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Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: AndroidNeox on 14/11/2018 19:12:06

Title: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 14/11/2018 19:12:06
Suppose you have a Schwarzschild black hole with an event horizon.

I presume that a light beam shone upward from an event horizon would be infinitely redshifted before it travels any distance above the event horizon. The redshift from an event horizon up to any point in space is infinite. This is because the gravitational potential energy difference between an event horizon and any point above the event horizon is infinite.

Conservation of energy requires that gravitational redshift is reversible. Infinite redshift up mean infinite blueshift down. The blueshift a light beam will undergo when traveling from any point in space to an event horizon is infinite.

Thought experiment: Place a laser at some point outside of the event horizon, stationary with respect to the black hole. Point the laser radially downward toward the center of gravity of the black hole. Turn on the laser.

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted. The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.

This is true no matter where in space the laser is located. Before light can travel from any point in space to an event horizon, infinite time must pass at that point in space. This is also true for every point in space that the light beam travels through on the way to the event horizon. Each of those points can be considered as a light source and infinite time must pass in those points before the light can travel to the event horizon.

If light cannot travel a path in finite time, nothing can. Not matter or energy or information.

It seems to me that this sort of reasoning could be why Einstein insisted black hole event horizons are impossible.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Bored chemist on 14/11/2018 22:05:24
"Is there an error in this relativistic thought experiment?"
Yes.

In principle, it is possible to cross the Event Horizon of a sufficiently massive black hole without noticing.

The change to an infinite blue shift happens at the singularity in the middle; not at the EH.

And we never get to see what happens there. We can safely assume that we shouldn't rely on the laws of physics as we know them.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 14/11/2018 22:36:21
You're wrong about light dilation. Light traveling from a point at higher gravitational energy to lower is blue shifted. It happens between Earth orbit and Earth's surface. It has nothing to do with any singularity.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: David Cooper on 14/11/2018 23:23:07
The solution is that the light never quite reaches the event horizon, but slows down to a near halt. The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands). The calculations that suggest that objects can cross the event horizon (and that light crosses it too) are based on the idea that clocks never really slow down, so objects are imagined to go on falling through the event horizon from their own point of view and continue on down to a singularity, but this could only happen after more than an infinite amount of time has gone by for the rest of the universe, which means there are no singularities yet and that all the stuff falling towards a black hole centre is frozen in place at the same distance from the centre as it was when it stopped at where the event horizon was at the time it stopped there. The black holes should evaporate away (due to Hawking radiation) before that material has a chance to move any further in, so in reality most of it can never reach the singularity, but perhaps the light can - as the black hole evaporates, the event horizon will migrate inwards as the energy density just outside the event horizon is reduced, so the light will get a chance to move a bit further in. At some stage when the event horizon disappears and the light is free to to go straight through what was the centre of the black hole, it will be shoot out the other side, liberated, never at any stage being infinitely blue-shifted.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 15/11/2018 01:31:58
The solution is that the light never quite reaches the event horizon, but slows down to a near halt.

Yes, this seems like the only explanation. The only thing it doesn't explain is why people think black hole event horizons can exist.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 15/11/2018 02:05:32
Suppose you have a Schwarzschild black hole with an event horizon.

I presume that a light beam shone upward from an event horizon would be infinitely redshifted before it travels any distance above the event horizon. The redshift from an event horizon up to any point in space is infinite. This is because the gravitational potential energy difference between an event horizon and any point above the event horizon is infinite.
Not because of that.  The gravitational potential between those two points is finite, but enough for escape speed to be c.  For it to be infinite would violate conservation of energy.

Quote
Thought experiment: Place a laser at some point outside of the event horizon, stationary with respect to the black hole. Point the laser radially downward toward the center of gravity of the black hole. Turn on the laser.

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted.
From the perspective of the point outside the EH, the beam never gets there.  I learned to envision a lot of this by exploring the Rindler horizon, which has most of the same properties. 

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The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.
Accelerate a ship at some constant proper rate, and shine a laser (why is a laser necessary?  Will not a candle do?) to the rear, and in the frame of the ship, the light will go only so far.  I suppose it blue shifts to infinity as you put it.  So at 1g of proper acceleration, this limit is just over a light year away, where there is a singularity with something like Hawking radiation and everything, but only in the frame of the accelerating ship.

The light does in fact get there, and beyond.  Rocks really do fall into black holes, with nothing unusual about the event.  No Hawking radiation observed by the rock for instance.  It just doesn't fall into the black hole in the frame of this distant observer is all.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: guest46746 on 15/11/2018 17:48:25
Disregarding all the reasons cited above, which are all mostly in unison, deter mining of the properties involved in the question may be of value.

If the beam of the laser is pointing downward into the BH, the laser beam is redshifted from the perspective of the observer. From the perspective of the BH, the laser beam is blueshifted via the oncoming beam and the force of gravity attraction from the BH, combined. Are the forces equal at this time?  Does the force of the BH's gravity in conjunction with the incoming laser beam create a blueshift that alters the redshift from the perspective of the observer to a blueshift? At what moment does the dual effect of the from the perspective of the BH, overtake the redshift of the observer?  Physic's at the event horizon may not and probably doesn't match anything we know. What is the dominant perspective? The BH's or the observers? my bet would be on the BH. lol

Can multiple forces working in conjunction overturn physic principles. In this situation can light be sped up to the point of where it alters the light spectum? can an infrared wave light be reversed into a gamma wave light by altering its wave length by force?  lol
Title: Re: Is there an error in this relativistic thought experiment?
Post by: guest4091 on 15/11/2018 18:21:36
By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted. The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.
What is the source of the unlimited energy?
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Bored chemist on 15/11/2018 19:48:46
The solution is that the light never quite reaches the event horizon, but slows down to a near halt. The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands). The calculations that suggest that objects can cross the event horizon (and that light crosses it too) are based on the idea that clocks never really slow down, so objects are imagined to go on falling through the event horizon from their own point of view and continue on down to a singularity, b
That very much depends on your perspective.
It's true from outside the hole.
But not true for the observer falling in.

