Singularity - Black Holes, Gamma Rays, Magnetars, etc

Palomar · 2003-03-29 08:23:19

*I posted a link to a story about a "runaway black hole" in the "New Discoveries" folder:

http://www.cnn.com/2002/TECH/space/11/2 … index.html

In the "Related" box is an Interactive: Anatomy of a black hole.

I went through the interactive. Near the end of it is mentioned the "Singularity" which caption reads: "Region of infinite density where matter is crushed out of existence."

I'm rather sure I've read and heard before (various sources) that matter is indestructible. How, then, can it be crushed out of existence? And, if matter can be crushed out of existence, what is in the area now where matter once existed? Doesn't SOMETHING have to now exist in the place where this matter was "crushed out of existence"? And if so, what?

I'm very VERY curious about this. Any input would be appreciated.

--Cindy

Shaun Barrett · 2003-04-02 01:55:05

Hi Cindy!
Black holes are very weird things to the minds of us humans - I think they're even weird to the minds of superhumans like Stephen Hawking and Paul Davies!! :laugh:

As you know, black holes are collapsed stars. At the end of their life, when they can no longer extract energy from fusion processes, the long battle between gravity and fusion power comes to an end. As was always inevitable, gravity wins!
As the star collapses, its matter becomes denser as its radius becomes smaller. And as the radius becomes smaller, the matter becomes denser. (A positive feedback loop.) If there's up to 1.44 solar masses of material present (the Chandrasekhar Limit), gravity will create a white dwarf star - a 'solar cinder', if you like, which will radiate weakly for tens of billions of years, ever so gradually dimming and cooling until it finally dies.
[Our Sun will do this, so we could move outwards, planet by planet, as it goes through its red giant stage, and then build habitats out of the wreckage of the solar system and huddle them in tight orbits near our new white dwarf star! ... But I digress.]
Beyond 1.44 solar masses, gravity is sufficiently strong to overcome quantum mechanical rules which say no two electrons may occupy the same state - this point is called electron degeneracy ( ... just imagine all those debauched little electrons disobeying all the rules and occupying the same state!! I can almost guarantee alcohol and drugs are involved! ) So, the star proceeds to collapse further by becoming just a logjam of neutrons - a neutron star.
If the matter exceeds about 2 solar masses (I believe there is some room for error in this figure and it could be as much as 3.5 solar masses.), then we reach the point known as neutron degeneracy (more debauchery!! ). At this stage, even the quantum mechanical rules which forbid neutrons blending into each other break down ( ... I just knew there'd be smut involved!! )

Now the collapsing star has jumped the last hurdle. There is now no force in the universe that can resist the collapse of this star's matter down into a mathematical point of infinite density. This point is called a singularity.
The closer you get to this singularity, the more powerful its gravity becomes. At a certain distance from it, the acceleration is so enormous that even light fails to escape. This boundary distance is called the event horizon - because beyond it, whatever happens is forever concealed from our view. We can never obtain any information from within that boundary and, therefore, we can never see a 'naked singularity' or measure any of its properties.
In fact, within the event horizon, our universe doesn't really exist! It's essentially meaningless trying to visualise what it's like in there because it's a region where the rules we understand and live by out here, no longer apply.
If you like, you can speculate about matter which has accelerated through the event horizon. Since it has reached light speed at the event horizon, its mass is now infinite and, from our point of view, time no longer passes for the atoms in it (not that we can view those atoms anyway, of course! ). Even though its mass is infinite, it is now encountering a rapidly increasing gravitational field as it approaches the singularity. As this unimaginable gravitational field exerts its influence on the matter, can it accelerate it further? ... Can an infinitely powerful gravitational field accelerate an infinite mass?!!

Since my own description of black holes is beginning to make me dizzy, this is where I get off!
That stuff about matter being "crushed out of existence" is really just a convenient way of describing the indescribable!! In a manner of speaking, once matter crosses the event horizon, it is "out of existence" - at least as far as this universe is concerned. Some people have speculated that the matter which disappears into a black hole in this universe, emerges out of a 'white hole' in another universe! But, again, there's no conceivable way of verifying this notion experimentally because no information can emerge from beyond the event horizon.

