4 April 2025 The Future is the Product of the Past

A Connection Between Viking Knots And Quantum Vortices Discovered

Scientists demonstrated how three vortices can be linked in such a way that they cannot be dismantled. Although this study focused on vortices in a special type of matter known as a Bose-Einstein condensate, the structure of the links resembles a pattern used by Vikings and other ancient civilizations. The findings have implications for quantum computing, particle physics, and other fields.

Postdoctoral researcher Toni Annala uses strings and water vortices to explain the phenomenon: ‘If you make a link structure out of, say, three unbroken strings in a circle, you can’t unravel it because the string can’t go through another string. If, on the other hand, the same circular structure is made in water, the water vortices can collide and merge if they are not protected.’

‘In a Bose-Einstein condensate, the link structure is somewhere between the two,’ says Annala, who began working on this in Professor Mikko Möttönen’s research group at Aalto University before moving back to the University of British Columbia and then to the Institute for Advanced Study in Princeton. Roberto Zamora-Zamora, a postdoctoral researcher in Möttönen’s group, was also involved in the study.

The researchers mathematically demonstrated the existence of a structure of linked vortices that cannot break apart because of their fundamental properties. ‘The new element here is that we were able to mathematically construct three different flow vortices that were linked but could not pass through each other without topological consequences. If the vortices interpenetrate each other, a cord would form at the intersection, which binds the vortices together and consumes energy. This means that the structure cannot easily break down,’ says Möttönen.

From antiquity to cosmic strands

The structure is conceptually similar to the Borromean rings, a pattern of three interlinked circles which has been widely used in symbolism and as a coat of arms. A Viking symbol associated with Odin has three triangles interlocked in a similar way. If one of the circles or triangles is removed, the entire pattern dissolves because the remaining two are not directly connected. Each element thus links its two partners, stabilising the structure as a whole.

The mathematical analysis in this research shows how similarly robust structures could exist between knotted or linked vortices. Such structures might be observed in certain types of liquid crystals or condensed matter systems and could affect how those systems behave and develop.

‘To our surprise, these topologically protected links and knots had not been invented before. This is probably because the link structure requires vortices with three different types of flow, which is much more complex than the previously considered two-vortex systems,’ says Möttönen.

These findings may one day help make quantum computing more accurate. In topological quantum computing, the logical operations would be carried out by braiding different types of vortices around each other in various ways. ‘In normal liquids, knots unravel, but in quantum fields there can be knots with topological protection, as we are now discovering,’ says Möttönen.

Annala adds that ‘the same theoretical model can be used to describe structures in many different systems, such as cosmic strings in cosmology.’ The topological structures used in the study also correspond to the vacuum structures in quantum field theory. The results could therefore also have implications for particle physics.

Next, the researchers plan to theoretically demonstrate the existence of a knot in a Bose-Einstein condensate that would be topologically protected against dissolving in an experimentally feasible scenario. ‘The existence of topologically protected knots is one of the fundamental questions of nature. After a mathematical proof, we can move on to simulations and experimental research,’ says Möttönen.

Aalto University

Cover Photo: In Borromean rings, each circle holds the pattern together by passing through the other two circles. Photo: Alexandr Kakinen / Aalto University

Related Articles

6th-Century BC Houses and Earthquake Evidence Discovered in Davti Blur, an Urartian Fortress City in Armenia

28 January 2025

28 January 2025

An Armenian-Polish archaeological team has uncovered remnants of 6th-century BC houses, a cremation cemetery, and signs of a significant earthquake...

Archaeologists found a 2,000-year-old Roman road in Cluj-Napoca in northwest Romania

23 January 2023

23 January 2023

Archaeologists from the National Museum of the History of Transylvania have discovered a well-preserved 2,000-year-old Roman road in the city...

Archaeologists have discovered sandstone blocks belonging to a pharaoh’s temple covered with hieroglyphs in Sudan

2 March 2023

2 March 2023

Polish archaeologists have discovered sandstone blocks belonging to a pharaoh’s temple covered with hieroglyphs during excavations at Old Dongola in...

Researchers Discovered Wreckage of a Schooner that Sank in Lake Michigan in Late 1800s

27 July 2024

27 July 2024

Maritime historians from the Wisconsin Underwater Archeology Association discovered the wreckage of a schooner that sank in Lake Michigan in...

Polish archaeologists discover papyruses containing a list of Roman centurions at Berenike

23 May 2024

23 May 2024

Papyruses with lists of Roman centurions stationed in Egypt were found by Polish archaeologists in Berenike. These unique documents were...

5500-year-old pentagon structure found in North China

13 November 2021

13 November 2021

Archaeologists discovered the remnants of a pentagonal structure going back 5,500 years in Taiyuan, Shanxi Province, north China. According to...

The Colossal Nordic Bronze Age Hall Unearthed in Germany May Be the Legendary King Hinz Meeting Hall

5 November 2023

5 November 2023 1

A colossal hall from the Bronze Age was discovered during excavations near the “royal grave” of Seddin (Prignitz district) northwest...

4750-year-old Megalithic Stone Plaza Discovered in the High Andes of Peru

15 February 2024

15 February 2024

Two anthropology professors from the University of Wyoming have discovered a prehistoric plaza high in the Andes, known as Callacpuma...

3500-year-old grape seed remains found in western Anatolia

12 September 2023

12 September 2023

Archaeologists at the Aşağıseyit Höyük (Aşağıseyit Mound) site in western Anatolia’s Denizli have uncovered a 3,500-year-old grape seed. Aşağıseyi Höyük...

Places to Visit in Oman

6 February 2021

6 February 2021

There are many places to visit in Oman. In this article, we wanted to talk about a wonderful country that...

An important discovery in Haltern: Mini temples and sacrificial pit discovered in Roman military encampment

16 November 2023

16 November 2023

Archaeologists from the Westphalia-Lippe Regional Association (LWL) have found remains of the foundations of two mini Roman temples and a...

Hagia Sophia’s Mysterious Underground Tunnels, Vaults, Tombs to Open for Visitors

7 January 2025

7 January 2025

The Turkish Ministry of Culture is carrying out a cleaning program aimed at opening to the public the underground spaces...

Scientists discover traces of paint on the Parthenon Sculptures that reveal their true colours

12 October 2023

12 October 2023

Recent research on the Parthenon Sculptures has found traces of the original paint used to decorate the Parthenon Sculptures, revealing...

White grape pips found in the Negev dated may be the oldest of its kind worldwide

29 April 2023

29 April 2023

Researchers from the University of York, Tel Aviv University, and the University of Copenhagen provide new insight into the mystery...

A 3200-year-old trepanned skull discovered in eastern Turkey’s Van province

12 November 2022

12 November 2022

A 3200-year-old trepanned skull was discovered in eastern Turkey’s Van province. In the prehistoric era, Anatolia served as a transitional...