TWO WAYS TO DISTINGUISH ONE INERTIAL FRAME FROM ANOTHER

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1 TWO WAYS TO DISTINGUISH ONE INERTIAL FRAME FROM ANOTHER (No general ausality without superluminal veloities) by Dr. Tamas Lajtner Correspondene via web site: ABSTRACT SPACETIME CONTINUUM BY EINSTEIN ACTION-REACTON OF SPACE AND MATTER Spae waves The inertial frames of referene an be distinguished by spae waves Calulation of the hange of wavelength of spae wave No aether, but spae waves SPACE-MATTER MODEL: SPATIAL DISTANCES GIVEN BY SPACE WAVES Wavelength and spatial distane Waves of spae are parts of the frames of referene TIME IN THE SPACE-MATTER MODEL Time expressed in meters in the speial relativity Light s speed is onstant in every (inertial) frame of referene Time as spatial waves Time wave and time unit ATTRIBUTIONS OF SPACE WAVES Veloity of spae waves is onstant Spae unit and time unit given by the same spatial wave Ation and frequeny of spae waves Spae as inertial frame of referene Constant veloity of mass in Spae WHAT IS MATTER, WHAT IS SPACE? Ation and density of spae and matter What is spae, what is matter? WAVE-PARTICLE DUALITY IS A TRIALITY Hidden presumption behind wave-partile duality Fast wave-wave-partile triality FREQUENCY LEVEL AND PRODUCT OF FREQUENCIES OF LIGHT TUNNELING: METAMORPHOSES OF PARTICLES Tunneling Tunneling partiles How does tunneling work? Travelling time in the barrier THE TWO PARTS OF THE PLANCK CONSTANT HIDDEN STRUCTURE OF ELEMENTARY PARTICLES INDICATOR OF MOVING SPEED OF SPACE WAVES GRAVITY CAUSED BY MASS AND PHOTON Gravity as the differene of wavelengths of Spae waves aused by masses Spooky ation at a distane as differene of wavelengths of spae waves aused by photons SUPERLUMNAL VELOCITY AND GENERAL CAUSALITY UNITS IN SUPERLUMINAL SPACES Calulation of units of superluminal spaes in the light s oordinate system Spae in spae in spae Superluminal veloity in the speial relativity? CONCLUSION ACKNOWLEDGEMENT REFERENCES...41

2 2 ABSTRACT Aording to physiists, the laws of physis don t allow us to disern one inertial frame from another. It does allow. This study shows two ways to distinguish one inertial frame from another. Physis hasn t defined what is spae, what is matter, what is time. In this study (in Spae- Matter Theory), spae is what matter uses as spae, regardless of its texture. Matter is what an exist as matter in the given spae. Both matter and spae have three spatial dimensions. When ation and reation ours between matter and spae, the result is time. Time appears as a given wave of spae. No partile, no frame of referene an exist without generating spae waves. A and B inertial frames of referene are not idential if e.g. two idential eletrons (eletron A and eletron B ) reate different wavelengths of spae waves. One way to distinguish one inertial frame from another is to alulate or measure the length of the wavelength of the spae wave. Via tunneling, a partile (with or without mass) travels through the barrier with superluminal veloity. In this ase the barrier is a speial spae made out of matter (matterspae), where the partile travels with veloity. This veloity appears in our spae as superluminal veloity. Saying this, there are more spaes and more times instead of one spaetime. The different spaes make hanges in the partile, too. The partile builds its ation out of Plank onstants h, where h has two parts whih depend on the veloity of the partile in the given spae. So there is also a phenomenon in the matter that makes it possible to distinguish one inertial frame from another. Keywords: spae-matter theory, wave of time, wave of spae, time, spae, matter-spae, matter. 1. SPACETIME CONTINUUM BY EINSTEIN The speial and the general theory of relativity 1, 2, 3, 4 5, 6, 7 introdued the definition of spaetime. Spaetime has three spatial dimensions and one time dimension, so spaetime is a four-dimensional model. Aording to Einstein's speial theory of relativity, every inertial frame of referene is equivalent. An inertial frame of referene is a system where there is no

3 3 aeleration but onstant veloities in a straight line. The speial theory of relativity introdued more new phenomena like time dilation and length ontration. If the inertial frames of referene A and B have different veloities, v v then both observers (A and B) an measure the time dilatation and the length ontration in their own oordinate systems. The observers A and B will measure different time and spae oordinates, but every physis law is the same in all inertial frames of referene. An inertial frame of referene is always loal. The next statement seems to be self-evident: neither observer A nor B an identify whih inertial frame of referene moves. In other words: the laws of physis don t allow us to disern one inertial frame from another 8 (p 13). This is not true, aording to Spae-Matter Theory. The inertial frames of referene an be distinguished. A B In Einstein s theory, mass energy equivalene is expressed as E=m 2, where E is the energy and m is the mass and is the speed of light in a vauum (299,792,458 meters per seond), and is the universal speed limit. The speed of light is isotropi in all inertial frames of referene. Einstein's general relativity theory gave a more omplex system of gravity than Newton's Law of Gravity 9. In Newton s Law of Gravity, gravity is given by the mass (mass density). The general theory of relativity is a geometri theory of gravity, where gravity is expressed as the urvature of spaetime generated by sixteen attributions of matter (mass, energy). The urvature of spaetime is given by the Einstein tensor, and the stress energy tensor ats as the soure of spaetime urvature. This is a non-loal model. Of ourse, there are lots of differenes between the speial and general theory of relativity. The speial theory uses the Minkowski geometry; the general theory uses the Riemann geometry. But there is a major theoretial differene between them in that the time dilatation and the length ontration doesn t reate urvatures in spaetime. The time dilatation and the length ontration are symmetrial mathematial onstrutions. If we suppose that they have real urvatures of spaetime, the symmetry disappears. The deteting of length ontration and time dilatation won t hange. The only hange is that it is possible to distinguish one inertial frame of referene from another.

4 4 2. ACTION-REACTON OF SPACE AND MATTER 2.1. Spae waves We know from quantum mehanis that partiles of matter are in onstant vibration. It is a physial impossibility for matter to ome into ontat with spae without its vibrations having an effet. Based on the Casimir Effet 10 and other physial phenomena like gravity waves 11 12, 13 measured by LIGO we an state that spae exists in waves and vibrations. Einstein's speial theory of relativity desribes how the mass of an objet inreases with its veloity relative to the observer. The inreasing veloity of mass dereases the spatial distane. When an objet is at rest, and both the objet and the observer are in the same (inertial) frame of referene, the objet has a rest mass ( m 0 ). The rest mass of an objet is the inertial mass that an objet has when it is at rest relative to the observer (in the given frame of referene). The rest mass is the smallest value of mass in the given (inertial) frame of referene whih is onneted with the longest spatial distane s 0. Note, the observer is mass and the objet is mass. Can we desribe a model of a moving mass using the waving spae? Yes, we an The inertial frames of referene an be distinguished by spae waves If the observer is able to measure the wavelengths of a spae wave λ, he would find the shortest wavelengths ( λ 0 ), if the mass is at rest that is, the mass does not move in the given inertial frame of referene, v 0 = 0. If the mass moves in the given inertial frame of referene λ > ). v 1 > v 0, its wavelength of spae wave is longer ( 1 λ Calulation of the hange of wavelength of spae wave The alulation is based on the speial theory of relativity. The known formula of the length ontration is in Eq. (1). 2 v 1 s0 1 2 s =, (1) where v is the veloity of the objet with mass. Aording to Spae-Matter Theory, the hange of wavelength of the spae wave is given by Eq. (2). λ 0 λ 1=, (2) 2 v 1 2