This subject is so mind-numbingly difficult to comprehend that I have nothing but the most awed and reverent respect for the theoretical physicists who tackle it and devise mathematical models to describe it! And it makes me all the more certain of, and humbled by, my own profound ignorance! There is a small group of people in this world who stand out from humanity as a Cro-Magnon must have stood out among Neanderthals.
Sobering stuff. But, for the sake of us Neanderthals, thank God they're there!!

Palomar · 2003-04-02 14:59:39

*Hi Shaun: Thanks for answering.

Now the collapsing star has jumped the last hurdle. There is now no force in the universe that can resist the collapse of this star's matter down into a mathematical point of infinite density. This point is called a singularity.
The closer you get to this singularity, the more powerful its gravity becomes. At a certain distance from it, the acceleration is so enormous that even light fails to escape.

*Yeah. Totally mind-boggling.

This boundary distance is called the event horizon - because beyond it, whatever happens is forever concealed from our view. We can never obtain any information from within that boundary and, therefore, we can never see a 'naked singularity' or measure any of its properties.
In fact, within the event horizon, our universe doesn't really exist! It's essentially meaningless trying to visualise what it's like in there because it's a region where the rules we understand and live by out here, no longer apply.

If you like, you can speculate about matter which has accelerated through the event horizon. Since it has reached light speed at the event horizon, its mass is now infinite and, from our point of view, time no longer passes for the atoms in it (not that we can view those atoms anyway, of course! ). Even though its mass is infinite, it is now encountering a rapidly increasing gravitational field as it approaches the singularity. As this unimaginable gravitational field exerts its influence on the matter, can it accelerate it further? ... Can an infinitely powerful gravitational field accelerate an infinite mass?!!

*That's one hell of a question.

Since my own description of black holes is beginning to make me dizzy, this is where I get off!

*You're just NOW starting to feel dizzy?

That stuff about matter being "crushed out of existence" is really just a convenient way of describing the indescribable!! In a manner of speaking, once matter crosses the event horizon, it is "out of existence" - at least as far as this universe is concerned. Some people have speculated that the matter which disappears into a black hole in this universe, emerges out of a 'white hole' in another universe! But, again, there's no conceivable way of verifying this notion experimentally because no information can emerge from beyond the event horizon.

*Yeah, I've heard about this "white hole"/other universe scenario too -- but I've encountered few ponderings about it/them.

This subject is so mind-numbingly difficult to comprehend that I have nothing but the most awed and reverent respect for the theoretical physicists who tackle it and devise mathematical models to describe it! And it makes me all the more certain of, and humbled by, my own profound ignorance! There is a small group of people in this world who stand out from humanity as a Cro-Magnon must have stood out among Neanderthals.
Sobering stuff. But, for the sake of us Neanderthals, thank God they're there!!

*Ah. I'm glad we live in an age where scientists (Western ones, at any rate) are open and share their knowledge with the non-scientific community. We can thank the efforts of the Enlightenment philsophers, in great part, for this attitude.

Well, Shaun -- thanks again for your response. I posted my initial post at another forum (which claims it is devoted to subjects such as black holes, worm holes, etc.); 40 members at that forum and no one has touched it yet. So, your input is extra appreciated!!

--Cindy

RobertDyck · 2003-04-02 16:38:44

Let me try to put it in simple terms. According to relativity, energy and matter can be interchanged and the formula to convert them is E=MC^2. Energy = Mass * (speed of light) squared. That does mean there is no fundamental difference between energy and mass, they are just different forms of the same thing. Think of water existing as ice or steam; they are the same thing, just different phases of matter. Mass can be considered the "ice", and energy can be equated to "steam". One theory to explain what matter is, states that matter is a fold in n-dimensional space. That means matter is basically a standing wave. The reason it is stable has something to do with relativity and the fact that time slows down close to the speed of light, and the quantum waves inside subatomic particles moving at the speed of light. But those waves reflect and refract off distortions in the dimensions of space, but those distortions are caused by matter itself, but matter is just distortions in n-dimensional space... (Ok, it's a circular argument that gives physicists headaches. This is why the unified field theory isn't finished yet.)

