Daryl Janzen, a Professor of Astrophysics & Philosophy, has an intriguing essay which asks-
'What if black holes never actually form?'How confusing inevitability with reality built decades of paradox'
Black holes are among the most captivating and scientifically intriguing phenomena in modern physics, inspiring both scientists and the public alike.
It is because there is so much evidence that they exist that they captivate us.
But do they really exist?
Yes. At least, that's the best explanation we currently have for what Astronomer's observe.
What if they are only ever forming, never formed?
If, there is a boundary beyond which we can't deter further 'forming', then all we can say, empirically speaking, is that the thing has formed.
Currently, Doctors use various protocols to determine when a person has died. It may be, in the future, these protocols will be changed because 'signs of life' or viability for resurrection currently undetectable become observable. Moreover, some procedure exists to restore life.
Just imagine — what if the whole edifice of black hole physics is built on an invalid logical inference that’s gone unnoticed (or unacknowledged?) for the better part of a century?
This wouldn't matter if the existence of the thing is empirically observed. Suppose Sherlock Holmes finds a clue that suggest Moriarty will be at the Charing Cross Hotel to kill the Archduke at 9 pm. This turns out to actually be the case. Mycroft Holmes points out that Holmes's logic was faulty. All that could be validly deduced was that there was a strong likelihood that a member of Moriarty's organization would seek to carry out the assassination at a particular time. Sherlock might reply 'look, my logic was good enough to serve my purpose. My job was to save the Archduke. The fact that I was also able to capture Moriarty was a bonus. I guess, he underestimated me. He should have sent some minion to do the dirty deed.'
Inevitability is not actuality — that’s obvious enough.
But it will be. Moreover, if it applies to a class of objects, then it is likely that some actual cases can be found. There is no proof that everybody currently alive will die but there is a lot of evidence that everybody who lived more than two centuries ago did actually die.
Yet for sixty years physicists have ignored relativity’s most basic rule,
which is that there are no privileged frames of reference. I suppose one could say 'for human beings who can only move forward in time, that which is inevitable will have actual examples. Maybe there are other sorts of beings for whom this would not appear to be the case.' But this doesn't greatly matter because we have no means to stop being human and become some other type of being.
and we’ve taken for granted that the latter is implied by the former. Like fools walking around imagining we’re all dead because someday we’ll die, they look at the evidence that nothing can stop black holes from collapsing toward their horizons and imagine that a process which remains forever incomplete has already come to its end.
Death may be a longer process than we realize. A thousand years from now, they may have the technology to revive a corpse which has been dead for twenty years. What is certain is that, as far as we are concerned, death is both actual and inevitable. We think the same is true of existing black holes and things which will become black holes.
Consider the following. We build a spaceship with three items onboard: a hot cup of coffee, a thermometer to measure the coffee’s temperature,
at some point the thermometer won't be able to find any difference between the coffee's temperature and that of the ambient atmosphere. Better and better thermometers may extend that limit from, let us say, 90 minutes to 90 minutes and three seconds or 90 minutes and 3.000001 seconds, etc. etc.
and a clock that measures the arctangent of elapsed time since launch.
The clock will soon show Pi/2 radians. Better and better clocks will only be able to distinguish tiny increments on elapsed time. But they are a convergent series. Thus we can say with certainty that there is an upper bound.
The ship, which has perfect insulating walls, is launched — and through some future technological innovation it is capable of constant proper acceleration away from Earth for all time.A continuous signal is transmitted back to Earth, sending two pieces of information: the coffee’s temperature and the arctangent time.
Quite soon, they both have an upper bound- i.e. improving the clock or the thermometer only makes an infinitesimal increment. Still, this may be important for testing the predictions of some other theory.
According to Newton’s Law of Cooling, the coffee’s temperature will approach the ambient cabin temperature exponentially and asymptotically — meaning it will very quickly approach the cabin temperature, but it actually takes infinite time to reach equilibrium.
For any given clock and thermometer, 90 minutes is that limit.
Therefore, the temperature value sent back to Earth will exponentially approach a finite value, but it will only reach that value exactly in the infinite future.
But that won't be observable. Our equations are artefacts of our mathematic model but that model is not reality.
Since the elapsed time is sent back as its arctangent, that value will also asymptotically approach a finite value of π/2 in the infinite future.
But the elapsed time, for any given receptor, will have quite a small upper bound.
And since the ship will be forever accelerating, the signal that transmits this information will quickly become practically invisible due to redshift. However, in principle the signal will forever be received back on Earth, as the coffee gradually cools and elapsed time increases — all while the ship’s velocity asymptotically approaches the speed of light.
In other words, there is no need to bring in a spaceship. My cup of coffee too will only reach ambient temperature after infinite time, though no clock and thermometer, however advanced, will be able to show elapsed time as more than about 90 minutes.
People die. Coffee cools down. Black holes have formed and will form. That is what empirical observation teaches us.
, when the radius of a star collapses to the finite value of its event horizon, only a finite amount of proper time will have passed on a clock carried by a particle at its surface. These two values — the star’s radius and the elapsed time since it started collapsing — are approached in essentially the same manner as the coffee’s temperature approaches its asymptotic limit while the arctangent time approaches π/2.