5 5 λ 1 is the wavelength of a modified spae wave. In this study a two-dimensional osine funtion as spae wave made by mass (mass density) will be used, beause it is simple. Of ourse, the model an be more preise, thinking about Newton's Law of Gravity. Using this approah results in different lengths of wavelengths of the given spae wave. See FIG. 1. If we use spae waves that ontain Einstein s impulse-energy tensor, we should alulate with more than one spae wave. FIG. 1. Wavelength of a spae wave that exists in the spae. y and x are spatial distanes. Mass is at the O point. Newton s Law of Gravity gives the idea of how the wavelength hanges. (Model, not proportional.) From Eq. (1) and (2) omes Eq. (3). λ s = λ. (3) 1 1 0s0 The theory of speial relativity uses s only and doesn t use λ. Therefore it annot be said who moves, the observer or the mass objet. Knowing λ 0 and λ 1, we know when the objet with mass moves and how fast it moves. If we study the spae waves, we an say when the mass aelerates. If λt+1 λt and t represents our time, where t = 0,1, 2..., then the aeleration of mass a 0. If λ t+1 = λt, then a = 0, that is the objet ontinues to move at a onstant veloity in the inertial frame of referene. Newton's First Law of Motion an be given as λ t+1 = λt, where our t = 0,1, 2..., that is, in an inertial frame of referene, an objet either remains at rest or ontinues to move at a onstant veloity, unless ated upon by a fore. Knowing spae waves, the modified version of this law sounds like this: λ t+ 1 > λt, where t = 0,1, 2..., that is, in spae, an objet aelerates, unless ated upon by a fore. See Eq. (13). Sine spae is always given, we an use it as a general frame of referene. Spae always has a ommon framework with every mass. Saying this, spae is an absolute entity behind the relativity. It sound like an old aether model, doesn't it? No, it doesn't.

6 No aether, but spae waves Aether theories propose the existene of a substantial medium, the so-alled aether. Aether is a spae-filling substane, and a transmission medium for the propagation of gravity fores (and even eletromagneti fore) aording to physiists at the end of the 19th and the beginning of the 20th entury. The works of Lorentz 14 represent the theory. In the aether model, time is a "loal time" that onnets systems at rest and in motion in the aether. In my model, there is no aether. The spae waves and the hanges in wavelengths of spae waves represent the re/ations that the re/ations of matter ause. And there is no "loal time". The definition of time makes a big differene between the spaetime model and the aether model. In the following model, there is neither "loal time", nor spaetime. In the next hapter, it will be shown that we an use a new model holding the results of the spaetime model. The name of the new model is the Spae-Matter Theory. 3. SPACE-MATTER MODEL: SPATIAL DISTANCES GIVEN BY SPACE WAVES Can we measure spae? Measuring spae, we measure matter. The meter is the length of the path travelled by light in a vauum during a given time interval 15. We annot measure spae at all. We measure only matter. Aording to the Spae-Matter Theory, spatial distane exists without having been measured Wavelength and spatial distane The given spatial distanes of the objet and of the observer an be given as the sums of the wavelengths of spae waves: where s observer = n n λ observer and s objet = objet 1 1 λ, s observer = s objet n n = observer = 1 λ λ. (4) Eq. (4) shows that the observer is in the objet s inertial system. If the objet moves relative to the observer, beause they are in different inertial systems, then v = 0 and vobjet v observer, so the observer will realize Eq. (5). 1 objet observer

7 7 sobserver s objet. (5) Eq. (5) shows the values we alulate using the theory of speial relativity. The observer that an see the wavelengths of spae waves finds Eq. (6). λ observer < λ objet. (6) That is, the objet has greater veloity than the observer aording to spae waves. Here Eq. (7) will be true. where out of n λ λ, (7) 1 = b observer objet 1 n> b. The same s spatial distane measured from Objet A1 to Objet A2 an be made n λobserver and out of b λobjet. The observer's wavelength of spae wave didn't hange, but the objet's wavelength of spae wave did. In other words, the s spatial distane as s observer is built out of more spae waves than the s objet, if v observer < vobjet aording to spae waves. The length ontration of s objet is a length dilatation of the wavelength of the spae wave. The length dilatation of the wavelength of the spae wave is not symmetrial; the wavelengths of spae waves are different. The objet travels the s spatial distane using its own spae waves, that is, the spatial distane for the objet is really shorter, now p piees long instead of n, where λ <. The λ observer < λobjet is a real phenomenon, not the viewpoint of the observer. observer λ objet Behind the relativisti length ontration is a real differene of the spae s wavelengths of observer and objet. Note the spae waves that onnet the observer and the objet are their ommon spae waves. These spae waves will hange between the observer and objet, if one moves. The deteting of length ontration and time dilatation remain true, both the objet and the observer are able to detet them, sine the length ontration and the time dilatation appear using these ommon, modified spae waves. The symmetry is broken, if we study the soure of the hange of the wavelengths of spae waves Waves of spae are parts of the frames of referene No frame of referene an exist without generating spae waves. So the spae waves are part of the frames of referene. They are also part of every inertial frame of referene, i.e. two inertial frames of referene are not idential, if they reate different wavelengths of spae waves. To be more preise, if there are e.g. two idential eletrons (eletron A and eletron B ) in

8 8 the frames of referene A and B, and an observer finds that the wavelengths of the eletrons are different, then the observer will know how fast the inertial frames of referene move. 4. TIME IN THE SPACE-MATTER MODEL What is time? Today s physiists laim that time is what we measure as time. What does the phrase "what we measure" mean? We an measure only matter. One seond is defined as a hanging harater of the aesium 133 atom 16 we an measure. One seond has its start and has its end that we measure. The main element of time is the hange. If there is no hange, there is no time. We measure hanges of matter measuring time. Aording to the Spae-Matter Theory, time exists without having been measured Time expressed in meters in the speial relativity An event an be speified with plae and time oordinates. It is a ommon, usual proedure in the Minkowski geometry 17 measuring time in meters or spatial distane in seonds. The onstant speed of light in a vauum makes these onversions possible. Now we an onstrut a oordinate system showed by FIG. 2. It has two dimensions: time and one spatial dimension, both expressed in meters (axis t is expressed ast ). Here an be used as one unit, that is =1. FIG. 2. The speed of light in the Minkowski geometry. t is time in meters, = 1, and s is the spatial distane in meters. s / t= 1=. We know that s / t= 1= is true in every (inertial) frame of referene in spaetime; this phenomenon is the ornerstone of the speial theory of relativity.

9 Light s speed is onstant in every (inertial) frame of referene How an the speed of light be onstant in every (inertial) frame of referene? There is no answer to this question in the theory of relativity, beause there are no spae waves in this theory. This is something missing in this theory. The speed of light an be onstant only in that ase, if light is in the given frame of referene. How an it be there? Using the spae wave reated by the inertial frame of referene. We know that these waves are part of the frames of referene. The light travels on the spae wave reated by masses. It will be demonstrated soon that spae waves (or spae) an also be seen as an inertial frame of referene Time as spatial waves Spae wave is a normal wave that has frequeny, veloity and ation. This veloity is onstant like the veloity of light aording to the frames of referene. Aording to LIGO, spae waves have veloity (although in the Spae-Matter Theory, spae waves have superluminal veloity). Saying this, spae waves an be displayed the same way in an inertial frame of referene like light in FIG. 2. In the Spae-Matter model, time omes into existene when matter and spae meet. Also, whenever matter and spae meet, the result is time. Time is the ation-reation phenomenon of matter and spae, and appears as a spatial wave. Time depends on two things: on the given spae and on the given matter that travels in the spae. Aording to modern physis, only mass has time. Aepting this, our time is the ationreation of mass and spae that exists as spae waves. This is not the only spae wave, i.e. not the only time, just our time. In other words, everything reates spae waves, that is, everything reates time. We use in our life (and in physis models) the time reated by mass, but "non-mass" objets may use different spae waves as time.

