Title: Solutions to some paradoxes in theoretical physics
Author: User

Comments on some paradoxes in theoretical physics
Jorma Jormakka

Let us start with the customary proof of the E=mc^2 formula. Einstein took the Lorentz transform to the special relativity theory and proposed that the mass m of a body moving with the velocity v is related to the rest mass m_0 as  
	 , where c is the speed of light. 
As for now, we take this formula as granted. From the formula we get

and differentiating it yields
, 
thus
 .
Next we take one equation for a force:
	.
A differential of the kinetic energy is 
	 .
Thus, 
	.
Integrating gives Einstein’s, or actually Olinto De Pretto’s, formula
	.
If v is close to zero we should get the rest energy . It is natural to assume that the rest energy is  and thus the total energy
	.
What part of this do we not understand? There are atomic and thermonuclear bombs, so we know that the mass is not constant. For instance, two deuterium ^2H atoms have the atomic weight 2*2.0141202=4.0282404 u while one helium ^4He atom has the atomic weight 4.002602 u, though both contain two protons and two neutrons. The mass difference releases lots of energy in a thermonuclear explosion and we can consider it verified that the rest mass is indeed correctly given by the formula . But the atoms are not moving close to the speed of light in a thermonuclear explosion. Therefore we may question if the Lorentz factor is necessarily correct. Let us just for fun see what would happen in this calculation if we generalize the Lorentz transform slightly. Let us select:
	 .
If this is our formula for the moving mass, then in a similar way
	 .
The kinetic energy is 
	 .
Solving v as a function of m gives
	.
Thus if k>>1 and  we get a series expansion
	
If k is large it is sufficient to take the first term, thus
	.
So, we get the same kinetic energy and therefore the same total energy from this approximation. Furthermore, there is no special reason to expect that the formula for the kinetic energy should be something simple to integrate. Indeed, if where is small, we always get the same first order approximation for the kinetic energy. 
	If there any reason why the equation of the moving mass should have the Lorentz factor? No, but there is a very good reason why it should not. If the mass transforms by the Lorentz factor, then time also transforms by the Lorentz factor and we get to the traveler paradox: if one of the twins travels with a speed close to the speed of light, he stays younger than the twin who remains at home:
 .
This is a paradox since the special relativity theory especially states that the results do not depend on the coordinate systems, and in the coordinate system of the traveling twin, it is the other twin who moves close to the speed of light. Thus, the other twin should be younger. I have listened to people who have tried to explain this paradox. Often they make a point from the fact that the twins cannot meet unless the traveling twin turns around and the turn has some effect on the times, but such explanations are futile. This is a real paradox in the theory and it cannot be removed as long as the Lorentz factor is kept. 
	The paradox can be removed if we take the generalized Lorentz transform and choose a sufficiently large k. Quantum effects forbid us from using the continuous time formulas as if they are the real description of the system. With a large enough k, the velocity v must be so close to c before any noticeable time difference can be obtained that the paradox cannot appear in reality: if v is so close to c, the model is not applicable. A small time difference will appear on smaller values of v, but it is so small that it is acceptable in a quantum system. 
	But do we not know that the transform must be the Lorentz transform? Earlier I believed that we knew it. Today I do not believe so. Today I question validity of the Michelson-Morley experiment, which is believed to have proven that there is no ether. In this experiment light travels in two ways. No speed difference is found and it is claimed to prove that there is no ether. The problem with this experiment is that even if we would assume that if ether moves relative to the earth and the testing equipment and light gets delayed when it struggles against the ether stream, the light beam turns back and gains the same time on the return trip before the two beams are again joined. There is no way this experiment could show a time difference between the two beams. And it does not. 
