PDA

View Full Version : Mirror falling towards event horizon.

WaxRubiks
2015-Jun-10, 03:57 AM
If a scientist threw a mirror towards a black hole, it would fall and fall towards the event horizon but never be seen to cross it.

If the scientist flashed a laser into the mirror, for how long would he see the flash reflected?

Assuming the scientist would live for billions of years, would he see the flash reflected for that long?

You may want to discuss red and blue shift, but when I say 'see the flash reflection', I mean that he is able to detect the radiation someone, even if it isn't in the visible range.

Is there a moment when the laser flash wouldn't be 'seen'? Even after billions of years?

malaidas
2015-Jun-10, 10:21 AM
Interesting question. Is this laser being fired from the moment the mirror is released towards the event horizon?

WaxRubiks
2015-Jun-10, 10:28 AM
Interesting question. Is this laser being fired from the moment the mirror is released towards the event horizon?

well yes.

Grey
2015-Jun-10, 12:31 PM
The answer here is more or less the same as if you drop a light source toward the event horizon. In principle, the light from the falling object is spread out over the entire future of a distant observer, but in practice, it rapidly diminishes to nearly nothing. If you take into account that light is made of photons, there will be a last photon emitted, and the average time for the observer to see that last photon is actually quite short (I think on the order of minutes to hours, depending on the size of the black hole and exactly how far away the observer is).

I was hoping someone would have a diagram of this, and found a great one here (http://www.quora.com/Suppose-you-cross-the-event-horizon-of-a-supermassive-black-hole-and-you-have-a-friend-just-outside-the-event-horizon-holding-a-mirror-If-you-fire-a-beam-of-light-at-the-mirror-and-measure-how-long-it-takes-to-return-how-will-the-result-be-consistent-with-the-constant-speed-of-light). It's a slightly different description, but it has Alice (who is falling into a black hole) and Bob (an observer at a fixed distance outside) bouncing light beams back and forth to each other. The light beams are the lines at 45 degree angles. You can see that light emitted (or reflected) when Alice gets close to the event horizon can in principle reach Bob arbitrarily late, but you can also see that light reflected very close together in time from Alice's perspective arrives at very different times for Bob. That's where the last photon issue comes in. There's certainly a chance that the last reflected photon could come at any arbitrary future point, but it's very unlikely (and there's also a point at which it would be hard to distinguish it from any other random photon).

Also, it's good to realize that the total amount of light reflected will be fixed. One thing the diagram makes very clear is that there is a definite point at which the laser from Bob will not make it to Alice's mirror in time to be reflected before the mirror crosses the event horizon. Light from Bob's laser emitted after that will never make it back to Bob. Similarly, there's a definite point at which light from Bob's laser won't reach Alice or her mirror before Alice reaches the singularity. So Alice won't see the entire future of the outside universe go by as she falls in.

Jeff Root
2015-Jun-10, 12:33 PM
The mirror also has a lamp on it. The scientist can see the
reflection in the mirror and the lamp side-by-side as the probe
falls toward the black hole, and easily tells the two apart.

The laser beam and lamp each emit light which encodes the
time it is emitted according to the local clock. The laser light
encodes the time the scientist's clock reads as it is emitted,
and the lamp light encodes the time the probe's clock reads as
it is emitted.

The scientist initially sees the two times as identical with the
time on his clock. As the probe moves away and accelerates
toward the black hole, both times lag behind his clock, but the
time in the reflection has a greater lag. If the probe was NOT
from the scientist at a constant, low speed, then the reflected
time would always lag twice as much as the lamp time. Both
lags would be due purely to the light travel time. The reflected
light would be redshifted by the speed of the probe by twice as
much as the lamp light is redshifted. The redshift would be
constant, the clock tick rates in the images would be constant,
and the rates at which the two time lags increase would be
constant.

In ALL cases, the amount of redshift is identical to the amount
of difference between the scientist's clock and the light images.
In ALL cases, the time in the lamp image is the time that the
reflected laser light (seen at the same instant by the scientist)
was being reflected. That is, light emitted by the lamp and laser
light reflected by the mirror at the same instant always travel
together side-by-side, and never get separated from each other.