"Observers crossing a black hole event horizon can calculate the moment they have crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon."
From
https://en.wikipedia.org/wiki/Event_horizon


You're wrong about light dilation. Light traveling from a point at higher gravitational energy to lower is blue shifted. It happens between Earth orbit and Earth's surface. It has nothing to do with any singularity.
I didn't say the light wasn't blue shifted.

I said that the infinite shift you are talking about is not observable from "outside".

Title: Re: Is there an error in this relativistic thought experiment?
Post by: David Cooper on 15/11/2018 21:11:25
That very much depends on your perspective.
It's true from outside the hole.
But not true for the observer falling in.

There is only one reality - if the material is evaporated away through the Hawking radiation process before it can progress beyond the point where the event horizon was when that material got stuck there, it cannot also go through an incompatible series of events in which it crosses the event horizon there and continues on down to a singularity. The calculations about it crossing the EV and continuing down to the singularity apply to a time beyond the infinite future for the black hole, and it's only a particular interpretation of GR in which no clocks are allowed to run slow where they are imagined to be able to take a shortcut into the future which can project them further forward into the future than the infinite. That would be an extraordinary trick to perform, but fortunately it doesn't have to do that because all that material will be destroyed (along with the black hole) long before it gets the chance, and that's something that hasn't been taken into account by the people who make claims about how material falls past the event horizon and on down to the singularity - they depend on the black hole lasting for an infinite length of time, and even then the material still can't move any further down towards the singularity, so it needs an infinite number of infinite lengths of time, and even that won't be enough.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Bored chemist on 15/11/2018 21:17:39
The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands).
If nothing ever falls in, how can it expand?
Title: Re: Is there an error in this relativistic thought experiment?
Post by: jeffreyH on 15/11/2018 22:52:09
There is a difference between information going into a black hole and information coming out. The escape velocity at the horizon equals the speed of light and points away from the centre of gravity. The clue is in the word escape. Things approaching the horizon will not slow down. Only the signals coming out from those objects slow down. This nonsense about objects never reaching the horizon needs to be shut down. It is simply wrong. Gravity accelerates objects towards the source. It certainly doesn't slow them down. It is the information sent out by the infalling objects that may give this impression.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Toffo on 16/11/2018 04:38:26
The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands).
If nothing ever falls in, how can it expand?

The black hole bends space-time. The stuff over the event horizon bends space-time some more.

The event horizon is a result of all mass in the neighborhood.




Title: Re: Is there an error in this relativistic thought experiment?
Post by: Toffo on 16/11/2018 05:13:33
The solution is that the light never quite reaches the event horizon, but slows down to a near halt.

Yes, this seems like the only explanation. The only thing it doesn't explain is why people think black hole event horizons can exist.

Near the center of a neutron star neutrons exchange gluons, the exchange process is slowed down by gravitational time dilation.

Then the neutron star pulls some matter out of a star. Now the gluon exchange process stops completely at some radius from the center of the neutron star. We have a event horizon there.  The event horizon is becoming larger as mass is moving towards the event horizon as the neutron star is shrinking.


(Hmm I guess neutrons do not actually repel by exchanging gluons. Well that's just a small error :) )

Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 16/11/2018 14:09:06
I didn't say the light wasn't blue shifted.

I said that the infinite shift you are talking about is not observable from "outside".
Nobody observes a blue shift.  The guy falling in looks backwards (or forwards to his buddy going in first) and sees both red shifted.  To see a blue shift, you'd have to be stationary and looking up.  That works on the surface of Earth, looking up to the signals from the orbiting stuff, but it doesn't work at the event horizon.  It isn't possible to be stationary there.  It isn't a valid inertial reference frame.

Am I right about that?  One can very much be stationary at the Rindler horizon, but the view from there (looking at the other observer that defines the horizon) is red shifted from both observers.  From the perspective of the outside observer, time does not pass for the observer at the event horizon, yet from the perspective of that (stationary) observer at the horizon, the first guy is red shifted.  Of course being stationary is the equivalent of an observer falling into a black hole.  To be equivalent to being stationary at the black hole, that observer would need to stay stationary relative to the accelerating frame of the first observer, and that perspecitive would make that first observer blue shifted (infinitely so).  So yes, I think I got it right.

Funny that one view has a red shift and the other a blue shift, but time is stopped for both.  That's the problem with playing with an invalid reference frame.  How can one be moving/accelerating without time?
Title: Re: Is there an error in this relativistic thought experiment?
Post by: MikeFontenot on 16/11/2018 15:11:45
Suppose you have a Schwarzschild black hole with an event horizon.
[...]

I'm in the tiny minority of people who believe that there is NOTHING beyond the event horizon, that there is no BEYOND the horizon ... i.e., that the event horizon itself is the closest thing to a "center" that a black hole has.

