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StevenG
2002-Aug-19, 11:41 PM
What is the speed of gravity? Is it constant or would it vary?

Would it be dependant on the mass of the object's exerting the force divided by the square of the radius as in
Gmm/(r~2)?

If the speed of light is the highest possible speed how can gravity catch up with it and pull it back into a black hole?

Thanks.

Paul Unwin
2002-Aug-20, 12:17 AM
On 2002-08-19 19:41, StevenG wrote:
If the speed of light is the highest possible speed how can gravity catch up with it and pull it back into a black hole?


For that matter, how can a mirror, which doesn't have any speed at all, get in front of a beam of light in order to reflect it?

Gsquare
2002-Aug-20, 12:32 AM
On 2002-08-19 19:41, StevenG wrote:
What is the speed of gravity?

Steven, this is a common question and is probably the most common question on physics forums.... I'm sure you'll get some replies...
It ought to get interesting. /phpBB/images/smiles/icon_wink.gif



Is it constant or would it vary?


Another good one for starting arguments./phpBB/images/smiles/icon_biggrin.gif



If the speed of light is the highest possible speed how can gravity catch up with it and pull it back into a black hole?


I like this one. Actually, according to Gen. Relativity, gravitational potential alters (slows down) the speed of light.

G^2


<font size=-1>[ This Message was edited by: Gsquare on 2002-08-19 20:33 ]</font>

Raz
2002-Aug-20, 12:47 AM
If I understand it correctly, gravity doesn't 'emanate' from a source in the way that, say, light and sound do. Instead it exists as overlapping fields of varying strengths. It can 'pull back light' because it is already present at the points in space through which the light is travelling.

Apologies in advance if I've muddied the waters /phpBB/images/smiles/icon_smile.gif

traztx
2002-Aug-20, 03:35 AM
On 2002-08-19 19:41, StevenG wrote:
If the speed of light is the highest possible speed how can gravity catch up with it and pull it back into a black hole?


I don't know, but here's an idea:

Imagine space is your waterbed and you have a bowling ball on it. While the bowling ball is at rest, it presses down on the mattress. The area around it is depressed because of the tension in the mattress.

Now imagine rolling the bowling ball a little. The place behind the ball comes up a little, and this change propagates outwards. The place ahead comes down a little and this change also propagates outward.

So even if light were moving faster than gravity, it would be moving through fields already in place. If it moves at the same speed, then it would be in the field as it was changing slightly. The field still exists.

JS Princeton
2002-Aug-20, 04:14 AM
The warping of space in GR does not "slow down" light at all. In a vacuum, light travels at the speed of light regardless of what the shape of that vacuum is.

xriso
2002-Aug-20, 07:28 AM
Okay, I've heard that gravity propogates at the speed of light (correct me if I'm wrong). Again, on the topic of black holes. If gravity is caused by little graviton particles, wouldn't the gravity be curved in upon the black hole by gravity? This would seem to remove the gravitational effects of the black hole, but I'm not sure how the particle interactions work.

Chip
2002-Aug-20, 07:33 AM
I'll have a go just for fun! Short and succinct - but not necessarily as clear. These are just thoughts after the questions rather than an essay - so anyone is free to refine, enhance, correct, or clarify.

What is the speed of gravity?
The speed could be measured from the standpoint of matter relative to pre-existing gravitational fields of curved space itself. And the speed could also be measured from the frame of light entering the fields, which would then be at "c" when light is involved. (In other words, relative to what enters the gravitational field, (light or matter,) rather than the field itself.)
As for matter in orbit or traveling past a massive star or planet, acceleration of matter through space due to gravity is dependent on it's location in space and time, and independent of the nature of the matter. Gravity accelerates all objects equally.

Light remains at "c" within it's own frame of reference in a vacuum. (Example: Light from a distant star near the sun in a solar eclipse being bent from an Earth observer's point of view, so that the distant star is in a different position than it is later in the year in the night sky.)

Is it constant or would it vary?
The measurable fact of it's action at a distance could perhaps be thought of as gravity's "constant" (unless negative mass were discovered.) Gravity is weaker the further an object is from the gravitational field. (That could be a measurable "constant" at various distances. I might be wrong.)

