קיימים מספר ערוצי קבלה.
בכל אחד מערוצים אלו, יש לעמוד בנוסף ביתר תנאי הקבלה. פירוט נוסף ניתן למצוא בקטגוריית מועמדים וכן במדריך לנרשם.
הלימודים מתחילים בסמסטר אלול. במהלך הסמסטר לומדים, בנוסף ללימודי קודש, גם את קורסי הקדם במתמטיקה, מחשבים ופיזיקה (משתנה מחוג לחוג). הסמסטר אורך כחודש ומטרתו לסייע לסטודנטים לחזק ולרענן את הידע בתחומים אלו לקראת הקורסים המתקדמים של סמסטר א'. לכל תלמיד חדש מפורט במכתב הקבלה אילו קורסים הוא מחויב ללמוד בסמסטר אלול.
שכר הלימוד במרכז האקדמי לב הוא שכר לימוד אוניברסיטאי מופחת ונקבע כל שנה על פי החלטת המועצה להשכלה גבוהה.
שכר הלימוד אינו כולל תשלומים עבור לימודי קודש, קורסי יסוד באנגלית, קורסי קדם ואגרות.
מבחן פוטנציאל שבודק כישורים ותכונות רלוונטיים ללימודים האקדמיים. מבחן זה מוכר כמקביל למבחן הפסיכומטרי עבור קבלה למרכז האקדמי לב, למעט למועמדי העתודה האקדמית ומועמדים לחוג לסיעוד.
המבדקים נמשכים כ-4 שעות ומתייחסים למידת ההתאמה לחוג המבוקש. המבדקים מוצגים באמצעות צג המחשב ואין כל צורך בהתנסות קודמת בהפעלת מחשב על מנת להצליח בהם. מבחן להתנסות עצמית ניתן למצוא באתר תיל אינטרנשיונל. לפרטים נוספים על המבחן ושאלות לדוגמא- לחץ כאן
ניתן לבצע שינוי כל עוד החוג פתוח להרשמה. השינוי חייב להתבצע ע"י פניה במייל למדור מידע ורישום.
במידה והנך עומד בכל תנאי הקבלה, מכתב הקבלה יישלח במייל בתוך שבוע ממועד קיום הריאיון.
1985, B.A. in Mathematics and Philosophy, University of Tennessee at Chattanooga, USA, graduated magna cum laude with Honors in Philosophy.
1989, M.A. in Mathematics, University of California, Berkeley, USA. Thesis: On Sierpinski’s Sets, supervisor: Jaime Ihoda (Chaim Judah)
2000, Ph.D. in Mathematics, Bar Ilan University, Ramat Gan, ISRAEL. Thesis: Compactifications of G-spaces, supervisor: Professor Hillel Furstenberg.
August 1988 – December 1989: Graduate Teaching Assistant, Department of Mathematics and Department of Astronomy, University of California, Berkeley, USA.
Courses: Discrete Mathematics, Introduction to Astronomy
February 1993 – June 1993: Exercise grader (בודק תרגילים), Department of Mathematics, Bar Ilan University, Ramat Gan, ISRAEL
Course: Mathematical Logic
October 1993 – September 1999: Graduate Teaching Assistant, Department of Mathematics, Bar Ilan University, Ramat Gan, ISRAEL
Courses: Calculus I and II, Topology, Logic for Computer Scientists
October 1997 – August 1999: Teaching assistant (מתרגל), Department of Applied Mathematics, Jerusalem College of Technology (Machon Lev), Jerusalem, ISRAEL
Courses: Calculus I and II, Complex Variables, Linear Algebra I, Linear Algebra for Business Majors, Differential Equations
August 1999 – present: Lecturer (מרצה), Department of Applied Mathematics, Jerusalem College of Technology (Machon Lev), Jerusalem, ISRAEL
Courses: Precalculus, Calculus I and II, Linear Algebra I and II, Discrete Mathematics, Differential Equations, Probability, Statistics, Partial Differential Equations, Mathematical methods in physics; teaching assistant (מתרגל) for Seminar in Modern Physics (August 2004)
a. Summary of Past Research and Development Activities
Theorem (Megrelishvili, Scarr) If G is an -bounded topological group which is not locally precompact, then G is not a V-group.