As the probe approaches the black hole, it accelerates, increasing
the redshift of both images, increasing the slowing of the timing
in the images, and increasing the lag of both times over what it
would be for a probe that was merely coasting away.

At the instant the probe crosses the event horizon, its lamp is
emitting light with a particular time stamp. At that same instant,
the mirror is reflecting laser light that has a particular time stamp.
That will be the last light that reaches the scientist.

How long after the probe crosses the event horizon the last
photons from the lamp and the reflected laser light can be
detected by the scientist depends on:

- The distance from the probe to the scientist (light travel time)

- The size of the black hole (affects how much the photons are
dispersed as they move upward away from the event horizon)

- The rate at which photons are being emitted or reflected
(the initial intensity of the light in photons per second)

- The rate at which the scientist can detect photons
(assume he can detect and identify even a single photon)

- The frequency or energy at which the photons are emitted
(the higher the frequency or energy, the more they can be
redshifted before they are too stretched out to detect)

- The frequency or energy at which the scientist can detect
photons (I don't think the scientist can detect photons which
are so redshifted that their wavelength is greater than the
distance between the point of emission and the "point" of
detection. Also, realistically, the longer the wavelength,
the more photons are required for detection.)

As a realistic thought experiment, discounting the light travel
be much less than a second. The images would not appear
frozen at the event horizon for any significant length of time
because they would be so weakened by thinning out of the
photons and redshifting of each individual photon.

The scientist can calculate the timestamp of the laser pulse
that reaches the probe as the probe crosses the horizon, and
the timestamp of the light emitted by the lamp on the probe
at the same instant.

I believe he can also calculate the time that his clock must be
showing as that happens, and the time his clock will show when
he observes those last few observeable photons. But it can't
be precise because the very last photons may be stretched out
so much that they cannot be detected.

-- Jeff, in Minneapolis

.

WaxRubiks
2015-Jun-11, 05:32 PM
So at what point would the last photon be received by the distant observer?

Grey
2015-Jun-11, 06:20 PM
So at what point would the last photon be received by the distant observer?As I said, in principle it can be any time in the future, depending on just how close to the event horizon it is emitted. But on average, it's likely to be very quickly. The exact details depend on things like the size of the black hole, but Jeff's right that it will generally be within seconds of the redshifting becoming really noticeable.

WaxRubiks
2015-Jun-11, 08:03 PM
As I said, in principle it can be any time in the future, depending on just how close to the event horizon it is emitted.

so if it weren't for black holes evaporating and having finite lives, there would be no ending of photons being reflected from the mirror?

Grey
2015-Jun-11, 08:33 PM
so if it weren't for black holes evaporating and having finite lives, there would be no ending of photons being reflected from the mirror?It depends on what you mean by "no ending", but this doesn't really have much to do with black holes having finite lives. If you didn't look at the diagram I linked to from my first response, I'd really encourage you to do so. There's a fixed total number of photons that will reach the mirror in time to be reflected. Those photons will in principle indeed be spread over the entire future of the outside observer. However, since photons are discreet, and there are a fixed number, in practice it's very unlikely that one will be received very late, even though it's technically possible. Think about it like an exponential decay in how quickly photons are arriving.

It's a little like the tail ends of positional probability that you find in quantum theory when dealing with a particle confined to a potential well. Yes, in principle, that electron has a finite probability of actually being a couple kilometers away, but in practice, the chance of that happening is so small that you can ignore it.

