[SimpleEngineer (OP)]

I watched a fantastic presentation on the BBC last night about the science of Dr Who, (a time travelling alien, worth a watch if you dont know it)

It explained a hell of a lot to me in nice laymans terms, but left me with a few questions

If a star collapses to a black hole and as time stops at the 'event horizon' (where the escape velocity becomes faster than the speed of light), we cannot observe the black hole due to it not releasing light, but due to time contraction as it approaches the event horizon, surely we could watch a star collapsing into one, in slow motion as such. Has this been observed?

If time stops at the event horizon due to gravitational forces 'bending' the light cone (or future possibilites) is there not a similar action around other gravitational masses? i.e. do we see comets 'slowing down' as they approach the sun.

Is time as we know it already affected by the sun, earth, moon and other planetary bodies? would this affect what we can learn about the speed of light? (i.e. are we subject to time dilation and record things slightly lower than a baseline?)

And finally, Dr Cox predicted the possibility of travelling to the past, using a black hole to 'turn' our future around so that our past becomes our future.. what limitations are there in the way of this being theoretically possible?

[David Cooper]

Is time as we know it already affected by the sun, earth, moon and other planetary bodies? would this affect what we can learn about the speed of light? (i.e. are we subject to time dilation and record things slightly lower than a baseline?)

Atomic clocks show up the effects of time slowing on the Earth compared to in orbit, so these are real, measured effects. They are fairly small though, even near the sun.

And finally, Dr Cox predicted the possibility of travelling to the past, using a black hole to 'turn' our future around so that our past becomes our future.. what limitations are there in the way of this being theoretically possible?

The worst problem would be the circular causality that would result. Having events cause themselves is probably impossible, so it may only be possible with an empty universe containing no events at all.

[evan_au]

do we see comets 'slowing down' as they approach the sun?

Comets are rather irregular and infrequent - and weren't even recognised as a periodic event until Halley predicted the return of Halley's comet.

However, the planet Mercury has been known since ancient times, and its orbit has been closely studied since the days of Kepler. It was noted in 1859 that the point of closest approach to the Sun deviated slightly from what Newton's laws of motions predicted. Einstein's theory of relativity identified time dilation as being roughly the right size to explain the discrepancy. See http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury

surely we could watch a star collapsing into one, in slow motion as such. Has this been observed?

A stellar-mass black hole is typically less than 100km across. You do not want to be within 10 light years of a supernova explosion, or your goose will be very thoroughly cooked. At this distance, the black hole is less than 1 pixel across on any conceivable telescope, so you could not resolve any details.
In addition, light from the stellar remnant falling into the black hole is rapidly red-shifted into radio wavelengths as it approaches the event horizon. Meanwhile, it is surrounded in all directions by a plasma so hot that it emits intense gamma rays, exploding into nearby space between the observer and the black hole. Seeing a dark and darkening object through this blaze of light is impossible with our current optical technologies.

It is possible that we could surround the imminent supernova with neutrino telescopes which may be able to produce some image of what goes on during a supernova - except that the matter collapsing into the black hole becomes dense enough to block and absorb neutrinos, producing the outward explosion.

Astronomers estimate the expected rate of supernovae in our galaxy, but it is much less than the observed rate. Some astronomers have hypothesised the existence of a "silent" black hole collapse, where an object collapses into a black hole without the telltale supernova explosion. In such a body, it may be possible to observe the collapse more closely. [...Assuming we manage to develop practical interstellar travel, and work out which stars are likely to collapse into black holes, and when... Avoiding getting cooked seems easy by comparison!]

[Bill S]

I watched the Prog on the BBC iplayer this evening; very enjoyable. Thanks for pointing it out SE.

A few points need thinking about before I attempt to comment or ask questions.

[Bill S]

…..time stops at the 'event horizon'

     


If what Dr Cox says is taken at face value, it must be that the entire accretion history of a black hole since the formation of its event horizon should be visible to any observer whose technology allows him or her to manoeuvre into the right position.  Of course, an observer will see these things by virtue of the light reflecting from them, but because the objects will not have crossed the event horizon, in the observer’s frame of reference, this should not be a problem.  Strange as this might seem, it is even stranger to realise that, outside the frame of reference of the observer, all this material is not there, because it has long since plunged down the ever steepening gravity well into the depths of the black hole; so how can light reflect off it?

This would also mean that any material not ejected into space in the supernova explosion would still be, in the frame of reference of an observer, forming an incandescent sphere at the event horizon.   

One has to remember that Dr Cox was presenting material in such a way as to make a particular point to a (largely) lay audience, so perhaps I am nit picking.  It could be that this situation is nothing more than a recurrence of Zeno’s paradox.  If we consider the situation from the point of view of the outside observer as an example of asymptotic decay, in which the infalling object is not simply stuck for ever in the same state, but is gradually vanishing, with its progress being recorded by an asymptotic curve, then, in theory, it would never actually vanish, but in reality, like Zeno’s arrow, it would come to a conclusion.  In other words, it would vanish.  This seems to be the simplest explanation, and the simplest may well be the best.         

[Pmb]

surely we could watch a star collapsing into one, in slow motion as such. Has this been observed?

A stellar-mass black hole is typically less than 100km across. You do not want to be within 10 light years of a supernova explosion, or your goose will be very thoroughly cooked.

A star that collapses into a black hole will not produce a supernova. That only occurs when the gravitational field is insufficient to over come the nuclear explosion caused by the compression of the collapsing star.

