{"id":487,"date":"2016-04-01T07:19:52","date_gmt":"2016-04-01T07:19:52","guid":{"rendered":"http:\/\/mrbiggs.net\/ron\/?p=487"},"modified":"2016-04-01T07:19:52","modified_gmt":"2016-04-01T07:19:52","slug":"the-event-horizon-a-cosmic-mirage","status":"publish","type":"post","link":"https:\/\/mrbiggs.net\/ron\/?p=487","title":{"rendered":"The event horizon – a cosmic mirage"},"content":{"rendered":"

Black holes – or more specifically, their event horizon – are a cosmic mirage.\u00a0 Not much different from a rainbow.\u00a0 Oh, they\u2019re real alright, I\u2019m not talking about leprechauns with the pot of gold at the end, but the way we experience them is totally different from the thing itself.\u00a0 There is no such thing as \u201cfalling though the event horizon\u201d because the \u201cevent horizon\u201d is precisely only our experience of it.<\/p>\n

Contradictions in last episode<\/strong><\/p>\n

The interesting thing about scientific inquiry is you\u2019re never satisfied with your answers.\u00a0 Answers always lead to contradictions, things that don\u2019t make sense, new questions.\u00a0 I had answered how something can accelerate to light speed in a black hole\u2019s pull.\u00a0 But what if it doesn\u2019t?\u00a0 What if some daring astronomer constantly decelerates himself as he comes closer and closer to the event horizon, constantly making sure he\u2019s both aiming for dead center, and making a nice slow descent?<\/p>\n

Now you could counter by saying that if you didn\u2019t let yourself freefall, the G forces would tear you to shreds.\u00a0 But here comes the complicating factor.\u00a0 Supermassive black holes exist which have relatively weak gravitational force at the event horizon.\u00a0 A black hole with a radius of about one light year, for example, would have a gravitation at its event horizon equivalent to here on Earth\u2019s surface (aka 1G).<\/p>\n

Not so coincidentally, if you were to accelerate for about a year at 1G, you would reach what I call nominal light speed \u2013 which is your actual speed if you accelerated to light speed in a simplified Newtonian universe\u00a0 That just happens to be 0.618c (0.618 the speed of light) \u2013 which is exactly the proportion of the golden rectangle (?) \u2013 but we\u2019ll save this tidbit for later.\u00a0 The question right now is how is such weak gravity at an event horizon even possible?\u00a0 Aren\u2019t black holes supposed to spaghettify us and tear us into subatomic shreds and stuff?<\/p>\n

What\u2019s an event horizon doing with such, well, EARTHLY gravity?<\/p>\n

Wait, what?<\/strong><\/p>\n

Yes, that\u2019s right. \u00a0\"radius<\/a>Supermassive black holes have very low gravity at their event horizon.\u00a0 It\u2019s a simple formula, really.\u00a0 The radius of the event horizon is the inverse of its acceleration \u2013 i.e. gravity.\u00a0 r*a is the same for each and every black hole.<\/p>\n

I could do some extra wizardry to show you the math, but you have the internet for that.\u00a0 Small black holes pull really hard on that photon to whip it in a circle.\u00a0 Large black holes can take their sweet time.\u00a0 And here\u2019s the fun part – if you were to free-fall into a black hole \"radius<\/a>\u2013 ANY black hole \u2013 from somewhere outside its influence, you\u2019d accelerate to the speed of light.\u00a0 Ve <\/sub>= velocity at event horizon = c (speed of light).<\/p>\n

But the twisted logic that happens at that event horizon remains the same.<\/p>\n

A lesson on geodesics<\/strong><\/p>\n

Well, how do we wrap our minds around that?<\/p>\n

\"black<\/a>

The non-euclidean geometry (geodesics) of a black hole, as discussed in our previous post<\/p><\/div>\n

For that we have to delve into the world of geodesics.\u00a0 And first in that, a beef.\u00a0 I don\u2019t like the term \u201cgeodesics.\u201d It conjures up hippy domes in the middle of the desert.\u00a0 I prefer the term \u201cnon-Euclidean geometry\u201d.\u00a0 It easily tells us\u00a0we\u2019ve left the familiar world of ancient geometers with their simple circles and triangles on a flat surface, and are falling down the rabbit-hole (so to speak) of curved spaces and planes.<\/p>\n

And that\u2019s what we need to know to understand a blackhole.\u00a0 It\u2019s how we can picture Einstein\u2019s theory of relativity.\u00a0 If you\u2019ll recall from my last post, this 3D well describes the spacetime around a black hole \u2013 how it curves down into an infinite well.<\/p>\n