This theorem establishes the existence of monothetic (even cyclic) non-V-groups, answering a question of Megrelishvili. We also obtained a characterization of locally compact groups in terms of G-normality. We also answered a question of E. Glasner by proving the following theorem:
Theorem (Megrelishvili, Scarr) Let G be a Polish group. Then G is a V-group if and only if G is locally compact.
Theorem (Megrelishvili, Scarr) Let G be a Polish group. Then every Polish G-space can be topologically embedded into a compact Polish G-space if and only if G is locally compact.
The proof of this theorem uses the strong Choquet game from descriptive set theory.
We also studied the actions of non-Archimedean groups on zero-dimensional spaces and proved the following theorem:
Theorem (Megrelishvili, Scarr) Let G be a non-Archimedean and second countable group, and let X be a compact, metrizable, zero-dimensional G-space. Let be the natural (evaluation) action of the full group of homeomorphisms of the Cantor cube . Then
(1) there exists a topological group embedding , and
(2) there exists an embedding , equivariant with respect to , such that
is an equivariant retract of with respect to and .
A better candidate is the covariant equation
where is the four-acceleration. However, current techniques have produced only one-dimensional hyperbolic motion as solutions to this equation. There are clearly some additional solutions, since this equation is covariant, while hyperbolic motion is not.
Yaakov Friedman and I proposed the relativistic dynamics equation
where u is the four-velocity and is a rank 2 antisymmetric tensor. We then defined a motion to be uniformly accelerated if it satisfies equation (1) for constant A. We then computed explicit solutions of equation (1). The solutions are divided into four Lorentz-invariant classes: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends one-dimensional hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion.
At this stage of the research, the following was still an open question:
Question 1 Does equation (1) model all uniformly accelerated motions?
We would eventually answer this question positively, but first we had to extend equation (1) to a uniformly accelerated frame. The solutions to
form an orthonormal basis to a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. In this so-called generalized Fermi–Walker frame, the solutions to equation (1) have constant acceleration.
Under B. Mashhoon’s Weak Hypothesis of Locality, we obtained explicit local spacetime transformations from a uniformly accelerated frame to an inertial frame. These transformations extend the Lorentz transformations. We also proved the following surprising result:
Theorem (Friedman, Scarr) Let and be uniformly accelerated frames with the same acceleration tensor . Then the spacetime transformations between and are Lorentz.
Application The spacetime transformations between an observer at rest on the Earth and an airplane flying at constant velocity are the Lorentz transformation, since both systems are uniformly accelerated with respect to the gravitational field of the Earth.
Our results on spacetime transformations led to the following question:
Question 2 Do the spacetime transformations between uniformly accelerated systems form a group?
Although we have some preliminary indications that the answer is no, this question is still open.
Our definition (equation (2)) of the uniformly accelerated frame is a system of uncoupled differential equations. This means that they are relatively easy to solve. B. Mashhoon, on the other hand, uses a coupled system defined by the Frenet frame. The advantage of Mashhoon’s approach is that it is frame independent, while our definition is with respect to a particular inertial frame. We showed, however, that the two approaches yield the same solutions. This equivalence led to the answer to Question 1:
Theorem (Friedman, Scarr) A motion is uniformly accelerated if and only if it satisfies equation (1).
Thus, equation (1) provides a complete and covariant description of uniformly accelerated motion.
Continuing to develop the theory, we adapted the off-shell technique of L. Horwitz and C. Piron to obtain both velocity and acceleration transformations from a uniformly accelerated frame to an inertial frame. We also obtained the time dilation between clocks in a uniformly accelerated frame. The power series expansion of our time dilation formula contains all of the usual terms, but also an additional term that had only been obtained previously in Schwarzschild spacetime. We applied these results to the case of an accelerated charge and obtained the Lorentz-Abraham-Dirac equation
The next step was to extend our theory to curved spacetimes. Given an arbitrary curved spacetime, we constructed a system of non-linear first-order differential equations which extends the geodesic equation and whose solutions are precisely the uniformly accelerated motions in the given spacetime.
This improved a result of D. de la Fuente and A. Romero, whose corresponding equation models only hyperbolic motion. We consider the particular case of radial motion in Schwarzschild spacetime and show that in this situation, there are no bounded orbits.
