Time dilation and Hawkins radiation.

[Jomazing]

As an object approaches the event horizon of a black hole, time dilation becomes increasingly more extreme, to the point where from an external observer's perspective, the object appears to freeze at the event horizon. However, due to the finite amount of time it takes for the black hole to decay via Hawking radiation, the object would never actually cross the event horizon and reach the singularity. In fact, it would take an infinite amount of time for the object to reach the singularity, as time dilation becomes infinite at the singularity. Therefore, from an external observer's perspective, the black hole would slowly decay over an incredibly long period of time, without ever seeming to fully "consume" the object that approached it. Please poke any holes in this as possible, i came up with if and am feeling cunfused.

[Halc]

11 hours ago, Jomazing said:

Therefore, from an external observer's perspective, the black hole would slowly decay over an incredibly long period of time, without ever seeming to fully "consume" the object that approached it.

This seems reasonable to me. Key here is 'from an external observer's perspective', which usually means 'relative to the coordinate system of some distant thing'. That coordinate system usually omits assignment of coordinates to events inside a black hole.

A black hole event horizon (EH) is nothing but a null surface, not a singularity. It is pretty much analogous to the Rindler horizon of a constantly accelerating coordinate system, which is also a null surface.  So say I am accelerating at 1G constantly forever at the front of a nearly light-year long ship. If I drop a rock, it will, relative to my accelerating coordinate system, fall to the Rindler horizon about a light year behind me. From my perspective, the EH would emit Unruh radiation (the accelerating equivalent of Hawking radiation) over an incredibly long period of time, without ever seeming to "consume" the object that approached it. From the rock's perspective, the ship speeds by in a year of rock time and the rock notices nothing as that EH passes by, just like it would not be able to detect anything funny about falling into a black hole. But the rock's perspective (frame) is a different one than that of your distant observer.

[OceanBreeze]

On 5/9/2023 at 9:43 AM, Jomazing said:

As an object approaches the event horizon of a black hole, time dilation becomes increasingly more extreme, to the point where from an external observer's perspective, the object appears to freeze at the event horizon. However, due to the finite amount of time it takes for the black hole to decay via Hawking radiation, the object would never actually cross the event horizon and reach the singularity. In fact, it would take an infinite amount of time for the object to reach the singularity, as time dilation becomes infinite at the singularity. Therefore, from an external observer's perspective, the black hole would slowly decay over an incredibly long period of time, without ever seeming to fully "consume" the object that approached it. Please poke any holes in this as possible, i came up with if and am feeling cunfused.

There are several things you have not taken into consideration in your analysis.

1).You are right in saying the infalling object will “experience” extreme time dilation. However, you have not mentioned that this means that light from the object will be extremely redshifted. In fact, from the distant observer’s point of view, as the object crosses the event horizon at the speed of light, time will slow to the point where it will take longer than the lifetime of the universe for the object to emit individual photons! Consequently, for the distant observer the object will become more and more redshifted to the point it fades out of sight.

2). You are also right that the distant observer will never see the object cross the event horizon, but you are wrong in thinking the distant observer will see the object frozen at the event horizon. As I wrote in (1) the object would fade out of sight.

3). However, we now have actual photos of black holes, and they all show they are surrounded by accretion disks. These disks are formed by infalling matter being accelerated to orbit the BH at high velocity (about 1/3 the speed of light) and due to friction reach temperatures of about 10 million degrees C. Any object caught up in such an accretion disk will be shredded into just streams of atoms before falling into the BH at the speed of light.

1 

 

As far as your thoughts about what happens inside the event horizon, that is currently outside the limit of our physics. We don’t even know for sure if there is a singularity inside the event horizon, let alone what happens there.

Some useful links:

https://astronomy.com/magazine/ask-astro/2022/11/can-an-observer-ever-see-anything-fall-into-a-black-hole

https://www.space.com/41923-black-hole-material-one-third-light-speed.html

https://science.howstuffworks.com/accretion-disk.htm

 

[Halc]

Some clarification commentary. Not trying to be contradictory, but sometimes it comes out that way.

On 5/11/2023 at 2:14 AM, OceanBreeze said:

You are right in saying the infalling object will “experience” extreme time dilation.

Well, dilation isn't something experienced. Per the principle of relativity, the laws of physics are locally the same in any frame, so the infalling guy will experience nothing out of the ordinary, including the passing through the EH.

Time dilation is a coordinate effect, the result of an arbitrary choice of some abstract coordinate system other than the one of the thing being measured.

On 5/11/2023 at 2:14 AM, OceanBreeze said:

However, you have not mentioned that this means that light from the object will be extremely redshifted.

Redshift is a non-local observer effect. Yes, a 'stationary' distance observer will see something near the EH redshifted. But the falling observer will see the distant observer redshifted. Somewhat similarly, any to observers moving inertially away from each other will see each other redshifted, but the symmetry isn't there with the black hole case.

So for instance, an observer hovering just above the EH will see the distant observer blueshifted, mostly due to his high acceleration in that direction, similar to distant galaxies appearing blueshifted if you accelerate towards them hard enough.

On 5/11/2023 at 2:14 AM, OceanBreeze said:

Consequently, for the distant observer the object will become more and more redshifted to the point it fades out of sight.

Yes. And the falling observer will still be able to see and receive messages from the distant observer even after he's passed the EH.

On 5/11/2023 at 2:14 AM, OceanBreeze said:

Any object caught up in such an accretion disk will be shredded into just streams of atoms

Yes, but most questions about infalling things assume a clean non-rotating black hole and falling pretty much straight in without first being nuked to atoms by orbiting plasma. We're also assuming a very large black hole to minimize second order effect (spaghettification). Tidal forces even near say a neutron star is enough to be fatal to a person, let alone the quick death of actually reaching the surface of one.