In the Schwarzchild derivation for a spherically symmetric, non-rotating mass, one encounters a quadratic equation in the variables r and t, which produces two solutions for r as a function of t.  One solution clearly corresponds to being "outside" the event horizon (where r >1), because it approaches the Newtonian solution as r -> infinity.  Most people conclude that the other solution (for r < 1) corresponds to the "inside" of a black hole, down to a "center" at r = 0.  But I concluded that the other solution of the quadratic equation is just a spurious mathematical result, with no physical significance (as often happens when quadratic equations arise in physics).  My conclusion was influenced by the fact that for r < 1, the variable r is not the spatial variable, but instead is the time variable.  So r = 0 ISN'T a spatial center, it corresponds to some sort of end of time.  (For r > 1 and large, r behaves like a Newtonian radius in spherical coordinates.  As r approaches 1, it still behaves like a radial coordinate, except that it becomes a nonlinear function of the Newtonian radius.)

I found out, some years ago, that my tiny group of like-minded people contains a very famous person: Paul Dirac come to exactly the same conclusion as mine, back in the 60's, and published a paper (which I read online) to that effect.  I'll take that company anytime.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: David Cooper on 16/11/2018 22:46:00
There is a difference between information going into a black hole and information coming out. The escape velocity at the horizon equals the speed of light and points away from the centre of gravity. The clue is in the word escape. Things approaching the horizon will not slow down. Only the signals coming out from those objects slow down.

Do you understand what you're claiming? (1) Are you saying that the speed of light outwards is not the same as the speed of light inwards at the event horizon relative to it? (2) Alternatively though, if you think the speed of light is the same there relative to the event horizon in opposite directions, do you imagine that matter overtakes light in order to cross the event horizon?

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This nonsense about objects never reaching the horizon needs to be shut down. It is simply wrong.

I've asked for confirmation of this business here before and the answer appeared to be that the speed of light is the same in all directions at the event horizon relative to the event horizon, so if you want this shut down, someone needs to point to a high-status source that spells out either that the speed of light at the EV relative to the EV is different in opposite directions OR which states unambiguously that matter overtakes light on the way into a black hole.

Quote
Gravity accelerates objects towards the source. It certainly doesn't slow them down. It is the information sent out by the infalling objects that may give this impression.

I am not being misled by that issue. The issue here is entirely about what the speed of light is at the EV relative to the EV. If it's the same both ways (i.e. zero), then for matter to cross the EV inwards would be an extraordinary phenomenon (particularly if you think of matter being made up of waves), but if the speed of light isn't the same both ways relative to the EV at the EV, that would also be problematic. I have been trying to establish for a long time what the official position is on this is because if the speed of light is different in different directions there, this must also apply above the EV all the way up through the gravity well, and the same should apply to the gravity well which we are in here.

So, can we settle this issue once and for all instead of having it come back again and again.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: jeffreyH on 16/11/2018 23:04:29
The frame of the infalling object is not inertial but if you ignore tidal forces it mimics an inertial frame at very small scales. You are comparing apples and orangutans.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: jeffreyH on 17/11/2018 11:58:10
The other point to note is time in the infalling frame. If we drop objects in the earth's gravitational field then the time of release makes a difference. If they are all released simultaneously then they will keep pace with each other. If they are released at intervals then they will not keep pace with each other. In this respect the falling frame appears like an inertial frame embedded in a series of accelerating frames. The objects further away from the source of the field fall behind. This looks like them accelerating away from our frame. The objects closer to the source move away, again looking like they are accelerating away. There is already directional bias. This is the bias caused by the vector direction of the gravitational force. Time is important for objects in the field but not positions within the field. They can be considered static for an idealised field.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: jeffreyH on 17/11/2018 12:05:56
The effect on an object depends upon its position within the field and its current velocity. It is the velocity that is time dependent. The position within an ideal stationary field is unaffected by time. This means that time dilation is a function of velocity alone. Gravity acts like a catalyst that only indirectly causes the time dilation.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: David Cooper on 17/11/2018 19:22:17
In case someone has an answer as to whether the speed of light inwards across the EV is higher than the speed outwards across it (zero), it would also be useful to get some picture of how high/low that inward speed is (i.e. whether it's c, 2c or some other value between 0 and 2c).
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 02/01/2019 16:52:56
The change to an infinite blue shift happens at the singularity in the middle; not at the EH.
That's wrong. The blueshift from any point in space to the event horizon is infinite just as the redshift up from the event horizon to any point in space above the EH is infinite. The blueshift downward is equal to the redshift upward. That's a simple consequence of conservation of energy.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 02/01/2019 16:58:51
The solution is that the light never quite reaches the event horizon, but slows down to a near halt. The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands). The calculations that suggest that objects can cross the event horizon (and that light crosses it too) are based on the idea that clocks never really slow down, so objects are imagined to go on falling through the event horizon from their own point of view and continue on down to a singularity, but this could only happen after more than an infinite amount of time has gone by for the rest of the universe, which means there are no singularities yet and that all the stuff falling towards a black hole centre is frozen in place at the same distance from the centre as it was when it stopped at where the event horizon was at the time it stopped there. The black holes should evaporate away (due to Hawking radiation) before that material has a chance to move any further in, so in reality most of it can never reach the singularity, but perhaps the light can - as the black hole evaporates, the event horizon will migrate inwards as the energy density just outside the event horizon is reduced, so the light will get a chance to move a bit further in. At some stage when the event horizon disappears and the light is free to to go straight through what was the centre of the black hole, it will be shoot out the other side, liberated, never at any stage being infinitely blue-shifted.

I agree with your interpretation (except for one point). I think you've correctly understood what happens.

