Dimensional Physics
Everything consists of space-time.
Everything consists of space-time.
The SR is based on only two principles
That sounds very simple. It is. Nevertheless, we will have to look at things here contrary to the textbook approach. With the DP, we have shifted an important aspect for the principle of relativity. It appears that a spacetime density and thus also the state of motion have an “absolute” value. We will see that this is not the case. However, there is information of smaller and larger between motion states. According to the textbook approach of the principle of relativity, this is not allowed. Every object can be considered at rest and there must be no smaller or larger. Even the word “motion state” is not correct there. This always depends on the chosen reference system. You cannot clearly assign a state to an object in motion. But that’s exactly what we’re going to do. To top it all off, we will necessarily create the principle of relativity for everything that exists in the universe from it. Sounds exciting, doesn’t it?
The counterargument of the Lorentz ether theory always comes up. It is important to note that we never use an ether. There is only spacetime. An additional ether in any form is explicitly prohibited by the DP. A suitable idea from the DP is that spacetime and the ether are a single identity
We have already shown in the previous chapter that the speed of light is the maximum speed. But that is not enough. It must also be shown why this limit is locally identical for every observer. If there is a smaller and a larger limit, then we can determine who is closer to the space-time limit, right? No, we can’t. This has nothing to do with the fact that the speed of light is defined identically for all observers. Once again, this is because all deformations of space-time are a change in the definition of geometry.
We are taking the classic route here. We start with Galileo and move on to Newton, Maxwell and Lorentz to Einstein. We will then see that Einstein did everything right by combining the speed of light and the principle of relativity, but also allowed himself a great deal of fun. This is often not recognized. But it is essential for us. Therefore, we will look at the sequence of developments in more detail. I realize that this section can be a bit tedious for the “initiated”. Please read it anyway. I am curious to see if you were already aware of this insight. Most people overlook it and jump straight to the calculations. But then you have not discovered the fun part of the SR.
Galileo is often regarded as the father of modern physics. For us, Galileo introduced the most important thought experiment into physics, the locked box. We need it in the SR without and in the GR with interaction. That was Galileo’s basic idea of the relativity principle. For him, the locked box was a ship’s cabin without the possibility of seeing outside. The whole thing on a very calm flowing water. In Einstein’s later work, it was a lift or a spaceship. Everyone is a child of their time.
If we are sitting in such a ship’s cabin, we cannot determine whether we are moving with the water or standing still. A reference system or point is missing to determine the movement. From this it is deduced that movement can only be determined relative to a reference point. We extend the thought experiment with two boxes that only have a small viewing slit. Nothing other than the boxes themselves cannot be seen.
Figure 21 shows two closed boxes with a “peephole”. There is no other reference point.
If we sit in a box and look out, we can see the other box passing by our box at a constant speed. If we cannot feel any acceleration, then we cannot determine for ourselves whether we are moving and the other is at rest or vice versa. It could also be that both boxes are moving at different speeds and no one is at rest. The only recognizable quantity is the difference in motion between the two boxes. We can only determine the relative motion of the boxes to each other. Both boxes could also move in the same direction at the same speed, in which case we would not detect any motion between the boxes. This is the result of the relativity principle.
A transformation is always part of a relativity principle. This is the change of perspective from one box to the other. This is called the Galileo transformation.
The principle of relativity is so simple and logically clear that Newton used it as the basis for his description of physics. Newton coined the term ‘inertial system’ here. This is not subject to acceleration and is therefore at rest or in a uniform and straight motion. This means that every inertial system is suitable as a reference system for determining relative motion. In particular, Newton’s axioms only apply in an inertial system. The crucial thing for us about Newton’s statement is that an inertial system can be at rest or in a rectilinear uniform motion. These are indistinguishable.
After Newton, the world was in order for about 200 years. Until James Clerk Maxwell came along. He achieved a similar feat to Newton. Newton combined all the individual loose ideas into classical mechanics in a single, almost completely consistent theory. Maxwell did the same with the individual parts of the description of electricity and magnetism, and with electrodynamics he also delivered an almost completely consistent theory.
