OER: ... a short distance above the horizon ...

To and from "a short distance above the horizon", the times are always finite, all you get is an extreme case of gravitational time dilation.

At zero distance above, the trampoline must fall in too so the thought experiment must assume an impossible situation before it creates a contradiction.

The version of this that I've seen before replaces the trampoline with a mirror and reflects light from it. The resolution is the same.

I corrected "infinitely many days" into "almost infinitely many days" in response to your criticism since this is what I had had in mind.

Now only a consensus remains between us, dear George. Right?

You need to correct to "almost infinitely" in paragraphs 3 and 4 as well and "The horizon has now become unreachable" is no longer true, it becomes "almost unreachable".

Make those extra changes and we have consensus, there is no contradiction and the large delay is similar to the plot theme in the movie "Interstellar" as you say, and the TV program "Andromeda", the script writers could choose any delay they like from almost none to almost infinite.

OER: overlooked the time-reversal-symmetry

No, the total delay can be thought of as part on the inwards trajectory and part on the outwards return but there is no universal definition of simultaneity that can be applied to say how much occurs on each part. It is only the total on the return to the starting point that matters and that is an invariant proper time. In addition, when falling in, gravity assists but when returning it acts against the engines so the situation is far from symmetrical.

Dear George:

I am very grateful for this dialog, but your attempt to defend the usual "equal rights interpretation" of the two time scales is unfortunately mistaken.

The outer-universe time is everywhere virtually the same, compared to the almost infinite delay that an object or observer suffers near the horizon. The trampoline argument reveals an 77 years old blunder in physics.

For example, no horizon ever got finished in the history of the universe, even if the latter were unbounded. Or would you contradict me here?

OER: I am very grateful for this dialog, but your attempt to defend ...

I am not "defending" anything, just pointing out that there was an error in your thought experiment and discussing the consequences of correcting that by adding "almost".

OER: ... the usual "equal rights interpretation" of the two time scales is unfortunately mistaken.

Ok, so you are saying UTC is not valid because it runs slower than the clocks on the GPS satellites, and slower than time in the rest of the universe between galaxies. I see no justification for that so there is no "blunder", you just have to take gravitational time dilation into account where appropriate.

I see no reason why the proper time of an infalling observer should be considered any less valid than that of a remote observer.

OER: For example, no horizon ever got finished in the history of the universe, even if the latter were unbounded. Or would you contradict me here?

I follow the science and in this case I think (YMMV) that the best way to look at that question is on a Penrose Diagram. On that, the past light cone of any observer outside the horizon runs parallel to the horizon itself hence we can say without dispute that the horizon can never be observed from a distance. Physics IMHO is about what is observable, but a ship that sails over the horizon still exists even if we can no longer see it.

The problem has always been that in the science that we call modern, we still think of things that can go back in time.  Unless all the conservation laws are just general rules time travel is not possible.  This means that time can not stand still for someone while it goes forward for others.  It can not slow down or stop at all unless the conservation of mass and energy are just jokes. 

Otto,

Thank you for pointing out one more place that the ridiculous science has shown us things that are not true.  When we stop letting the math show us the way and start leading with science instead of math we will find our way again.

When we set limits that are limitless or stopping points that do not stop we are just pointing out how little we truly understand.  At times I feel like I am back in the time of the middle ages where spirits and essences ruled the world.

There are many ways to point out how some of the science is not and could not be correct.  I like the point of reference issues that we tend to ignore and Otto has pointed out so well in this example of reference frames....

  Say that one is setting at the north pole, your friend is on mars, you have a friend on the equator, and one on a ship orbiting the earth at a vary fast speed and a vary far distance from the earth say ten thousand miles.  By the science today every single one of these people will measure a different mass for the orbiting ship.  The problem is that with respect to the person at the pole and the one at the equator and the ship that is orbiting in synchronous orbit they are not moving with respect to each other.  So the person on mars that measures different masses for these objects is just using the old science of the day to show how wrong the science is today?  

Otto, Thank you.        

Dear George.

I did not get which statement of mine you consider unacceptable for you. Thank you.

None are unacceptable.  I think you are saying things that are correct.  Are you speaking of Mr Dishman?

I thank both Georges, but my question had been directed to the George without the added E.

OER: I did not get which statement of mine you consider unacceptable for you.

