If we cannot see past the event horizon of a black hole, how do we know how big the black hole actually is?

We currently use orbital mechanics to estimate the mass and radius of black holes – this basically involves inferring the mass/radius of the black hole by observing the motion of objects (i.e., stars) around it. This sounds good enough in principle, but it's important to remember that we don't really know if our current laws of physics hold at extremities like inside a black hole as things are masked behind the event horizon. Our current calculations assume the validity of general relativity at these points.

This is an example of where a theory of quantum gravity would be needed. Until we figure that out (if we ever do), I suppose our current estimations will have to suffice.

The flow of time

Objects traveling at speeds lower than the speed of light (3 x 10^8 m/s) experience the flow of time. While that flow of time may be relative (i.e., an organism living on a planet with a gravity which is much stronger than Earth's would experience the ticking of time at a slower pace relative to a human on Earth), it still does flow.

Objects traveling at the speed of light (i.e., light itself) do not experience the flow of time. The Lorentz transformation describes how space and time coordinates change between two inertial (non-accelerating) references frames. This transformation is just written as t' = t / sqrt(1 - (v/c)^2). In the case where v=c, the denominator becomes 0 (the Lorentz factor becomes undefined). This means that from the perspective of an object traveling at v=c, time dilation becomes infinite. This mathematical result is consistent with the principle that no massive object (an object with a mass greater than 0) can reach or exceed the speed of light. As an object approaches the speed of light, its relativistic mass increases, and the amount of energy needed to accelerate it further approaches infinity. So, while we can't directly show the experience of timelessness mathematically for an object traveling at the speed of light due to the undefined nature of the result, we can deduce it based on the behaviour of the Lorentz transformation.

Entropy is a quantity which seems to play an important role in the dimension of time. Entropy describes the order of a system. If a system is highly ordered, it is referred to as being in a low-entropy state. If there is a lot of disorder in a system, then it is referred to as being in a high-entropy state.

As the universe expanded and cooled down, matter and energy spread out, leading to an increase in entropy (as things became more disordered). The second law of thermodynamics states that in a closed system, entropy tends to increase or remain constant, but it never decreases. Now it's technically possible for a system to spontaneously move toward a lower entropy state at any given moment, but the law of averages state that that overall entropy in the universe will increase. This means that entropy tends to increase with the arrow of time pointing forward. If you find yourself in an environment with decreasing entropy, then just know that you're moving backwards in time!

published: 11/02/24 by kaan evcimen