There\u2019s a few things going on in that diagram, so we\u2019ll try to take it a bit at a time.<\/p>\n

The thing to remember about this well is, it\u2019s not like gravity is pulling everything down it.\u00a0 It mainly describes how light, a massless particle that always travels in a perfectly straight line, can still seem to bend.<\/p>\n

Now there\u2019s difference in the specifics of how light and massive entities\u00a0 fall towards a gravitational center.\u00a0 But what\u2019s the same is the acceleration.\u00a0 Here on Earth, we are constantly accelerating towards it at 9.8m\/s2<\/sup>.\u00a0 And light is no different.<\/p>\n

Even though it travels in a straight line.<\/p>\n

And that\u2019s my second beef with \u201cgeodesics\u201d\u00a0 – the definition of a straight line as the closest distance between two \u201clocal\u201d (i.e. \u201cclose\u201d) points.\u00a0 That\u2019s a bit of a copout, like saying \u201cwell we\u2019re reducing this to a map\u201d.\u00a0 I prefer the term \u201cno sideways pull\u201d.<\/p>\n

\"plane<\/a>

The (air)plane rotates, twisting the (geometric)plane it’s on, and then lifts into a turn. Get it?<\/p><\/div>\n

But let\u2019s go back to our analogy of the plane from last chapter.\u00a0 There\u2019s rudderless planes out there.\u00a0 By just rotating the plane with ailerons, and using the elevators in back, you can turn every which way without ever having sideways pull.\u00a0 Just rotate the plane, and go up or down.<\/p>\n

So if you look at what makes the plane \u201cturn without turning\u201d, the factor here is \u201cwhich way is up\u201d.\u00a0 As it rotates, it changes that \u201cupwards\u201d direction, and then goes up or down in that upwards direction.<\/p>\n

And BTW, this works equally for spaceships in zero gravity.\u00a0 So gravity has nothing to do with which way is up.\u00a0 In more complicated math, it\u2019s called \u201corthogonal\u201d which is defined as the perpendicular to the plane.\u00a0 This allows us to pile on more dimensions.<\/p>\n

But we\u2019re here to discuss black holes, not study math.\u00a0 So let\u2019s translate this \u201cupness\u201d into black holes. \u00a0\"earth<\/a>Compare Earth\u2019s gravitation of a beam of light \u2013 a1<\/sub> \u2013 and compare it with a REALLY massive black hole, whose acceleration near the event horizon is less than at Earth\u2019s surface.<\/p>\n

As a light beam approaches earth, it enters Earth\u2019s gravity, changing its \u201cupness\u201d and starts to \u201ccurve\u201d around Earth.\u00a0 What causes the curve is the \u201cupness changing\u201d.<\/p>\n

Now, compare that to a supermassive black hole.\u00a0 By the time you\u2019re near the event horizon (as seen by this incredibly drawn cut-out) you\u2019re practically vertical.\u00a0 But there\u2019s not much \u201cupness\u201d left to change.\u00a0 You\u2019re just being whipped around in what seems like a flat surface, in a very large cylinder, \u201cupness\u201d pointing directly into the middle.<\/p>\n

Any way you look at it, it\u2019s the speed of light<\/strong><\/p>\n

The problem though, with such small scale cutouts, is they conveniently leave out just how far we\u2019ve come to get to this \u201cvertical space\u201d in the supermassive black hole.\u00a0 As I hinted earlier, before we get to this spot in a supermassive black hole, we\u2019d have been freefalling literally for years and years.<\/p>\n

But what if we decided not to freefall?\u00a0 What if we got some theoretical rocket thrusters and slowed down our descent, so we avoided being anywhere near the speed of light at the event horizon?<\/p>\n

Einstein\u2019s Theory of Gravitation<\/strong><\/p>\n

The answer is it doesn\u2019t matter.\u00a0 Because how would you do that?\u00a0 You would manually accelerate yourself in this gravitational field.\u00a0 If you did the same manual acceleration outside a gravitational field (i.e. deep space), you would go from 0 to light speed.\u00a0 So no matter what your behavior is around the event horizon \u2013 hovering, freefalling, or some combination of the two (i.e. orbiting) \u2013 you\u2019d be at near light speed.<\/p>\n

This is what Einstein is talking about, that we experience a spacetime dilation in a gravitational field, even if we\u2019re hovering\/standing\/using rocket thrusters.\u00a0 The spacetime dilation is basically equal to the sum of acceleration from deep space to whatever surface you\u2019re at.<\/p>\n