	I thought about this problem. There are at least three different cases of adding velocities. One case is that a man is walking in the train against the direction of the train. The man walks 5 km/h, the train moves 100 km/h. An outside observer sees the man moving 95 km/h to the direction of the train. This is certainly not the case with light in the ether. Here the man is in contact with the train floor. The second case is that the man shoots a bullet to the opposite direction than the train moves. The bullet leaves the gun with the speed 400 m/s, that is 1440 km/h. For an outside observer the bullet leaves the gun with the speed 1340 km/h, so it moves a bit slower. This is also not the case with light in ether. Light does not move because of the initial speed like the bullet. The case I think is correct is a helicopter dropping divers to the sea. After coming to the surface, the divers swim in the sea with their swimming speed. It makes no difference at all, apart of an initial push, what the direction and the speed of the helicopter was. Thus, the speeds do not add. This is the case with light in the ether: light moves in the ether with the maximum speed that anything can move. The speed of a light source does not matter any more than the speed of the helicopter. I prefer to think of the maximum speed in the ether as if the space were a discrete world: the maximum speed is one unit of space to the target direction in one moment of time. That means, I think time, the real time, the present time, consists of moments, and the space consists of discrete units. With this model for the ether, the speed of light is always the maximum and it is constant. It is not possible to add or to subtract velocity from the speed of light, since it is determined by the structure of the space. 
	Smaller speeds do add, but when we go to speeds that are very close to c, the model fails: we cannot use a continuous time model but have to take the real structure of the space into account. As an approximation we can use a generalized Lorentz transform, but it is only an approximation. Any paradoxes that may be derived from the approximation only show that the model is not applicable. 
	Of course it is quite fine to use the Lorentz transform for practical calculations. The paradox with the twin astronauts traveling close to the speed of light does not often appear in practice. When it does, it is sufficient to note that the ether time may well exist and the time with the Lorentz factor is a calculation devise. Probably some quantum effects will change the situation if it ever comes practical to test the traveling twin case with humans. Elementary particles certainly can behave in strange ways, that is known from Quantum Mechanics.
One can use theories that have certain known problems, but give correct results when used as intended. It is even possible to calculate the places of fixed stars in the night sky from the world axis theory. The star locations are given rather correctly by this theory even though there is no word pillar with elephants turning the mill. 
	The astronaut twins were just a thought experiment, but quantum entanglement in Quantum Mechanics seems to be a more serious source of paradoxes, as there are some experiments that support the logically problematic standard interpretation of Quantum Mechanics.  
In the two slot experiment there are two ways a particle can choose. In the midway there may, or may not, be an observer making a measurement. The paths are joined in the end and there is a detector. If there is no observer in either path making measurements, the detector shows an interference picture. The explanation for the interference picture is that the particle took both ways and interfered with itself by quantum interference.  If there is an observer making a measurement, a single line will be seen in the detector. The explanation is that the particle travels on one of the paths. One particle is enough in this experiment, thus it is not an effect caused by a chain of particles. The particle does not split to the two paths: if there is a measurement, it will in 50% of the cases find a particle from the observed path, and in 50% it will tell that there was no particle. So, this seems very confusing, but it can be explained by the disturbance that the measurement causes to the particle. An observation in Quantum Mechanics is today often understood as simply meaning a measurement. The observer does not need to be a human: it can be the measuring equipment. The wave function of the particle gets entangled with environment represented in this case by the measurement equipment. This entanglement causes the wave function to lose coherence and it loses the ability for quantum interference. Therefore, if the particle is measured, there will not be quantum interference and we see a single line. It is not necessary to understand this situation in the way the standard interpretation of Quantum Mechanics says: that the particle travels two ways if there is no measurement but only one way if there is a measurement, as this would mean that some part of the wave function disappears when the measurement is done.
In the Copenhagen interpretation it does happen exactly so that some of the wave function disappears. If the wave function is physical, a physical field must disappear when the measurement is done. Physical fields cannot disappear like that. Therefore the Copenhagen interpretation denies that the wave function is physical: it is simply a calculation devise for deriving probabilities for measurements. Obviously this is not a very satisfactory explanation: there must be something that exists if it can be measured. But as said, the two slot experiment does not require using the Copenhagen explanation.
