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#38078 - 04/11/11 05:53 PM Light From Distant Galaxies.
Bill S. Offline
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When I first met the idea that light from an object that was moving away from us at superluminal speed would never reach us, it seemed quite reasonable. However, I seem to have developed a problem arising from the fact that light must always be observed as travelling at c, irrespective of any relative movement between emitter and receiver. It goes something like this.

A distant object is moving away, relative to Earth, at superluminal speed. At a given point (say 15 billion l y away, which we will call “point A”) it emits a photon. This photon should reach Earth 15 billion years later.

Assume the emitting object is receding (relative to Earth) at 1.5c. One year later it is at point B, which is 16.5 l y from Earth. There it emits another photon, which should reach Earth after 16.5 years; ie, 1.5 years after the arrival of the photon emitted at point A.

Whatever the speed of recession of the emitting object, any light emitted must, from the viewpoint of Earth, be approaching Earth at c, so it must eventually arrive.

I accept that there must be something wrong with this reasoning, but at the moment I can’t see what it is.
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#38079 - 04/11/11 07:18 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill Offline
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The reason we don't receive light from the edge of the observable universe is simple. The Doppler Effect causes the light to be red shifted to a frequency of zero. Well, that is what we say. I better qualify that a little bit. The stretching of space due to the continued expansion of space causes the wavelength to be so long that it is undetectable.

Bill Gill
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#38082 - 04/12/11 01:30 AM Re: Light From Distant Galaxies. [Re: Bill]
Bill S. Offline
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Thanks Bill.
I had progressed as far as considering the expansion of space. In fact I had made a distinction between the Doppler Effect caused by moving vehicles and that caused by the expansion of space. I was stuck on the idea of the observed speed of light being constant, and overlooked the fact that it would have red shifted away to nothing by the time it reached Earth.
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#38124 - 04/16/11 03:14 AM Re: Light From Distant Galaxies. [Re: Bill S.]
KirbyGillis Offline
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Bill S.

I must say; You have a knack for posing some interesting questions (problems).

BTW; they say that the acceleration rate of gravity within the event horizon of a black hole is super luminal and that no light of any wavelength escapes.
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#38129 - 04/16/11 02:25 PM Re: Light From Distant Galaxies. [Re: KirbyGillis]
Bill Offline
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That's right. No light escapes from a black hole horizon because the gravitational red shift stretches the wave length so that it can't get out. Of course the other way to look at it is that time for the wave, in the reference frame of the light wave, is slowed down to 0, in comparison with clocks in our reference frame. The original conception of the black hole was that the escape velocity for a black hole is greater than the speed of light. So there are several ways of thinking of it, depending on what way you want to look at it.

Bill Gill
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C is not the speed of light in a vacuum.
C is the universal speed limit.

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#38132 - 04/16/11 04:51 PM Re: Light From Distant Galaxies. [Re: Bill]
Bill S. Offline
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Is it me, or is nothing straight forward? Let’s take your points one at a time.

“No light escapes from a black hole horizon because the gravitational red shift stretches the wave length so that it can't get out.”
Does this imply that the wavelength would have to be infinite in order to escape? If so, could it not escape when it became "effectively infinite"?

“…that time for the wave, in the reference frame of the light wave, is slowed down to 0, in comparison with clocks in our reference frame.”
Elsewhere, we met the argument that light could not be said to have a frame of reference. How could one re-phrase your statement in order to avoid ascribing a F of R to light?

“The original conception of the black hole was that the escape velocity for a black hole is greater than the speed of light”
Initially, this interpretation seemed to present no problems, but, light must always be measured as travelling at c, so it must be seen (or presumed, if there is no-one to see it) to be approaching the event horizon, from the inside, at c. What stops it from going through?
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#38133 - 04/16/11 05:23 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill Offline
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I told you to stop trying to make me think!

Ok, let's take your points 1 at a time.

re: Red Shift - I am trying to avoid the use of the word infinite, because no body seems to be able to come up with a good working use for it. But yes, the wavelength becomes infinite, and the frequency drops to zero. Keep in mind that an infinite wavelength means that the wave is smeared over the whole universe. Actually I believe that some work has been done which suggests that the light quanta are smeared over the surface of the horizon. I think, but am not sure, that I kind of got that idea from "The Black Hole War" by Leonard Susskind.

re: time slowed to zero - The idea of a rest frame for light is problematic, so let's say that time in a reference frame located at the horizon would apparently be slowed to zero as compared to our clocks. Keep in mind that in the frame at the horizon time would appear to move normally. If you were to fall into a sufficiently large black hole you would be able to fall all the way into it without the tidal effects pulling you apart, because the center of mass would be far enough away that they would be minimal. So as you fell through the horizon you would not notice any special effects. But from a distant observer you would appear to be torn apart and swallowed up. Hey, you thought just QM was crazy?

