Julian Barbour is an independent theoretical physicist who has gained some attention of late. Minkowski is dead. From my soapbox here, I will channel Minkowski in this gentlemen’s disagreement. Links to Julian’s work will be provided, they are worthy of your time. Nothing I say against Barbour’s ideas are personal, they are all technical in nature, as is my way. I have a bullet with “The Nature of Time” written on it. At this moment, I am not sure if it will kill the paper. I will have to find out and report the result at the end of this blog.

Julian has a real theoretical physics Ph.D.   He has been an independent theoretical physicist since 1968, only recently hooking up to visit with uber old Oxford. I have no idea how he financed that run, could be inheritance, marrying up, a part-timer, some brilliant idea sold to the engine of commerce. He has a nice house in Oxfordshire, England.
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There are several ways to get up to speed about his world view. On blogging heads TV, he has an hour long chat with UCSD Philosopher Craig Callender. Julian has a real British accent so sounds wiser. No hard math questions were asked. Instead there are hard philosophy questions, which means they discuss issues where we do not have the math chops yet.

In 2008, The Foundational Questions Institute (FQXi) sponsored an essay contest titled “The Nature of Time”. Here is a description of the organization:
“FQXi catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.”
The Science Director is Prof. Max Tegmark of MIT, a guy who is smarter and nicer than I will ever be. They have some cash from the John Templeton Foundation. Their members are either big wigs in physics now, or moving on up to the East Side, to a deluxe apartment in academia. Groucho and I are not members.

Both Julian and Craig have pulled down $100k grants out of FQXi, ranking #2 and #8 in the list of top money winners, respectively. Sweet. Questioning time is worth money. Lots of people submitted essays to the contest, another sprinkling of big names. The winner, el numero uno, taking home$10k to Oxfordshire, was Julian Barbour’s essay titled “The Nature of Time”
(discussion here). I thought that was a joke, the winning essay having the same title as the contest. It turns out that is a method. The winning essay in the 2011 contest “Is Reality Digital or Analog?” was “Is Reality Digital or Analog?”

Julian has written a few books. The one that I had heard about was “The End of Time: The Next Revolution in Physics (2001)” If you are not a speed reader, you can get a flavor of that work in Bekijk de Noorderlicht-aflervering 'Killing Time', 23 minutes of Dutch TV (spoken in English).

Go out, do your research, the blog will be here when you return.

Start the fight with Hermann “Take me and my mustache seriously you lazy ass Einstein” Minkowski, Einstein’s teacher at ETH who was initially unimpressed with Einstein and his work ethic:
"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
He preached this to the 80th Assembly of German Natural Scientists and Physicians in 1908, 4 months before he died. There is “The International Society for the Study of Spacetime" whose own pulse I needed to check as their once every 2 year conference stopped in 2010. A personal communication indicates that is only a sign the organizer is busy, busy, busy.

Good riddance as far as Julian is concerned. He wanted to say Minkowski is wrong in the blogging heads TV interview, but does a two step to avoid being that radical in his assessment.

I suffer from Minkowski vision. “Time In Bed With Space” says not only are they both naked, but time and space are doing the nasty in ways we have not been able to quantify or qualify. Mostly they do nothing, the key to a 13.6 billion year life.

I do suffer. The contest should have been titled “The Nature of Spacetime”. Say you come up with a great definition of time. Bully for you. We set up an experiment in a lab and show your definition works. Excellent. Then a clown points to cosmic rays raining down on the experiment. Cosmic ray riders would see a definition for time and space (clowns can see cosmic rays?).

I decided to subject the paper to a quantifiable test. Special relativity is about how events in spacetime are viewed by different inertial observers. Those observers report on the time and distances between the events. No events, no marks for time or distance. I set the bar at a ratio of 5/1: five mentions of time to every one for events. The paper failed this specific test because the word event never appeared in the document.  Julian knows the math. He can do all the calculations for observers in rocket ships. He will get the twin problem right for the right reason, the asymmetry in the energy put into the rocket. Julian is a pro. He does not hear the cosmic ray clown whispering in his ear like I do. Live a life with just space, then I will use the factor of c to convert it to an equal amount of time, that thing Julian wishes to banish. I took something real (space) and made it not real (time), which is either a great disappearing trick or the pitch of a good snake oil salesman.

Julian focuses on slices of 3D space. He gets a 75% mark for this, a solid C. The fourth element where he loses points is time. Those 3D slices are vital, don’t get me wrong. I have a huge amount of experience with such slices. They make up each frame of my quaternion analytic animations. How much time goes in between each frame can be changed as a command line option. If I put in zeros for the time variables, no animations result. Time is different from space.