10 Time wave and time unit The ations between spae and matter, from the view point of matter, an vaillate between strong and weak. It osillates. The hange is periodi, and one period is one unit of time 18. This unit of time has two parts: a) the hit, when spae ats upon matter most strongly; and b) the period between hits, when the fore of spae ats less strongly upon matter. If we employ a osine funtion to desribe time, we get a periodi wavelength. Hene, it appears to be a good model: where a) equals the positive amplitude of the osine funtion, and every other value of the funtion is b). In a time unit (in a single time wave), there is only one positive amplitude. Time is a repetition of these units. Time is the ontinuous alternation between a) and b). From the viewpoint of matter, time is harateristi of the periodi way that spae ats upon mass. FIG. 3. Time as the spae wave. x and y are spatial distanes. (Model, not proportional.) FIG. 3. shows that a pulse of time exists, if os( x ) = 1, here marked as point. This is followed by a lak of time pulse, when os( x ) < 1. The longer the wavelength of the spae wave, the rarer the time impulse. Here we get bak the well-known formula of time dilatation of the speial theory of relativity. t t 0 1=, (8) 2 v 1 Sine the time is given by the spae wave, we get bak Eq. (2) putting the wavelength of the spae wave in Eq. (8) 2

11 11 5. ATTRIBUTIONS OF SPACE WAVES 5.1. Veloity of spae waves is onstant If time waves are derived from spae waves generated by mass, there arises a strange phenomenon the time and the distane are the two sides of the same oin from the viewpoint of mass. Saying this, it is impossible for an objet with mass to hange any spatial distane without hanging time, and hanging time means hanging the position in the given spae. See Eq. (9-11), where f means frequeny. and f = f (9) spaewave timewave timewave λ = λ (10) spae wave If a mass generates growing wavelengths of spae, the frequeny of the spae wave dereases, that is, the time unit for the mass grows in the same portion. v spae wave λ λ t λ = = = = = λ0f 0 (11) t / onstant v v t Spae unit and time unit given by the same spatial wave Knowing Eq. (11), we an use the idea of the Minkowski geometry to make the new time and distane model visible. Time is expressed in meters (axis t is expressed astv shortest distane for mass. t 1 is the shortest time unit for mass. spae ). s 1 is the s1_ 3. a s1_ 3. b v spae wave = = = 1 (12) t t 1_ 3. a 1_ 3. b FIG. 4.a. and 4.b. Wavelength of spae wave; time and spatial distane of mass i.e. the veloity of spae wave and time wave. The λ spae is the shortest time unit and the shortest

12 12 spatial unit, i.e. t 1 and s 1 annot be shorter. The veloity of an objet with mass hanges the length of λ spae wavelength of the spae wave but not its veloity. FIG. 4.a. and 4.b. show the same mass, when v Mass _ 4. a. < vmass _ 4. b. Knowing the speial theory of relativity, we an also say that FIG. 4.b. shows a bigger mass, i.e. m Mass _ 4. a. < mmass _ 4. b.. FIG. 4. explains how spae and matter reate time. An observer or an objet gets moved in the spae. This is the ation. The reation of spae is the hange of wavelength of the spae wave. This is followed by a reation of the objet. It moves faster. This is followed by a reation of spae the wavelength of the spae wave grows Therefore time is an ation-reation phenomenon and not a dimension. Eq. (13) expresses it more preisely with terms of logi: ( v λ ) ( λ v ) v λ (13) mass Spae Spae mass mass Spae In the following, spae m or Spae (written with apital S) are synonyms of spae, where mass exists. In terms of modern physis: Spae is where fermions interat with the Higgs field 19, 20 getting mass this way. Aording to the modern physis, the interation is onneted with the spins of the elementary partile of the standard model. Sine a photon isn t a fermion, and its spin is 1, it doesn t interat with the Higgs filed. The spin is a good attribution that is able to explain the interation between the Higgs field and fermions in Spae. But spins desribed in the standard model are not able to explain why fermions lost their mass in a non-spae spae. If a fermion entered a different spae, it lost its mass. Why? I think that the hange of the spins of fermions ould be a part of a possible explanation, and it will be mentioned one more in this paper. The question is open: an fermions hange their spins? In the following, I will show you a different notion. My explanation is in harmony with the standard model 21 of physis (in Spae), but it opens new ways. Here it is supposed that photons and fermions travel in different spaes (and we don t know their spins). Eq. (13) shows more than just the ation-reation of Spae and mass. It shows that mass in Spae will aelerate, if it started moving, unless ated upon by a fore. The aelerating gravity fore an be traked bak to Eq. (13). From the viewpoint of Spae waves Newton s First Law of Motion remains unhanged. In an inertial frame of referene, the veloity of an objet v t = v t+ 1 unless ated upon by a fore, where t represents our time, and t=0,1,2, In

13 13 the following it will be shown that the Spae waves are speial inertial systems, where there is no aeleration. where 5.3. Ation and frequeny of spae waves Let s study Eq. (14). E = h f, (14) Spae Spae E Spae is the energy and h Spae is the ation of the Spae wave. If, E Spae _ 1 > ESpae _ 2, Spae then v 1< v 2 or m 1< m 2. Mass Spae Mass Spae Mass Spae Mass Spae Solely through the use of Spae waves, we an express spatial distane, time and energy. Every spatial distane an be expressed using the wavelength of Spae waves. In our physis terms: This is the shortest unit of distane. Every unit of time an be expressed using the frequeny of Spae waves. In our physis terms: This is the shortest unit of time. Every amount of ation (energy) an be expressed using the value of the ation of Spae waves. In our physis terms: This is the smallest unit of ation. The time dilatation and the λ Spae dilatation (spae ontration) do not hange our metris. See the wave number k in Eq. (15). Let s see FIG 4. one more. The shortest distane unit in Spae is λ Spae (FIG. 4. s 1 ). 1 meter spatial distane is made out of k piees of λ Spae no matter how long λ Spae is. In other words, 1 meter has always the same spae units. 1meter k= = onstant. (15) λ spae 1 seond time is as long as the Spae wave reates f Spae is t shortest (FIG. 4. t 1 ); see Eq. (16),. The shortest time unit in Spae t shortest 1 =. (16) f Spae The lengths of the meter and seond are dependent upon the spae waves. Note this is not the theory of speial relativity; here we re speaking about real hanges of spae waves. One Spae wave has one h Spae ation. Eq. (17) omes from the Plank onstant 22 h.

14 14 where spae. h spae i h = h Spae H Spae or more generally h = h spae _ i Hi, (17) _ depends on the given spae i (e.g. on Spae) and it is onstant in the given H i has no dimension, it shows the relationship between h and h spae_i. Sine in spae i v onstant, and h onstant the unit spatial distane, the spae _ i = spae _ i = time unit and the ation unit are embedded in λ spae _ i (in spae i f _ ) and in h spae _ i Spae as inertial frame of referene FIG. 5. Mass, light, Spae waves. y and x are spatial oordinates. Spae s wavelength as spatial unit distane and frequeny as time unit for the mass. A bigger or a faster mass (irle in the piture) makes longer wavelengths in Spae waves. The mass meets just the d setion. The light uses a big setion of the Spae wave. (Cosine model, not proportional.) FIG. 5. offers a new way to explain the ooperation of Spae and matter. The Spae wave is a speial inertial frame of referene, where the veloity of the Spae wave is onstant from the viewpoint of mass and the veloity of mass is onstant from the viewpoint of the Spae wave. The hanging veloity of mass hanges the wavelength of the Spae wave, but even the aelerating motion of mass seems to be a onstant veloity from the viewpoint of the Spae wave. Even more, sine λ spaewave is a very short distane, it seems to be a motion in a straight line at a onstant speed. The Spae waves are speial, non-mass inertial systems Constant veloity of mass in Spae FIG. 4. shows the onstant veloity of the Spae wave. The basi unit of spatial distane and the basi unit of time are small. So masses may use more basi units; matter s basi unit of spatial distane and time are built out of more Spae units.