So what you'll see as the mirror falls is that, at first, the laser will be reflected normally. As the mirror gets closer to the black hole, you'll see the beam start to redshift and the intensity will drop as the time between each photon arriving gets longer. Shortly after that, the redshift will become very large and the intensity will drop very rapidly, dwindling to almost nothing. Toward the end of that, the reflected beam will consist of individual photons separated by longer and longer amounts of time. By the time you notice that happening, you'll pretty much stop seeing any photons within a few seconds. Now, it is true that there will never be a point when you can be absolutely certain that you've seen the very last photon; another one could arrive any time, for the rest of the life of the universe. But it's not very likely. And even if you did suddenly observe a photon arriving a day (or a century) later, by that time there wouldn't really be any way to be sure it wasn't just a random CMB photon, rather than a photon from your laser.

WaxRubiks
2015-Jun-11, 08:39 PM
Shortly after that, the redshift will become very large

on that point: wouldn't the redshift be cancelled by the ingoing blueshift?

Grey
2015-Jun-11, 08:56 PM
on that point: wouldn't the redshift be cancelled by the ingoing blueshift?No. A freely falling observer near a black hole (like the mirror) will not see incoming light significantly blueshifted (in fact, it will see slightly redshifted, but not greatly). An observer hovering near an event horizon will see light from the rest of the universe greatly blueshifted, but that's a different situation.

WaxRubiks
2015-Jun-11, 08:58 PM
No. A freely falling observer near a black hole (like the mirror) will not see incoming light significantly blueshifted (in fact, it will see slightly redshifted, but not greatly). An observer hovering near an event horizon will see light from the rest of the universe greatly blueshifted, but that's a different situation.

so the blueshift is cancelled out during the reflection?

Grey
2015-Jun-11, 09:10 PM
so the blueshift is cancelled out during the reflection?There is no blueshift. Again, an observer hovering close to the event horizon will see light from further away blueshifted, but an observer freely falling toward the event horizon will not see that same light blueshifted. Redshift and blueshift aren't things that can be said to happen in any absolute sense. It's always with regard to how one observer will see light emitted by a source that is moving differently or is in a different place in a gravitational field (or maybe both).

WaxRubiks
2015-Jun-11, 09:18 PM
doesn't light that is bent by a BH first blueshift as it gets closer to the BH, and then redshift on its way out, or is that too Newtonian a way to look at it?

Grey
2015-Jun-12, 12:15 AM
doesn't light that is bent by a BH first blueshift as it gets closer to the BH, and then redshift on its way out, or is that too Newtonian a way to look at it?Too Newtonian. You're trying to imagine that something is happening in absolute terms to the light. But relativity is all about how different observers will see things, depending on their frames of reference. For an observer holding stationary near a black hole, it is true that such an observer will see light coming from farther away as blueshifted. If the observer is close to the event horizon, the light will be very blueshifted. But an observer who is freely falling into a black hole is in a different reference frame from one who is holding stationary (under huge acceleration to maintain position against the black hole's gravity). As such, the freely falling observer won't necessarily observe the same things, and one of the things in particular that is different is that light from further away is not seen to be blueshifted.

That's just relativity: observers in different reference frames see different things. And under relativity, we pretty much accept that it's not appropriate to ask whether the light "really" blueshifts or not. All observers are equally valid, even though they'll see different things.

Maybe it will help if I point back to something Jeff said, that the amount of redshift is the same as the amount of delay for a pulse of light. If you think about it, that has to be true. If you were to send out a series of light pulses, and they end up delayed, that just means the time between each pulse is longer. But a light beam can be seen as a series of wave crests and troughs, which are just as much markers as pulses would be. So the time between two successive wave crests has to get longer by exactly the same proportion as the time between two pulses. If the time between two wave crests is longer, that means the frequency is lower, and the light is redshifted. Since the light that comes back from the falling mirror is spread out over a longer time than it was emitted, it also has to be redshifted, by the same amount.

jartsa
2015-Jun-12, 04:31 PM
doesn't light that is bent by a BH first blueshift as it gets closer to the BH, and then redshift on its way out, or is that too Newtonian a way to look at it?

Yes. It goes something like this:

Light has normal energy when it leaves the laser.
Light gains 10000% more energy as it falls down.
Light gives most of its energy to mirror, light's energy becomes about half of the original energy.
Light loses 99 % of its energy as it climbs up.
99.5 % of the original energy of the light was "lost" in this process, all lost energy became kinetic enrgy of the mirror.

