Introduction to Black Holes: Newbie Questions Answered

[Guy From Alberta]

Hello. I am new to this board. I hope it is acceptable to ask some foolish questions here once in a while. I am a novice when it comes to physics; but I have always been quite interested in such subjects.

I have been looking for some reliable information regarding what is usually called "black holes." If this is not the forum to ask my questions, please let me know before I go on and on...

I will keep it short until I see if this is the right forum for this topic. The first thing I would like to find is a definition of a black hole.

More later...

 

[Chen]

Start with:
http://en.wikipedia.org/wiki/Black_hole
This is probably the wrong place for this thread, but a mentor will move it shorly so don't worry.

 

[Guy From Alberta]

Thanks Chen

I was hoping to uncover info like this here. The link you provided is very helpful; and EASY to understand! I really appreciate it. I will be back in about 2 days; and if this subject gets moved; I totally understand. I will appreciate being able to ask a few more questions here, and learning more. Now that I look things over closer; it may be that some of my questions will over-lap into your Philosophy Forum here; but for now; I am interested in exploring black holes and related topics in this thread, if that is OK.

 

[Guy From Alberta]

Gravity And Time??

I don’t understand a lot of what I read on these topics, as I am untrained in them; but I do enjoy the physics related topics I see here for personal research. I know my questions may sound really simple to many here; but I am sincerely interested in getting at the facts with certain areas of physics.

I once did a science project in elementary school on Einstein’s theory of relativity – drove my Dad nuts; asking him all kinds of questions about it, so I could complete my project…

Am I correct in understanding that gravity can be seen as the result of the basic “geometry” of space time? (that geometry being curved by matter and energy). And that, therefore, certain predictions are made possible, such as black holes, and time being slowed by gravitational fields?

From my studies of black-holes; I have been able to see the connection with gravity, I think; in my own simple way. But, as I mentioned; I am interested in not just black holes, but some other related subjects.

Can I also ask then, what kind of “gravitational field” would slow time? Perhaps, I need to better understand the definition/s of time as I ask this question; I have always thought of time as something we measure by hours and minutes; yet as I look into the physics of black holes, and gravity, etc., I am starting to sense some other possibilities, which I would like to understand better.

Any comments, or links that you could refer me to are appreciated.

 

[Imparcticle]

Am I correct in understanding that gravity can be seen as the result of the basic “geometry” of space time? (that geometry being curved by matter and energy). And that, therefore, certain predictions are made possible, such as black holes, and time being slowed by gravitational fields?

Gravity does indeed curve the spatial geometry of the universe. A black hole is an example where the intense gravitational concentration causes a massive indentation in the "fabric" of spacetime. A certain phenomenon regarding black holes I find particularly fascinating is Hawking Radiation. Have you heard of this phenomenon?

Can I also ask then, what kind of “gravitational field” would slow time?

Precisely what do you mean by "what kind of gravitational field.."?

Perhaps, I need to better understand the definition/s of time a
s I ask this question; I have always thought of time as something we measure by hours and minutes; yet as I look into the physics of black holes, and gravity, etc., I am starting to sense some other possibilities, which I would like to understand better.

True, what we measure by hours, minutes etc. are only accurate within particular premises on earth. Universal time on the other hand is relative.
I would define time as the increase in entropy. That is, the increase of disorder.

 

[Mr. Robin Parsons]

Time is simply the metering of movement or motion, nothing else non-existent...

Gravity is 'The energy' contracting space in the Universe, rather then expanding it, like heat (energy) can also do...

Black Holes are exceedingly difficult to go at as so little is actually verifiable, lots of speculation though, most that has been proven is the observation of a place in Space that is empty, devoid of background light passing through that particular spot, and something has been, apparently, 'videoed' falling into one...just means it disappeared into 'apparent' emptiness...

 

[turin]

Am I correct in understanding that gravity can be seen as the result of the basic “geometry” of space time? (that geometry being curved by matter and energy). And that, therefore, certain predictions are made possible, such as black holes, and time being slowed by gravitational fields?

Yes to all.

what kind of “gravitational field” would slow time?

The kind that has a variable g₀₀, off the top of my head, but I'm probably leaving out other kinds as well. You have to remember that time is relative, and it doesn't "slow down" in an absolute sense, only wrt other frames of reference. In GR, time can actually "speed up" too (again, this means in a relative manner).