15 15 out of v Mass always needs the same time expressed as q tshortest to travel the unit distane made p λ Spae wave, where p and q are onstant. That is, the veloity of mass in the Spae is p _ in _ Spae, beause λ Spaewave and t shortest are basi units. q mass = The veloity of mass is onstant; it an travel neither faster nor more slowly in the Spae. This is true aording to Spae waves, too. See Eq. (10) and (11). Every hange of frequeny and wavelength of Spae gives the same veloity: λ t 0 = onstant. The wavelength of the Spae wave depends on the mass of the objet. Objets with bigger mass will reate longer wavelengths in Spae. Every mass is onneted only with the d (i.e. p d ) setion of the Spae wave. d (without p) is shown by FIG. 5. So the wave of Spae is the d setion for a mass. If the mass enters the d setion, it generates a new d setion. The Spae wave itself is the ationreation of mass and spreads in the Spae. How does the frame of referene made out of the Spae wave show the aeleration of mass? It will appear as the hange of wavelength of the Spae wave. The Spae waves are like light waves. So we expet there to be no aeleration in the frame of referene of Spae aording to the veloity of Spae waves. The alulation with the wavelength of the Spae wave is in Eq. (18). The Spae wavelength is the unit wavelength from the viewpoint of mass; its value is always 1 for the given mass, sine λ is the basi unit distane in Spae. Look at Eq. (19). λ a= t 0 λ λ0 1 1 a= = t t 1 = 2 t0 λ0 v / = v t = 0. (18) Indeed, there is no aeleration in the inertial system of the Spae wave. Aelerating motion an appear in a non-spae frame of referene aording to the mass, but it annot appear in the framework of waving Spae; aording to the veloity of the Spae wave there is no aeleration. Therefore the Spae wave is a speial inertial frame of referene. 0 (19)

16 16 What else does Eq. (19) show? It shows that travels with v=. In the spae m (Spae of mass) mass p _ m veloity. Note spae_ m works inside the spae m from the viewpoint q spae = of Spae. This is the only veloity of masses in spae m. Sine there is only mass in this spae m, this is the only veloity in this Spae. (Spae=spae m ) This veloity is not the speed of light; this is the veloity that appears between the spae m and the mass. Light travels on the Spae waves generated by mass. Light doesn t hange these waves. That is, it travels in a different spae, see FIG. 5., and its veloity is. The spae of light, i.e. Spae wave, is a part of the frame of referene of mass, it is glued to the mass, that is, the mass and the spae of light is one inertial frame independent of the veloity of mass in the Spae. In this inertial frame, the veloity of light is onstant. The speed of _ seems to be a very important onstant. This is the veloity at spae i = whih the objets travel in their own i spaes. In other words, in every i spae the objets travel with _ i veloity, but different i spaes have different values of spae_ i from spae = our point of view; spae spae i is a spae, where objet i generates time i, and where objet i travels with i _ an be different from our from our point of view. In general, _. spae i = Of ourse, the aeleration motion of mass an be measured by a non-spae observer in a given non-spae frame of referene. 6. WHAT IS MATTER, WHAT IS SPACE? There are more spaes, and not all objets are able to use all spaes. So it has to be defined what spae and matter mean. First let s see some simple definitions. Spae is what matter uses as spae. Matter is what spae allows to exist as matter in the given spae. There are spaes that the given matter annot use as spae, and there is matter that annot exist in given spaes. For example, light (normally) doesn t exist in the Spae. There are more spaes and more forms of one given matter. For example, the partile we

17 17 know as the eletron an exist in a speial spae as a fast wave. In some ases the spae an be made out of an objet that we know as matter Ation and density of spae and matter The simplest way to define a spae is to give its smallest h value shown in Eq. (20) h spae Spae h i i _ value. Our known Spae has the h = é, (20) where h i is the ation of any different spae or matter and 0 <é < 1. It is possible to use the density of spae, too. If we alulate with little Spae ubes whose 3 3 size an be given as λ ( m ), knowing the ation of the Spae wave and knowing spae λ Spae (m), we an alulate the density of spae. It is D Spae. Using the simplified Spae-Matter model with osine funtions, we an onlude that the density of the proton is nineteen orders of magnitude beyond the density of Spae. See Eq. (21). The nulear density of a proton is 53 3 = ev / m. (The radius of the proton D proton is disussed 23. The disussion may influene the alulation, but not the onlusion.) D Spae >> D proton, (21) The density of Spae is very important. It hanges, beause of the growing wavelength of the Spae wave. If Spae s density is small enough, Spae an turn into matter What is spae, what is matter? If the ations and the density are given by Eq. (22). h objet = h Spae i.e. objet DSpae D = (22) then this objet is always Spae for masses and never matter in our known world. The Spae has the smallest ation and the biggest density. The ation of matter is always bigger than h Spae. The density is always smaller than D Spae. If h objet > h Spae (or objet DSpae D < ), (23) then this objet is matter in Spae, says Eq. (23). If the ation of an objet is bigger than the ation of Spae, or in other words, the density of an objet is smaller than the density of Spae, this objet an at as spae from the viewpoint of a third objet, and an at as matter from the viewpoint of another objet. Tunneling works this way. The barrier is made out of

18 18 matter, but eletrons and photons use it as spae. The barrier an be alled a spae made out of matter, or in short: matter-spae. Without a new definition of spae and time, we will neither understand the working method of spaes like matter-spae, nor understand how matter objets exist in matter-spae. Here we an use the new, above-mentioned definition of time in a wider meaning: Time is the ation-reation of spae and matter, where spae is either Spae or matter-spae. In every mass made out of more elementary partiles, there is a big portion of Spae. How an it be that matter doesn t hange its size while the wavelength of Spae hanges? This effet doesn t hange the size of the objet, this statement rystallized in the early years of the 20th entury in the disussions about aether and relativity. Mass is one unit. It has its own rules inside the matter. Or a simpler answer: matter an be seen as matter-spae in Spae. Matterspae is an independent spae, so its internal units an be independent from Spae. 7. WAVE-PARTICLE DUALITY IS A TRIALITY Wave partile duality is the onept that all matter an exhibit two behaviors a partilelike behavior and a wave-like behavior. In other words, every elementary partile or quanti entity may be partly desribed in terms not only of partiles, but also of waves. The wellknown de Broglie wavelength 24 λ shows the onnetion between the momentum of the wavelength of the given partile p and Plank s onstant. See Eq. (24). h λ = (24) p In general, the momentum of a partile that has mass is p = m v. The momentum of a partile that has no mass, e.g. a photon, is written in Eq. (25). where E is the photon's energy. E p=, (25) 7.1. Hidden presumption behind wave-partile duality The original version of the de Broglie wavelength means that the partile turns into a wave, if Eq. (26) is true: λ partile l partile, (26) where l partile is the size (length) of the partile. λ partile is the wavelength of the partile if it

19 19 is a wave. Atually, there is a hidden presupposition behind the formula of the wave-partile duality: the spae wave doesn t exist. De Broglie didn t know about spae waves, therefore there is no spae wave in Eq. (24) Fast wave-wave-partile triality If we involve the wavelengths of spae waves in the formula of wave-partile duality, and Eq. (27) is true, that is, if the wavelength of the spae wave is longer than the wavelength of the wave of the partile, then the fast wave-wave-partile triality omes into being. See ó in Table 1. λ >λ l, (27) spae partile partile Tunneling is a good example for fast waves. To understand how tunneling works, we need to understand how light works. 8. FREQUENCY LEVEL AND PRODUCT OF FREQUENCIES OF LIGHT When the medium is not the vauum, Eq. (28) is used in alulations of phase-mathing in nonlinear optis. E p= n, (28) where in general n = > 1 is the refrative index of a transparent optial medium, also alled v l the index of refration of the material in whih the signal propagates. v l is the veloity of light in a non-vauum, that is, in medium. The index of refration 25 is the fator by whih the phase veloity v phase is dereased relative to the veloity of light in a vauum. In the ase of one photon wave v phase veloity in the vauum and _ > v and v phase _ M phase M _, where v phase_ represents light n phase = v _ represents the light veloity in medium. During the refration, the frequeny of the light wave remains unhanged f phase_ = fphase_ M, while the wavelength of the light wave dereases λ > λ. phase _ phase _ M Let s take a look at the fast light experiment arried out at the University of Rohester,

