3 dimensions of space and 1 of time

[Frame Dragger]

Well... that didn't end in the best possible way... which I have to say, I think Gatchaman summed up nicely.

EDIT: @ Hoku... Ok... this is my last attempt: The parable of the apple from MTW.

Once upon a time a student lay in a garden under an apple tree
reflecting on the difference between Einstein's and Newton's views
about gravity. He was startled by the fall of an apple nearby. As he
looked at the apple, he noticed ants beginning to run along its
surface. His curiosity aroused, he thought to investigate the
principles of navigation followed by an ant. With his magnifying
glass, he noticed one track carefully, and, taking his knife, made a
cut in the apple skin one mm above the track and another cut one mm
below it. He peeled off the resulting little highway of skin and laid
it out on the face of his book. The track ran as straight as a laser
beam along this highway. No more economical path could the ant have
found to cover the ten cm from start to end of that strip of skin. Any
zigs and zags or even any smooth bend in the path on its way along the
apple peel from starting point to end point would have increased its
length.

"What a beautiful geodesic," the student commented.

His eye fell on two ants starting off from a common point P in
slightly different directions. Their routes happened to carry them
through the region of the dimple at the top of the apple, one on each
side of it. Each ant conscientiously pursured his geodesic. Each went
as straight on his strip of appleskin as he possibly could. Yet
because of the curvature of the dimple itself, the two tracks not only
crossed but emerged in very different directions.

"What happier illustration of Einstein's geometric theory of gravity
could one possibly ask?"

murmured the student.

"The ants move as if they were attracted by the apple stem. One might
have believed in a Newtonian force at a distance along his track. This
is surely Einstein's concept that all physics takes place by 'local
action'. What a difference from Newton's 'action at a distance' view
of physics! Now I understand better what this book means"

Light follows a geodesic INTO the black hole, which is allowed! It is not "dragged" in, but by each step is informed by the local topography/geometry. That is Relativity. If you're proposing something else, then it's a personal theory you should make clear, because that isn't Briane Greene's stance. I think everyone on this forum can surmise that he probably would know a geodesic and what that meant if it bit him on the heiney. :grimace:

 

[Dale]

1) Brian Greene says that normal spacetime moves at the speed of light.

This is wrong. You probably misunderstood what Brian Greene said. I suspect that he was probably saying something about the magnitude of the 4-velocity being equal to c. The 4-velocity is a property of a particle, not spacetime.

But I can see that there is no compassion for this logic

That is a strange comment. I have never thought that logic would need compassion. If it is sound it stands on its own.

 

[Frame Dragger]

Hell, logic by definition is DISpassionate. Hell, you'd expect people on PF to be VERY familiar with Spock!... and yes, I am too.

 

[Hoku]

I wish I could cut and paste that portion of the video. It's one of the first things he talks about. I've watched it a few times and it doesn't confuse me at all. That doesn't mean I'm not wrong in my interpretation, but it seems straightforward enough that "interpretation" isn't necessary. I think it might help people have more "compassion" for my logic if they could see that portion of the video. Frame Dragger, yes, logic is, by nature, dispassionate. However, one can go through a dispassionate logical process and, for one reason or another, come to an incorrect conclusion. Another person can have "compassion" for that faulty logic when they can say, "...but I see where you were coming from". As it is, I'm not sure anyone is seeing where I'm coming from. I accept responsibility for that.

Frame Dragger, thanks for your ant/apple post. It does help me understand the concept of geodesics better. I had read wikipedia's entry on it and your additional input helped me get more out of it.

Without being able to show you the video, I can only think of one other way to try and resolve this. If it doesn't work, it doesn't work.

Picture in your mind a source of gravity. There is a null geodesic path to this point and one out of it, right? So, why then can light follow this null geodesic away from a point of gravity in normal spacetime but not in a black hole?

 

[Gatchaman]

If it doesn't work, it doesn't work.

It doesn't work.

 

[atyy]

Picture in your mind a source of gravity. There is a null geodesic path to this point and one out of it, right? So, why then can light follow this null geodesic away from a point of gravity in normal spacetime but not in a black hole?

http://physics.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html

Look at the light cones. The top half of a light cone points to the future. Outside the event horizon, the cones are standing upright, so there is a future that is away from the singularity, just as there is one into the singularity. Inside the event horizon, the cones are tilted, so that the only future goes into the singularity.

