[jeffreyH (OP)]

We have two situations where light reaches absolute limits. The first is the speed of light itself. The so called universal speed limit. The second is the event horizon of a black hole, past which point light is trapped. These two absolutes have a variety of properties which are similar in aspect. They both involve a momentum. The first momentum is the constant c and the second the momentum is induced via gravitation which is thought to require an escape velocity of c. This will be discussed further later on. Another property is the dilation of time. This is a property which mathematically applies to both situations. This is also thought to be true of length contraction. Matter density is different as it only really applies to the black hole situation but it could be argued that this could be mirrored by a density of spacetime when nearing light speed. Though this is speculative.

With respect to the escape velocity at the event horizon, it could be argued that light speed would not be violated if the event horizon was also a universal absolute that collapsing matter would never actually reach.

[jeffreyH (OP)]

The interaction of electromagnetic radiation with gravitation relates directly to c at two distinct points. An accelerating mass approaching c can be thought of in the same way as a collapsed mass by examining the interactions with gravitation. The mass approaching c would appear to be experiencing very similar gravitational effects as those experienced at the event horizon. If we presume that the event horizon is in fact an absolute we can then examine the behaviour of light in both situations. Under intense time dilation light has to slow down and take an extended length of time time to leave the vicinity of the event horizon. Approaching light speed we are extremely time dilated and to an outside observer in another frame light would appear to be taking an extended length of time to leave our vicinity.

Considering the region around the event horizon light speed would not be violated if spacetime contraction occurs. This could suggest that light years of spacetime could actually be compressed around the immediate vicinity of the event horizon depending upon the mass of the black hole. Light would then still be travelling at c for all observers.

[jeffreyH (OP)]

Considering my previous post it becomes obvious that both spacetime contraction and mass-energy density increase would apply to both situations. It would be interesting to investigate this at the Planck scale. Although how that could be done is beyond me.

[jeffreyH (OP)]

The fact that electrons tend to the lowest energy state is of interest with respect to matter compression. Proton/electron balance in compressed matter states is something to investigate. How does this fit with the Pauli exclusion principle? This question needs to be answered.

Phonon vibration frequencies in condensed matter could be investigated using helium atom streams. This would be useful in investigating the vibrational states of solid hydrogen.

[Ethos_]

Considering my previous post it becomes obvious that both spacetime contraction and mass-energy density increase would apply to both situations. It would be interesting to investigate this at the Planck scale. Although how that could be done is beyond me.

You make some very interesting comparisons and I agree that the circumstances suggest a possible connection. From my position, it's clear that black hole dynamics may very closely parallel conditions necessary for the production of infant universes. Not sure if you're familiar with this theory but as you stated in a former post, light years of space/time may exist within and or adjacent to the event horizon. Interesting Jeff, very interesting indeed.

[jeffreyH (OP)]

Considering my previous post it becomes obvious that both spacetime contraction and mass-energy density increase would apply to both situations. It would be interesting to investigate this at the Planck scale. Although how that could be done is beyond me.

You make some very interesting comparisons and I agree that the circumstances suggest a possible connection. From my position, it's clear that black hole dynamics may very closely parallel conditions necessary for the production of infant universes. Not sure if you're familiar with this theory but as you stated in a former post, light years of space/time may exist within and or adjacent to the event horizon. Interesting Jeff, very interesting indeed.

Well I am finding that either some mass leaves our universe through a brane at the event horizon or I am out in my thinking. I don't like the mass loss idea although this could explain a big bang scenario to some extent. However it can't explain where continuing universal expansion will end up. If it is heat death then the system isn't balanced and I really don't like that concept.

[Ethos_]

If it is heat death then the system isn't balanced and I really don't like that concept.

Neither do I Jeff, heat death seems an extreme answer and counter intuitive, if intuition has any value. While it may be the possible fate our universe is destined to face, one must still ask a few simple questions.