20 20 USA 26. In this experiment, a normal light impulse (with veloity and made out of a group of lights) travels on an optial medium and a fast light impulse (made out of a group of lights) travels on the normal light. Fast light has a longer wavelength than normal light traveling with λ > λ and a measurable superluminal veloity of fast light: fl impulse is group veloity (envelop), where generally the following is true: v fl = v v. group phase v fl >. This veloity of In the fast light experiment, the envelop (fast impulses) is built out of a spread of optial frequenies: out of sinusoidal (sine, osine) omponent waves 27 ; that is phase veloities v phase. In the given experiment, every omponent s wave has one wave number. So the following must be true, beause if v = v = v is not true, the fast wave impulse fl group phase ollapses. (Here n 1< 0, and n is a great number with negative sign.) In the experiment, the wavelength of the fast light inreased ompared to the wavelength of the normal light traveling with veloity in a vauum. It means that the wavelengths and veloities of its spetral omponent waves inreased in the given medium 28 ( λ ), phase _ M ompared to the wavelengths and veloities of spetral omponent waves of light in a vauum v _. The veloities of the omponent waves of fast light are also superluminal phase veloities see Eq. (28), that is, v phase > and λ > λ. phase _ M phase _ From the above-mentioned, we know that during refration the frequeny of the light wave remains unhanged while its wavelength grows. So we may suppose that in a given spae the hanging wavelength λ < λ and the unhanged frequeny f f phase _ phase_ M _ v. phase_ = phase _ M are a general working method of light, if phase phase _ M v We an write this law in a more general form in Eq. (29) and (30). Light holds its frequeny level onstant ompared to the frequeny of the spae wave of the given spae. The gravitational red shift shows learly that the frequeny isn t onstant, but the frequeny level of light is onstant. Aording to a given light (or photon), Eq. (29) is true in the whole lifetime of the given light (photon) in a given spae. f f light spae_ i = onstant. (29)

21 21 Beause there are more spaes, photons use Eq. (30), too. We an all it produt of frequenies. f light f spae _ reator = onstant, (30) where f _ is the frequeny of the given spae, where the photon was reated. spae reator Eq. (30) is true in the whole lifetime of the given light (photon) in every spae. We haven t identified Eq. (30), sine today s physis works with spae-time, where Eq. (30) doesn t ome up. Eq. (29) seems to be in ontradition with Eq. (30). There is no onflit here, sine spae waves are also time waves. barrier In a matter-spae the frequeny level of light is reated by using the frequeny of the f spae_ i and by using spae reator f _. Aording to Eq. (30) in the barrier a very high frequeny ours, therefore a very high veloity. This veloity is realized in the matter-spae, so we annot measure it. Instead of it we measure e.g. the tunneling veloity (whih is smaller). More in the hapter on tunneling. In FIG we an see the light before hanging its wavelength and frequeny. FIG.6.1., 6.2. and 6.3. show how the photon (light) works. t and s are expressed in meters and 6.2. show the photon in its spae, when the wavelengths of the Spae wave grow shows a tunneling light in a barrier, i.e. in a matter-spae. onstant in the lifetime of the photon ( f system, whih results in a onstant veloity. s t s s = = = 1 t2 t3 onstant. This is 1 = ) i.e. every photon has a onstant oordinate t FIG shows a Spae with greater gravitation. The wavelength of the Spae wave is longer here. We know that the big gravity reates a red shift of the light, that is, the wavelength of the light grows, and its frequeny dereases. Why? Beause the light holds its

22 22 frequeny level onstant. We find that the light has less energy here, but from the viewpoint of light everything remains unhanged, sine its frequeny level remains unhanged. 9. TUNNELING: METAMORPHOSES OF PARTICLES 9.1. Tunneling Quantum tunneling refers to the quantum mehanial phenomenon where a partile (with or without mass) tunnels through a barrier that it lassially ould not surmount. Partiles that travel with superluminal veloities in tunneling will be alled fast waves in the following. (The above mentioned fast light is a fast wave, too.) Nimtz 29, Enders and Spieker first measured superluminal tunneling veloity with mirowaves in Aording to them, the puzzle is that the jump of the partile over the barrier has no time (it spends zero time inside the barrier) and the partile is undetetable in this ondition. The tunneling does take time, so this time an be measured. Aording to Nimzt, the partile annot spend any time inside the barrier 30, beause the wave funtion has no missing part (and no missing time). The tunneling method of the partile is unknown and immeasurable. If the wave doesn t spend time inside the barrier, what is the tunneling time? Nimtz supposes that the measured barrier traversal time is spent at the front boundary of the barrier. The seond riddle in tunneling: experiments show 31 that the tunneling partiles are faster than light, and these fats are not ompatible with the theory of relativity. The growing veloity of the partile with a mass (for example an eletron) auses growing mass aording to the theory of relativity, and if v, then m. Sine the mass (of the eletron) won't be, and the tunneling is fat, we have to suppose that v= never ours. There is a disrete jump in the veloities, and after v< ours v> Tunneling partiles Every tunneling or not tunneling wave and every partile wave uses Eq. (29) and (30). In tunneling, the light meets a barrier, a matter-spae. The light deides whether it an enter this spae. It depends on the unit ation, wavelength and frequeny of the matter-spae. If it an enter this matter-spae, it has to adapt itself to the new spae. (Probably it hanges its

23 23 spin, too.) Different spae and different time fore a metamorphosis of the objet 1. Objet 1 will appear in a form that is not written in our books. In tunneling, objets exist as fast waves. Let's see the eletron during tunneling. The tunneling shows that v tunneling _ objet>, aording to us. It is a fat measured. The eletron has mass. The tunneling eletrons seem to violate the speial theory of relativity 32. They don't violate it, if we suppose eletrons have different forms in different spaes, and the barrier ats as matter-spae. In matter-spae, the tunneling eletron beame a fast wave 33. The metamorphoses (from partile into fast wave and bak) do not mean that the eletron hanges its identity the essene of the eletron always remains the same, just the form of the eletron hanges. Partile, fast wave, partile. Let's see the two metamorphoses of an eletron during tunneling 34. Tunneling from the viewpoint of the form of the eletron (or other tunneling partile): o Before the barrier: eletron partile or wave. Metamorphosis 1. o In the barrier: unknown objet (fast wave). Metamorphosis 2. o After the barrier: eletron partile or wave. It means that the unknown, faster-than-light-objet is the same eletron we know, but it does have a new form we don't know. The given form of an eletron depends always on the spae in whih it travels. So there is a 'fast wave wave partile triality' instead of the 'wave partile duality'. The tunneling shows that photons (with no mass) make metamorphoses too. That is, generally speaking, the given form of objet 1 (with or without mass) depends on the spae in whih it travels. Objet 1 has more forms, and its forms depend on the spaes where it travels. Its every form seems to have its own (range of) veloity. In tunneling it appears as a fast wave and it has superluminal veloities, from our viewpoint.