However, with a quantum singularity the matter is squished so any distinction between matter and energy is gone. All the energy waves and dimensional distortions that are the quarks that make up subatomic particles are all squished together and merged into one big distortion. The total mass of the quantum singularity does not increase, but its size becomes mathematically zero. That means its density is infinite, although its mass remains finite.

A couple interesting things happen during formation. When a big star dies, its core becomes so dense that the electrons and protons cannot hold themselves apart. The outer shell of the stellar core has such an intense gravity that electrons and protons combine to form neutrons. This causes one hell of an explosion, and the inner core is crushed so it also combines into neutrons. This is called a super nova, and the outer part of the star is blow off. The remnant is a neutron star. If the remnant is big enough, the neutrons combine to form a quantum singularity. Some people think this second reaction is what causes gamma ray bursts. So each gamma ray burst may be the formation of a new quantum singularity.

One theory holds that inside the quantum singularity all the dimensions of space are collapsed. However, there is significant mass. A new set of dimensions may form which are discontinuous from ours, including a new dimension of time. That means the quantum singularity may be a pocket universe, and the formation of a quantum singularity may be the big bang for that universe.

Palomar · 2003-04-03 07:18:34

A new set of dimensions may form which are discontinuous from ours, including a new dimension of time. That means the quantum singularity may be a pocket universe, and the formation of a quantum singularity may be big bang for that universe.

*Wow, thanks Robert.

I take it, then, that it is possible (or even likely) that our own universe may have begun in this manner.

--Cindy

Palomar · 2003-04-03 13:51:27

Let me try to put it in simple terms. According to relativity, energy and matter can be interchanged and the formula to convert them is E=MC^2. Energy = Mass * (speed of light) squared. That does mean there is no fundamental difference between energy and mass, they are just different forms of the same thing. Think of water existing as ice or steam; they are the same thing, just different phases of matter. Mass can be considered the "ice", and energy can be equated to "steam".

*I re-read the first paragraph, because I knew I wanted to come back to this, Robert (if you'll be kind enough to respond once more); I'll try to phrase my question as precisely as possible:

How do energy and mass BECOME different forms of the same thing? I understand the ice and steam analogy, as it relates to water, but I don't understand this analogy as it relates to mass and energy.

I ask, because this is the closest I have yet come to understanding what "mass" is. I didn't know it was a different form of energy, which is why I'm asking HOW they come to be different (the process or catalyst or whatever).

Thanks in advance, if you care to answer.

--Cindy

clark · 2003-04-03 14:25:11

How do energy and mass BECOME different forms of the same thing?

I always thought it was TIME.

But I'm no physicist.

RobertDyck · 2003-04-03 15:29:12

How do energy and mass BECOME different forms of the same thing? I understand the ice and steam analogy, as it relates to water, but I don't understand this analogy as it relates to mass and energy. ... I'm asking HOW they come to be different (the process or catalyst or whatever).

Molecules are what we experience in daily life. Our bodies do not undergo nuclear reactions, only chemical. The static electric charge of protons holds electrons in orbit about the nucleus. Moving electrons move the static charge, so they are responsible for chemical reactions that bind atoms into molecules. Likewise those static electric forces push molecules apart when their electron clouds do not merge. The vast majority of an atom is empty space. When you place your hand on a table top, the thing which prevents your hand from passing through is the static charge of the atoms in your hand pressing against the charge of the atoms in the table top. You don't feel the static charge until your hand comes into contact because freely moving electrons equalize the static charge from the protons resulting in no charge. It is only when you hand contacts the table top that the electrons are forced away by the static charge of the electrons in the table top, whose electrons are also forced away. This can expose protons of the atoms of both your hand and the table top to the positive charge of each other. At this point the distance between nuclei is very close, so the inverse square law dictates the force is relatively great. The harder you press your hand down, the harder you push the electrons out of their orbital so the more distorted the static charges become, resulting in stronger like charges pushing each other away. This is what feels like a hard surface. In reality all solid matter is just forces.