On 5/11/2023 at 2:14 AM, OceanBreeze said:

before falling into the BH at the speed of light.

That seems to be a misrepresentation. From the distant observer's PoV, it comes to a halt at the EH, never falling in at all. From the falling guy PoV, he's stationary and the EH (a null surface) passes him at the speed of light. From nobody's PoV is anything with mass moving at the speed of light.

On 5/11/2023 at 2:14 AM, OceanBreeze said:

As far as your thoughts about what happens inside the event horizon, that is currently outside the limit of our physics. 

Well, physics says that nothing is especially different inside. As stated before, you'd not notice anything different and would have to compute when the EH was crossed since there's no obvious way to measure it. OK, the nature of the singularity itself probably requires a unified field theory. GR says that a Schwarzschild BH has a sort of 1D line singularity. A Kerr BH has a 2D ring singularity, maybe like a garden hose. The Reissner–Nordström metric describes a charged BH with more than one event horizon (including a Cauchy horizon) inside of which the 'singularity' gets sort of fuzzy.

All real black holes are a combination of these metrics, none being a nice clean example of any one of them.

[OceanBreeze]

21 hours ago, Halc said:

Some clarification commentary. Not trying to be contradictory, but sometimes it comes out that way.

We appreciate clarification commentary, even when it is contradictory. That is what we are here for.

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Well, dilation isn't something experienced. Per the principle of relativity, the laws of physics are locally the same in any frame, so the infalling guy will experience nothing out of the ordinary, including the passing through the EH.

Time dilation is a coordinate effect, the result of an arbitrary choice of some abstract coordinate system other than the one of the thing being measured.

 

There is a reason I placed “experience” in quote tags. Maybe I should have used “undergoes” instead.

But I do not agree that the laws of physics, as far as we know them, necessarily hold beyond the event horizon. Certainly, Newtonian physics does not hold.

 I also didn’t realize we were talking here about an infalling “guy”. As I understood the OP, the discussion is about an object. But that’s fine; we can assume the object is an astronaut.

Now, if said astronaut was stretched by tidal forces into spaghetti, as some theories predict, I would think he might be having a rather unpleasant “experience”. Even if he were not turned into spaghetti, he would be moving at such a high velocity that collisions with other matter that is near the BH would heat him until he is glowing hot! Finally, I do believe he would experience many g’s of acceleration. But I could be wrong. . . .

 

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Redshift is a non-local observer effect. Yes, a 'stationary' distance observer will see something near the EH redshifted. But the falling observer will see the distant observer redshifted. Somewhat similarly, any to observers moving inertially away from each other will see each other redshifted, but the symmetry isn't there with the black hole case.

So for instance, an observer hovering just above the EH will see the distant observer blueshifted, mostly due to his high acceleration in that direction, similar to distant galaxies appearing blueshifted if you accelerate towards them hard enough.

 

Agreed. (I did mention that the time dilation and the redshift is referenced to the distant observer)

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Yes. And the falling observer will still be able to see and receive messages from the distant observer even after he's passed the EH.

OK.

 

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Yes, but most questions about infalling things assume a clean non-rotating black hole and falling pretty much straight in without first being nuked to atoms by orbiting plasma. We're also assuming a very large black hole to minimize second order effect (spaghettification). Tidal forces even near say a neutron star is enough to be fatal to a person, let alone the quick death of actually reaching the surface of one.

Most questions may assume such a thing but the OP’s question wasn’t that specific. As far as I know, the only BHs we have positively detected all have these accretion disks around them. In fact, it is the presence of the accretion disks that allows for us to positively detect and identify them; otherwise they would be invisible. We can speculate there may be “clean” non-rotating BHs out there in space but they would be hard to detect or even undetectable. Their presence may be suspected by secondary effects they have on other objects, but suspicions of a BH is not quite the same as confirmation. I think the accretion disks deserve mentioning since they confirm the presence of a BH and they are what we actually see and can photograph.

 

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That seems to be a misrepresentation. From the distant observer's PoV, it comes to a halt at the EH, never falling in at all. From the falling guy PoV, he's stationary and the EH (a null surface) passes him at the speed of light. From nobody's PoV is anything with mass moving at the speed of light.

How about with respect to the BH? Isn’t the stream of atoms passing through the EH at, or near, the speed of light with respect to the BH itself?

The speed limit of light for objects with mass may be broken inside the event horizon of the black hole because It is believed that time and space inside the BH are not the same as outside.

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Well, physics says that nothing is especially different inside. As stated before, you'd not notice anything different and would have to compute when the EH was crossed since there's no obvious way to measure it. OK, the nature of the singularity itself probably requires a unified field theory. GR says that a Schwarzschild BH has a sort of 1D line singularity. A Kerr BH has a 2D ring singularity, maybe like a garden hose. The Reissner–Nordström metric describes a charged BH with more than one event horizon (including a Cauchy horizon) inside of which the 'singularity' gets sort of fuzzy.

All real black holes are a combination of these metrics, none being a nice clean example of any one of them.

 

The OP was speculating about an object approaching the “singularity” and that is what I was responding to, although I could have made that clearer. What happens deep inside the black hole is unknown; our current theories of physics do not apply in the vicinity of a singularity. We just do not know what happens there or even if there is a singularity. There are a lot of theories and just plain speculation, as your post shows, but I still claim we really do not know anything about what is at the center of a BH.

[Halc]

On 5/14/2023 at 12:21 PM, OceanBreeze said:

There is a reason I placed “experience” in quote tags. Maybe I should have used “undergoes” instead.

It can be 'experienced', at least under GR.  I look up at somebody at the top of the stairwell and notice that despite us maintaining constant separation, his watch runs faster than mine, and he sees mine run slow. That's experienced dilation, no?