24 How does tunneling work? Tu. Topi Experiment 35 1 Experiment 36 2 Experiment 37 3 Remark vtunneling v ú= ú= 1 T = t (se) T = f 1 f 0 frequeny of light before tunneling (1/se) λ 0 wavelength of light before tunneling (m) L length of the barrier (m) λ = L (m) L 1 wavelength of fast wave λ L ó= = ó ú λ 0 λ 0 f = 1 T (1/se) v f = λ á f t 0 = = á ú f t0 h kineti ő =. 11 hrest indiator of moving Table 1. Here are shown the tunneling times and the lengths of barriers in three experiments. The ó values show that λ is longer than λ 0. It an be supposed that the unit of the spatial distane of matter-spae is longer than the unit of the spatial distane in light s spae. The á value shows that in matter-spae there is different time unit than in light s spae aording to the given partile. A single time unit in matter-spae mustn t be shorter than a time unit in Spae. Partiles use a set of time units, this set an be shorter. ő is the indiator of the moving of the partile showing the effet of matter-spae on the light s ation, or in other words, the effet aused by interrelations of units of matter-spaes are displayed in FIG. 11. v > on the light s ation. The ó ú and á ú show that the different units of spatial distane and the different time units explain together the superluminal veloity measured by us: f ( ú) = f '( á) f ''( ó).

25 25 The tunneling partile travels in the matter-spae with matter spae =. This viewpoint is presented in FIG. 11. The barrier is a spae i, where the units of time and spatial distane are different from time and spatial distane units of our Spae and of light s spae. Saying this, every spae i has its own unit of time and spatial distane. The given values depend on the spae i and the given matter that travels in spae i. _ i in every spaes i, the matter spae = travels always with veloity in every spae i. If it annot travel with veloity in spaes i, then the given spaes i is no spae for this matter. (Note this is not about the Cherenkov radiation, it is about spaes.) How does tunneling work? The question an be answered using the new spae and time definitions and knowing the working method of light. The barrier is a spae made out of matter, a matter-spae, where h > h. Therefore the photon in the barrier exists as fast barrier Spae waves, and it travels inside the barrier with matter spae =. If a matter, a barrier ats as matter-spae, the light here works the same way as in its spae. It holds its frequeny level and oordinate system onstant. Light enters the matterspae. This is a very simple step, and is shown by FIG This situation is one step aording to light, but an adequate model that desribes its details is made out of four steps see Tu in Table 1. Light detets the length of the barrier and adopts it as wavelength. Its frequeny will be given by the produt of frequenies from Eq. (30). It develops its f. In the following light holds the frequeny level f / onstant in this mater-spae f spae _ i aording to Eq. (29). Travel in spae or travel in matter-spae are different onditions even for the light itself, see the produt of frequenies in Eq. (30). The longer or shorter t and s don t make a differene, if they are a simple hange of wavelength of Spae. But here the units are hanged. Longer units means bigger ations. Matter-spae has a bigger ation than light s spae. This is the reason for the metamorphosis. Light and other tunneling partiles should be able to use this bigger ation. Using this bigger ation unovers that elementary partiles have struture.

26 Travelling time in the barrier We are able to measure only the tunneling time, but the tunneling time is longer than the traveling time in the barrier. As mentioned above, aording to Nimzt, the partile doesn t spend any time inside the barrier. It spends, but its atual travelling time inside the barrier is shorter than the tunneling time. t = t + t + t, (31) tunneling Metamorphosis1 travelling Metamorphosis2 Eq. (31) shows that a partile needs time to adapt itself to the new spae. Why do traveling partiles need time for metamorphosis? Beause they must resale the struture of their ation h. 10. THE TWO PARTS OF THE PLANCK CONSTANT Let s use the funtions of Table 1. L ó=, where λ 0 means the wavelength of light λ 0 before tunneling. f 1 =, where the tunneling partile in the barrier is a fast wave from t tunneling our point of view. Now we an study the same partile in two different spaes using a very simple method often used in eonomis but not in physis. See Eq. (32-38) f λ = v and f 0 λ 0 = (32) f = (33) f á 0 f 0 λ = v á and 1 á λ 0 λ = v f 0= (34) λ 0 (35) 1 á v λ =λ 0 (36) Let s study the de Broglie wavelength of λ 0 h p 1 = λ λ 0 =, (37) á v v h v 1 λ = á = á( h). (38) p p

27 27 If v = and á = 1, then we get bak the original formula. Sine h is the attribution of the partile (photon), we an write Eq. (39). h partile 0 h partile =. (39) v Let s use the expression ( h) in the Plank law aording to Eq. (40-43) where v 0, and f v = E0 = á f ( ) ( h) = á f h. (40) f v á 0 is the rest energy part and E 1 v = á f ( h) ( ), (41) h v 0 h h h = h (42) v rest v = h (43) kineti is the kineti energy part of the Plank onstant in the ase of light and seen from our Spae. Physis hasn t defined Eq. (42, 43) previously. If h = h rest kineti, then the speed of the light is ; Plank s law remains untouhed, if where its spin is 1. v =. If h = h then we speak about photon, rest kineti If h > h rest kineti, we are speaking about partiles with mass i.e. fermions with half-integer spins. If h rest < h we annot measure this fast wave via the tunneling, but both photons kineti and fermions (e.g. eletrons) an realize the tunneling. Therefore fermions are able to lose their mass, so we may suppose that they an hange their spin (into an integer or other) spin via tunneling, though hanging of spin is not an option aording to the standard model. Fermions (and photons) as waves adjust their frequeny levels to the waves of Spae, using h rest and h kineti. If we don t want to onflit with the standard model, we an suppose that the hange of spaes makes it possible for fermions that they loose their masses. On the other hand, loosing mass in tunneling seems to be onneted to the QFT.

28 28 Sine h is the attribution of the photon partile, it remains the same in Eq. (44). E 1 v = f ( h) ( h). (44) h v 11. HIDDEN STRUCTURE OF ELEMENTARY PARTICLES Today s physis doesn t use the expression rest energy, just 'rest mass'. As the speed of the objet is inreased, the inertial mass of the objet also inreases, while the rest mass remains unhanged. In the given inertial frame of referene, the value of the rest mass of an objet annot hange 38, 39. The fast wave-wave-partile triality shows that the rest ation exists in the ase of eletrons and photons too. Aording to above-mentioned, the rest ation an hange in the given inertial frame of referene. If the rest energy redues, how is it possible that the objet remains the same? It seems that the rest ation is not the partile (wave) itself. What is the partile itself? The dimension of h ation is Js. Js is also the dimension of the angular momentum. In physis, angular momentum is the rotational equivalent of linear momentum. The hanging rest energy part of h is supposed to mean that the rest energy of the elementary partile is reated by a smaller unit of energy (ation) that rotates inside the elementary partile. This smaller unit of energy is supposed to be the information apsule of the elementary partile that defines the elementary partile as a partile. The distane from the enter of the elementary partile hanges depending on the veloity of the partile. The faster the partile is, the shorter this distane is. This makes it possible that the rest energy of the partile an derease and inrease without hanging its information. The dimension of the information apsule an be given as (ev/ 2 ). In the ase of eletrons it is obvious, and it an be also aepted in the ase of the photon, sine photons an have mass in a quantum nonlinear medium 40.