Perhaps, I need to better understand the definition/s of time as I ask this question;

Probably. Time is traditionally defined as the parametrization of physical processes. It is also traditionally defined according to some physical standard process.

I have always thought of time as something we measure by hours and minutes;

Not "by" hours and minutes. We measure time by clocks "in" hours and minutes. Hours and minutes are different units of time, but they are not very fundamentally defined.

... as I look into the physics of black holes, and gravity, etc., I am starting to sense some other possibilities, which I would like to understand better.

Such as ...?

 

[cephas]

I also have a question on black holes. It kind of crosses over to quantum mechanics though. I hope that is ok. Since a black hole is considered to be a singularity wouldn't that violate the uncertainty principle?

 

[chroot]

cephas,

Yep. General relativity is incompatible with quantum mechanics. Most physicists are hopefully that a successful quantum gravity theory will remove the singularity.

- Warren

 

[Imparcticle]

Chroot:

Is that what they call LQG? What about 5 demensional gravity theory (it's something like that)? What's the difference?

 

[chroot]

Both string theory and loop quantum gravity are competing theories of quantum gravity. The difference is largely that LQG is just a quantized theory of gravitation, while string theory is more ambitious and attempts to unify all four fundamental forces.

- Warren

 

[Guy From Alberta]

Figuring it out...a bit!

Gravity does indeed curve the spatial geometry of the universe. A black hole is an example where the intense gravitational concentration causes a massive indentation in the "fabric" of spacetime. A certain phenomenon regarding black holes I find particularly fascinating is Hawking Radiation. Have you heard of this phenomenon?


Precisely what do you mean by "what kind of gravitational field.."?


True, what we measure by hours, minutes etc. are only accurate within particular premises on earth. Universal time on the other hand is relative.
I would define time as the increase in entropy. That is, the increase of disorder.

Hello

I appreciate all the responses here; and feel I am SLOWLY learning a few things that will be very worth-while. I will not always take this long to respond - but I am a Dad with 2 growing boys!

The question here re "gravitational field" may be a good place for me to continue here. I think, that by using this term; I was referring to anything that causes a concentration of gravity.

I am trying to figure out as much as I can re how gravity, or concentration thereof, affects "time." And; I would like to understand "time" much better. I think that my first question may be a lot harder to grasp, if I do not correctly understand the basic concepts of time - according to modern physics. I know what it is, according to the clock on the wall; but what is it really? The black hole concept seems like a good place to understand these other two concepts I am wanting to study?

I agree; that Hawking Radiation is a really interesting area of study; but until last week; it was a new subject to me; so it will take a little time to get it all absorbed.

I am in the middle of formulating some questions about this; and will get back here this week end to ask them!

 

[Guy From Alberta]

I would like to try out this one question first, if I may??

As I read through these posts, and other, related materials I have been referred to; it is appearing to me that "time" can be assessed from more than one point of reference?

For eg., we can assess time, by using our clock. it looks like some here have stated that "time" can also be assessed from a gravitational point of reference; which is DIFFERENT than the clock on the wall.

Would someone be able to compile a list of all the different ways that we can view time? I would really like to look into that.

Someone above mentioned a brief definition for time: "the amount of entropy." From what I understand; "entropy" is energy that cannot do work? Is this then, an accurate definition of "time" in consideration of the above list I have asked for? Please remember; I am a layman/novice at all this; so you have to bear with me, if some of this seems really elementary. I don't understand much of the math I have seen here; but the rest is really interesting!

 

[Mr. Robin Parsons]

Entropy is the enregy lost doing work, like the heat off of a car motor that cannot be used in the work process...sorta...

Concentrating gravity is sort of a mis-conception, but if you compact mass, as gravity tends to want to do, then the gravitational field Appears as increased in strength, hence the appearance of a BH is a result of highly compacted mass (A singularity, for now) that generates the appearance of the absence of emissions of light/EMR...

 

[turin]

Guy From Alberta,
If you really want to understand black holes, or how physicists use time, then I believe it will only confound the issue to list every possible way imaginable to consider time. Firstly, the physical processes themselves may not lend to you any strong significance, and merely serve as neat little abstractions. Secondly, the term "time" can have dramatically different meanings to different people in different contexts. What I suggest is that you learn the meaning of time in the particular physical context of interest to you (I'm assuming that to be GR), for which there are two important types: coordinate time and proper time.