The Problem Consider a disk rotating with constant angular velocity with respect to an inertial frame. Compute the spacetime transformations from the disk to the inertial frame.
This problem has been debated for over 100 years and continues to the present day. The recent book of Rizzi and Ruggerio makes it clear that there is still no universally accepted theory. Moreover, many of the current approaches make arbitrary assumptions about the form of the transformation of the
radius of the disk, the radial coordinate. There is still no theory which derives the transformations from first principles.
In our paper, Yaakov Friedman and I derive explicit spacetime transformations using only the basic tenets of Special Relativity, the inherent symmetries of the problem, and our previous results on uniform acceleration. We do not make any arbitrary assumptions about the form of the transformations.
We avoid the horizon problem
Our transformations imply that the speed, with respect to an inertial frame, of a rest point on the disk at any radius does not exceed the speed of light. This implies, contrary to standard reasoning, that
Special Relativity does not impose a limitation on the size of a rotating object. That is, we avoid
the horizon problem. According to the horizon problem, global rigid rotations are forbidden in
relativistic theories, because at large distances, the angular velocity will exceed the speed of
light. In our approach, the horizon problem does not arise. We obtain a global reference frame, with no limit of the distance from the axis of rotation, and all speeds are bounded by the speed of light.
No time gap
We show how to synchronize the clocks on the disk, not only to each other, but also to
the clocks in the lab frame. Clock synchronization on a rotating disk was heretofore thought
impossible because a time gap invariably arises. We give a clear description of our synchronization procedure and explain how to avoid the time gap. We were also lead to the following conjecture:
Conjecture (Friedman, Scarr) A system is uniformly accelerated if and only if all of the clocks in the system can be synchronized to each other, and the clocks will remain synchronized as long as the acceleration remains uniform.
This conjecture is still open.
Bernhard Riemann was a strong advocate of a geometric approach to physics. His lifelong dream was to develop the geometry to unify the laws of electricity, magnetism, light and gravitation. In fact, Riemann believed that the forces at play in a system determine the geometry of the system. In other words, force equals geometry.
General Relativity (GR) is a direct application of “force equals geometry.” Consider a particle freely falling towards the Earth. In Newtonian Dynamics, the particle accelerates in response to the force of gravity, but in GR, the same particle has zero acceleration as it moves along a geodesic, a straight line in a curved spacetime. Gravity is no longer a force. It changes the geometry of spacetime from flat to curved and creates a new stage for particles to move on.
On the other hand, an electric field does not create a common stage on which all particles move. Indeed, a neutral particle does not feel any electric force at all. The way spacetime curves due to an electric field depends on both the field and intrinsic properties of the object. This leads to the following question:
Question Can Riemann's principle of “force equals geometry” be applied to other forces?
In Relativistic Newtonian Dynamics (RND), the answer is “yes.” We first introduce the relativity of spacetime. This means that spacetime is an object-dependent notion. An object lives in its own spacetime, its own geometric world, which is defined by the forces which affect it. For example, in the vicinity of an electric field, a charged particle and a neutral particle exist in different worlds, in different spacetimes. In fact, for the neutral particle, the electric field does not exist. Likewise, in the vicinity of a magnet, a piece of iron and a piece of plastic live in two different worlds.
The next new idea stems from the observation that an inanimate object has no internal mechanism with which to change its velocity. Hence, it has constant velocity, or zero acceleration, in its own world (spacetime). This lead us to formulate a new principle, the Generalized Principle of Inertia, which unifies Newton's first and second laws and states that: An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it.
In GR, a freely-falling object in a gravitational field moves along a geodesic determined by the metric of the spacetime. With respect to this metric, the object's acceleration is zero. The Generalized Principle of Inertia extends this idea so that every object moves along a geodesic in its spacetime. This geodesic is with respect to an appropriate metric, which we call the metric of the object's spacetime. The metric in GR is determined solely by the gravitational sources, while in our model, the metric of the object's spacetime depends on all of the forces affecting the object. In the case of static, conservative forces, the metric will depend only on the potentials of these forces.