29 INDICATOR OF MOVING h kineti ő =, (45) hrest where ő is the indiator of the moving of a partile. The pronuniation of ő is ɜː (like her). If we know the value of ő written in Eq. (45), we know how fast the partile travels ompared to the given spae. It means that we are able to detet that our inertial frame of referene moves without using other inertial frames of referene. If we study the ő of an eletron or photon of our inertial frame of referene, we an expet how fast our inertial frame of referene moves in the given spae. Comparing values of two ős from two different inertial frames of referene, we are able to say whih system is the moving one. Does the loss of mass mean hanging spin? If yes, spins depend on ő, i.e. the spin written in the standard model is hangeable in different spaes. New spae needs new onditions of partiles, and maybe new ondition of spins. How does ő work in the ase of masses? Masses travel in Spae with veloity spae _ m = whih is unhangeable. How an ő work in this ase? ő works, beause the wavelengths of Spae waves hange. That is, the density of Spae hanges, so ő hanges, too. ő shows that the Plank onstant has a lose onnetion to the speial theory of relativity. If ő < 1, that is h kineti < hrest, so ( v = v< ), we an write the well-known formula this way: 2 v h = 1 ő = 1 h 1 2 kineti rest, (46) Eq. (46) shows that there is a disrete jump in the veloities of masses that travel in Spae. If ő = 1, then we speak about light travelling with veloity in spae (and not in Spae). This means that it is possible to hange spaes. Eq. (47) shows the fast wave form of mass. If ő > 1, (47) then mass has a new form: fast wave. The veloity of mass is surprising. From veloity it develops its veloity into this: veloities. v< v> without travelling with. There is a disrete jump in the This disrete jump at this big sale is unexpeted, but we know other shoking disrete jumps like this. Physiists at the Ludwig-Maximilians University and the Max Plank Institute of Quantum Optis in Germany reated an atomi gas in the laboratory that

30 30 nonetheless had negative Kelvin values. These negative Kelvin values ame into existene out of positive Kelvin values. The atomi gas had no zero Kelvin value. There was a disrete jump on the Kelvin sale 41. If a partile with mass (e.g. eletron) or without mass (e.g. photon) has a superluminal veloity, then ő > 1. In this ase we are speaking about a fast wave that has no measurable mass. This annot work without hanging of spaes. ő works in every partile. ő an be seen as the mirror of wavelengths of a spae wave, that is, here an we find a new kind of symmetry. Beause of this symmetry, light must reate spae waves, i.e. gravity is ourred by light, too. where 13. SPEED OF SPACE WAVES GRAVITY CAUSED BY MASS AND PHOTON Gravity as the differene of wavelengths of Spae waves aused by masses Gravity ours when Spae aelerates masses, see Eq. (48): Spae F 0, (48) F Spae are vetors of the fore (ation) of Spae waves from the viewpoint of mass. Mass moves the diretion of the resultant vetor (exept in speial ases not detailed here). Among bodies experiening gravity, the frequeny of Spae waves dereases. That is, the Spae pressure between the bodies dereases. Gravity arises, beause the portions of Spae with higher fore (ation) shift the masses. If on one side of a mass the Spae wave has f S1 frequeny, and on the opposite side of this mass the Spae wave has f S2 frequeny and f S1< fs2, then the mass goes into the diretion of S1 f. The greater f S2 frequeny the greater fore (ation) of spae moves the mass forward. This fore will give the diretion of the objet s moving in the gravitation. Saying this, the wave of Spae flows in the diretion of mass. This is logial, sine the density of Spae is smaller around the mass. The gravitational wave measured by LIGO is not the Spae wave, just the hange in the Spae waves generated by energy and sent away in the Spae. The energy travels with, then the hange in the gravitational wave is also. Aording to the Spae-Matter Theory, this hange is not the veloity of Spae wave.

31 31 Let s see now FIG.1. this way: a big mass is at O and a small mass is at a. If the small mass is muh smaller than the big one, so it doesn t signifiantly hange the wavelength of the Spae wave, then from the viewpoint of the small mass the wavelength of the Spae wave is an aelerator for the small mass, where a t a 1 and time t=1,2,3 = t+ If the smaller mass hanges the wavelength signifiantly, the aelerator effet of spae remains untouhed; see FIG. 4. The aelerating Universe an be explained with Spae waves. The onstant aeleration of gravity has been explained above. The growing aeleration measured in the Universe omes from the growing wavelengths of Spae waves between galaxy lusters, sine gravity makes Spae waves longer. In Einstein s model, the gravity as urvature of spaetime has no veloity it is a deformity of spaetime. Therefore gravity as a Spae wave must have suh a large veloity as it was unhanged aording to masses; the veloity of the Spae wave and time wave must be a very high superluminal veloity independent of our viewpoint. That is, we ll find that Spae waves (time waves) are over-superluminal or they seem even motionless. The wavelengths of the Spae wave an be onneted with the general relativity. A geometri transformation is possible shown by a draft in FIG. 7. FIG. 7. The spaetime urvature an be transformed into a Spae wave as gravity. There is a new theory growing out of the general theory of relativity holding its values. This new theory is the Spae-Matter Theory. In the theory of relativity, there is no plae for spooky ation at a distane. Aording to Spae-Matter Theory, spooky ation at a distane works using a speial kind of gravity gravity between photons, in other words: the spooky ation works with the photon s spae waves.

32 Spooky ation at a distane as differene of wavelengths of spae waves aused by photons The spooky ation at a distane is the nikname of the non-loal orrelation in quantum entanglement (nlqe) given by Einstein 42. Quantum entanglement is a physial phenomenon that ours when two partiles interat in suh ways that the quantum state of eah partile annot be desribed independently. The most known example is the hange of spins of photons. Two independent measurements prove that v nlqe > 10, 000, where v nlqe is the speed of non-loal orrelation in quantum entanglement 43, 44. These measured times are longer than the travelling time of the spin-hanging information; it is the whole proess of the non-loal orrelation in quantum entanglement, where even photon 1 and photon 2 need time to develop their spin, so these measurements show three different veloities. t = t + t + t, (49) nlqe developing _ spin _1 traveling _ message developing _ spin_ 2 where t nlqe is the whole time measured. Eq. (49) remembers us for Eq. (31). This is orret, sine the spooky ation also has more steps that need time. The spooky ation at a distane has four steps. If photon 1 meets something, this is the first ation. In reation, it develops its spin this is a real hange in spin. This real hange is followed by a reation of spae waves made by photon 1, the wavelength of the spae wave grows. This is one single ation, this growth is a short period of the wavelength that travels to the photon 2. The grown wavelength appears as an ation for photon 2. As a reation, photon 2 hanges its spin. Saying this, the veloity of the spae wave must be a very minor part in the measured values of time of the spooky ation, sine if Eq. (50) is not true t traveling _ message << tdeveloping _ spin _1, traveling _ message tdeveloping _ spin _ 2 t <<, (50) then photon 2 may develop its own spin independent from photon 1, sine it doesn t have information about the hanged spin of photon 1. See FIG. 8. FIG. 8. y and x are spatial distanes. Here is the photons spae wave between photon 1 and photon 2 that hange their spins. The longer wavelength shows: photon 1 has already hanged its spin. (Model, not proportional.) The measured veloity of the spooky ation is The spae wave of photon s spae must be at least so fast.