Coordinate time is an axis label, and designates one of the four space-time directions. This is the one that you have probably heard called "the fourth dimension."

Proper time is the kind of time that is experienced and almost always serves to characterize a process in relativity. This is the time that any physical clock will tick by. The particulars of the physical mechanism that causes the clock to literally tick are somewhat inconsequential, so long as you consider the reason behind the ticking to be physically fundamental.

All physically processes are trajectories of a physical state, and there is some parameter against which this state can be said to change. Furthermore, the effect of this parameter is shared by direct relationship with all other physical systems. Time meets these criteria. The physical processes only reflect the incrementation of this parameter. A physical process that is dedicated to just that purpose is a clock. You will find many types of these, based on many types of physical processes, but they all operate on the same fundamental principle.

 

[Grizzlycomet]

I would like to try out this one question first, if I may??

As I read through these posts, and other, related materials I have been referred to; it is appearing to me that "time" can be assessed from more than one point of reference?

For eg., we can assess time, by using our clock. it looks like some here have stated that "time" can also be assessed from a gravitational point of reference; which is DIFFERENT than the clock on the wall.

Would someone be able to compile a list of all the different ways that we can view time? I would really like to look into that.

Someone above mentioned a brief definition for time: "the amount of entropy." From what I understand; "entropy" is energy that cannot do work? Is this then, an accurate definition of "time" in consideration of the above list I have asked for? Please remember; I am a layman/novice at all this; so you have to bear with me, if some of this seems really elementary. I don't understand much of the math I have seen here; but the rest is really interesting!

Indeed, the time measured will depend on the frame of reference. The faster you travel, the slower time will tick for you. Also, the stronger a gravitational field you are subjected to, the slower time will tick for you. These effects are known as "time dilation", and are further explained in This Link

 

[Nereid]

Chroot:

Is that what they call LQG? What about 5 demensional gravity theory (it's something like that)? What's the difference?

There's a sub-forum
here at PF devoted to discussion of just this topic.

 

[Mr. Robin Parsons]

Is this place great for finding knowledge, or what!...whooohoooo!

 

[Guy From Alberta]

Hi Turin

I really appreciated your reply in particular this time. I will need a few days to get back to this forum with some other questions/comments.

 

[Erich Schoedl]

Just like to add that there is a lot of speculation involving black-holes. Gravity is "causing" time to slow, but the other way to look at it is that the curved space-time (in the topological sense) is causing gravity. In 4d topology, the gravity is a result of the curvature. Energy present in the spacetime is what we consider causes the curvature. John Wheeler writes excellent books with great visual capacity to describe these connections.

I'd also like to spark my personal idea that if space is stretched out (instead of contracted) in the region of a singularity, then the Planck scale is relative to the rate of aging within a given region. In other words, the Planck scale limitation of space-time could be stretched out to form event horizons or the topological surface of the "strings" or membranes in m-theory.
Then spacetime itself is considered the underlying structure of such objects, and contains various topological properties to carry energy.

Even if a swolen Planck area was the surface of an event horizon of a black hole, it would still not emit light other than Hawking radiation, but it would technically be "naked" and still contain no singularity. The math of an expanded Planck length would eliminate the mathematical singularity within an event horizon.

 

[Mr. Robin Parsons]

Lots of this is nice but, until we have an accurate measure of lightspeed, (c) outside of our Solar system, we are still simply making, well educated, uhmmmm 'guesses' actually...

 

[Nereid]

Lots of this is nice but, until we have an accurate measure of lightspeed, (c) outside of our Solar system, we are still simply making, well educated, uhmmmm 'guesses' actually...

Er, there have been many, many observations of just that! :tongue:

For a start, how about two sets of observation of (as many dozen as you care to specify) pulsars, six months apart? This is a variation on a http://www.colorado.edu/physics/2000/waves_particles/lightspeed_evidence.html .

 

[Mr. Robin Parsons]

Uhmmm Nereid, Jupiter is still within our solar system, least last time I heard...

 

[Nereid]

Uhmmm Nereid, Jupiter is still within our solar system, least last time I heard...