Schrödinger cat though experiment can also be dismissed. It describes how Quantum Mechanics sees the problem, but as it is only a thought experiment, we cannot know what actually happens: as long as the box is not opened we do not know if the cat is dead or alive or in a mixed state. 
The only paradox that has been well studied in theoretical and empirical ways seems to be the EPR thought experiment. Einstein, Padolsky and Rosen posed this problem in 1935. Much of it was solved by John Stewart Bell in 1964.
The problem is of two entangled particles. Measuring e.g. spin or polarization in one entangled particle allows deducing the property in the other particle even though the particles move far away from each other. There does not seem to be any exchange of information between the particles, and indeed, if information would be changed, it would have to happen faster than the speed of light because the correlations between the measurements of the two particles appear to be instantaneous. The phenomenon is well tested and used today in quantum cryptography. 
	Bell showed that the explanation for this phenomenon cannot be that the particles have the values of spin or polarization when they are together. They do not have values for these properties but instead their wave functions are in mixed states. The proof is quite simple: if the particles had values for these parameters before they are measured, then the values would satisfy Bell inequalities. One such inequality is the following: for any numbers A, B, C, D that take values 1 or -1 holds the inequality 
.
The reason is that one of  or  is zero and the other is  and
.
Assuming that the measured properties have values before measurement, we can integrate AC over the probability space and get what is called in quantum physics the correlation C(A,B) between measurements of A and B. The correlation is , twice the probability that A and B are equal minus one. This correlation can be measured in an experiment and calculated from Quantum Mechanics. In Quantum Mechanics the correlation is determined by the coefficients of the wave function. That is, the wave function is a linear combination of the base vectors, which we can for instance select as eigenvectors:
	  .
The measurement collapses the wave function and the eigenvalue of   is measured with the probability. It is possible to construct wave functions with such coefficients  hat the correlations C(A,C), C(A,D), C(B,C) and C(B,D) do not fulfill the inequality that all probabilities taking values in 1 and -1 must fill. Experiments agree with predictions from Quantum Mechanics and do not agree with the Bell inequalities. Thus, it is virtually certain that particles do not have values for spin, polarization and similar things before they are measured. The only two limitations in this Bell’s theorem are that information could be transferred to far away places in some unseen way faster than light, which is not only against the special relativity theory but also highly doubtful, or that the universe is so totally determined that a researcher does not have a free choice in selecting what he wants to measure, which is even more questionable claim. We have to conclude that Quantum Mechanics is correct in this point: particles are in mixed states before they are measured, they do not have values for measurable parameters before these parameters are measured. 
	This brings us to the real paradox: Quantum Mechanics predicts correctly and consequently the reality becomes paradoxical. 
If the wave function corresponds to something real, history changes in the EPR experiment. This is so because the wave function of both particles cannot have collapsed before the measurement as in that case we have no choice what to measure, but after the measurement the wave function of both particles has collapsed, meaning it has collapsed also at the time before measurement when the particles were still together. As that is history at the time of the measurement, history at the time when the particles were together changes from a non-collapsed wave function to a collapsed wave function.   
	The Copenhagen interpretation is that the wave function does not exist in space-time, but there must be something real since properties can be measured. There are some logically sound explanations that do not change the predictions from Quantum Mechanical calculations, but try to give a logically more understandable explanation to the EPR paradox. 
One explanation is the many worlds theory of Hugh Everett. It claims that the space splits into multiple worlds and the observer chooses where he is. This does work with the EPR experiment, but it is very problematic when continued to more particles: the universe splits all the time and so do humans, who are in the universe. 
	Another is called the transactional interpretation of quantum mechanics, TIQM, and it was proposed by John G. Cramer in 1986. It is only an interpretation of Quantum Mechanics, so it agrees with all calculations of Quantum Mechanics, but gives some theoretical reasons why the calculations are as they are. It assumes that wave functions are real physical objects, but waves travel also to the history, do a handshake in the history and exchange information there. The result is that the history changes.
	A third alternative, not worked out in any formulas, is the simulation world. It is not possible to change the real past because what has happened cannot be changed, but it is possible to change the past in a simulator because simulation time is not real. It only requires recalculating the past.
