# If photons don't experience time then why can't they escape a black hole?

From the point of view of a photon released from the sun its reaches your eye in NO TIME AT ALL because photons do not experience time. From the point of view of you, it takes roughly 8 and a half minutes for the photon to travel the 150,000,000 km and reach your eye because from our point of view light travels at 300,000,000 m/s.

So if, as I understand it, a black hole, at its event horizon, pulls space towards it faster than the speed of light due to the fact that although you can't travel through space faster than the speed of light, space itself can stretch faster than the speed of light. Then this would explain why we can't observe any light escaping from the black hole.

However, from the point of view of the photon, that does not experience time, surely, no matter how fast space is being stretched it should be able to travel though space faster than this, because time does not exist to a photon. So from the photons point of view, it should be able to escape a black hole even though from our point of view it can't.

Are photons both escaping and not escaping from black holes simultaneously?

• Well, you will never see a photon escape. Not even if you live forever. And what does it mean for a thing that does not experience time to have a "point of view"? – Solomon Slow May 11 '17 at 15:50
• I think he means hypothetically if a photon could have a point of view. Or if a human could travel at the speed of light. – Brad S May 11 '17 at 17:11
• "From the point of view of a photon" - sigh... As has been stated here more times than I care to count, there is no point of view of a photon. This follows quite straightforwardly from the Lorentz transformation; an entity with speed $c$ in any inertial reference frame has speed $c$ in all inertial reference frames, i.e., a photon has no point of view, no frame in which it is at rest, no frame in which a ruler or clock is at rest with respect to it, no frame... sigh – Alfred Centauri May 12 '17 at 1:53

Speed of light:

Because from our point of view light travels at 300,000,000 m/s.

While it's certainly true that we see light traveling at $c = 3 \times 10^8 ~\textrm{ms}^{-1}$, it's equally important to note that it's not just us who see the light traveling at that speed. The speed of light is, in fact, invariant to any observer in the universe, regardless of how fast or slow they were themselves moving through the space.

Please see this link on Length Contraction and Time Dilation to know how scale of your measurements change at relativistic speeds.

Black Hole:

At its event horizon, pulls space towards it faster than the speed of light due to the fact that although you can't travel through space faster than the speed of light, space itself can stretch faster than the speed of light. Then this would explain why we can't observe any light escaping from the black hole.

You're right in the first statement. However, at the Event Horizon, a Black Hole doesn't pull the space (, time and matter) simply to stretch / expand it. It actually warps and shrinks the space (, time and matter) down infinitesimally to what is known as Singularity. The gravitational pull of a Black Hole at the Event Horizon is so strong that anything falling down would need a speed of more than $c$ to escape. And because even light itself can only travel at $c$, it would forever fail to escape the black hole once caught at / inside the Event Horizon.

Light escaping from the black hole.

There are a few things to consider here. So let's ignore light / photon for a brief moment.

Point of view of an observer falling inside a Black Hole:

An observer $O_{bh}$ falling inside a Black Hole would be subject to infinite Time Dilation caused by its immense gravity. Therefore, put simplistically, from the point of view of an external observer $O_{ext}$, it would seem that $O_{bh}$ is nearly stuck at the Event Horizon. However, this is not the same as $O_{bh}$ literally being stuck at the Event Horizon. $O_{bh}$ wouldn't feel anything special happening with their experience of time. They could theoretically still experience hitting the singularity in a finite amount of time.... if they can survive getting spaghettified first, that is.

Inside the Event Horizon:

Now, before getting to anything escaping a Black Hole, we can begin to ask what would happen to light / photon inside a Black Hole. As the following excellent Q&A would point out, anything falling inside a Black Hole must essentially forego its original state and be reduced to Singularity.

Can a sufficiently large black hole be singularity-free?

It's also important to consider that photons have a rest mass of zero. In other words, they can't ever be at rest. However, they interact easily with any other particles with mass, can get absorbed by such particles, and transfer their energy to them, and then that particle with mass can be made to come to a rest.

Now, the Black Holes are theorised to evaporate in a finite time via mechanism called Hawking Radiation, although neither has this been verified nor has enough time passed for any Black Hole in the universe to evaporate just yet. It can (possibly?) be argued that the Hawking Radiation may be emitted via / as photons, but it's too big a bite for me to chew upon!

However, with these pointers above, here's something that could be surmised on your primary question....

With two mutually contentious subjects:

(a) Infinitesimally small spacetime (Singularity), and

(b) No stillness for photons

It can't be said whether a photon remains a photon once caught in the Event Horizon of a Black Hole (even if it could escape as one later!). With that uncertainty, if we still consider the speculative case of a photon escaping the Event Horizon due to Hawking Radiation (again, being totally clueless about whether it's the same photon that fell into the Black Hole or a new one that was emitted due to radiation), the time that it would / could experience between its capture and escape (which would meaninglessly be zero, anyway) is not so much of a spot of bother as the other issues are.

Finally, as a closing text, you might perhaps like to read more on an unresolved problem in Physics, namely: Information Paradox.