If the speed of light is the highest possible speed how can gravity catch up
with it and pull it back into a black hole?
If the light moves within the gravitational field, the gravity doesn't
"catch up" with the light because the field is already "there." For matter, the gravity of a massive object is equivalent to an accelerating frame of reference without
the massive object.
Light traveling at "c" in a vacuum, remains at "c" in the presence of gravity, but matter traveling into the field is accelerated. A massive object creates the effect of gravity by bending the nearby space around itself. Light travels (from "light's frame of reference") in a straight line, but the space near a massive star is curved, and the space in a black hole is infinitely curved. To an outsider, the light's path is curved. To the "light," it is straight, and the journey is instantaneous.

In the case of matter, traveling below the speed of light, the direction of a "worldline" when accelerated by gravity has a longer timespan. The expanding cosmos is Euclidean in nature yet matter within it defines gravity within spacetime in a non-Euclidean geometry. The curvature of space in the vicinity of matter is created by the presence of matter.

None of this tells you exactly what gravity "is".

John Kierein
2002-Aug-20, 09:55 AM
I think gravity is a push from the electromagnetic background radiation. Thus if you try to quantize the "pull" of gravity to identify the graviton, you are quantizing the shadow cast by the mass in this field. Like light this shadow also moves at c.
Tom VanFlandern has a different view. He thinks that if gravity travels at c the earth would be orbiting the place where the sun was 8 minutes ago as the sun travels around the galaxy, not where the sun is now. He thinks that is not the case but rather that the earth travels around the place where the sun is now, not where we see it to be as it was when its light left 8 minutes ago. Consequently, he disagrees with me and thinks that gravity travels much faster than c. I discuss this briefly in my paper in the book "Pushing Gravity".

2002-Aug-20, 10:28 AM
<a name="20020820.2:13 A.M."> page 20020820.2:13 aka the "RATE" of travle of select Gravity Wave Pods
1: now and then there are large eruptions on the surface of the Sun
2: lets call some [X] and `poise for now they lie in the 10^30 erg range
3: you can do the math and calculate the mass loss
4: {ok so you can't forget Math untill 2020}
5: What May? take place then might be
6: Gravity wave pods travel from X to Earth
7: & when it gets here it Causes a 7.4 Quake
8: in you neighbors yard {when shes out BBq`N}
9: it takes 50 hours [when you can do the math] for those to take place ..? HUb' 2:21 A.M. PST

nebularain
2002-Aug-20, 11:20 AM
What little I know about gravity:

In the equations we used in my physics class, gravity was given the same place as acceleration (i.e. where applicable, the equation F=ma was changed to F=mg, where F is force, m is mass, a is acceleration, and g is gravity). Acceleration is defined as the change in velocity.

As per black hole, I have not heard it being explained as the speed of gravity being greater than the speed of light. What I have heard is that the escape velocity (the initial velocity an object needs to escape from a celestial body) is greater than the speed (velocity) of light.
I don't understand the mechanics, but for reference, the gravity on Earth is 9.8 m/s. The escape velocity from the Earth's surface, however, is 11km/s.

I also know that anything with mass has gravity. I wonder if this is why when you are walking next to someone, the two of you tend to keep walking into each other!

Celestial Mechanic
2002-Aug-20, 01:08 PM
On 2002-08-20 05:55, John Kierein wrote:
[snip!]
Tom VanFlandern has a different view. He thinks that if gravity travels at c the earth would be orbiting the place where the sun was 8 minutes ago as the sun travels around the galaxy, not where the sun is now. He thinks that is not the case but rather that the earth travels around the place where the sun is now, not where we see it to be as it was when its light left 8 minutes ago. Consequently, he disagrees with me and thinks that gravity travels much faster than c. I discuss this briefly in my paper in the book "Pushing Gravity".

This argument for a superluminal speed for gravity goes back at least to Laplace. Actually, if you treat the Lagrangian properly in the first Post-Newtonian approximation, you get a Lagrangian called the Einstein-Infeld-Hoffman Lagrangian in which all of the retarded fields are replaced with the coordinates and velocities of the present time in a suitable frame. Although you started out with a field theory you end up with an effective Lagrangian that has action at a distance to this order, and of course if you omit the relativistic corrections you get back the standard Lagrangian for Newtonian gravity.

