In The Beginning...
By Johannes Koelman | February 12th 2013 09:08 AM | 20 comments | Print | E-mail | Track Comments

I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune

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1:1 In the beginning Newton declared space and time. 1:2 And space was without form, and void; and darkness was upon the face of the deep. 1:3 And Newton said, Let there be force: and there was force. 1:4 And Newton saw the force, that it was good: and Newton divided force from straight motion. 1:5 And Newton called force change of momentum, and straight motion he called momentum conservation. And the evening and the morning were the first day.

1:6 And Newton said, Let there be a force in the midst of matter, and let it divide matter from energy. 1:7 And Newton divided matter which were under influence of the force from energy which were above the force: and it was so. 1:8 And Newton called the force Gravity. And the evening and the morning were the second day.

1:9 And Maxwell came and said, Let the matter under influence of gravity be gathered together unto one place, and let the vacuum appear: and it was so. 1:10 And Maxwell called vacuum the field; and the gathering together of matter called he Source: and Maxwell saw that it was good. 1:11 And Maxwell said, Let the field bring forth electricity, magnetism yielding north, and the waves yielding light, whose Source is in itself, upon the field: and it was so. 1:12 And the field brought forth electricity, and magnetism yielding North, and the waves yielding light, whose Source was in itself, and Maxwell saw that it was good. 1:13 And the evening and the morning were the third day.

1:14 And Einstein came and said, Let there be movement between the light to divide absolute from relative; and let them define time: seasons, and days, and years. 1:15 And let them render space and time one: and it was so. 1:16 And Einstein created a principle; a single principle to rule the dynamics of matter and also to rule fields. 1:17 And Einstein applied it to the firmament of the heaven to cast light upon the doubters, 1:18 And to divide reality from the darkness of the ether: and Einstein saw that it was good. 1:19 And the evening and the morning were the fourth day.

1:20 And Einstein said, Let matter and field bend space and time, and Let all movements maximize duration. 1:21 And the shape of space and time created gravity, and gravity moved the planets and bended light: and Einstein saw that it was good. 1:22 And Einstein blessed the unity of space and time. 1:23 And the evening and the morning were the fifth day.

1:24 And Bohr and Heisenberg came, and they said, Let energy bring forth quanta: and it was so. 1:25 And Heisenberg and Bohr said, let there be quanta for the harmonic oscillator, and quanta for the hydrogen atom, and quanta for everything that creepeth upon the earth: and they saw that it was good.

1:26 And Feynman and others came, and they said, let us make quantum fields: and let them have dominion over over every creeping particle that creepeth upon the earth. 1:27 So Feynman and others created quantum fields, bosonic and fermionic they created them. 1:28 And All blessed the quantum fields, and said unto these, Be fruitful, and multiply, and replenish the vacuum, and subdue it: and have dominion over reality.

1:29 And All said, Behold, we rule the quantum field, which is upon the face of all the universe, and every piece of space and time, yet we fail to understand how the quantum bends space and time. 1:30 And it was so. 1:31 And All saw every quantum gravity theory that was made, and it was not good. And the evening and the morning were the sixth day. 2:1 Thus space and time refused to yield to the quantum. 2:2 And despite all their work they made; nobody found rest on the seventh day.

Centuries of fundamental physics condensed in a single Euler diagram. The various theories are grouped according to which aspects of reality are ignored. Red oval (1/c = 0, vanishing slowness of light): theories ignoring relativistic effects, blue circle (h = 0, vanishing quanta): theories ignoring quantum effects, green circle (G = 0, vanishing gravity): theories ignoring spacetime curvature.

Specific theories are labelled as follows:

NM: Newtonian mechanics (Isaac Newton, 1687)
NG: Newtonian gravity (Isaac Newton, 1687)
EM: Electro-magnetics (James Maxwell, 1862)
SR: special relativity (Albert Einstein, 1905)
GR: general relativity (Albert Einstein, 1916)
QM: quantum mechanics (Erwin Schrödinger, Werner Heisenberg, 1925)
QFT: quantum field theory (Sin-Itiro Tomonaga, Julian Schwinger, Richard Feynman, and Freeman Dyson, 1948)

Quantum gravity, the elusive theory of everything, is represented by the area external to the two circles.

Six down, one to go...

This is fantastic. This Euler diagram works well because it reveals truths about the symmetries created and broken when the physical coupling constants are taken to the indicated limits. The scripture satire was incredibly clever, but those dudes were discovering, not declaring... prophesying perhaps, but not creating.

Finally: the King James Version of the history of physics!

In my Physics 101 class we have just started talking about Newton's Laws. This blog uses Newton's Law in a unique way of explaining Newton's laws by showng it in a conversation between Newton and other scientists. As you said in your blog all of Newton's three laws have to do with force. Newton's laws explain why objects behave the way they do when a force is applied. Newton's law is very useful in physics because it help you better understand the problems and be knowledge of what the question is asking. This blog was very injoyable and interesting.

