6. What Are the Evidences If We Are Moving In 4th Dimension Direction With The Speed Of Light?

Below post is a back-up of my posts in my Quora blog. I take a copy of them to here in case if something goes wrong in there.

(If you somehow have ended up on this page without any background knowledge, before continue, you better know that all below scenario is based on the idea that our universe is expanding in time -4th dimension- direction with the speed of light. You can check the previous 2 posts of: 1. Do We Travel in Time Direction With Speed Of Light and 2. Expansion of the Universe as Travel in Time Direction if you are willing to understand this concept)

I would like to note here some of the compliances that I have noticed between the modern Physics facts and this expansion model. (By the way, it is better to give this model a name, because I don’t know how to call it shortly, every time when I need to mention it. The model is about Expansion with the Speed Of Light in 4th Dimension. So, for easy reference, I guess ESOL from some of the first letters would be a good name for it. I will call the model with this name, from now on.)

1. Space-Time Metric:

ds² = (c*dt)² - (dx²+ dy²+ dz²)

According to Special Theory of Relativity, this is the way to find the distance between 2 events in space-time. It is a simple Pythagorean Theorem application. It takes the squares of the distances on x, y, x axes and makes it equal to the square of the total distance. It would be very simple if it was only limited to that. But you can also see the term c*dt here. Physicists explain that as a way of converting the time amount into a distance amount and therefore, c becomes a conversion factor between those 2.

With ESOL model, you don’t need that. It is still perfectly in compliance with that metric but in this model c is no longer a conversion factor but it is the speed of light, itself. If you are in motion in 4th dimension direction with the speed of light, how would you measure the distance that you have covered on that dimension direction? You would simply multiply your speed on that direction with the time you spent. This metric is exactly doing that. No need any modification.

P.S. With the little exception of that minus sign, of course. I don’t have the exact explanation for that, yet. I suspect that the answer lies in the i*c*dt form instead of c*dt but I am not sure about that, yet. So, I will pass that, for now.

2. Energy-Mass Equivalence:

Everybody knows E=mc² but not so many people know that this formula is only applicable in a special case. Specifically, to the objects which are at rest, which doesn’t move in any spatial dimensions relative to your reference point. Its general case is not as beautiful but more descriptive. It is:

E² = (m*c²)² + (p*c)²

In this form, the first m*c² term is for the resting objects potential energy and p*c term is the term for the moving objects kinetic energy. p is the momentum of the object, which means:

p = m * v

v is speed of the object in any spatial dimension. If we write it again in this form, we get:

E² = (m*c²)² + (m*v*c)²

According to ESOL model, we are moving in 4th dimension direction with the speed of light. In this case, even our resting position shall have a momentum, because it says we are in motion on 4th dimension direction. If that’s correct, then we should also be able to see it in above formula. And it is very easy if we write it in below form:

E² = (m*c*c)² + (m*v*c)²

Didn’t see it yet? Have a look now:

E² = (m*c*c)² + (m*v*c)²

The bold characters are showing our momentum. m*c term is our momentum on 4th dimension direction while the m*v term is our momentum in any of the other 3 spatial dimensions.

If we call those as Pp (potential) and Pk (kinetic), we can write our equation as:

E² = (Pp*c)² + (Pk*c)²

Interestingly, this is exactly the same energy-mass equivalence formula which is equal to;

E² = (m*c²)² + (p*c)²

3. Lorentz Factor:

I have already explained this one in detail, before. In short, if you assume that you are travelling in 4th dimension direction with the speed of light, when you move in any other spatial dimension, that will cause a new combined speed which will be greater than the speed of light. According to special theory of relativity, that is not possible. So, I have assumed that your motion in any spatial dimension direction shall cause your speed on 4th dimension direction to decrease, as much as keeping your new combined speed exactly at c. The rate of that decrease can be calculated easily and the result will be found equal to the Lorentz Factor. You can find the longer explanation here: 1. Do We Travel in Time Direction With Speed Of Light?

4. Hubble Constant:

This was also comprehensively explained here before. As a summary, if the universe has a 4D hypersphere geometry and if its diameter is expanding with the speed of light, the 3D surface of that 4D hypersphere will also be stretching with a rate. I have assumed that this stretching rate shall be equal to the Hubble constant for my model to be valid. If that’s true, then I should be able to calculate the radius of our universe using the expansion rate of the radius and stretching rate of the surface. Expansion rate of the radius shall be equal to the speed of light as per this model and the surface stretching rate shall be the Hubble Constant, as I mentioned. When I did that, I found that the radius of our 4D hypersphere universe shall be about 14 billion light years, which seems to be true according to our current knowledge. You can read about it in detail, here: 2. Expansion of the Universe as Travel in Time Direction

5. Gravitational Time Dilation:

ESOL model also has a potential to explain the cause of gravitational time dilation. You can read it in detail here.

If I will find any other compliances, I will add them here, in future.

5. Is Our 3D Space an Infinitely Length Contracted 4D space?

Below post is a back-up of my posts in my Quora blog. I take a copy of them to here in case if something goes wrong in there.

(If you somehow have ended up on this page without any background knowledge, before continue, you better know that all below scenario is based on the idea that our universe is expanding in time -4th dimension- direction with speed of light. You can check the previous 2 posts of: 1. Do We Travel in Time Direction With Speed Of Light and 2. Expansion of the Universe as Travel in Time Direction if you are willing to understand this concept)

One of my biggest bemusements about “travelling in a 4D universe with the speed of light” idea for me was; what would be the consequence on the objects which travel with that speed. I guess, I finally have an opinion and it is actually pretty simple.

As we usually do, in order to figure out what will happen in any 4D case, we can have a look at its analogue in 3D and try to apply the same logic to our 4D scenario. In this case, we should first understand what is happening in 3D.

In wikipedia description of the Length contraction it says;

Length contraction is the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any non-zero velocity relative to the object.

and futher it adds;

Length contraction is only in the direction parallel to the direction in which the observed body is travelling.

So, when an object is in motion, the observers outside of its reference frame sees that it gets shortened on its travel direction. But at the same time, since everything is relative to each other, the object which is in motion observes the other objects in its rest frame are being length contracted while not observing any length contraction on its own body. The travelling object also sees that the length contraction of the other objects is only happening on its travel direction.

The amount of the length contraction can be found by using the formula:

where;

L0 is the proper length (the length of the object in its rest frame),

L is the length observed by an observer in relative motion with respect to the object,

v is the relative velocity between the observer and the moving object,

c is the speed of light,

So, all you need is to know the proper length and the velocity of an object. If you insert your velocity same as the speed of light into the formula, contracted length becomes “zero”. If you want, you can interpret this as; an object which travels with the speed of light, will be infinitely length contracted and its length on its travel direction will become zero for other observers (the ones in its rest frame). Meaning, our 3D objects will turn into 2D objects for the observers in its rest frame.

More interestingly, as I wrote above, the object in motion will also see all the other objects around it (the ones in its rest frame) as infinitely length contracted. We can also interpret that as; for an object which travels in 3D space with the speed of light, the space around and everything else in its rest frame will be infinitely length contracted on its travel direction and it will become a 2D universe for that traveler.

Now we have everything that we need to know to investigate our 4D case. The most important thing to consider is:

Length contraction is only in the direction parallel to the direction in which the observed body is travelling.

With that feature, comes our conclusion;

In a 4D universe, if any object is in motion with the speed of light, all the universe will be infinitely length contracted in its travel direction and will turn into a 3D universe for that traveler.

I am not a physicist but am pretty sure that this conclusion is not against the Relativity Theory (Except the fact that any object with mass cannot travel with the speed of light. That can be true for a 3D universe but can be different for a 4D universe model, I am not so sure). And if that’s true, there is no way for us to tell if we are living in a (3D only) universe or travelling in a 4D universe with the speed of light, therefore observing it as a 3D one. I put this conclusion in my pocket in favor of this universe model for now. Just wanted to note it here for the record.

Gravitational Time Dilation Due to Expansion of the Universe in 4th Dimension

Below post is a back-up of my posts in my Quora blog. I take a copy of them to here in case if something goes wrong in there.

(If you somehow have ended up on this page without any background knowledge, before continue, you better know that all below scenario is based on the idea that our universe is expanding in time -4th dimension- direction with speed of light. You can check the previous 2 posts of: 1. Do We Travel in Time Direction With Speed Of Light and 2. Expansion of the Universe as Travel in Time Direction if you are willing to understand this concept)

In previous posts, I have tried to explain a model which our universe expands with the speed of light in the 4th dimension direction and the speed of light was the universal speed limit. In that universe, within 3 spatial dimensions, we can only observe the stretching of the universe which we call the expansion today, while the real expansion is happening in time direction with the speed of light. We did not have any other knowledge in our hand except that the gravity is the dominant force in galaxies and universe doesn’t expand according to our observations where the gravity is dominant. But as I said; the expansion which they call today, corresponds to stretching in our expanding universe model. Now, we will apply this idea to our universe model and see what happens.

Do you remember below graph from the 2nd post?

We have used this graph to explain how the distance between objects increases while they travel in time direction. We have called them objects but we did not give them any feature like mass or gravity since we didn’t know about the basics of such concepts. Calling those points as objects was nothing more than calling them “things”.

If we want to understand the basics of any idea, we need to go deep down to its lowest level, to its simplest form. And a point is the simplest form that we can define in our universe. It has 0 dimensions. No width, no length and no height. Even its existence is a miracle under such conditions. But they are the most useful tools for thought experiments like ours and we will use them as our base. So our A, B, C objects are our points, the smallest parts of our universe. Remember that they don’t have any mass or size yet.

I will not claim yet that I know what the cause of the expansion is and what is happening to the structure of the universe during that expansion. What I know is; all the points must spread away from a center towards every direction during an expansion (if the fabric of space is made of points, of course. If it is wave based, then it is another scenario. But I am only capable of dealing with points; therefore I will proceed with them). We will build our gravitational time dilation mechanism on this idea.