However, this has given rise to a problem that we are familiar with. The two major theories, which were supposed to describe all of physics at the time, did not fit together in some places. Somehow, over time, the problems keep repeating themselves. We will pick out two important points.
The problem with the description is that \epsilon_0 is the electric field constant and \mu_0 is the magnetic field constant, both of which are unchangeable natural constants. This is independent of the state of motion. Then c must also be an unchangeable natural constant. The speed of light must always be the same, regardless of the reference system. All natural constants must be identical in every reference system. These reference systems were still inertial systems. This allowed them to move in a uniform and rectilinear manner. How can the speed of light remain the same if it is observed from an already moving inertial system?
At that time, Newton was the demigod of physics. Therefore, a solution was sought that had to match Newton’s description. The solution was the ether. It was already known that light is an electromagnetic wave. So this wave description had to have a medium. Like waves in water or sound in air. This medium for the propagation and excitation of electromagnetic waves is said to be the ether. Thus, the speed of light has this absolute and fixed value of speed only with respect to the ether. Galileo’s principle of relativity would thus be saved.
It was recognized early on that this ether must have very strange properties for all this to work. In addition, this ether could not be detected in any experiment. In particular, the experiment by Michelson and Morley in 1881 and 1887 caused a great deal of trouble for an ether theory. The purpose of the experiment was to find an ether by observing the movement of the earth through the ether. The result was negative and has remained so to this day.
Lorentz then came to the rescue of the ether for this experiment. A new transformation was developed, the Lorentz transformation. This is constructed in such a way that the existence of an ether is compatible with the Michelson-Morley experiment. However, for this to be the case, a length had to be shorter and time had to be slower in the direction of motion. Length contraction and time dilation were already known as mathematical facts before the SR. For Lorentz, length contraction only existed in the electromagnetic field (ether) and time dilation was a pure mathematical tool.
Purely mathematically, Lorentz had found a solution. Now comes the joke. This has been developed for an ether theory. This means that the Lorentz transformation only works with an absolute zero point and the associated absolute speed. That should be clear. If an absolute speed is assumed, then there must be an absolute zero point. Here, everything is in relation to an ether.
But now finally to our joker. Einstein made the following assumptions when developing the ST, in my opinion:
These points are sufficient to arrive at the SR. We can use them to build the following logic:
This almost gives you the SR. For a proper justification of the length contraction and time dilation of space-time, which was a very bold assumption at Einstein’s time, Einstein argued a lot with the simultaneity in space-time. Or rather, with the no longer existing simultaneity. To do that, he had to make an additional assumption that was not there before. The speed of light is not only constant, but also maximal. According to Maxwell, c is simply constant for electromagnetic waves. For Einstein, this now had to be the maximum for any effect in space-time. Only with this extension does SR result. Therefore, this condition looks like a “foreign body” in the theory for many.
Due to the maximum speed, there can no longer be simultaneity for an effect from one point in space-time to another. The effect always requires time between the space-time points. If there is a length contraction and a time dilation between these space-time points, this becomes more and more visible. We will soon set up a different approach that is better suited to DP and avoids the discussion of simultaneity for length contraction and time dilation.
Ok, so much for the historical digression. What’s the joke now?
If we follow this logic, then, in my opinion, we do not see the joke of it. The same applies to the argument with simultaneity, which we will not pursue further here. But that is exactly how it is explained in the textbooks. That is why almost no one notices. Einstein did not just change Galileo’s old principle of relativity. He built a completely different principle of relativity. The basic assumptions of the Galileo transformation and the Lorentz transformation are mutually exclusive.
No problem, then Einstein is right and Galileo is not. Unfortunately, this is not so easy in DP. We will build a third concept as an argument for a principle of relativity. This follows more the assumptions of Galileo and Newton. However, Einstein must also be right, although the approaches are mutually exclusive. The SR has been flawless in all calculations of the experiments for 120 years. It cannot be wrong. The different approaches to relativity must be mathematically identical under certain circumstances. This feat is only possible because all deformations of space-time are a change in the definition of space-time geometry.