While researching this article, I came across a great page by Richard Conn Henry, The page was about teaching special relativity. Let me quote a poignant section:
"I can visit Rome, but I cannot visit Julius Caesar. So we need some distinction between space and time. Suggestions, please?"
Almost always, after some Socratic prodding, I do get "use imaginary numbers for one, and real numbers for the other?" I reward the student by announcing "you have just discovered Einstein's theory of special relativity!"
The notion that the Minkowski metric describes spacetime is entirely plausible to the students. It is not counter-intuitive, in any way, at least on its face. I announce to the students that experiment is the test!
Once students agree that the Minkowski metric might describe the world, it is of course extremely easy to deduce that if this should be our world, then there must be a limiting velocity. Everything else then follows with ease, and the students emerge comfortable with special relativity as a marvellous insight into the mathematical structure of the observations—the observations that we naively interpret as a universe.
There is an important observation from my research: while there is one dimension for time, there are three for space. One therefore needs three imaginary numbers, a perfectly tailored fit for quaternions. With Minkowski gone, the lesser lights of Conway and Silberstein tried to represent the Lorentz group with quaternions but failed, bailing out to biquaternions instead which are not a division algebra. That shortcoming is enough for professionals to ignore this apparently perfect tool for the job. The glaring gap was corrected in an earlier post:
$b'=h^*b h +\frac{1}{2}\left(\left(h^*h^*b\right)^*-(h h b)^*\right) \quad eq. 1$
where b is the quaternion to be boosted and h is a hyperbolic cosine and sine quaternion.

Scalars are fundamentally different from 3-vectors. Real numbers are different from imaginary numbers. I cannot justify using only 3-vectors or only three imaginary numbers. One can use 3-vectors to generate scalars, as one can use imaginary numbers to make real numbers. Special relativity provides the rules for rotating one into the other.

Here is an important question for Julian:
“How can we say that a second today is the same as a second yesterday?”
It is stunning that we all use the same unit devised by the Babylonians. Lengths, weights, counting systems, language, and money are all wildly different, but agreeing to time was central to being able to agree. There are some examples of people disagreeing about noontime (Indiana and Iran come to mind), but the basic unit is the same.

A second for one observer is necessary exactly the same as a second for another observer. A second has a precise definition. Different people using the same definition get the same result, a founding principle of the scientific process. If we compare two seconds, those can be different in both special and general relativity.

Nature never uses a second. Nature never uses a meter. Hydrogen atoms do not use angstoms when emitting the light that appears in the Balmer lines. One must be systematically dimensionless. The way to start down such a road is to think about events in spacetime. What caused the event? Was it an electron emitting a photon, good old EM? Was it beta decay or the weak force? Was the event between gluons keeping the nucleus together? Was the event involved with gravitational attraction (details to be understood at a later date)?

Events are invited to all the interactions of the four fundamental forces. They still have units, at least the way most people write them. It is easy enough to make an event dimensionless - just divide time by Planck time and distance by Planck distance. Done. Some in the audience will squawk about how small Planck units are. You have a size issue? We can all look monster truck big this way, but move like snails in a vat of superglue. I could avoid Comité international des poids et mesures which sounds like a French international conspiracy committee by develop all my own darn units for everything. And yet I would end up with the same dimensionless numbers. Space aliens could even agree once we figured out how to compare our numbering systems.

Julian ends his essay with a definition of time. Excellent. Now we can test the paper, design a bullet, shoot for a head. First I need to explain what a covariant equation is. At a practical level, it means the form of the equation will stay the same for all observers, whether they are different inertial observers or non-inertial observers. Even as values changes for this kaleidoscope of observers, the form of the equations stay the same. The Maxwell equations have this property as do general relativity. The rules for special relativity are constrained to inertial observers, an important limitation.

