QuestionCan someone help me visualize the General Theory of Relativity in 3 dimensions?

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IG2007

"Don't criticize what you can't understand..."
We all know about the General Theory of Relativity. It was proposed by Albert Einstein, the most controversial physicist of all time. The theory is the best theory (till now) we have got about Gravity. There's no better theory about Gravity than this till now, accepted by a majority of the Scientific Community. Till now, we have described GR like this:
But, you know, I find this image of GR to be kind of vague. Because, you know, it's kind of 2-dimensional, which contains only Latitude and Longitude. We all know that there are infinite planes in the universe, this is just one plane. I want to visualize it in a 3D way which consists Altitude as well. Can anyone help me visualize it in a 3-dimensional way?

PS: It would be good if you can help me visualize it in a 4D way as well,

Catastrophe

"Science begets knowledge, opinion ignorance.
Gosh! You do ask some questions.

Let's try a black hole. The normal representation falls down because you can only approach the bh on a flat plane like your diagram. Flat, that is, until you start getting closer.
Instead of looking down from above, and seeing a hole in the centre, imagine you are in space. You see (or don't see) a sphere into which matter is being drawn. You may see, according to some descriptions, a static image at the even horizon.
Anyway, to start answering your question, see a sphere which can be approached equally from any direction. What happens if you look at your bh on paper from underneath the paper. This problem disappears when you imagine it as a sphere. We'll have to leave any more dimensional jumps for the moment.

IG2007

Geomartian

General Relativity uses geodesics.

Friends don’t let friends use geodesics.

To help you see in 4D I would have to get a medical release before doing the upgrade.

Current displays are in 2D and there are high level engineering programs that can move you through 3D models.

A fourth dimension can be ported through a haptic interface.

Einstein was said to be able to hold (not visualize) three and four dimensional objects in his mind. Your mind knows where your hands and feet are at all times. This (sense) can be repurposed as a non-visual form of spatial imagination. The amount of concentration required is not trivial. Some intellectually challenging professions have their people work with their hands in order to strengthen this talent.

Einstein appeared slow as a child so this talent can have a price.

IG2007

"Don't criticize what you can't understand..."
Gosh! You do ask some questions.

Let's try a black hole. The normal representation falls down because you can only approach the bh on a flat plane like your diagram. Flat, that is, until you start getting closer.
Instead of looking down from above, and seeing a hole in the centre, imagine you are in space. You see (or don't see) a sphere into which matter is being drawn. You may see, according to some descriptions, a static image at the even horizon.
Anyway, to start answering your question, see a sphere which can be approached equally from any direction. What happens if you look at your bh on paper from underneath the paper. This problem disappears when you imagine it as a sphere. We'll have to leave any more dimensional jumps for the moment.
But, you know, I am trying to figure out why a plane that is going through the center of an object bend.

Catastrophe

Catastrophe

"Science begets knowledge, opinion ignorance.
But, you know, I am trying to figure out why a plane that is going through the center of an object bend.
If I understand correctly:
It is like we 'think' the Earth is flat - not actually, but the curvature is so slight that it is as if it were flat. My sphere is just like the Earth with all gravity pulling inwards (perpendicularly) towards the centre. Now you know that is a simplification so I will say I understand that gravity is directed towards the CoG and not the actual centre of the planet - also that large masses can distort gravity very slightly from that.

IG2007

Mental Avenger

We all know about the General Theory of Relativity. It was proposed by Albert Einstein, the most controversial physicist of all time. The theory is the best theory (till now) we have got about Gravity. There's no better theory about Gravity than this till now, accepted by a majority of the Scientific Community.

I disagree. IMO, the warping of “space” is a poor representation of gravity. It lends itself to many

But, you know, I find this image of GR to be kind of vague. Because, you know, it's kind of 2-dimensional, which contains only Latitude and Longitude. We all know that there are infinite planes in the universe, this is just one plane. I want to visualize it in a 3D way which consists Altitude as well. Can anyone help me visualize it in a 3-dimensional way?