Atomic nuclei have strong and weak nuclear forces holding them together. This operates over a very short distance, and the strong force operates over a shorter distance than the weak force. It is believed these forces are evidence of higher dimensions. The reason the weak nuclear force does not exert itself far outside the nucleus is the inverse rule. That is, any force that operates over 3 dimensions will decrease in strength by 1/(distance)^2, but any force that operates over 5 dimensions will decrease by 1/(distance)^4, and any force that operates over 7 dimensions will decrease by 1/(distance)^6. The exponent is always 1 less than the number of dimensions. I'm not sure, but I suspect the weak and strong nuclear forces operate over dimensions of prime numbers; for example 5 dimensions for the weak force and 7 dimensions for the strong force.

Photons have been speculated to be waves in 3-dimensional space. That is the dimensions of space itself fluctuate as a wave. Photons can be polarized to any of the 3 dimensions, resulting in the wave fluctuating up and down only in that one dimension. Gravity has been called a similar distortion (warp) in the 5th dimension. I suspect it is more complicated than that. Actually, I suspect the dimensions are partially collapsed so that in a gravity well there is a fraction less than 4 dimensions of space-time. If we only have 3.9999 dimensions of space and time, that would explain why the mountains, clouds, waves, etc. all have fractal shapes. Fractal mathematics is the mathematics of fractional dimensions.

A subatomic particle with mass has all forces working together: static, strong nuclear, and weak nuclear. The result is a set of waves operating over curved space that is warped in at least 7 dimensions. The waves keep getting curved and reflected back upon themselves. So each wave is altering the path of the other waves, resulting in the waves getting caught on each other. In the process these waves can exchange energy between the various dimensions by causing waves to curve, like a skate boarder riding up along the wall at a skate park. The distortions in the dimensions of space can extend outward, like a ball bearing sitting on the rubber sheet of a water bed; the greatest depression is close to the ball bearing but the depression extends outward all the way to the edge of the bed. The electromagnetic force can extend outward in 3 dimensions. The nuclear forces have more dimensions. I suspect gravity is a collapse of dimensions themselves rather than a distortion in another dimension. So this means subatomic particles with entangled waves actually pull the dimensions into themselves. Ack; I'm getting into my own flexible-dimension theory.

In any case, waves can only react with each other if their result is a stable harmonic. Since electrostatic forces extend out beyond the particle, that harmonic must include all particles involved in the system. This means an electron can only absorb a photon if the result is an electron moving an orbital that is a stable harmonic including all electrons in the atom. You not only have to include the waves inside the electron, but the motions of all electrons: complicated. These stable harmonics are the quantum states. If the result is not a stable harmonic, at least for a fraction of a second, then the photon does not get "caught" in the tangle of other waves which is the electron: it would just wiggle as it passes through.

Now getting back to your original question: how does energy become matter and vice versa? Well, movement over time (one of the dimensions) must be translated into waves in one or more of the other dimensions. If you translate movement over time into one of the 3 dimensions we are familiar with (length, width, height) then the result is a photon. That translates kinetic energy into electromagnetic energy. Whacking electrons can convert kinetic energy into photons. A photon entering a nucleus can convert energy into mass: this "curves" energy from the wave in one or more of the 3 conventional dimensions into the 5th dimension of gravity (or as I am postulating, into the collapse of dimensions). A nucleus is necessary because that is where waves interact which have 3 dimensions and the dimension which is mass. Hmm. I wonder if a bare proton or neutron would do this conversion as well? To convert photons into a new subatomic particle you must have enough energy for that particle, and enough energy for sufficient kinetic energy (speed) for the particle to get out of the nucleus. If there isn't sufficient speed, the new particle will just fall back in and disintegrate.

If you want more detail into how kinetic energy becomes other forms of energy, that gets into the definition of what is time. I would have to do some more research into that.

There; a basic primer for unified field theory.

dickbill · 2003-04-03 17:32:24

gosssh ! difficult to follow, but nice explanation and theory.
Is there some issue with the thermodynamic principles ? That in any process, more entropy or disorder should be created when the time advances.

does the formation of a black hole respect this rule, which, I believe, overcome all the other physical rules and forces ?

I read the S. Hawking's book a "brief history of time" but it would be interesting to see your opinion on that, Robert.
If the time dimension inside the black hole is changed, then the arrow of time has changed too and so for the entropy generated...

Palomar · 2003-04-03 21:58:19

If you want more detail into how kinetic energy becomes other forms of energy, that gets into the definition of what is time. I would have to do some more research into that.