Nice parody. But what a pity the red oval divides the blue-green intersection so EM and SR are degenerate. Oh, wait a minute, you wanted to get seven theories... But, umm, why stop at seven? :)

Thanks for the comments. Terry, Derek, the story covers 7 days and 8 theories...
Ah yes, the elusive seventh day turtle! :)

Johannes:

To think that for all these years I have been using Euler diagrams and calling them Venn diagrams.  :}

Unfortunately, your Euler diagram violates a "rule" of "wellformedness", given within the reference you linked.  It has two disconnected zones, thus giving the mistaken impression that EM and SR are not within the same region.

A possibly better version of the Euler diagram is the following (though it also violates a "rule" of "wellformedness" since it has a triple point):

Of course, when we include the region with h ≠ 0, and G ≠ 0, there is no reason not to expect that a "Quantum Gravity" theory would be able to yield a limit within the 1/c = 0 ("vanishing slowness of light") while maintaining nonzero h and G.  This, then, yields the following Euler diagram (that violates no "rules" of "wellformedness"):

Of course, this is not to say that anyone will, necessarily, try to create a theory within the realm of 1/c = 0 ("vanishing slowness of light") while maintaining nonzero h and G, except as a limiting case of a more full fledged theory.

David

David, surely you seem attracted to Venn diagrams rather than Euler diagrams, as you end up with the former. Unfortunately, that makes you reinvent the wheel that I have discarded. ;) The present diagram I consider highly preferable over the corresponding Venn diagram. The Euler diagram correctly shows electromagnetism and special relativity as two distinct theories both belonging to the class of classical Lorentz invariant theories.
Yes. From the outset, I thought that the degeneracy in the diagram is actually meaningful. I am struggling to determine if it is merely accidental that such a diagram is possible, or if there is some deeper principle that correlates the compatible but distinct theories with a simple 2-d line drawing....

The degeneracy is meaningful, but don't read too much into the diagram. It's a way to order and visualize the succession of fundamental physics theories devised, nothing more than that. The fact that two Lorentzian regions show up is related to the existence of massive and massless particles.
Actually, Johannes, the fact you are feeling the need to make this sort of reply to "GDS" indicates a failing in the degeneracy of the diagram.

Of course, if we were to illustrate the proper relationship between SR and EM, we would show EM as being enclosed by SR.  SR is properly considered as the "label" for the region h = 0 and G = 0 (it includes the 1/c = 0 portion of this region as a limiting case), while EM is a particular "citizen" of this region.*

(Similarly, GR is the "label" of the entire h = 0 region, with the G = 0 and 1/c = 0 sub-parts as limiting cases.  Again, similarly with QFT [exchanging G and h], of course.)

David

*  Of course, this is referring to Maxwell's formulation of EM, before being generalized (via the principle of "minimal coupling") to be a "citizen" of GR, and, later, by other means, becoming the "premier" "citizen" of QFT.

The diagram provides some good food for thought, and like GDS I think the apparent symmetry is most compelling. On the degeneracy: SR describes the dynamics of material objects, and EM the dynamics of electromagnetic fields. Without bending definitions, one can not enclose EM by SR. It occurs to me that the proper label for the central h=0 and G=0 region would be "Poincare covariant theories". EM and SR are distinct theories in this region. The red region can be labeled "Galilean covariant theories".

I agree with your remark that EM and SR are distinct examples of Poincaré covariant theories. However, not just the central region but he whole green G=0 area should be marked "Poincaré covariant theories". The central (G=0, h=0) region represents "classical Poincaré covariant theories".
Johannes:

You stated

... However, not just the central region but [t]he whole green G=0 area should be marked "Poincaré covariant theories". The central (G=0, h=0) region represents "classical Poincaré covariant theories".

This is correct if (and only if) we take G=0 as strictly meaning flat (or certain classes of uniformly curved) space-and-time/spacetime, while only G≠0 is allowed to be (more generally) curved.  While this is true for all the particular theories you have mentioned within your article (and illustrated within your diagram), this need not be the case for all conceivable theories.

However, I'm willing to make this identity for the sake of the diagrams.

On the other hand, the portion of the G=0 area that intersects with the red 0=1/c area is not truly "Poincaré covariant", but, as Justin said, more properly "Galilean covariant".  (Of course, one may take "Galilean covariant" as a special case of "Poincaré covariant", for the singular case of 0=1/c.)

(There does remain a potential issue with the portion of the red 0=1/c area that is outside the green G=0 area.  While NG is a denizen of this area, and it is a "Galilean covariant theory", since it uses the same, flat, Galilean space-and-time of NM, there are other curved, only locally "Galilean covariant theories" that dwell therein.)

David

Justin:

If, as with the "Poincare covariant theories", you are using the full Galilean group (including translations), then the "red region" of only Johannes' diagram (at least the particular theories of NM*, NG, and QM) may properly be referred to as "Galilean covariant theories".