 

[Gatchaman]

Just look at the Kruskal diagram. Learn how to interpret it and it tells you everything you ever wanted to know about the spacetime near a BH.

 

[Frame Dragger]

Just look at the Kruskal diagram. Learn how to interpret it and it tells you everything you ever wanted to know about the spacetime near a BH.

Agreed, it's a terrific tool, but do you really think that someone who's already telling us honestly that this is something from Nova and such should be told, "hey buddy, just grasp the mathematics of Kruskal-Szekeres coordinate systems". That's about as useful as explaining QM to someone by telling them to look at a Feynman diagram; most people asking that question would be unable to bridge the gap you're presenting them with. Perhaps a staged plan to get from where we are now to Point "Kruskal Diagram"?

 

[Dale]

I wish I could cut and paste that portion of the video. It's one of the first things he talks about. I've watched it a few times and it doesn't confuse me at all. That doesn't mean I'm not wrong in my interpretation, but it seems straightforward enough that "interpretation" isn't necessary.

Are you thinking about the part where he mentions that gravitational waves move at the speed of light? If so, then you are really misunderstanding. Here is an analogy, the speed of sound vs wind speed. Just because a wave goes through the air at 760 mph does not mean that the air is moving at 760 mph. Similarly with the Einstein field equations. The fact that gravitational waves propagate through spacetime at c does not imply that spacetime moves at c.

 

[typical guy]

Just to move away from the current conversation for a second, I want to go back to quantum entanglement because I'm fascinated by it. On the first page of the thread, it's mentioned that entanglement cannot be used to send information faster than the speed of light.

Lets say, for the sake of argument that two scientists are each watching one half of a pair of entangled particles. It was previously agreed that if the entanglement is destroyed on and odd second that they would have pizza for lunch. If the entanglement is destroyed on an even second, they would have burgers for lunch. one of the scientists (who is very hungry) destroys the entanglement on an odd second because he wants pizza. We don't have to set up any kind of complicated morse code, we can simply have a previously agreed upon definition to define what a 1 or 0 means for a single entangled pair.

Maybe I'm completely off-base here because of my lack of edumication but I just feel like you could communicate something with these pairs of entangled particles faster than the speed of light by simply agreeing to what is meant by stopping the entanglement on a previously agreed upon moment.

We could even go one step further and say that the scientists have previously agreed upon the lunch scenario described above but instead of forcing it to stop on an odd second, the scientists simply allow the entanglement to be stopped naturally by environmental factors. These factors make the entanglement cease on either an odd or even second. When this occurs, both scientists learn if they will be having pizza or burgers at the exact same moment. Information was received by both at the same time even though no information was intentionally sent. It would be like the two people each rolling a die and those dice landing on the same numbers every single time they attempt a roll. Even though they have no control of the outcome of the roll, they have previously agreed upon the what happens as a result of the outcome and the information of pizza or burgers is transmitted instantly to each.

I hope that makes sense?

 

[Hoku]

atty: I am familiar with the light cone. I will research it again in "light" of this discussion. Thanks for you input and direction.

Frame Dragger: I like your idea of a "staged plan". I assure you that I'm taking everything here very seriously. I've done A LOT of work since I've been on the forums and I expect that to continue.

Dale: YES! That's exactly what I'm talking about. Thank you. Your analogy doesn't immediately clear up any confusion for me, but I will take some time to research the light cone and reflect on the analogy you've proposed.

I will undoubtedly be back to this thread. Whether any of you choose to resume discussion with me or not is fine. Actually, Gatchaman, I encourage you NOT to resume it.

 

[Frame Dragger]

atty: I am familiar with the light cone. I will research it again in "light" of this discussion. Thanks for you input and direction.

Frame Dragger: I like your idea of a "staged plan". I assure you that I'm taking everything here very seriously. I've done A LOT of work since I've been on the forums and I expect that to continue.

Dale: YES! That's exactly what I'm talking about. Thank you. Your analogy doesn't immediately clear up any confusion for me, but I will take some time to research the light cone and reflect on the analogy you've proposed.

I will undoubtedly be back to this thread. Whether any of you choose to resume discussion with me or not is fine. Actually, Gatchaman, I encourage you NOT to resume it.