Still, that's a non-local observation and there wouldn't be a local test for either one of them to determine if dilation is being experienced.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

But I do not agree that the laws of physics, as far as we know them, necessarily hold beyond the event horizon. Certainly, Newtonian physics does not hold.

Well, Newtonian physics doesn't hold here on Earth, but it's closer here. By saying the laws still hold beyond the EH, I'm saying there isn't a local test to determine if you've passed it. Of course if the BH is small, then 'local' starts getting seriously local since second order effects become quite noticeable even over incredibly short distances.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

I also didn’t realize we were talking here about an infalling “guy”. As I understood the OP, the discussion is about an object. But that’s fine; we can assume the object is an astronaut.

Now, if said astronaut was stretched by tidal forces into spaghetti, as some theories predict, I would think he might be having a rather unpleasant “experience”.

Key was 'infalling'. It being a 'guy' doesn't seem to matter much except that it is more pointless to say that the object isn't going to notice the EH being passed. Most small rocks say don't care.

There are valid theories that don't predict spaghettification?  Phobos is a pretty big rock at it is definitely noticing the 2nd order effects and is beginning to crack due to 2nd order gravitational effects. And Phobos is nowhere near the EH of Mars. They figure it has some millions of years before it breaks up (spaghettifies), which is pretty imminent at astronomical scales. Even Newtonian physics predicts it.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

Even if he were not turned into spaghetti, he would be moving at such a high velocity that collisions with other matter that is near the BH would heat him until he is glowing hot! Finally, I do believe he would experience many g’s of acceleration. But I could be wrong. . . .

We're assuming he doesn't pass through say an accretion disk, which yes, tears apart just about anything before it reaches a real black hole. It's pretty much plasma that actually falls in. But we're playing with a nice clean one with nothing orbiting it.

Something falling in would experience no more g's than does an astronaut in the ISS. It's freefall, zero g's by definition, taking a geodesic path. Of course the 2nd order effects would be felt if they were significant, but they're not for the really black holes, at least not until well after the event horizon has been crossed. Spaghetification would always tear apart any extended object before the singularity was reached.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

I did mention that the time dilation and the redshift is referenced to the distant observer

You did, but I was adding that they'd both see each other redshifted.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

Most questions may assume such a thing but the OP’s question wasn’t that specific. As far as I know, the only BHs we have positively detected all have these accretion disks around them. In fact, it is the presence of the accretion disks that allows for us to positively detect and identify them; otherwise they would be invisible.

Yes, one without an accretion disk is just an ideal mathematical thing that's easier to describe. They don't exist in reality. In reality they have stuff around them, they have nonzero angular momentum and charge. A black hole could be identified by its gravitational effects on somewhat nearby things.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

Their presence may be suspected by secondary effects they have on other objects, but suspicions of a BH is not quite the same as confirmation.

Maybe some binary system has a star orbiting nothing that can be seen, from a distance sufficient to not draw material from the visible star. Maybe it has insufficient material accreted to be visible. That would be indistinguishable from just some dark heavy object except possibly for the way light would bend as it eclipsed things behind it. That's something that can be photographed.

 

On 5/14/2023 at 12:21 PM, OceanBreeze said:

How about with respect to the BH? Isn’t the stream of atoms passing through the EH at, or near, the speed of light with respect to the BH itself?

I don't think the BH defines a frame. It isn't say a location in space that can be said to be stationary. Sure, the BH is stationary from the distant observer frame, but in that frame things 'stop' at the EH. There is no black hole at all in that frame. Events within have no valid coordinate values relative to such a frame.

 

On 5/14/2023 at 12:21 PM, OceanBreeze said:

The speed limit of light for objects with mass may be broken inside the event horizon of the black hole

Speed of light can be broken anywhere, as long as it is elsewhere. The limit is only a local one, relative to some local inertial frame. So a few examples: A laser pulse shone to the moon and reflected back will travel the round trip faster than c. That's just because the gravitational potential along the path is higher than where the speed is being measured (Earth's surface). Similarly, we can shine a pulse to a reflector on Mercury and back and it will make the trip slower than c because most of the trip is made at lower potentials.

2nd example: Neptune is moving faster than c relative to the frame of Paris, but that's because Paris's frame is a rotating one.

A planet 20 GLY away is receding from us (increasing its proper separation) at a rate greater than c due to the expanding metric used to measure that recession rate. The metric isn't an inertial one.I suppose there is a metric in which the speed of things (light, something else) exceed c inside a black hole, but I can't think of one that doesn't utilize one of the 'tricks' mentioned above.

On 5/14/2023 at 12:21 PM, OceanBreeze said:

What happens deep inside the black hole is unknown; our current theories of physics do not apply in the vicinity of a singularity. We just do not know what happens there or even if there is a singularity.

Well, not entirely 'deep inside' the tidal forces will tear apart things into component parts, sort of like a big rip. Once it gets to the quantum level, it gets really speculative without a unified theory. GR just says that time ends and that's that. I doubt it's so simple.

I don't think any model suggests a collection of infinitely dense matter, stuff all squished together far worse than what goes on in a neutron star. It would seem wrong for all this pulling apart action to suddenly become squishing.

[OceanBreeze]

6 hours ago, Halc said:

Speed of light can be broken anywhere, as long as it is elsewhere. The limit is only a local one, relative to some local inertial frame. So a few examples: A laser pulse shone to the moon and reflected back will travel the round trip faster than c. That's just because the gravitational potential along the path is higher than where the speed is being measured (Earth's surface). Similarly, we can shine a pulse to a reflector on Mercury and back and it will make the trip slower than c because most of the trip is made at lower potentials.

2nd example: Neptune is moving faster than c relative to the frame of Paris, but that's because Paris's frame is a rotating one.