In the first case scenario, where our universe is singular and alone in the so-called bulk, it seems quite unlikely that if we happened once, we will likely happen again. And speaking of course as WE being our present universe.

In the second case scenario, where we are living on a brane, it appears quick likely that the only possible outcome is another big bang given the close proximity of each brane to their associate member branes and the probable  collisions between them.

IMHO, the heat death solution is a drastic remedy to the question and should be discarded. 

[jeffreyH (OP)]

If it is heat death then the system isn't balanced and I really don't like that concept.

Neither do I Jeff, heat death seems an extreme answer and counter intuitive, if intuition has any value. While it may be the possible fate our universe is destined to face, one must still ask a few simple questions.

In the first case scenario, where our universe is singular and alone in the so-called bulk, it seems quite unlikely that if we happened once, we will likely happen again. And speaking of course as WE being our present universe.

In the second case scenario, where we are living on a brane, it appears quick likely that the only possible outcome is another big bang given the close proximity of each brane to their associate member branes and the probable  collisions between them.

IMHO, the heat death solution is a drastic remedy to the question and should be discarded.

Well with the brane solution you would have to answer the question of what happens to the mass that is not consumed by black holes? If only a percentage of mass leaves our universe then the rest effectively keeps on expanding. If gravitation is also lost as an integral part of matter that makes the situation worse. This cannot be a satisfactory answer either.

[Ethos_]

Well with the brane solution you would have to answer the question of what happens to the mass that is not consumed by black holes? If only a percentage of mass leaves our universe then the rest effectively keeps on expanding. If gravitation is also lost as an integral part of matter that makes the situation worse. This cannot be a satisfactory answer either.

I am a firm believer in the conservation of mass and energy. Just exactly where it becomes located under these circumstances is a little beside the point. We know that the gravitation remains even though the mass seems to have disappeared.  But the mass has really not evaporated into nothingness, it has just passed from here to there, where ever and what ever "there" means. And whether one believes in M theory and branes, or whether they believe in the multiverse of budding infant universes, the passage from our universe to the one adjacent by matter and energy should not doom either one to heat death. If mass and energy can transverse from here to there, the opposite must also be true. And just because we haven't detected the exchange from there to here yet does not mean that it is not occurring.

I still have my doubts about exactly what this observed expansion really means anyway. It may be too early to really understand the significance taking into account that these measurements are still a bit new to us, especially the acceleration we think is taking place. Quite beyond our predicted assumptions about how all this is supposed to work.

[jeffreyH (OP)]

Well with the brane solution you would have to answer the question of what happens to the mass that is not consumed by black holes? If only a percentage of mass leaves our universe then the rest effectively keeps on expanding. If gravitation is also lost as an integral part of matter that makes the situation worse. This cannot be a satisfactory answer either.

I am a firm believer in the conservation of mass and energy. Just exactly where it becomes located under these circumstances is a little beside the point. We know that the gravitation remains even though the mass seems to have disappeared.  But the mass has really not evaporated into nothingness, it has just passed from here to there, where ever and what ever "there" means. And whether one believes in M theory and branes, or whether they believe in the multiverse of budding infant universes, the passage from our universe to the one adjacent by matter and energy should not doom either one to heat death. If mass and energy can transverse from here to there, the opposite must also be true. And just because we haven't detected the exchange from there to here yet does not mean that it is not occurring.

I still have my doubts about exactly what this observed expansion really means anyway. It may be too early to really understand the significance taking into account that these measurements are still a bit new to us, especially the acceleration we think is taking place. Quite beyond our predicted assumptions about how all this is supposed to work.

One of the puzzling aspects of my work has been the fact that the smaller the initial mass the more densely packed the mass has to be beyond the event horizon. Larger masses actually lose less mass. This is not what I expected. I want to see what happens at the Chandrasekhar mass limit. Right now I could even come to believe that a proportion of the mass never reaches the event horizon at all.

BTW This could indicate an inverse proportionality of mass lose with respect to the size of the mass and the Schwarzschild radius.