Er, I think I said (my emphasis) "a variation on a technique first used by Roemer". Roemer observed occultations, eclipses, etc of the Galilean moons of Jupiter; Mr. Robin Parsons - as he has a good radio telescope and a very accurate atomic clock - can observe the timing of the pulses from the Crab Nebula pulsar (or any other of the hundreds of pulsars - observable from Canada - found to date). Mr. Robin Parsons, being a diligent scientist, will note that pulses observed when his radio telescope is on the 'far' side of the solar system arrive at later times than when he is on the 'near' side (compared with his expectation that they will all arrive as if he is moving towards - or away from - the pulsar at a constant speed). Mr. Robin Parsons will then use high school math to calculate the speed of light - between his radio observatory and the pulsar - and he will tell PF members and readers ... {what will you tell us Robin?}

As I think I also said, this is just one of many methods which can (and have) be used to measure "lightspeed, (c) outside of our Solar system".

 

[Mr. Robin Parsons]

Uhmmmmm and if that light traveled at speed X then when entering the local gravitational environemnt, (solar system) sped up. or slowed down. to speed c, then we would have no way of knowing that, nor proving it, because of relativity of the observation...cause what you are measuring, is measured here, on earth, not out there...

 

[Nereid]

Uhmmmmm and if that light traveled at speed X then when entering the local gravitational environemnt, (solar system) sped up. or slowed down. to speed c, then we would have no way of knowing that, nor proving it, because of relativity of the observation...cause what you are measuring, is measured here, on earth, not out there...

Quite so. And if the mighty CIA were monitoring all internet forum discussions, and secretly altered the text which you (or I) typed before anyone on PF could read them, ...

William of Ockham had something to say about this, IIRC, ... or do you require that someone bring back samples of ⁵⁸Ni and ⁶⁰Co from SN1987 (in the LMC), to be sure that they were the cause of the decay in the light curve?

But, as I said, there are plenty of other techniques and observations; are you interested in hearing them? E.g. 'light echoes'

 

[Mr. Robin Parsons]

Bad dodge Neried, no need of the samples because experimentally it makes eminent sense that the visible line spectra would be as arising from the same reasoning...

But that is NOT a measure of lightspeed outside of our solar system, neither is the method you referred to reliable enough as to be taken as 'absolute' proof, even though I too, would accept it, on it's present basis, untill better proof is found, and knowing that it is not a very Solid piece of evidence, it is lacking, somewhat...

 

[Nereid]

Bad dodge Neried, no need of the samples because experimentally it makes eminent sense that the visible line spectra would be as arising from the same reasoning...

But that is NOT a measure of lightspeed outside of our solar system, neither is the method you referred to reliable enough as to be taken as 'absolute' proof, even though I too, would accept it, on it's present basis, untill better proof is found, and knowing that it is not a very Solid piece of evidence, it is lacking, somewhat...

So we're down to personal taste re the extent to which the data is consistent with predictions from a theory (or hypothesis), right?

If we go back to the 'pulsar variation' of the Roemer technique, you will see that it does provide (in principle) a test of c being different 'in the solar system' from everywhere else in the universe (well, at least out as far as the furthest pulsar). It depends, of course, on just how 'c' varies within 'the solar system'; for example, does it have a value of c_a out to 50 au (from the Sun, or baricentre), then c? Or is it a function of distance from the Sun?

Simplest case would be a step function; imagine two pulsars, each in a binary system, more or less in the same line of sight as Jupiter (or Saturn, ...). Analysis of the differences in eclipse times and pulsar 'ticks', ~six months apart, should be able to recover the step function. Always assuming it were large enough, of course.

BTW, since this is science, not math, I propose 'proof' is impossible, let alone 'absolute proof'.

[Edit: the phrase in blue added; clearly I typed my post in too much haste earlier today ]

 

[DrMatrix]

Lots of this is nice but, until we have an accurate measure of lightspeed, (c) outside of our Solar system, we are still simply making, well educated, uhmmmm 'guesses' actually...

Well, yes and no. I hope you're not one of those who think scientific theory is "just a guess". A theory explains obervations and makes testable predictions. Relativity explains observations and makes predictions. Every test of the theory has supported relativity. Unless someone can come up with a compelling reason that the laws of physics should be different outside the Solar system, we have no reason to suppose that we live in a privileged region.