Here is Julian’s definition of duration at the end of the paper:
$\delta t = \sqrt{ \frac{\sum_i m_i (d_i)^2}{2 (E - V)} } \quad eq. ~2$
What happens to each side of the equation under a Lorentz boost along one axis? The left hand side is easy: it transforms like the first term of a 4-vector [corrected primes]:
$t \rightarrow t’ = \gamma t - \gamma \beta x/c \quad eq ~3$
The right hand side is...scary. The numerator has a Lorentz invariant mass, that is easy. Then there is the spatial part of a 3-vector:
$\\x \rightarrow x’ = \gamma x - \gamma \beta t c \quad eq. ~ 4\\ y \rightarrow y’ = y \\ z \rightarrow z’ = z$

The energy terms will transform like the first term of a 4-vector, like time:
$E-V \rightarrow E’-V’ = \gamma (E-V) - \gamma \beta P c \quad eq ~4.5$
How can I test how all these things transform together? I like to do things numerically. If it works for numbers, it will work for symbols. To be generous to Julian, we will choose simple numbers and see how it goes. Sum for one particle. Give it a boost of 0.5c. Set the values on the right hand side like so:
$\\m_i = 1 \quad \quad \quad eq. ~5\\ d_i = (3, 4, 5)\\ E - V = 1\\ P = (0, 0, 0)$
Therefore the calculated duration is
$\delta t = 5 \quad eq. ~6$
Now we need to boost 2 4-vectors, one for position, the other for energy-momentum:
$\\(5, 3, 4, 5) \rightarrow (4.0414, 0.57735, 4, 5) \quad eq. ~7 \\ (1, 0, 0, 0) \rightarrow (1.1547, -0.5773, 0, 0)$
Here is one problem with covariance. I don’t know where to put the value of momentum in the x direction for Julian’s equation. As someone who worked at a lab bench, it feels wrong to just ignore it. If the values are plugged in, we get:
$\delta t = 5.6734 \quad eq. ~8$
The Lorentz boost lowered the value of the duration, while the calculation raised it. There is no hope to make this expression make sense under a Lorentz transformation. This bullet has killed the paper to my eye. I don’t think the paper has any lasting value. None.

Am I going to go yell at Julian? Gentlemen don’t yell. As a skeptic, I have done my job: I have been precise about my technical difference about his proposal. He can point to sources outside himself to say he is on to something. He has received six-figure grants, he has collaborators, he gets invited to speak at the Perimeter Institute, and he has won a competitive essay contest. He may claim to be outside of academia, but that is the behavior of a professor. His long walks have constructed a web of connections in his own mind that will remain. He has a doubt circuit since he is a punctual fellow who looks at clocks often.

As I said before, Julian understands special relativity. He knows the history better than I. Yet when he goes into his area of research, the rules of special relativity are not applied. Special relativity is about events, events, events.

I recall someone in a sci.physics.research discussion saying that you should not complain unless you have an alternative. I cannot answer the contest question, but can deal with “The Nature of Spacetime”. Treat empty spacetime as a continuous quaternion differential manifold with is sprinkled with discrete, dimensionless events. Again I disagree with the questions posed by FQXi since reality looks like it is both discrete/digital and continuous/analog. An event in isolation is just that: in isolation. Durations and distances come into being for two or more events. Calculate the square of the difference between two events e and e’:
\begin{align*} (e - e’)^2 &= (\sqrt{\frac{c^5}{G \hbar}}~((t, x/c, y/c, z/c) - (t’, x’/c, y’/c, z’/c)))^2 \\ &= \frac{c^5}{G \hbar}(d t^2 - dR^2/c^2, 2 ~dt ~d\vec{R}/c) \quad eq. ~9 \end{align*}
This definition will work for different inertial and non-inertial observers. One fun thing about this definition is that it will produce the same numerical values for similar observers even if their systems of measure are different. There is the Système International d'Unités and the English system. Both will provide identical numerical results. According to Hollywood, we should expect an alien invasion since the President is African-American. The aliens would not have seconds, meters, or slugs. We could all agree that the 3->2 Balmer series transition is 4.06 x 1030. The ability to have folks agree to values using arbitrary systems of measure is in the spirit of general covariance.

This is dull accounting stuff done in small slivers of time late at night. It is "unlikely to be supported by conventional funding sources" or unconventional funding sources. I have failed the social component of theoretical physics. But I like a companion in my basement that knows how to transform. Power math tools rule in the end.

Doug

Snarky puzzle. Imagine a pair of machines that can measure 1044 dimensionless time to a high degree of accuracy (a little over 5 seconds for you guys still clinging to the bosom of units). One is at sea level, the other at Mount Everest base camp, 5,380 m. Calculate the square of both of these intervals (the formula with standard units is delta t = -t G M h/(c2R2). Imagine a bullet train going at 3 x 10-7 (a little over 200 mph) along one axis gets data from both clocks. What would they report?

Google+ hangout: 11:00-11:45pm Eastern time, Tuesday-Friday. http://gplus.to/sweetser
This could be an efficient way to exchange a few ideas. If you have a question or two or need an invite, send me a message.

Next Monday/Tuesday: Sex and Unified Field Theory R&D