Maximum Velocity for Matter in Relation to the Schwarzschild Radius Predicts Zero Time Dilation for Quasars

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1 Maximum Veocity for Matter in Reation to the Schwarzschid Radius Predicts Zero Time Diation for Quasars Espen Gaarder Haug Norwegian University of Life Sciences November, 08 Abstract This is a short note on a new way to describe Haug s newy introduced maximum veocity for matter in reation to the Schwarzschid radius. This eads to a probabiistic Schwarzschid radius for eementary partices with mass smaer than the Panck mass. In addition, our maximum veocity, when inked to the Schwarzschid radius, seems to predict that partices just at that radius cannot move. This impies that radiation from the Schwarzschid radius not can undergo veocity time diation. Our maximum veocity of matter, therefore, seems to predict no time diation, even in high Z quasars, as has surprisingy been observed recenty. Keywords: Schwarzschid radius, maximum veocity of matter, probabiistic Schwarzschid radius, quasars, time diation. Haug s Maximum Veocity for Matter Haug s newy introduced maximum veocity for matter has been pubished in a series of papers and working papers; see, for exampe [,, 3]. It is given by v max = c p λ () where p is the Panck ength; see aso [4, 5]. This formua can be derived simpy by putting a Panck ength imit on ength contraction, or one can set the maximum reativistic mass (energy) for an eementary partice to the Panck mass (energy), for exampe. Aternativey, one can even derive this formua from Heisenberg s uncertainty principe, if one assumes that the minimum uncertainty in position is the Panck ength, see [7]. Haug has aso recenty shown that the Panck ength is given by p = Rs λ () where R s is the Schwarzschid radius and λ is the reduced Compton waveength of the same mass. An important point is that the Schwarzschid radius and the reduced Compton waveength can be found independent of any knowedge of Newton s gravitationa constant or any knowedge of the Panck constant as shown by [6]. This means the maximum veocity is given by v max = c p λ = c Rs λ = c Rs (3) λ λ We think this formua ony gives meaning for eementary partices; we have suggested in other working papers that a eementary partices have a probabiistic Schwarzschid radius. More precisey, they have a Schwarzschid radius equa to the Panck ength with a frequency (probabiity) of ony p λ. That is to say, the probabiistic Schwarzschid radius for an eementary partice is R s = p p λ (4) e-mai espenhaug@mac.com. Thanks to Victoria Terces for heping me edit this manuscript.

2 This version of the Schwarzschid radius formua aso hods for masses arger than the Panck mass, but then the interpretation is no onger simpy probabiistic, as the probabiistic factor (frequency): p λ wi be higher than one. Integer numbers above one indicate the number of Panck masses, and there is certainty for Panck masses. The fraction above one indicates an additiona probabiistic factor for the remaining mass. This means that probabiistic effects dominate beow the Panck mass and determinism dominates above; see [7]. Be aware that the Schwarzschid radius of any mass, incuding the probabiistic Schwarzschid radius of eementary partices such as eectrons, can be found independent of any knowedge of G. The Panck ength can aso be found independent of G and ; see Haug s recent working papers [8]. Even if the maximum veocity formua ony hods for eementary partices, it can give a good indication of the maximum veocity of composite masses (e.g. partices such as protons). As suggested by [, 7], the maximum veocity of the composite object wi be imited by the heaviest eementary partice in the object. Our theory predicts that the heaviest partice wi start to dissove into energy when it reaches the maximum veocity. Any eementary partice is then a Panck mass Gravitationa Time Diation Pus Veocity Time Diation at the Schwarzschid Radius For a Panck Mass Gravitationa Object If we take into account gravitationa time diation pus veocity time diation from genera reativity utiizing the Schwarzschid metric, we have (see [9] for an exceent introduction to this ) dτ = dt Rs r v (5) c where R s is the Schwarzschid radius, and r = R + h where h is the height (distance) from R. Further, v is the orbita veocity of the object traveing around the gravitationa object. Assume we now want to ook at the specia case of a Panck mass partice. This is the smaest known mass with a Schwarzschid radius. A partice with a smaer mass wi have a Schwarzschid radius ess than the Panck ength according to the standard formua of R s = Gm c (6) that again is equivaent to R s = p p λ. We coud get into a engthy discussion over whether the factor actuay shoud be instead of in a very strong gravitationa fied, but that is beyond the scope of this short paper. Instead, et us assume a gravitationa object with Panck mass m p and that something is moving just at the Schwarzschid radius. In other words, we assume h = 0 and r = R s + 0 this eads to dτ = dt Rs v (7) R s c As Rs R s =, this eads to the square root of a negative number for any v > 0. Does this mean that the time diation at the Schwarzschid radius is imaginary? We don t think so. However, the maximum veocity, as given by Haug s maximum veocity formua for a Panck mass partice, is v max = c p λ = c p λ = c p = 0 (8) p where λ is the reduced Compton waveength of the partice in question. For any observed eementary partice, such as an eectron, this veocity is very cose to c, but far above what has been accompished by the Large Hadron Coider. In the specia case of a Panck mass partice, we have λ = p; this means the maximum veocity for a Panck mass partice is zero. Thus, for a Panck mass partice we must have p. 75