[jeffreyH (OP)]

I have come to the conclusion that g = GM/r^2 is wrong and will not fit with a proper theory of quantum gravity. It needs adjusting. How the hell I do that I really don't know.

The equation rs=2Gm/c^2 has to be modified as well because the mass is not always compressed at this radius so what happens to rs at lower densities? Interestingly a function of rs within elementary particles may be to produce a potential well trapping photon energy in energetic particles. Counter-intuitively this may have a negative gravitational effect so that hot air rises although it has more mass and can be considered heavier than other atmospheric gasses. I know the cry of buoyancy will ring out against this.

[Ethos_]

The equation rs=2Gm/c^2 has to be modified as well because the mass is not always compressed at this radius so what happens to rs at lower densities?

I'm not following you here Jeff, the Schwarzschild radius is necessarily defined by this equation. Escape velocity is determined by the ratio of the rs/mass critical = 2G/c^2 compression and will always be less than c until this compression ratio is reached. You can't have a black hole until escape velocity reaches c. You just can't have a black hole unless these densities are reached.

[jeffreyH (OP)]

The equation rs=2Gm/c^2 has to be modified as well because the mass is not always compressed at this radius so what happens to rs at lower densities?

I'm not following you here Jeff, the Schwarzschild radius is necessarily defined by this equation. Escape velocity is determined by the ratio of the rs/mass critical = 2G/c^2 compression and will always be less than c until this compression ratio is reached. You can't have a black hole until escape velocity reaches c. You just can't have a black hole unless these densities are reached.

OK then let me restate the problem. What does rs = 2Gm/r^2 mean where r > rs and r < c?

BTW This is not considered as a function of g.

When the denominator r = c we get the Schwarzschild radius when it equals rs we get 2c^2. Where the lower bound is a variable radius the upper bound is a constant. What does that tell us. Can we consider the upper bound as a radius also? If not why not? If we however consider this as a density function it describes quite well the effect on light by a gravitational field. 2c^2 could be considered a potential that can only be broken by two photons, one travelling forward in time and prompted by one travelling backward in time. This would apply at the microscopic scale and be at the lower end of the density spectrum involving single atoms. As density increases r starts to approach c. This would involve molecules and move on through the gas and liquid phases into solids and on to condensed matter states. Basing this progression on the Planck mass would be very interesting and graphing the data would be very interesting. Using the Planck mass we would move from 2c^2 to 2 times the Plank length. This also progresses from and expanded 2 dimensional space to a reduced 1 dimensional space. Once we get into the one dimensional space length contraction and time dilation are greatly intensified and spacetime is point-like.

[Ethos_]

OK then let me restate the problem. What does rs = 2Gm/r^2 mean where r > rs and r < c?

     (rs = 2Gm/r^2)

that equation is meaningless Jeff, ............should be written as:  (rs = 2Gm/c^2)

[Ethos_]

You're loosing me my friend..........

Here is an example of this equation at work:

Let's find the mass that would be required for an object with the radius of the electron to collapse to a black hole.....

radius of the electron = 2.81794092 E-15
speed of light squared = 8.98755179 E 16
gravitational constant = 6.673 E-11

[rs = 2Gm/c^2]  or [ M critical = re * c^2/(2 * G)]

mass critical = (2.81794092 E-15 * 8.98755179 E 16)/(2 * 6.673 E-11)

mass critical equals 1.89767645 E 12 Kilograms

In conclusion, a mass equal to 1.89767645 Kilograms compressed to a radius of the electron will collapse to a black hole. Likewise, any mass compressed to a sufficiently small radius will also collapse. However, the smaller the collapsed object is, the faster it will evaporate due to Hawking radiation. Supermassive black hole will take billions of years to complete this process.

[jeffreyH (OP)]

You're loosing me my friend..........

