# A Hypothetical Correspondence with Einstein on Modern Physics
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Chapter 1: A Letter from the Future
In a light-hearted but thought-provoking exercise, two Princeton physicists imagine writing a letter to the legendary Albert Einstein, sharing groundbreaking developments in physics. While the concept of time travel might seem far-fetched, the essence of this letter illustrates how far our understanding has come since Einstein's era.
This section provides a unique perspective on an imaginary dialogue with one of the greatest minds in science.
Section 1.1: The Legacy of Einstein's Work
Dear Albert,
First and foremost, let us express our admiration—your contributions to physics are unparalleled. The equation E = mc² is universally recognized, and Time magazine even honored you as the Person of the Century. Although Einstein jokes have become somewhat predictable, your legacy continues to resonate. Despite the existence of numerous nuclear weapons, humanity has managed to avoid total annihilation thus far. The atomic bombs used during World War II remain the only instances of their intended use against people.
Currently, our focus is on general relativity and black holes, especially since the LIGO observatory detected gravitational waves from a black hole collision that happened over a billion years ago. We even authored a book on black holes, knowing of your keen interest in Schwarzschild's solution. We hope to share some exciting updates from the decades following your passing.
Section 1.2: Insights on Black Holes
The fascination with general relativity has only grown. A key feature in Schwarzschild's solution is the event horizon—once crossed, escape becomes impossible without exceeding the speed of light. This solution exhibits peculiar traits when the radius equals mass, leading to the vanishing of the time-time component of the metric. This point defines the event horizon. Further, as the radius approaches zero, we encounter a singularity where the fabric of spacetime ceases to function normally. Should one enter a Schwarzschild black hole, they would inevitably meet this singularity, but what happens afterward remains a mystery.
Section 1.3: The Evolution of Black Hole Theory
We wish you could witness the remarkable advancements in general relativity in the decades following your death. John Wheeler played a pivotal role in this evolution, coining the term "black hole" to describe Schwarzschild's solution. Notably, Roy Kerr derived a more complex metric that represents rotating black holes, further enhancing our comprehension of stellar collapse.
Current consensus suggests the universe contains numerous black holes. As theorized by Chandrasekhar, Tolman, Oppenheimer, and Volkoff in the 1930s, if a star's core is left with roughly three solar masses post-fusion, it will collapse into a black hole. Even more astonishing are the supermassive black holes located at the centers of galaxies, including our own Milky Way, which hosts a black hole with a mass of approximately 4 million solar masses. Tracing the orbits of nearby stars has confirmed its existence.
The first video, Artifacts: Albert Einstein Letter | The Florida Holocaust Museum, provides a deeper look into Einstein's legacy and impact on science.
Chapter 2: Gravitational Waves and Modern Discoveries
One of the most thrilling moments in recent physics was the LIGO detection of gravitational waves. This large Michelson interferometer, spanning 4 kilometers, was poised for a significant scientific run when it fortuitously captured a gravitational wave pattern from the merger of two black holes, each around 30 solar masses.
The second video, Einstein's 1922 letter reveals he was fearful for Germany's future, sheds light on Einstein's perspective during tumultuous times.
Section 2.1: The Cosmological Constant Revisited
Your notion of the cosmological constant has also evolved. Once deemed your greatest error, it is now recognized as a crucial aspect of your field equations. This constant appears to account for approximately 70% of the universe's energy, particularly when explaining the universe's accelerated expansion. Rather than maintaining a static universe, dark energy accelerates this expansion, prompting intense studies in higher-dimensional spacetimes.
Section 2.2: Quantum Theory's Validation
We are increasingly confident in the validity of quantum theory. Stephen Hawking demonstrated that quantum mechanics implies black holes can emit radiation, albeit at exceedingly low temperatures. Intriguingly, black holes exhibit a high entropy, despite being unique solutions to your equations. Even your collaborative work with Podolsky and Rosen remains relevant, influencing modern developments in quantum computing.
In closing, many Princeton faculty members have abandoned ties, but socks remain common attire. Lake Carnegie continues to be a picturesque sight, and an eagle has taken residence along its banks. While a unified field theory eludes us, we remain hopeful for future discoveries.
Yours sincerely,
Steve and Frans
Steven S. Gubser is a professor of physics at Princeton University and author of The Little Book of String Theory.
Frans Pretorius is also a professor of physics at Princeton University.
This letter is inspired by The Little Book of Black Holes by Steven S. Gubser and Frans Pretorius, copyright © 2017 by Steven S. Gubser and Frans Pretorius. Published by Princeton University Press and reprinted with permission.