I personally interpret the situation a bit differently. Since Relativity is based on the universality of c, I interpret the time delay of  light passing through a gravity well as space dilation... essentially, the rubber sheet model. If space didn't dilate exactly the same amount as time then c wouldn't be universal when measured within every frame of reference. 
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 02/01/2019 17:01:15
The gravitational potential between those two points is finite, but enough for escape speed to be c. 

No, this is wrong. The event horizon is defined as the point where the gravitational potential energy barrier is infinite and that is why the escape velocity is c. To accelerate a test mass to c requires infinite energy. It's not a finite energy barrier unless there's no event horizon.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 02/01/2019 18:07:17
But not true for the observer falling in.
This is not correct. The falling observer measures finite time in their fall to the event horizon. That does not in any way imply that the fall ever ends. Time for the falling observer (even ignoring special relativistic effects) slows asymptotically approaching zero time passage as the observer approaches the event horizon. Just as the area under a decaying exponential curve is finite while the curve is infinitely long, the forever slowing observer never reaches zero.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 02/01/2019 18:10:44
The light does in fact get there, and beyond.  Rocks really do fall into black holes, with nothing unusual about the event.  No Hawking radiation observed by the rock for instance.  It just doesn't fall into the black hole in the frame of this distant observer is all.

As with all of Relativity, the observations of all observers are consistent. However, there is no possible way to make the infinite value of the time observed by any observer (not only distant) stationary with respect to the black hole match the finite time you suggest. If the falling object reaches the event horizon in finite time then that event must be observable outside of the event horizon within finite time. But, as you say, it is not observable.

The Shapiro delay is infinite. That means light cannot travel to an event horizon in finite time. Unless you are suggesting that Shapiro is wrong?
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 02/01/2019 18:20:45
The blueshift from any point in space to the event horizon is infinite just as the redshift up from the event horizon to any point in space above the EH is infinite. The blueshift downward is equal to the redshift upward. That's a simple consequence of conservation of energy.
Energy is not conserved over different reference frames, so that property is being applied in an invalid manner here.  In fact, yes, the guy at the EH appears stopped (infinite redshift) to some outside observer, but that guy on the EH sees the distant observer finite redshifted.  There is light reaching the falling guy from the distant point at exactly one moment, and light from earlier times already fell in, and light from later times hasn't yet got there.
The two are moving apart from each other, so just like Joe and Bob in different galaxies see each other both redshifted, so do these guys, one falling into a black hole.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 02/01/2019 18:30:58
The gravitational potential between those two points is finite, but enough for escape speed to be c.
No, this is wrong. The event horizon is defined as the point where the gravitational potential energy barrier is infinite and that is why the escape velocity is c. To accelerate a test mass to c requires infinite energy. It's not a finite energy barrier unless there's no event horizon.
Well, it would take infinite acceleration to keep something outside of the EH, so I'm willing to concede this.  It doesn't violate energy conservation, so it works.
Escape velocity might be c there, but only for light pointed directly out.  At 1.5x the radius of the EH, light orbits the black hole.  It is moving at more than escape velocity, but it doesn't escape.  Light orbiting below that point will not orbit, but be pulled in.  So clearly there are two different escape velocities that are the same for minor objects like Earth, but quite different for relativistic anomalies like black holes:  One is the velocity needed going straight up, and the other is the velocity needed tangential.  For a black hole, the latter is c at 1.5 the radius of the event horizon, so the value is greater than c anywhere between the two.

This can be observed by seeing a black hole eat material from a nearby star.  The material falling in comes from well outside the event horizon and you'd think it would pick up enough speed to orbit like a comet, but it actually gets sucked in by the bent space and spirals in just like the light does.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 02/01/2019 21:07:27
Energy is not conserved over different reference frames, so that property is being applied in an invalid manner here.

No, that's incorrect. All frames under consideration in this problem are stationary with respect to the black hole. All light is traveling only radially. Energy is conserved.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 03/01/2019 00:23:09
Energy is not conserved over different reference frames, so that property is being applied in an invalid manner here.
No, that's incorrect. All frames under consideration in this problem are stationary with respect to the black hole. All light is traveling only radially. Energy is conserved.
OK, I was speaking of the frame of an observer falling in.  The frame you speak of (inertial, stationary with the BH, at the event horizon) is an invalid reference frame, but an observer in a frame close by (one meter outside the EH) will observe an arbitrarily large blue shift of the distant observer, so I agree in that sense.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 03/01/2019 00:38:06
Energy is not conserved over different reference frames, so that property is being applied in an invalid manner here.
No, that's incorrect. All frames under consideration in this problem are stationary with respect to the black hole. All light is traveling only radially. Energy is conserved.
OK, I was speaking of the frame of an observer falling in.  The frame you speak of (inertial, stationary with the BH, at the event horizon) is an invalid reference frame, but an observer in a frame close by (one meter outside the EH) will observe an arbitrarily large blue shift of the distant observer, so I agree in that sense.

No, it's not invalid. The thought experiment is a perfectly valid relativistic thought experiment. Nothing in the experiment entails anything being stationary at the event horizon. Maybe you should read the original post and work through the thought experiment.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 03/01/2019 03:15:23
No, it's not invalid. The thought experiment is a perfectly valid relativistic thought experiment.
You seem to contradict yourself between these two statements:
Quote
All frames under consideration in this problem are stationary with respect to the black hole.
Quote
Nothing in the experiment entails anything being stationary at the event horizon.
Red and blue shifting of light is a frame-dependent thing, not an actual thing light does.  You need to specify a frame, but your contradicting statements don't tell me which one to use.