I've noticed that you've progressed here in the short time I've been around the forums actually. It's impressive... you've managed to get past preconceptions that really hobble most people and I'd be proud of myself in your place. As for DaleSpam's analogy, think of waves in water: The energy moves in a wave, but the water doesn't move much. Molecules "bang into each other" and exchange energy/momentum... the water is the VEHICLE for the energy of the wave. Just as in the classic "executive toy" Netwon's Cradle, which of course is why the water of a tsunami that strikes land, is really not the water that we see and say is "racing towards the coast". The WAVE is, but the water is mostly stationary except at the Incident point to the point of expression (the wave, the ball the swings on the other end of the cradle).

So it is thought to be with gravitational waves. Spacetime doesn't race along with the wave, any more than the rock you toss into a pond rides its own waves to the shore. The energy makes the trip, not the matter, or in this case, spacetime.


EDIT: @Typical Guy: That's probably a question you should do a search on first here on PF, because it's been talked about a LOT. The answer is, as always, no. Communication of Information follows Classical routes, not quantum ones. There is also the matter of that being an issue of QM, so, maybe the Relativity forum and a 3+1 spacetime thread isn't the place?

EDIT 2: @Typical Guy: Just to illustrate... In your case, let's call the two people "Bob and Alice" (the usual formality). Remember, you say they AGREED on what the communication is, right? There is your "Classical means of communication", because THAT had to be non-FTL. If they met, then parted, the information was already shared when they met. If they use radio, or lasers etc... well.. that's still limited to c at best. You could use Entanglement to communicate as quickly as your fastest Classical means of sharing information, but no faster than 'c'.

 

[JesseM]

Lets say, for the sake of argument that two scientists are each watching one half of a pair of entangled particles. It was previously agreed that if the entanglement is destroyed on and odd second that they would have pizza for lunch. If the entanglement is destroyed on an even second, they would have burgers for lunch. one of the scientists (who is very hungry) destroys the entanglement on an odd second because he wants pizza. We don't have to set up any kind of complicated morse code, we can simply have a previously agreed upon definition to define what a 1 or 0 means for a single entangled pair.

How would they know if entanglement is destroyed? The only way to judge whether two particles are entangled is to compare the measurements on each particle and see if they are correlated. But there's no way to control what result a particle gives--you can't choose if it's 1 or 0 (spin-up or spin-down, say) for whatever variable you're measuring (like spin in a particular direction), you can only choose what variable to measure and the result will appear to be random, but if you later compare your result with the other experimenter, you'll find that if she chose the same variable to measure, then you'll have gotten correlated results if the particles were entangled (she's either guaranteed to get the same result or the opposite result depending on the type of entanglement).

 

[Hoku]

Well, I'm just proud of myself for putting up with, well, you know. But, don't worry, I'm sure I'll give you reason to regret any kind words soon enough, possible in 2-short paragraphs from now...

Entanglement really isn't too far off the topic and it wouldn't surprise me if it naturally found it's way back into the discussion. However, because of it's complexity (for me, anyway), I would like to try and keep this thread simplified and organized. I don't think entanglement is appropriate at this moment. There is a nice new discussion of it in the "quantum physics" section of the forums. The thread is entitled, "entanglement".

I've been thinking more about the "waves moving through a medium" analogy and I think I can explain why it doesn't immediately clear things up. I do understand the difference between a wave and the medium through which the wave travels. However, I'm not sure that gravity and spacetime can really be separated like that. I'll explain why, but please be patient. This may take more than one post.

From what I've gathered, gravity IS spacetime. New Scientists says, "General relativity describes gravity as geometry. ...whenever anything - be it you, me, a piece of space dust or a photon of light - tries to travel through the universe in a straight line, it actually follows a trajectory that is curved by any mass and energy in the vicinity. The result of this curvature is what we think of as gravity." http://www.newscientist.com/article/mg20227122.700-gravity-mysteries-what-is-gravity.html

But is this geometry really enough to affect the movement of things? Now, this is where I really need your help, so try to understand my point of view before formulating your answer. The way I understand it, gravity IS enough to affect movement of things as long as those things already have momentum. It even says that in the New Scientist quote; just piece together the magenta words. Planets, for example, are not in orbit simply because gravity is there. Momentum is also required. Is this not true? So, if gravity is described as geodesics, then light/matter, whatever, must have momentum in order to follow those geodesics. right?