Otto, my objection is to your provocative use of the word "blunder" to describe an understanding of the nature of time and space which is accurate, what you call the "equal rights interpretation".

If we met to have a drink in a pub and I walked to the bar and got the round in while you stayed in your seat, when I rejoin you, I will have aged less than you. The reason is that a watch on my wrist will measure the length of the path I took through spacetime while your watch measures your path. Each measurement is correct for the wearer.

The UK astronaut, Tim Peake, spent some months on the ISS and recently returned to his family. The paths are more complex but the same principal applies, the gravitational time dilation at altitude simply alters the proper time measurement of the path he took. Your example is a more extreme version of that scenario in terms of the numbers but is no different in principle.

Otto,

I think your use of the word Blunder is correctly placed.

Dear George D: We have not the slightest dissensus. You are repeating my argument.

Right, I don't think there's any technical disagreement. That's why "blunder" was not appropriate.

I have interest in this question but not being an expert in the field I am not sure of exactly what the problem is.  I will explain why and ask for clarification to my thinking. 

As I understand it the mistake is in the claim that the two time courses of an astronaut’s downfall onto the horizon of a stellar black hole – two days in proper time vs. almost infinitely many days in outer time, are both equally valid points of view. But they are not and the correct point of view is that it takes an infinite amount of time to fall into a black hole.  Is this the point?

The point is that it takes an infinite amount of time in outer universe time, and that the shorter astronaut time has no physical reality in the whole universe. For talking about something that may or may not happen after an infinitely long future (since for example another black hole may come along and pluck the frozen astronaut from this one) is irreal.

So almost everything the textbooks teach in theorem form about black holes is, unfortunately, based on a logic blunder.

And Oppenheimer and Snyder are responsible with their elegant mathematics: A tragedy.

Dear George D, what do you say here? Did I open up a new wound?

I don't know what you mean Otto, from what you've said, as far as I can see, there is no difference in our understanding of the science.

Thank you very much! 

Being eager to make sure I understand and teach this idea correctly, I have a followup question. Perhaps the greatest discovery in the past year is the binary black hole merger detected by LIGO.  The LIGO detectors are in outer universe time, correct? If so how can LIGO ever observe two black holes merging? Would this not take an infinite amount of time?  Even if Oppenheimer and Snyder were correct, in my mind this is still a problem. Since the entire gravitational wave community is comfortable with detecting mergers, it obviously is allowed.  So my head hurts trying to reconcile this with the fact that to us it should take an infinite amount of time to occur.  

First dear George:

I am  happy that you agree that never so far in the history of the universe did any particle reach the horizon of a black hole.

Second, dear Joseph:

Even unfinished black holes have properties very close to those of finished ones - this follows from Birkhoff's very intuitive theorem which says that when you have matter inside a given radius around a prospective black hole, this object behaves for all practical purposes as if the matter in question had already reached a smaller radius since from the outside there is no difference.

What this means for the dynamics of mergers is open. My hunch is that the matter in-falling onto the smaller "almost black hole" (a term I introduced in 1998) is getting "deviated" from their own prospective center of attraction so as to "switch over" to the stronger one. Hereby, a manifold needs to be crossed along which neither attractor acts on the particle in question. I consider it possible (as a conjecture) that this unstable manifold extends indefinitely towards the outside world. If so, the whole matter in-falling onto the smaller black hole would be re-injected into the outer universe. 

But this is but a conjecture at the time being. It, by the way, shows that Hawking's idea of "evaporation" re-emerges in a qualitatively (but not at all quantitatively) related fashion.

I thank Tobias Winkler for a discussion.

OER: I am  happy that you agree that never so far in the history of the universe did any particle reach the horizon of a black hole.

Nowhere did I agree that Otto, I didn't comment on that aspect at all.

What I said was this:

GD: If we met to have a drink in a pub and I walked to the bar and got the round in while you stayed in your seat, when I rejoin you, I will have aged less than you. The reason is that a watch on my wrist will measure the length of the path I took through spacetime while your watch measures your path. Each measurement is correct for the wearer.

That is the basic "Twins Paradox" version based on movement only. The next paragraph extended it to the gravitational case but the same logical argument:

GD: The UK astronaut, Tim Peake, spent some months on the ISS and recently returned to his family. The paths are more complex but the same principal applies, the gravitational time dilation at altitude simply alters the proper time measurement of the path he took. Your example is a more extreme version of that scenario in terms of the numbers but is no different in principle.

