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"Big bang" is a phrase you hear everywhere, but the idea that makes it testable is less well known: if the universe was once hot, it should still be glowing faintly. George Gamow and his younger colleagues worked that out in 1948, and it was 17 years before the glow turned up, found by people who were not looking for it. This post covers what Gamow contributed, the prediction, a Wien's law calculation you can do with Class 11 thermal physics, and what students can learn from how the work was done.
Who was George Gamow?
Gamow was a Russian-born American physicist and a former student of Alexander Friedmann, one of the first people to find expanding-universe solutions of Einstein's equations. That is how the physicist Jean-Pierre Luminet describes him in a history of early cosmology (2015).
Before cosmology, Gamow made his name in nuclear physics. In a 1928 letter to Nature, The Quantum Theory of Nuclear Disintegration, he noted that Gurney and Condon had used wave mechanics to explain alpha decay qualitatively, and said that with similar assumptions it was possible to give "a quantitative explanation". This is the quantum tunnelling picture of alpha decay: an alpha particle escapes a nucleus even though classically it lacks the energy to cross the barrier. It is a good example of Gamow's habit of taking a new idea from quantum mechanics and asking what numbers it predicts.
What was the hot big bang idea?
In 1948, Ralph Alpher, Hans Bethe and Gamow published The Origin of Chemical Elements in Physical Review. Luminet summarises the argument: if the early universe was very hot, nuclear particles could fuse into the lightest nuclei, deuterium, helium and lithium, during the first few minutes, when the temperature was around 10 billion degrees.
Later, as the universe expanded and cooled to a few thousand degrees, it became transparent and light could travel freely for the first time. That light would still be around, stretched and cooled by the expansion.
How did Alpher and Herman correct Gamow?
Here the story becomes a lesson in checking work. In a short letter, Evolution of the Universe (Nature, 1948), Alpher and Herman wrote that in checking Gamow's recent article they found errors, including "an arithmetical error". They corrected his calculation. Luminet records that Alpher and Herman calculated the present-day temperature of this leftover radiation at about 5 K.
Gamow was the senior, famous scientist. His younger colleagues checked his arithmetic, found mistakes and published the corrections, and the science moved forward because of it.
When was the prediction confirmed?
According to Luminet, the prediction caused no excitement and nobody tried to detect it. In 1965, engineers Arno Penzias and Robert Wilson at Bell Labs found an unexplained excess of about 3.5 K in their antenna's noise, coming from every direction. Their measurement and the Princeton group's explanation appeared side by side in the Astrophysical Journal that July. Neither paper mentioned Alpher and Herman's prediction. Gamow died in 1968.
Penzias and Wilson received the 1978 Nobel Prize in Physics "for their discovery of cosmic microwave background radiation". The modern value, from a 2009 analysis by D. J. Fixsen, is 2.72548 ± 0.00057 K.
Worked example: why is it called microwave?
Wien's displacement law says a black body at temperature T emits most strongly at wavelength λ_max = b/T, where b is Wien's constant. The CODATA value from NIST is b = 2.897771955 × 10⁻³ m K.
Today's temperature, T = 2.725 K:
λ_max = 2.898 × 10⁻³ / 2.725 ≈ 1.06 × 10⁻³ m ≈ 1.06 mm.
Alpher and Herman's prediction, T = 5 K:
λ_max = 2.898 × 10⁻³ / 5 ≈ 5.8 × 10⁻⁴ m ≈ 0.58 mm.
Both are around a millimetre, in the microwave band. That is why the glow was found with a radio antenna rather than a telescope.
Common mistakes:
Using °C instead of kelvin. Wien's law needs absolute temperature. 2.725 K is about −270.4 °C; putting a negative number in the formula gives nonsense.
Losing a power of ten. Write b as 2.898 × 10⁻³ m K and keep the units until the end, then convert metres to millimetres.
Thinking colder means shorter wavelength. It is the opposite: halving T doubles λ_max.
Our post on black body radiation covers Wien's law and Stefan's law with more examples. To see how the peak shifts as temperature changes, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
What can a student take from Gamow's way of working?
Ask what a new idea predicts in numbers. Gamow turned qualitative tunnelling into a quantitative theory, and a hot universe into a temperature.
Work with people who will check you. The 5 K prediction exists because Alpher and Herman checked and corrected Gamow.
Write predictions down. The 1948 papers are why we know the glow was predicted before it was found.
For the earlier half of this story, read about Georges Lemaître and the expanding universe.
This week, take one formula from your thermal physics chapter and use it to predict a number you can check, such as the peak wavelength of the Sun at 5772 K.
