## SWaB: does gravitational redshift slow BH growth?

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### SWaB: does gravitational redshift slow BH growth?

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### Re: SWaB: does gravitational redshift slow BH growth?

I also find the proposition that time stops highly interesting....for an outside observer who sees matter falling into a black hole, it will appear as though the material:

- takes on a redder color (as the photons get gravitationally redshifted),

- falls in slower and slower as it asymptotically approaches the event horizon (due to time dilation),

- appears fainter and fainter over time (as the number of photons per "amount-of-dilated-time" progressively decreases),

- and eventually gets "frozen" infinitesimally close to, but still outside, the event horizon.

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### Re: SWaB: does gravitational redshift slow BH growth?

correct me if i'm wrong, but my understanding is the in-faller sees their watch continue ticking as normal as they approach and cross the horizon, but if they were able to compare the elapsed time before crossing with the elapsed time of an observer hovering at fixed altitude far outside the horizon, the hovering observer's watch shows that much more time has elapsed on their watch compared to the in-faller... same goes if the in-faller only closely approaches the event horizon on an elliptical or hyperbolic orbit without actually crossing... their watch shows less time has elapsed compared to the hovering observer.

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### Re: SWaB: does gravitational redshift slow BH growth?

It only stops near the event horizon in the reference frame of a distant observer though. For a freely falling observer's inertial reference frame, only valid locally, no slowing happens. "Locally" means a volume so small that tides aren't important.helicon wrote: ↑Sun Jan 12, 2020 5:36 pmI also find the proposition that time stops highly interesting....for an outside observer who sees matter falling into a black hole, it will appear as though the material:

- takes on a redder color (as the photons get gravitationally redshifted),

- falls in slower and slower as it asymptotically approaches the event horizon (due to time dilation),

- appears fainter and fainter over time (as the number of photons per "amount-of-dilated-time" progressively decreases),

- and eventually gets "frozen" infinitesimally close to, but still outside, the event horizon.

**Scopes: Refs:**Orion ST80, SV 80EDA f7, TS 102ED f11

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### Re: SWaB: does gravitational redshift slow BH growth?

Yes. Of course a hovering observer's watch also runs slower the closer the hover point is to the event horizon. A very distant hovering observers watch is unaffected.metastable wrote: ↑Sun Jan 12, 2020 6:47 pmcorrect me if i'm wrong, but my understanding is the in-faller sees their watch continue ticking as normal as they approach and cross the horizon, but if they were able to compare the elapsed time before crossing with the elapsed time of an observer hovering at fixed altitude far outside the horizon, the hovering observer's watch shows that much more time has elapsed on their watch compared to the in-faller... same goes if the in-faller only closely approaches the event horizon on an elliptical or hyperbolic orbit without actually crossing... their watch shows less time has elapsed compared to the hovering observer.

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### Re: SWaB: does gravitational redshift slow BH growth?

My understanding is (correct me if i’m wrong) if you could synchronize 7 atomic clocks on the space station— 6 at rest with respect to each other in a box with no wiggle room (the bottom of the box has the same shape as the curvature of the earth, and the box is always kept "top side up" with respect to the ground)— & bring the 6 clocks in the box down to Earth along with the next set of returning astronauts, they could then place the box next to a roller coaster and load the clocks, one per car, in such a way that each clock remains the same distance from the ground and each other during the loading process. If the roller coaster starts accelerating on a perfectly level track in the sense that the track exactly follows the curvature of the earth (and in an idealization the earth is a perfect sphere as well), the 6 clocks are still in sync, but when the coaster starts turning wildly and doing loop the loops, the clocks are out of sync with each other during the turns and loops, but when the coaster returns to the straight & "level" stretch of track, the 6 clocks are back in sync. When the clocks are carefully unloaded without changing their elevations or separation distances, returned to the box, & the box is kept right side up and returned to the space station on the next launch, & in space, the box is opened and the clocks checked for synchronization with the 7th clock, it would be found that the 6 clocks in the box agree on the elapsed time but are out of sync with the 7th.

The part I don’t understand is if to the hovering observer, the in-faller’s clock stops at the event horizon, how could the hovering observer witness the stoppage since no signal can escape said horizon?

The part I don’t understand is if to the hovering observer, the in-faller’s clock stops at the event horizon, how could the hovering observer witness the stoppage since no signal can escape said horizon?

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### Re: SWaB: does gravitational redshift slow BH growth?