Let’s ask a simple question again: Why is there a principle of relativity? We had already discussed this with the boxes. It’s so simple, why even discuss it? If you don’t understand this, you don’t need to bother with the SR. That’s exactly the problem. Everyone understands the logic with the boxes. The mathematics for this is simple and we’ll start with the calculations. That’s why the fundamental question is never asked. Now I’m going to make a bold statement. When we look at different textbooks on the SR, it is clear to me that almost no one has understood the actual idea behind the principle of relativity.
Let’s address the fundamental question. The approach comes from the example with the boxes. A relativity principle only arises if we can only determine differences between objects (boxes). We expand this statement in a very general way. This is not only the case at speeds. This is a general problem of measurement. We move away from speed and do this for length. Then the examples become a bit simpler.
We can make a measurement if we have at least two measuring points. With a length, this is clear to us. With one measuring point, we cannot determine a length. But neither can we determine a speed or an electrical charge. The second measuring point is just not always immediately clear to us. The other measuring point is often the zero point. However, this can also be a maximum value. It does not matter whether we take a measurement at a maximum or minimum value. To specify a value, we always need two measuring points. A measurement is a comparison. For us, this was the two boxes. Then we can measure a difference.
We want to give an absolute value. This is a value that must not change for any observer. Then we need an identical measuring point for all observers. Intuitively, we always equate this with the origin. This means that as soon as we can define a general reference point for the measurement that is common to all observers, a relativity principle is no longer possible. This is important for the ST. We may agree on the measured value of a difference. We call this an invariant quantity. However, the measuring points that led to this invariant quantity must not be “invariant” themselves. These must then be explicitly different, otherwise we do not get a relativity principle.
The fundamental question now formulated differently: When can we only determine a difference? To put it bluntly, when we have lost our zero point. It is not possible for us to give an absolute value if we cannot give a generally valid reference point. Then a relativity principle is inevitable. The only information that can be given are differences. With this idea in mind, we will go through our variants again (and I promise, this is the last time). After that, we will build the new idea for the relativity principle for the DP.
Newton and Galileo agreed on the principle of relativity. We stick with good old Newton. Based on the definition of his axioms, we see Newton’s view as the best for the Galileo transformation. An inertial system is either at rest or in a rectilinear uniform motion.
Both states of motion are explicitly mentioned there, and in particular, rest is listed separately. This means that we have a point of origin and there can be no principle of relativity. What is the error in reasoning here? The word “or” is not simply a list. This “or” is to be understood in such a way that the two states of rest and rectilinear uniform motion are indistinguishable. It can be one or the other, since we cannot distinguish the states of motion. That was the approach with the boxes. We cannot determine whether we are moving or not. This means that we cannot determine one thing, the zero point. A relativity principle follows.
A minimum value is not given. What about a maximum value? The two probably agreed on that too. In their time, no one thought about a maximum value for a speed. This means that there is no general reference point.
If we take this as an image, this is what emerges.
Figure 22 shows two lengths for which the zero point is not recognizable.
We have two lengths. However, we cannot determine the absolute values of the lengths. The only recognizable features are the two red edges. We get a difference. In order to assign a value to this difference, we simply set the origin (at a speed of rest, this is rest) on one of the red edges. We can set the origin arbitrarily purely from a mathematical point of view. We do not know the “real” origin. Intuitively, we choose one of the edges. It is also important for us that this difference is necessarily symmetrical. So far, everything should be clear. I also assume that many people have understood this as we have described it. In the next section, it looks different.
What did Einstein do that I think of him as such a joker and make my daring statement about understanding SRT? His two principles are:
The two principles are mutually exclusive. That is what I meant, that the Galileo and Lorenz transformations do not agree on basic assumptions.
We can also see this very well at another point. In the Galileo transformation, the boxes may be at rest or in rectilinear uniform motion. Just an inertial system. But rest has been thrown out because we cannot determine it. For Einstein, every box must be a system at rest. Each box sits on an absolute reference point, each for itself. If anyone ever comes across a textbook that even begins to address this line of argument, please let me know.
