scholarly journals Does Special Relativity Lead to a Trans-Planckian Crisis?

2019 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Special Relativity ◽  
Gravitational Constant ◽  
Maximum Velocity ◽  
Relativity Theory ◽  
Speed Limit ◽  
Planck Length ◽  
Planck Constant ◽  
General Relativity Theory ◽  
Time Intervals ◽  
Planck Time

In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time. The trans-Planckian problem is easily solved by a small modification that assumes Haug’s maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton’s gravitational constant or the Planck constant.

scholarly journals Special Relativity Leads to a Trans-Planckian Crisis that Is Solved by Haug's Maximum Velocity for Matter

2018 ◽  
Author(s):  
Espen Haug
Keyword(s):  
Special Relativity ◽  
Maximum Velocity ◽  
Gold Rush ◽  
Relativity Theory ◽  
Theoretical Physics ◽  
Speed Limit ◽  
Planck Length ◽  
Time Intervals ◽  
Slow Progress ◽  
Planck Time

In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time. The trans-Planckian problem is easily solved by a small modication that assumes Haug's maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton's gravitational constant or the Planck constant. After a long period of slow progress in theoretical physics, we are now in a Klondike "gold rush" period where many of the essential pieces are falling in place.

scholarly journals A New Mass Measure and a Simplication of Modern Physics that Make Gravity Predictions Independent of G

2019 ◽  
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Maximum Velocity ◽  
Relativity Theory ◽  
Particle Accelerators ◽  
Planck Length ◽  
Speed Of Light ◽  
Planck Constant ◽  
Arbitrary Mass ◽  
Subatomic Particles ◽  
Modern Physics ◽  
Important Exception

Recent experimental research has shown that mass is linked to Compton periodicity. We suggest a new way to look at mass: Namely that mass at its most fundamental level can simply be seen as reduced Compton frequency over the Planck time. In this way, surprisingly, neither the Planck constant nor Newton's gravitational constant are needed to observe the Planck length, nor in any type of calculation or gravitational predictions. The Planck constant is only needed when we want to convert back to the more traditional and we would say arbitrary mass measures such as kg. The theory gives the same predictions as Einstein's special relativity theory, with one very important exception: anything with mass must have a maximum velocity that is a function of the Planck length and the reduced Compton wavelength. For all observed subatomic particles, such as the electron, this velocity is considerably above what is achieved in particle accelerators, but always below the speed of light. This removes a series of infinity challenges in physics. The theory also offers a way to look at a new type of quantum probabilities. As we will show, a long series of equations become simplied in this way. Further Newton's gravitational constant G is clearly not needed for gravity calculations or predictions; it is the Planck length and the speed of light (gravity) that are essential for gravity, and both can be measured easily with no knowledge of G.

scholarly journals BIANCHI I SOLUTIONS OF EFFECTIVE QUADRATIC GRAVITY

2012 ◽  
Vol 21 (04) ◽  
pp. 1250037 ◽  
Author(s):  
DANIEL MÜLLER ◽  
JULIANO A. DE DEUS
Keyword(s):  
Numerical Solutions ◽  
Relativity Theory ◽  
De Sitter ◽  
General Relativity Theory ◽  
Spatial Metrics ◽  
Effective Gravity ◽  
Bianchi I ◽  
Quadratic Theory ◽  
Quadratic Gravity ◽  
Planck Time

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.

Non-Kinematicity of the Dilation-of-time Relation of Einstein for Time-intervals

2000 ◽  
Vol 55 (6-7) ◽  
pp. 563-569 ◽  
Author(s):  
Sidney Golden
Keyword(s):  
Special Relativity ◽  
Relative Velocity ◽  
Relativity Theory ◽  
Einstein Relation ◽  
Time Interval ◽  
Time Intervals ◽  
Light Pulses ◽  
Time Relation ◽  
Special Relativity Theory ◽  
Inertial Systems