A planet 20 GLY away is receding from us (increasing its proper separation) at a rate greater than c due to the expanding metric used to measure that recession rate. The metric isn't an inertial one.I suppose there is a metric in which the speed of things (light, something else) exceed c inside a black hole, but I can't think of one that doesn't utilize one of the 'tricks' mentioned above.

 

A bit more non-contradictory clarification may be called for here.

All your examples are just the phase velocity apparently exceeding the speed of light. However, in none of those examples is information being sent from one point to another FTL speed.

Take the laser beam moving across the face of the moon as an example. The information is being sent from the laser you are holding in your hand. When you sweep the beam across the face of the moon you move the laser a distance of 2 inches, approximately, but you see it travel across the face of the moon from point A to point B, across the diameter of the moon  (3.5 million meters). So, because you see the beam moving a greater distance in the same time, you might infer that the beam moved FTL across the face of the moon.

But the important point is that no information was passed from point A to point B FTL because the information is being sent from the laser in your hand and that information arrives at the exact same time as the swept beam and it is traveling to the moon at the speed of light.

The swept beam is just the phase velocity and it doesn’t get the information from point A to point B any faster than the laser in your hand sends the information to point B.

Another way to see this: Say you are standing on the shore watching a wave coming in to you at an angle.

You watch the wave crest at sea coming to you from a distance of 200 meters. Because the wave is at an angle, you also notice where the wave is already breaking on the shore about 500 meters from you.

As you watch, both the wave crest at sea and the breaking wave on the shore reach you at the exact same moment. We can call the wave moving along the shore a phase wave.

Now suppose that was a light wave from some source at sea that has a direct wave traveling to you moving at light speed. Again, the phase wave traveling along the shore is moving a greater distance than the direct wave and it reaches you at the exact same time as the direct wave.

As you can see, although the phase wave traveled a greater distance along the shore as the direct wave, both waves reach you at the exact same time and no information from the source traveled to you FTL.

Sorry about the long explanation. I think you, Halc, already understand phase velocity but some other readers may benefit from an expanded explanation.

 

 

I do want to explain why I said that matter can infall into the BH at FTL speed. It isn’t really violating the universal speed limit. My earlier post probably was not very clear on that but I didn’t want to delve too deeply into the BH theory, and frankly I still do not want to do that but here is an excellent link that demonstrates the off-beam phase velocity much FTL.

I am a marine engineer, not an astro-physicist, but I am exposed to all sorts of scientific minds on our expeditions and I try to learn as much as I can or just pick things up by osmosis.

My understanding of the Schwarzschild BH is that space itself is falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light.

There is no restriction on how fast space can move, and it can carry objects such as a stream of atoms that have mass, along with it at the same speed. We see this same thing with the expansion of the Universe. The speed limit is that nothing with mass can move through space FTL. It says nothing about space itself moving FTL and carrying entire galaxies along with it. The galaxies are not moving through space FTL; they are moving with space and may even be stationary with respect to space itself.

Rather than I spend my whole day boring you with my description I ask you to visit this fine site.

Here I quote some relevant points:

“A more insightful way to conceptualize how a black hole works is to picture space as flowing like a waterfall into the black hole.”

“Inside the horizon, the space waterfall falls faster than the speed of light, carrying everything with it.”

“Physically, the Gullstrand-Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light. Technically, the Gullstrand-Painlevé metric encodes not only a metric, but also a complete orthonormal tetrad, a set of four locally inertial axes at each point of the spacetime. The Gullstrand-Painlevé tetrad free-falls through the coordinates at the Newtonian escape velocity.”

 

 

That is as deep as I want to get into this subject due to constraints on my time.

The thread is still open and Halc and others are free to continue this interesting discussion as long as you please, but my participation ends here. Thanks for the great discussion!

 

 

 

 

Edited May 16, 2023 by OceanBreeze

[Halc]

10 hours ago, OceanBreeze said:

All your examples are just the phase velocity apparently exceeding the speed of light.

They are nothing of the sort. The moon one treats light like a particle and messages can be sent to the moon faster than c (not faster than light).

It's a fraction of a microsecond faster since the potential difference isn't much, but it could be extended to seconds and hours with a more extreme scenario.

The other two examples were of planets moving at a rate considerably greater than c. I don't think I was talking about the phase velocity of a planet. I was just giving examples of where the rule 'nothing moves faster than c' does not apply.

10 hours ago, OceanBreeze said:

Take the laser beam moving across the face of the moon as an example. The information is being sent from the laser you are holding in your hand. When you sweep the beam across the face of the moon you move the laser a distance of 2 inches, approximately, but you see it travel across the face of the moon from point A to point B, across the diameter of the moon  (3.5 million meters). So, because you see the beam moving a greater distance in the same time, you might infer that the beam moved FTL across the face of the moon.

I wasn't talking about a moving pointer. We were timing a signal that goes to the moon and back, not tracking the speed of the red dot.

I did do a whole topic once about what the cat (who can move at nearly c if he wants) sees when chasing a red dot around a circle at various speeds greater than c. You're quite right that in this case there is no information traveling faster than c because the whole thing is expressed relative to an inertial frame. None of my examples used a Minkowskian frame.

10 hours ago, OceanBreeze said:

Another way to see this: Say you are standing on the shore watching a wave coming in to you at an angle.

Another example I sometimes use is a Moire pattern, which can easily move faster than c, but does not represent FTL information transfer nor does it involve anything actually moving fast.

All my examples were of actual information transfer faster than c, and none utilized phase velocity.

10 hours ago, OceanBreeze said:

I am a marine engineer, not an astro-physicist, but I am exposed to all sorts of scientific minds on our expeditions and I try to learn as much as I can or just pick things up by osmosis.