Why introduce needless complications? It's symptomatic of bad thinking. So I'm not interested in decoding this word salad. There are so many unnecessary complications it's ridiculous. Clocks are synchronized if the path integrals of their proper times agree.metastable wrote: ↑Sun Jan 12, 2020 10:39 pmMy understanding is (correct me if i’m wrong) if you could synchronize 7 atomic clocks on the space station— 6 at rest with respect to each other in a box with no wiggle room (the bottom of the box has the same shape as the curvature of the earth, and the box is always kept "top side up" with respect to the ground)— & bring the 6 clocks in the box down to Earth along with the next set of returning astronauts, they could then place the box next to a roller coaster and load the clocks, one per car, in such a way that each clock remains the same distance from the ground and each other during the loading process. If the roller coaster starts accelerating on a perfectly level track in the sense that the track exactly follows the curvature of the earth (and in an idealization the earth is a perfect sphere as well), the 6 clocks are still in sync, but when the coaster starts turning wildly and doing loop the loops, the clocks are out of sync with each other during the turns and loops, but when the coaster returns to the straight & "level" stretch of track, the 6 clocks are back in sync. When the clocks are carefully unloaded without changing their elevations or separation distances, returned to the box, & the box is kept right side up and returned to the space station on the next launch, & in space, the box is opened and the clocks checked for synchronization with the 7th clock, it would be found that the 6 clocks in the box agree on the elapsed time but are out of sync with the 7th.

The distant observer, of course, does not "witness" it, What the distant observer "witnesses" is that as the falling observer nears the event horizon the rate of the clock slows to approach zero at the event horizon in accordance with the metric which predicts zero rate at the event horizon.The part I don’t understand is if to the hovering observer, the in-faller’s clock stops at the event horizon, how could the hovering observer witness the stoppage since no signal can escape said horizon?

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### Re: SWaB: does gravitational redshift slow BH growth?

So it sounds like you’re saying no observers can see the clock stop completely.

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### Re: SWaB: does gravitational redshift slow BH growth?

Not exactly. To be more direct, I'm saying that that the question "Can an observer see a clock stop completely as it approaches an event horizon?" is an incoherent and unphysical question.metastable wrote: ↑Sun Jan 12, 2020 11:22 pmSo it sounds like you’re saying no observers can see the clock stop completely.

To answer the question requires 1) a ticking clock approaching an event horizon and 2) an infinitely long lived observer who at the "end" of an infinitely long life can say "it hasn't ticked again".

The fact that it indicates an experiment that cannot be realized means the question itself is a bad question. It's metaphysical, not physical and as meaningless as asking the number of infinitesimal angels that could be included to perform Swan Lake on a pinhead.

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### Re: SWaB: does gravitational redshift slow BH growth?

Won’t the in-faller cross the horizon in a finite time as measured by the hovering observer’s clock, even if the in-faller’s clock appears to almost stop to the hoverer just before crossing?

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### Re: SWaB: does gravitational redshift slow BH growth?

No. A distant observer will se the infaller approach the event horizon ever more slowly and never reach it. See the link in the first post.metastable wrote: ↑Mon Jan 13, 2020 12:01 amWon’t the in-faller cross the horizon in a finite time as measured by the hovering observer’s clock, even if the in-faller’s clock appears to almost stop to the hoverer just before crossing?

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### Re: SWaB: does gravitational redshift slow BH growth?

Since GR isn’t a quantum theory, can I make the following statements on a quantum basis:

1) The black hole does not change the speed of the photons transmitted or reflected by the in-faller which are received by the hovering observer

2) The last photon received from the in-faller by the hovering observer will happen at a finite time according to the hoverer’s clock

1) The black hole does not change the speed of the photons transmitted or reflected by the in-faller which are received by the hovering observer

2) The last photon received from the in-faller by the hovering observer will happen at a finite time according to the hoverer’s clock

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### Re: SWaB: does gravitational redshift slow BH growth?

It is true that GR is not a quantum theory. But ordinary QM can be done in local Lorentz (i.e. inertial) reference frames as long as all length scales are larger than the Planck length. So on that basis one can answer your questions.metastable wrote: ↑Mon Jan 13, 2020 12:39 amSince GR isn’t a quantum theory, can I make the following statements on a quantum basis:

You do not specify the reference frame in which the photon speed is measured.1) The black hole does not change the speed of the photons transmitted or reflected by the in-faller which are received by the hovering observer

Now consider the velocity (not speed) of a photon. If gravitational fields did not affect photon propagation then gravitational lensing wouldn't happen and the deflection of starlight near the Sun's limb wouldn't happen either.

Meaningless question as already discussed in post #11. It takes an infinite time for the last photon to be observed.2) The last photon received from the in-faller by the hovering observer will happen at a finite time according to the hoverer’s clock

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### Re: SWaB: does gravitational redshift slow BH growth?

