It’s all relative as you fall headlong into a black hole

Physics is seriously cool sometimes. And weird. Want to live longer? Albert Einstein knew how. Move into a house at sea level and don’t go up hills or tall buildings. Seriously. Time runs slower on the ground.

Albert Einstein lecturing in 1921 - after he'd published both the Special and General Theories of Relativity. Public domain, via Wikimedia Commons.
Albert Einstein lecturing in 1921 – after he’d published both the Special and General Theories of Relativity. Public domain, via Wikimedia Commons.

The phenomenon is a consequence of Einstein’s General Theory of Relativity, which supplanted Newton’s theory of gravitation and states that time dilates in gravitational fields. The closer you are to the source of gravitation (treated as a point-source in the centre of the planet you’re standing on) the slower time goes.

Cool, isn’t it.

Of course, here on Earth the effect is pretty small. GPS satellites typically gain 45 nanoseconds daily at their orbital distance. Proving Einstein was right…again. And how cool is that?*

Zip across to the centre of the Galaxy though, visit the 4.3 million stellar mass black hole, and you could see for yourself.  What’s a black hole? It’s a mass, at least 1.4 times that of the sun (‘Chandrashekar’s Limit’), that has collapsed into a ‘singularity’ whose escape velocity exceeds the speed of light. The radius where that happens is known as the Schwarzchild radius, or ‘event horizon’, and is the effective diameter of the black hole. On it, time stops. Inside, Einstein’s equations solve to nonsensical answers – and space-time curvature becomes infinite. A ‘singularity’.

For a long time it used to be thought that anything that fell into a black hole would never escape, because nothing can exceed lightspeed.

The Horsehead nebula, Barnard 33, as seen by Hubble. Wonderful, wonderful imagery.
The Horsehead nebula, Barnard 33, as seen by Hubble. Wonderful, picture. Why is it here in this post? Just because. Click to enlarge.

Weirdly, though, stuff CAN escape. Quantum superposition tells us  that the position of a particle on an event horizon is uncertain. It is both inside and outside. When the probabilities collapse to one or the other, some actually are outside. In other words, black holes radiate. It’s why tiny ones evaporate. The phenomenon was discovered by Stephen Hawking and (inevitably) is known as Hawking radiation.

So what would it be like to fall into a black hole? Let’s suppose you survived the tidal forces. (Black holes, being very small but hugely massive, have a wicked gravitational gradient –  r-i-i-i-i-i-p.)

First off, you’d be swan-diving with huge acceleration – hitting the speed of light at the event horizon. Anybody looking at you from outside would see you redden as wavelengths of light reflected off your body were stretched by Doppler effects. The longer the wavelength, the redder it is. Eventually the reflected light would be red-shifted to the radio spectrum and below.

But if you were still detectable as you reached that event horizon, you’d never be seen to enter. Time stops there, relative to an external observer, thanks to gravitational time dilation. So you – and everything else the black hole ever ‘swallowed’ would appear to be frozen there for eternity.

Not that you would notice. On the contrary, as you accelerated towards the black hole, you’d be slammed by wavelengths that were being shortened – blue-shifted – by your velocity. They would climb through blue to ultraviolet, x-rays and gamma rays. Nasty. And you’d see the universe apparently moving ever-faster as your own relative time slowed down as a function of your velocity.

See what I mean about Einsteinian extreme physics being weird in an everyday sense? And after that…well – we don’t know. Even Einstein’s physics break down inside a black hole. All sorts of things have been imagined, usually exotic ‘wormholes’ – Einstein-Rosen bridges.

Actually…nobody knows.

What’s more, I’m not keen to find out – not personally, anyway. Are you?

Copyright © Matthew Wright 2013

* If you’re curious, the equation is as follows, where t0 is the ‘slow reference frame’ time, tf is ‘fast reference frame time’, c is the speed of light, r is the distance from the centre of the gravity field, G is the gravitational constant  – it’s 6.67384 × 10-11 – and M is the mass of the object.

t_0 =  t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}}

Just saying. My niece calls me Uncle Sheldon, I can’t think why.

13 thoughts on “It’s all relative as you fall headlong into a black hole

  1. My favourite of Einstein’s theories (that has also since been proven) is that a gravitational field can even influence light, making it possible to see stuff that’s actually behind other stars. I read about that in high school and remember thinking that’s so cool. The time-thing as well. Of course, another way to prevent aging is moving very fast. The closer you get to the speed of light, the slower time progresses, doesn’t it? Though one has to wonder at the guys aboard the ISS. Are they ageing slower because of the speed they’re travelling, or faster because of their distance from the earth’s gravitational core?

  2. Redshift… Blueshift… When Einstein rode his beam of light into a new understanding of reality, he towed behind him an entire paradigm shift! Had he ridden into a black hole, let’s hope his hitch would have held lol. Personally, I prefer to keep all my molecules in the same timezone. Thanks for writing so clearly and engagingly about a topic that usually causes brain-shift into the dreaded dimension of ‘what-the-?’ 🙂

      1. Definitely! I often assign myself little ‘thought experiments’ to let my brain grind away on (generally) while I’m busy concentrating on something else. I check in occasionally to see if there’s been any progress and/or to revise the parameters. Usually after 2-3 days (don’t know the neurological basis for the specific time frame, but it’s fairly consistent)… Poof! The connections formalize and I’ve got a working solution. I remember feeling so validated when I learned that Einstein’s had given his own form of brainstorming the same vocabulary. Up to that point, I’d had the nagging feeling that I was just being weird. Ok, so maybe I still have that nagging feeling, but at least now I can say I’m in good company lol. I can’t believe how many ideas you come up with! With all those idea balloons floating around, careful you don’t drift off over the Pacific 😉

        It’s a shame that now everyone spends their public transit commutes bent-necked over their little screen worlds. Frightening what we would have lost out on if Einstein had had an iphone! His musings about speeding trams and clock towers bring a whole new meaning to “watching time tick by.”

  3. Ah, where would sci-fi writers be without those handy wormholes to get characters from one side of the galaxy to the other!

    I chuckled at a scathing comment on the Doctor Who site recently, deriding the poor science in having a gold arrow pierce the hull of a spaceship and make it go faster. Quite ridiculous, they said. (But a wooden box that can travel through space and time? Apparently that’s perfectly acceptable!)

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