The derivation is used as a series of exercises in Chapter 39 of Gravitation by Misner, Thorne, and Wheeler, and Carmeli in his book (sorry, I can't remember the exact title right now) has a very lengthy derivation that includes electromagnetic fields as well. ***WARNING***: these derivations are fairly complicated and not for the faint of heart!

HankSolo
2002-Aug-20, 09:56 PM
HUb': You certainly seem to know your stuff, but I'll be darned if I can ever figure out what you're saying! /phpBB/images/smiles/icon_smile.gif

I've posed this question a couple of times before in other threads, and I'm still not satisfied with any answer. I'm no scientist, but there seems to be a lot of hocus-pocus that goes on when we try to explain gravity, space, and the light speed barrier. Things that would make my ideas seem mainstream. Maybe it's a stupid question, but in plain english, how does mass increase with speed? I also never bought the "bending of space" theory. The 2D example of a bowling ball on a waterbed only works because there is gravity below the waterbed. I understand the point, but it assumes that space is a physical object or material that can be bent or warped. That's too "new age" for me (and this coming from the resident Nibiru-believer!). To me, space is just that... space. There's nothing to bend or warp. There's a pulling force generated by every object (don't know what it could be) but I don't believe it's due to the displacement or curvature of space. We don't say that magnetism warps the fabric of space, yet it has a similar attractive (and repulsive) force. The mathematics and physics may end up working the same, but I believe things tend to have the simplest explanation, and we're just not there yet.

In my totally non-scientific opinion, light is nothing more than photon particles travelling at a very high speed. When they collide with an object, the impact releases energy which our eyes can sense and our brains can make patterns out of. Different types of light are generated by different speeds and/or types of photons releasing different types of energy. Since they are particles, they can be affected by gravity, and they can be slowed down or sped up (as in the black-hole example). The path of light bends slightly around a massive object for the same reason an asteroid's path would be affected by a massive object: the tug of gravity. Furthermore, things can travel faster than light if there is a propulsion system that will overcome some fuel barriers. Gravity could be a potential propulsion agent if we could keep it focused in front of us.

If there is a speed limit to gravity, wouldn't falling objects travelling at different speeds in a vacuum have different rates of acceleration? The faster objects would accelerate at a lower rate, and that acceleration rate would keep getting lower until the speed of gravity was reached. I would think someone has tested this, although we would need some super-sensitive equipment. Any info on such an experiment? If the acceleration rate of gravity remains constant regardless of speed, that would seem to indicate that gravity can produce an infinite speed.

I realize I'm no expert but I do have a lot of interest in the possibilities. I just need them in plain English (or Spanish)!

Wiley
2002-Aug-20, 10:36 PM
I have time to answer some these questions:


On 2002-08-20 17:56, HankSolo wrote:
Maybe it's a stupid question, but in plain english, how does mass increase with speed?


It depends on what you mean by mass. There is "relativistic mass" and there is "rest mass". Rest mass is, I think, what you're interested in, and it does not increase with speed. The rest mass, or the amount of substance, is speed invariant. Relativistic mass is really a measure of inertia, or in normalized units (c = 1) energy. Quoting from Ned Wright's cosmology FAQ:


In one sense, any definition is just a matter of convention. In practice, though, physicists now use this definition because it is much more convenient. The "relativistic mass" of an object is really just the same as its energy, and there isn't any reason to have another word for energy: "energy" is a perfectly good word. The mass of an object, though, is a fundamental and invariant property, and one for which we do need a word.

The amount of substance does not depend on speed, but it's energy does.



I also never bought the "bending of space" theory. The 2D example of a bowling ball on a waterbed only works because there is gravity below the waterbed. I understand the point, but it assumes that space is a physical object or material that can be bent or warped.

It's not just General Relativity that has curved space; all modern theories, e.g. Brans-Dicke, of gravity assume space is curved. Why? They are based on three postulates:

Inertial mass and gravitional mass are equivalent: the trajectory of a freely falling body is independent of its internal structure and composition,
The outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling reference frame in which it is performed,
The outcome of any local non-gravitational experiment is independent of where and when in the universe it is performed.