*Thank you, Robert. I will have to give more study time to your most recent post, before I can make any response to it.

I would very much like to hear more, especially "what is time." My curiosity is going into overdrive!!

But Robert, I don't want you to feel obligated. If you'd like to go further in this thread and explain "what is time" and how kinetic energy becomes other forms of energy, well -- I leave that decision entirely up to you. I'll ::gladly:: read and try to understand what you've written, of course. Apparently some other folks are following this thread, too, which is a good thing; I wouldn't want you spending extra time and energy for just one person (me) who admittedly has to struggle to understand these concepts.

--Cindy

dickbill · 2003-04-03 23:58:10

To continue with the entropy issue, the 2nd principle (any physical system increases its entropy with time) is a universal priciple, if I understand it well.
Meaning that systems like living organisms, which locally produce neg-entropy to keep and grow their content of information over time, are not counterexamples of the 2nd principle since their metabolism heat their environnement and so, globally, they still produce more entropy than negantropy. So the global content in disorder of the universe is always increasing.
This has been very well explained in Erwin Schrodinger's book "what is life" . If we accept the identification of living process with the local production of neg-entropy, then the metabolism of living organism is not at all a "definition" for life, metabolism is merely a side effect of the neg-entropy generation. This has also something to do with the arrow of time. The best example is the pool, the billiard:
Imagine a camera recording 2 balls incoming in staight line to hit each other on the billiard. If the record did not include the players hitting the balls and we play the record forward or reverse, their is no way actually to say which way correspond to the real event. their is just not enough information in the system and we could say that the arrow of time is not strong enough to be able to say for sure if the movie plays towards the past or the future.
Now imagine the same scene with 3 balls, the players's hits are still not included, all you see are the balls moving straight. Even in that case, it will be difficult to say accuratly in what sense, forward or reverse, the movie has to be played to fit the real game. So we are unable to attribute an arrow for the time.
with 4 balls, say 3 balls hit one white ball which then moves away, the chance are that the right sense to play the movie is the white ball is hitting the 3 other balls, not the reverse. It's just a little bit more likelly. so you see that the arrow of time strongly depends of the information content of the system.
A system devoid of information (nothing happens) has a very weak arrow of time. Where stands the black hole in that story since their information content is hidden from the rest of the universe ?

Also, that mean that the whole universe reacts globally to very local thermodynamic process. This is where it is less clear in the case of a black hole, since no information escapes the horizon, how can the universe adjust its entropy if the black hole entropy changes ? Is that something to do with the quantic evaporation of the black holes, postulated by Hawkings ?

Shaun Barrett · 2003-04-04 00:27:24

Yeah ... well, I'm .. er, "following this thread ,too ...", Cindy, as you so optimistically put it!!
If you need any moral support in the 'struggling department', I'm right there with you, kiddo!!
:laugh:

I often plow my way through articles on this kind of thing in publications like "Discover" and "New Scientist". I usually end up with the same dull pain in my head as I got just now reading Robert's dimensional tour-de-force! Not that I mean any slight against Robert - on the contrary, I am impressed as usual by the scope of his knowledge. No, I fear the whole problem lies in my head, and with the hardware it contains, rather than with the software Robert provides!

I've never come across the notion that gravity results from "partially collapsed" dimensions. I assume it must be part of Robert's "flexible-dimension" theory - and I'm not even going to ask about that!!
Sounds interesting though.

Years ago on a British T.V. science show called "Horizon", they described matter as just 'pinched up energy'. I decided that was something I could live with because it's not too hard to imagine huge quantities of energy waves getting bundled up together and squished into a small volume - voila! - matter!
As for your question, Cindy, as to how or why some energy stayed energy and other energy got compressed into matter ... I never thought to ask! I know that some time after the big bang, the universe cooled enough for matter to condense out of the fireball of energy. And I know there are smart people who have devised mathematical models for that early time which predict how much hydrogen and how much helium should have been produced. Current estimates for the abundance of those elements in the universe today, mesh well with the theoretical amounts calculated, too.
So, those models would presumably also explain why or how a certain percentage of the initial available energy became matter. But then again, there are now question marks over other forms of energy - the so-called 'dark energy'.
Maybe nobody really knows the answer to your question yet! ???