This immediately raises the crucial question: how does the SR work at all? It can never result in a principle of relativity. But it does, only not in the way that anyone would imagine. In the two theories of relativity, fundamentally different things are compared with each other. But no one comes up with it. The line of argument in the textbooks is always first Galileo and then this relativity principle, modified by Einstein, to the SR. Here I am also not sure whether this difference was recognized by Einstein himself. By this approach, we simply transfer the idea of Galileo’s relativity principle to the SR. This approach is wrong. To clarify this, we have to do what? Exactly, ask the next fundamental question.
What kind of objects are compared in Galileo’s principle of relativity? First of all, our two boxes. The boxes in relation to what? Only to themselves, since we have lost the reference point. The reference point in relation to what? The surrounding space. We can only speak of space with Galileo and Newton. A space-time with a dynamic definition of length and time was not yet known here. In general, this means that we compare the different objects in identical space. That is clear to everyone, what else could it be? This unquestioned basic structure is now transferred to the SR. As we have learned from the two principles, the SR cannot do this. The SR must do something different.
I’ll spare you the next round of questions and just give you the answer. The SR is still a relativity principle. These objects must compare. But these are not our boxes in a spacetime. The SR compares spacetimes, which are each assigned to a box.
Can we create a relativity principle between spacetimes? Let’s take a look at a comparison according to the SR.
Figure 23 shows two lengths with an identical end point (speed of light) and different start points (rest)
Here we see two lengths again. Both start from zero with a different length in relation to each other. Both lengths start from zero in their space-time. Then we still need the end point, the speed of light. This must be identical for all. Otherwise, a comparison is not possible with different geometries.
Figure 24 shows two lengths with an identical end point (speed of light) and different start points (rest) with the measurement divisions
For this, a different length scale must be chosen at B. The number of scales must be the same in both cases. From zero to the speed of light should be the same for everyone. This comparison is symmetrical again. We could set the rest system at A and at B. Thus A and B can each be an absolute value in space-time A and B. That’s not a problem. No comparison is made in the respective space-time. The space-times A and B are compared. We see that the relativity principle also works between differently defined space-times.
Then our condition, no reference point, must work for the space-times themselves and not just for an object in the space-time. The space-times in relation to each other must not have an absolute reference value. To do this, let’s look at the structure of a normal space-time diagram.
Figure 25 shows various possibilities for a movement in a space-time.
Let’s look at the possibilities:
In all cases, we are moving, even if only in time or only in space. What does not exist explicitly for a space-time is rest. Even if there is no object in the space-time and only the space-time itself would be present, time passes. This is also a movement in the mathematics of the SR. A space-time as an independent object does not know a state of rest. Fortunately, we have lost our way again. Within space-time, we simply set a point of rest and generate absolute values. This is not possible for space-time itself.
But what about a maximum speed? We do have the speed of light. Yes, but it is now absolutely necessary for a comparison to be possible at all. If both space-times have different geometries, there must be a common reference point for a comparison. Otherwise we could not even specify a difference.
For spacetimes, we can only define a reference point, the speed of light, and obtain a genuine principle of relativity between spacetimes, due to variable geometry in spacetime. That is the ST. With that, we can solve several problems at once. We can use it to explain why the twin paradox is so difficult for the SR, which we will do in 4.7. We can clarify a point that I have called cherry picking, which we will do in 4.6. We can explain why the SR fits better with QFT than with GR, in 4.8. We will see that with this interpretation, the SR really makes sense.
Before all these points can be resolved, we need to approach it differently, then these solutions will become even clearer. We first have to build the new view of the DP. This should combine Galileo’s relativity principle, everything in one spacetime, and Einstein’s relativity principle, comparison of spacetimes. We have compiled all the necessary components for this in 4.2.
We do not introduce a new name for this variant of SR. The old variant according to Galileo and Newton is simply the principle of relativity. The variant according to Einstein is SR and we have now realized that this is indeed very special. For our new variant, we simply stick with the name SR. Since SR is mathematically identical in both variants, we do not need new names.
