Protected by cylindrical walls of reinforced concrete, the steel and glass “depthscrapers” extend hundreds of metres underground. Only a single floor of each inverted 35-storey skyscraper is visible at ground level.

Giant mirrors mounted directly above the central wells reflect sunlight to the apartments below. Prismatic glass ensures even light throughout the day, while fresh, conditioned air is pumped down from the surface.

“The whole structure, in case of an earthquake, will vibrate together, resisting any crushing strain,” declared a 1931 edition of Everyday Science and Mechanics that called the design the product of “the best engineering brains of Japan”.

The idea was to future-proof Tokyo against the threat of another tremor to rival the 1923 quake, which had devastated and traumatised the city less than a decade earlier.

Like many fantastical projects featured in the popular technology magazines of the 1930s, 40s and 50s, the depthscraper was never likely to become reality. It remains part of unbuilt Tokyo, an alternate city of unrealised plans: some conceptual, some speculative and some derailed by economic or political shocks.

Depthscrapers featured in the November 1931 edition of US magazine Everyday Science and Mechanics

One of the most potentially transformative and best known of these was the Plan for Tokyo 1960 by Kenzo Tange, Japan’s most influential architect and a future winner of the Pritzker prize.

Tange – who had been in charge of the reconstruction of Hiroshima after the second world war and designed its Peace Centre and Memorial Park – proposed an extensive expansion of bomb-damaged Tokyo into the shallow waters of its bay. His manmade islands, bridges and floating platforms offered the capital an adaptable space for future growth and change – and an alternative to uncontrolled expansion of the city proper.

Paul Dobraszczyk, a teaching fellow at the Bartlett School of Architecture and the author of Future Cities, says a number of floating cities were proposed in the aftermath of the second world war, inspired by sea forts and large pontoons developed by the military.

He sees the Tokyo Bay plan of Tange, and another by the French architect Paul Maymont, as being “driven by a modernist faith in the power of technology and the mass production of building components” in an effort to create “an entirely new type of urban environment … free from the traditional restraints of land-based cities”.

By the 1970s this technological optimism had waned, says Dobraszczyk. Future proposals for floating cities would emphasise organic forms and were often entirely separated from terrestrial cities.

Kenzo Tange’s 1960 masterplan for Tokyo. Images: Tange Architects

Tokyo Bay was also the proposed site for the Shimizu Mega-City Pyramid, a 2,000-metre-tall structure with accommodation for an incredible 1 million people. The conceptual project was announced in 2004 by the Shimizu Corporation – the engineering giant behind the Aqua Line tunnel-bridge across the bay and the Cocoon Tower in Shinjuku – and featured on the Discovery Channel’s Extreme Engineering series.

The whole city would be built by automated robots. Its carbon nanotube struts would allow it to withstand earthquakes and tsunamis, and power would be generated from a photovoltaic coating and algae.

Although the project is (very) theoretically due for completion by 2110, Shimizu is also busy with the Ocean Spiral city under the sea, a space hotel and a 250-mile belt of solar panels around the moon, so that date may be subject to change.

The Shimizu Mega-City Pyramid. Image: Shimizu Corporation

While unbuilt Tokyo is packed with conceptual structures and skyscrapers – such as the 4km-tall X-Seed 4000 project from 1995 – the Millennium Tower is one that might have made it off the drawing board.

Designed in 1989 by the venerable British architect Norman Foster, the 840-metre steel tower was to have been divided by “town squares” every 30 floors and would have featured high-speed lifts the size of buses. Helical bands around the tower were to give structural support, and water tanks at the top could be rotated as a counterweight against strong winds.

It was commissioned by the Obayashi Corporation, the construction firm behind the Tokyo Skytree and the Roppongi Hills development. The company was also responsible for the Tokyo Laputa Plan for a series of 1 sq km “platform cities” built six to eight storeys above ground level to relieve overcrowding and provide much-needed open space.

The Millennium Tower was more serious but it was never built anyway – a victim of the city’s burst real estate bubble in the 1990s.

A model of the Norman Foster-designed Millennium Tower. Photograph: SSPL/Getty

The American firm Kohn Pedersen Fox came up with the Sky Mile Tower, a 420-storey skyscraper, as part of its Next Tokyo 2045 proposal, which outlines ways an eco-friendly district could combat rising sea levels in Tokyo Bay.

The tower would be almost double the size of the world’s current tallest building, Dubai’s Burj Khalifa, and significantly higher than the 1km-tall under-construction Jeddah Tower in Saudi Arabia.

The skyscraper would contain housing for around 55,000 people, linked by multi-level “sky lobbies”, and feature shops, restaurants, hotels, gyms, libraries and health clinics. The design includes plans to harvest water from clouds, while farms floating in the surrounding waters help provide food for the 500,000 residents of the wider development.

The Sky Mile Tower was announced in 2016 with no funding.

The Sky Mile Tower was the centrepiece of Kohn Pedersen Fox’s Next Tokyo 2045 project. Images: KPF

The most high-profile recent addition to unbuilt Tokyo is Zaha Hadid’s futuristic design for Tokyo’s 2020 Olympic stadium. The late British-Iraqi architect won the original design competition in 2012, but three years later, when costs ballooned to almost twice the original estimate, Japan’s prime minister, Shinzo Abe, scrapped the plan. Unimpressed Tokyoites had already likened it to a potty and a bike helmet.

Construction on a new stadium, by Japanese architect Kengo Kuma, began in 2016 and is due for completion later this year.

Zaha Hadid’s design for the National Stadium for the 2020 Tokyo Olympics. Images: Japan Sport Council/EPA/AP/Zaha Hadid Architects

Additional reporting by Nanako Yamamori

Guardian Cities is live in Tokyo for a special week of in-depth reporting. Share your experiences of the city on Twitter, Facebook and Instagram using #GuardianTokyo, or via email to cities@theguardian.com