Quote
Maybe you should read the original post and work through the thought experiment.
The OP doesn't specify any frame.  It says these things:
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The blueshift a light beam will undergo when traveling from any point in space to an event horizon is infinite.
...
By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted.
These are frame dependent claims.  I can look at light from a distant galaxy and the light is red shifted to one observer moving away from that galaxy, and blue shifted to another observer in the same place, but moving towards the galaxy.  The light is not actually shifted in either case, but appears red or blue relative to different frames.

Ditto for the black hole.  Light is finite red shifted for a falling observe at (or even beyond) the EH of a black hole.  For an observer stationary to the distant light source, the light appears blue shifted due to the time dilation of the gravity well, and yes, this approaches infinite dilation as the point approaches the horizon, but at the horizon itself is no more a valid inertial frame than is the inertial frame of a photon. Such a frame violates the principle of relativity.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 07/01/2019 05:47:59
The light from the lasers platform is indeed blue shifted, but only as measured at the Event horizon. Passing that EV it is part of the singularity and might be described as 'infinitely blue shifted', although that makes no sense from the position of making a measurement. Outside, or at, the EV it can't be infinitely blue shifted.

The light the platform possibly can measure on will be reflected light, and that, as it comes back from the vicinity of the black hole, must be red shifted. You always need to be clear about what frame of reference you use when setting up a thought experiment like this. 

When it comes to the time dilation then you should be correct about the platform finding it to take a very long time to get any reflections of that light, if it now was possible to measure. But from the frame of reference of the infalling 'photons' the time it will take to reach the Event Horizon is defined by 'c', locally measured, so it should have no trouble reaching the EV in a 'finite time'. And as soon as you're outside a 'singularity' of some sort you can't speak of something being 'infinitely slow', because that will fall under the physics we know.
=

This is presuming we could use a frame of reference for a photon  :)
You can't really, but it doesn't matter for this, 'c' is 'c', and it's always a local measurement. And something assumed to 'propagate', as a 'photon', must then have some sort of locality in Space and Time. We can simplify it by imagining you to throw a rock at the Black Hole from the platform. Then let someone on that rock constantly measure 'c' as he 'falls' into a geodesic towards the Black Hole. He will reach it too in a, to him, finite time.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 07/01/2019 09:47:22
" I'm in the tiny minority of people who believe that there is NOTHING beyond the event horizon, that there is no BEYOND the horizon ... i.e., that the event horizon itself is the closest thing to a "center" that a black hole has. "

I've seen that definition too Mike and it makes sense. Once you passed a event horizon, if we define that as being inside the region from where light can't leave, it seems to me that there will be no real definition of what a center should be. You're already inside a region where physics breaks down.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 07/01/2019 12:14:42
The light from the lasers platform is indeed blue shifted, but only as measured at the Event horizon. Passing that EV it is part of the singularity and might be described as 'infinitely blue shifted', although that makes no sense from the position of making a measurement. Outside, or at, the EV it can't be infinitely blue shifted.

The light the platform possibly can measure on will be reflected light, and that, as it comes back from the vicinity of the black hole, must be red shifted. You always need to be clear about what frame of reference you use when setting up a thought experiment like this. 
And yet you don't specify one.  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.  Not so if the mirror is falling.  But you didn't specify above, which is the gist of most of my prior post.
You can get arbitrarily high blue or red shift, but the only infinite shift I can think of is that from a laser falling into the black hole as seen from the platform outside.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 07/01/2019 13:11:18
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. "

Sorry
Fail
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 07/01/2019 13:13:33
A frequency is the number of occurrences of a repeating event per unit of time. That means that the platform watching the red shifted light also will find it to be at another frequency. Light is 'observer dependent'. meaning that you can see a light quanta as being constant, no matter if it seems to red or blue shift from another frame of reference.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 07/01/2019 14:09:15
The point being, you have a good mind Halc, I enjoy reading you.
 Adapt and overcome.

you will get there.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 07/01/2019 16:35:35
A frequency is the number of occurrences of a repeating event per unit of time. That means that the platform watching the red shifted light also will find it to be at another frequency.
Assuming it is red shifted, yes.  But you haven't justified your assertion that it is red shifted.

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Light is 'observer dependent'. meaning that you can see a light quanta as being constant, no matter if it seems to red or blue shift from another frame of reference.
Correct again, but we're looking at the reflected beam from the frame of the platform from which it was sent, reflected by a mirror stationary relative to that platform.  Regardless of any gravity well in which the mirror might be, that is going to result in no red or blue shift as seen by our platform observer.  If it were otherwise, you run into contradictions.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 08/01/2019 11:45:38
Want to show me the contradictions?
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 08/01/2019 19:25:56
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. "

Sorry
Fail
Quote from: Halc
Regardless of any gravity well in which the mirror might be, that is going to result in no red or blue shift as seen by our platform observer.  If it were otherwise, you run into contradictions.
Want to show me the contradictions?

1) The system is in steady state.  There is a black hole, a mirror nearby that, and a platform a good distance away, all stationary.  There is a light emitted by the platform which is reflected by the mirror back to the platform where it is measured.  By steady state, I mean if you look at the system an hour later, you cannot tell the difference.  Nothing has changed but the time on clocks, wherever you want to put them.

2) The platform is putting out say green light (578 THz) and it takes 2 days for the beam to get back, as measured by the platform.  That means they turn it on and 2 days later they see the light come back from the mirror.  From this they cannot compute the distance to the mirror since space/time might be contracted, depending on how you choose to measure distance.  But we know exactly how many waves of light are 'in flight' since we know the frequency that we're emitting them, and how long it has been since the light was turned on.  That number is say 1e20 (2 days of green light) waves.  Once the light returning is seen, the system is in steady state.