re: escape velocity - That is one of the poorer ways of describing the black hole horizon. However, it was what the first discussion of a sort of black hole was based on. Escape velocity is the velocity a mass has to have to escape from the gravitational attraction of another mass. If you throw a rock into the air it will slow for some period of time, then come back down and hit you on the head. If you throw it harder it will go up farther and take longer to hit you on the head. At some velocity it will reach a velocity that it will never come back down. That is escape velocity. Well, somebody started looking at that and imagining larger and larger planets, and figuring the escape velocity. This was a purely Newtonian calculation, done long before Einstein. He reached the conclusion that a sufficiently large star could have an escape velocity greater than the speed of light. He was pretty much ignored, but the idea was still kind of floating around. Then when Einstein invented GR Chandrasekhar used to conclude that they were theoretically possible. But escape velocity is still one of the relatively simple ways to explain it. Now after that digression, back to your problem. When a photon, traveling at light speed, reaches the horizon, it has used all the energy it has, and falls back into the interior. Of course since it now has zero energy, it also has a zero frequency, so we are back to the red shift. In fact just about all the ways of looking at how a black hole works are just different ways of saying pretty much the same thing.

Now I hope that is confusing enough.

Bill Gill
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C is not the speed of light in a vacuum.
C is the universal speed limit.

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#38134 - 04/16/11 07:20 PM Re: Light From Distant Galaxies. [Re: Bill]
Bill S. Offline
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Originally Posted By: Bill
When a photon, traveling at light speed, reaches the horizon, it has used all the energy it has, and falls back into the interior.


Would it not have to stop in order to do that; like that rock that kept hitting me on the head. smile
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#38136 - 04/16/11 10:28 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill Offline
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Well, it would have to stop moving away from the center, but that doesn't mean it would stop moving. If it was moving at an angle it would just change direction.

Bill Gill
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C is not the speed of light in a vacuum.
C is the universal speed limit.

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#38139 - 04/17/11 06:24 AM Re: Light From Distant Galaxies. [Re: Bill]
Bill 6 Offline
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Registered: 02/28/11
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Originally Posted By: Bill
re: escape velocity - That is one of the poorer ways of describing the black hole horizon.


This is a derogatory classification of what you later more suitably describe as being one of the relatively simple ways to explain it.

I happen to agree with Einstein that we should keep things as simple as possible...unfortunately many people have the habit of latching onto new concepts such as 'black holes' and adding their own usually much more extreme aspects (such as worm tunnels) in attempts to have their name associated with such phenomena.

I believe that the person who "...reached the conclusion that a sufficiently large star could have an escape velocity greater than the speed of light." was the British astronomer the Rev. John Michell who, in the 1700's, reasoned that if a star had a strong enough gravity it would choke off its own light but I don't see this as suggesting that having been emitted by the star that light would then be pulled back into same but that the light would not escape in the first place.

In 'Einstein's Universe' Nigel Calder wrote (62, BBC, 1979):- "Light travels faster...toward the centre of gravity than away from it."

The stronger the object's gravitational field the greater that variation and on that basis - as a star collapses the rate of departure of a beam of light traveling away from that (fixed location) source gradually reduces to zero in some cases.

This is, of course, from the point of view of a far distant observer whereas a local observer (located alongside the light source) would determine c for both beams however this is solely due to the fact that his measuring rods and clocks are physically distorted by that field.

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#38146 - 04/17/11 12:04 PM Re: Light From Distant Galaxies. [Re: Bill 6]
Bill S. Offline
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Originally Posted By: Bill6
"Light travels faster...toward the centre of gravity than away from it."

This is, of course, from the point of view of a far distant observer whereas a local observer (located alongside the light source) would determine c for both beams however this is solely due to the fact that his measuring rods and clocks are physically distorted by that field.


Let me get this straight. Are we saying that light does not always travel at c; it only seems like that to an observer?
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#38147 - 04/17/11 12:12 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill S. Offline
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Originally Posted By: Bill
Well, it would have to stop moving away from the center, but that doesn't mean it would stop moving. If it was moving at an angle it would just change direction.


(Thinking aloud, here): A change of direction = a change in velocity; light changes velocity without reducing speed, so it (sort of) goes into orbit inside the event horizon. (?)
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#38150 - 04/17/11 05:13 PM Re: Light From Distant Galaxies. [Re: Bill 6]
Bill Offline
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Originally Posted By: Bill 6
The stronger the object's gravitational field the greater that variation and on that basis - as a star collapses the rate of departure of a beam of light traveling away from that (fixed location) source gradually reduces to zero in some cases.