Abstract Light-pulses that are reflected recurrently to one another by two kinematically equivalent dynamically identical inertial systems moving collinearly and irrotationally with uniform relative velocity generate sequences of contiguous time-intervals in both. By means of clocks stationed in the two systems, each time-interval is both measurable locally and calculable non-locally in accord with basic requirements of special relativity theory. Their ratio yields the velocity dependent dilation-of-time relation of Einstein, but an equivalent spatially dependent version of it is obtained as well, because the time-intervals involved are actually determined by the distances that exist between the systems when the reflections occur. As a result, the Einstein relation involves no time-rates of clocks that are actually affected kinematically by the systems containing them.

scholarly journals HOMOGENEOUS SOLUTIONS OF QUADRATIC GRAVITY

2011 ◽  
Vol 03 ◽  
pp. 111-120 ◽  
Author(s):  
DANIEL MÜLLER
Keyword(s):  
Relativity Theory ◽  
General Relativity Theory ◽  
Homogeneous Solutions ◽  
Bianchi I ◽  
Quadratic Theory ◽  
Quadratic Gravity ◽  
Generalized Potential ◽  
Planck Time ◽  
Limiting Case ◽  
Einstein’S General Relativity

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3 + 1 decomposition for the zero vorticity case for arbitrary spatially homogenous spaces. We specialize for the particular Bianchi I diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi I case is a limiting case where this potential is negligible to the dynamics. The spirit should be analogous, in some sense to the BKL solution. In this sense, a better understanding of the Bianchi I case could shed some light into the general Bianchi case.

scholarly journals A Bridge between Quantum Mechanics and Astronomy

2015 ◽  
Vol 8 (1) ◽  
pp. 16 ◽  
Author(s):  
Anna C.M. Backerra
Keyword(s):  
Quantum Mechanics ◽  
Large Scale ◽  
Massless Particle ◽  
Relativity Theory ◽  
Small Scale ◽  
Speed Of Light ◽  
Planck Constant ◽  
General Relativity Theory ◽  
Constant Amount ◽  
The Universe

<p class="1Body">Small-scale physics called quantum mechanics, is still incompatible with large-scale physics as developed by Einstein in his general relativity theory. By using twin physics, which is a dualistic way of considering the universe, and following Einstein’s later advice it is possible to create a bridge between these extremes. The formulation is carried out using complementary language in which time and space necessarily occur as two distinct qualities, although they are treated analogously. The basic item in the theory is the Heisenberg unit, which has a constant amount of potential energy, and which is supplied with mathematical attributes; by interaction with another Heisenberg unit, these attributes are transformed into physical qualities. With this theory, a photon can be described such that its velocity is constant without using the related postulate, showing how the speed of light is the link between small- and large-scale physics. The Planck constant emerges from the explanation. The photon is accompanied by a so-called anti-photon, being a charged, massless particle, traveling with the same velocity and exchanging electromagnetic energy.</p>

VII.—On the Geometry of Dirac's Equations and their Expression in Tensor Form

1938 ◽  
Vol 57 ◽  
pp. 97-127 ◽  
Author(s):  
H. S. Ruse
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relativity Theory ◽  
Tensor Form ◽  
General Relativity Theory ◽  
Spinor Theory ◽  
Two Component

The purpose of the present paper is to give as simple an account as possible of the general-relativity theory of two-component spinors, and to investigate its geometrical and analytical consequences. The work was suggested by courses of lectures given at Edinburgh in 1932 and 1935 by Professor E. T. Whittaker, who, on the basis of the special-relativity spinor theory of van der Waerden (1929), obtained the completely tensorized form of Dirac's equations given by him in a recent paper (1937).