In other words, black holes form as inevitably and ubiquitously as cups of coffee cool down. True, we may have a theory that says it takes infinite time for the boundary to be reached but that just means that any cut off we observe could be infinitesimally bettered if we had better tech. Thus, instead of saying the patient died at 3.02 AM, we may be able to say time of death was 3.0199999997 A.M.
And from the standpoint of external observation, the light emitted outwards from a collapsing star exponentially fades and quickly becomes invisible
in other words, the thing ceases to be observable- unless you are moving away from it at the speed of light.
— though in principle, no matter how long an external observer waits, they will forever “observe” that when the light they are now receiving was emitted,
there is no such light save in the case mentioned above.
the star still had not collapsed below its event horizon — just as the future civilization above will forever see that the coffee hadn’t yet reached equilibrium when the signal now being observed was sent.
No. Future beings won't be able to detect any difference in the coffee's temperature just like us. They won't see the black hole after we stop seeing it. Obviously, if an astronomer says 'there used to be light coming from this patch of the sky. Today, that light disappeared.' then his peers will understand that if the object is 3000 light years away, a particular object became a black hole 3000 years ago.
But regardless of which past events are observed now, we’d also like to know whether collapsing stars should be thought to have already crossed this observational threshold,
the moment you cease to observe them, you know that they became black holes x number of years ago where x is the number of light-years separating us from the collapsing star.
or if they are more accurately thought of as still approaching their event horizons.
If at 10 AM some light was received but none was at 10.01 AM then we know the thing became a black hole x number of years ago.
In essence, while the image of the star freezes and fades, we’d like to know: Do gravitationally collapsing stars really pass through their event horizons and form massive singularities in our universe?
Currently, that is the best hypothesis. In 2015, a massive star, designated N6946-BH1, that was expected to explode as a supernova was observed to disappear entirely, a phenomenon called a "failed supernova". The star's quiet demise suggests it collapsed directly into a black hole, and instruments like the Hubble and Spitzer space telescopes helped confirm its disappearance, say NASA scientists. It may
Or, do they instead remain forever collapsing towards their event horizons, approaching asymptotic limits in both radius and proper time just as, in reality, the coffee’s temperature approaches equilibrium with the ship’s cabin while the arctangent time approaches π/2?
The 'failed supernova' mentioned above is still detectable on the infrared frequency. Currently we think it is generated from stuff falling into the black hole.
General relativity is agnostic about which distant events are coincident with one another.
Not for inhabitants of this tiny planet. We have a common frame of reference. It's just that we finding 'simultaneous' some species on a planet far far away might not.
This is by design: whether or not any two particular events occur “simultaneously” is not supposed to have any objective meaning in standard general relativistic descriptions.
No. The thing is well defined for a local frame of reference- e.g. the one all mankind currently shares.
In principle, we can hear Lord Jesus deliver the sermon on the Mount. However, it is likely that there is a limit beyond which coherence is irretrievably lost.
What happens to an astronaut as he falls into a black hole? To an observer, the astronaut would appear to slow down and freeze at the event horizon, eventually fading from view completely. However the last photon to reach us will be so 'redshifted' as to only reach us much later. But this doesn't mean that we can't say 'in (2015 minus x, where x is distance in light years) such and such failed supernova became a black hole'.
The only thing external reality can ever know for sure is that when the information now being received left the star, it had not yet reached its event horizon.
Sadly we can't know anything for sure. The Universe may be a hologram.
Since no external event is ever causally connected to the horizon formation event,
so far as we know.
this is the only empirically valid claim that can ever be made.
For the moment.
Naming the fallacy
Empirical claims may be false. Logical claims may be fallacious. The question, for the former, is whether the best available information confirms them or, at the very least, does not contradict them. There may be a 'structural causal model' associated with the empirical claim or prediction. It may feature logical fallacies which it may or may not be worthwhile to correct.
The primary problem with the canonical picture of black holes emerging through gravitational collapse is one of metaphysical overreach:
if a problem is metaphysical, physicists need not bother with it. I suppose, since Janzen wears two hats- that of a philosopher as well as that of a physicist- he has a certain scruple which others need not share. I suppose a Theologian who is also a Physicist may have a different scruple. Why is God not being mentioned by the theory?
we infer one of two essentially different potentialities to be true while ignoring the other, even though both must remain forever unobservable.
One might say 'we can't point to the exact moment when Achilles overtook the tortoise, we can only say 'with current 'photo-finish' technology, this is our best guess of when that happened.' But this doesn't mean there is any fallacy in deducing that Achilles swiftly overtook the tortoise.
The inference is therefore scientifically illegitimate, unjustified metaphysics.
It is scientifically legitimate if the physics community overwhelmingly considers it to be so even if they also believe that the inference will be 'sublated' at a later date. Still, it may be some valuable Research Program is motivated by the scruple raised by Janzen.
This does not bear on the Penrose-Hawking singularity theorems themselves. Rather, the issue is with ontological overreach in drawing specific physical implications on the basis of these mathematical theorems.