If you disagree with those postulates, you are free to develop your own theory of gravity which does not curve space. If however you agree with them, there is nothing you can do, space is curved.



I believe things tend to have the simplest explanation, and we're just not there yet


I agree. But look at the three postulates, they are very simple and reasonable. Scientists and mathematicians have take these simple postulates and have taken them to their logical conclusions. The mathematics required to reach the conclusions are nightmarish, but the underlying physical postulates are quite simple.

Hope this helps,

Raz
2002-Aug-20, 10:45 PM
On 2002-08-20 17:56, HankSolo wrote:
Maybe it's a stupid question, but in plain english, how does mass increase with speed?


Basically, it doesn't /phpBB/images/smiles/icon_smile.gif This came up recently elsewhere and Doctor Don covered it nicely. Have a look at his first post on this page (http://www.badastronomy.com/phpBB/viewtopic.php?topic=1852&forum=2&start=25).



I also never bought the "bending of space" theory. [...] That's too "new age" for me [...] There's a pulling force generated by every object (don't know what it could be) but I don't believe it's due to the displacement or curvature of space.


But with respect, you can't ignore it just cos it's too hard to understand. That's like saying, "hmmm, I'm not sure how I see pictures in my TV - people say there's a gun in there firing electrons at tricolor phosphor, but that can't be true; all I see is a flat piece of glass". /phpBB/images/smiles/icon_smile.gif I don't really get curved space myself, but I'm trying to!

Raz

Wiley
2002-Aug-20, 10:55 PM
On 2002-08-20 17:56, HankSolo wrote:
In my totally non-scientific opinion, light is nothing more than photon particles travelling at a very high speed. When they collide with an object, the impact releases energy which our eyes can sense and our brains can make patterns out of. Different types of light are generated by different speeds and/or types of photons releasing different types of energy. Since they are particles, they can be affected by gravity, and they can be slowed down or sped up (as in the black-hole example). The path of light bends slightly around a massive object for the same reason an asteroid's path would be affected by a massive object: the tug of gravity.


I got more time. /phpBB/images/smiles/icon_smile.gif

What you're describing is very similar to the Newton's light as a particle idea. Newtonian gravity predicts an angle of deflection of 2*m/R. However GR predicts an angle of deflection of 4*m/R. In 1919 scientists measured the deflection of star light by the sun, the reported results were 1.98 0.16 and 1.61 0.40 seconds and GR predicted 1.75 seconds of angular deflection. For more information see the Math Pages: Bending of Light (http://www.mathpages.com/rr/s6-03/6-03.htm).

HankSolo
2002-Aug-21, 04:54 PM
Raz: Thanks for the link to Doctor Don's explanation. I understand the principle. However one thing still doesn't sit right with me. He says:


As you get closer to the speed of light, the same amount of force produces less acceleration.

That is assuming the force pushing the object is equal to the speed of light. I understand that it will never have enough force to budge the mass to the exact speed of light. It will always be just below the speed of light.

But.... why does the force have to have the speed limit of light? That sounds like a self-imposed limitation. Why would we think that forces are equal to, or slower than, light?

I agree with your TV comparison. But I can "get" things like that. To me, curved space reeks of a theory created to fill a void in our knowledge. I guess that would be the definition of any theory! But it still gives me the impression of a "filler" theory until we can get a better one. The mathematics and physics may work, but the assumption that space can be warped, bent, or curved, seems to defy common-sense. It gives me a feeling that someone will be looking back 100 years from now, laughing "Can you believe they thought that?!?" That's one of the few things that gives me that feeling (besides light-speed limitations and people who think rap is music). I realize it's subjective, and I may "see the light" one day. Until then, I'm coming up with my own...

Wiley: I think I understand the three postulates. Sounds like legal mumbo-jumbo almost... Like something you hear at the end of a car-dealer commercial /phpBB/images/smiles/icon_smile.gif

But it sounds good. I just don't see the connection with the curvature of space. Please... no nightmare mathematics... I believe it...

