# Visualization of space time contraction and gravity

1. Apr 7, 2012

### dustinthewind

I am glad for a place like this where I can come to discuss what is on my mind with those interested. My delema is expanding my conceptual understanding of relativity and how it realates to space time and gravity.

To begin I will go over how I have come to understand space time contraction. It would seem a frame S observing another moving frame S' will percieve S' frame as contracted in space and time. For simplicity they are both traveling in the x and -x axis direction. Lets say we are in a space craft near the speed of light and we see our selves as normal. However the other frame is moving near the speed of light and is contracted. It has velocity towards us. This suggests to contract it then we would add time to to the front of its frame bringing it closer but the rear of the frame we would recieve even more additional time setting the rear closer to the front of this moving frame. This would contract the observed frame. Of course we would do this using the math of the Lorentz contraction. Then you could consider the far end of the S' frame set further ahead in time symbolizing you traveling into the S' frame future. This would seem to make sense as you would live much longer traveling at near light speed. It also hints at the unseperable relation between space and time.

Ok so then we have some one on the ground observing a space craft directly above their head at near the speed of light. It appears contracted but for different reasons. It has forward velocity and appears to be contracted. It having a forward velocity then you subtract time from the front of the craft and add time to the rear of the craft and this contracts it. You can then visualize as the craft travels forward continually subtracting time from it and preserving the occupants life span. This also seems to suggest the connection of space and time but from the S frame perspective.

However the contraction in space time dosn't seem to change at constant velocity. This suggests the culprit of space time contraction as being due to acceleration. So then as we accelerate this distortion in space time would seem to contract space and distort time.

Ok now lets consider gravity and the earth for instance. If we placed a clock high above the earth at a lower acceleration and another clock at the base of the earth at higher accleration the clocks should be distorted in time and desynchronize due to the contraction of time and space. However for the earth this contraction of time and space would seem to be in all directions. Almost suggesting the flow of time and space into the earth or matter. Or that the future is flowing into a gravitational well.

Now this seems to suggest to me matter as possibly being a hole in time and space in which time and space are flowing into it? It would seem to suggest an appropriate naming for the black hole I guess. Or that this suggest gravity is a relativistic effect. I wonder if this would mean that this demands that what is cuasing gravity is a relativitic effect in it self?

And that leads to my ultimate question that is assuming that all my other assumptions are correct above. If not let me know. My question being lets now consider matter and down to the atom. What relatistic effect do we know of in the atom that could cause gravity and the distortion of space time. Could it be the differences in between the velocities of the proton and the electron? Is there some other relatistic effect that occurs in the atom that I could not be taking into account?

Also are we sure that all mater has the same gravitational constant? For instance does lead have the same gravitational constant as say helium? How would we know this. The closest example I can think of is the Cavendish experiment http://en.wikipedia.org/wiki/Cavendish_experiment I would expect in that experiment we could possibly measure some elements to determine this but here is another problem. How do we know the electron and protons alone have a gravitational atraction? I would think it would be impossible to tell with the electric force being so much greater than the gravitational force. And here is anoteher problem. What if the gravitational force is a result the electrons and protons coming together but the electrons are much faster than the protons. It would certainly explain the 1/r^2 behavior of the gravitational force and the similarity of the electric to the gravity force. But it would have to always be atractive on the other hand. Could the positive proton to the electrons always have a greater aparent charge than the electrons because the protons is what seems to be moving the fastest? And to the protons the electrons always have a greater aparent charge than the protons because they apear to be traveling faster? But for the electrons in orbit around their nucleus there is no change in aparent charge because of the lack of time distortion to objects with velocity perpendicular? Any suggestions where I might be getting lost? I appreciate any ideas on this as I can't seem to get it off my mind.

2. Apr 8, 2012

### Vorde

You seem to have a decent understanding of Special Relativity, but little knowledge of General Relativity (which is fine). I will proceed assuming that is the case, I apologize if I am wrong. Your whole concept of 'subtracting time/space from one end and adding it on to the other' to explain length contraction/time dilation isn't really accurate, but I think it will be fine.

All of Special Relativity is simply the math for adjusting two inertial (not accelerating) reference frames to be consistent with relativistic effects (time dilation, length contraction etc...). Special Relativity doesn't deal with acceleration, and it doesn't deal with gravity.

When you want to consider one of those two things, you need to switch to General Relativity, which is quantitatively incredibly complicated but qualitatively very simple and beautiful. What GR (Gen. Relativity) says, in addition to the two SR postulates, is that matter (or mass, really) bends spacetime around it. If you don't understand what that means, I'd search a bit around because there are lots of great discussions of it, but it can be applied to your question.

It's not that matter is a 'hole in spacetime' as you say, but rather that matter bends space around it so that other matter is attracted to it. So it is not some SR movement in matter that causes the gravitational attraction, but rather the very fact that they have mass causes other matter to be attracted (as dictated by GR).
So you are right in saying that relativity causes gravity, but not in the way you think.

Regarding your query about the gravitational constant. G (as it is called) is the same for any mass. However, the exact value of G varies with the units of measurement being used, and there are specific units (called natural units) where G is 1 and therefore is not needed.

3. Apr 8, 2012

### dustinthewind

Thanks for separating the terms. That let me know there was a difference so I looked it up.

I get this from http://en.wikipedia.org/wiki/Relativity_of_simultaneity or the Relativity of simultaneity. And this equation $t’=\left(t-\frac{v x}{c^{2}}\right)\gamma$ Where you take an object and set all clocks in it to t=0. Then assign it a velocity. At different positions x this distorts time. This time distortion also contracts the object because of its velocity which is equivalent to doing a length contraction but easier because you only consider points along its frame.

