Einstein’s brilliant elevator Gedankenexperiment (thought experiment).

Graham writes ...

Credit: Image generated by AI Gemini.

I read with great regard last month’s blog post from John, in which he discussed a topic of interest to himself, but of great importance for the rest of us – photosynthesis. John’s career focussed mainly on the study of the genetics of plants and, as we all know, the ability of plants to utilise an external energy source (the Sun) to fix carbon for their own development changed the planet around 2.5 billion years ago when oxygen-producing photosynthesis began. Clearly, the oxygenation event changed the future development and evolution of all life (including us) on planet Earth.
 
This motivated me to go back to my origins in terms of long-term science interests to produce something this month. Throughout my career in the space sector, I have always had a fascination with gravity. Effectively, there two theories in current use to describe gravitation – Newton’s theory which was published in 1687, and Einstein’s (the general theory of relativity (GTR)) which hit the physics community in 1915. The two theories are fundamentally different. Newton’s theory regards gravity as a ‘force’ and has a mathematical structure which is relatively simple in comparison to its more recent counterpart. Strangely, Einstein’s theory does not regard gravity as a force, but instead proposes that gravity is a manifestation of curved space and time, which makes the mathematical framework of the theory extremely complex. Both theories have lasted well – Newton’s theory reigned for around two centuries before observations caught up with it and revealed anomalies when the theory’s predictions were compared to the real world. Einstein too has yet to be found wanting in this respect after about 110 years, which is amazing since the recent tests of his theory (in the strong field regime) have been more demanding.

The young Albert Einstein (aged 5 years) taken in 1884. Credit: public domain.

However, before we get into all that, it’s worth giving a brief account of Einstein’s first major contribution to the world, his special theory of relativity (STR) which was published in 1905. That year marked the end of classical physics, when Einstein’s new insights into the nature of reality swept away the Newtonian view of the Universe. We need to keep in mind that at the time Einstein was unknown to the physics community and was working as a lowly patent clerk in the Federal Office for Intellectual Property in Bern, Switzerland. Initially, his contribution was overlooked, but there were some eminent physicists, notably Max Planck, who appreciated that a ‘new Newton’ had burst upon the scene.
 
Einstein’s efforts in developing the STR were sparked by various issues arising in classical physics around the turn of the 20th Century (see, for example, references to the Michelson-Morley experiment). Perhaps the first question is – why is the special theory special? This is simply because it describes a special case, in as much as it does not account for gravity or accelerated motion. Consequently, it concerns itself with observers in ‘inertial frames of reference’; that is, observers travelling at constant speed in a straight line. This sounds like quite a constraint, but then you’ve got to start somewhere. The second main outcome of all this is that our understanding of the nature of reality was transformed. Newton’s concept of space and time was represented by a rigid and unchanging 3-dimensional spatial grid against which the motion of objects was measured, while in the background a clock ticked away marking the universal passage of time. Einstein’s theory swept this away, and introduced the concept of a 4-dimensional entity called ‘spacetime’ to manage the notion that space and time are flexible (varying, depending upon observers) and inextricably connected to each other – in other words, space and time are not absolute as Newton had supposed.

A simple spacetime diagram of a moving object. Credit: University of Toronto.

To develop his special theory Einstein proposed two principles or starting points. Firstly, that the laws of physics are the same for all inertial frames of reference – that is, there is no special ‘absolute rest’ frame of reference in the Universe. Secondly, that all observers measure the same value of the speed of light c in a vacuum (c ~ 299,792,458 m/s) no matter how fast they are moving. The second of these, which has been experimentally verified, is the key attribute that forces space and time to behave differently to what our everyday intuition might expect. The outcome of adopting these axioms resulted in a paradigm-changing theory with a number of consequences. The most significant of these can be summarised as follows:
 

• Kinematic time dilation

If someone travels very fast relative to you then their time passes more slowly compared to yours. This leads to the famous ‘twin paradox’ – a twin who travels at near the speed of light on a cosmic adventure and then returns ends up younger than their twin who stayed home. It is also not generally appreciated that the mathematics of SRT implies that each of us is travelling through spacetime at the speed of light! So, if you observe someone passing you very rapidly through space, then the rate at which they ‘travel’ through time is correspondingly slower – that is their clock ticks more slowly than yours – a curious consequence that has again been verified experimentally.
 