3) One hour later, there are still 1e20 waves in flight.  For that number to be anything else would violate the steady-state established in 1).

4) Suppose the light returning is not green, but some different frequency.  Let's suppose the return light is red shifted to a lower-frequency/longer-wavelength.  That would mean that more waves are being created than are finishing their trip, which results in a net increase of waves 'in flight'.  That would represent a change that violates the steady state in 1).  Similarly a blue shift would result in a net decrease of waves in flight, which is a similar contradiction.

Notice that the black hole in the picture doesn't effect the argument at all.  It does not break up the steady state, and so the argument holds.  It would not hold if the mirror was moving because that would not be a steady state.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 08/01/2019 19:51:31
Halc, okay, see how you think but when it comes to 'compressing' or 'stretching' a wave then that is a measurement of 'peaks and troughs' in time. If you think of cosmological red shift for example then that can be described by two ships passing/leaving each others perimeter as they exchange light signals. The signals will 'stretch' and so be come red shifted after they passed each other. It's the same here, as in the classical ambulance example with a siren sounding high pitched before meeting you, to then become lower pitched as it leaves you. What changes it is 'relative motion' and 'time'. There is no real 'loss' of those 'photons' (intrinsic) energy in either example, at least not as I see it, but thought of as waves their frequency change due to it.
=
The 'relative motion' I mentioned can also be referred to as a 'accelerating expansion of space' but it is essentially the same idea, then called cosmological red shift. What we're discussing is a equivalence but now using 'gravity' and 'time' instead.

( Exchange the bouncing for someone standing at the 'bottom of a gravity well'/event horizon sending a light signal to our platform. It must red shift. https://astronomy.swin.edu.au/cosmos/G/Gravitational+Redshift ). The point with me saying that I don't see it as a photon losing energy is due to the fact that this is a relation (observer dependencies), but that is a case of interpretation, you can choose the one there although I won't agree :)

spelling

Or maybe I will change my mind there? Damn, one reason why I don't want too is that no matter how you treat 'gravity' here that light is in a geodesic, it's not 'decelerating', it's just a equivalence. One way around it would be to define it as a 'field' in where there exist observer dependencies. Then define a 'photon' to be non propagating, but still behaving 'as if' to our measurements. That should mean that as the 'field strength' of 'gravity' diminish with distance the 'photon' would 'reclaim' its original energy.

Anyway, it's still observer dependent.
And gravity as a 'field'?
=

Here, read this and decide for yourself Halc :)
http://iopscience.iop.org/article/10.1088/1742-6596/600/1/012055/pdf

It's soo tricky that one. And btw, you can let a 'photon' propagate for that 'field' too if you like, reaching a same conclusion, but it's more to my taste treating it as a result of your measurement in time and space, no 'motion' necessary :)
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 00:06:07
Halc, okay, see how you think but when it comes to 'compressing' or 'stretching' a wave then that is a measurement of 'peaks and troughs' in time.
If you are compressing the time, then yes, but we're not since we're measuring it by the same clock as the source.  Compressing the distance doesn't change the frequency, just the wavelength.  That wavelength is back to its full size by the time the signal gets back, and may never have changed, depending on how it is measured.

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If you think of cosmological red shift for example then that can be described by two ships passing/leaving each others perimeter as they exchange light signals.
I know what red shift is, but what is 'cosmological red shift'?  How is that different?

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The signals will 'stretch' and so be come red shifted after they passed each other.
Doesn't work like that at all.  The signals are not observing each other.  No signal changes at all due to what the other ship is doing.  Red shift is observed by one ship if the path from source to observation is increasing, which happens after the ships pass, not after the signals pass.

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It's the same here, as in the classical ambulance example with a siren sounding high pitched before meeting you, to then become lower pitched as it leaves you. What changes it is 'relative motion' and 'time'.
Again, you describe it as the sound changing, and not just a different observation of the same sound.

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The 'relative motion' I mentioned can also be referred to as a 'accelerating expansion of space' but it is essentially the same idea, then called cosmological red shift.
OK, you're talking about distant things tending to move away from us, and thus appearing red shift to us.  That's not the cosmos doing anything, that's just us moving away from the thing being observed.  The same light would appear not shifted at all at the same location as us, but to an observer stationary relative to the source of the light.  The long cosmological separation doesn't change that a bit.

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Or maybe I will change my mind there? Damn, one reason why I don't want too is that no matter how you treat 'gravity' here that light is in a geodesic, it's not 'decelerating', it's just a equivalence. One way around it would be to define it as a 'field' in where there exist observer dependencies. Then define a 'photon' to be non propagating, but still behaving 'as if' to our measurements. That should mean that as the 'field strength' of 'gravity' diminish with distance the 'photon' would 'reclaim' its original energy.
You're overthinking this. How about you point out the error in my prior post.  It doesn't depend at all on all these complications.  It depends only on fixed path length, and not on how that length is computed.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 00:42:47
Here, read this and decide for yourself Halc :)
http://iopscience.iop.org/article/10.1088/1742-6596/600/1/012055/pdf
This is an article about how and when relativity should be taught to students, to avoid the misinterpretations of the concepts involved. It uses gravitational redshift as its example since it has different interpretations.
It doesn't apply to our example since we're not worried about how the light appears to an observer near the mirror.  We only care about our observer who is at the same gravitational potential (and same location actually) as the light source.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 09/01/2019 05:53:38
No, it was discussing the last part I wrote about, how to see the 'energy' contained in a 'photon' as it propagates.