I'm a file-systems software engineer, hardly a physicist. I took no relativity or QM classes ever, but I read. I had questions to which I wanted answers, answers that I could not find on the web. So picking up the necessary skills was part of finding those answers. It took me into places totally unexpected.

10 hours ago, OceanBreeze said:

My understanding of the Schwarzschild BH is that space itself is falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light.

OK, I've heard that, but it makes 'space' sound like a thing. I've mostly heard this view from the aetherists, calling it aether wind. Funny that this stuff is immune to time dilation when all the pebbles and such falling in come to a halt, seemingly with the aether wind whizzing by it. I don't find this to be a particularly useful model.

For instance, the one general absolutist model I know is the one by Schmelzer where there is the one preferred frame (the one in which the aether, if he calls it that) is stationary. In this model, there is a big bounce instead of a big bang and 'frozen stars' instead of black holes. There is no interior to a frozon star, and nothing falls in at any speed.

10 hours ago, OceanBreeze said:

The speed limit is that nothing with mass can move through space FTL

Nothing can move locally through Minkowski spacetime faster than c. All spacetime (except at singularities) is locally Minkowskian, so it is a speed limit only so long as spacetime remains Minkowskian. The expanding metric relative to which very distant objects are said to be increasing their proper distance from us at greater than c is no a Minkowskian metric. If one was to remove the energy (mass and dark energy) from the metric, the expansion would be linear (not accelerating). That metric (the Milne metric) is completely flat spacetime and thus can be mapped to Minkowski spacetime. Relative to that Minkowskian spacetime, those really distant galaxies are not currently so distant (and not so old), and nothing in that universe can move faster than c.

A big difference in comparing the same metrics is the way velocities add. So for instance, using the expanding metric (comoving coordinates, proper distance), galaxy X is 10 GLY away and receding at something like 0.75c. Galaxy Y is 10 GLY away from X, and receding from X at 0.75c. Under the expanding metric, velocities add normally, so Y is receding from us at 1.5c.

Now do the same thing but using the Minkowski metric. Galaxy P is 10 GLY away and receding from us at 0.75c. Galaxy Q is 10 GLY away from P (as measured by P), and receding from P at 0.75c. Under the Minkowski metric, velocities add the relativistic way, so Q is receding from us at 0.96c. Nothing recedes fast than c in that metric.  All that works only for flat spacetime, which actual spacetime isn't, so the expanding metric is all we have, and yes, motion in that metric is absolute, and thus it makes more sense to talk about 'motion through space' instead  of 'motion relative to some object'.

11 hours ago, OceanBreeze said:

“Inside the horizon, the space waterfall falls faster than the speed of light, carrying everything with it.”

Ouch. They make it sound like the a radial line from a distant point to the 'center' of the BH is space-like all the way.

11 hours ago, OceanBreeze said:

The thread is still open and Halc and others are free to continue this interesting discussion as long as you please, but my participation ends here. Thanks for the great discussion!

Not a problem. I left up my replies for the general audience if there is anyone following this. Been an interesting exchange.

[OceanBreeze]

13 hours ago, Halc said:

They are nothing of the sort. The moon one treats light like a particle and messages can be sent to the moon faster than c (not faster than light).

It's a fraction of a microsecond faster since the potential difference isn't much, but it could be extended to seconds and hours with a more extreme scenario.

 

"faster than c (not faster than light)" Just what is that supposed to mean?

The speed of light IS c. You are saying messages can be sent to the moon faster than c (the speed of light) but not faster than light, which makes no sense at all.

You were doing fairly OK until now, although I did not agree with everything you posted, I didn't see anything too absurd until now.

Now you will need to provide a link from a reliable source to support this rather absurd statement, or withdraw it.

Here is a link about Earth-Moon-Earth communication and there is nothing mentioned about any message exceeding c.

 

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2nd example: Neptune is moving faster than c relative to the frame of Paris, but that's because Paris's frame is a rotating one.

Since the observation is from a rotating frame, that is a phase velocity.

 

Edited May 17, 2023 by OceanBreeze

[Halc]

Ooh, I earned a 'sceptical' emoji!

4 hours ago, OceanBreeze said:

The speed of light IS c.

No. Light (and other massless things) moves at c relative to an inertial frame. c is the fundamental constant, not light speed.

You asked for links, so excerpts from https://en.wikipedia.org/wiki/Speed_of_light with my bold

"In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and is independent of the motion of the light source"

"In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light can differ from c when measured from a remote frame of reference, depending on how measurements are extrapolated to the region."

Your confusion seems to be that you think the law (light moves at c) is unconditional, not 'relative to an inertial frame'. The quotes above don't mention a vacuum, but I hope we agree that a vacuum is assumed here.

So in the moon case, suppose we measure the time for a round trip signal from Earth to moon and back (and we're ignoring the atmosphere, and we stop the spin and orbits of everything so nothing 'moves' relative to the frame in which everything is stationary) and a moon device is doing the exact same experiment using a reflector on Earth. The round trip distance of both experiments is the same, but the clocks on Earth and moon run at different rates due to differing gravitational potentials and so will log different elapsed time. So the measured average speed (distance/elapsed time) is going to be different. If the speeds are different, they can't both be c, and it turns out that neither is and c is somewhere between the two measured values.  All this is because there is gravity involved which isn't something covered by the rules special relativity.

Even under SR, the 'light moves at c' rule doesn't apply to non-inertial frames, such as my example with Neptune, and also with Rindler frames, such as light not moving at c as it goes between the ends of an accelerating rocket. I didn't give an example of an accelerating frame. I get lots of members that deny for instance that proper acceleration at opposite ends of an accelerating rigid object (like a rocket) is not the same.

Edited May 17, 2023 by Halc

[OceanBreeze]

22 minutes ago, Halc said:

Ooh, I earned a 'sceptical' emoji!

Since you like it so much I give you another one.