• The relativity of simultaneity

Two spatially-separated events, simultaneous in one reference frame, are generally not simultaneous in another frame moving relative to the first. Simultaneity is not absolute, but relative to an observer’s frame of reference. Intriguingly, this has the consequence that there is no universal ‘now’ moment. If you are travelling at a different speed relative to me, your ‘now’ is different to mine. This leads to all sorts of interesting questions about whether the future, present and past coexist 'now' -  to quote Einstein "For we convinced physicists, the distinction between past, present and future is only an illusion, however persistent." (1) Unfortunately, there is no space in this post to explore these notions – maybe another blog post sometime?
 

• Mass-energy equivalence

This is Einstein’s ‘famous’ equation – E equals m times c squared (in words). This implies that mass and energy are different forms of the same thing. Given that c is such a large number, it means that a tiny bit of mass contains a huge amount of energy. For example, the destruction of Hiroshima in August 1945 by an atomic weapon was the result of the conversion of 0.7 grams of mass into energy. This ‘simple’ equation has led to the understanding (among many other phenomena) of the creation of matter particles in the early Universe, energy production in stars and, closer to home, nuclear energy generation here on planet Earth.

Albert Einstein (1879-1955). Credit: Image generated by AI, courtesy freepik.com.

Getting back to gravity, and to help appreciate what follows, it’s worth describing briefly what is meant by the idea that gravity is produced by the curvature of space and time. If you have a copy of the book (2), then you can skip this section and read a fuller, and hopefully more helpful, explanation on pages 52 to 56.

Einstein’s general theory of relativity was developed during the period 1907 to 1915, when he wrestled with the physics and, in particular, the mathematics required to create his theory. He considered his own mathematical skills to be poor (!), and given the complexity of the mathematics required to describe his theory, he was grateful for the help of others (including Marcel Grossmann, a close friend and one-time classmate and David Hilbert, a renowned mathematician who finalised the field equations for general relativity around the same time as Einstein). Fortunately, despite this complexity, the basics of his theory can be explained in relatively straightforward terms.
 
The foundation of his theory is the principle that massive objects, like the Sun, distort the geometry of the spacetime surrounding them. This is the celebrated ‘warped space’, which has become so ‘familiar’ to us all, from science fiction books, TV and cinema (“warp-factor 5 Mr. Sulu”!). However, although we have heard a lot about it in sci-fi stories, an intuitive appreciation of what a ‘curved four-dimensional spacetime continuum’ means is still difficult to comprehend, even for those equipped to cope with the mathematics! Einstein’s basic idea of motion in a gravity field is that objects move in such a way as to take a path which gives the shortest distance between two points in the curved geometry. These paths are referred to as geodesics, and examples of these in simpler contexts are straight lines in flat (Euclidian) space and great circles on the curved 2-dimensional surface of a sphere. The accompanying pictures illustrate what geodesics look like in the setting of the Solar System.

Planetary orbits in Einstein’s gravity theory. Credit: the author.

The deflection of light in a curved space-time. The angle of deflection of the light has been exaggerated for the sake of clarity. Credit: Artwork by Luis Maria Benitez (public domain).

In summary, to describe how the theory works you could say that “matter (e.g. the Sun) tells spacetime how to curve, and the curvature of spacetime tells matter how to move”. For readers interested in more technical details see Text Box 3.3 on page 56 of the book (2).
 
As an aside, this picture of gravity as a result of the curvature of space and time, rather than being a ‘force’, poses a significant problem when physicists try to unify gravity with the other three fundamental forces of nature – which is something that the physics community has been trying to do for the last hundred years or so. It is also worth noting that Einstein became a Nobel Laureate, not for developing his two monumental theories of relativity, but for his work on the quantum-mechanical implications of the  photo-electric effect!
 
Einstein's elevator thought experiment was crucial in aiding Einstein in his struggles to introduce gravity and accelerated motion into his relativistic theories, serving as the "happiest thought" of his life (around 1907-1908) that bridged special relativity and general relativity. By imagining an accelerating elevator, he developed the principle of equivalence, which states that gravity and acceleration are indistinguishable, allowing him to propose that gravity is the curvature of spacetime, not just a force.

Fig. 1. Einstein in his elevator in a 'normal' 1 g environment. Is it caused by gravity or acceleration? Credit: Image generated by AI ChatGPT.

