[AndroidNeox (OP)]

If I put a mirror stationary (relative to the platform) near a black hole

How do you define, "near a black hole"?

Outside the event horizon somewhere, but deeper in the gravity well than is the light source.

As the experiment shows, and the Shapiro Delay confirms, light cannot travel from any point in space to an event horizon in finite time. How are you defining two points, stationary WRT each other, to be "near" each other when light cannot travel from one to the other in finite time?

The light is not traveling to the event horizon.  It goes to the mirror and back.

How are you defining distance?

I didn't specify any distance.

Yes, in the experiment the light goes to the mirror and back. But, if the event horizon is a finite distance from the platform then, if the mirror is lowered into the event horizon, the light beam will cease to be reflected when the mirror reaches and passes into the event horizon. The length of rope would be finite.

But, as the experiment makes clear, an infinite length of rope must be paid out for the mirror to reach the event horizon.

[AndroidNeox (OP)]

I did this diagram to help make the thought experiment easier to visualize:
https://photos.app.goo.gl/2BqU6nZW85oToXw77

All sorts of invalid conclusions can be drawn from invalid premises.
The picture shows an infinite strength rope which can be shown to violate special relativity.  You cannot lower a mirror to an event horizon even in principle.

Anyway, the mirror is depicted as having not yet arrived there, so the rope has finite tension on it, and it works.  So long as the winch is not moving the mirror, the scenario pretty much is what I'm talking about.  The picture says the winch is moving at some constant rate, and that means the mirror is not stationary, so a redshift will be observed at the platform because the path is getting longer.  Relativity has something to say about exacty how redshifted that light will be, since it will not be a constant redshift like you would get for a mirror moving away but not into a gravity well.

This is a correctly structured thought experiment. If you study Relativity you'll learn about Einstein's train that travels near and even at the speed of light. The physical constraints of normal matter are not relevant in thought experiments. The mirror is just a metaphor to identify a point in space where the light beam is imagined to reverse direction. The entire experiment is set up to make conceptually clear how a light beam behaves in a gravity well.

The Doppler redshift due to the motion of the mirror is fixed and finite. Because its finite it is insignificant compared to the infinite blueshift/redshift due to gravity.

If you accept that the blueshift of the light beam down to the event horizon will be infinite then you must accept that infinite time must pass at the light source before the front of the light beam can reach the event horizon.

[AndroidNeox (OP)]

Yes, in the experiment the light goes to the mirror and back. But, if the event horizon is a finite distance from the platform then, if the mirror is lowered into the event horizon, the light beam will cease to be reflected when the mirror reaches and passes into the event horizon.

Agree with all that.

The length of rope would be finite.

That depends how it is measured.  Using Schwarzschild coordinates, yes, it would be finite.
The rope is stretched due to tension and also contracted due to dilation, so using the rope as a measurement isn't the best tool.

But, as the experiment makes clear, an infinite length of rope must be paid out for the mirror to reach the event horizon.

That's using different coordinates than Schwarzschild coordinates then.

I don't use the Schwarzschild coordinates because the Schwarzschild Radius, Rs, is not a unit of distance through space. Rs is the apparent radius at which an event horizon would form if viewed from an infinite distance. The fact that it takes longer for light to travel from 3 Rs to 2 Rs than it takes to go from 4 Rs to 3Rs shows that it's not a measure of distance in space.

The fact that it takes light infinite time to travel from 2Rs to 1Rs means nothing can ever fall to an event horizon. This is because the Shapiro Delay is infinite.

[Halc]

This is a correctly structured thought experiment. If you study Relativity you'll learn about Einstein's train that travels near and even at the speed of light.

Einstein did not posit a train moving at light speed.  Near isn't the same, since it is in fact stationary, not moving at all in its own frame.  I'm moving at near light speed right now, just in a different frame than the one we typically use.

The physical constraints of normal matter are not relevant in thought experiments.

Which is why I said 'even in principle'.  One can communicate faster than light with such a rope.  I can build an infinite energy engine with such material.

The mirror is just a metaphor to identify a point in space where the light beam is imagined to reverse direction.

That is all fine.  I didn't have a rope either.  I just said the mirror was stationary, and somewhere outside the event horizon.