Gravity field did a lot of work on falling light. Climbing light did a small amount of work on gravity field. Energy lost by gravity field became kinetic energy of the mirror.

Shaula
2015-Jun-12, 05:06 PM
Gravity field did a lot of work on falling light. Climbing light did a small amount of work on gravity field. Energy lost by gravity field became kinetic energy of the mirror.
Energy is not conserved in general in GR. It is only a local conservation law (in effectively flat spacetime). If you are getting to extreme redshifts as you are describing then the energy pseudotensor is path dependent.

jartsa
2015-Jun-12, 05:23 PM
Energy is not conserved in general in GR. It is only a local conservation law (in effectively flat spacetime). If you are getting to extreme redshifts as you are describing then the energy pseudotensor is path dependent.

Energy is conserved when running a machine consisting of a mirror, a laser, and a black hole. Do I need to justify this?

Shaula
2015-Jun-12, 05:35 PM
Energy is conserved when running a machine consisting of a mirror, a laser, and a black hole. Do I need to justify this?
In your scenario you had a gravitational redshift that led to an apparent 'loss of energy' of 99% and a gain of 10000%. That is pretty extremely curved space. And you further claim that 95% of the photon's energy is imparted as KE to the mirror and make a series of other claims about the relative amounts of energy gained/lost. So yes, you do need to show, in GR, what you think is conserved and how it is conserved if you are to make that claim.

jartsa
2015-Jun-17, 10:22 AM
In your scenario you had a gravitational redshift that led to an apparent 'loss of energy' of 99% and a gain of 10000%. That is pretty extremely curved space. And you further claim that 95% of the photon's energy is imparted as KE to the mirror and make a series of other claims about the relative amounts of energy gained/lost. So yes, you do need to show, in GR, what you think is conserved and how it is conserved if you are to make that claim.

Well, I don't think so. :)

First I postulate that there's a 10000% energy increase when light falls down.

Then I say light's energy becomes about half of the original. Well, that was wrong. Light's energy becomes ... millionth of the original, and that is just a made up number.

Then I say climbing takes so much energy that only one hundreth remains, this we know from the fact that falling made energy hundred times larger, climbing is a reverse process.

Quite obviously light's energy when it returns back is one millionth times one hundredth of the original energy. One millionth is still a made up number.

Then I say any "lost" energy must become kinetic energy of the mirror, we know this is true, because otherwise we would see a definite violation of conservation of energy.

I guess you were right, there was a unfounded claim about "about half of the original energy".

Shaula
2015-Jun-17, 05:38 PM
Then I say any "lost" energy must become kinetic energy of the mirror, we know this is true, because otherwise we would see a definite violation of conservation of energy.
And as I pointed out when you are dealing with highly curved space then you have to take GR into account. And GR doesn't have a globally conserved energy, it has a pseudotensor that is approximately conserved locally but is highly path dependent when looked at globally in curved spacetime. So this statement makes no sense and, as I said, you have to define what you are calling energy and why you expect it to be conserved. Because the GR stance is that your reasoning here is flawed because you cannot define a conserved global energy.

Jeff Root
2015-Jun-17, 07:25 PM
Redshift and blueshift aren't things that can be said to
happen in any absolute sense. It's always with regard
to how one observer will see light emitted by a source
that is moving differently or is in a different place in a
gravitational field (or maybe both).
That is why I disagree with those who say that light loses
energy when it is redshifted by cosmic expansion. If blue
light is emitted from a source, and is seen as red by distant
observers due to cosmic expansion, you may understandably
get the impression that the light has lost energy. But each
of those distant observers would say that the light reaching
observers on the far side of the source is blueshifted to UV
relative to them by the expansion, not redshifted. I think
the redshifting and blueshifting may exactly cancel for the
overall energy account of the volume of expanding space
that the light reaches. Meaning no change in the total
energy in the expanded volume, although a decrease in
energy density.