Every observation is consistent with a constant speed of light. Does that mean that the speed of light is necessarily constant? No, not really. We cannot measure the speed of every beam of light in the Universe. Therefore we can never prove that the speed of light is constant. But since every test is consistent with a constant speed of light, a reasonable conclusion is that the speed of light is constant everywhere.

 

[Nereid]

Of all the observations which, directly or indirectly, attest to the constancy of c, outside the solar system, right out to the surface of last scattering, perhaps the most powerful are those which looked at time variation of $$\alpha$$, the fine structure constant.

The best observations show that $$\alpha$$ is constant to ~2 parts in 10⁸, here on Earth, over the past ~2 billion years, and to ~<1 part in 10⁶, in many parts of the universe, over the past ~10 billion years.

Of course, as $$\alpha$$ contains h-bar and e, as well as c, one could argue that these observations are consistent with the idea that c, e, and h-bar (or some combination) vary - over time - in just such a way as to keep $$\alpha$$ constant. And then we would examine independent observations of the constancy of e and h-bar (as well as others into c).

And such a discussion could lead us to a point in another thread (in Theory Development?), where Janitor (?) quoted John Baez on the constancy of c. We could then discuss - probably in HPS rather than any Physics sub-forum - how the constants and units which many (most? all?) of us take for granted are just as dependent on theoretical constructs* as the constancy of c.

*Albeit constructs which are consistent, to high degrees of accuracy, with observation and experiment.

 

[Guy From Alberta]

Physics Post 2

Thanks Grizzlycomet for the link to “time dilation.” I am finding this all very interesting. I want to come back to this time dilation theme in a short bit.

I have a number of questions arising; hope it is OK to just spout them out. In this topic, some of us have touched on how gravity does indeed “curve the spatial geometry of the universe.” Can we further define “spatial geometry?”

Now, we have also been talking about “time.” ; and how a definition of time would be dependent upon the frame of reference being used. A “frame of reference;” I presume as meaning a collection of condition, axis, or assumption; which establish how something will be approached or understood. As “Turin” mentioned in a post above “coordinate time;” and “proper time;” and he mentioned how some call “coordinate time, the “fourth dimension;” I came up with more questions, possibly related to some of my earlier questions here about time.

From what I see so far, time is not really the fourth dimension of space; but of “spacetime.” It is within the sphere of general or special relativity where we see time, plus three dimensional space being treated together as a single, four dimensional “manifold,” called “space time.” And spacetime cannot be viewd as a fixed background; but rather, a networking and developing of certain evolving relationships. And, it is a spacetime interval between two events, that results in an entity analogous to distance?

What exactly are a) the dimensions of space?
b) the dimensions of spacetime?

What does it mean to say “a spacetime interval between two events?” How is an “interval” best defined, and what is an example of this kind of “event,” in a case like this?

How are “coordinate time,” and “proper time,” affected by/related to said “Intervals,” and “events?”

Do black holes teach us anything about coordinate time, or proper time?

 

[turin]

For someone who does not have a strong mathematical or physics background, you sure do know who to ask ambitious questions. Let's see what we can say about them.

I have a number of questions arising; hope it is OK to just spout them out.

You(r questions) are one of the reasons I visit the forum. Please ask all the questions you want, or I'll start to get bored.

In this topic, some of us have touched on how gravity does indeed “curve the spatial geometry of the universe.” Can we further define “spatial geometry?”

Gravity curves space-time, as well as space in itself. Geometry is what gets curved. Imagin a volume. This volume is filled with points. Each point has an identity. They form a set. There is also some notion of points being close to each other and points being far away. This notion (called topology, I think, I'm still learning this stuff) is not sufficient to support a notion of curvature. So the points are endowed with a more specific notion of, not only close or far, but how close or how far. This notion is called geometry. (This notion does not have to arise from the same closeness relationships as the topology, as I understand it, but I might not understand it.) It was inspired by Euclid, but later on, people like Gauss and Riemann came along and decided that Euclid put unnecessary restrictions on his geometry.

You can think of geometry as the collection of distances between all the points together with those points between which the distance is defined. Spatial geometry implies that these distances are always positive definite for any two distinct points.