BORN'S RECIPROCAL GENERAL RELATIVITY THEORY AND COMPLEX NON-ABELIAN GRAVITY AS GAUGE THEORY OF THE QUAPLECTIC GROUP: A NOVEL PATH TO QUANTUM GRAVITY

2008 ◽  
Vol 23 (10) ◽  
pp. 1487-1506 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Planck Scale ◽  
Relativity Theory ◽  
Target Space ◽  
Speed Limit ◽  
General Relativity Theory ◽  
Curved Space ◽  
Maximal Speed ◽  
Proper Force

Born's reciprocal relativity in flat space–times is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved space–times and construct a reciprocal general relativity theory (in curved space–times) as a local gauge theory of the quaplectic group and given by the semidirect product [Formula: see text], where the non-Abelian Weyl–Heisenberg group is H(1, 3). The gauge theory has the same structure as that of complex non-Abelian gravity. Actions are presented and it is argued why such actions based on Born's reciprocal relativity principle, involving a maximal speed limit and a maximal proper force, is a very promising avenue to quantize gravity that does not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other approaches based on deformations of the Poincaré algebra, quantum groups. It is discussed how one could embed the quaplectic gauge theory into one based on the U(1, 4), U(2, 3) groups where the observed cosmological constant emerges in a natural way. We conclude with a brief discussion of complex coordinates and Finsler spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant closed-string target space backgrounds where Born's principle may be operating.

scholarly journals Measurements of the Planck Length from a Ball Clock without Knowledge of Newton’s Gravitational Constant G or the Planck Constant

2021 ◽  
Vol 3 (6) ◽  
pp. 15-20
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Gravitational Constant ◽  
Planck Scale ◽  
Simple Approach ◽  
Planck Length ◽  
Planck Constant ◽  
Physics Teachers ◽  
Teachers And Students ◽  
Plank Length ◽  
Newtonian Gravitational Constant

We demonstrate how one can extract the Planck length from ball with a built-in stopwatch without knowledge of the Newtonian gravitational constant or the Planck constant. This could be of great importance since until recently it has been assumed the Planck length not can be found without knowledge of Newton’s gravitational constant. This method of measuring the Planck length should also be of great interest to not only physics researchers but also to physics teachers and students as it conveniently demonstrates that the Plank length is directly linked to gravitational phenomena, not only theoretically, but practically. To demonstrate that this is more than a theory we report 100 measurements of the Planck length using this simple approach. We will claim that, despite the mathematical and experimental simplicity, our findings could be of great importance in better understanding the Planck scale, as our findings strongly support the idea that to detect gravity is to detect the effects from the Planck scale indirectly.

scholarly journals Gravity without Newton's Gravitational Constant and No Knowledge of Mass Size

2018 ◽  
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Gravitational Constant ◽  
Universal Constant ◽  
Einstein Gravity ◽  
Relative Mass ◽  
Planck Length ◽  
Speed Of Light ◽  
Planck Constant ◽  
The Earth ◽  
Mass Size ◽  
Schwarzschild Radius

In this paper we show that the Schwarzschild radius can be extracted easily from any gravitationally-linked phenomena without having knowledge of the Newton gravitational constant or the mass size of the gravitational object. Further, the Schwarzschild radius can be used to predict any gravity phenomena accurately, again without knowledge of the Newton gravitational constant and also without knowledge of the size of the mass, although this may seem surprising at first. Hidden within the Schwarzschild radius are the mass of the gravitational object, the Planck mass (their relative mass), and the Planck length. We do not claim to have all the answers, but this seems to indicate that gravity is quantized, even at a cosmological scale, and this quantization is directly linked to the Planck units. This also supports our view that the Newton gravitational constant is a universal composite constant of the form G = l p 2 c 3 ℏ , rather than relying on the Planck units as a function of G. This does not mean that Newton&rsquo;s gravitational constant is not a universal constant, but that it is instead a composite universal constant that depends on the Planck length, the speed of light, and the Planck constant. Further, G &times; 1 &thinsp; weight &thinsp;unit c 2 = G c 2 is the Schwarzschild radius off one weight unit. So G is only needed when we want to use gravity to find the weight of an object, such as weighing the Earth. This is, to our knowledge, the first paper that shows how a long series of major gravity predictions and measurements can be completed without any knowledge of the mass size of the object, or Newton&rsquo;s gravitational constant. As a minimum we think it provides an interesting new angle for evaluating existing gravity theories, and it may even give us a small hint on how to combine quantum gravity with Newton and Einstein gravity.

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