Life involves 'ontological overreach'. How can we be sure we aren't already dead. Anyway, that's the reason I put off doing the washing up.
The theorems tell us that if certain energy and causality conditions hold, and if space-time is extended in a particular way, then geodesic incompleteness is inevitable. The upshot in the case of black hole singularities is that these must be a global feature of the space-time manifold.
In 1783, John Michell hypothesized 'dark stars' on the basis of Newton's theory. In 1916, Karl Schwarzschild found the first solution to Einstein's equations that described a black hole. But it was only in 1971 that the first strong evidence for a black hole was found in the X-ray source Cygnus X-1- which is now widely regarded as the first black hole identified.
But inevitability and actuality are not the same, and conflating them is a modal fallacy.
No fallacy arises where empirical evidence supports the existence of an object predicted by a theory. However, that empirical evidence might turn out to be wrong.
We might name this the tense-import fallacy
which isn't really a fallacy. It is merely a linguistic misunderstanding. But nothing of the sort arises here.
— or, more specifically, the present-tense import fallacy — the slide from atemporal mathematical features (event horizons, singularities) to present-tense claims about what has “already” occurred in our universe.
There is no such slide. What happened was that mathematical physics theorized a type of object which, many years later, empirical observation confirmed as actually existing. Mathematics is a separate language from that of Astronomy- which is concerned with objects existing in the cosmos. It turns out that black holes exist in the same way that galaxies exist.
The canonical interpretation of black holes as real, already actualised objects within our universe is tied to a deeply problematic view by which space-time manifolds, along with the individual events such as those in the regions “inside” event horizons — including singularities at r = 0 — physically exist.
One would only say so if one also felt that believing you are alive, and thus can do the washing up, is deeply problematic.
But the points in space-time should not be confused with physical reality.
Nor should an infinite series be confused with the passage of time as we humans experience it. Achilles really does overtake the tortoise because the distance between them is a 'converging sequence' till he overtakes it.
Rather, space-time should be understood as
a model or map. It isn't the actual terrain.
a set of events that happen in our existing reality.
No. Stuff that happens may, for some particular purpose, be given a mathematical mapping.
From this perspective, the manifold is a descriptive tool, not the fabric of reality itself.
No one has suggested otherwise. It is not the case that by manipulating a manifold we can turn into rabbits living on a planet in the Andromeda galaxy.
It does not have to be maximally extended in any ontological sense; it only has to describe the physical events that occur in our existing universe in its domain of applicability.
Such descriptions are either useful or useless. It is fair to say, the philosopher's 'domain of applicability' is different from that of the physicist. It may be that the scruple expressed by Janzen is motivating some potentially very useful Scientific Research Programs.
Janzen concludes thus
In a universe that continues to expand and undergo hierarchical structure formation, ultra-compact Kerr-like bodies will continue to merge and grow.
but we don't have to assume they contain actual singularities. Even if this is not the case, it is useful to have people working on theories which account for existing observations without the relevant assumption.
But from any external vantage point, each collision will always be observed in its pre-horizon phase. The observational future of the universe is
dependent on the compossibility of observation. It may be that everything really interesting about the Universe is essentialy unobservable. But it may still be very useful. Observation is like verification. A lot can be done- and the most interesting things may be of this sort- without either observation or verification savein the sense that a superior outcome becomes available.
thus not one of mergers between completed black holes, but of ever-larger, ever-more-compact collapsing objects whose horizons are approached only asymptotically from the outside universe’s perspective.
Emerson, grieving for his dead son, wrote in his essay 'Experience'- ' Was it Boscovich who found out that bodies never come in contact? Well, souls never touch their objects. An innavigable sea washes with silent waves between us and the things we aim at and converse with.' Emerson was aware of the new 'field' theories (which the Jesuit Boscovich may have learnt about from a translation of the Vimalakirti sutra. It turned out that the 'sea' which washes between us is composed of forces- e.g. electro-magnetism- which we can very profitably harness to our own ends. But, for now, death remains death and black holes remain black holes.
1 comment:
This is partly a semantic question. Are the dark objects that astronomy has inferred, still black holes if they don't actually have event horizons? If usage is dictated by the technical criteria of general-relativists, the answer is no, but if Janzen turned out to be right, popular usage might dictate a redefinition.
This question of event horizons shows up in Frank Tipler's Christian-transhumanist "Omega Point Theory". For his theo-physical teleology to work, there can only be one true singularity in the history of the universe, into which all information eventually falls. But in classical general relativity, there is also a singularity inside each event horizon that forms. So Tipler concludes that the cosmos-spanning robot civilization of the future must actively prevent all event horizons from forming!
Among the ideas in *quantum* gravity is a "membrane paradigm" due to Leonard Susskind (also called "black hole complementarity"), according to which the space behind the event horizon is actually just a scrambled description of the space immediately about the event horizon. It would mean that there's a description of Hawking radiation in which nothing ever crosses an event horizon, but instead just becomes part of the membrane hovering above it. I should think about how this relates to the purely classical debate that informs Janzen's remarks.
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