui-tshik kui-la̍p sán-sing ê kiat-kó kóng, oo-tōng tsah ê sìn-sit m̄-sī àn i pau tī lāi-té ê thé-tsik kuat-tīng ê, sī àn sū-kiānn-sī-kài ê piáu-bīn-tsik kuat-tīng ê. Tsit-ê-sù "Tsuân-siōng" sī uì "Tsuân-siōng tâu-iánn luī-pí" lâi ê. Sī kā kng-suànn tâu-iánn tī pênn-bīn tshòng-tsok tshut-lâi ê sann-D iánn-siōng. M̄-koh ài tsù-ì! Ū tsi̍t-kuá lâng khuànn tsit-tiunn-tôo khó-lîng ē siūnn kóng lāi-té m̄-nā kan-na tshit-tsa̍p-la̍k bān pueh-tshing ê uī-guân, mā m̄-sī nn̄g-pah-gōo-tsa̍p-la̍k-bān sann-tshing uī-guân ê pâi-lia̍t. In khó-lîng ē kóng lāi-té ū tsi̍t-ê sann-D ê tê-kóo.

[English] The Holographic Principle and a Teapot

Sure, you can see the 2D rectangle of colors, but can you see deeper? Counting color patches in the featured image, you might estimate that the most information that this 2D digital image can hold is about 60 (horizontal) x 50 (vertical) x 256 (possible colors) = 768,000 bits. However, the yet-unproven Holographic Principle states that, counter-intuitively, the information in a 2D panel can include all of the information in a 3D room that can be enclosed by the panel. The principle derives from the idea that the Planck length, the length scale where quantum mechanics begins to dominate classical gravity, is one side of an area that can hold only about one bit of information. The limit was first postulated by physicist Gerard 't Hooft in 1993. It can arise from generalizations from seemingly distant speculation that the information held by a black hole is determined not by its enclosed volume but by the surface area of its event horizon. The term "holographic" arises from a hologram analogy where three-dimension images are created by projecting light through a flat screen. Beware, some people staring at the featured image may not think it encodes just 768,000 bits -- nor even 256^3,000^ bit permutations -- rather they might claim it encodes a three-dimensional teapot.

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