Introduction
Epstein's theory, while providing a valuable framework for understanding relativity, is described by Epstein himself as a good myth. This paper aims to address what I perceive as a contradiction in Epstein's explanation of the fourth dimension and length contraction, and to propose an alternative good myth that can explain the same phenomena.
Epstein's Myth
Epstein's theory posits that we are always moving with speed \( c \) through 4D spacetime. Hence we can imagine for our convenience a 2D plane and a perpendicular time axis. So an object stationary in space will be moving through time at speed \( c \). This can be thought of as a vertical vector. (see Figure 1)
When that object starts moving in its 2D space as well, the vector tilts a bit. Hence through that vector we can see that it is still moving through spacetime at speed c but the vertical component of that vector(along time axis) decreases and that results in the object moving through time slower. Also, the tilt of the object (from moving straight up in time to moving a little in space along with time) causes the rear end to be a little in the future and the front end to be in the past. This explains relativity of simultaneity. Also, the projection of this tilted object on the 2D plane will be shorter in the direction of tilt and this is what causes length contraction in the direction of motion.
According to this model, we always feel ourselves moving straight through time and others moving in space. And others feel they are straight and we are tilted in spacetime and hence are moving through space. Just like if we see a painting of a man and turn it sideways such that it appears shrunk to us, they haven’t really shrunk but their projection has. Whereas for them, they are straight and we are oblique. In relativity, this tilt occurs not in a spatial dimension but in the temporal dimension.
Epstein then explains as to why there are 3 dimensions of space and 1 dimension of time. Epstein's theory posits that we are always moving with speed c through 4D space, and that we experience length contraction in the direction of motion. This contraction, according to Epstein, renders the fourth dimension invisible to us, making it a ghost dimension or time dimension.
Critique of Epstein's Theory
While Epstein's theory provides an interesting perspective, it appears to be contradictory. It uses the fourth dimension to explain length contraction, and then uses that same length contraction to argue that the fourth dimension becomes infinitely contracted, leading us to perceive only three dimensions.
A Different Perspective on the Fourth Dimension
I propose that the fourth dimension should be thought of as perpendicular to the existing three dimensions, as per the definition of a dimension. Using the example of a 3D sphere, I suggest that the fourth dimension of this sphere would be an expanding/contracting sphere. This idea is supported by the novella Flatland, which describes a 4D hypersphere passing through a 3D universe as an expanding/contracting 3D sphere.
We can represent that expanding sphere with the imaginary unit \( i \) (i.e. \( \sqrt{-1} \)) because the physical interpretation of \( \sqrt{-1} \) is being perpendicular.
Even Einstein has mentioned this use of \( i \) in his Relativity book.
My Good Myth
The new theory suggests that we are 4D beings, with 3D spatial dimensions and a fourth dimension represented by the light emanating from us. This light, continuously expanding at speed \( c \), forms our existence in the fourth dimension.
Now, we are 3D people. How do we make ourselves understand that we are 4D people? When an object comes into existence in the universe. Light starts emanating from it and it continues as an expanding sphere outward. After the first layer of light there is the second then third and it goes on forever after the object has come into existence. Now far away when some part of that spherical light reaches some person, he perceives the first layer of light, then the second, etc. So, he perceives the past of that object (due to finiteness of speed of light).
So basically, we are 4-dimensional objects with 3D spatial dimensions and the light from us forever emanating. We can visualize it like this. There is a man waving. The light from his first move is moving straight ahead. then the light from his second move (dx amount different after first move) etc. So we get long stretching light waves in front of the man which is constantly getting longer and any slice in that will give the 3D equivalent of that person's waving of that time!
Implications for Relativity
The proposed model offers a unique perspective on the three fundamental effects of special relativity: time dilation, length contraction, and relativity of simultaneity. As per Epstein, all objects are moving with speed c through spacetime and the tilt of objects cause time dilation, length contraction and relativity of simultaneity. We will understand that this tilt is nothing but the perceiving of the 4D objects.