Palomar · 2003-04-04 11:08:47

I read the S. Hawking's book a "brief history of time" but it would be interesting to see your opinion on that, Robert.

*I've got that book too, and am working my way through it.

How about Hawking's other book, "Black Holes and Baby Universes and Other Essays"? I plan to buy and read it soon.

--Cindy

Phobos · 2003-04-04 13:20:17

Another good book is "The Elegant Universe" by Brian Greene. It's my favorite pop-sci book.

Palomar · 2003-04-04 13:31:11

Another good book is "The Elegant Universe" by Brian Greene. It's my favorite pop-sci book.

*Thanks for referring it, Phobos. I've seen it at the bookstores; may get to it, one day.

--Cindy

Palomar · 2003-04-04 14:03:02

Yeah ... well, I'm .. er, "following this thread ,too ...", Cindy, as you so optimistically put it!!
If you need any moral support in the 'struggling department', I'm right there with you, kiddo!!
:laugh:
I often plow my way through articles on this kind of thing in publications like "Discover" and "New Scientist".

*That's good to know, Shaun; I'll likely need some moral support.

I love all the articles and info on the internet I can find. I used to get "Discover" magazine, but now just "Astronomy."

And heeeeeeeere's a little gem I found earlier today:

http://www.alumni.ca/~lijam/introd.html

--Cindy

Palomar · 2003-04-05 08:15:15

Atomic nuclei have strong and weak nuclear forces holding them together. This operates over a very short distance, and the strong force operates over a shorter distance than the weak force. It is believed these forces are evidence of higher dimensions. The reason the weak nuclear force does not exert itself far outside the nucleus is the inverse rule. That is, any force that operates over 3 dimensions will decrease in strength by 1/(distance)^2, but any force that operates over 5 dimensions will decrease by 1/(distance)^4, and any force that operates over 7 dimensions will decrease by 1/(distance)^6. The exponent is always 1 less than the number of dimensions. I'm not sure, but I suspect the weak and strong nuclear forces operate over dimensions of prime numbers; for example 5 dimensions for the weak force and 7 dimensions for the strong force.

*Robert: I think I've got a pretty good grasp of the material to this point (I still need to go over the remainder once more). However, I have 2 questions:

1. Why does the stronger force operate over a shorter distance than the weaker force? Is this due to some sort of level of resistance (higher for the stronger force)?

2. "Dimension" -- how defined? I think of science fictionish "dimensions" of other times and realities, etc. Please define?

Thanks.

--Cindy

RobertDyck · 2003-04-05 19:29:46

*Robert: I think I've got a pretty good grasp of the material to this point (I still need to go over the remainder once more). However, I have 2 questions:
1. Why does the stronger force operate over a shorter distance than the weaker force? Is this due to some sort of level of resistance (higher for the stronger force)?
2. "Dimension" -- how defined? I think of science fictionish "dimensions" of other times and realities, etc. Please define?

1. the strong force does operate over a shorter distance than the weaker force. I'm not sure why; I'm am just speculating this is due to it operating over a larger number of dimensions.

2. What is a "dimension"? There are 3 dimensions of space that we are familiar with: length, width, and height. There is a fourth dimension: time. Time operates over a single dimension; that is it can be measured forward or backward, there is no sideways to time. These 4 dimensions are often referred to as space-time. Einstein's theory of relativity speculated that gravity is explained by warping a 5th dimension. This dimension is not directly visible other than affecting the path of travel of objects passing through it. I am speculating that the time dilation effect that Einstein described is accurate; however the other effects are caused by a collapse of the 3 dimensions rather than a fifth dimension.

Physicists have since starting declaring that every effect they observe in subatomic physics is explained by yet another dimension. They are now up to 11 total dimensions, including the 4 dimensions of space-time. I suspect many of these additional 7 dimensions are not real, they are explained by simpler phenomena. However, do expect there are more than the 4 dimensions we experience. This means at a subatomic level our universe is a multi-dimensional thing.