Humans are stuck to the Earth because of gravity, but what is the momentum that we have that makes use of the geodesics? As far as I can tell, we are at rest relative to gravity at the Earth. So why do we keep following the geodesic? Why are we actually stuck to the Earth?

 

[A.T.]

The way I understand it, gravity IS enough to affect movement of things as long as those things already have momentum.

No, if you mean classical 3-momentum, it is not necessary. Apples accelerate from rest, so they are affected by gravity before they have any velocity / momentum.

As far as I can tell, we are at rest relative to gravity at the Earth. So why do we keep following the geodesic?

The apple is at rest in space relative to Earth. But it still advances in space-time, and that is where it follows a geodesic, once it detaches from the tree.

Have a look here:
http://www.relativitet.se/spacetime1.html

 

[atyy]

I do understand the difference between a wave and the medium through which the wave travels. However, I'm not sure that gravity and spacetime can really be separated like that.

Yes, generally you cannot split spacetime up into background + wave. Misner, Thorne and Wheeler say it is like a wave on the ocean, which is the wave and which is the ocean? But sometimes splitting up the ocean into wave and ocean is quite a good approximation. Similarly, such a split is sometimes quite a good approximation of the full mathematics of general relativity.

So, if gravity is described as geodesics, then light/matter, whatever, must have momentum in order to follow those geodesics. right?

You have the right idea - if you talk about 4-momentum, not 3-momentum. The curvature is that of spacetime, and we are always moving in spacetime, because we are always moving in time.

 

[Hoku]

Further down the rabbit hole, things get curiouser and curiouser. Let me piece together things I've picked up:

1) Frame Dragger said, "Light follows a geodesic INTO the black hole... It is not "dragged" in..."

2) A.T. said, "[an apple] still advances in space-time, and that is where it follows a geodesic..."

3) atyy said, "...we are always moving in spacetime, because we are always moving in time."

4) New Scientist says, "...whenever anything...tries to travel through the universe... it follows a trajectory that is curved... The result of this...is what we think of as gravity.

5) In this thread, https://www.physicsforums.com/showthread.php?p=2617230#post2617230, Maurol2 says, "What is needed is a dynamical theory of gravity."

What I'm piecing together here, is that gravity has no more power than a hill. A hill is a noun, not a force. It seems like momentum is the only real force in play and things with momentum - in space or in time - follow geodesics because it's the easiest, quickest path. Could this be why they can't make gravity fit with the other 3-forces? I'm no longer certain that gravity IS a force.

 

[A.T.]

It seems like momentum is the only real force in play and things with momentum - in space or in time

You have a default "movement" in space-time, which cannot be stopped, but only changed in direction:
http://www.adamtoons.de/physics/relativity.swf

follow geodesics because it's the easiest, quickest path.

Follow geodesics, means go straight ahead like a car without steering. It is only locally the "easiest, quickest" path.


In the http://www.relativitet.se/spacetime1.html" a toy car is used to model geodesics:

 

[Frame Dragger]

I love it when these things come together! Hoku, I do believe you've gotten it! Thois is fun!

 

[atyy]

What I'm piecing together here, is that gravity has no more power than a hill. A hill is a noun, not a force. It seems like momentum is the only real force in play and things with momentum - in space or in time - follow geodesics because it's the easiest, quickest path. Could this be why they can't make gravity fit with the other 3-forces? I'm no longer certain that gravity IS a force.

Test particle GR:
T1 Energy-momentum curves spacetime
T2 Test particles move on spacetime geodesics

Test particle GR is a very good approximation, but there is a flaw in it. What is a test particle? It is something which has no energy-momentum and does not curve spacetime. So all real particles cannot obey the test particle equation T2, they should obey T1.

Also, most matter is not point particles, at least not in GR. Point particles are black holes in GR. So in GR, everything is a field, which matches up with our view of all the other forces and matter - such as the electromagnetic field (a gauge force field) and the electron field (a matter field), and it is in fact possible to make a quantum theory of gravity.

The problem with quantum general relativity is that it doesn't seem hold at very, very high energies (this is not proven yet, it may turn out that gravity is asymptotically safe). But neither does quantum electrodynamics. So the geometric test particle view of GR is not the reason for the failure of quantum general relativity at very, very high energies.

