Relativity Equations derived in one line, and without assuming the two Relativity postulates

Posted by M.G.Hocking on 18 November 2009 | 0 Comments

Strong evidence for absolute motion can be taken from the "Big Bang" of cosmology, which locates a point of origin in the universe.  In contrast, the First Principle of Special Relativity denies the existence of any absolute point of reference which could be used to measure distances from.

Relativists try to avoid this problem by postulating, ad hoc, that space itself was also created at the same time as the Big Bang, like a very tiny rubber balloon which was then inflated (the expanding Universe) so that at any later time all points on the balloon (i.e. all points in space) were effectively at the point of origin of the Big Bang.

But the well-known and experimentally verified equations of Special Relativity can be derived assuming absolute motion instead, and the derivation (in just one line) is far simpler than that from Special Relativity.

Also, the contentious Second Principle of Relativity on which Special Relativity is based, is avoided: The Second Principle of Relativity states that the velocity of light is independent of both the velocity of the light source and the velocity of the observer !   (My exclamation mark)   

Mass Dilation formula, without Special Relativity:

The (real) existence of higher dimensions is supported by particle physicists who postulate ten spatial and one time dimension.  The absolute motion derivation below also uses a much earlier observation of Besant & Leadbeater [1], not only that there are more than 3 dimensions in space, but that an energy welling-up from 4-D space enters 3-D space, and particles at rest in 3-D space are created by this energy entering from a 4th spatial dimension.  A theory of “rest mass” is provided by this explanation.  

Rest Mass:  Assume that a welling-up of electromagnetic energy from 4-D space creates a stationary particle in three-dimensional space, of rest mass m_o.

Electromagnetic energy (light, radio, etc) travels at c, the velocity of light.

If the particle is then made to move in 3-D space, by giving it momentum in a direction in 3-D space, it will have an extra momentum of mv.  The particle’s total mass then increases from m_o to m to incorporate this extra kinetic energy.

All dimensions must be at right angles to each other, so the 3-D mv must be at 90º to the 4-D m_oc, and so a triangle of momenta can be drawn, closed by a hypotenuse mc.

A triangle cannot be drawn on a blog, so please draw one on a paper, with long side m_oc, short side mv  and hypotenuse mc.

Then, from Pythagoras’ Theorem: (m_oc)²  +  (mv)² =  (mc)²

The m_oc axis is in a 4th spatial dimension.   

The mv axis is in the 3rd spatial dimension. 

Re-arrange the above Pythagoras equation:  

m_o = m√(1 – v²/c²).

This is Einstein’s mass dilation equation, derived in 1 line!

Five lines of very elementary physics then give:  E=mc².

The time & length dilation formulae can be obtained similarly [2].

These derivations are far simpler than Einstein’s derivations and so by Occam’s Razor principle, it could be more likely that they are correct.

Comments:

Orthodox physicists have accepted Einstein’s complicated derivation of the above mass equation for the past hundred years, and so it is very difficult to get them to consider that the same equations can be obtained very simply by assuming absolute motion instead of relative motion (relativity).

Well-known physicists like Prof Stephen Hawking and Prof Paul Davies say they

receive hundreds of letters annually about relativity and so they can’t even try to reply to them.   The only way I felt that could get a reply from an eminent physicist was by sending a single page only, to a fellow professor (whom I have never met) at Imperial College (where I am also at):

So I sent the above Pythagoras triangle mass equation derivation only, on a single page, to a Relativity physicist, an F.R.S., at  Imperial College.

His response (2008) is given below (with my answers in italics):

He commented that the theory of relativity has very extensive & diverse support.  But I have derived the exact same equations, so I can also claim the same experimental support.

He also said that my derivation is based on an unmotivated assumption. 

I could not explain this within 1 page!  I think he means that my theory that “rest mass” is created by an energy welling-up from a 4th spatial dimension, is unproven, but so are both of Einstein’s Special Relativity postulates (which were contrived by him to derive the correct Special Relativity equations). 

The real physical evidence of Einstein’s assumptions are only that his equations are experimentally verified.   My equations are identical, but derived alternatively by assuming absolute motion instead of assuming there is only relative motion. 

My basic motivation is that if there are hidden spatial dimensions (which particle physics now does accept as a possibility), then it would be very strange if these extra dimensions have no effect at all on the basic equations of physics!

He finally said that Einstein's theory has real beauty, which mine lacks. 

Although I agree that Einstein’s theory has a mathematical beauty, my physical-based derivation has beauty in its simplicity:  Pythagoras’ Theorem is a beautiful piece of geometry.  

But beauty does not always equate to physical reality and mathematical beauty does not mean a theory corresponds to physical reality. 

Mathematical fractals are beautiful but no plant leaves in nature look like them.  I have a beautiful crystal of silicon carbide, but this compound does not exist in Nature. 

I can evoke the Occam’s Razor principle (“The simplest explanation is probably the correct one”, or, “If it looks like a duck, it is probably a duck”!).

The above derivation was published by me in 1968 and again in 2007 [2] along with derivations of the other equations of Special Relativity (including E = mc²).

References:

1.  www.4-D.org.uk

2.  M.G. Hocking:  J Scientific Exploration 21 (1), 13-26 (2007).  Available as a (free) web download from

 www.4-D.org.uk