Here is an example of this equation at work:

Let's find the mass that would be required for an object with the radius of the electron to collapse to a black hole.....

radius of the electron = 2.81794092 E-15
speed of light squared = 8.98755179 E 16
gravitational constant = 6.673 E-11

[rs = 2Gm/c^2]  or [ M critical = re * c^2/(2 * G)]

mass critical = (2.81794092 E-15 * 8.98755179 E 16)/(2 * 6.673 E-11)

mass critical equals 1.89767645 E 12 Kilograms

In conclusion, a mass equal to 1.89767645 Kilograms compressed to a radius of the electron will collapse to a black hole. Likewise, any mass compressed to a sufficiently small radius will also collapse. However, the smaller the collapsed object is, the faster it will evaporate due to Hawking radiation. Supermassive black hole will take billions of years to complete this process.

Yes that is true but what is the actual kg per volume and is it a constant density or does it vary with mass? What is g at this density? Does it vary with mass? There is something wrong here. g must be a constant value at the radius and it should ideally be infinite to stop light. How do we get there at the radius?

[jeffreyH (OP)]

Thank you Ethos_ I have been bending my brain over this and you have just given me the answer. You are a genius!

[Ethos_]

Thank you Ethos_ I have been bending my brain over this and you have just given me the answer. You are a genius!

I'm pleased to be of help Jeff but, sorry to say, I must correct you once again. I'm a long way from being a genius. Truth is, I flunked my first year of algebra. No sir, not even close to being one of those rare breeds.

[jeffreyH (OP)]

Thank you Ethos_ I have been bending my brain over this and you have just given me the answer. You are a genius!

I'm pleased to be of help Jeff but, sorry to say, I must correct you once again. I'm a long way from being a genius. Truth is, I flunked my first year of algebra. No sir, not even close to being one of those rare breeds.

Don't underestimate your abilities. Now then if the speed of light slows nearing the event horizon and nothing can exceed the speed of light then if gravitational waves move at c or near it they are also slowed and the wavelength gets longer. BTW escape velocity was what I hadn't taken into account. How stupid and so easy. Now if gravitation slows in effect at the event horizon it too can't escape. This may well have rid me of the density issue except that all calculations of g have to be outside the mass being modeled. If c stops then there is effectively no g. If there is no g then what stops light. This is chicken and egg. So we are back to density.

BTW Have you ever read up on phonons? There are some experiments I have thought of that may be interesting but the medium would be important and the type of wave to produce. Light or sound may do although water is a good model for gravitation too.

[Ethos_]

 Now if gravitation slows in effect at the event horizon it too can't escape. This may well have rid me of the density issue except that all calculations of g have to be outside the mass being modeled. If c stops then there is effectively no g. If there is no g then what stops light. This is chicken and egg. So we are back to density.

Now I see what you're having trouble with Jeff. Consider what the term "relativity" really means. Relativity is about the relative differences between the local events and what someone at a distance observes. For anyone falling into a black hole, time marches along exactly the same way it passed before they started their fall. However, for an observer the light coming from the black hole seems to be frozen. You may be thinking a bit backwards about this issue and this is very common for people to confuse the understanding about the dilation of time.

Local to the black hole, light still travels at c. Local to the black hole, gravity is the same as it was beyond the region. What has changed it what the distant observer sees.

I'm sure you've heard about how speed and gravitational forces slow the advance of time. But this slowing of time is only observed by those outside the local frame. For those experiencing the speed or the gravitational forces of huge masses like a black hole, time advances as it always has.

Remember the example of the astronaut leaving the earth and speeding around the galaxy and returning to find those he left much, much older than himself. People confuse who's time has slowed. If the people on earth are much older, it appears to the astronaut that their time has accelerated and his has slowed. When we talk about speed and huge gravity causing time to slow, this slowing is only apparent to the observer, not the ones under observation. And conversely, those who remained on earth seeing their astronaut returning many years later and looking only months older would cause them to think his time had slowed. But for the astronaut, his interpretation remembers his time as advancing quite normally.

BTW Have you ever read up on phonons?

No, can't say that I have.