Exploring The Intellectual Odyssey of Stephen Hawking

We have all likely heard the statement that “nothing escapes a black hole”. The gravitational pull of a black hole (not really a hole, as you know, but since light cannot escape it, it looks very dark) exceeds most objects’ escape-velocity (minimum velocity that a body must have in order to escape the gravitational attraction of a particular planet or other object) ability, so those objects are pulled into the singularity. Webster’s defines singularity as a point at which a function takes an infinite value, especially in space-time when matter is infinitely dense, as at the center of a black hole. I prefer the word singularity over “black hole” simply because it is a more accurate, descriptive name.

Is information truly lost in a singularity? This question arises because of the premise that the speed of light is represented as C in most science and calculus classes and its numerical value is 299,792,458 m/s (meters per second). “The event horizon of a black hole is the boundary around the mouth of the black hole, past which light cannot escape. Once a particle crosses the event horizon, it cannot leave. Gravity is constant across the event horizon” (Redd). If nothing can escape a singularity, not even a photon (which, at the time of this writing, is the commonly known “speed limit” of the universe), especially considering the escape velocity necessary at the event horizon of a singularity: C= sqrt(2Gm/R), how does information escape?

In this example, C takes on a new value which is the square root of the entire quantity represented by twice the gravitational pull (G) times the mass of the object (M) divided by the center of radius between the two objects (R).

To put that in perspective:

• the gravity felt on Earth is roughly 9.8 m/s
• stellar-mass singularities are typically in the range of 10 to 100 solar masses (the mass of our Sun)
• supermassive singularities at the centers of galaxies can be millions or billions of solar masses

Our Earth’s mass is estimated to be 5.972 × 1024 kg, and our sun is estimated to be 2 × 1030 kg. Substituting in the mass of our star to the range of masses for singularities increases the mass by 10 to 100: a singularity would have a mass approximately between 2 × 10300 and 2 × 103000 kg. ( That is a ten followed by 3000 zeroes.) In any calculation of force, the mass of the object is key. A boiled-down equation useful for measurements of force in physics is:

Where the sum of the forces is measured in Newtons, mass in kilograms and acceleration is in meters per second, squared. In short, it’s a lot faster than three hundred thousand meters per second, based only on the gravity of a singularity, because their mass is tied to the equation. If, then, it’s true that nothing can escape the event horizon, how does information not get sucked in, with no chance for escape? Further compound this question by asserting that there is a singularity (typically a supermassive black hole) at the center of each galaxy. The supermassive black hole at the center of the Milky Way, Sagittarius A*, is 4.3 million solar masses. There are billions of galaxies known to us… with all those event horizons, how does information survive?

In short, we have set up an impossible situation. We know that information is all around us, especially in the digital age. We have established that nothing can escape a singularity, and nothing can exceed the speed of light. Well, then, if it’s true that information cannot escape a singularity’s gravitational attraction, how is that information all around us… at all?

Stephen Hawking first stated that it’s true: “…information can be recovered in principle, but it is lost for all practical purposes” (Hawking, The Information Paradox for Black Holes), then, a few years later, he revised his original statement. Using a special branch of mathematics (Virasoro algebra), he hypothesized that it is indeed possible for the backwards transfer of information from particle to particle as they enter the event horizon (Hawking, Black Hole Entropy and Soft Hair). It’s like a rather large-scale version of Tag! where each particle entering passes information to particles that have not reached the event horizon, thereby saving information. Is your head spinning, yet? It’s a bit of a lark to read about this, now, but imagine if you were Mr. Hawking – and this conversation was happening inside your own head. There are some physicists who continue with the old statement that nothing can exceed the universal speed limit. As is usual in the scientific world, they likely have their own hypotheses that they are actively working on, so they are not about to abandon their work and simply state that Hawking is correct. You see, in the scientific process, there are certain steps one should undertake in proving/disproving a hypothesis:

1. Make an observation;
2. Ask a question;
3. Look for research already conducted;
4. Form a hypothesis or testable explanation;
5. Make a prediction based on your observation and on your understanding of the hypothesis on the outcome of the experiment;
6. Test the prediction;
7. Iterate; that is, use the result to form a new hypothesis or set of predictions.