 

[Hoku]

You have a default "movement" in space-time, which cannot be stopped, but only changed in direction:

The real mystery with this is the "time" part. I did look at the "free fall" page you gave a link to a few times last night. I even kept it open and looked again this morning. The problem that I'm having with it is that it let's space be infinite but time ends at, what, .11s, .12s? Obviously, time cannot be less infinite than space.

In this graph, it seems the only reason the event returns to 0.0m is because of this limitation imposed on time, which closes the curved surface. The adamtoons link you included in your last post seems better because it doesn't make time finite. BUT, then it doesn't become clear why the object should return to 0.0m.

Test particle GR:
T1 Energy-momentum curves spacetime
T2 Test particles move on spacetime geodesics

Test particle GR is a very good approximation, but there is a flaw in it. What is a test particle? It is something which has no energy-momentum and does not curve spacetime. So all real particles cannot obey the test particle equation T2, they should obey T1.

This is confusing for me because, if a test particle has no energy-momentum, then why should it obey T1 any better than T2, aside from proving that it doesn't curve spacetime? Or is that the point?

Point particles are black holes in GR. So in GR, everything is a field...it is in fact possible to make a quantum theory of gravity.

I can see the connection between gravity and general relativity, but you seem to be using these interchangably, which is confusing me. From what I understand, gravity is a component of GR, but GR is ultimately describing relationships between different moving things. Gravity is just a path to follow, right? On it's own, gravity has little to do with relationships. Even when something is following gravity there is still no "relativistic value" without the the movement of something else to compare it with. Do you see my confusion? So, to help clear this up, I'd ask if we're trying to make QM fit gravity or relativity.

 

[Gatchaman]

The real mystery with this is the "time" part. I did look at the "free fall" page you gave a link to a few times last night. I even kept it open and looked again this morning. The problem that I'm having with it is that it let's space be infinite but time ends at, what, .11s, .12s? Obviously, time cannot be less infinite than space.

Spacetime does end. That's why its called a singularity.

 

[Gatchaman]

From what I understand, gravity is a component of GR, but GR is ultimately describing relationships between different moving things. Gravity is just a path to follow, right? On it's own, gravity has little to do with relationships. Even when something is following gravity there is still no "relativistic value" without the the movement of something else to compare it with. Do you see my confusion? So, to help clear this up, I'd ask if we're trying to make QM fit gravity or relativity.

I think the problem you have is that you're thinking too much of Newtonian gravity and somehow this still exists as a force in general relativity (GR). In GR, gravity is a purely geometrical/stress-energy construction. There are no "forces" involved.

 

[atyy]

This is confusing for me because, if a test particle has no energy-momentum, then why should it obey T1 any better than T2, aside from proving that it doesn't curve spacetime? Or is that the point?

I should have said - a test particle is a particle whose energy momentum does not curve spacetime. There are no such things. In real life, we treat a real particle as a test particle if its energy-momentum is so small compared to the rest of the universe that its contribution to spacetime curvature is negligible.

I can see the connection between gravity and general relativity, but you seem to be using these interchangably, which is confusing me. From what I understand, gravity is a component of GR, but GR is ultimately describing relationships between different moving things. Gravity is just a path to follow, right? On it's own, gravity has little to do with relationships. Even when something is following gravity there is still no "relativistic value" without the the movement of something else to compare it with. Do you see my confusion? So, to help clear this up, I'd ask if we're trying to make QM fit gravity or relativity.

Yes, I would say that general relativity is not a theory of relativity (but this can be debated). General relativity is a theory of gravity in which the spacetime metric is affected by mass-energy and is the gravitational field. In comparison, in special relativity, the spacetime metric is not affected by mass-energy.

 

[A.T.]

from : http://www.relativitet.se

The real mystery with this is the "time" part. I did look at the "free fall" page you gave a link to a few times last night. I even kept it open and looked again this morning. The problem that I'm having with it is that it let's space be infinite but time ends at, what, .11s, .12s?

No, time doesn't end there, it continues on a new layer of the diagram. Think of the diagram as a roll. You can extend this diagram along both dimensions into infinity.

In this graph, it seems the only reason the event returns to 0.0m is because of this limitation imposed on time, which closes the curved surface.

No, the limitation of the displayed time interval has nothing to do with the shape of the world lines. They are just affected by the local curvature.

The adamtoons link you included in your last post seems better because it doesn't make time finite. BUT, then it doesn't become clear why the object should return to 0.0m.