 

Quote

 

No. Light (and other massless things) moves at c relative to an inertial frame. c is the fundamental constant, not light speed.

You asked for links, so excerpts from https://en.wikipedia.org/wiki/Speed_of_light with my bold

"In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and is independent of the motion of the light source"

"In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light can differ from c when measured from a remote frame of reference, depending on how measurements are extrapolated to the region."

Your confusion seems to be that you think the law (light moves at c) is unconditional, not 'relative to an inertial frame'. The quotes above don't mention a vacuum, but I hope we agree that a vacuum is assumed here.

So in the moon case, suppose we measure the time for a round trip signal from Earth to moon and back (and we're ignoring the atmosphere, and we stop the spin and orbits of everything so nothing 'moves' relative to the frame in which everything is stationary) and a moon device is doing the exact same experiment using a reflector on Earth. The round trip distance of both experiments is the same, but the clocks on Earth and moon run at different rates due to differing gravitational potentials and so will log different elapsed time. So the measured average speed (distance/elapsed time) is going to be different. If the speeds are different, they can't both be c, and it turns out that neither is and c is somewhere between the two measured values.  All this is because there is gravity involved which isn't something covered by the rules special relativity.

Even under SR, the 'light moves at c' rule doesn't apply to non-inertial frames, such as my example with Neptune, and also with Rindler frames, such as light not moving at c as it goes between the ends of an accelerating rocket. I didn't give an example of an accelerating frame. I get lots of members that deny for instance that proper acceleration at opposite ends of an accelerating rigid object (like a rocket) is not the same.

 

You claimed that a message can travel faster than c.

That is a claim for information traveling faster than c and that is what is absurd.

Light can travel a path slower than c due to gravitational wells along its path, but never faster than c.

It is you who is confused. Your links do not back up your claim that "The moon one treats light like a particle and messages can be sent to the moon faster than c"

And you challenge a model provided by:

Andrew J. S. Hamilton Ph.D (Astronomy), Professor, APS (Dept. of Astrophysical and Planetary Sciences) University of Colorado and Fellow, JILA (formerly the Joint Institute for Laboratory Astrophysics) while admitting that you have not taken any relativity or QM classes ever.

That alone earns you a skeptical smiley.

[Halc]

2 hours ago, OceanBreeze said:

You claimed that a message can travel faster than c.

This comment (the bold indicating a distinction between a message and a not-message) implies that a message/information cannot be send via light pulse. Is one of your problems with my scenario? You've not actually said where I go wrong. Just these assertions.

Your choice of language makes it sound like something that comes from a discussion that spooky action at a distance doesn't count as information, which it indeed doesn't.

2 hours ago, OceanBreeze said:

Light can travel a path slower than c due to gravitational wells along its path, but never faster than c.

Ah, but this isn't a well (a lower potential) along the path, it is a higher one, a hill of higher potential. In this case. Your comment results in a contradiction. If light goes slower than c in Earth's gravity well, then an observer would measure a slower lightspeed in a lab on Earth. He doesn't because his clock runs slower than a clock not in that well, so light on Earth is measured at c, and light at higher potentials (away from Earth's well) would be measured faster than c.

Do you perhaps deny the Earth clock running slower than the moon one? They've measured the difference on different floors of the same building. Is one clock objectively wrong maybe?

Do you perhaps deny the distance between the two points being different for one than the other. Everybody is stationary so we can run a tape measure between the two if that helps.

If you don't deny these things, then do you deny the mathematics that D/T1 is different than D/T2 (same D, different elapsed Time)?

2 hours ago, OceanBreeze said:

And you challenge a model provided by:

Argument from authority, which would hold more weight if I saw the model. Does it take relativity into account? Does it do that and still deny the sort of thing I'm describing?

I mean, they put a man on the moon using slide rules and such. They didn't bother factoring in relativity when it only made a difference in the 8th decimal place. The Newtonian model sufficed.

2 hours ago, OceanBreeze said:

admitting that you have not taken any relativity or QM classes ever.

Well I'm a moderator as well on a different science forum, and the relativity expert there at that. That puts the two of us at least on equal footing, even if my tenure here is still at the contributor level. That claim to authority is pretty thin given the expertise level at said forum. There are those at say physicsForums that blow me away with their knowledge, never mind a place like stackExchange.

[OceanBreeze]

 

23 hours ago, Halc said:

This comment (the bold indicating a distinction between a message and a not-message) implies that a message/information cannot be send via light pulse. Is one of your problems with my scenario? You've not actually said where I go wrong. Just these assertions.

I have said exactly where you are going wrong.

Let's look at your statement again: The moon one treats light like a particle and messages can be sent to the moon faster than c (not faster than light).

Any number of sources will confirm that information can never be sent faster than c.

What does "messages" mean if not information?

Here is yet one more link for you to study:

Some excerpts from that link:

"Faster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (c). The special theory of relativity implies that only particles with zero rest mass (i.e., photons) may travel at the speed of light, and that nothing may travel faster."

"In the context of this article, FTL is the transmission of information or matter faster than c, a constant equal to the speed of light in vacuum, which is 299,792,458 m/s (by definition of the metre[7]) or about 186,282.397 miles per second. This is not quite the same as traveling faster than light, since:

    Some processes propagate faster than c, but cannot carry information (see examples in the sections immediately following).
    In some materials where light travels at speed c/n (where n is the refractive index) other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation (see phase velocity below).

Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as FTL as described here."

 

Can you see where your statement is wrong yet?

It may have been a bit more correct if you wrote:  The moon one treats light like a particle and messages can be sent to the moon faster than light (not faster than c). That would still be wrong but at least it has a snowball's chance in hell as light speed varies under certain circumstances but c is the universe's speed limit for information and is never violated.