All of these theories agree with the calculations of Quantum Mechanics and in all of them the physical world is in fact unreal. In the Copenhagen interpretation the wave function does not exist in space-time. In the TIQM the past changes and therefore the physical time cannot be real and therefore the physical world cannot be real. In the many world theory the wave functions splits all the time implying that energy grows infinitely. In a simulation world theory the world is a simulation, the past can be changed but the world is not real.
	Additionally there are the possibilities that there is no free will and that information can be transferred faster than light (or faster than any maximal speed), but these seem improbable.
I conclude that the physical time and the physical world cannot be the real time. It follows that there must be real time and there must be real space because the present time cannot move forward without a real time and the real time must exist somewhere. 
What do we know about reality from immediate observation? Immediate observation we can do only because we possess a conscious mind and a free choice. We can notice that we have the conscious mind, that time moves forward and that there is present time and everything that exists seems to be in the present time. Future cannot be determined if we have a free choice. 
Let us reconsider an observer in quantum physics. It is common to hear that an observer has nothing to do with a conscious mind and that the measurement equipment can be an observer, but is this so? A human does not need to be present in a measurement for the wave function to collapse, but must somebody look at the results? If nobody looks at the results, how do we know if the equipment had a failure? Does measurement equipment collapse a wave function even if it has a failure? If we answer no, then we can ask what kind of a failure is sufficient. Does it collapse the wave function if the detector head is broken, what if the printer lacks ink or the wire to the computer is loose? If we answer yes, then what if the equipment is incorrectly designed? Assume it could not have worked. Does it still collapse the wave function? If so, does a wooden stick collapse a wave function? There are people, who look for places for wells with a wooden stick thinking it is a magic wand. Some researcher may have thought that a magic wand can detect the spin of an electron. Clearly, it is very unclear when the measurement equipment can collapse the wave function. Disturbing the wave function does not seem as the issue: a bubble chamber can detect the speed and location of electrons quite well and it does not seem to disturb the wave function much. The observer is something else: it must deal with a connection of the world of possible wave functions and the reality. 
	What do we know of the physical world? The wave function, which may or may not exist in the space-time, but something exists somewhere in some sense, either develops along the Schrödinger equation or it collapses. Development according to the Schrödinger equation is the dynamics of the physical world. There is no real time in the physical world, so this is not movement in time: it is movement in the (virtual) time axis. The physical past changes is it is necessary to avoid contradictions, as in the EPR experiment. The collapse of the wave function can only happen in the present time. That is where the wave function meets the reality. 
What we actually know about reality? We have an immediate observation that our conscious mind exists. All measurements produce real numbers, that is, the coefficients of the wave function as complex numbers but the measured values are real. It seems possible that nothing really exists except for the present time in a three-dimensional world. The past may or may not be how things actually happened. The past in the physical world is always without contradictions. No strange quantum things can happen in the macro-world. The craters in the dark side of the moon were there in the same places even before a spaceship photographed them, but in the quantum world electron does not have a value for the spin before it is measured. This means that up to very recent times the physical world seemed to behave as a real world behaves. 
	In the last one hundred years humans found ways to make experiments where the human free will forces the history to change. It is hacking into a system that is meant to look real but is not. The elementary particles do not behave as they should if the physical world is real. From this we should conclude that the physical world is not real and all history that has been found for the origin of the universe and the life on the earth is highly suspicious: that need not be the real history. There are too many too nice coincidences in the far past: the universe emerged from nothing, the interactions are fine tuned, life emerged from non-life, oxygen was nicely produced by cyanobacteria, species evolved while I cannot see how exons got the mutations, and humans have a conscious mind and a free will. Where did they come from? And besides, the time goes only forward but one should be able to move an axis to any direction.   
I know this sound a bit dubious, but have become slightly skeptical of science and everything in genera, must be the side-effect of reading The Unz Review. I will try to do some theory in equations, starting maybe from the TIQM, but it will take some time. It is a bit too long time since I did such calculations in studies.