-- Jeff, in Minneapolis

WaxRubiks
2015-Jun-17, 07:40 PM
I wonder if light even exists between emitter and receiver.

Grey
2015-Jun-17, 08:52 PM
That is why I disagree with those who say that light loses
energy when it is redshifted by cosmic expansion. If blue
light is emitted from a source, and is seen as red by distant
observers due to cosmic expansion, you may understandably
get the impression that the light has lost energy. But each
of those distant observers would say that the light reaching
observers on the far side of the source is blueshifted to UV
relative to them by the expansion, not redshifted. I think
the redshifting and blueshifting may exactly cancel for the
overall energy account of the volume of expanding space
that the light reaches. Meaning no change in the total
energy in the expanded volume, although a decrease in
energy density.If I'm understanding you correctly, it sounds like you're trying to add up the energy observed by every potential observer to get some kind of total "meta-energy" value. I don't think that's going to give you anything useful. I don't think that it's meaningful to try to add the total energy (or even just the changes in energy) of the same objects, but from more than one reference frame.

WayneFrancis
2015-Jun-18, 07:56 AM
If a scientist threw a mirror towards a black hole, it would fall and fall towards the event horizon but never be seen to cross it.

If the scientist flashed a laser into the mirror, for how long would he see the flash reflected?

Assuming the scientist would live for billions of years, would he see the flash reflected for that long?

You may want to discuss red and blue shift, but when I say 'see the flash reflection', I mean that he is able to detect the radiation someone, even if it isn't in the visible range.

Is there a moment when the laser flash wouldn't be 'seen'? Even after billions of years?

This is a pop science misunderstanding of what happens to a free falling object and what an external observer would see.
The reality is that an external observer would see an object falling into the black hole, quickly red shift and within a very finite amount of time stop emitting/ reflecting photons.
There comes a point outside the EH where the last photon from that object will be emitted to any external observer.
So you wouldn't even have to wait billions of years. You would probably only have to wait slightly longer then an object falling onto the surface of a similarly sized object.

WayneFrancis
2015-Jun-18, 07:58 AM
The answer here is more or less the same as if you drop a light source toward the event horizon. In principle, the light from the falling object is spread out over the entire future of a distant observer, but in practice, it rapidly diminishes to nearly nothing. If you take into account that light is made of photons, there will be a last photon emitted, and the average time for the observer to see that last photon is actually quite short (I think on the order of minutes to hours, depending on the size of the black hole and exactly how far away the observer is).

I was hoping someone would have a diagram of this, and found a great one here (http://www.quora.com/Suppose-you-cross-the-event-horizon-of-a-supermassive-black-hole-and-you-have-a-friend-just-outside-the-event-horizon-holding-a-mirror-If-you-fire-a-beam-of-light-at-the-mirror-and-measure-how-long-it-takes-to-return-how-will-the-result-be-consistent-with-the-constant-speed-of-light). It's a slightly different description, but it has Alice (who is falling into a black hole) and Bob (an observer at a fixed distance outside) bouncing light beams back and forth to each other. The light beams are the lines at 45 degree angles. You can see that light emitted (or reflected) when Alice gets close to the event horizon can in principle reach Bob arbitrarily late, but you can also see that light reflected very close together in time from Alice's perspective arrives at very different times for Bob. That's where the last photon issue comes in. There's certainly a chance that the last reflected photon could come at any arbitrary future point, but it's very unlikely (and there's also a point at which it would be hard to distinguish it from any other random photon).

Also, it's good to realize that the total amount of light reflected will be fixed. One thing the diagram makes very clear is that there is a definite point at which the laser from Bob will not make it to Alice's mirror in time to be reflected before the mirror crosses the event horizon. Light from Bob's laser emitted after that will never make it back to Bob. Similarly, there's a definite point at which light from Bob's laser won't reach Alice or her mirror before Alice reaches the singularity. So Alice won't see the entire future of the outside universe go by as she falls in.

Sounds like one of Susskind's lectures.