Here is a simple visualization to help explain dimensions: draw a line on a chalk board (or white board). Now draw a line perpendicular to it so the second line crosses the first at 90?. The first line is in one dimension and you can measure the number of inches or centimetres any point is from the crossing point. The second line is in a second dimension and has a second number distance from the crossing point. Any point on the board has an X and Y coordinate; that is the distance "up" from the horizontal line, and a distance "across" from the vertical line. These are 2 dimensions of a plane. Now draw a line that is perpendicular to both of the others so it is 90? to both of them. The only way to do that is to draw it out from the board. This is the 3rd dimension, often designated by the letter Z. Now try to draw a line that is perpendicular to the previous 3 lines. You can't do it. That would require 4 dimensions of space. Our experience only has 3 dimensions. However, bozons (protons and neutrons) have more than 4 dimensions of space-time. The strong and weak nuclear forces operate over other dimensions.

Fractal mathematics is interesting. Visualize a single line drawn on a chalk board. That line has 1 dimension. Now draw a wiggly line. That line has more than 1 dimension, but less than 2 dimensions. Now make the wiggles larger and more complicated, but keep repeating the wiggle pattern. That line has still more dimensions but it is still less than 2. The line becomes steadily more wiggly and the wiggles become more complicated as the dimension fraction become larger. When the number of dimensions becomes 2, the wiggles merge so the line becomes a plane and fills the entire board. If you continue to increase the number of dimensions beyond 2, the plane starts to curve, bend, and wiggle away from the wall. Again, the wiggles become larger and more complicated until they merge together to form a solid cube when the dimension number becomes 3.

Physicists have found that electrons have random behaviour within an atom. Furthermore they have found they cannot measure the exact speed of an electron, its path of travel, and the time it passes through a point in space. They can measure its location, but not the time it is there. They can measure the time an electron passes through a plane, but not exactly where it passes. I believe this is due to the fact that the electron has 3 dimensions of space-time. They are trying to measure 4 dimensions simultaneously for something that just doesn't have 4 dimensions. They can rotate which dimension is missing, but there is always something they can't measure. Furthermore, since the electron exhibits random behaviour, I believe this is due to a fractional dimension. So the electron has 3 and a little bit of a dimension.

Einstein's theory of relativity states that a theoretical spaceship that travels ever faster, approaching the speed of light, will become shorter in the direction of travel. If the spacecraft could reach the speed of light it would shorten so it has zero length. I believe this is due to the fact that the dimension of travel is literally collapsing as you accelerate close to the speed of light. If you could travel at exactly the speed of light, your spacecraft would become a 3-dimensional space-time object in our 4-dimensional space-time universe. An electron travels close to the speed of light, so this is why it has one dimension almost completely collapsed. If a spacecraft could travel as fast as an electron, it would experience quantum tunnelling and other random effects just as an electron.

Stephen Hawking's book "A Brief History of Time" was an excellent book, and I do have a first edition copy in hardcover. Great reading, though in places it left me wanting much more detail. I'm afraid to use the word "simplistic" for a book like that. I am trying to read Albert Einstein's book "The Meaning of Relativity" but the math is a bit heavy. I'm still looking for a good calculus tutor. I do disagree with Stephen Hawking on one point. He said Albert Einstein was completely wrong when he said "God does not play dice with the universe" in response to the Heisenberg uncertainty principle of quantum mechanics. Dr. Hawking argued that the randomness of the uncertainty principle is a fundamental property of physics. Dr. Einstein could not accept it because he thought everything should have a specific reason and sufficiently described physics should calculate everything. But quantum mechanics was developed by observing subatomic particles and generalizing those observations by producing mathematical formulae to match the observations. Quantum mechanics did not attempt to explain why; it simply stated that it is because it is, and these formulae match the observations. Einstein had to have a reason for everything. Now this theory of "flexible dimensions" that I am trying to develop states there is a specific, finite reason; however fractal mathematics still results in random behaviour when projected into a 4-dimensional space-time universe. So Dr. Einstein was correct when he asserted there must be a reason, but Dr. Hawing was right when he said the uncertainty principle is a fundamental principle of physics. Both gentlemen are right and both are wrong, depending on your point of view.

dicktice · 2003-04-06 07:37:39

Gee, RobertDyke, your "dimension" examples are very easy to follow and, more importantly, easy to remember. I know that Cindy will reply in good time (oops, I mean: 4th dimension). Anticipating her--thanks, for your thoughts.