What do we want? We want a comparison of two objects in a spacetime. Because that’s what we actually mean when we speak of a principle of relativity (Galileo). Then we have to be able to deal with different geometries of spacetime in a single spacetime, without the need for an absolute value. As mentioned at the beginning, we do this with our spacetime density. This must contain all the required properties from both variants. Sounds very difficult again, but it’s easy. We have already incorporated this through our approach. We do not distinguish between stage and actor. A space-time density is always space-time itself. Thus, the property only has to be present, then it is automatically present in both variants. We can also divide the variants differently. In Galileo, the actors on a stage are compared. In Einstein, the stages are compared. We no longer recognize this difference.
What makes life easy for us now is that a space-time density is always energy, geometry and state of motion in one.
If we want to compare two space-time densities, there must be no zero point for a space-time density. We have covered this in detail in chapter 3. There can be no space-time density of zero. Otherwise, the point in space-time is not present in the space-time. That’s all we need to know for this section. By definition, there can be no zero point for a space-time density.
At a higher momentum, we have more space-time density. I can relate this to the speed of light. The limit for the space-time density is infinity. Thus, there is no limit. However, for the state of motion, there is an absolute value, the speed of light. This means that there is a reference point. Thus, there should be no principle of relativity in DP at speeds. Unfortunately, it’s not that simple.
For the ST, it was important that the speed of light is always identical for each space-time, otherwise we would not be able to compare space-times at all. We have to be able to determine a clear difference. This is only possible between spacetime if there is an edge/measuring point from which we can measure. Without the absolute speed of light, the comparison between spacetime makes no sense. For different geometries, there must be a starting point for the comparison, otherwise not even the comparison is possible. Otherwise we would have no suitable edge/measuring point for comparison.
We have the speed of light in spacetime. This is clearly defined by the geometry and thus an absolute value. The statement is correct. Nevertheless, we have no reference point in space-time. We only have it between space-times. We do the trick here as with Newton with rest. There we had rest or rectilinear and uniform motion. Since we cannot distinguish between the two states, the zero point has been eliminated. Something similar happens to us with the speed of light. This is always identically far away for every object and therefore cannot be used as a reference point for a measurement within a space-time. That was Einstein’s basic idea. But there it is a postulate. We cannot use it that way. We have to derive this constancy of the speed of light. We will do that in the next section.
We have discussed the existence of the speed of light in detail in chapter 3. As a structure element of space-time, it is necessarily given by the space-time boundary. However, this is only the first step. We have an identical condition. This explicitly does not produce the constancy of the speed of light.
The second step is that we have to show that, despite this condition, we have an identical distance to each object. There are two possibilities. One of them is wrong. Unfortunately, the wrong possibility is used very often. Let’s take a closer look at the two possibilities.
We already had this topic with the Planck values. The velocity is a fraction \frac{length}{time}. This means that there are an infinite number of values that lead to the identical velocity. In the SR, the length and time dimensions change identically. This means that the value of the fraction as a whole does not change. The length and time become smaller and larger to the same extent. The speed does not change and must remain the same locally.
One part of the argument is correct. We cannot detect any change. Unfortunately, the second part, that this happens because the speed does not change its value as a fraction, is wrong, even though it looks right.
The best counterexample is the Shapiro delay, as it is well confirmed experimentally. We discuss this in more detail in the next chapter for the equivalence principle of GR. What is important for us now is that light in a gravitational field can also move more slowly for an external observer. Locally, however, the light must travel at c again. Here, length and time change in opposite directions. This never results in a locally constant speed over a fraction. We need a more general solution that also works in the presence of gravity.
The first thought was that we can detect the changes, but that they cancel each other out. For the constancy of the speed of light to work, we must not be able to detect a change in the components of space-time locally. Then it is irrelevant what the environment looks like or how the space-time components behave in relation to each other. We achieve this by defining the geometry as the determining factor for the space-time density. Since everything in the universe is a space-time density, the local constancy of any given quantity is achieved.
Let’s start with length. The change in the space component can be whatever we want, we can never detect it locally. The meter as a reference size is not squashed. It is defined differently locally for the object. If a spaceship flies at about 86% of the speed of light, then the meter is only half as long for us in the direction of motion. However, there is physically no way to determine this in the spaceship. Absolutely everything in the spaceship now has the new length definition. A meter always remains a meter locally. We cannot even recognize the change.