Well, that is obviously wrong. The speed of light, measured in any reference frame, is always the same, approximately 300 million meters per second. What happens as light travels away from the star is that it is red shifted until the frequency gets to zero. Since energy is equal to Planck's constant multiplied by the frequency (e = Hf) then at that point it has effectively zero energy. The energy it had before has been transferred to the gravitational energy of the star. Possibly the source you are quoting misunderstood the way it works.

Bill Gill


Edited by Bill (04/17/11 05:13 PM)
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C is not the speed of light in a vacuum.
C is the universal speed limit.

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#38151 - 04/17/11 05:19 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill Offline
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Originally Posted By: Bill S.
A change of direction = a change in velocity; light changes velocity without reducing speed, so it (sort of) goes into orbit inside the event horizon. (?)


Well, I guess that is one way of looking at it. Another way is that it is that, since it's wavelength has become infinite, it is smeared all over the surface of the event horizon. The fact is that this is one more of those things that just really don't have any kind of a real analog in the world we can see around us. I doubt if even physicists that work with GR really have a good feel for what is going on, but they do know the math and can understand what is happening.

Bill Gill
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C is not the speed of light in a vacuum.
C is the universal speed limit.

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#38152 - 04/17/11 05:44 PM Re: Light From Distant Galaxies. [Re: Bill]
Bill S. Offline
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Registered: 08/20/10
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Loc: Essex, UK
Originally Posted By: Bill
Another way is that it is that, since it's wavelength has become infinite.....


I think you said that on purpose, because you knew I would ask how you fit an infinite wave in a finite space, inside an event horizon. smile
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#38154 - 04/17/11 06:22 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill S. Offline
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Anyway; how did we get from talking about distant galaxies to black holes?
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#38156 - 04/17/11 08:15 PM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill Offline
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They call it thread drift. If you have ever looked at some of the things discussed in the news groups on USEnet you would have seen some really drastic thread drifts.

Bill Gill
_________________________
C is not the speed of light in a vacuum.
C is the universal speed limit.

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#38160 - 04/18/11 01:42 AM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill 6 Offline
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Registered: 02/28/11
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Originally Posted By: Bill S.
Let me get this straight. Are we saying that light does not always travel at c; it only seems like that to an observer?


The speed of light is always measured as being c due to the fact that the devices employed - clocks and rods - can be physically affected either by relative motion (SR) or respective locations in a gravitational field (GR).

In his book 'Albert Einstein' Banesh Hoffmann (Paladin, 1975) makes no less than six references to Einstein's 'heretical' discovery of the variable speed of light and in 'Relativity, the special and general theory' Einstein wrote that the results of special theory are invalidated by gravity (76, Crown, 1916).

In the introduction to general theory Einstein wrote that the special theory law of the constancy of the speed of light required modification (Annalen der Physik 773, 49 1916).

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#38161 - 04/18/11 02:41 AM Re: Light From Distant Galaxies. [Re: Bill]
Bill 6 Offline
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Registered: 02/28/11
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Loc: Australia
Originally Posted By: Bill
Originally Posted By: Bill 6
The stronger the object's gravitational field the greater that variation and on that basis - as a star collapses the rate of departure of a beam of light traveling away from that (fixed location) source gradually reduces to zero in some cases.

Well, that is obviously wrong.


Imagine that you are looking at a light source located in your reference frame and some distance away from you. The source emits beams of light in opposite directions which, in a certain period of time as determined by your clock, travel identical distances away from that source:-

<----------•---------->


The source now starts accelerating across your line of vision and again emits beams of light in opposite directions which, in a certain period of time as determined by your clock, travel different distances away from their source:-

<---------------•----->

From your point of view, as a distant observer, the beams are moving at different speeds relative to you due to the fact that their source is accelerating.

The light source is now (hypothetically) located at a fixed distance from a black hole. On the basis of the principle of equivalence the respective beams will similarly travel at different speeds away from their source:-

<---------------•----->

From your (distant observer) point of view the beam that is traveling radially toward the centre of gravity is moving faster away from its source (and relatively to you) than the beam that is headed in the opposite direction (you cannot, of course, actually see those beams).

"Light travels faster...toward the centre of gravity than away from it." (Nigel Calder, 'Einsteins Universe')

Originally Posted By: Bill
The speed of light, measured in any reference frame, is always the same.

In the above detailed event relative to a black hole... the speed of light is only determined to be constant by a local observer whose rules and clocks are physically affected by the gravitational field.

The speed of the respective beams of light is not the same as far as the distant observer is concerned.

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#38162 - 04/18/11 02:46 AM Re: Light From Distant Galaxies. [Re: Bill S.]
Bill 6 Offline
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Registered: 02/28/11
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Originally Posted By: Bill S.
Anyway; how did we get from talking about distant galaxies to black holes?

Because of the principle of equivalence - the fact that light emitted by an accelerating source is analogous to light emitted by a source located in a gravitational field.

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