A “frame of reference;” I presume as meaning a collection of condition, axis, or assumption;

Not exactly. There is a more exact definition in the context of relativity. This is one of the things to which I think Einstein (the man himself) gives a decent portrayal. He gives a working definition of a frame of reference is a set of intersecting planes. The (perpendicular) distance that would be measured to these planes gives the (spatial) coordinates of any point in this frame. If you imagine that two sets of such intersecting planes can exist without mutual interference, and then further imagine that they move wrt each other, then these two sets of intersecting planes give two distinct frames of reference.

A frame of reference is something to which you refer to give meaning to your expression. In relativity, this means a set of intersecting planes that allow you to label points with a set of numbers.

From what I see so far, time is not really the fourth dimension of space; but of “spacetime.” It is within the sphere of general or special relativity where we see time, plus three dimensional space being treated together as a single, four dimensional “manifold,” called “space time.”

Exactly

spacetime cannot be viewd as a fixed background;

This is a GR notion. In SR, spacetime is fixed for sure. Since you really want to talk about BHs, then you are correct to say that the geometry is dynamical. Whether spacetime itself, on which the geometry is endowed, is dynamical is more of a philosophical debate (as I understand it). Actually, this is another item for which I rather liked the treatment of Einstein. (See Relativity, 5th ed., pp. 135-57, "Appendix V: Relativity and the Problem of Space", or the first chapter in The Meaning of Relativity, I forget what it's called.)

but rather, a networking and developing of certain evolving relationships.

Very good. When you get right down to it, physics can only go so far as to make epistemic judgements.

What exactly are a) the dimensions of space?
b) the dimensions of spacetime?

The dimensions of space are the degrees of freedom that a point particle may utilize. A point particle can go up, right, or out. Any other behavior of a strict point particle is a combination of scaled versions of these behaviors (including negative and vanishing multiples). The dimensions of spacetime are not quite so understandable. They do not indicate degrees of freedom for a point particle. The reason why spacetime is treated like a 4-D space is that, there are results of a certain type of transformation (Lorentz transformation), which are very much like what rotations would be in 4-D space.

Imagine just a 1-D space, like a line. A particle in this space has 1 degree of freedom. It can go, let's say, to the right. (Going to the left is just a negative scaled multiple thereof.) Now, let us consider the behavior wrt time. This behavior can most readily be considered from a 2-D type construct called the 1+1 D spacetime for this particle. If we further posit onto this structure the rules of SR, then there is a characteristice wedge in this 2-D construct. I will hereafter refer to this wedge as the "lightcone." The interior of the lightcone is allowed, however, the exterior is forbidden. This lightcone follows the particle through the 2-D construct. It would look kind of like a tiny car with its headlights shining out front with a spread beam (though this is not why it is called a lightcone). The car is allowed to drive wherever the beam shines. 2 stipulations on the car: 1) Regardless of the direction of the car, the beam always shines in the same direction, 2) the car always moves forward at the same speed. Clearly, this car does not have the freedom to enjoy every point in this 2-D construct, so the time dimension doesn't exactly add a degree of freedom, at least, not like a spatial degree of freedom, not a direction that a particle can choose.

What does it mean to say “a spacetime interval between two events?” How is an “interval” best defined, and what is an example of this kind of “event,” in a case like this?

The only way I really know how to field this one is with some math. An event is a "point" in spacetime. Return again to the 1+1 D spacetime (forget about the car for the moment). Imagine 2 distinct points in this spacetime (any two will do). Imagine the straight line segment connecting them. This line segment represents the interval. In Euclidean geometry, this interval would be quantified by the Pathagorean theorem. In spacetime geometry (which is not Euclidean), the Pathagorean theorem is generalized to a metric.

Imagine that the time axis is verticle and the space axis is horizontal. Then, qualitatively, the more verticle the interval, the greater it is. Intervals that are not verticle are shorter, to the limit that the interval coincides with the edge of the lightcone (as in the car example, the edge of the head light beam). If the interval is even more horizontal than the edge of the lightcone, then it is negative. This is clearly not possible using the Pathagroean theorem. (Note: you may have heard of a treatment that invokes an ict axis, and that claims the validity of the Pathagroean theorem therefrom. This is OK if all you ever want is a cursory understanding. The idea of non-Euclidean geometry is mathematically more sophisticated and will take you further. I have never tried to understand GR in terms of the ict notion, but I don't think that the ict notion can even be carried that far, so, even for our purposes, it is useless.)

How are “coordinate time,” and “proper time,” affected by/related to said “Intervals,” and “events?”