RobertDyck · 2003-04-06 11:16:57

Robert, you are wrong. ... By definition dimensions of an universe is an positive integer number.

Ah, the criticism of a new theory begins. Every new theory has been strongly criticized at first, and it should be. That is the scientific method: analyze, examine, look for inconsistencies, thow out theories that fail examination. Then test your assumptions again by looking for new data, and deliberately look for things that do not fit in the remaining theory. Come up with a new theory to explain the new data, criticize that new theory, etc. It is a continuing, on-going process. I would like to give more details, but I need to work on the math. If I had all the math down I could publish it as a new Grand Unified Theory.

Before getting into too great of a debate, let me quote Albert Einstein who said "Great thoughts have always encountered opposition from mediocre minds." Please do criticise my ideas, but don't get too caught in what has already been done.

BGD, you are quite correct when you describe basic Euclidean geometry. Euclid was a Greek mathematician who lived circa 300 B.C. and produced the principles of geometry you describe. However, Albert Einstein's theory of General Relativity is based on objects with mass (like the Earth) warping space in the 5th dimension. That means you cannot use Euclidean geometry to calculate trajectories. Normally the distance between two points (X1, Y1, Z1) and (X2, Y2, Z2) would be calculated by the formula sqrt( (X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 ). However, General Relativity states that there is another dimension and that space in that dimension is curved; it is warped by massive objects like a planet. That means you are actually tracing the path along a curved surface in 4-dimensional space, and those dimensions do not include time. Time is also warped by a massive object, so time dilation affects the speed of the object, which affects its trajectory. Tracing an object's trajectory along curved 5-dimensional space-time requires Riemann geometry; Euclidean geometry is just not good enough.

Furthermore, General Relativity states that gravity is not a force, it is an effect. I know, this means throwing out all of Newtonian physics. The first proof of General Relativity was actually done by Albert Einstein himself. He calculated the orbit of Mercury at a time when people noticed perturbations in its orbit that could not be accounted for by the gravity of the other planets. At first scientists thought those perturbations were caused by a new planet orbiting very close to the sun, but when they looked they couldn't find one. Dr. Einstein calculated the orbit of Mercury using General Relativity and the result was correct within the accuracy of the measurements taken. His calculation of the orbit of Mercury was based on the planet following the straightest line possible within curved space-time.

I could give a simple explanation how a differential time dilation gradient could cause acceleration, but rather than use an explanation I came up with, let me first refer you to General Relativity and Riemann geometry. What I am trying to do is unify General Relativity with Quantum Mechanics using Fractal Mathematics as the glue. Yes, I know, unifying these two theories would be the Unified Field Theory. Benoit B. Mandelbrot developed Fractal mathematics in the 1970s so it wasn't available in Albert Einstein's life time.

I do have one question, since you are a math teacher. Could you please explain Fractal mathematics over a continuous domain? Computer graphics and virtual reality image models use integer formulae, but the real world uses continuous phenomenon so you must use Real numbers.

Palomar · 2003-04-06 11:21:25

I hope Cindy will understand what everything is about when i finish. Cindy, i expect your input about this. Robert, read it too.

*Hi BGD. I'll read your post more carefully and give whatever input I can, but please know I'm still working my way through Robert's *first* post about these matters. It's challenging for me, and please keep in mind I also have long work days, duties regarding my home and spouse, etc. I've also just had a nasty bout of food poisoning and am still not quite up to par.

I will read your post again (and probably again) very carefully and will give whatever input I'm able to, but please be patient and give me some time.

When it comes to this subject matter, you and Robert are the hares...and I'm the tortoise.

--Cindy

RobertDyck · 2003-04-06 18:21:35

Robert, some time ago there was posted on the net a theory of a doctor Schroeder, called EPSM (elementary particle spatial model). I quite liked it for a time, and i'm still considering it in my pet theories now. Have you ever heard of that? A plain Y/N answer will be enough.

I believe EPSM (elementary particle spatial model) is quantum chromodynamics (QCD). I have heard about it, although I won't claim to be any sort of expert.

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