Time behaves identically to length. The second is now defined differently. There is no way to determine this. But we have defined time as a measure of distance to the space-time boundary. The spaceship has moved closer to the space-time boundary. Yes, that’s right. Locally, we can’t determine that either. We would have to be able to detect a length contraction or a time dilation to be able to determine this. We lack this possibility. From the point of view of the spaceship, it has not moved an inch towards the space-time boundary. Therefore, locally everything remains as it is.
Locally, it is not possible to detect a change
Locally, no approach to the space-time boundary is recognizable. This must always remain identically distant. Constancy of the speed of light
This “locally no change recognizable” not only has the constancy of the speed of light in its luggage. This also explains why, according to the SR, we can put everything in a rest system. The distance to the space-time boundary does not change locally and there is no zero point. Thus, any object can be considered at rest without acceleration. This is the connection between the SR, the comparison of space-times, and the old relativity principle, the comparison of objects in a space-time.
Let’s look at the relativity principle in the DP using an example. We’ll do the classic here and take one person on Earth and one in a spaceship moving away from Earth
Figure 26 shows the Earth at rest and the spacecraft moving at a speed below the speed of light.
Then we have to discuss two points of view. One from Earth and one from the spaceship. We start with the simple case.
Here, SR and DP agree on the point of view. Therefore, the case is simple. The person on Earth experiences no change in the state of motion. Thus, the space-time density remains identical. For the SR, this person simply remains in the rest system. The spaceship is accelerated and thus actually acquires a higher space-time density. The spaceship experiences length contraction and time dilation. This can be measured from Earth. However, nothing can be recognized in the spaceship. So far, there is agreement.
Length contraction and time dilation are a real physical change in the spaceship. It is precisely this statement that leads to the assumption that the space-time density is not subject to a relativity principle.
With the SR, everything seems very simple at first. When the spaceship has completed its acceleration phase, it can claim to be at rest. The Earth has accelerated and is flying away from the spaceship. The Earth must now be subject to length contraction and time dilation. A perfectly symmetrical view.
This is exactly where the problems begin in understanding the SR. The acceleration phase has only and exclusively taken place on the spaceship. Why should the Earth be any different than before? The Earth is not enough. In the direction of motion, the entire universe must have accelerated. No, certainly not. The universe does not change just because a spaceship has had an acceleration phase somewhere. This is the best way to see that the SR does not compare two objects (Earth and spaceship) in one space-time. Depending on the point of view, the objects are assigned a suitable space-time, which always goes from zero to the speed of light. Then the comparison of the spacetimes is made. Therefore, from the point of view of the spaceship, the entire universe must have undergone a change. Only the spaceship has been given this new definition of spacetime. However, it is a definition of a complete spacetime.
However, the SR only knows one direction when making a comparison. The other object always has the “smaller” definition with time dilation and length contraction. In a relativity principle, there should only be a difference and no specific direction. This, in turn, is a forced result of the approach with the Lorentz transformation from an ether theory. This only assumes an identical zero point throughout the entire universe. Therefore, we get this preferred direction in the comparison in the SR.
In the DP, only the spaceship may have the higher space-time density. Only there has an acceleration occurred. Then the spaceship has a changed definition of geometry. The spaceship recognizes, just like the Earth, that there is a difference in the definition of geometry. Only this difference is recognized. Even if it is clear to the spaceship which one must be the one with the higher spacetime density, we cannot measure this from the spaceship. In the spaceship, a different definition of geometry is now in place. The spaceship may now only recognize all outward observations with its definition. Let’s proceed strictly according to SR. Then the spaceship is at rest and the earth has accelerated. What does it look like for the spaceship after the DP? The earth has definitely maintained its speed. But with that, so has its space-time definition. The meter of the earth is defined longer than the meter in the spaceship. Then the earth, from the point of view of the spaceship, creates more length at the same speed. Thus, from the point of view of the spaceship, the earth must have accelerated. Not just the earth, the whole damn universe. Only the spaceship has changed its space-time density. Thus, for the spaceship, the entire universe must necessarily be subject to change.