There is a concept called a "worldline." This is the collection of all events that represent the existence of a particle through time. Returning once again to the 1+1 D spacetime, any particle in the 1-D space will actually be a line (or, in general, a curve) in the 1+1 D space time. This line, which can be considered the posisition of the particle at all points in time, is the worldline. According to the rules of relativity, two distinct events on the worldline of a particle are separated by an interval that is always more horizontal than the edge of the wedge. Therefore this interval is positive. The proper time (between these two events) is one way of quantifying the length of this interval. The proper time can be directly related to the coordinate time interval (&Delta;t) by the time dilation (Lorentz transformation).

The proper time usually implies an interval that does not "violate" the light cone. For intervals that do extend outside the light cone (more horizontal than the edge of the lightcone), the value changes sign (becomes negative), and it is usually denoted as the proper distance instead of the proper time. Fundamentally, proper time and proper distance are the exact same thing (with the occasional exception of a sign convention), and it is just a matter of context that determines the particular label.

Do black holes teach us anything about coordinate time, or proper time?

Yes. For instance, "inside" a BH, the distance from the center becomes another time like axis. That is, once a particle enters a BH, it loses another degree of freedom, because it now not only must move forward in time, but its distance from the center of the BH must consistently decrease. At the center, the worldline of the particle terminates.

 

[Guy From Alberta]

For someone who does not have a strong mathematical or physics background, you sure do know who to ask ambitious questions...
You(r questions) are one of the reasons I visit the forum. Please ask all the questions you want, or I'll start to get bored.

Thanks Turin...I appreciate the vote of confidence. My mother always used to say something similar - that I asked a lot of questions which kept her hopping. But, believe it or not; I am just a simple trucker type guy who is really interested in certain scientific fields, such as physics. When a person is really interested in something; it seems to help. I have about 14 years experience in nursing, before what I do now, so the sciences seem to ring a bell with me.

One of the several reasons I am trying to explore the black hole angle, in relation to time, and/or space time; is that I believe human beings can understand themselves better; when they understand the "physics" of who they are; and where they are in space/time. This is why I mentioned in the beginning of this thread that some of the many ideas ruminating in my cerebrum, may at some point delve into the philysophical end of things here.

But, before I can really explain all that; I feel I need to study more into some of the basic, physical concepts. There are some things that I would like to understand better.

For now; I just have one, quick, clarifying question about black holes. My recent studies indicate that there are atleast 4 different kinds of black holes...the Kerr Black Hole; the Kerr-Newman, the Reisner-Nordstrom; and the Swarzchild Black Hole.

Now, in your last post to me; you stated: ""inside" a BH, the distance from the center becomes another time like axis." I apologize; but I don't quite get what is meant by a "time axis;" or a "time like axis." What is meant by "axis" in this context? And, if we can figure me out that far; I find myself wondering about some pertinent differences:

a) between black holes that are rotating (Kerr-Newman), and black holes which have an "angular momentum." (Reisner-Nordstrom).
b) between BHs that are "charged" and BHs which have zero charge; (as in Kerr-Newman vs the Swarzchild BH).
c) If BHs teach us something about "time," or "space-time;" how would the things we can learn about time differ, with each of these 4 types of BHs?

I have some other questions; but I need to take this all just a bit at a time. If I shift gears too fast; I'll stall my "rig." And I am thinking my current questions may change a bit, if we can answer these ones.

Thanks everyone for taking the time to reply here. I am enjoying it.

 

[turin]

in your last post to me; you stated: ""inside" a BH, the distance from the center becomes another time like axis." I apologize; but I don't quite get what is meant by a "time axis;" or a "time like axis." What is meant by "axis" in this context?

There are a few ways to look at it.

You don't have access to the future (classically speaking). You only gain information in the future by "going there;" processes do not flow from the future to the past, and neither do you. In fact, the future doesn't even really exist. You move along and constantly "lay down" your worldline as you go, like building a road right in front of you (or maybe like leaving footprints). The only stipulation is that you do not violate the light cone. This is not a philosophical issue, this is more of a definition. There is a fundamental principle in (classical) physics called "causality." When we speak of a path that is time-like, we mean that the points at larger values of the parameter along this path are a direct result of the points at the lesser values of the parameter, thus the parametrization. Another consequence is that we may orient this axis with the time axis in a meaningful way. Essentially, any path/line/curve that doesn't violate the lightcone is (potentially) somebody's timeline.

