When the Age of Earth > Age of Universe and how this paradox was resolved
There is an entertaining book that captures the reminisces of Nobel Prize-winning physicist Richard Feynman: “Surely You’re Joking, Mr Feynman”. A champion of quantum electrodynamics, particle physics, the Manhatten Project, plus much more, in reality the book is only tangentially related to his successes in his field and instead focused on his interesting character and rather extraordinary life experiences. Though it must be noted that nowadays the disrespectful way he at times describes his interactions with women is joyless to read.
In one of the chapters (“An Offer You Must Refuse”), Feynman recounts his difficulty in choosing whether to pursue his professional career back at Cornell, or start anew at Caltech, following a year-long sabbatical spent in Brazil. Ultimately his decision was based on a fortunate day spent on campus at Caltech, where he was told of two separate, tremendous scientific discoveries by his friends, the excitement convincing him to not leave such a cutting-edge environment.
One of these friends was astronomer Walter Baade, who had found that there are two types of Cepheid stars (which we will describe further), that allowed a head-scratching paradox to be resolved, which I had not been aware of before. To quote the book:
“I knew the problem. In those days, the Earth appeared to be older than the Universe. The Earth was four and a half billion, and the Universe was only a couple, or three Billion years old. It was a great puzzle. And this discovery resolved all that: The Universe was now demonstrably older than was previously thought. And I got this information right away — the guy came running up to me to tell me all this.”
In this article we explore the age of Earth and explain what Cepheid stars and their contribution to solving this paradox.
Why was Earth older than the Universe?
Discoveries in physics (and I bet science in general) rarely happen in parallel and can contradict each other. Before the day Baade came running to Feynman to explain his important correction to the Universe’s age in 1952, work towards doing the same for Earth had been steadily progressing. Today, the age of Earth is estimated to be 4.54 ± 0.05 billion years, but at the turn of the century estimates were often a factor of thousand smaller. This was greatly revised when radiometric dating started to be effectively adopted (after years of resistance from the geological community).
Radiometric dating works like this: I’m sure you have been taught that for many of the elements, atoms may have several isotopes (containing equal number of protons but different numbers of neutrons), and some isotopes decay into smaller daughter atoms due to nuclear instability — radioactivity. An example is Uranium, which has several isotopes, each having 92 protons, the two most common in existence being U-235 and U-238 (U-235 has 143 neutrons, U-238 146). The rate of decay is exponential, and through experimental measurement the half-life of an atom may be derived (the time it takes for half the nuclides in a sample to decay, a parameter which is assumed constant). Therefore by looking at the proportions in rock samples of the parent and daughter nuclei can the Earth’s age be estimated.
The equation looks like this:
Where D* is the amount of daughter nuclei today, D⁰ the original amount of daughter atoms, N* the amount of parent nuclei, t the sample age, and λ is the decay constant of the parent nuclei, inversely proportional to its half-life. D* and N* may be measured for a sample, and the half life known, but D⁰ cannot be found directly, as you can’t travel back in time.
First thing to consider for effective dating of Earth is to pick a radioactive element that has a sufficiently-long half life to be useful. Carbon-14, with a half-life of 5,730 years, is great to estimate ages of historical artefacts or ancient burials, but it is not suited to measure the Earth’s age since it would have gone through many half-life cycles until there is not enough C-14 atoms left in a sample. Conversely, U-235 and U-238 have half lives of 700 million and 4.5 Billion years respectively, making them a good choice. Secondly, a closed system is required, i.e. no isotopes could have left or entered the sample. This is more difficult to control, since the Earth has undergone many geological changes over millennia. To get around this, terrestrial meteorite samples are often used, since they are not affected by the Earth’s geological evolution.
Creating an isochron of several minerals in a sample to look at relative proportions solves the mentioned problem of deriving D⁰. In various samples, the amount of parent and daughter nuclei are compared with an isotope of the daughter element that is stable (i.e. non-radioactive) and therefore its amount in a sample can be assumed unchanged over time. If we denote this nuclei as D_ref, we can change the above equation to:
This actually look similar to a simple linear y = mx + c equation, where the gradient m contains the exponential minus 1, and the intercept gives us the initial value D⁰( / D_ref).