Wiley II: If Einstein's revised equation is a better gauge of reality, I can accept that. But (as above) I don't see how that shows that space is curved. It's just showing the amount of deflection based on mass, but not showing the underlying cause of the deflection.

Does anyone have a good link for a site detailing the cause of the attractive effect of gravity?

Here's another thing that causes me to lose sleep at night:

Imagine a planet (or a large object) with a large hollow core. I can use a thick handball floating through space as an example too, but it's easier to picture using a planet. Let's say you drilled down and reached that hollow core. Which way would gravity be pulling you inside that core? Towards the empty center? Back to the solid mantle? Or would an object dropped into this hollow core simply float because of the counteractive forces from all sides?

DoctorDon
2002-Aug-21, 05:31 PM
On 2002-08-21 12:54, HankSolo wrote:
He says:


As you get closer to the speed of light, the same amount of force produces less acceleration.

That is assuming the force pushing the object is equal to the speed of light.


No, force is not the same thing as speed. The force (as defined in the problem) is acting on a fast-moving object, but is itself completely independent of the speed that object is moving. You can increase the force as much as you want (as much as you have energy available to do so), and you will never increase the object's velocity to the speed of light, because its acceleration will continue to drop, the faster it goes.



But it still gives me the impression of a "filler" theory until we can get a better one. The mathematics and physics may work, but the assumption that space can be warped, bent, or curved, seems to defy common-sense.


So does quantum tunneling. So does the interference of quantum states. One of the most important points of 20th century physics (in my opinion) is that when you pass into a regime outside your common experience (moving too fast, shrinking too small, etc.), then "common sense" is simply an unreliable guide and must be discarded. It's like insisting that a particular animal be called a "cat", and not a "gato" or "Katze" or something else. Your experience as an English-speaker leads you to associate certain sounds with certain concepts, but if step outside the realm of that experience, other rules apply, and you have to learn what they are. If the mathematics lead you to a counter-intuitive result, *and* experiment verifies that this result is realized, then you have to let go of your preconceptions and tackle the implications of the theory.



But (as above) I don't see how that shows that space is curved. It's just showing the amount of deflection based on mass, but not showing the underlying cause of the deflection.


Einstein's Field Equations link the curvature of space to the amount of mass/energy within it. In English, they can be expressed as: "stuff tells space how to curve, and the curvature of space tells the stuff in it how to move". That is, in essence, the theory of general relativity. The more mass is there, the stronger the curvature, and the greater deflection of a passing photon. This *is* the underlying cause of the deflection, since a massless particle like a photon will always take the shortest possible path, which in a curved space is itself curved (like airplanes that follow great circles over the earth's surface, because they want to take the shortest path and conserve fuel). Curved space solves two problems: a massless particle like a photon shouldn't feel a gravitational force a la Newton (since F=GmM/r<sup>2</sup>, if m=0, then F=0), and secondly, curved space allows the information as to where masses are to propagate without violating light speed.

If one bases a theory in the mathematics of curved space (as Einstein did), and experiment verifies its predictions (as is so far the case with GR), then you have to consider that space might indeed be curved. You could play semantic games and say "it's not really curved, it just has all the properties of being curved", to which one can only say that since there is no effective difference between those two options that can be measured in any experiment, one might as well just say that space is curved.



Imagine a planet (or a large object) with a large hollow core. Or would an object dropped into this hollow core simply float because of the counteractive forces from all sides?


Yup. (Not counting its initial momentum from being dropped, which would cause it to float across the hollow core, unless the shell were rotating, in which case, centrifugal and coriolis forces would cause it to float back and stick to the inner wall.)

Hope that helps,

Don

MartinM
2002-Aug-21, 06:39 PM
On 2002-08-21 12:54, HankSolo wrote:
But.... why does the force have to have the speed limit of light? That sounds like a self-imposed limitation. Why would we think that forces are equal to, or slower than, light?



Not sure what you're asking here. Are you asking why an event here cannot exert a force way over there faster than c? If so, the resolution is simply that forces are mediated by particles which themselves cannot travel faster than c.



To me, curved space reeks of a theory created to fill a void in our knowledge. I guess that would be the definition of any theory! But it still gives me the impression of a "filler" theory until we can get a better one.



