Black Holes#
A boundary to the universe#
Why should you care about some fuzzy black hole photo? For the first time in human history, humans have indisputable proof that the universe has boundaries and that other dimensions exist. And that has not only scientific implications, but philosophical ones as well.
Event Horizon Telescope Collaboration
Despite strong evidence for the existence of black holes, until yesterday I was always seriously dubious. The equations are fascinating, but the implications were too strange and frightening. But it's hard to doubt something I see with my own eyes. I poured over the research methods, hoping for a flaw or trick or misrepresentation, but found nothing.
The photo is a compilation radio image of the plasma surrounding a supermassive black hole created from an interpolation of data points collected from a global array of radio telescopes. Or more fundamentally, it's a picture taken by an Earth-sized telescope. It seems legitimate.
But if black holes exist and confirm the predictions and models for general relativity, it means that gravitational time dilation is true. This is far scarier than the time dilation related to velocity. There is a divide between speeds close to light and our normal life. We don't move very fast relative to our environment or each other, so don't ever observe substantial distortions of time.
But a black hole is just a place. It's somewhere you could actually go. Yes, the M87 black hole is far away, but that's irrelevant. Shanghai is far away too, but it's there whether I have access to an airplane or not. And if you go to the x, y, z locations where any of the millions of black holes in our own galaxy reside, you can leave the universe.
Imagine moving toward a black hole that is not rotating and is much smaller than the one in the photo. Imagine this black hole is 25 times the mass of the sun and is close enough to reach in a lifetime at subluminal speeds. There may be many such black holes matching this description.
You can easily calculate the diameter of the event horizon (the "black" part of the black hole). It's a strangely tiny 150 km across. Assuming you were protected from radiation and tidal effects, you wouldn't notice the collapsed star until you were nearly upon it, because the effects of time dilation only increase rapidly when very near the event horizon.
But you would eventually know something was wrong as you approached. Because your local time would slow down, you would perceive the time of distant points moving progressively faster. First, the discrepancy would be hours, then days, then years, decades, millennia and eons. Assuming the survival of the universe into the distant future, before you crossed the event horizon, you would see stars streaming across the sky, nebulae forming and evaporating, galaxies whirling, morphing and colliding. Unimaginable ages would blur past in fractions of seconds until you crossed the boundary.
At the instant you reached the event horizon, your local time will have stopped. This logically infers that all possible time will have passed in the universe - similar to how a velocity of zero implies an infinite amount of time required to reach any distance.
Before reaching this place in space, you were a part of the universe. But inside the event horizon, you have moved past the end of time, regardless of how long time may last. It sounds like nonsense, but the very same physical equations which predicted the structure of the black holes we see in the images, also predict this disturbing behavior of time.
This fuzzy orange photo means that this "nonsense" is a reality. For sure now. Let that sink in. Philosophically, this has multiple implications that I haven't worked through yet. But what is immediately obvious is that if the universe has a boundary, there must be at least one other dimension of which our universe is a subset.
With the numbers#
This concept is easier to understand if you drop a dimension to visualize it. A sphere has no boundary on it's surface. You can move through latitudes and longitudes, but will never reach an edge. The only edge is up, which requires a third dimension. Likewise, a three dimensional universe may only have a boundary if it exists in a fourth dimension.
A fourth dimension allows all kinds of fantastic phenomena, like movement over vast distances in an instant without moving through the space in between. It allows a four-dimensional being to observe multiple places simultaneously and perceive the interior of objects in seemingly impossible ways. It has implications concerning the nature of time, because the boundary of the event horizon isn't only a boundary of space. What does it mean to experience all time as now? We can't even imagine it, but the verification of black holes, and the confirmation of general relativity demands that we try.
You can play around with time dilation yourself by adjusting the mass of the black hole M and the distance of the observer from the event horizon r in the following equation: \(t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}}\). The mass of the sun is \(1.989 × 10^{30} kg\), \(G\) and \(c\) are constants and \(t_f\) can be set equal to 1 unit of time (to represent any time unit in a system outside the gravitational influence of the black hole). The radius of the event horizon is called the Schwarzschild radius and uses a related equation: \(r_s = \frac{2 G M}{c^2}\).
For instance, the event horizon radius for a 25 solar mass black hole is \(\frac{2*6.67 × 10^{-11}×25×1.989 × 10^{30}}{299,792,458^2}\) = 73,830 meters. The event horizon is 73.83 km away from the singularity. If we were to move within 50 km of the event horizon, we would be 123,830 meters from the singularity. If we use this value for r in \(t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}}\) we calculate a time ratio of 1 to 0.5962. This means that an hour-long event for the observer 50 km from the event horizon, would seem to take 35 minutes to a distant observer outside the gravitational field. It would also mean that a year-long event for a distant observer would seem to the observer near the black hole to take \(\frac{1}{0.5962}\) years or 1 year and eight months. The time difference grows more extreme with increased mass or decreased distance.