Your right special relativity doesn’t specifically state this but I realized it naturally by accident as it seemed to be implied by my trying to visualize it. It seemed to be what would be the cause of space time contraction. This is where I looked up General Relativity.

http://www.thebigview.com/spacetime/relativity.html

and it basically states, "Eleven years after On the Electrodynamics of Moving Bodies, Einstein published his second groundbreaking work on General Relativity, which continues and expands the original theory. A preeminent feature of General Relativity is its view of gravitation. Einstein held that the forces of acceleration and gravity are equivalent."

I didn't realize Einstein published this later but yes I agree with this. However I sense that you may be implying that a linearly accelerating object such as a rocket also wraps space time around it. I don't think I understand that because I assumed the contraction of space time was in the direction of acceleration. Therefore the space ship would view space as flattening in its direction of travel. But for a gravitational body it would tend to contract space time in on itself in all directions. However you may be right in that if the gravitational attraction to a near light speed object would increase with its apparent mass and this would cause contraction of space all around it… so that’s something new I hadn’t thought of before. This last one might be a new insight for me! D . But on the other hand for a ship at near c why would y' not equal y. That dosn't seem right. But it would happen if the ship started to become a gravitational well. Thats strange. I'll have to look into this one.

Thats kind of what I was getting at when I stated

So how I was visualizing it is that space time is flowing into the earth in all directions or it is warped around the earth in all directions in spherical symetry.

Well the reason I can think of matter like a hole in space time is that I can see the clocks of space changing time unevenly and contracting space as a ship accelerates. These clocks bring space time closer together because of its velocity relative to the craft. That is all velocity being relative to space time or the speed of light. I can then translate that to the equivalence of acceleration on earth. This contraction of space time would distort clocks differently at different distance from the central radius but not at the same radius. So further away from the earth gravity is less and I can imagine space time contracting to the earth slower. Space time would contract at earth’s surface more quickly due to larger acceleration. It almost looks like a space time fluid going down a drain but in 3 dimensions. Then we go inside the earth and this fluid motion is decreasing as if it is disappearing. Possibly into matter? Ya kinda see it? When I realized that it started to make sense how this competing flow of space time would cause atraction between objects as well. Between 2 object there would be a low pressure region between them and they would attract. Or its mathmatically symbolized by the potential field being lower between the 2 objects. Like the unstable lagrange point between 2 objects.

What bothers me is saying space time bends around or flows into mass because mass has mass. You see the problem? It seems there must be a deeper reason for this. But what it is I am a bit stumped about.

Ok yeah I was wondering about that. How do we exactly know this gravitational constant is the same for all mass? Especially I wonder about protons or electrons. I would imagine the only way we have to measure them is when they are together.

Last edited: Apr 8, 2012
4. Apr 8, 2012

### Vorde

Not incorrect, but the more proper view of the equation you mentioned (and I'd say easier to conceptualize) is that if you have two clocks (c and c') at the same location at time t=0, and c' moves away with velocity v, when c' is at a distance x from c, and c reads the time elapsed as t, c' will read the time elapsed as t'. There isn't actually any length contraction unless you are talking about contraction in the time dimension, but thats a roundabout viewpoint that isn't really useful here.

I think this whole problem stems from the misconception of thinking mass contracts space instead of what I describe below. If thats not it then I think it was a misstep on my art as you are right, space would only contract for the rocket in the direction of motion.

The SR terminology of 'contracting' doesn't transfer directly over to gravitational attraction. saying a massive body contracts space around it isn't really correct, I'll try to rephrase it but I need to explain a word first. A geodesic is described often as 'the generalization of the notion of a straight line to curved spaces', a more useful way to use the word in this scenario would be to say that if you throw an object with a set velocity, and the object never experiences another force again, that object's path will be a geodesic.
With that in mind, massive bodies do not contract space around them, but rather they bend the geodesics of any passing object towards the center of mass. Applied: an object in motion seems to follow a straight line, but that is only because the geodesic it is following is straight. When an object in motion passes a mass the geodesic is bent and the object seems to be attracted to the mass.

Regarding a later question you had in that paragraph: does the gravitational attraction increase as a bodies velocity increases (which you think it would because mass increases). My tentative answer is sort of. I've received a lot of different answers to that question, and I am not really equipped to answer it definitely, but the general consensus I've gotten is that yes gravitational attraction does increase with velocity, but there are complicated elements that don't make it a straight answer.

In your later paragraph you say a lot of things I would regard as incorrect but they are all stemming from the visualization of space contracting with mass instead of the correct view with geodesics, are your questions still relevant, having read that?

In GR, mass (or energy, they are interchangeable) bends spacetime. As for why, its because it does, as far as I know (and I am pretty damn sure) any reason why is purely philosophical.

This is the way I've explained it before and it seems to work.

The universe computes the force a massive object applies on another object a distance r away by the equation:
$f= \frac{m1m2}{r2}$
I don't know why this isn't working, but its the force equation without the G

This is all fine and dandy, but we (the human race) use very specific units that we are used to. When we want to compute the force with our units, we have to include a constant of proportionality (G) for the units to all work out. We could use the natural units and not have to worry about G, but that would give an answer in units we aren't familiar with so we use G.

5. Apr 11, 2012

### dustinthewind

I believe when you go to post you have to select advanced mode for it to take. I ran into the same problem.

I also wanted to say thanks for your helpfull tips. It got me thinking about other ways of looking at relativity.