That could also describe any theory.



The mathematics and physics may work, but the assumption that space can be warped, bent, or curved, seems to defy common-sense.



Common sense has no place in Science. And the classical notion of space and time as immutable has held Science back for far too long. Why should spacetime not be curved?



Wiley: I think I understand the three postulates. Sounds like legal mumbo-jumbo almost... Like something you hear at the end of a car-dealer commercial /phpBB/images/smiles/icon_smile.gif

But it sounds good. I just don't see the connection with the curvature of space. Please... no nightmare mathematics... I believe it...



OK - in special relativity, spacetime is flat. Flat, but not Galilean - velocities do not add trivially, for example.

Nevertheless, the fact that it is flat allows us, in principle, to extend a single co-ordinate system to infinity in all directions. An observer in an SR Universe can look out in all directions to any distance and know that spacetime looks just the same from over there. All of which means, if you're sailing along at a constant velocity, a single co-ordinate system will do the job nicely. And you can keep that co-ordinate system for ever - it will never fail you.

Now, what if you accelerate to a new velocity? Well, once your acceleration ends, you are travelling at constant velocity again, and the previous situation reoccurs. Your co-ordinate system can be extended to infinity in all directions. But - if you do this, it will inevitably overlap with your old co-ordinate system. And the two cannot be reconciled. The only resolution to this conflict is to accept that our seemingly perfect reference frame in reality can only describe spacetime locally.

Now, take a look at the second postulate that Wiley quotes - "The outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling reference frame in which it is performed"

This means that in freefall, the equations which describe reality are identical to those we see when stationary in zero-g. Our acceleration does not affect this. Locally, SR laws hold. But only locally. If we extend our co-ordinate system out too far, it will again break down.

To conclude, then -

1)Spacetime is locally flat everywhere.
2)These locally flat patches cannot be extended outwards and trivially 'stiched together', since they are mutually inconsistent.
3)Thus, the only way we can take all of these locally flat patches and put them together into a single Universe (as must be possible) is to accept that spacetime is curved.




Imagine a planet (or a large object) with a large hollow core...would an object dropped into this hollow core simply float because of the counteractive forces from all sides?



Yes - a consequence of Gauss' Law. There are no sources nor sinks for gravity inside the hollow planet (yourself excluded!), thus no net gravitational flux through any arbitrarily small surface within the hollow core. Thus, no gravitational force at any point.

Wiley
2002-Aug-21, 10:49 PM
On 2002-08-21 12:54, HankSolo wrote:
To me, curved space reeks of a theory created to fill a void in our knowledge. I guess that would be the definition of any theory! But it still gives me the impression of a "filler" theory until we can get a better one.

All theories are "filler" theories. All theories have a range of validity, and one of the most important aspects of science is determining this range of validity. For instance, electromagnetic theory and Newtonian mechanics do not jive; one has to bend. Einstein came along with SR which said Newtonian mechanics is not valid as velocity approaches the speed of light. Newtonian mechanics is not wrong, but we now know its range of validity. Similarly SR is a "filler theory" since it does not account for acceleration. Einstein knew this and immediately after publishing SR began work on GR. Einstein also knew that GR is an incomplete theory and started work on a unified field theory soon after GR was completed. One could also show how electromagnetics is "filler theory" which leads to (non-relativistic) quantum mechanics which is a "filler theory" leading to quantum field theory ...

Wiley
2002-Aug-21, 11:22 PM
HankSolo wrote:
The mathematics and physics may work, but the assumption that space can be warped, bent, or curved, seems to defy common-sense.



DoctorDon wrote:
You could play semantic games and say "it's not really curved, it just has all the properties of being curved", to which one can only say that since there is no effective difference between those two options that can be measured in any experiment, one might as well just say that space is curved.


I think it may be helpful to take a step back and define what is meant by "space is curved". If you remember from your middle school geometry class, the distance between two points (x1,y1) and (x2,y2) is ( (x2 - x1)^2 + (y2 - y1)^2 )^1/2. When we say space is curved, all we mean is that the formula we learned in 8th grade is not true. In GR speak, we're interested in the metric, the metric is how we measure the distance between two points. It turns out that the mathematics for GR, differential geometry, is the same as for curved surfaces. So to paraphrase Doc Don: Space has all the properties of a curve; hence if it walks like a duck and it quacks like a duck, we just may be dealing with a small aquatic water fowl.

DoctorDon
2002-Aug-22, 05:43 PM
This is where I think "common sense" messes us up. If one thinks "of course space is flat!", well, you have to ask yourself why you think space is flat. My guess is it would be a combination of (a) our sense that we can look in straight lines in all directions if nothing is blocking the view, (b) the way we usually associate curvature with some thing, and empty space is nothing, so it's hard to imagine nothing being curved, (c) maybe we remember seeing x-y-z cartesian axes at some point, and those are straight lines, and (d) we all either inherit or intuit an aristotalean image of what "empty space" is, and it's a euclidean (flat) geometry.

The key is that all these images/concepts are rooted in our experience, and modern physics has shown that when you get into regimes outside our regular experience, common sense doesn't help us, in fact, it actually hinders us. How we think of things behaving is based on observations of conglomerations of 10<sup>23</sup> atoms or more; when you're dealing with just one atom, you will find it behaves quite differently than common sense would indicate.

Here's an example that's not quite as esoteric: we're talking about whether space can be curved. Part of the problem is that we generally (unless you've had a fair amount of math) don't properly generalize those words: space, curved, straight, etc. So what is "space"? I'm sure mathematicians can give you a better definition, but I think it will be sufficient to say that space is an abstract collection of points with some arbitrarily small distance between them. We say the space is n-dimensional if we need n numbers to characterize those distances. Whether space is flat or curved depends on how you can characterize that distance. In a flat space, the Pythagorean theorem (extended to n dimensions) will adequately describe the distance. If you want to define a finite extension within that space, you need to add up (i.e. integrate) the tiny distances between all the points in the space along the extension. The surface of the earth (if you ignore mountains and valleys) can be approximated as a two-dimensional curved space. What does that mean? Well, in technical terms, it means that the metric is no longer ds<sup>2</sup> = x<sup>2</sup>+y<sup>2</sup>. That is, all the rules of euclidian geometry no longer apply: the interior angles of a triangle do not sum to 180, parallel straight lines do cross, etc.

Let's take that last one: how can parallel straight lines cross? Well, what exactly is the definition of "straight"? We can all recognize a straight line when we see it (in a flat space), but what property defines it uniquely as "straight"? The definition of straight is this: pick a point on the line and take a tiny step in the direction of the line at that point. If you are still on the line, and you can do this at any point on the line, then it's straight. Parallel straight lines are thus two lines that fit this criterion, and the "tiny step" is in the same direction for both lines.

Note that in a flat space, straight parallel lines are the same distance apart everywhere, but this is not true for curved space. Back to the curved surface of the earth, we apply our definition of "straight", and we get a curved line! Specifically, we get a great circle. Any other type of line on the surface of the earth will not fit this definition. Longitude lines are straight, latitude lines are not. Parallel lines do cross each other on the surface of the earth (you might think latitude lines are parallel, but that is not so).

My point in all this long-windedness is that we are taught to think in terms of euclidean (flat) geometry, but there is absolutely no reason to think that the universe has to conform to our conceptions about it. Indeed, as I have illustrated with the surface of the Earth example, there are simple cases well within our experience where it does not conform. When moving out into realms where our common sense simply does not apply, we need to be careful that we have properly generalized our conceptions (like the straight line), and then we need to take those tiny steps forward, and test to see if we are still on the line. If we pass those tests, then we need to open our experience up to new realms and widen our definition of common sense. Once you train yourself with math and experiment, the weirdest behavior of a quantum particle will also make sense to you, and then (and only then) can you start to trust your intuition about what "seems" right. Until then you are just trying to draw straight lines on the curved surface of the earth.

Yours,

Don

<font size=-1>[ This Message was edited by: DoctorDon on 2002-08-22 13:49 ]</font>

nebularain
2002-Aug-22, 06:35 PM
OK, space is curved.
/phpBB/images/smiles/icon_rolleyes.gif Maybe that's why everything in life tends to follow a bell curve.