Both times are valid, but each time is valid only for the person carrying the watch.

I don't think your thought experiment differs from those, nor does the conclusion. If we agree that science, did I miss something in your logic?

Thank you , George, for making it clear that you had only the ordinary twins paradox in mind and not the gravitational one.

So what is your answer to the trampoline situation: When will the astronaut reappear outside?

Otto, the chaps at the bar was the SR version, the Tim Peake example is the gravitational version. He goes to the ISS for a few months then returns and his watch shows a different elapsed time from one that he left on Earth. Both times are equally valid, one for him and the other for his family. You trampoline experiment is no different from that in principle though the magnitude of the time difference is of course much greater.

OER: When will the astronaut reappear outside?

The time difference depends on the mass and how close he gets to it so I can't give you a numerical answer. It is however going to be a finite time.

Yes, it is a finite, near-infinite, time. We agree.

And what follows?

A party to celebrate his return?

After twice (almost) infinitely many years?

After a finite number.

Dear George - of course.

I am most grateful to you for your insisting.

To me and maybe others, the impossibility of a single horizon ever having formed even in an infinitely old cosmos, is a most interesting insight.  For if you and everyone else continue being unable to object, something is wrong with the kingdom of Denmark.

Right? Do you come over?

I am doing my own investigation into the nature of black holes so until I get some answers from that, I'll not comment on that aspect.

What I am absolutely sure of is that the only time of physical significance is the proper time in the (possibly infinitesimal) frame of the physical process being described. "Equal rights" as you put it is valid, and the finite proper time for a spaceman falling through the horizon is as valid for him as the near-infinite time he appears to take even to approach the horizon as seen by an outside observer.

This also applies in cosmology, there is a cosmological event horizon and what happens in galaxies beyond that cannot ever impact our existence. Equally, from the point of view of a scientist in one of those galaxies, it is we who are and always will be beyond their horizon, yet time still passes for us.

The blunder I have seen many people make is the intuitive idea that there has to be some universal concept of time, that is not valid.

Dear George:

You gave a perfect example for the common logic blunder I tried to expose.

Maybe a RG discussion is not sufficient to get this clear (although  I already once profited a lot from a clarification of yours regarding the intensity of the background radiation).

My point is very simple. Do you agree that the in-falling time as seen from the outside is infinite?

And: Do you agree that if there were a trampoline right above the horizon, the return time seen in the external universe would be twice almost-infinity?

If you agree to both answers, I can continue. My hunch is, however, that you do not agree. And that would be very important for me to understand.

Otto, there are subtleties involved but let's gloss over them for a moment just for the sake of argument. This is an over-simplification but for the moment let's see where you want to go:

OER: Do you agree that the in-falling time as seen from the outside is infinite?

It is unbounded but the past is always a finite duration. For the moment though, take that as a "yes".

OER: Do you agree that if there were a trampoline right above the horizon, the return time seen in the external universe would be twice almost-infinity?

No I don't, but can we agree that the time is finite? Saying "almost-infinity" for a finite number is meaningless and will only create confusion.

Saying "twice" is also probably meaningless BTW since the time of the impact with the trampoline in the distant observer's coordinates is ill-defined. In general the return will take a lot longer than the in-fall time but that's dependent on your choice of coordinates.

George:

It is not clear to me whether or not you agree that the astronaut returning after twice two days (say) re-arrives on the outside after twice "very very very many" days, Do you?

OER: It is not clear to me whether or not you agree that the astronaut returning after twice two days (say) ...

No Otto, I don't agree with "twice" anything.

The astronaut going from the ground to the ISS is moving upwards while a passing free-fall object moves downwards. His trip takes some time, say two days. Now on the return he passes free-fall object and both are moving downwards. If he is moving at the same speed relative to the free-fall objects, then his return trip must take less time than the upward trip, less than two days, so the total is not twice the duration of either. For your total of four days, it might be three days on the upward trip but just one day downward (in reality the numbers are much closer of course but you get the idea).

@Otto

The question is does any body really believe that there is infinite time dilation at the event horizon?