Here is the more complex version:
http://www.adamtoons.de/physics/gravitation.swf
Keep in mind that this diagram is also multilayer like a roll.

It shows the space-time along an axis all the way trough to the other side of a massive sphere, and the world line of a test particle moving on this axis. You can set:
initial position : 1
initial speed : 0.16
To get a body thrown up vertically and come down again.

Press "Help" for more info.

 

[Hoku]

Spacetime does end. That's why its called a singularity.

Whether or not spacetime actually "ends" is in the realm of philosophy. Your statement is presumptious. Fortunately, whether or not spacetime actually has an end is irrelevant to my point for 2 reasons:

1) It hasn't ended YET so we cannot close the curve.
2) Since spacetime is a "singularity", as you point out, then space and time both need to be closed on the graph simultaneously to maintain consistency. Space cannot extend beyond time.

No, the limitation of the displayed time interval has nothing to do with the shape of the world lines.

I think it does. The world line is defined by geodesics, right? Closing the curved surface affect it's geometry, which, in turn affects geodesics.

This is bringing me back to the question of why we actually stick to the Earth. Why do objects return to 0.0m? I did click the help button on the new adamtoons site that A.T. last posted. In the help menu, under the "samples" heading, it says "When you push play, you see in the 3-D view, how the object is moving along its world line. The world line changes it's direction in regard to the dimensions because it is taking the straightest possible way." But this makes me ask:

1) The straightest possible way to where?
When it is answered, "Back to the Earth, of course." Then I need to ask:
2) Why does it want to get back to the Earth?
From this, I expect the answer to be, "because it's the straightest possible way."

Do you see what I'm having trouble with? Circular reasoning.

A.T. said movement in space-time cannot be stopped but it can change direction. Evidentally, that's not entirely true. As I said early in this thread, we only really have control over 2-dimensions. We need planes, rockets, etc., to gain control of the third. Why? Why are we stuck to the Earth?

I might pose this question in a new thread in hopes of finding others that haven't been following this one to help answer. But I will let it sit here for a minute to see how far we can get it.

 

[Gatchaman]

Whether or not spacetime actually "ends" is in the realm of philosophy. Your statement is presumptious. Fortunately, whether or not spacetime actually has an end is irrelevant to my point for 2 reasons:

1) It hasn't ended YET so we cannot close the curve.
2) Since spacetime is a "singularity", as you point out, then space and time both need to be closed on the graph simultaneously to maintain consistency. Space cannot extend beyond time.

No philosophy here. Just your lack of understanding GR in a mathematical manner.

 

[Mentz114]

we only really have control over 2-dimensions. We need planes, rockets, etc., to gain control of the third.

I can walk up a hill without rocket assistance.

Why? Why are we stuck to the Earth?

Oh, the futility of human existence !

Ah, you mean literally. Well, there's this thing called gravity you see, blah blah ...

 

[Gatchaman]

I'm no longer responding to this thread. I really think Hoku is trolling now. All of the mumbo-jumbo metaphysics he throws in here along with legitimate GR contributions from other forum members just doesn't sit right with me.

Good luck.

 

[Gatchaman]

Hoku,

As easy as this may sound for me to say:

Go grab an introductory book about General Relativity and start learning the MATH. Without knowledge of the MATH, you will have absolutely no understanding of GR.

But, I think you need to grab yourself an introductory physics book to review basic Newtonian Laws. Its obvious from your statements that you lack the basic knowledge.

 

[Frame Dragger]

Way to hold to post #64!

 

[Hoku]

I can walk up a hill without rocket assistance.

I'm going to assume that you're serious with this statement and respond accordingly. I think a 2-dimentional surface is allowed to have "hills". I also think that a Flatlander can "ascend" those hills. Does this mean Flatlanders have control over the 3rd dimension? I don't think so.

"Why? Why are we stuck to the Earth?"

Oh, the futility of human existence !

Ah, you mean literally. Well, there's this thing called gravity you see, blah blah ...

Thanks for the comic relief, Mentz! That should carry me through the day...

Gatchaman, this is a second request for you to withdraw from this thread. I will report you for harrassment if you continue.

 

[JesseM]

Whether or not spacetime actually "ends" is in the realm of philosophy. Your statement is presumptious.