That’s easy. I did that about 12 years ago. This is the 3D segment from a larger explanation.
In order for the wormhole/space travel concept to work, the wormhole would have to be a “shortcut” to another area of space. Now, this is not a mathematical explanation, but it explains graphically why the “fold in space/wormhole hypothesis is unrealistic in the real universe. The inaccurate and totally misleading misrepresentation of space as a flat sheet or membrane makes it look easy. But, space is not flat like a sheet of paper, it is solid like a bowling ball. It is easy to fold a sheet of paper, but not quite so easy to fold a bowling ball. IMO, too many people have taken the woefully inadequate 2D flat sheet model and applied it literally to the 3D Universe.

A better and more reasonable representation of space and gravity would be that of a giant sponge the size of the Universe. The effect of gravity (i.e. a star) would be like reaching in to a point deep within the sponge and pinching some of the sponge material. You would end up with a region of dense sponge at the point of the “pinch”, immediately surrounded by a region of rarified density which gradually reverts to the original density as you move further from the “pinch”. The density of the sponge surrounding the “pinch” is analogously inversely proportional to the gravitational force of the star. Notice that no matter how hard you pinch an area, it never brings it any closer to any other area. It only changes the density of the sponge in that immediate vicinity, and that change in density varies inversely with distance from the pinched area. With this more accurate model, all those notions about folding space vanish.

MaxGaofeiYan

The drawing Figure 2.4 in the following paper may help:

Figure 2.4 – A dot representing matter that stretches the elastic field inward in a 3D space.

Geomartian

How do you show the rate of time at one point in space?

What you need is a cursor that can be moved through three dimensional space.

That cursor will have a readout of the properties for that point in space. It can leave a marker that will show up in a database. You can then compare the properties of several points.

If you try to display all of the information in a static form it will be opaque and useless.

You can sample the field to make sense of it.

voidpotentialenergy

My take on relativity (bad base math idea) works but for the wrong reason.
Speed of light and more important black holes and the ability of black holes to alter the speed of light are proof that relativity cause is wrong.

Quantum fluctuation as the beast that is space and time, a black hole compresses the local area of fluctuation space and compresses time.
Why light can travel at a different speed near a black hole because it is in compressed space/time.
Black hole simply an area of compressed time/space and reason it doesn't shrink forever and become an infinite mass point is the compression of time in that region.
No singularity and no crazy physics in a black hole.

IMO relativity looks at the effects of everything but not the cause.

Our universe quantum fluctuation forever with endless big bang universe's in all formats of size and activity in it. JMO

MaxGaofeiYan

Here is a good video on 3D visualize general relativity.

A new way to visualize General Relativity

5:21 in the following video and some other times, the 3D visualize general relativity is the same as the "Figure 2.4 – A dot representing matter that stretches the elastic field inward in a 3D space." in my paper which link shared in above post.

Our explanation on Gravity is much simpler, without a timeline as the 4th dimension which causes so many paradoxes and so much confusion.

Wolf28

We all know about the General Theory of Relativity. It was proposed by Albert Einstein, the most controversial physicist of all time. The theory is the best theory (till now) we have got about Gravity. There's no better theory about Gravity than this till now, accepted by a majority of the Scientific Community. Till now, we have described GR like this:
But, you know, I find this image of GR to be kind of vague. Because, you know, it's kind of 2-dimensional, which contains only Latitude and Longitude. We all know that there are infinite planes in the universe, this is just one plane. I want to visualize it in a 3D way which consists Altitude as well. Can anyone help me visualize it in a 3-dimensional way?

PS: It would be good if you can help me visualize it in a 4D way as well,
Sure: In essence, the image in your post does represent 3 dimensions, almost. The only 2D part of the image is the fabric or membrane. What you're missing is velocity. The membrane that the spheres rest upon is merely a 2D representation of space-time. Without orbital velocity one would assume that the small sphere would simply roll down the slope towards the bottom of the large sphere at the center - but that's false! We all know that in reality, the larger sphere's gravity would pull it towards it's center of mass.

Without it's orbital velocity, the small sphere would avoid the space/time representation's slope, and make a bee-line to the central mass of the larger sphere. Here's how to convert that 2D membrane into 3D reality. So what you have to imagine is that instead of the large sphere creating a slope in space/time - it is creating a well that objects can fall into equally from all directions. The only thing that can keep a smaller object from falling in is orbital velocity. If it's fast enough it can escape by increasingly larger orbits. If it's too slow it will spiral down into the larger sphere's gravity well towards it's point of center mass. The more massive the object, the greater it's gravity or it's gravity "well", it's attraction.