(Don't mind me; I don't know what I'm talking about.)

Wiley
2002-Aug-22, 07:01 PM
DoctorDon wrote:
So what is "space"? I'm sure mathematicians can give you a better definition ...


I would not bet on that. I've asked mathematicians this question, and the best answer I've heard is "space is where you solve your problem." There may be a precise mathematical definition, but it seems to be one of those terms that no one has ever bothered to define because everyone just knows it (sic).

This brings me to a question. When astronomers speak of a space, do they mean the stuff (or lack thereof) that keeps things seperated, or do they mean the mathematical definition? Or, perhaps, a specialized mathematical space like a n-dimensional vector space? From your post I inferred the mathematical definition. I've always kept the mathematical space abstract and only apply it after determining the PDE. It sounds like you're doing the opposite. But perhaps not. Are you starting with the Einstein field equations, and then applying the appropriate space to them?

-Wiley

"What the hell do you mean, I should be using a negative one-half order Sobolev space!" -Me to a UD math professor.

<font size=-1>[ This Message was edited by: Wiley on 2002-08-22 15:04 ]</font>

DoctorDon
2002-Aug-23, 06:13 PM
On 2002-08-22 15:01, Wiley wrote:
This brings me to a question. When astronomers speak of a space, do they mean the stuff (or lack thereof) that keeps things seperated, or do they mean the mathematical definition?


I know this sounds like a cop-out, but I think it would be whatever works for the situation you're dealing with. I was thinking about how to explain curved space in terms of how you (i.e. a photon) would move through it from point A to point B, so I thought of it in terms of a path integral over the metric where you take the limit as ds goes to zero. There are certainly situations where I would think of it in terms of an n-D mathematical space. And then, of course, there's "phase space". I confess to being something of a pragmatist on this one. /phpBB/images/smiles/icon_wink.gif

Yours,

Don

2002-Aug-25, 07:37 AM
<a name="JD2452511.HS"> page JD2452511.HS aka H.M.S.
On 2002-08-20 17:56, HankSolo wrote:
HUb': You c /// been there // DONE THIS

curvature of space.
HUb' 11:21 P.M. IF, U stand close enough (I stood 2 close)
to the release of 100,000 Kt {really I should attempt the E=mc crap here and give you Grams}
lets see[E_kt = .1e9] So E_Er would = {maybe later} and M {maybe around X}(If c were to = 300,000 K/s) {um .3e9} roughly 1/3Gram ?
If there is a speed
yeah yeah it takes a while / try this / think of an auto race
and each car possessing a moving Gravity Wave POD [ just POD for short ] around and about it.
those PODs around & about CAR travel across a "SPECTRUM" OF "sPEEDS" best i can do 4U [sorry]

2002-Aug-25, 07:57 AM
On 2002-08-25 03:37, HUb' wrote: to? HUb' 11:41 P.M.
1: in the prior post [um to H.M.S.]
2: i ommited the step of converting
3: from E_Kt To E_Er
4: and thats severl Megs _Just a second?
5:10 e 6 Joule
6:3.6 e 12 kWhr
7:4.2 e 18 kTonn
8:from _Kt down to _Jd same as _Er
9:looks like 18-6=12 for the after e part
and from 4.2 down to 10
would be about aTWo so maybe its
1/3 Gram * 2e12 {which makes no cents at all}
my second guess 2/3 [11:49 P.M.] mah be no closer than my first 1

Wiley
2002-Aug-27, 08:43 PM
On 2002-08-23 14:13, DoctorDon wrote:
I know this sounds like a cop-out, but I think it would be whatever works for the situation you're dealing with. I was thinking about how to explain curved space in terms of how you (i.e. a photon) would move through it from point A to point B, so I thought of it in terms of a path integral over the metric where you take the limit as ds goes to zero. There are certainly situations where I would think of it in terms of an n-D mathematical space. And then, of course, there's "phase space". I confess to being something of a pragmatist on this one. /phpBB/images/smiles/icon_wink.gif

Yours,

Don


Thanks, Don. It's not a (total /phpBB/images/smiles/icon_smile.gif) cop-out since it does actually answer my question. So "space" is where ever you're solving your problem.