So, it’s not unlike scientists to sit in their laboratories or offices for years repeating those steps. While they may be aware of Hawking’s hypothesis (via looking for other research in step 3), that is not the end of the road. Of course, we must remember that it was Hawking that “discovered” black holes back in 1974 (Ouellette). The understanding of singularities was his life’s work (Ferguson). This can create challenges to those scientists who are attempting to complete, or at least, continue, Hawking’s work. This was all the man did from the time he opened his eyes in the morning until his head hit the pillow at night. This resulted in spending a lot of time on the subject, which led to his notoriety as an expert in the field. It is commonly known that Hawking suffered from ALS, amyotrophic lateral sclerosis, which is a progressive neurodegenerative disease that affects nerve cells in the brain and the spinal cord. It typically leaves the patient paralyzed, as it did in Hawking’s case. To speak to his celebrity, his wheelchair recently sold for 300,000 pounds at auction (Rawlinson).

We could, as one scientist has, hypothesize that there are some undiscovered particles that are able to travel superluminal (Gonzalez-Mestres). This is not unheard of, but don’t wait for the proof to come any time soon. Peter Higgs hypothesized about a particle that was the glue holding other, larger (yet still sub-atomic) objects together back in 1964. While firmly proved by mathematics, he had to wait until 2012 for the physical proof (Arbey). The outlook for this is promising, however. At CERN’s LHC (Large hadron collider), it was revealed that certain neutrinos have been recorded at slightly over 300,000 kilometers per second

We should consider that some scientists do not believe that anything can exceed the speed of light (Harris). This is the generally accepted hypothesis, because as your speed increases to near-light speeds, your mass also increases exponentially. If you were to reach the speed of light, it’s thought that your mass would become infinitely large. When we are talking about subatomic particles, that’s not really a big change. But imagine if your mass were to increase exponentially and became infinitely large. You would require one hell of a diet. There is currently no explanation for reducing mass once your speed decreased to sub light speed, but there are plenty of opinions.

It’s a wonderful thing to watch this argument being bandied about, and most interesting to see opinions change because of new information.

In conclusion, the text delves into the intriguing realm of black holes and the associated information paradox. By questioning the fate of information within a singularity and examining differing perspectives, the author prompts contemplation on the intricate nature of these cosmic phenomena. The ongoing discourse, fueled by scientific advancements and hypotheses, keeps the enigma of black holes alive in the pursuit of understanding the universe's most captivating mysteries.

Works Cited

1. Gonzalez-Mestres, L. 'Cosmological Implications of a Possible Class of Particles Able to Travel Faster than Light.' Nuclear Physics B - Proceedings Supplements, Volume 48, Issues 1–3 (1996): 131-133. Print.
2. Hawking, Stephen. Black Hole Entropy and Soft Hair. Cambridge, UK: Cambridge University, 2018. https://arxiv.org/abs/1810.01847. pdf.
3. —. The Information Paradox for Black Holes. scholarly article. Cambridge, UK: University of Cambridge, 2015. https://arxiv.org/pdf/1807.05864.pdf. pdf.
4. Ouellette, Jennifer. 'Why Stephen Hawking's Black Hole Puzzle Keeps Puzzling.' Quanta Magazine 24 March 2018. https://www.quantamagzaine.org/stephen-hawkings-black-hole-paradox-keeps-physicists-puzzled-20180314.
5. Siegel, Ethan. 'The Black Hole Information Paradox, Stephen Hawking's Greatest Puzzle, is Still Unsolved.' Forbes 29 March 2018. https://www.forbes.com/sites/startswithabang/2018/03/29/the-black-hole-information-paradox-stephen-hawkings-greatest-puzzle-is-still-unsolved/#13926ce91c66.