So, what they try to represent by showing a sloped membrane is the method by which the smaller object "falls" towards the larger one - how the larger object creates a well in space-time - what causes the attraction. All you have to do is change it from a membrane to more like a sea urchin, with spikes radiating from all possible points to the center of mass yet still remember that it's the warping of space-time that creates the attraction.

A note about velocity and time - the 4th dimension. If an object is massive enough it can create a black hole. An infinite gravity well - per say. The 4th dimension is time. On Earth a skydiver with air resistance reaches terminal velocity at 118 MPH or so. But a black hole - ahhhh... the faster you are pulled into the gravity well the slower time passes. Once your terminal velocity reaches the speed of light (and believe me, it is terminal) - time stops - for you - and your fall into the central mass of the black hole lasts forever. So - imagine falling forever - there's your 4D visual. It's a bit more complicated than that, what with all the stretching your body experiences as your head is at the speed of light while your feet are not quite there yet but for simplicity's sake, let's just leave it at falling - forever. You won't be needing a parachute.

IG2007

voidpotentialenergy

Here is a good video on 3D visualize general relativity.

A new way to visualize General Relativity

5:21 in the following video and some other times, the 3D visualize general relativity is the same as the "Figure 2.4 – A dot representing matter that stretches the elastic field inward in a 3D space." in my paper which link shared in above post.

Our explanation on Gravity is much simpler, without a timeline as the 4th dimension which causes so many paradoxes and so much confusion.
Or gravity simply travels between quantum fluctuation with no speed limit because it is between quanta orbits and (void) has no speed limit or size.
Gravity just a compression of fluctuation.

Light travels at the valley of fluctuation with a set speed limit and why light interacts with everything.
Neutrinos at the crest with set speed limit and why the can travel through planets without interacting since they travel at the same place as the crest nothing else can exist at that point other than a freak event of fluctuation particle creation/ destruction.

JMO

marty369

look at a dice so your seeing it as a cube length, height and width then take away time

Ancient One

We all know about the General Theory of Relativity. It was proposed by Albert Einstein, the most controversial physicist of all time. The theory is the best theory (till now) we have got about Gravity. There's no better theory about Gravity than this till now, accepted by a majority of the Scientific Community. Till now, we have described GR like this:
But, you know, I find this image of GR to be kind of vague. Because, you know, it's kind of 2-dimensional, which contains only Latitude and Longitude. We all know that there are infinite planes in the universe, this is just one plane. I want to visualize it in a 3D way which consists Altitude as well. Can anyone help me visualize it in a 3-dimensional way?

PS: It would be good if you can help me visualize it in a 4D way as well,

Ask Cat, he has an answer for everything. I'm not sure he believes in wormholes, so his explanation may take longer than others?

Good luck

Mars Hall

Catastrophe

"Science begets knowledge, opinion ignorance.

Well, thank you for that! I am gad you did not suggest that my answers are aways correct (because I am sure that they are not). However, when it comes to GR, I think that IG is already ahead of me.

One thing I am trying (but still Newtonian) is to elaborate my flatlander analogy to include mass, energy and gravity. I have found it very successful in elucidating spatial characteristics, so it is worth a try,

Cat

IG2007

Ancient One

Well, thank you for that! I am gad you did not suggest that my answers are aways correct (because I am sure that they are not). However, when it comes to GR, I think that IG is already ahead of me.

One thing I am trying (but still Newtonian) is to elaborate my flatlander analogy to include mass, energy and gravity. I have found it very successful in elucidating spatial characteristics, so it is worth a try,

Cat

I'd love to hear more about your concepts of bad wars & good peace, if you don't mind?

All Ears (I/we have much yet to learn) :O

IG2007

Catastrophe

"Science begets knowledge, opinion ignorance.
This is a philosophical question which I believe is beyond the scope of this forum. It is certainly way out of my science orientated province.

It is probably epitomized by the saying:
"One man's terrorist is another man's freedom fighter " on which I have no comment.

Cat

IG2007

Ancient One

This is a philosophical question which I believe is beyond the scope of this forum. It is certainly way out of my science orientated province.