The entire experiment is set up to make conceptually clear how a light beam behaves in a gravity well.

We're not measuring the light beam in the gravity well, so I'm not sure how your experiment demonstrates how it behaves in there.  The answer is very dependent on how the light is observed down there, but you're not observing it at all.

The Doppler redshift due to the motion of the mirror is fixed and finite. Because its finite it is insignificant compared to the infinite blueshift/redshift due to gravity.

It isn't infinite anything if the light doesn't reach the event horizon.  If it does, nothing is reflected, so there is no light observed at all coming back, shifted or not.

You say the mirror motion is fixed and finite, and you measure it by counting winch revolutions of your hypothetical unstretchable rope.  I can allow that I think, but I don't think you ever reach the black hole using such coordinates.

If you accept that the blueshift of the light beam down to the event horizon will be infinite

You have no observer specified, so I cannot accept this.  Our observer is on the platform and any relativistic shift is undone by the return trip.

I don't use the Schwarzschild coordinates because the Schwarzschild Radius, Rs, is not a unit of distance through space. Rs is the apparent radius at which an event horizon would form if viewed from an infinite distance. The fact that it takes longer for light to travel from 3 Rs to 2 Rs than it takes to go from 4 Rs to 3Rs shows that it's not a measure of distance in space.

Depends who's measuring the time, but yes for that distant observer.  I tend not to put too much stock into non-local measurements.

The fact that it takes light infinite time to travel from 2Rs to 1Rs means nothing can ever fall to an event horizon. This is because the Shapiro Delay is infinite.

And yet gravity waves from objects falling in cease abruptly as the event horizon is crossed.  Sounds like it falls in to me.  If the time to fall in was infinite, the gravity waves would get slower and fade (redshift) to nothing after a while, don't you think?  Not claiming to be able to answer this myself.  The signature of the waves was predicted, so people smarter than me computed that before it was ever witnessed.  It was one of Einstein's falsification tests.

- - -

How is any of this relevant to the stationary (not being lowered) mirror that doesn't reach the event horizon?  Yes, it blueshifts (in the frame of the mirror) on the way in, and redshifts on the way out.  Net shift is zero.

[David Cooper]

What?

are you telling me that  " If I put a mirror stationary (relative to the platform) near a black hole, the observer on the platform will see his own reflected light coming back the same frequency as it left. "

If this hasn't been resolved yet, the answer's yes. The observer will see no change in the frequency. Indeed, the frequency of the light does not change at all on any part of its journey down to the mirror and back. The light's frequency is perceived as being of higher frequency by observers lower in the gravity well due to their slowed functionality, but the light's frequency has not gone up - extra waves cannot be inserted into the signal to increase the frequency. In the same way, on the return journey the light's frequency does not go down - it remains constant at all times.

[In a theoretical case where the mirror is at the event horizon rather than any higher up, then the light will reach it at the same frequency as the light had when emitted (assuming that it's possible for light to reach the event horizon, though we needn't discuss that issue here), but it won't be able to make the return journey out, so it cannot return to the mirror, therefore demonstrating that this example is not the kind of case Halc was discussing where he made it clear that light was returning to the mirror).

[AndroidNeox (OP)]

And yet gravity waves from objects falling in cease abruptly as the event horizon is crossed.  Sounds like it falls in to me.

No, they don't. In fact, the ringdown of merging black holes lasts longer than predicted and does not show an abrupt termination. It fades but does not present an abrupt cutoff.

[David Cooper]

The fact that it takes light infinite time to travel from 2Rs to 1Rs means nothing can ever fall to an event horizon. This is because the Shapiro Delay is infinite.

And yet gravity waves from objects falling in cease abruptly as the event horizon is crossed.  Sounds like it falls in to me.  If the time to fall in was infinite, the gravity waves would get slower and fade (redshift) to nothing after a while, don't you think?  Not claiming to be able to answer this myself.  The signature of the waves was predicted, so people smarter than me computed that before it was ever witnessed.  It was one of Einstein's falsification tests.