"  Okun et al. note that in the literature there are two interpretations of the gravitational redshift in a static gravitational field: either the photon frequency is modified en route between emitter and receiver (and the clock rate unaffected by gravitational potential) or the clocks at lower potential are slowed down (and the photon unaffected en route).

They advocate strongly the clocks-slow-down view, stating that the gravitational redshift should be taught in a way that “centers on the universal modification of the rate of a clock exposed to a gravitational potential”. 

But the situation is subtle and confusing because an important heuristic principle in GR is that the local effects of gravity can always be eliminated with a coordinate transformation. This follows from a version of the principle of equivalence of gravity and inertia that asserts that inertial forces and gravitational forces are one and the same physical effect "

And that one is tricky, at least I think so. The one with it becoming a red shift when reflected back from a event horizon, not so much. And a cosmological red shift is due to a accelerating expansion of the vacuum (space). Turning it around it is a equivalence to those ships passing each other producing a Doppler redshift. The same effect is there, distance growing between ships/galaxies etc.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 09/01/2019 06:14:41
No Halc, I'm not overthinking it. Relativity is simple as well as confusing, the more one learn the trickier it becomes :) And the red shift shown in this example is no different from the red shift you get sending a light signal from Earth to space. Clocks ticks differently depending on elevation in a gravitational potential and that affects the frequency of light. Infalling light blueshifts, light leaving a gravity well will be found to redshift.

" The wavelength and frequency of light are closely related. The higher the frequency, the shorter the wavelength. Because all light waves move through a vacuum at the same speed, the number of wave crests passing by a given point in one second depends on the wavelength. "

There is one difference more btw between Doppler and Cosmological red shift. In the later case the redshift continue to grow as the light propagate as the universe constantly is expanding. In the first case the light sent doesn't :) But in reality, as all space is accelerating expanding, that difference seems of a lesser importance to me. Expressed otherwise: The difference between Doppler and Cosmological redshift is just a question over what distance you measure.

https://einstein.stanford.edu/content/relativity/a11859.html

Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 12:22:34
No, it was discussing the last part I wrote about, how to see the 'energy' contained in a 'photon' as it propagates.
Energy of a photon is defined when it is a local measurement. The article points out that various interpretations are valid when the measurement/calculation is not local.
Again, that changing energy is irrelevant to my reasoning since it doesn't matter what happens to the energy or wavelength of the photon as it moves in and out of the gravity well.



But the situation is subtle and confusing because an important heuristic principle in GR is that the local effects of gravity can always be eliminated with a coordinate transformation. This follows from a version of the principle of equivalence of gravity and inertia that asserts that inertial forces and gravitational forces are one and the same physical effect "

Quote
And a cosmological red shift is due to a accelerating expansion of the vacuum (space).
Wrong twice.  It is due to the path length increasing between us and objects being viewed.
Secondly, there would be a redshift even if the expansion was constant or slowing, as was long suspected.
The expansion was deduced from the redshift in the 30's, but the acceleration of the expansion was not worked out until at least 6 decades later.

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Turning it around it is a equivalence to those ships passing each other producing a Doppler redshift. The same effect is there, distance growing between ships/galaxies etc.
There is no growing distance in our example with the mirror.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 12:30:06
No Halc, I'm not overthinking it. Relativity is simple as well as confusing, the more one learn the trickier it becomes :)
I didn't have to invoke relativity once to show that the light observed back at the platform is not redshifted.  That's what I mean by you overthinking it.  You're invoking a theory that isn't needed.

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And the red shift shown in this example is no different from the red shift you get sending a light signal from Earth to space.
Yes it is.  I'm not measuring it in space.  I'm measuring it back at the light source.  Put a stationary mirror in space (and stop Earth's motion) and the situation would be no different.

You keep posting about what the light does en-route, but it doesn't matter.  I'm not disagreeing that there is a shift to the light as it moves in and out of gravity wells, but since we're not measuring it out there, it doesn't matter.


Again, you've not found anything wrong with my post showing a contradiction with your assertion.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 09/01/2019 13:32:53
Hmm

The idea of different clock rates impending on wavelength and frequency is a easy idea to check, and it has been checked over and over again. But I won't spoonfeed, check it up yourself, It's not me you will need to convince of your interpretation btw, it's the physics you need to correct first, aka relativity.

that will be interesting.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 13:51:41
Hmm

The idea of different clock rates
Again you sidetrack.  There is but the one clock in our example.  Discussion of the rate of another is irrelevant.

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It's not me you will need to convince of your interpretation btw, it's the physics you need to correct first, aka relativity.
I've expressed no interpretation of relativity in my post showing the contradiction.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 09/01/2019 14:51:23
Look Halc, this is what you wrote. "   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. "

That's what I reacted on, the rest of it is you not checking your sources to see if I'm correct or not. The lasers light will red shift as it is reflected from a gravity well (EV) back to the 'platform' with the laser. The red shift involves a slower frequency and a longer wave length, due to different time rates, as it 'climbs' the gravity well.

Check it
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 15:40:32
Look Halc, this is what you wrote. "   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. "

That's what I reacted on, the rest of it is you not checking your sources to see if I'm correct or not. The lasers light will red shift as it is reflected from a gravity well (EV) back to the 'platform' with the laser. The red shift involves a slower frequency and a longer wave length, due to different time rates, as it 'climbs' the gravity well.

