Special Relativity
and
Space Deformation
Han Erim
29 October 2009
Revised on 16 November 2009 and 10 October 2010
Space deformation is one of the newest topics I have been working on. After my work on Ghost and Pınar, it became inevitable for me to focus on this subject. I was expecting an interesting result, but I was truly surprised by what came out.
Nature is three-dimensional, and the images that reach us come from three dimensions. In other words, our field of view has depth. In the Ghost and Pınar section, if the reference frames are in motion, the real position of an object (Pınar) is different from the position we see (Ghost).
If we combine this effect with the three-dimensional structure of nature, we obtain a perception that we may call “Space Deformation”. Space deformation consists of the deformations on the Ghosts we see. Now let us see how this deformation arises.
Flash
In the Alice Law Version 6 book I used a train. Here,
instead of a train, we have a city. The observer on the right is looking
towards the city. To understand how space deformation occurs, we need to
think about how the image of the city reaches the observer.
In the animation, we see an image packet (wagon) that starts empty from the farthest point of the city. Along its path, the packet collects the images that newly set out from the point it is currently passing and, at the end of its journey, reaches the observer. I called this situation “brotherhood of electromagnetic waves”. In the animation, the electromagnetic waves are represented by photon figures wearing caps. We see that within the same packet there are many electromagnetic waves that set out at different times and from different distances. This image packet, together with all its content, reaches the observer at a single instant and as a single packet. When the packet reaches the observer, the observer interprets this image packet and reconstructs the image of the city in his or her mind.
We saw in the Ghost and Pınar section where the observer would see the GHOST. In order to understand space deformation, we will perform this calculation for each photon inside the packet. Each photon will represent a specific part of the ghost and form a portion of it. If, as a result, the resulting GHOST image is different from PINAR, then SPACE DEFORMATION has occurred. In our example here, since the Observer and the City are at rest with respect to each other, the Ghost and Pınar will overlap. That is, there is no deformation.
However, if they were in motion relative to each other, a deformation would occur on the Ghost image seen by the observer. If, for each photon that sets out, we show in our animation where the ghost belonging to that photon appears, we will also see how space deformation takes place.
In the animation, we see an image packet (wagon) that starts empty from the farthest point of the city. Along its path, the packet collects the images that newly set out from the point it is currently passing and, at the end of its journey, reaches the observer. I called this situation “brotherhood of electromagnetic waves”. In the animation, the electromagnetic waves are represented by photon figures wearing caps. We see that within the same packet there are many electromagnetic waves that set out at different times and from different distances. This image packet, together with all its content, reaches the observer at a single instant and as a single packet. When the packet reaches the observer, the observer interprets this image packet and reconstructs the image of the city in his or her mind.
We saw in the Ghost and Pınar section where the observer would see the GHOST. In order to understand space deformation, we will perform this calculation for each photon inside the packet. Each photon will represent a specific part of the ghost and form a portion of it. If, as a result, the resulting GHOST image is different from PINAR, then SPACE DEFORMATION has occurred. In our example here, since the Observer and the City are at rest with respect to each other, the Ghost and Pınar will overlap. That is, there is no deformation.
However, if they were in motion relative to each other, a deformation would occur on the Ghost image seen by the observer. If, for each photon that sets out, we show in our animation where the ghost belonging to that photon appears, we will also see how space deformation takes place.
Flash
In the animation above, which shows space deformation,
I used only two points for the photons — the front and the back of the
city. When a photon that sets out from the back of the city reaches the
front of the city, it forms an image packet together with another photon
that sets out from the front at that instant, and both photons reach the
observer together.
Since each photon pair that reaches the observer determines where the front and the back of the Ghost will be, the ghost of the city, for the observer, will lie between these two points.
Notice that the image packet travels across the field of the observer. If the observer is in motion, the (c+v)(c−v) mathematics naturally arises, and the time it takes for a photon starting from the back of the city to reach the front of the city changes. It is precisely this change that leads the observer to perceive the dimensions of the city differently.
Space deformation is an effect that occurs along the direction of motion. It takes place in the form of space expansion or space contraction. We can write a rule on this subject.
Rule: Objects in motion will see the region of space in front of them stretching in depth, and the region of space behind them compressed in depth.
I would also like to answer the question: what can be the magnitude of space deformation? If the observer is moving towards the object being seen, the (c−v) mathematics will arise, and if the observer approaches the object with a speed very close to c (the speed of light), the time it takes for the photon starting from the back of the city to match with the photon starting from the front will become very long. In other words, in this case the amount of space expansion tends to infinity.
If the observer is moving away from the object, the (c+v) mathematics will arise, and if the observer is receding with a speed very close to the speed of light, then the matching time of the photons will become progressively shorter. As a result, the amount of space contraction approaches half of the original size. Space contraction can at most be half of the original dimension.
I said that space deformation is a matter of perception. However, since we have to live in nature as we perceive it, space deformation also represents a major reality. Especially when very high speeds are involved, the magnitude of the deformation increases significantly, and an observer in such an environment will find himself or herself in a space that is very different from normal. The effect of space deformation is always present — more or less depending on speed — whenever we are in motion.
The two graphs that follow show how we can calculate space deformation. The first is for (c−v) and the second is for (c+v).
Since each photon pair that reaches the observer determines where the front and the back of the Ghost will be, the ghost of the city, for the observer, will lie between these two points.
Notice that the image packet travels across the field of the observer. If the observer is in motion, the (c+v)(c−v) mathematics naturally arises, and the time it takes for a photon starting from the back of the city to reach the front of the city changes. It is precisely this change that leads the observer to perceive the dimensions of the city differently.
Space deformation is an effect that occurs along the direction of motion. It takes place in the form of space expansion or space contraction. We can write a rule on this subject.
Rule: Objects in motion will see the region of space in front of them stretching in depth, and the region of space behind them compressed in depth.
I would also like to answer the question: what can be the magnitude of space deformation? If the observer is moving towards the object being seen, the (c−v) mathematics will arise, and if the observer approaches the object with a speed very close to c (the speed of light), the time it takes for the photon starting from the back of the city to match with the photon starting from the front will become very long. In other words, in this case the amount of space expansion tends to infinity.
If the observer is moving away from the object, the (c+v) mathematics will arise, and if the observer is receding with a speed very close to the speed of light, then the matching time of the photons will become progressively shorter. As a result, the amount of space contraction approaches half of the original size. Space contraction can at most be half of the original dimension.
I said that space deformation is a matter of perception. However, since we have to live in nature as we perceive it, space deformation also represents a major reality. Especially when very high speeds are involved, the magnitude of the deformation increases significantly, and an observer in such an environment will find himself or herself in a space that is very different from normal. The effect of space deformation is always present — more or less depending on speed — whenever we are in motion.
The two graphs that follow show how we can calculate space deformation. The first is for (c−v) and the second is for (c+v).
Flash
Flash
Space deformation is another important result shown to
us by the (c+v)(c−v) mathematics. The amount of space deformation on the
Ghost is calculated according to the following equation: deformed
dimension = original dimension · c /(c±v)
Appendix (10 October 2010)
When I finished writing Alice Law Version 6, I had not yet recognized the direct relationship between the Doppler Effect and Alice Law. My work on the Doppler Effect has revealed its relationship with space deformation as well. The existence of the Doppler Effect means that space deformation occurs. I have published two studies on this subject.
DOPPLER EFFECT and SPECIAL RELATIVITY
THE RELATIONSHIP BETWEEN THE DOPPLER EFFECT AND SPECIAL RELATIVITY. ERIM EQUATIONS
Link