On the other hand, if, instead, we use "local" versions of the groups (analogous to "local symmetries", as used in QFT), then the entire "red region" (including my expanded version, like unto the "green region" in Johannes' linked article) can be referred to as something like local "Galilean covariant theories", while the entire region outside of the "red region" can be referred to as something like local "Poincare covariant theories".  (Note:  Present QFT, within the green, G=0, region is globally "Poincare covariant", but this need not, strictly, be the case for all conceivable theories.)

David

*  E. Cartan has shown how NG can be reformulated as a curved Galilean space-and-time theory.  In this case, there is no longer global Galilean covariance, but local Galilean covariance still holds.

Johannes:

Surely you jest.  Surely you know that because even the last diagram—just as with the diagram you referenced—includes the region outside of all the circles (the region of non-zero h, G, and 1/c), these cannot be Venn diagrams (because all the sets, represented by the circles, and all their intersections and unions, are all wholly included as a proper subset of the enclosing set represented by that outer region).

The last diagram—just as with the diagram you referenced—only appears similar to the Venn diagram of three (3) sets.  However, they are actually Euler diagrams of four (4) sets, where the three Venn diagram like sets are all proper subsets of a fourth containing set.

David

Where would little-loved thermodynamics go in such a figure?

One of my ongoing interests is one-math-tool-that-does-it-all, like everything in the diagram. Quaternions were a good swing of the bat, but as defined, it does come up short. One thing that exercise indicated to me is this idea of saying a constant is zero is silly. That ends up implying the universal constants do a job they just don't do. When writing out Newtonian laws with quaternions, there are always terms that end up being zero.  For example, there is Newton's dimensionless second law:


To make a relativistic law, there are exactly zero zeroes. I like seeing the hbars in this expression cancel out.  There might be a message in those tea leaves.

What is required to get to equations used in quantum mechanics are operators that will necessarily generate real and imaginary numbers (Newton's law above creates only three imaginary numbers).  A dimensionless version of the Klein-Gordon equation has this property:
$\left(\frac{\hbar}{m c^2}\left(\frac{\partial}{\partial t}, c \nabla\right)\right)^2 \psi=(1, 2 \beta \gamma^2) \psi$

The Klein-Gordon equation is the first term here.  Some might think the other three are signs of quaternion "junk", but I bet they are just not used based on current math toolsets.  I don't see anything malformed in the math expression, so I would bet on the math expression being valid.  The extra terms will not be invariants like unity, but will be covariant (we know how they change, by beta gamma squared).

Good post, it was fun to read.
Doug:

In talking about your (quaternion) "version of the Klein-Gordon equation", you state:

The Klein-Gordon equation is the first term here.  Some might think the other three are signs of quaternion "junk", but I bet they are just not used based on current math toolsets.  I don't see anything malformed in the math expression, so I would bet on the math expression being valid.  The extra terms will not be invariants like unity, but will be covariant (we know how they change, by beta gamma squared).

As has been amply shown throughout the history of the "principle of general covariance", and as is re-illustrated in your case, this principle has "no forcible content" [Misner, Thorne, and Wheeler].  As they state:

...  Any physical theory originally written in a special coordinate system can be recast in geometric, coordinate-free language.  Newtonian theory is a good example, with its equivalent geometric and standard formulations (Box 12.4).  Hence, as a sieve for separating viable theories from nonviable theories, the principle of general covariance is useless.

Now, admittedly, you haven't written your work in "geometric, coordinate-free language".  However, this same argument of how the "sieve" of "covariance" is "useless" applies, a fortiori, to what you have expressed, above.

I'm sorry to have to break this bad news to you, but you need to learn this hard won lesson.

David

Congratulations Johannes,
you made a very original composition and a remarkable job in summarizing physics discoveries.

As a personal contribution, let me propose a small amendment for the sake of making everybody rest the seventh day.

Our troubles arise just because we strive to find a unified theory of everything basing on quantum physics; we want this so badly because we strongly believe in the success of the atomistic approach.

In few words, following discoveries in HEP and going deeper and deeper towards the infinitely small, we are striving to find a basic block for everything.

Well - just to start with - HEP is also showing us there are some “strange” effects, somehow incompatible with the idea of isolation and interaction of a single particle from or with the “whole”, such as the wave/particle duality. For instance, what’s the real meaning of wave? And in what is this wave propagating?

Still, the same atomistic approach seems to be quite reductive (so we can even say that the word “paradox” is a good synonym for “not compliant” with the generally accepted model) when we get experimental effects such as entanglement, that may suggest us not just to consider a single particle as a separate entity, but as a instance of the whole or, in other words, the whole itself.

In few words, the above said principle would seem to drive us in considering each particle and the universe a new duality.

With this paradigm, we don't need to reconcile gravity (a global effect) with the quantum world (a local effect), as they are always and simply co-existing.

Not to mention that this could be a good application of Einstein's principle "we can't solve problems by using the same kind of thinking we used when we created them" or - put in modern talking - “to think out of the box".

Ok, given the afore said statements, let's correct your composition: