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.
