Feb. 27  2007

Detecting and analyzing higher dimensions

via the EM radiation field


 by Hans de Vries 



     Modern day theoretical physics and higher dimensions.


The very successful  "Standard Model"  in theoretical physics was established in the seventies and the eighties. It united the Electromagnetic force with the Weak and the Strong nuclear force. This model could predict the outcome of numerous 

experiments performed at the large particle accelerators which were probing the mysteries of Nature.


A major part of the physics community, then full of confidence, went on to study models embracing both the Standard Model and Einstein General theory of relativity. These models, mostly referred to  as "String Theory" have a remarkable aspect: They

presume extra spatial dimension above our three current ones.


The successful years of the Standard Model in which rapid developments came one after the other has turned in a silent period now for more then two decades without real results. Was the assumption of higher dimensional spaces to speculative? Can we ever hope to probe these higher dimension? Can we disprove their existence?  


The higher dimensional String Theory is undergoing somewhat of a crisis, even while scoring huge successes on the public relation front. A startling example: 

The Chinese government, always keen on new knowledge and technology, opened up the symbolic center of its power:  Beijing's Great Hall of the People, the meeting place of the communist party, to host the yearly conference on string theory in the summer of 2006.

It also invited around 3000 of its brightest and most intelligent students to attend the meeting in an apparent attempt to create an 'army' of new string theorist. 


Higher Dimensional Theories in

Beijing's Great Hall of the People


     Higher dimensional Electro Magnetic fields. 


In this paper we derive and describe how the EM field looks like in an arbitrary higher dimensional space. It strongly suggest that we should have seen signs from these higher dimensions already, that is, if they exist. We should have seen the effects directly via the nature of the electromagnetic radiation originating from charges moving and accelerating within these higher dimensions.


How can we derive the behavior of the EM fields  in higher dimensions?  It turns out that we can go from, say, a four or five dimensional space to 3d, in the same way as we go from 3D to a one or two dimensional space. 


A two dimensional (x,y) space looks in 3D as a collection of parallel lines, infinitely extended into the z direction, while a one dimensional (x) space looks like a collection of planes infinitely extended into the y and z directions.


This means that the n-dimensional EM field, must always produce the laws of physics, as we know them, in 3D space when we extend the objects in n-dimensional dimensions in the same way as we have to do when we go from 3D  to 2D or 1D. 


One very remarkable difference one finds, is how the magnetic field of a particle depends on the speed and acceleration of the charge. In 3D space the magnetic field is proportional to the speed of the charge (the current). In higher dimensional spaces one finds a very different relation.


The largest term is dependent on a higher derivative of the speed. See the image on the right. The particle's speed is given in all situations by a smooth curve, made out of parabolic curves. Starting with v=0, then gradually accelerating and de-accelerating again to a standstill.   


In 3D the charge will generate a magnetic field which is proportional to the speed. In 5D however the largest term of the magnetic field is proportional to the acceleration of the charge. This is basically a triangular pulse since the motion of the charge is following a curve made out of parabolic curves. 

Magnetic field of a particle moving with the same speed the same way but in different higher dimensional spaces.


In 9D space, which together with the time dimension, is the usual 10 dimensional space associated with string theory we see even stronger effects. The major component of the magnetic field B is proportional to the third derivative of the speed. The discontinuities were the separate parabolic curves are connected together, hardly visible in the 3D situation, now become strong Dirac pulses. 


The magnetic field and the radiation associated with it are very different from that in the usual 3D space.  This would suggest that higher dimensions, even if they are compacted at Planck's scale should produce measurable effects. Something which hasn't been seen so far. Some newer versions avoid problems by a priory stating that the Electromagnetic, the Weak and the Strong nuclear force can only propagate in a limited 3D space, (The 3D Brane theories) while gravitations would be able to propagate in all 9 spatial dimensions. There still remain problems with the latter since gravitons which are considered being mass less, have similar propagators as the ones described in the paper ( ref[3] ) and similar effects occur for the gravito magnetic fields.


      The paper.


The paper itself can be accessed by clicking on the PDF logo. It requires a graduate physics level for a good understanding. Care has been taken to make it accessible as possible. As often happens, after finishing the document I found out that much of the paper isn't really original work. It is mentioned that a full derivation mass less propagators in the space-time domain of any dimension is also given in reference [1]. Reverences [2] and [3] show identical results as we do. Interestingly, reference [3] discusses gravitons instead of photons. The correspondence is of course the result of both having mass less propagators with the difference that the gravitons correspond to a spin 2 tensor field and the photons to a spin 1 vector field.   



     Other sources 


[1] S. Hassani, Mathematical Physics, (Springer-Verlag, New York, 1998)

Is mentioned to contain a complete derivation of the massless propagators in the space-time domain in any dimensional space.

[2] D. V. Gal'tsov,  Radiation reaction in various dimensions, Physical Review D 66, 025016 (2002). hep-th/0112110
[3] Cardoso et. al. Gravitational Radiation in D-dimensional Spacetimes, Physical Review D 67 064026 (2003). hep-th/0212168



Regards, Hans