Hi. I am new to forum. So, I am not sure if any similar subject has been discussed here before. I can remove the thread if it is a duplicate. My native language is not English, so also apologies for any typos, in advance.

I have been thinking about the expansion of the universe a lot lately and I believe that I have developed a different look on the subject. It requires some higher dimensional imagination capability; therefore, I think it wasn’t quite understood where I have tried to explain it before. Since this forum is focused on higher dimensions, I thought some of you might find it interesting and relate with it easily. It will get quite long in order to have a clear explanation, though.

The idea is simple; what if our universe is expanding in 4 spatial dimensions instead of 3? To visualize what it would be like, I have gone 1 dimension below, as most people do. So, I have imagined our universe like a balloon in a 3D environment and replaced our 3D space with the balloon's 2D surface, therefore we also became 2D creatures living on this surface.

When this 3D balloon is expanding, as 2D creatures living on its surface, we only notice that the surface is being stretched and all the points on this surface will be moving away from each other, similar to what our astronomers define what happens when the universe expands today.

But while the surface is stretching for the 2D creatures on it, the balloon’s radius is also increasing. This increase is happening on 3rd dimension direction and the creatures on its surface are not able to observe this motion since they are limited with their 2D reality. If we apply this to our 1 higher dimensional real universe, it means that; when we measure the expansion of the universe, we only measure the stretching of its 3D surface on a 4D hyper sphere but cannot notice any increase on its diameter which takes place in 4th dimension direction. (This seems easy to understand, but it is usually the point where people miss to grasp and get lost. So, if you want to continue, it is important to relate with this part well.)

But of course, there is a link between the surface and the radius. If you increase one of them, the increase of the other should be possible to be calculated. So, I draw a section of this balloon as below:

The black arc in this sketch represents the surface section of our 3D balloon. It extends in –x and +x directions completing a circle. It has a radius R and there are 2 point objects; "A" and "B" standing on it. Since the radius is quite big, its center point (let’s call O) is not visible here but I guess you’ve got the picture.

This was showing what the static version of the balloon looks like. If this balloon would be expanding as explained above, after an amount of time we should have a scenario like the one below :

While the balloon is expanding, A and B would be following the paths shown with the red lines. Such a movement would increase the L distance to L’, balloon’s radius will increase from R to R’ and t - t’ amount of time will be passed.

We want to calculate the relation between R and L when one of them increases. So, in order to have a clear picture, let’s get rid of the unnecessary parts of this sketch:

“O” represents the center of our balloon. The distance between A and B increases when the balloon expands. We know the expansion rate of our universe today which is about 70 km/sec per each megaparsecs (3.26 million light years). This will correspond to increase of the distance between A and B in our model. If we could know how much the radius of the balloon has increased during this process, we could calculate the radius itself using the similar triangles method very easily.

For some reason, I wanted to set the speed which the radius increases to the speed of light, so I decided to try this value. If we insert all our values into our sketch, we get this:

This is showing what happens after 1 second of time while our balloon is expanding. Since its radius is increasing with speed of light, BB’ must be equal to 300.000 km. So, let’s calculate what is our radius represented by |OB| above. OAB and OA’B’ are similar triangles in the sketch. So we can write:

|A’B’| / |AB|=|OB’| / |OB|

(|AB| + 70) / |AB| = (|OB| + 300.000) / |OB|

1 + 70 / |AB| = 1 + 300.000 / R

R= 300.000 x |AB| / 70

R = 300.000 x (3.260.000 x 9,47376 x 10^12) / 70

70R= ~ 9,26534 x 10^24

R= ~ 1,323 x 10^23km

R= ~ 13,97 x 10^9 light year.

So our balloon has a 13,96 billion light year radius. If this radius is expanding with speed of light every moment, and if it has been the same since the beginning of the universe, it would take 13,97 years for it to expand to this radius value.

13,97 billion years…

I don’t know this was convincing for you or not, but reaching to a value which is really close to age of our universe after such a simple calculation using only the speed of light and expansion rate of the universe was too much of a coincidence for me. So, I have decided to pursue this idea and see where it leads. But before that, let’s try to find out if this model is consistent with our modern Physics theories.