It is probably epitomized by the saying:
"One man's terrorist is another man's freedom fighter " on which I have no comment.

Cat

The soldier is the last one to want war, for he/she is the first to die

IG2007

"Don't criticize what you can't understand..."
However, when it comes to GR, I think that IG is already ahead of me.
I am really honoured by that, sir, I appreciate it.

One thing I am trying (but still Newtonian) is to elaborate my flatlander analogy to include mass, energy and gravity. I have found it very successful in elucidating spatial characteristics, so it is worth a try,
Hey, tell us more about that! That sounds good, I would like to know more about your theory.

The soldier is the last one to want war, for he/she is the first to die
That depends whether the soldier is fighting for a cause or not.

Catastrophe

Ancient One

I am really honoured by that, sir, I appreciate it.

Hey, tell us more about that! That sounds good, I would like to know more about your theory.

That depends whether the soldier is fighting for a cause or not.

"It depends on what your definition of the word is (cause), is."

Sometimes if the soldier has (all) the information the DOD/War Dept./generals/Sec. of Defense/powers that be/leaders have, he/she may agree with them on the cause/going to war, & sometimes not. I feel too naked & afraid/uninformed going to battle/war with too little knowledge, especially when I am carrying the gun, & the generals don't think I & mine can handle the truth/information & facts, before spilling blood. Of course the powers that be can't (usually/don't/won't) do that, but then again, maybe I won't fight so hard/determined either?

"A well informed soldier, is a wise/determined soldier."

Mine eyes have seen the glory ... <> <>

IG2007

"Don't criticize what you can't understand..."
"It depends on what your definition of the word is (cause), is."

Sometimes if the soldier has (all) the information the DOD/War Dept./generals/Sec. of Defense/powers that be/leaders have, he/she may agree with them on the cause/going to war, & sometimes not. I feel too naked & afraid/uninformed going to battle/war with too little knowledge, especially when I am carrying the gun, & the generals don't think I & mine can handle the truth/information & facts, before spilling blood. Of course the powers that be can't (usually/don't/won't) do that, but then again, maybe I won't fight so hard/determined either?

"A well informed soldier, is a wise/determined soldier."

Mine eyes have seen the glory ... <> <>
Well, I actually tried to mean "good cause" by "cause", but yes, I should have elaborated on that. I agree that not every person on Earth has the courage to fight for a great cause that can have huge effects in the future of Humanity, and diplomacy is a more useful tool.

Ancient One

Well, I actually tried to mean "good cause" by "cause", but yes, I should have elaborated on that. I agree that not every person on Earth has the courage to fight for a great cause that can have huge effects in the future of Humanity, and diplomacy is a more useful tool.

"Ours is not to reason why, ..."

Avoid that idea

Like the plague

Epiphany

We all know about the General Theory of Relativity. It was proposed by Albert Einstein, the most controversial physicist of all time. The theory is the best theory (till now) we have got about Gravity. There's no better theory about Gravity than this till now, accepted by a majority of the Scientific Community. Till now, we have described GR like this:
But, you know, I find this image of GR to be kind of vague. Because, you know, it's kind of 2-dimensional, which contains only Latitude and Longitude. We all know that there are infinite planes in the universe, this is just one plane. I want to visualize it in a 3D way which consists Altitude as well. Can anyone help me visualize it in a 3-dimensional way?

PS: It would be good if you can help me visualize it in a 4D way as well,

Great question, and a lot of great responses. I wonder if you created a VR model that represented space time distortions by a “fog” of color varying by gravity. So, in a VR flight through a solar system, you would see Jupiter as embedded in a fog going from a light blue to an intense red as you went closer to the planet, with the moons having similar “colored fogs”.

IG2007

"Don't criticize what you can't understand..."
Great question, and a lot of great responses. I wonder if you created a VR model that represented space time distortions by a “fog” of color varying by gravity. So, in a VR flight through a solar system, you would see Jupiter as embedded in a fog going from a light blue to an intense red as you went closer to the planet, with the moons having similar “colored fogs”.
That's a really great idea to be frank, but I guess I do not have the equipments to do that. Might try later though.

"Ours is not to reason why, ..."

Avoid that idea

Like the plague
I don't really get what you mean to say. Can you please elaborate?

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