Time Dilation
The model suggests that time dilation arises from the difference in perceiving the rates of the emanating light waves. As a 3D object moves, the light waves are bunched up ahead and dispersed at the back. The object itself, unable to interpret its own 4th dimension (emanating light), experiences proper time. However, when these waves are perceived by others at different rates, time dilation occurs. This can be mathematically represented by integrating the ratio of the difference of two consecutive waves over a sphere or circle, yielding the Lorentz factor. For example, integrating the time dilations as per different orientations of a photon clock in a circle would involve an integral like this:
\[ \int \sqrt{c^2 - v^2 + 2vc\cos\theta} \, d\theta \]Length Contraction
According to the model, length contraction occurs due to the perception of the emanating light, which is considered as the projection of the object. As the object moves, the light waves bunch up ahead and disperse at the back, leading to a perceived contraction in the length of the object by others. This aligns with Epstein's explanation that the tilt of an object in the 4th dimension causes its projection to shorten.
Relativity of Simultaneity
The model explains the relativity of simultaneity by considering the distribution of the emanating light waves. As the rear end has things spread out and a more expanse of it is there, it is slightly in the future, while the front end, where things are bunched up, is in the past. (Note that the waves will be continuous.) This differential perception of time at different points of the object accounts for the relativity of simultaneity.
Also, just like for doppler effect in light where it doesn’t matter who is moving, even here it does not matter who is moving. Neither can we ever know it because we will always feel ourselves stationary and others moving. (The Doppler effect for light provides the explanation for this symmetry).
The model also agrees with Epstein's assertion that we are always moving in 4 dimensions with speed \( c \). This is because the light waves continuously emanating and expanding are moving at speed \( c \), which represents our movement in the 4th dimension. This interpretation provides a novel way of visualizing our existence in the 4-dimensional spacetime of relativity.
Extension: Mass and Spacetime Distortion
The concept of mass distorting spacetime has been traditionally understood in terms of curvature, but this paper offers a different perspective. Mass causes more space to be clumped together near it. For a person far away from a massive object, a given volume of space near the mass contains more space than the same volume would far from the mass. This means that near a massive object, there is effectively more space, leading light to take more time to travel which in turn leads to the perception that time is slowed down near the mass. This interpretation aligns with the previously discussed idea that time and light are synonymous.
This perspective also explains gravitational phenomena. Light moving near a massive object appears to slow down because, although the speed of light remains constant, it has to traverse more "space" near the mass. For an observer far away, this manifests as time dilation near the mass.
Additionally, gravity can be explained through this model. A light ray passing near Earth bends because the part of the ray closer to Earth traverses more space than the part further away. This differential in space traversed causes the light ray to bend, similar to Epstein's explanation of time dilation near masses (which says that time slows down near masses because of which the light bends).
An object left at some height above Earth will emanate light as it moves through time. However, because there is more space below and less space above, the light emanated will not form perfect spheres around the object. Instead, these light spheres will be skewed towards the bottom, resembling the shape described by the Doppler effect for a moving object. This skewing causes the object to be perceived in motion, leading to gravitational attraction.
Conclusion
While Epstein's theory provides a valuable starting point for understanding relativity, the author's critique and alternative explanation offer a new perspective on the fourth dimension and its implications for our understanding of length contraction and time dilation. This paper contributes to the ongoing discussion on the nature of the fourth dimension and invites further exploration of this fascinating topic.
We can extend this into quantum mechanics as well. The light waves emanating from the object is the past of the object (for another person perceiving those rays). And the object is the present. And within the object is the Future. Hence quantum mechanics is unpredictable because it is the future. And the collapse of the wave function is the present.
However, it proposes that light is synonymous with time, and hence if we say that light slows down near masses, then obviously time slows down. This suggests that general relativity cannot be further explained by saying that time is slowing down near masses. Since time is not independent of light anymore. Hence, to understand this, we can say that the density of space near mass has changed. This automatically leads to a change in time which then can be continued with regular general relativity explanations.