No, it's just a statement of how general relativity deals with cases like black holes. GR may well be wrong about this, but aren't we just discussing the theory's predictions on this thread, not speculating about what might be true in a theory of quantum gravity that supercedes it?

1) It hasn't ended YET so we cannot close the curve.
2) Since spacetime is a "singularity"

Spacetime is not a singularity. In GR spacetime can contain singularities at certain points like the center of black holes and the Big Bang, and according to GR these are the only points where worldlines can "end".

I think it does. The world line is defined by geodesics, right? Closing the curved surface affect it's geometry, which, in turn affects geodesics.

A.T. was just giving a diagram which is an imperfect representation of actual 4D spacetime geometry. The fact that time "ends" at a certain point on the surface in the diagram doesn't reflect how it actually works in GR, although the diagram may capture other aspects of it.

This is bringing me back to the question of why we actually stick to the Earth. Why do objects return to 0.0m?

If our bodies were solely affected by gravity (meaning we all followed geodesic paths at all times) we would fall right through the surface of the Earth and pass near the center at high speed and then pop up on the opposite side of the Earth, following something like a highly eccentric orbit around the center. But other forces can prevent objects from following geodesics, in this case the electromagnetic force between the ground and our feet which prevents us from falling down towards the center.

I did click the help button on the new adamtoons site that A.T. last posted. In the help menu, under the "samples" heading, it says "When you push play, you see in the 3-D view, how the object is moving along its world line. The world line changes it's direction in regard to the dimensions because it is taking the straightest possible way." But this makes me ask:

1) The straightest possible way to where?
When it is answered, "Back to the Earth, of course."

No, the straightest possible path on the curved spacetime around the Earth, where the spacetime curvature is determined by the distribution of mass and energy in this region of spacetime according to the Einstein field equations, mainly by the mass of the Earth itself.

A.T. said movement in space-time cannot be stopped but it can change direction. Evidentally, that's not entirely true. As I said early in this thread, we only really have control over 2-dimensions. We need planes, rockets, etc., to gain control of the third. Why? Why are we stuck to the Earth?

Here you are talking about mere questions of biology, not physics. If we didn't have legs (if we were plants for example), then we wouldn't have "control" over 2 dimensions. If we had wings (if we were birds or pterodactyls for example) we would have "control" over 3 (and obviously we already have a limited sort of control since we can jump). This sort of control is always a matter of electromagnetic interactions between parts of our body (legs, wings) and the environment (ground, air) which allow us to move along non-geodesic paths.

 

[Mentz114]

Thanks for the comic relief, Mentz!

You started it. Some of the stuff you're saying is ludicrous. Don't take my post as agreement. I can move around in 3 dimensions. I suspect you'll start pushing some crackpot theory soon.

 

[Dale]

"When you push play, you see in the 3-D view, how the object is moving along its world line. The world line changes it's direction in regard to the dimensions because it is taking the straightest possible way." But this makes me ask:

1) The straightest possible way to where?
When it is answered, "Back to the Earth, of course." Then I need to ask:
2) Why does it want to get back to the Earth?
From this, I expect the answer to be, "because it's the straightest possible way."

Do you see what I'm having trouble with? Circular reasoning.

It is not circular reasoning, but it does require a bit of understanding what it means for a line to be "straight". There are essentially two different but equivalent ways of determining if a path is straight. The first (global) definition is that a straight path is a path which locally minimizes the distance between the start and the end (the shortest distance between two points is a straight line). To use this one you need a beginning point and an ending point. The second (local) definition is that a straight path is a path which doesn't turn anywhere (parallel transports its tangent vector). To use this one you need a beginning point and an initial tangent direction.

So, how do we understand this idea wrt gravity? First, we consider the path of a particle to be represented by some line in spacetime, a particle at rest will be represented by a line in the time direction, while a particle which is moving will be represented by a diagonal line with a slope which is related to the velocity. Inertially moving particles travel along geodesics. So, if we hold our hand still and drop a rock, the event of our dropping the rock is a point in spacetime and at that point the rock is at rest so its worldline's tangent is in the time direction. From that point, it travels straight (in the local sense), parallel transporting its own tangent vector through spacetime, until it hits the ground, at which point it is no longer traveling inertially.

Gatchaman, this is a second request for you to withdraw from this thread. I will report you for harrassment if you continue.

Good luck with that. I looked back and couldn't find a single thing that Gatchaman said that was out of line.