3 3 dτ = dt Rs v max R s c ( c p R s p dτ = dt R s c c ( p ) dτ = dt p c dτ = dt ) + p = 0 (9) p That is to say, we have zero time diation at the Schwarzschid radius for a Panck mass. It is not a new concept that time must stand sti at the Schwarzschid radius. However, what we have not seen discussed before is that any object (with mass) at the Schwarzschid radius must itsef stand sti in order for this to happen. This is consistent with Haug s predictions where he has caimed that the Panck mass partice must stand absoutey sti, see [, 7]. However, it ony stands sti for one Panck second before it bursts into energy. We can think of standard eementary partices moving at very cose to the speed of ight towards the Schwarzschid radius. They are getting dramaticay compressed, due to the very strong gravitationa fied. Just at the Schwarzschid radius, they are compressed to Panck mass partices m = v max c λ c ( c p λ c ) = = mp (0) p c The Panck mass partice then suddeny stand sti for one Panck second before they burst into energy. One coud imagine some of this energy eaving the Schwarzschid radius in sudden bursts of energy. This eads to a breakdown of Lorentz symmetry at the Panck scae. A breakdown in Lorentz symmetry is not that controversia, as it is aso predicted by severa quantum gravity theories; see [0,, ]. Aternativey, one needs to introduce imaginary time diation (the square root of negative one), but this does not seem to be very ogica. In modern cosmoogy, it is commony assumed that a quasar is supermassive object, often caed a back hoe. Further, it is assumed that the radiation from the quasar ikey comes from a ayer of matter cose to the back hoe. If quasars are radiating back hoes, then even high Z quasars wi ikey not have any time diation. This because it is just at the Schwarzschid radius that the partices burst into energy after standing sti for one Panck second. This prediction of no veocity time diation in quasars (back hoes) is exacty what modern observationa physics has shown [3, 4]. Hawking studied a series of high red-shift (high Z) quasars and surprisingy did not find the expected time diation predicted by standard physics. His observationa study is a great achievement, but we are sti critica towards postuates associated with the growth of the centra supermassive back hoe in quasars/active gaactic nuceus (AGN) to offset the missing expected time diation in the standard theory. Coud this aso mean there is a very different expanation for cosmoogica red-shift than today s theory caims? At a minimum, it suggests that we shoud, once again, study other aternative theories in more detai. One coud even suggest that the ack of time diation in quasars is one of the first observations possiby is confirming that Lorentz symmetry breaks at the Panck scae, the Schwarzschid radius is the Panck scae. Our newy introduced maximum veocity aso indicates so caed back hoes are possiby a misnomer. A eementary partices must be compressed to Panck mass partices at Schwarzschid radius as they then reaches the veocity of v max = c Rs = c p λ λ, they then stand sti and then burst into energy. So they go from a veocity just beow the speed of ight to standing sti for one Panck second and then bursting into energy and moving at speed c. Some of this energy ikey goes inward into the so-caed back hoe, so in this sense it is back, but some of it ikey aso bursts out. Remember this is at the very boundary of the back hoe. This indicates the Schwarzschid radius is a radiation horizon where matter is compressed and then bursts into energy. Back hoes are, for this reason, ikey white hoes (with this we simpy mean bright), and one wi not observe any time diation from the radiation coming from the Schwarzschid radius itsef, and very itte time diation from partices at a distance of a few Panck engths away from the the Schwarzschid radius.