Now we can proceed. Let’s go back to the idea of gravity being dominant within the galaxies and universe is not expanding there. We don’t know what is gravity or mass but we can simply fit this idea into our model like that: If universe is not expanding (actually not stretching) where the gravity is dominant; it means that; the distance between the points in that region of the universe does not increase. That means, the points in that region are travelling with the speed of light on time direction with a fixed distance from each other as below:

This is very similar to our previous graph. We have 2 points which we call A and B on their blue observable 1D universe while that universe is expanding on time direction with speed of light which is indicated with the red arrows. This time, there is one difference, though. Instead of keep following their routes, A and B points somehow keep the distance between them and expand towards the black arrows direction instead of the red ones, just as the matter would do where the gravity is dominant in our universe. This is the only feature we can appoint to matter right now since we don’t know any other features of it. And this feature results a slight deviation from the previous route of our points.

After t’-t amount of time, A point reaches to A’’ instead of A’ and B point reaches to B’’ instead of B’. We don’t know what did cause them to move together or what the distance from each other was when they have started their joint movement first. But one thing we know for sure; the stretching rate of our universe. That means, 2 points with 1 mega parsec distance from each other should move apart on x direction by ~70,8 km after 1 second. If we assume 2 points with that much of distance apart from each other starts to move keeping their distance between them fixed, we can check what will happen to their speed in time direction. If |BB’’| is longer than |BB’|, covering that distance in 1 second will mean that they are travelling faster than the speed of light which is not possible. So their speed in 4th dimension direction should decrease accordingly to keep that speed within the speed of light limit.

In order to calculate |BB’’|, we can neglect the curvature of our universe (green arc) and treat our BB’B’’ shape as a right triangle and use Pythagorean Theorem since the curvature will be very small considering size of the universe:

|BB’’|² = |BB’|² + |B’B’’|²

|BB’’|² = 299792,458² + 35,4²

|BB’’| =~ 299792,460 km

It is a very small difference (about 2 m/sec) but it anyway exceeds the speed of light. Therefore, our objects must be subjected to a time dilation and relative to other points in the universe which doesn’t jointly move, their 1 second shall be different than the others. If we wanted to find the amount of time dilation we could simply divide |BB’’| to |BB’’’|. We will come to that soon, but first let’s take a broader look on where we are right now.

As a summary; our points were first supposed to end up on A’ and B’, then they have started to move jointly and they were supposed to end up on A’’ and B’’, then they have been subjected to a time dilation due to their joint speed and they have ended up on A’’’ and B’’’. Final status is something like in the below sketch.

Now, we are sure that there must be a time dilation. But this calculation is only based on the points which are 1 MegaParsec apart from each other. What if our points had a different distance between them? It is better to leave that distance as a variable and write a formula for the amount of time dilation depending on the distance between 2 points. In order to do that, let’s find out a formula where our previous 35,4 km |B’B’’| figure is the variable L distance between 2 points.

|B’B’’| = (Expansion Rate /2) x L / 1 Megaparsec

|B’B’’| = 35,4 x L / 3,1 x 10^19

|B’B’’| =~ 1,47 x (10^-18) x L

Now we know the length of |B’B’’| as a function of L. So, we can calculate |BB’’| from Pythagorean Theorem and reach to time dilation amount after that.

|BB’’|² = |BB’|² + |B’B’’|²

|BB’’|² = 299792,458² + (1,47 x (10^-18) x L)²

|BB’’| = (299792,458² + 1,3152 x 10-36 x L²)^(1/2)

And the time dilation shall be calculated as:

t’/t’’’ = |BB’’| / |BB’’’|

t’/t’’’ =~ (299792,458² + 1,3152 x 10-36 x L²)^(1/2) / 292792,458

As a summary, our A and B points which were travelling in time direction with speed of light on their own routes were supposed to end up on A’ and B’ locations after 1 second due to expansion of the universe in 4th dimension direction. But instead of following their routes defined by the expansion, they somehow have started to keep their distance between them and started to follow a new joint route. That should have cause them to end up on A’’ and B’’. But to reach A’’ and B’’ in 1 second, they should be travelling with a little bit more than the speed of light. So instead, their speed in new joint direction have decreased to speed of light and caused a time dilation.

Our formula shows us that; if the L between 2 points is not a big amount, the time dilation effect will be really, really small. In order to have a considerable gravitational time dilation effect, there should be a lot of joint points moving together on the same direction at the same time. Since I don’t know any details about the structure of space or the finest elements of the matter, I will not attempt any calculation on the gravitational time dilation effects of such bigger structures. It should be also noted that since the above formula is only related with the distance between points, it means it only deals with the density of 2 space points. To see the gravitational time dilation effects on multiple jointly moving points, the formulation shall be improved to deal with more than 2 points. I suspect that the effect will not be increasing linearly with the number of points but will probably be increasing exponentially. Anyway, I will not go into that detail right now.

What I have tried to explain in this post was; how the gravitational time dilation concept can be achieved in our expanding universe model with a simple idea like jointly moving points. It is also possible to reach the concept of gravity with jointly moving points idea based on the same model and the next post will probably be about that subject if I can warp my head around it well.