First thing you can argue about the model can be; nothing with mass can travel with speed of light according to today’s Physics theories. We have used the analogy of us being 2 dimensional creatures on the surface of the balloon before, but this was actually only for easier understanding. The basic version of the model only includes space, speed of light and expansion of the universe. We didn’t introduce any concepts such as; mass, gravity, energy, force etc. yet. If you accept the fact that the only thing expands in the above scenario is space, then there is no contradiction. Because in modern Physics, there is no speed limit to how fast the space itself can move.

Another argument can be that; we don’t have any observational evidence about such physical motion around us. If the objects were moving with that speed, they would be infinitely length contracted and we would notice that. The answer to that is simple; everything is moving with the same speed in the same direction, therefore it is not possible to notice any relativistic effects. It is not so difficult to grasp that I guess.

You can also argue that there is no evidence in our current Physics theories that shows we are moving in such speed. I guess that is not true. I can show you something in front of us all the time but we were not seeing it this way:

Many of you probably know that the coordinates of any event in space-time is expressed as x, y, z, t in modern Physics . Space-time is a 4 dimensional environment and t represents the 4th spatial coordinate. But since x, y, z has a unit of distance, the “t” coordinate which has a unit of time, has to be converted into a spatial coordinate, as well. The conversion rate for this purpose is; -yes you guessed it correct- is the speed of light “c”. Since the speed of light has a unit of distance/time, when you multiply it with time (c*t), the remaining value has a unit of distance, as it is supposed to be. Therefore, the coordinate of an event is usually expressed as x, y, z, c*t. This also implies that; even if an object is stationary in x, y, z coordinates in space-time, after “t” amount of time it will cover a distance in 4th dimension direction which is equal to c*t.

Let’s keep that in mind for a second and go back to our model. What happens to an object in our above scenario when an object stands still on balloons surface? It will stand still on the surface but at the same time it will be dragged outwards while the balloons radius is increasing, right? And if we want to calculate the amount of this drag, we should multiply the time passed with the speed which our balloon’s radius expands. We have set this speed to the speed of light when we have calculated the age of the universe, so this distance should be equal to c*t, as well.

So, this shows that the way our current Physics models use to calculate the distance between 2 events in space-time is exactly the same way which I have used the above scenario. I think this is a quite interesting coincidence.

Even though it surprisingly complies with the current Physics theories, I still have many unexplained questions about the theory. One of them is; the sign of time. Time has an opposite sign compared to all other spatial coordinates in Physics. So, if you call spatial coordinates with a + sign, the time has a – sign or vice versa. In above model, the displacement of any object shall be calculated with; S^2=x^2 + y^2 + z^2 + (c*t)^2 whereas in Physics, it is calculated with; S^2= x^2 + y^2 + z^2 - (c*t)^2. It is very difficult for me to visually explain how this opposite sign works physically and it is probably the answer to many of my troubles but anyhow, I am still trying to figure out. Time will tell the answer.

Before finish, I would like to mention a little bit about how this model can be useful. When you try to explain things in a new model, one of the arguments of the Physicists usually is; “What does your model explain better than the current model does?” After trying to understand what happens when the objects move on surface of the balloon in such a universe model, I have reached to an explanation about motion based time dilation using simple Pythagorean Theorem calculations. I will not go into the details of it here not to make this already long post any longer. You can read more about this in my blog post here: https://erens.quora.com/1-Do-We-Travel-in-Time-Direction-With-Speed-Of-Light. In addition to that, I also tried to show how you can reach the basics of gravitational time dilation in this post: https://erens.quora.com/Gravitational-Time-Dilation-Due-to-Expansion-of-the-Universe-in-4th-Dimension.

Sorry this was quite a long post, but I have tried to be as clear as possible. It will be nice to discuss with anyone who gets interested.

P.S. I think the essence of this post fits into the Spatial Dimensions section better. But I saw that the description of Non Spatial Dimensions section includes the real universe subjects, so I have posted it here. Admin can move the thread where he/she feels it fits into, if that matters.