4 4 3 Heisenberg Uncertainty Principe Extended to the Schwarzschid Radius In 97, Heisenberg [5] pubished what today is known as the Heisenberg Schwarzschid principe; (see aso [6]) p x () In 93, during his Nobe ecture Heisenberg himsef suggested the existence of a universa east ength. Later on (in 958), he assumed that the east ength was the atom nucei diameter 0 5 m; see aso [7]. A series of researchers have argued that the Panck ength is indeed the shortest ength that gives any meaning; see [8, 9], for exampe. Modern quantum gravity theories are aso returning to the idea that the Panck ength is the universa east ength, even though there is sti considerabe scientific debate on this. Here we wi assume that the smaer possibe uncertainty in the position is the Panck ength. We can then repace our expression for the Panck ength with p = Rs λ and see what we get. Further, we wi assume that eementary partices must have a momentum smaer than or equa to the Panck mass momentum; the maximum momentum is then m pc = p. If this is the maximum momentum of an eementary partice (incuding the Panck mass partice), then this must aso be the maximum uncertainty in the momentum for an eementary partice. Based on this we get p p x p p Rs λ Rs p λ Rs m λ pc Rs p p Rs λ c c λ R s p λ = p p λ The correct interpretation of this is ikey that the Schwarzschid radius is probabiistic for eementary partices. A eementary partices have a Schwarzschid radius equa to the Panck ength, but they ony have this at the Compton periodicity, and the Schwarzschid radius ony asts for one Panck second for each unit of Compton time. That is the Schwarzschid radius is the reduced Compton frequency over the shortest possibe time interva mutipied by the shortest possibe ength. This means the probabiity inside a Panck second for observing the Schwarzschid radius is p λ. For the Panck mass partice (aso known by modern physics as a micro back hoe), this probabiity is one, because we then have λ = p. That is why the Panck mass partice is the smaest mass that has a Schwarzschid radius. Smaer partices sti have a Schwarzschid radius, but it is then probabiistic. 4 The Panck Constant A sma side note is that we can rewrite the Panck constant as = Rs λc 3 (3) G This is simpy because the Panck constant is embedded in Newton s gravitationa constant, as the gravitationa constant is simpy G = p c3 ; see [], that is ()

5 5 = Rs λc 3 G = p 3 p λ λc = pc 3 G G = pc 3 p c3 (4) 5 Concusion In this paper, we have shown that there is a ink between the Schwarzschid radius and our maximum veocity of matter. An important point is that the Schwarzschid radius can be found independent of any knowedge of Newton s gravitationa constant or any knowedge of the Panck constant. This again eads to the idea that we can derive a probabiistic Schwarzschid radius for eementary partices using the Heisenberg uncertainty principe. Our maximum veocity of matter, when inked to the Schwarzschid radius, aso seems to predict that even high Z quasars cannot have time diation, something that has been confirmed by experiments. References [] E. G. Haug. The gravitationa constant and the Panck units. A simpification of the quantum ream. Physics Essays Vo 9, No 4, 06. [] E. G. Haug. The utimate imits of the reativistic rocket equation. The Panck photon rocket. Acta Astronautica, 36, 07. [3] E. G. Haug. Newton and Einstein s gravity in a new perspective for Panck masses and smaer sized objects. Internationa Journa of Astronomy and Astrophysics, 08. [4] Max Panck. Naturische Maasseinheiten. Der Königich Preussischen Akademie Der Wissenschaften, p. 479., 899. [5] Max Panck. Voresungen über die Theorie der Wärmestrahung. Leipzig: J.A. Barth, p. 63, see aso the Engish transation The Theory of Radiation (959) Dover, 906. [6] E. G. Haug. Finding the Panck ength independent of newton s gravitationa constant and the Panck constant: The Compton cock mode of matter [7] E. G. Haug. Revisiting the derivation of Heisenberg s uncertainty principe: The coapse of uncertainty at the Panck scae. preprints.org, 08. [8] E. G. Haug. Gravity without Newton s gravitationa constant and no knowedge of mass size. preprints.org, 08. [9] Ø Grøn. Lecture Notes on the Genera Theory of Reativity. Springer Verag, 009. [0] F. Kisat and H. Krawczynski. Panck-scae constraints on anisotropic Lorentz and CPT invariance vioations from optica poarization measurements. Physica Review D, 95, 07. [] G. Ameino-Cameiaa, B. J. Eisc, N.E. Mavromatosa, D.V. Nanopouosd, and Sarkar S. Potentia sensitivity of gamma-ray burster observations to wave dispersion in vacuo. Nature, 393, 998. [] Reyesa C. M., S. Ossandonb, and C. Reyesc. Higher-order Lorentz-invariance vioation, quantum gravity and fine-tuning. Physics Letters B, 746, 005. [3] M. R. S. Hawkings. On time diation in quasar ight curves. Mon. Not. R. Astron. Soc., 406: , 000. [4] M. R. S. Hawkings. Time diation and quasar variabiity. The Astrophysica Journa, 553:97 00, 00. [5] W. Heisenberg. Über den anschauichen inhat der quantentheoretischen kinematik und mechanik. Zeitschrift für Physik, (43):7 98, 97. [6] E. H.. Kennard. Zur quantenmechanik einfacher bewegungstypen. Zeitschrift für Physik, (44):36 35, 97. [7] R. L. Wadinger and Hunter G. Max Panck s natura units. The Physics Teacher, pages 58 59, 988. [8] T. Padmanabhan. Panck ength as the ower bound to a physica ength scaes. Genera Reativity and Gravitation, 7, 985. [9] R. J. Ader. Six easy roads to the Panck scae. American Journa of Physics, 78(9), 00.