Back to where we started<\/strong><\/p>\n

Which takes us back to the incredible shrinking black hole, except this time we take it a step further.\u00a0 In the last post, we talked about the fact that a black hole shrinks away from any object approaching it.\u00a0 But just how?\u00a0 We don\u2019t want to just WATCH something fall into a black hole, we want to KNOW what it\u2019s like.\u00a0 We want to BE whatever it is that falls in.<\/p>\n

Well, considering we nixed any realistic possibility of crossing the event horizon with strange tricks, let\u2019s pretend\u00a0 we\u2019re freefalling directly to a black hole\u2019s heart.\u00a0 And orbits are boring.\u00a0 We want to go straight in.\u00a0 So we have this craft that doesn\u2019t try to resist gravity, and doesn\u2019t let us slip to the right or left.\u00a0 And we\u2019ll start well outside a nice supermassive black hole, about 1 light year diameter.<\/p>\n

The best way to picture this is pretend we\u2019re falling in a Newtonian universe, and at periodic intervals, we\u2019ll recalibrate to allow for how spacetime changed around us.\u00a0 Don\u2019t worry, if someone gives us flak for this, just tell them delta apporoaches zero.\u00a0 If it doesn\u2019t shut them up, send them my way.<\/p>\n

If you were to freefall to what you think is the event horizon, you\u2019d hit what you\u2019d think was light speed in a Newtonian universe \u2013 i.e. \u201cnominal light speed\u201d, or to put it another way, Newtonian velocity = momentum divided by mass = light speed (v=p\/m=c).\u00a0 So let\u2019s take our new bearings.<\/p>\n

Distance to center is still r.<\/p>\n

Actual relativistic speed is now ?c (~.618c).<\/p>\n

At ?c, distances shrink to ??.\u00a0 So the radius of the new black hole is r*??.<\/p>\n

Time also dilates to ?(1+?) for those outside of you, but we don\u2019t care about them, so that\u2019s kind of irrelevant.<\/p>\n

Recalibrate your instruments for your new reality, and freefall AGAIN to \u201cnominal light speed\u201d \u2013 the speed you\u2019d reach at the new event horizon at r*??.<\/p>\n

Distance to center is now r*??.<\/p>\n

Except now you\u2019re at ?c compared to where you were before, or basically, your momentum doubled from your starting point.\u00a0 You\u2019re at\u00a0 ?c compared to your last point.\u00a0 Or, to put It another way, Newtonian velocity is twice the speed of light (p\/m=2c).<\/p>\n

New event horizon is now r*?.<\/p>\n

\"freefall<\/a>

While “light speed” is maximum, momentum is infinite. Here’s how momentum compares to the relative size of an event horizon. You would even out where the event horizon was ?? times the distance from the singularity as you are.<\/p><\/div>\n

And so on, in the grand progression of the golden rectangle.\u00a0 The ultimate equation is that y=r*a\/ ?0.5(x-1) <\/sup>. Where y is your Newtonian velocity (momentum\/mass) and x is the radius of the black hole.<\/p>\n

Here, you know what?\u00a0 Let\u2019s draw a graph.<\/p>\n

Notice there\u2019s no time here.\u00a0 Acceleration is whatever it is to get you to the light speed you\u2019d reach at event horizon.<\/p>\n

How far down do you want to go?\u00a0 How much can your imaginary ship take?\u00a0 How infinitely fast do you want to go?\u00a0 How far do you want to escape those boring confines of flat spacetime and see the universe from the perspective of the infinite?<\/p>\n

That is what it\u2019s like to fall down that well.<\/p>\n

\u00a0<\/sub><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Black holes – or more specifically, their event horizon – are a cosmic mirage.\u00a0 Not much different from a rainbow.\u00a0 Oh, they\u2019re real alright, I\u2019m not talking about leprechauns with the pot of gold at the end, but the way we experience them is totally different from the thing itself.\u00a0 There is no such thing […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[5],"tags":[293,294,297,296,299,301,298,295,300],"_links":{"self":[{"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=\/wp\/v2\/posts\/487"}],"collection":[{"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=487"}],"version-history":[{"count":1,"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=\/wp\/v2\/posts\/487\/revisions"}],"predecessor-version":[{"id":495,"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=\/wp\/v2\/posts\/487\/revisions\/495"}],"wp:attachment":[{"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=487"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=487"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mrbiggs.net\/ron\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}