33 33 The veloity of the photon s spae wave is a very high superluminal veloity; and photons need time to hange their struture. Saying this, photons have strutures. 14. SUPERLUMNAL VELOCITY AND GENERAL CAUSALITY Superluminal veloity annot destroy general ausality, beause in the Spae-Time Theory time travel is impossible, sine time has no dimension. General ausality remains untouhed in theory and in praxis, too. The superluminal veloity (of fast light, fast wave) exists; it has been measured. This veloity doesn t and annot violate general ausality 45. Even more, the superluminal veloity is the explanation of many unexplained phenomena. Here will be shown a geometrial explanation of how fast waves don t work, using a draft of Minkowski geometry in FIG. 9. FIG. 9. t and s are expressed in meters. Aording to Minkowski geometry (of speial relativity) the superluminal veloity in the st oordinate system is a time travel in the past in the s t oordinate system. AB and BD events are in the past aording to s t. Superluminal veloity in one system (e.g. st) is time travel in another system (e.g. s t ). In the speial theory of relativity, it is not possible to display an event with a superluminal veloity. There is a main problem in FIG. 9. It is supposed that the superluminal veloity ours in a spaetime, where the angle of the axis of the symmetry is in Eq. (51). α = 45 (51) Objets travel in every spae with veloity. The superluminal veloity is fat, so Eq. (51) must be false in the ase of fast waves. The angle of the axis of the symmetry of the oordinate systems of fast waves is in Eq. (52). α < 45 (52)

34 34 of matter-spae. Eq. (52) shows that there are more kinds of spae with different times. See FIG. 10. Spaes in a Minkowski-like geometry. FIG. 10. t and s are expressed in meters. Here there are two different oordinate systems, that is, two frames of referene in different spaes. (In this hapter if I speak about spae I mean a frame of referene in the given spae, sine it is impossible to be in a spae without having reated time, so axis t annot represent a motionless observer in the spae but in a frame of referene.) Both frames of referene st and s t time and spatial distane are in basi units and given in meters. The oordinate system st is a known oordinate system that an be used in the Minkowski geometry of speial relativity, too. Here the veloity of light (marked as event OA or BC) is 1, sl i.e. = = 1 and α st = 45. Event AB doesn t appear in spae st we don t know what t L happens in the blue area; here α < 45 that annot be in the oordinate system st aording to FIG. 9. The event BC has no reason in frame of referene st, and if we suppose that event AD is the path of the light and this is the fastest path here, event BC remains a mystery, sine it annot originate from events OA or AD. Though event AB is not in the frame of referene st, we an observe it indiretly. The event AB uses s t = v, where v > from our viewpoint. The veloity v is a alulation aording to our known system st. The event is in a fast spae s t e.g. a matter-spae, where objets travel with a superluminal veloity from the viewpoint of the

35 35 frame of referene st. This superluminal veloity we measure is from the viewpoint of matter-spae s t. Matter-spae s t doesn t exist as spae without travelling partiles in it. It exists as matter-spae as long as the partile travels in it. After and before it is just matter. So it doesn t have time without travelling matter in it. Time will be reated by travelling partiles. Time is the ation-reation of spae and matter. s' Aording to the oordinate system s t : = ' = = 1. The axis t of the t ' oordinate system s t lies on the line of the light in the oordinate system st. The axis AB of the symmetry of s t is defined by α, where < α < 45. The OA+AB+CB 0 setions show the path and veloities of the light in the experiment. There is no missing part of the path of the light. Eq. (53) states, if v, then α 0. (53) The smaller is α, the faster is the fast wave from the viewpoint of st. 15. UNITS IN SUPERLUMINAL SPACES Let s see the onrete units of the three tunneling experiments. Entering the matter-spae means hanging the unit distane and the time unit. See FIG 11.

36 36 FIG. 11. Here there are two oordinate systems. t and s are in meters. The light (veloity ) and all the three experiments of tunneling are shown in both systems. The oordinate system s 1 st is the light s spae. The unit is given by light with this funtion: unit U L = = = 1=. t 1 Every veloity lies on the axis of symmetry (45º). The axes of the oordinate systems of matter-spaes s1t1 are marked with brown. Here are their units 1, sine U' i OU ' 2 Exp _ i = = 1 e.g. Exp 2 = = 1=. In this example OU 2 is the time unit of U OU i 2 experiment 2 U Exp2. This is more times longer than U L. U Exp2 is 1 unit long in the oordinate system of experiment 2. This 1 time unit exists in the matter-spae of the experiment 2, in different matter-spaes are different units Calulation of units of superluminal spaes in the light s oordinate system Seeing FIG. 12., we will understand immediately why a is matter-spae faster than our Spae. Its basi units are longer than ours. Here waves travel with Exp _ i =. This veloity seems to be a fast wave from the viewpoint of st, but it is from the viewpoint of the given matter-spae. The units of the different matter-spaes are in Table 1. "Same step, different ountry. A step in the ountry of dwarves is shorter than in the ountry of giants." FIG. 12. This piture is a different view of FIG. 11. Now here are the veloities in the Cartesian oordinate systems. t and s are in meters. The first square is the known oordinate system of our light s spae. Here U L =1, aording to our units. The following squares display

37 37 the hidden units of the matter-spaes in our units. The veloities in these matter-spaes is (dashed lines), but for us they appear as fast waves (thik lines). Why? Beause the units of matter-spaes are longer. For example, in the Experiment 2 the fast wave has v = veloity. The unit of this matter-spae is longer than our st unit, but from the viewpoint of the 8.56 matter-spae: UExp 2 = = 1= Exp2 = The waves shown in the oordinate system xy are spae waves in the different spaes. x and y are spatial distanes. (Model, not proportional.) The wavelengths of spae waves are longer in faster spaes. In tunneling there are one traveling time and time of two metamorphoses. I think, the real travelling speed is muh higher than the speed of tunneling measured. Aording to my alulation the travelling time is shorter than one yoto seond. Untill now we haven t measured values about the metamorphoses, so we annot exatly alulate the pure travelling time. So the values given above are orret aording to today s measurements. As it is written above, the spatial units and the time units of the different matter-spaes have different multipliation fators, see ú, ó and á in Table 1. Using ú, ó and á and the units from FIG. 12., it is easy to alulate the atual unit of spatial distane and time of the given matter-spaes. (Naturally, it is also possible to study the oordinate system st from the others systems.) Spae in spae in spae It is possible to put a new oordinate system s t in the oordinate system of s t. I won t go into details here Superluminal veloity in the speial relativity? FIG. 10. shows that the event OA is the reason of the event AB whih is the reason of the event BC. Without fast waves, the BC event has no reason. How an we put the fast wave in the speial relativity? There are two solutions. There is a way to put the superluminal veloity in the speial relativity. I ll use here two

38 38 Cartesian oordinate systems, beause they are easy to understand. FIG. 13. Time and spatial distane are in meters. The figure shows, how to put a fast wave into the speial relativity. st and s t are two different oordinate systems, but every rule remains the same in both. In st is the light. In s t is the fast wave with veloity from the viewpoint of matter-spae, here t = s= 1. Here are different (longer) units than in oordinate system st. Using these different units, we an alulate with fast wave like with lights. The green area is the region of fast light. In this figure the E of unified fast light in s t and the D of light in st are the same point. How to display that E and D are the same point? We an use more than two oordinate systems: st, s t and s t, see FIG. 14. Here s t and s t are oordinate systems of fast waves. They are the same oordinate system, the differene between s t and s t is a rotation. Now we have to show how the hain of ausality goes. So the oordinate system s t must be rotated at K, so a new oordinate system s t will appear. In reality there isn t any rotation; this is a visual solution to show the ausality more learly.

39 39 FIG. 14. Time and spatial distane are in meters. The figure shows how to put a fast wave into the speial relativity. st and s t are two different oordinate systems, but every rule remains the same in both. s t is the same s t rotated. The AGEF region is the region of fast waves shown in three oordinate systems. (AF and FB are in st.) sl s' Note st and s t have different units, but = = 1. The two oordinate systems are not t t' independent, onnets them together. To use Eq. (54) we have to know α, that is, the veloity of fast wave v. where time and distane have the same dimension. L sl t ' = tl s' = 1, (54) The very visual version of the general ausality is FIG. 15. FIG. 15. Light and fast light in the same figure displayed by four oordinate systems. The best way to make the ausality and the importane of fast waves visible is using four oordinate systems. The veloities are in every oordinate system. The light OA and the fast wave AB result in light BC. These are measured values. Using the oordinate systems of matter-spae after OA omes AK. KK is the next step and K B results in BC. The OK and the K C lines aren t broken while the three yellow setions are the regions of fast waves. The oordinate systems like these an be used in the speial theory of relativity. Note the earlier symmetry of the viewpoints of objet and observer annot be held with or without fast waves, beause the spae waves are parts of the inertial frames of referene. Longer and shorter wavelength of spae waves are real differenes.