In the particular case of an object moving in a static, spherically symmetric, conservative force field, the explicit form of the metric of the object's spacetime may be derived from a set of Euler-Lagrange type equations and conservation laws, in addition to spherical symmetry and a carefully defined classical limit. For the gravitational force, this metric turns out to be the Schwarzschild metric. We thus obtain a simple derivation of the Schwarzschild metric, one that does not require the field equations of GR. Furthermore, the resulting dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and exactly reproduces the following tests of GR:
Thus, RND is a viable alternative to GR and, moreover, has a much simpler mathematical derivation. In addition, the techniques of RND are applicable to all conservative force fields, not just gravitation.
GR versus RND
We apply RND to a static, spherically symmetric gravitational field, without assuming that the metric is diagonal. Spherical symmetry implies that all off-diagonal components are zero except , the coefficient of drdt. We construct an infinite series of metrics, analytic everywhere except , for which . The dynamics of these metrics all lead to the same trajectories as in the Schwarzschild model and therefore pass all classical test of GR. However, GR and RND predict different velocities on the trajectories, both for massive objects and massless particles. The total time for a radial round trip of light in RND is the same as in the Schwarzschild model, but RND allows for light rays to have different speeds propagating toward and away from the massive object. One of these metrics keeps the speed of light toward the object to be c. We are designing experiments, some of which may be possible on a chip, to test whether .
RND extends to multiple non-static forces, each of which obeys an inverse square law and whose field propagates at the speed of light.
RND needs to be extended to non-conservative forces, in particular, the magnetic force, and ultimately, the self-force. We also want to extend RND to the microscopic region. One possible approach is to use a complex scalar prepotential which is in fact a wave function. We already have some preliminary results.
We explore the role of symmetry in deriving the theory of Special Relativity (SR). The Lorentz transformations are isometries preserving the Minkowski metric. One then defines velocity addition and shows that the domain of all relativistically admissible velocities in SR is a bounded symmetric domain with respect to the group P of projective maps. The invariance of the metric between inertial frames enables one to use the Newtonian limit and the Lie algebra of P to derive a 3D relativistic dynamics equation. This equation canonically embeds into a fully covariant 4D version.
If one describes relative motion using symmetric velocities, the corresponding bounded domain is symmetric with respect to the conformal maps. This description leads to a spin-half representation of the Lorentz group and is useful in obtaining analytic solutions of the relativistic dynamics equation.
I will develop these ideas fully in a paper for the special issue of the journal Symmetry entitled “Relativity based on Symmetry.” I plan to present the paper at the 2nd International Conference on Symmetry in Benasque, Spain, in September 2019.
a. Peer-Reviewed Papers in Refereed Journals
Before latest appointment
G-Tychonoff, Topology and its Applications 86 (1998), 69 – 81, 12 pages. Impact factor 0.549,
citations 18, SCImago Q2
Applications 105 (2000), 113 – 119, 7 pages. Impact factor 0.549, citations 2,
of the Cantor Cube, Fund. Math. 167 (2000), 269 – 275, 7 pages. Impact factor 0.609, citations
10, SCImago Q3
Covariant: Explicit Solutions for Constant Force, Phys. Scr. 86 (2012) 7 pages. 065008.
Impact factor 1.032, citations 15, SCImago Q3
Accelerated System, Phys. Scr. 87 (2013) 8 pages. 055004. Impact factor 1.296, citations 10,
Since latest appointment (October 2014)
47:121 (2015) 19 pages. Impact factor 1.668, citations 14, SCImago Q2
Gen. Rel. Grav. 48:65 (2016) 9 pages. Impact factor 1.618, citations 4, SCImago Q2
conservative force, Int. J. Geom. Meth. Mod. Phys. 16 (2019) 1950015. 17 pages. Impact
factor 1.068, citations 0, SCImago Q2
Europhys. Lett. 125 (2019) 49001 7 pages. Impact factor 1.957, citations, SCImago Q2
Before latest appointment
1.Tzvi Scarr, Loops in Relativistic Dynamics, Proceedings of the Mile High Conference on
Quasigroups, Loops and Nonassociative Systems (July 2005) in Quasigroups
and Related Systems 14 (2006), 91 – 109, 19 pages. Impact factor n/a, citations 0, SCImago
Conference Series 437 (2013) 012009, “The 8th Biennial Conference on Classical and
Quantum Relativistic Dynamics of Particles and Fields (IARD 2012)” 27 pages. Impact
factor n/a, citations 7, SCImago Q3
Since latest appointment (October 2014)
Acceleration, Jour. Phys. Conference Series of “The 10th Biennial Conference
on Classical and Quantum Relativistic Dynamics of Particles and Fields (IARD 2016)”
12 pages. Impact factor n/a, citations 0, SCImago Q3
Jour. Phys. Conference Series of “The 11th Biennial Conference on Classical and
Quantum Relativistic Dynamics of Particles and Fields (IARD 2018)” 19 pages. Impact
factor n/a, citations 0, SCImago Q3
Relativistic Dynamics, submitted to Proceedings of the Fifteenth Marcel Grossman Meeting
on General Relativity, edited by Elia Battistelli, Robert T. Jantzen, and Remo Ruffini, Open
access e-book proceedings, World Scientific, Singapore, 2019
Before latest appointment
Homogeneous Balls, Progress in Mathematical Physics, volume 40 (2005),
Birkhauser, Boston, 278 pages.
