Renormalising the Entanglement Island in the Information Paradox

Julian De Vuyst
Persbericht

The Black Hole War: zwarte gaten als (slechte) versnipperaars

Foto van het M87 supermassieve zwart gat. Copyright: EHT Collaboration

Black Holes are where God divided by zero - A. Einstein

Velen van ons schrijven een dagboek: een plaats waarin je al jouw gedachten en geheimen kwijt kan, niet bestemd voor de ogen van onbekenden. Echter, wat als er toch iemand is die achter jouw geheimen probeert te komen? Je wilt absoluut zeker zijn dat dit nooit zou gebeuren, dus kan je maar best jouw dagboek vernietigen. Je beslist daarom om met de Starship Enterprise naar Sagittarius A* te reizen. Daar vind je het dichtstbijzijnde zwart gat en je gooit jouw dagboek erin. Nu ben je gerust, het dagboek is verdwenen en iedereen die erachter duikt kan nooit aan een ander vertellen wat het bevat: immers, niets ontsnapt een zwart gat. Alhoewel, is deze opvatting correct?

Zwarte gaten zijn niet zo zwart

Zwarte gaten blijven tot de verbeelding spreken: objecten in ons universum waar de zwaartekracht zo sterk is dat niks eraan kan ontsnappen eenmaal erin gevallen, zelfs licht niet. Het bestaan hiervan vloeit voort uit Einsteins Relativiteitstheorie en was het onderwerp van de Nobelprijs in Natuurkunde 2020. Er is natuurlijk ook de beroemde eerste foto en in juli namen onderzoekers voor het eerst licht waar van achter een zwart gat.

De naam 'zwart gat' is misleidend. In de jaren 70 toonde Stephen Hawking namelijk aan dat deze objecten wel degelijk stralen op een temperatuur die de Hawkingtemperatuur wordt genoemd. Dit fenomeen van Hawkingstraling zorgt er dan ook voor dat een zwart gat kan verdampen, het krimpt tot er niks van overblijft. Een proces dat enorm lang duurt, een zwart gat met de massa van de zon verdampt slechts volledig na 10^66 jaren. Vergelijk dit met de leeftijd van het heelal, nl. 13,8·10^10 jaren.

Een zwart gat verdampt totdat enkel Hawkingstraling overblijft.

Is tijd wel relevant?

De alombekende wetten van Newton kennen een brede toepassing en leidden tot het wiskundig modelleren van de wereld rondom ons. Gooi een bal in de lucht en we kunnen voorspellen waar en wanneer hij neerkomt. In de klassieke mechanica staat tijd centraal als onafhankelijke parameter, elk object heeft een positie en een snelheid die evolueren naargelang de tijd vordert. Newton vertelt ons hoe dit gebeurt: gegeven een beginpositie en -snelheid kunnen we met Newton berekenen wat de verdere evolutie is van de bal. Evenwel kunnen we ook terug in de tijd evolueren: vertrekkende van de eindpositie en -snelheid kunnen we berekenen in welke toestand de bal vertrok. In zekere zin bevatten beide toestanden, en alle toestanden daartussenin, dezelfde informatie. Dit behoud van informatie wordt ook wel unitariteit genoemd. Dit geldt niet enkel voor de klassieke wereld, de kwantumwereld wordt namelijk beschreven door een vergelijking die ook unitair is, de Schrödingervergelijking. Het kost nu geen grote gedachtensprong om te denken dat heel ons heelal unitair is.

The Black Hole War

Wat hebben de bovenstaande concepten nu met ons dagboek te maken? Allereerst, waarom hebben we niet voor een simpelere manier gekozen om onze geheimen te vrijwaren? We konden het dagboek verbrand hebben. Dit is niet enkel veel efficiënter, het bespaart ons ook veel kosten. Nochtans weten we dat de wereld unitair in elkaar zit. Dus iemand zou in staat zijn om het dagboek te reconstrueren indien we alle restanten opvangen: het as, de uitgezonden straling, enz. Verwachten we dan niet hetzelfde bij een zwart gat en haar Hawkingstraling?

Deze vraag was dan ook de aanleiding tot de Black Hole War tussen Hawking en Leonard Susskind. Gaat informatie verloren in Hawkingstraling of wordt ze behouden? Samen met de initiële ontdekking van Hawkingstraling, ontdekte Hawking namelijk ook dat we informatie verliezen over het zwart gat tijdens haar verdamping. Een zwart gat ontstaat wanneer een te zware ster aan het eind van haar leven onder haar eigen zwaartekracht bezwijkt, maar deze initiële toestand kunnen we niet te weten komen zelfs al hebben we alle Hawkinstraling opgevangen. Bijgevolg kunnen we niets te weten komen over objecten die tijdens de verdamping in het zwart gat vielen. In het kort: jouw geheimen zijn veilig! Maar hadden we niet enkele minuten geleden besloten dat fysica unitair is?! Deze berekeningen komen ten slotte van een combinatie van relativiteitstheorie en kwantummechanica, wat beide unitaire theorieën zijn. Deze informatieparadox houdt fysici al decennialang bezig, maar de afgelopen jaren kwam er wat schot in de zaak.

Ontbre... info

In mijn scriptie onderzocht ik juist deze laatste ontwikkelingen binnen de puzzel. Dit werd gedaan in een 2-dimensioneel model voor zwaartekracht, nl. Jackiw-Teitelboim zwaartekracht die nog enige relevantie heeft met onze 4-dimensionele wereld. De wiskunde in zulke modellen is vaak gemakkelijker dan diezelfde wiskunde in vier dimensies. Op die manier hopen we resultaten te extrapoleren naar onze realiteit. Een centrale maatstaf in dit onderzoek is de entropie van het zwart gat en van de straling. In zekere zin geeft de entropie een maat voor de ontbrekende informatie. M.a.w. als het verdampingsproces unitair is dan verwachten we dat de entropie zakt tot nul op het einde van haar leven. Dit is uiteindelijk wat ik uitkwam binnen het model: het verdampingsproces is unitair.

Is de puzzel dan helemaal af? Neen, totaal niet. De berekeningen berusten op benaderingsmethoden, een exacter antwoord zou komen van een theorie die kwantumzwaartekracht beschrijft. Hierin is snaartheorie de bekendste koploper. Daarbovenop wordt de fysische relevantie van de onderliggende assumpties tegenwoordig in twijfel getrokken. De paradox kan fysici dus nog enkele jaren entertainen.

Zijn jouw geheimen nu veilig?

De conclusie van mijn onderzoek is dat binnen dit model het verdampingsproces informatie behoudt. Dat is maar goed ook, want anders zou dit breken met de natuurwetten zoals we ze nu kennen. Aan de andere kant betekent dit dat jouw geheimen dus niet veilig zijn, voor niemand... Zoals eerder vermeld is er geen totale zekerheid over dit eindresultaat. Gelukkig kunnen we soelaas vinden in het feit dat de verdampingstijd vele malen langer is dan de leeftijd van het heelal.

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Universiteit of Hogeschool
Master of Science in de Fysica en de Sterrenkunde
Publicatiejaar
2021
Promotor(en)
Dr. Thomas Mertens; Prof. Dr. Henri Verschelde
Kernwoorden
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