Can I say in QM, since we can only sensibly discuss quantities that are measurable, if the hovering observer decides to end the experiment after the number of photons received from the in-faller asymptotically approaches zero for a given detector sensitivity, then the last photon measured by the hovering observer will happen in a finite time according to the hovering observer’s clock?

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### Re: SWaB: does gravitational redshift slow BH growth?

No. The asymptotic approach to zero takes an infinite time. That's what asymptotic approach to zero as time goes to infinity means. Of course the hovering observer can get tired of waiting for infinity.metastable wrote: ↑Mon Jan 13, 2020 1:16 amCan I say in QM, since we can only sensibly discuss quantities that are measurable, if the hovering observer decides to end the experiment after the number of photons received from the in-faller asymptotically approaches zero for a given detector sensitivity, then the last photon measured by the hovering observer will happen in a finite time according to the hovering observer’s clock?

How many ways can you ask the same question expecting a different answer?

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### Re: SWaB: does gravitational redshift slow BH growth?

I thought very close to the horizon the in-faller’s transmitted or reflected photons would be so gravitationally and doppler redshifted as to be undetectable to the hovering observer for a given detector sensitivity range.

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### Re: SWaB: does gravitational redshift slow BH growth?

When was there a shift from an idealized infinite bandwidth detector of perfect efficiency to a finite bandwidth lossy detector? I must have missed that and the numerical values associated with those specifications?metastable wrote: ↑Mon Jan 13, 2020 1:25 amI thought very close to the horizon the in-faller’s transmitted or reflected photons would be so gravitationally and doppler redshifted as to be undetectable to the hovering observer for a given detector sensitivity range.

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### Re: SWaB: does gravitational redshift slow BH growth?

According to this the lowest frequency detectable individual photons are in the 200mhz range:

https://physics.stackexchange.com/quest ... 740#248740

If we can only sensibly discuss measurable quantities in QM, and the lowest frequency at which we can reasonably detect individual photons is ~200mhz, won’t the last detectable photon reflected or transmitted by the in-faller that is received by the hovering observer occur within a quite finite amount of time according to the hovering observer’s clock?

https://physics.stackexchange.com/quest ... 740#248740

If we can only sensibly discuss measurable quantities in QM, and the lowest frequency at which we can reasonably detect individual photons is ~200mhz, won’t the last detectable photon reflected or transmitted by the in-faller that is received by the hovering observer occur within a quite finite amount of time according to the hovering observer’s clock?

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### Re: SWaB: does gravitational redshift slow BH growth?

There is no "in principle" limit to how low in frequency a photon can be detected. The question shows ways that technology can be improved to go to lower frequencies. The link discusses limits of current technology and cites methods that can go below that frequency.metastable wrote: ↑Mon Jan 13, 2020 2:35 amAccording to this the lowest frequency detectable individual photons are in the 200mhz range:

https://physics.stackexchange.com/quest ... 740#248740

If we can only sensibly discuss measurable quantities in QM, and the lowest frequency at which we can reasonably detect individual photons is ~200mhz, won’t the last detectable photon reflected or transmitted by the in-faller that is received by the hovering observer occur within a quite finite amount of time according to the hovering observer’s clock?

By changing the question from "in principle" to "with current technology" you are changing the logic of the original question to get an answer you want.

Your premise "we can only sensibly discuss measurable quantities in QM" is dubious. I can go with "we can only sensibly discuss measurable quantities" period. But there are antennas and receivers that operate at much lower frequencies. I've worked on extremely low frequency systems in the 3-30 hz range.

So a falling observer can broadcast a signal at much lower than 200 Mhz.

It is annoying to deal with changing the question after the fact because one doesn't like the answer to the question as originally asked.

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### Re: SWaB: does gravitational redshift slow BH growth?

Wouldn’t infinite duration imply the mass distribution of the singularity is more like an eggshell than a point mass?notFritzArgelander wrote: ↑Mon Jan 13, 2020 1:19 amNo. The asymptotic approach to zero takes an infinite time. That's what asymptotic approach to zero as time goes to infinity means. Of course the hovering observer can get tired of waiting for infinity.metastable wrote: ↑Mon Jan 13, 2020 1:16 amCan I say in QM, since we can only sensibly discuss quantities that are measurable, if the hovering observer decides to end the experiment after the number of photons received from the in-faller asymptotically approaches zero for a given detector sensitivity, then the last photon measured by the hovering observer will happen in a finite time according to the hovering observer’s clock?

How many ways can you ask the same question expecting a different answer?