If you are standing on the Earth’s surface and you drop something, it will accelerate towards the Earth’ centre at a rate of 9.81 metres per second per second (m/s/s) (neglecting other forces such as friction or aerodynamic drag). This means that the object will increase in speed by 9.81 metres per second for each second of its fall. This is referred to as a 1 g environment, and it is this gravitational influence that keeps us firmly attached to the ground. The essence of the thought experiment can be summarised by the considering the following scenario. Imagine yourself (or indeed Albert Einstein – see Fig. 1) in a small elevator compartment with no windows, and experiencing a ‘normal’ 1 g environment. The easiest conclusion to draw from this is that the elevator is indeed stationary in a gravity field while resting on the Earth’s surface. However, there is another possibility. The elevator could be in deep space, very distant from any gravitating objects such as stars, and accelerating ‘upwards’ at a rate of 9.81 m/s/s (it’s obviously a very strange elevator with some sort of rocket attached to it!). Albert will experience the same 1 g environment as he did with the elevator resting on the Earth’s surface, and if he drops something it will appear to fall at a rate of 9.81 m/s/s as the floor of the elevator is accelerating upward at this rate towards the object. So, the two cases are indistinguishable, in one case the 1 g environment caused by gravity and in the other by acceleration.

Fig. 2. The bending of light due to 'upward' acceleration of the elevator. The degree of bending has been exaggerated for the sake of clarity. Credit: Image generate by AI ChatGPT.

This equivalence principle helped Einstein realise that an observer in a ‘sealed room’ cannot distinguish between being at rest in a gravity field or being accelerated in free space. So how did this help him to take the crucial step of considering gravity to be a manifestation of spacetime curvature rather than a ‘force’? Going back to Albert in his elevator, imagine an intense pencil beam of light (a laser beam?) entering through a small hole on one side of the compartment. If the elevator is accelerating ‘upwards’ in free space, then in the time it takes for the beam to traverse the compartment, the elevator would have moved upwards a little. Hence the beam will arrive at the opposite wall at a slightly lower position compared to the entry hole. The beam will appear to have been bent slightly downwards (see Fig. 2, in which the effect is greatly exaggerated for the sake of clarity). Einstein figured that the equivalence principle would suggest that the same thing – the bending of light – will also happen in a gravity field. This marked the beginning of a torturous eight-year journey, enabling Einstein to shift away from treating gravity as a Newtonian force and toward understanding it as the effect of the curved geometry of spacetime.
 
Another curious feature of Einstein’s general theory is the notion that time slows down (clocks tick more slowly) when they are close to a gravitating object. This gravitational time dilation has been experimentally verified, and is furthermore incorporated into the engineering of the GPS system that we all use in our cars these days. Without taking account of this effect, positioning estimates would be kilometres in error after a couple of days. This attribute can also be predicted using the elevator model, but the explanation is a little bit more difficult, so I have decided to pass over the details. 

Fig. 3. Einstein experiencing weightlessness. Is it caused by zero gravity or free-fall? Credit: Image generated by AI ChatGPT.

Finally, Einstein’s elevator can help in the understanding of weightlessness. Imagine you (or Albert – see Fig. 3) are floating freely inside the compartment, and around you other objects are floating as well, and you feel totally weightless. Does this mean you are far away from all gravitating objects, somewhere in deep space? Again, you cannot be sure. Alternatively, you and the elevator could be in a gravitational field but in a state of free fall. In this case you and everything else within the elevator, and the elevator itself, would all be accelerating at the same rate so that, inside, no influence of gravity can be detected, hence establishing that a free-falling frame is equivalent to an inertial frame in empty space. This aids understanding of the kind of weightlessness experienced by astronauts on the International Space Station (ISS). The spacecraft has not escaped Earth’s gravity, but is in a continuing state of free fall. Its forward motion along its orbit curves towards Earth in this falling state, but of course the Earth’s surface curves away as well, so that, fortunately, the spacecraft’s trajectory never intersects the Earth’s surface!

Astronauts aboard the ISS enjoying a state of weightlessness. Credit: NASA.

I hope you have enjoyed this excursion into the realm of thought experiments, and have found it helpful. Einstein was a master of this art, and used it continually to challenge the advocates of quantum mechanics at a time in his life when he felt the theory was incomplete.
 
Graham Swinerd
Southampton, UK
March 2026.
 
​(1)   Einstein and Besso: Correspondence 1903-1955, Editor P. Speziali, Hermann Academic Press, 1972.

(2)  From the Big Bang to Biology: where is God?, Graham Swinerd & John Bryant, Kindle Direct Publishing, 2020.