Abstract
We often say that the physics of “small distances” is equivalent to the physics of “high energies.” This is indeed true, as a direct consequence of the celebrated Heisenberg’s principle (or uncertainty principle) stating that, in order to explore (and measure) smaller and smaller distances, we need probes with higher and higher momenta, namely with larger and larger kinetic energies. According to the uncertainty principle, in particular, the required energy E turns out to be inversely proportional to the considered distance d, so that E tends to infinity when the distance d goes to zero.
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Notes
- 1.
The famous Andromeda Galaxy, whose picture is also used as a desktop background in recent versions of Mac computers, is one of the nearest galaxies, and is approximately 2.5 million light-years away from Earth (corresponding to a distance of about 2. 4 × 1019 km).
- 2.
This occurs when the radiation reaches a temperature that is about a 1,000 times larger than the current one: more precisely, a temperature of 2,973 K. Such a temperature is reached at the so-called “decoupling epoch,” see for instance the textbooks by Durrer [1], Weinberg [2], Gasperini [3] (in Italian).
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Gasperini, M. (2014). Prologue: Inside the Energy Walls of Our “Cradle”. In: Gravity, Strings and Particles. Springer, Cham. https://doi.org/10.1007/978-3-319-00599-7_1
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