DP only makes a spacetime change to the object that has also had an acceleration phase. But then there is a global change for the object. SR does this by always assigning a complete spacetime to each object. Then the DP and SR perspectives seem to be identical. So why all the fuss? Because they are not identical.
In DP, the spaceship actually has a higher spacetime density. In SR, we cannot determine this in this way. We can only use a symmetrical approach. In DP, it is clear that length contraction and time dilation are only local phenomena. In SR, these are always global depending on the point of view. We will clarify these two points in the next two sections.
According to the SR, time dilation and length contraction always occur identically and physically measurable in all of space-time. But then we get a logical problem. Mathematically, everything is clean because it is symmetrical. Logically, it becomes critical here. The approach from the DP solves this problem very easily.
As always, I have named this problem “Cherry Picking” by virtue of sovereign arbitrariness. When I sit in my chair and write the text, I have a defined time and a defined length between my two hands in front of me. Now muons are continuously approaching this length from all sides of the earth’s atmosphere. Since muons are very fast, the length must be different for these particles, depending on the angle to my hands. We cannot really imagine that.
Almost all discussion partners make a rather idiosyncratic distinction here. Each muon must have a different time than mine. These are different objects from my hands. These can have different time courses. Since time remains a mystery, this is simply accepted. This is a good thing, since time dilation has since been verified with impressive accuracy in experiments. Chop on that.
According to the SR, however, the length must also change physically. Time dilation only exists with length contraction. If time dilation is measured experimentally, then, conversely, length contraction must also occur physically. This means that the distance between my hands must constantly be different. Depending on the angle at which the muon moves in relation to my hands. Almost no one accepts this. Many people leave the path of virtue and go for what is logically understandable. Length contraction is only a point of view; time dilation is real. From a logical and mathematical point of view, this makes no sense in the SR. Either both are just a point of view or both are physically measurable. We are certain about time because it has been measured. We do not want to accept it when it comes to length, which is just “cherry picking”. The problem arises from the fact that the ST always assigns a complete space-time. In fact, it does not make logical sense. However, since the math works very well => shut up and calculate.
In DP it is clear. There is always a real physical effect. However, this is only local in the object. From the object, the appropriate view of the rest of the unmodified universe then arises. Cherry picking is not needed.
Sorry, but if we go through the SR, the twin paradox must not be missing. In particular, we can use this paradox to clarify the problem with information about a greater or lesser density of space-time. Most of the other paradoxes (e.g. garage paradox) are rather uninteresting. These can always be explained by the symmetrical view, by the non-existing simultaneity. But in the case of the twin paradox, there is no symmetrical result. There must be a reason for this..
In mathematics, there is no difference. Even the SR has the result that the twin in the rocket is always the younger one. This is also the expected result in the DP. In the SR, however, it is not clear why this is so. The argument is often a symmetry break or something similar. For a better understanding, we extend the twin paradox to triplets.
Figure 27 shows the Earth at rest and the two spaceships with their motions in space.
There is a triplet on the left (DL), a triplet on the right (DR) and a triplet on Earth (DE). DR has a single destination and DL visits several places. DE stays on Earth and only moves forward in time. What may not be 100% recognizable in the picture, the distance traveled by DL and DR should be identical in total.
The result is clear. The triplets are the same age at the starting point. When they meet again, DL and DR will be the same age because both have traveled the same distance through space-time, and DE will be the older of the three.
In the DP, the result is logically to be expected. Only DL and DR experience an increase in space-time density. Only DL and DR can experience time dilation compared to the starting condition. It does not matter in which direction the time dilation occurs. Only the sum of the time dilation, that is the distance traveled, is relevant in the end. There is information here from younger and older or from smaller and larger space-time density.
This is not clear from the SR. The SR is always symmetrical. Thus, between DE and DL, the other should experience an identical time dilation and there should be no difference. However, the result looks different. Why is that? I have not yet read a good explanation for this. What comes up most often is the most obvious explanation. If the symmetry is no longer given, then it must have been violated. Because nothing else is there, the culprit is quickly found. The evil, evil acceleration. This must break the symmetry. Then come even worse statements, such as: “The SR cannot deal with acceleration”. What nonsense. The SR just can’t handle gravity. Any kind of classical acceleration can be incorporated 100% error-free into the diagram or the calculations.