Check it
Not disputing that at all.  My comment above doesn't say otherwise.
But light does the opposite effect (negative redshift) when 'falling' into the gravity well in the first place.  Net effect from the platform is zero since it is at the same potential as the platform.  As I keep repeating, all these effects are quite real, but irrelevant.

I ran your assertion into a contradiction, so the analysis must be wrong according to you, but you don't point out where.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 17:10:37
Correct again, but we're looking at the reflected beam from the frame of the platform from which it was sent, reflected by a mirror stationary relative to that platform.  Regardless of any gravity well in which the mirror might be, that is going to result in no red or blue shift as seen by our platform observer.

Exactly correct. Gravitational redshift is entirely reversible. Traveling into space of lower gravitational potential energy, the light is blueshifted. Then, when the light travels back to the platform, the gravitational blueshift is exactly reversed by the gravitational redshift because the light is returning to a point of the same gravitational potential energy as it started.

If the mirror is moving downward at a constant speed, there will be a Doppler redshift of the light beam but that will be constant throughout the experiment.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 17:15:36
If I put a mirror stationary (relative to the platform) near a black hole

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

How are you defining distance?
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 17:26:09
As I keep repeating, all these effects are quite real, but irrelevant.

I think I see where you're getting confused. The blueshift is not irrelevant but the very crux of the argument.

If the light beam travels from the platform to the event horizon, the beam will be infinitely blueshifted. That means the downward beam will contain infinitely many wave cycles. That means, *before* the front of the light beam can reach the event horizon, the light source must generate an infinite sequence of light waves. This requires infinite time at the light source. This means, before the front of the light beam reaches the event horizon, infinite time must pass at the light source. That is a causal sequence and is therefore frame independent. There are no valid frames of reference from which the front of the beam can reach the event horizon before infinite time has passed at the platform.

And, because the location of the platform is irrelevant to the validity of the thought experiment, the result is true for all points in space.

I hope this clarifies it for you.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 17:31:17
I did this diagram to help make the thought experiment easier to visualize:
https://photos.app.goo.gl/2BqU6nZW85oToXw77
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 17:34:35
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.

Quote
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.

Quote
How are you defining distance?
I didn't specify any distance.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 17:41:03
As I keep repeating, all these effects are quite real, but irrelevant.

I think I see where you're getting confused. The blueshift is not irrelevant but the very crux of the argument.
You said in post 52 that the shift in the two directions cancel each other.  That makes it pretty irrelevant in this example.  I'm not claiming it doesn't happen, but I've not bothered to specifiy any distances or difference in potential since the light will be measured without redshift regardless of the values specified.  All I specified was that nothing was moving: the path is unchanged.

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If the light beam travels from the platform to the event horizon, the beam will be infinitely blueshifted.
I never posted light going to the event horizon in my statement.  It doesn't come back if it does that.
I know you are the OP and may be imagining a different scenario, but the scenario I've been describing is reflecting light from a mirror somewhere outside the event horizon.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 17:44:33
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.

Quote
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.

Quote
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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 17:49:18
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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 18:03:54
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.

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The length of rope would be finite.
That depends how it is measured.  Using Schwartzchild 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.

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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 Schwartzchild coordinates then.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 18:08:46
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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 18:12:39
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.

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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.

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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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 18:46:17
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.

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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.

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

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.

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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.

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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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 09/01/2019 19:04:13
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.

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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.

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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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: David Cooper on 09/01/2019 19:22:08
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).
Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 19:41:04
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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: David Cooper on 09/01/2019 19:43:47
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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: guest47899 on 09/01/2019 20:52:24
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. 


Title: Re: Is there an error in this relativistic thought experiment?
Post by: AndroidNeox on 09/01/2019 21:28:34
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.

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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.

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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.

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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.

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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.

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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.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: Halc on 10/01/2019 02:56:37
[quote =Halc]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.[/quote]
Then Einstein would have been wrong.  He wasn't in the habit of that, especially for such trivial things.
You have a reference for this?

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Quote from: Halc
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.
Not wrong.  An observer at a moving mirror (in particular, one falling from the platform) will see the light from the platform redshifted, while an observer stationary with everything will see a blueshift.  So that makes it 'very dependent on how the light is observed'.  You sort of described a mirror slowly being lowered, so assuming you don't do that too fast, blueshift it is.
These both are quite easy to verify using the equivalency principle.  The light coming back to the platform is easier to envision with the gravity case.  Acceleration equivalence I think actually makes that one less intuitive.

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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".
Understood.  An observer at the slow mirror will see a blue shift that goes arbitrarily high as you approach the horizon.  But the platform guy sees no change at all as the mirror slowly approaches the event horizon.

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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.
From an outside measurement of time, this seems to be true, and from the local perspective, it also seems to be the case.  I see contradictory descriptions of surviving the fall or not, but the least contradictory description seems to be instant death by compressed radiation, after which the black hole no longer exists.  I'm therefore quite willing to agree with you on this.

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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.
Agree.  Never mind the winch.  Just rocket your butt in.  You still can't get there with the description above.  So the mirror never makes it, but it doesn't reflect light anymore either.  That seems almost like a contradiction, but not quite.

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quote]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.[/quote]
My mirror is not at the event horizon.  It is some distance from it, and there are no infinities involved.  I never claimed the platform would see reflected light from a mirror at the event horizon.

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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.
But I did do that, which is how zero redshift is observed by a stationary mirror.  Anything else would not conserve energy.  There is no loss anywhere to account for an energy difference of seeing a different light.
Title: Re: Is there an error in this relativistic thought experiment?
Post by: yor_on on 10/01/2019 06:04:16
" 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