We haven't observed gravity waves from objects falling in, but from black holes merging and their event horizons warping from two spheres into one sphere. While the maximum speed anything can move at an event horizon may be zero both outward and inward (and the rest of this paragraph will be based on that assumption), the event horizon itself can move at any speed up to c and take any material that might be stuck at the event horizon with it, so there can be a rapid rearrangement of shape which reveals nothing about whether anything has crossed an event horizon. The speed of approach of two event horizons to each other may slow down in the final stages as they get closer and closer together, but only if you're tying them to the material stuck with them, but their proximity to each other will actually increase the local energy density and make the real event horizon migrate to enclose the entire gap between the two old event horizons, this merger capable of propagating at c.

[guest47899]

The fact that it takes light infinite time to travel from 2Rs to 1Rs means nothing can ever fall to an event horizon. This is because the Shapiro Delay is infinite.

And yet gravity waves from objects falling in cease abruptly as the event horizon is crossed.  Sounds like it falls in to me.  If the time to fall in was infinite, the gravity waves would get slower and fade (redshift) to nothing after a while, don't you think?  Not claiming to be able to answer this myself.  The signature of the waves was predicted, so people smarter than me computed that before it was ever witnessed.  It was one of Einstein's falsification tests.

We haven't observed gravity waves from objects falling in, but from black holes merging and their event horizons warping from two spheres into one sphere. While the maximum speed anything can move at an event horizon may be zero both outward and inward (and the rest of this paragraph will be based on that assumption), the event horizon itself can move at any speed up to c and take any material that might be stuck at the event horizon with it, so there can be a rapid rearrangement of shape which reveals nothing about whether anything has crossed an event horizon. The speed of approach of two event horizons to each other may slow down in the final stages as they get closer and closer together, but only if you're tying them to the material stuck with them, but their proximity to each other will actually increase the local energy density and make the real event horizon migrate to enclose the entire gap between the two old event horizons, this merger capable of propagating at c.

I gravitated towards your suggestion that the merger of two black holes is the result of one BH coming to rest atop of a second BH. I envision this as an Oreo cookie, one cookie (BH) on top, the other cookie (BH) on the bottom, with a cream filled center. The resulting gravity wave comes about as the top BH and the bottom BH when merging, push/compress the crème filled center (their respective gravity fields) outward in their merger to create a singular identity. Please excuse my simplicity. 

[AndroidNeox (OP)]

Einstein did not posit a train moving at light speed.

Wrong. Einstein noted that if his train moved faster, he would see the clock tower clock move more slowly and if it went at the speed of light, the clock would appear to slow to a halt.

Which is why I said 'even in principle'.  One can communicate faster than light with such a rope.  I can build an infinite energy engine with such material.

Wrong. If you learn how to set up relativistic thought experiments you'll learn that the only physical traits you are allowed to idealize are those that do not alter the outcome of the experiment. As I explained, the rope and mirror are metaphors to show the point of reflection of the light beam.

The answer is very dependent on how the light is observed down there, but you're not observing it at all.

Wrong. There needn't be an observer at the mirror. If you want to set up a different experiment and place an observer at the mirror, that's fine. I didn't do that because this setup is simpler and reveals the result I was trying to find.

It isn't infinite anything if the light doesn't reach the event horizon.  If it does, nothing is reflected, so there is no light observed at all coming back, shifted or not.

This thought experiment uses what is called "reductio ad absurdum". I begin by assuming that a Schwarzschild black hole is possible and that it is possible for matter to travel to the event horizon. Then I show that this is impossible because it would require infinite time. Because anything that cannot happen in finite time is impossible, I conclude Einstein was correct that black hole event horizons are impossible.

You say the mirror motion is fixed and finite, and you measure it by counting winch revolutions of your hypothetical unstretchable rope.  I can allow that I think, but I don't think you ever reach the black hole using such coordinates.

Correct. Nothing moving at a finite speed can travel to an event horizon in finite time. Not light and certainly not anything moving slower than light.

You have no observer specified, so I cannot accept this.  Our observer is on the platform and any relativistic shift is undone by the return trip.

I don't really care if you understand it or can accept it. It is a fact of causality that the light beam cannot have an infinite sequence of light waves until after the source has generated the light waves. If you aren't able to apply conservation of energy (gravitational blueshift/redshift) and causality to solve a physics problem, I can't help you.

[yor_on]

" I ran your assertion into a contradiction "

?
You mean that I'm wrong, right :)
Good on you, now you just have to convince the rest of the physics community.

Let this rest