Let's call the r-axis (in the Schwarzschild geometry) the distance from the center (of the coordinate system/BH). There is a characteristic radius, outside of which, there are three spatial degrees of freedom and one temporal dimension, the coordinate of which is always increasing for physical processes. This is the "flow of time" if you will. This is the feature of time that I think will make things most clear. You must increase your time coordinate value. You must pass from one hyperplane of 3-space onto another with a greater value of t. You cannot pass to a hyperplane with a lesser value of t. This is a timelike quality of t, or of the temporal axis/direction. (Of course, you can design a clock that moves its hands counterclockwise, but that is not the point. The real point is not that time always increases, but that it changes monotonically. You can say that the parameter you have chosen is actually decreasing throughout a physical process; that is arbitrary. The convention is to denote the variation as an increase; whether the parameter be increasing or decreasing, the parameter is consistently doing so throughout the entire physical process. This is what makes it a time-like parameter, the fact that the variation cannot take place in the other sense.)

What does this have to do with the r-axis being timelike? Simply this: inside a BH, the r coordinate of a particle cannot increase. It is doomed to decrease monotonically. Thus, any physical process (I use the term freely) inside a BH can be parametrized according to its distance from the center, or r coordinate. Thus, this parameter, the r coordinate, can be
isomorphically transformed into time, and is therefore timelike.

If it's philosophy that you're after, then here's a thought (not an answer, but a thought): Physical processes must have a monotonic variation in their timelike parameter. Is consciousness so intimitely connected to physical process that it too must follow such a parameter, or is it possible to survive a conscious eternity within a BH? I suppose this could give some indirect insight into the nature of consciousness.

a) between black holes that are rotating (Kerr-Newman), and black holes which have an "angular momentum." (Reisner-Nordstrom).

I don't understand the difference. I will have to do some research. I am only moderately familiar with the Kerr metric, and I have been under the impression that the only two types of metric are the Schwarzschild and the Kerr. You see, you have stimulated an investigation. This is an example of why I want you to come here and ask your questions.

b) between BHs that are "charged" and BHs which have zero charge; (as in Kerr-Newman vs the Swarzchild BH).

Again, I will had to do some research. I know absolutely nothing about the influence of charge on the metric.

 

[Guy From Alberta]

Quote by Turin

You don't have access to the future (classically speaking). You only gain information in the future by "going there;" processes do not flow from the future to the past, and neither do you. In fact, the future doesn't even really exist. You move along and constantly "lay down" your worldline as you go, like building a road right in front of you (or maybe like leaving footprints). The only stipulation is that you do not violate the light cone. This is not a philosophical issue, this is more of a definition. There is a fundamental principle in (classical) physics called "causality." When we speak of a path that is time-like, we mean that the points at larger values of the parameter along this path are a direct result of the points at the lesser values of the parameter, thus the parametrization. Another consequence is that we may orient this axis with the time axis in a meaningful way. Essentially, any path/line/curve that doesn't violate the lightcone is (potentially) somebody's timeline.

Thankyou for this interesting reply.

I just need to ask re the causality principle for now; and will get back to some of the other items when time permits.

Are you mentioning "causality" here in the context of "time axis;" and if so, how would we reconcile the phenomena or occurrence of "causality problems," (or exceptions)? I know that S. Hawking's "chronology protection conjecture," states that the laws of physics do not allow time machines, for eg., and that "time travel," is only possible "microscopically," whatever that might mean. But in a "causality problem" a real paradox can occurr when some given particle moves faster than the speed of light...the "causality problem" happening from the fact that when 2 events, A and B, happen faster than the speed of light; (for a stationary frame of reference), then, accordingly, event B can happen before event A?

A fellow named K. Thorne, has proposed that something called "wormholes" could be used as "time machines," but I don't understand how a human being could access a "wormhole," since, admittedly they are hypothetical. According to special relativity, from what I understand, traveling faster than light is equivalent to traveling backwards in time? I guess all this is suggesting to me that perhaps, there may be a way we do have access to the future; as we consider "causality loops," where events of the future cause events of the past...it is getting really interesting as I study this; but I do not feel as though I yet understand it all in it's correct context...O well; with more study; I am bound to figure this out better.

Till next time.