Before latest appointment
2011-2012, German–Israel Foundation for Scientific Research and Development (GIF),
Before latest appointment
September 2003 Completed the Dale Carnegie course on Interpersonal Relationships, Jerusalem
July 2004 Attended the “Non-commutative Geometry and Representation Theory in
Mathematical Physics” Satellite Conference to the Fourth European
Congress of Mathematics, Karlstad University, Karlstad, Sweden
Title of Talk: Conformal Triumphs over Projective
July 2005 Attended the “Mile High Conference on Quasigroups, Loops and Nonassociative Systems” University of Denver, Denver, Colorado, USA
Title of Talk: Right versus Left: Relativistic Dynamics in the Einstein Loop
July 2006 Attended a COMSOL Multiphysics (FEMLAB) Minicourse, Bnei Brak
2010-2011 I wrote a 90-page חוברת for our Statistics courses (both the engineering course and the business course). These notes include theory, examples, and solved problems.
2011-2012 TMPJ Theoretical Mathematics and Physics Jerusalem Seminar.
I gave seven our-hour lectures in this weekly seminar held at Machon Lev.
February 2012 I served on the Organizing Committee of the 2nd GIF Workshop “Exploring the Full
Range of Classical Electrodynamics: from Applied Physics to General Relativity”
Jerusalem College of Technology (JCT), Jerusalem, Israel
I also gave a talk: Covariant Uniform Acceleration
May 2012 Attended “The 8th Biennial Conference on Classical and Quantum Relativistic
Dynamics of Particles and Fields (IARD 2012)” Galileo Galilei Institute
for Theoretical Physics, Florence, Italy
Title of Talk: Extending the Lorentz Transformations to Accelerated Systems
December 2012 Attended “The 58th Annual Israel Physical Society Meeting (IPS 2012)”
Title of Poster: Making the Relativistic Dynamics Equation Covariant
June 2013 Attended the 3rd GIF Workshop “Exploration of Electrodynamics” ZARM,
Universitat Bremen, Bremen, Germany
Title of Talk: Velocity and Acceleration Transformations and Time
Dilation in a Uniformly Accelerated Frame
July 2014 I served on the Organizing Committee of the 4th GIF Workshop “Exploring the Full
Range of Classical Electrodynamics: from Applied Physics to General Relativity”
Jerusalem College of Technology (JCT), Jerusalem, Israel.
Title of Talk: Relativistic Rotations
Since latest appointment
June 2016 Attended “The 10th Biennial Conference on Classical and Quantum Relativistic
Dynamics of Particles and Fields (IARD 2016)” Ljubljana, Slovenia
Title of Talk: The Frenet Frame and Applications
February 2017 Attended workshop on “Rotating Systems in Relativity” Lev Academic Center,
Title of Talk: Avoiding the Horizon Problem
June 2018 Attended “The 11th Biennial Conference on Classical and Quantum Relativistic
Dynamics of Particles and Fields (IARD 2018)” Merida, Yucatan, Mexico
Title of Talk: Geometric Dynamics
September 2019 I have registered for the 2nd International Conference on Symmetry in Benasque,
Spain and have submitted an abstract for my talk entitled “Special Relativity from