So, now let’s calm down and tackle the solution. If the information is not already present, we could not get it. We cannot create additional information. The information must always be included. In the DP, we always have this information. We just can’t determine it in the SR. This can only be obtained under certain conditions. That’s the right approach.
It can’t be the accelerations. We expanded the twins to triplets so that this would become visible. We could also let DL fly through space-time at a faster pace. If the sum of the distance traveled in space-time is identical, DL and DR are identical in age. The number and direction of the accelerations do not matter. The acceleration is only necessary so that there is any change in the space-time density at all and the triplets can meet again.
What many people do not realize is that in the classic twin paradox, the twin in the spaceship breaks symmetry twice. The first time when he starts from Earth. The second time when he starts again from the intermediate destination. Then the first symmetry break is a “good” one, since everything is still symmetrical, and the second symmetry break is a “bad” one that ruins everything. That doesn’t fit.
Let’s go back to the basics. When did we have to switch from an absolute value to a relativity principle? When we lost reference points for measurement. If we want more information, there must be a reference point again that can indicate this information. The picture again with the two important points.
Figure 28 shows the triplets with a reference point
What is special about this paradox is the starting and end point. The starting point is identical for everyone in every piece of information. The end point has remained identical in space and shifted in time. It should be the identical point in space and time for the triplets. We have created an additional reference point for the measurement within the relativity principle. This gives us all the information about space and time that differs from this reference point in the relativity principle. Then, in the SR, there is also a younger and older one.
The last section in this chapter deals with the fact that the naming of SR and GR, well, let’s say, was a disaster. We can’t change the names anymore. These suggest that the SR is the little sibling of the GR. I want to contradict this here. From a purely mathematical point of view, I can still understand the statement. From a logical point of view, it is simply wrong. At this point, too, it is clear to see that a great many people can do calculations well with the SR. But only a few have understood the SR. We will stick with the approach from the DP.
What does the GR do? This theory states how the space-time components change due to space-time density. This statement only makes sense within a single space-time. The space-time density is only the source here. The actual statement does not concern the space-time density. We can see this from the fact that the GR creates a singularity. This is not possible with the approach of a space-time density. For the GR, only the amount and distribution of the space-time density over the space-time dimensions is of interest. The curvature of space-time must then compensate for this. The GR makes statements about the curvature of space-time. Thus, the surrounding space of the space-time density in a single space-time. There can also be several space-time densities, spatially separated. This statement of the GR concerns the surrounding space-time.
What does the SR do? In the old view, different spacetimes are assigned to the objects and compared. This only makes it appear that the SR makes a statement about spacetime. The SR cannot do that. Different spacetimes are compared. The SR cannot make a statement about a single spacetime or a single object. We always need at least two objects, otherwise the SR makes no sense. In DP it becomes a bit clearer. SR compares the definition of the space-time geometry of different space-time densities. These are statements about one space-time density. Just because the rest of the space-time appears different from this definition, we believe that SR makes a statement about space-time. Clearly in DP, everything is space-time, so every physical statement is somehow a statement about space-time.
The SR makes absolutely no statement about the surrounding space-time of a space-time density. This is only the comparison of space-time densities. The GR needs a space-time density as the source of space-time curvature. Otherwise, however, the GR is not interested in the space-time density and only makes statements about the surrounding space-time. From this we conclude:
The GR and the SR result in two completely different statements
The SR is simply contained in the GR because the relativity principle must be incorporated into all physical statements in the DP by definition. Everything is spacetime density and this is always subject to the relativity principle.
So what does QFT do? It describes the “inner structure” of a space-time density through low-dimensional spaces (fields). However, QFT is only interested in the space-time density. The space-time density is not aware of any space-time curvature. QFT only uses the surrounding space-time of a space-time density as a “given possibility”. A low-dimensional space-time density cannot determine whether this surrounding space-time has a curvature. Thus, the surrounding space-time is uninteresting for QFT. Therefore, SR and QFT can be unified to a certain extent. Both look at space-time densities and not at the surrounding space
We will end the chapter here and take a closer look at GR in the next chapter.