Quote

Ah, but this isn't a well (a lower potential) along the path, it is a higher one, a hill of higher potential. In this case. Your comment results in a contradiction. If light goes slower than c in Earth's gravity well, then an observer would measure a slower lightspeed in a lab on Earth. He doesn't because his clock runs slower than a clock not in that well, so light on Earth is measured at c, and light at higher potentials (away from Earth's well) would be measured faster than c.

Still wrong.  Under certain circumstances light carrying information can travel slower than c but never faster.

 

Quote

Argument from authority, which would hold more weight if I saw the model. Does it take relativity into account? Does it do that and still deny the sort of thing I'm describing?

You saw the model! You said it was "not useful" and accused the author or being an etherist, or something of the sort.

An argument from authority is perfectly valid when that authority has a PhD is astronomy, and the one challenging his model has no formal training in the subject.

 

Quote

I mean, they put a man on the moon using slide rules and such. They didn't bother factoring in relativity when it only made a difference in the 8th decimal place. The Newtonian model sufficed.

non sequiter.

Quote

Well I'm a moderator as well on a different science forum, and the relativity expert there at that.

You are not qualified to call yourself a relativity expert when you make such basic mistakes as you are making here.

Quote

That puts the two of us at least on equal footing, even if my tenure here is still at the contributor level.

 

What you are on another forum means absolutely nothing here.

 

Quote

That claim to authority is pretty thin given the expertise level at said forum.

What "said forum"? That model and other information is from the Home Page of Andrew J. S. Hamilton Ph.D (Astronomy), Professor, APS (Dept. of Astrophysical and Planetary Sciences) University of Colorado and Fellow, JILA (formerly the Joint Institute for Laboratory Astrophysics)

Quote

There are those at say physicsForums that blow me away with their knowledge, never mind a place like stackExchange.

Perhaps you will have better luck than showing off your expertise with Black Holes on those forums. Why waste your valuable time with us?

If you do decide to stay here, I expect you to correct your mistake, no need to apologize or anything, but you need to show that you now understand where you went wrong or I will be forced to close this thread.

[Vmedvil]

On 5/8/2023 at 10:43 PM, Jomazing said:

As an object approaches the event horizon of a black hole, time dilation becomes increasingly more extreme, to the point where from an external observer's perspective, the object appears to freeze at the event horizon. However, due to the finite amount of time it takes for the black hole to decay via Hawking radiation, the object would never actually cross the event horizon and reach the singularity. In fact, it would take an infinite amount of time for the object to reach the singularity, as time dilation becomes infinite at the singularity. Therefore, from an external observer's perspective, the black hole would slowly decay over an incredibly long period of time, without ever seeming to fully "consume" the object that approached it. Please poke any holes in this as possible, i came up with if and am feeling cunfused.

Your favorite black hole dude named Vmedvil, fully agrees with that line of thought and thinks it is plausible.

[Halc]

5 hours ago, Vmedvil said:

Your favorite black hole dude named Vmedvil, fully agrees with that line of thought and thinks it is plausible.

I also agree, so long as we keep in mind that it is coordinate time being referenced.

 

7 hours ago, OceanBreeze said:

Any number of sources will confirm that information can never be sent faster than c.

I will agree with the fact that 'any number of sources' make such a claim. But most of those sources are pop sites that don't properly qualify such a statement. Einstein didn't say it. The statement contradicts the wiki site I quoted. Find a site that specifically talks about making such assertions about light speed relative to a non-inertial frame, such as in every one of my examples.

First of all, a more correct way of saying it is that information can never be sent faster than light.  But light can go faster than c relative to a non-inertial frame, and few sites (there are some, including your posts) explicitly deny this. Also, I do agree that the local speed of light is c, not just in an inertial frame, but any of the frames that we've discussed. All my examples are not only non-inertial, but they involve non-local light signals. Relative to an inertial frame, the 'local' requirement isn't necessary.

The more simple experiment is simple. Take a rod that is about 149.9 meters long, arrange it horizontally in a lab in a vacuum. You emit a pulse of light from a device at one end and it reflects from a reflector at the other end where it gets detected right by the source. I've actually done this in school (less than 150 meters). It should take exactly a microsecond if the reflector is placed at just the right spot. We presume we have super-accurate methods to measure the elapsed time. We did not in school and got 1.5 digits of precision at best.  Do you agree with the validity of this, that it constitutes information making the round trip at c? If you don't agree with that, then we have to figure out why.

7 hours ago, OceanBreeze said:

Here is yet one more link for you to study:

From that very site I see my 2nd example (the Neptune one, except they use Proxima Centauri):

"In this [rotating] frame of reference, in which Proxima Centauri is perceived to be moving in a circular trajectory with a radius of four light years, it could be described as having a speed many times greater than c"

My only gripe with that wording is the usage of the word 'perceived'. It isn't just perceived to be moving at over 10000c relative to that frame. It really is moving at over 10000c relative to that frame. That's why I picked Neptune, which is just far enough away to be moving at over c relative to the rotating frame of Earth.

It talks about proper distance and proper speed, the latter which is unlimited. The recession rate of a distant galaxy is a proper speed. Proper speeds add the regular way, not the relativistic way that regular velocity does. In this way a traveler can reach a point 1000 light years distance despite having a half-century life expectancy. He gets there in say 10 years of his life if he moves at a proper speed of 100c.  All this is discussed on that page.

They do discuss the phase velocity that you brought up, but that was not one of my examples since it isn't information traveling faster than c.

They talk about apparent motion of stars faster than c, but that one is just a perception, not coordinate motion faster than c.

A final quote that states the rules more correctly, with my bold.

"In special relativity the coordinate speed of light is only guaranteed to be c in an inertial frame; in a non-inertial frame the coordinate speed may be different from c."