The reason why this works is because one can imagine that at the start of Earth’s formation, all samples should have equal ratio of D⁰ / D_ref, but may have varying values of N / D_ref, since they are different elements. As the Earth gets older and N decays, the ratio D / D_ref increases at the expense of N / D_ref decreasing, so the slope starts to increase. Hence the gradient calculated from samples can derive the current age (time lapsed since horizontal line). This shift is illustrated in the figure below:
By 1950, several experiments had already produced estimates that were in the realm of a 2-3 billion years. Experiments made in Caltech in 1956 already came very close to the accepted figure today (source).
A star-tling discovery
The Earth having such an early birthday did not seem to agree with the estimations of the day regarding the age of the Universe, and this was perhaps one of the key motivators to re-evaluate some of the prior results. By that time, scientific understanding of what the Universe is had already been, to put it lightly, turned on its head. Since Einstein’s theory of general relativity was published in 1917, advocating for a steady-state Universe in which its size stayed unchanged, physicists like Edwin Hubble had shown otherwise experimentally that this is in fact not the case, and the Universe is in fact expanding. From this was born the desire to calculate the rate of expansion of the Universe, also called the Hubble constant, to get the time when expansion first started — the Big Bang.
The age of the Universe can be estimated by trying to find the farthest objects with your telescope, and by calculating the distance the light took to travel to Earth. This also gives you the time it took to reach you, since light travels at a constant speed, c = 3 x 10⁸ m/s. Cepheid stars are a special type of variable star with predictable brightness variations — that is, they pulsate at a consistent brightness and period, usually on the scale of days-weeks. Additionally, the period is linearly related to the star’s absolute brightness — the slower it pulsates, the brighter the star is. If absolute brightness of a star is defined as being 10 parsecs from earth, and using the fact that brightness is inversely proportional to square-distance d from Earth, we can estimate the distance of a Cepheid star simply by measuring its apparent brightness and period P:
So, in essence, a cepheid with a longer period = brighter absolute magnitude and the dimmer it is, the further away it is = the longer the time took for light to reach Earth.
Strides had been made to use this method, which was standardised by physicist Harlow Shapley using stars found in our Milky Way. Hubble used these parameters to estimate the distance to the Andromeda galaxy at 800 thousand light years. However, this approach had a flaw- the standardisation assumed that all Cepheid stars observed were the same, when in reality they are not. The age estimation was around 1.5 billion years at this point, which as we know from the previous section, is far too small.
This is where Baade’s discovery brought some relief. Whilst observing the Andromeda galaxy during the clear blackout skies of the Second World War, he found there was not one, but in fact two types of Cepheid stars. Type II Cepheids are older, dimmer, and found in Andromeda’s inner globular cluster and outer halo (same as those in Milky way). But type I (classical) Cepheid, are brighter and found in the outer clusters. The two had differing Period-luminosity relationships, as seen in the graph below:
Since type I Cepheids are systematically brighter than type II for the same period values, this means that in fact a type I with the same dimness as type II must be much farther away. Hubble re-calculated the distance to Andromeda and it increased to 1.8 million years away. The discovery had an overall effect of doubling the previous estimate of the age of the Universe, eliminating the controversy of before.
It should be noted that by no means Baade’s discovery was (and is) the last estimate. The estimation has been greatly refined numerous times since by looking at the evolution of stars in globular clusters found in distant galaxies (more reading). Furthermore, the theory of expansion of the Universe has been greatly accepted due to the discovery of Cosmic Background Radiation (more reading — possible topic of future article). Using these techniques, the current best estimate of the age of the Universe is 13.787±0.020 billion years.
Conclusion
When one reads about Feynman & his contemporaries experiences in the 20th century, it is fantastic to picture how it must have been to be caught in the middle of a very turbulent period in understanding of physics. Many at the time, including Einstein himself, would come up with radical theories and then vehemently find ways to dispute them. In the case of Baade, I believe the excitement of finding a key piece of the puzzle to solve an obvious contradiction must have been rather satisfying, to say the least.