[David Cooper]

…..time stops at the 'event horizon'

I think he could have explained things a lot more clearly. If you could dangle a clock on a long string so that it is sitting at the event horizon, that clock would stop. If you send a clock across the event horizon at speed though, it will continue to tick, but viewed from outside the event horizon it will appear to stop and will fade to darkness so that there will be an eternal frozen image of zero brightness.

[Bill S]

Let’s look at the possibility of rotating an individual’s light cone so as to loop back into the past.      On a two-dimensional space-time diagram (One day I will find out how to put a diagram on a thread, but in the meantime, you will have to draw your own) a world line that loops back to meet itself in the past must at some point tilt at an angle of more than 45⁰ from the time axis, which would, of course, mean that the body of which it was the world line would be travelling at superluminal speed.  This unrelativistic situation can be circumvented if the light cones of the moving body can be tilted in such a way that, locally, the world line of that body never exceeds 45⁰. 

 Although this might look like cheating, it is, apparently, possible given that spacetime becomes, locally, sufficiently curved.  Such curvature could, in theory, be encountered close to a very massive body, such as a black hole; or could be created in the vicinity of one of Tippler’s infinitely long, rotating cylinders.  It seems that it could also occur in a Gödel-type rotating universe.

What does it mean to say that we rotate the light cone of an object?   Dr Cox demonstrates this in the case of a traveller who crosses the event horizon of a black hole.  Obviously this will not do in terms of returning to a past event, as the traveller is probably nearing oblivion.  The rotating cylinder, or rotating universe, would seem to present better possibilities. 

On the face it Tippler’s rotating cylinders seem the simplest model to consider; as long as we ignore the fact that they have to be infinite.  We can equate the fixed x/y co-ordinates of our space-time diagram to the whole of the Universe, and tilt the individual light cone, together with its local x/y co-ordinates, in the region of the rotating cylinder; this tilting being caused by the local curvature of spacetime. 

If on our spacetime diagram we draw a line at 45⁰ to represent “c” we can start by drawing the world line of a traveller, taking its local light cone with it as it approaches “c”.  Smoothly we take this world line round until it loops back on itself; eventually meeting itself in the “past” at what we will call point X. 

That wasn’t so difficult, was it?  Let’s not rest on our laurels yet, though.  In fact, point X is where our troubles start.

Before I dig myself further into a hole, I must run this past the experts to comment on it.

[dlorde]

…..time stops at the 'event horizon'

If what Dr Cox says is taken at face value, it must be that the entire accretion history of a black hole since the formation of its event horizon should be visible to any observer whose technology allows him or her to manoeuvre into the right position.  Of course, an observer will see these things by virtue of the light reflecting from them, but because the objects will not have crossed the event horizon, in the observer’s frame of reference, this should not be a problem.  Strange as this might seem, it is even stranger to realise that, outside the frame of reference of the observer, all this material is not there, because it has long since plunged down the ever steepening gravity well into the depths of the black hole; so how can light reflect off it?
...
If we consider the situation from the point of view of the outside observer as an example of asymptotic decay, in which the infalling object is not simply stuck for ever in the same state, but is gradually vanishing, with its progress being recorded by an asymptotic curve, then, in theory, it would never actually vanish, but in reality, like Zeno’s arrow, it would come to a conclusion.  In other words, it would vanish.  This seems to be the simplest explanation, and the simplest may well be the best.

Yes; as I understand it, light can reflect off the infalling object until it reaches the EH. Beyond this point, all light paths lead to the singularity. However, as the object approaches the EH, the external observer sees it slow, but the reflected light is red-shifted proportionally, so just before reaching the EH, the reflected light takes an extremely long time to emerge and it's frequency will be shifted far into the long wave radio spectrum. So the very last reflected light takes forever to emerge and has an infinitely long wavelength. Or something... []

But in terms of infalling objects being represented on the EH, there is the Holographic Principle, that says that the information content of a volume of space can considered to be encoded on the 2D boundary of that space, so that for a black hole, the information content of whatever it has absorbed is encoded on its event horizon and isn't lost, resolving the black hole information paradox.

[Bill S]

If we look at our diagram; those of us who drew one; we can imagine that the two versions of the traveller, when they part company at point X, may not both have to travel round the loop.  The younger version has to go round the loop, but the older one is, presumably, free to go off in any direction. 

The younger one must go round the loop, and must meet a younger version of herself at point X, and that younger version must always have been there.  Now we have a problem: The “self” who has just completed the loop, left point X to go round the loop, so she cannot now leave point X in any other way, nor can we say that she has to go round the loop again, because there is no “again”.  The younger self left point X to go round the loop, so she must always leave point X to go round the loop, but however many times we think of this as happening, there is in fact only one occurrence.  Above I said that the older self might not have to go round the loop, but when we stop and think about this we realise that she must have been round the loop in order to be at point X as an older “self”, so she would not be free to frisk off anywhere else.  It seems that none of this makes any sense, at least, not in a single Universe, unless, perhaps, it is the static, timeless universe of Julian Barbour; in which case, at point X, we would have an “infinite” accumulation of selfs, all of whom would actually be one self, and each of which would set off to travel round the loop, but all these departures would be just one departure. 

If all this sounds utterly ridiculous, do not despair, because it is just possible it could all be persuaded to make perfect sense if only we had more universes in which to manoeuvre, but somehow I doubt it.  Alternatively, it might also make sense if we could really grasp the concept of infinity, instead of having to try to understand it within the confines of our four dimensional cosmos.  Infinity must dispense with the exigencies of time and space.  As with Barbour's "Platonia", everything simply "is" now; movement, be it from A to B, or round a closed time-like loop, is an illusion, as is change of any sort.   

When I suggest that change is an illusion I certainly do not mean that it is unreal in our frame of reference.  Our reality is reality.