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Future Train Wreck: Mine or Modern Physics talk Next Thursday, Jan. 26

If you are in Cambridge, MA on Thursday, Jan. 26, you can see me live at MIT in room 3-270 from...

Holiday Physics Card, 2016

Just put them in the mail on December 24...It was a fun year of thinking, whether the idea is right...

Unified Mathematical Field Theory Talk

I gave a 15 minute talk at a local Americal Physical Society Meeting.  Here is the title and...

Holiday Card 2015

Here is my holiday card for 2015, a tradition of mine going back to 1990.  Enjoy.On the back...

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Doug SweetserRSS Feed of this column.

Trying to be a semi-pro amateur physicist (yes I accept special relativity is right!). I _had_ my own effort to unify gravity with other forces in Nature. It ran into quite a number of technically... Read More »

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In this blog, I challenge the vaulted role that tensor calculus enjoys today. I will define a concrete example of what I consider to be a technical flaw in the tools of tensor calculus in all modern physics theories. The complaint is about completeness, that partial stories are not good enough. Please feel free to defend the status quo in the comments.


The relativistic quantum field equation for a spin 0 particle is the Klein-Gordon equation (written in natural units):




One takes the first derivative of the wave function. Also take three spatial derivatives. Then take the second time derivative of the wave function, and similarly for the three spatial derivatives.

In my last blog, I wrote in detail about zero, one, real numbers, complex numbers and quaternions (or as I now prefer to call them, space-time numbers although I use them interchangeably). For each sort of number, there were rules for addition, rules for multiplication, and a relevant animation. The rules happened to get more complicated going from zero out to the space-time numbers, but they were all of the same form. That makes sense since zero, one, the real numbers, and the complex numbers live inside the tent of space-time numbers.

In Part A, the core idea behind the space-times-time invariance as gravity was detailed. When one treats events as a 4-vector, the contraction of that 4-vector generates one number. When one treats events as quaternions, the square of a quaternion generates 4 numbers. If for two observers, the first number in the square is identical while the other three (I call space-times-time) are different, then the two observers are moving at a constant velocity relative to each other. The space-times-time proposal is exploring the case where the observers disagree about the interval, but have the same space-times-time.

In this blog, I will again define the space-times-time invariance proposal using simple graphics, an explanation intended for a wider audience, videos, and information for nerds. It is taken directly from my own web site that has nearly exactly the same information. In Part B, the equations of motion will be derived, something technical people would reasonably ask for.


An Overview

[Note: many of the images were upgraded to include more information about addition and multiplication, 10/25/2015]

What is a quaternion? Mathematicians might claim it was the independent inventions of Gauss, Hamilton, and Rodrigues. Unit quaternions are useful to do 3D rotations and as an esteemed member of the standard model. They are also one of many Clifford algebras, Cl(0, 2) being its formal name.

This poem is too good to just quote the final stanza.

The Road Not Taken
By Robert Frost

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,

And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.