I do not see gravitational cases or accelerated reference frame explicitly mentioned on that site. Both fall under the heading of non-inertial frame, but the specific frame types are not discussed. There are wiki pages that do this.

7 hours ago, OceanBreeze said:

You saw the model! You said it was "not useful" and accused the author or being an etherist, or something of the sort.

Ah, the waterfall site was his. Didn't catch that, sorry. I didn't call him an aetherist, but I said I've seen similar descriptions from them.

I cannot find how I could compute the scenario in question using this waterfall model. Imagine not a black hole, but something almost one. You have an observer (a bit of gadgetry and a clock) sitting on a shell around a stellar-mass black hole just outside EH, something like the surface of a neutron star. On this surface we build at 300 km tower and put a mirror up there. Light has 600 km to traverse which should take 2 milliseconds in an inertial frame. My claim is that the clock on the surface will measure far less than 2 ms between emission and detection. It's the same thing as the moon case, but far more extreme so the difference isn't in the 10 decimal digit.

I presume the waterfall model computes the same numbers as GR does, which would not say that it must take at least 2 ms as measured by the clock at the bottom. Of course the same round trip would take more than 2 ms if measured by the same setup at the top, reflecting light from the bottom. The closer the bottom is to the EH, the bigger the difference.

You seem to acknowledge that light slows in a gravity well (of lower gravitational potential), but you seem in total denial that light would correspondingly speed up when going through regions of higher potential, as if light somehow remembers where it was emitted and changes speed only when it crosses into regions of lower potential than the potential where it was emitted, in which case you could have two light pulses moving on identical paths at different speeds, which seems pretty contradictory to me.

7 hours ago, OceanBreeze said:

What "said forum"?

The one where I'm a moderator, and you've not demonstrated my mistakes, only asserted them. Pretend I'm trying to help for a minute and actually consider what I'm saying and stop assuming I'm one of the cranks. Your assertions lead to contradictions. I've shown how the same trip will be measured by two different observers to take different times. You've not actually denied any of that. It's light, and it's in a vacuum, and it's a straight line. But you say one measures the trip at c and the other observer does not. At least I think you say that. You seem to avoid my explicit questions about where I'm wrong, instead just falling always back to this assertion that this blanket statement is unconditionally true when it isn't. And yes, I do acknowledge that you'll find plenty of web sites that make that assertion. It's a good example of how much pop science does a lot of damage.

I found somebody asking this question on physics stack exchange, which is probably the most reputable site I know. (with quora being one of the least reputable).

https://physics.stackexchange.com/questions/33816/does-the-speed-of-light-vary-in-non-inertial-frames

Part of the question is ours: "If [speed of light] is not constant in non-inertial frames, is it still bounded from above?"

This seems to address your claim that light is bounded by c from above, but it can be slower for various reasons (gravity, non-vacuum, etc). The case discussed is that of an accelerating system, which (per the equivalence principle) is applicable to an Earth observer accelerating upward at a proper 1g. We can place our reflector not at the moon but only 149.9 meters up (a 15 story building stairwell) in an effort to keep that acceleration reasonably near 1g all the way.

"If you consider an accelerating reference frame with respect to Rindler coordinates (where time is measured by idealized point-particle accelerating clocks, and objects at different locations accelerate at different rates in order to preserve proper lengths in the momentarily comoving reference frames), then light may not move at c, and can in fact even stop."

So far so good. 'Stop' is the event horizon (Rindler horizon here) case. We're both good with that. Cut to the chase:

"So in natural units, the speed of light in Rindler co-ordinates is
c(x)=gx

[in non-natural units,gx/c]"

That says that the speed of light is dependent on x (the x coordinate of our observer), with it being less than c in the direction away from acceleration, and greater than c for displacements in the direction of acceleration, which is 'to the right' in their example. It says light speed ranges from 0 (at x=0) to c (at the observer) to any arbitrarily high value (for x > where the observer is).

This formula works on Earth for a bit, but light speed increases to a finite limit with Earth because (gravitational) acceleration drops off faster with altitude faster than it does in a Rindler frame.

 

The post admittedly isn't as comprehensive as the wiki site. The latter mentions several different kinds of frames, but omits the accelerating (and equivalent gravitaional) one that is applicable in our case. The stack exchange post addresses this case.

Edited May 19, 2023 by Halc

[OceanBreeze]

On 5/17/2023 at 11:57 PM, Halc said:

This comment (the bold indicating a distinction between a message and a not-message) implies that a message/information cannot be send via light pulse. Is one of your problems with my scenario? You've not actually said where I go wrong. Just these assertions.

I am closing this thread because you just can't seem to stay focused on the issue or maybe you still do not understand what the issue is.

I will place it in bold one last time: Information cannot be transmitted at a speed greater than c.

You keep going on and on about "light" when I have already given examples of light going faster than c, such as in phase velocity, but that light carries no information.

Information is the key point and you keep intentionally or otherwise keep on missing the point.

One final link:

"The answer to whether meaningful information can travel faster than light is currently no. We're only at the level of moving a few quantum particles at speeds that may possibly be over the speed of light, if the data pans out on subsequent experiments. To have a practically applicable form of data transfer, you have to be able to send organized bits of data that mean something, uncorrupted, to another machine that can interpret it. The fastest transmission in the world will mean nothing otherwise. But you can be sure that if the speed of light is broken, we'll be applying it to our Internet transmissions far sooner than to interstellar travel. Our ability to watch the highest quality television and surf the net at the fastest speeds will be paramount. And perhaps for those purposes, even getting ourselves to truly as-fast-as-light transmission would do wonders."

Frequently Answered Questions
Is it possible for information to travel faster than light?
No, it is not possible for information to travel faster than light.

 

If you can find a reputable link that contradicts that "assertion", send me a PM with that link and I may reopen this thread.

Thread Closed.