That means that a black hole cannot accrue mass (false), two black holes cannot merge (false), the ring down of gravitational waves from that merger is instant (false), etc etc etc.

The maths off GTR can be re-analysed without the infinite recurring terms. This results in a new equation which agrees with time dilation in sat-nav systems i.e billions of experiments a day. Importantly it also agrees with the experimental gravitational red shift of the K alpha lines emanating form the accretion discs in close proximity to the event horizon of a black hole.

The answer to your question is 2 days of proper time is equivalent to 3 days of event horizon time. Specifically the time dilation is a factor of 1.5 at the event horizon.

Surprised, well this has been published, in a highly reputable journal (see below).

Both time frames are proper time frames to the observer and the in-falling object are the same. But the observer will perceive a slowing of the clock  in  the gravitational field very much as we observe with the slowing of time we see near the Earth in sat- nav systems.

Article Finite Gravitational Time Dilation In Black Holes Using Dyna...

Here is the paper.

Fact is that the infinite time dilation at the event horizon does not in reality exist.

Its just a quirky paradox of the maths of GTR 

These along with other paradoxes can be lifted by reformulating the maths

Einstein did not predict the existence of black holes, in fact he denied their existence in a paper published in 1936, Simply because that would imply the existence of singularities, with infinite density and zero time passage at the event horizon.

The force of gravity in General relativity  (GTR) is thought to come form the curvature of space-time.

Unfortunately the maths of GTR implies infinite curvature and zero time passage at the black hole event horizon  and the black hole becomes a singularity- and yet the black hole has a radius.

The Misner Wheeler Thorne interpretation partially resolved this in  that the singularity rests inside the event horizon.

But yet another paradox arises if time stops at the event horizon (frozen star) no matter would fall in hence  black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon, hence the firewall.

The solution is to alter the maths of GR.

Additionally GR falls down in a number of areas, so any new maths should also resolve these problems

Yes GR works in the weak fields of the the solar system, and Intermediate

fields of neutron stars. 

1). It produces infinite density singularities in the very strong fields

such as in black holes.

2).It does not necessarily explain dark matter in galaxy cores where we

know super-massive black holes exist and the galactic dark matter

therein,

3). It does not explain dark mater present in galactic halo's,and galactic

clusters such as the bullet cluster,

4).It does not explain the presence of cosmological dark matter as a whole.

5). It has not yet been fully corroborated by the studies of neutron stars

and in black holes.

6). It does not easily explain the presence of dark energy and cannot be

translated in quantum gravity.

7). It predicts that time stops at the event horizon

Here I enclose a number of publications which explain all of these

phenomena, whilst agreeing with the results of GR where it has been

thoroughly tested.

1).First to obviate the infinite density singularities.

1a)

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)

https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the

galaxy.

2a)

https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the

galactic halo.

3a)

https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation

damping ) and is corroborated by black hole studies.

5a)

https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).

https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

7). It does not offer infinite time dilation at the event horizon

https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg

Article Finite Gravitational Time Dilation In Black Holes Using Dyna...

Article An advanced dynamic adaptation of Newtonian equations of gravity

Article The formulation of Dynamic Newtonian advanced gravity, DNAg

Article Advances in Black Hole Gravitational Physics and Cold Dark M...

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

Article An advanced modification of dynamic gravitation

Article Corroboration of Dynamic Black Hole Gravitational Physics fr...

Article String quintessence and the formulation of advanced quantum gravity

Thank you,Andrew, for this impressive learned summary of current knowledge and convictions.

The Oppenheimer-Snyder trampoline cuts in here as a playground that can be fully understood independently of the state of learnedness of the reader.

All of the above views will have to stand the test of this example. I am sure you will not contest this statement, right?

it is rare to be confronted with such a litmus test. Thank you for having seriously entered into the discussion of the trampoline.

In short the down and up journey are time symmetric. But the time dilation will be at maximum a factor of 1.5 at the event horizon - so not  almost infinite  days

Dear Andrew: Your statement is at variance with accepted views and so. for example, with the movie "Interstellar" - right?

Can I mention this continuation?

https://www.researchgate.net/post/Logic_Blunder_regarding_Black_Holes_collectively_maintained_over_77_Years_Can_anyone_make_the_Resolution_palpable_to_the_disgraced_Physics_Community#57a4428e93553bcd1f7d57c3