god-given units

October 9, 2010

A bigger Ben

Continuing the themes of religion and big construction works from the last post, a while ago the construction of a gargantuan clock in Mecca was reported in various news outlets (like here):

Saudi Arabia hopes the four faces of the new clock, which will loom over Mecca’s Grand Mosque from what is expected to be the world’s second tallest building, will establish Mecca as an alternate time standard to the Greenwich median.

This effort has been ridiculed (i.e. here, here) as a cargo-cultish attempt to steal away the reference point for global time keeping from Greenwich, just by building a bigger clock than the Big Ben in London. This may not be true, what I have read at least leaves open that it is perfectly understood in Mecca that the clock will have merely a powerful symbolic function… but on the other hand, what I have read about the local understanding of the earth magnetic field, isn’t exactly rational either:

According to Yusuf al-Qaradawi, an Egyptian cleric known around the Muslim world for his popular television show “Sharia and Life”, Mecca has a greater claim to being the prime meridian because it is “in perfect alignment with the magnetic north.”

This claim that the holy city is a “zero magnetism zone” has won support from some Arab scientists like Abdel-Baset al-Sayyed of the Egyptian National Research Centre who says that there is no magnetic force in Mecca.

“That’s why if someone travels to Mecca or lives there, he lives longer, is healthier and is less affected by the earth’s gravity,” he said. “You get charged with energy.”

Western scientists have challenged such assertions, noting that the Magnetic North Pole is in actual fact on a line of longitude that passes through Canada, the United States, Mexico and Antarctica.

Anyway, before I get sidetracked on magnetic fields, the topic I wish to discuss is that of the arbitrariness of how we measure universal quantities like space and time. Just how arbitrary is our time unit, for example? We have time zones related to Greenwich for purely historical reasons and measure the passage of time in minutes, hours and days that neatly divide up a single earth’s rotation. But if we were to encounter the proverbial alien species, would we be able to draw upon a system of units for time, energy, momentum, distance that makes equal sense to them as to us? The answer to this question turns out to be yes. And whether we should be surprised by this or not, is one of the deeper questions one can ask in physics.

Gravity

Part of the mystery is that the ingredients for a universal set of measurement units can be found at an even deeper level than, say, the rest mass of some particle, like the electron, which would still allow the freedom of choosing a different particle. We will take our ingredients from the very structure of the physical laws governing the interactions in the universe instead. And we’ll start with gravity’s constant G.

It is known since the days of Newton that all masses attract each other, and nowadays it probably takes a conscious effort to realize just how incredibly radical this idea was: that the motion of the sun, the moon and the stars is dictated by the same force (another concept that wasn’t even formalized before Newton) that makes sure an apple drops to the ground when we let go of it. Newton’s law of gravity is given by F = mMG / r^2, high school physics now. In other words, any massive object feels a force F from the massive objects around it, proportional to both their masses (m, M) and the square of their relative distance r. This square feels natural, it is after all also how the area on a sphere grows as we increase its radius (so any quantity on the surface of the sphere gets diluted in this fashion when the sphere expands). But don’t read to much into this, for there exist forces with different reach. For now, the element of interest in the equation is the gravitational constant G, which has a very specific value and dimension: G = 6.67428 x 10^11 m^3 kg^-1 s^-2. To the best of our knowledge (and confirmed observationally through a variety of means), this value holds true also at the other end of the universe. We’ll take it as the first building block when constructing our set of universal rulers. This one measures some combination of distance (m), mass (kg) and time (s).

The speed of light

It was only in college that I learned to appreciate just how phenomenal Newton’s insight into nature was. He realized for example something special about masses which completely passed us by in high school even though it was right in front of us on the blackboard: The mass that determines the strength of gravitational attraction doesn’t need to be the same as the mass that features in F = m a. The former kind of mass is akin to electric charge -but without the complication of pluses and minuses. It dictates how much a particular particle feel gravity, just as electric charge dictates how much a particle feels the electric force. The second kind of mass is more general. It tells us how much a particle will budge when a force, any force, is applied to it. When the forces F applied to them are equal, a very massive particle will only undergo a small acceleration a compared to a very light particle -which will accelerate a lot to compensate for its small mass in order to keep the product m and a equal to that of its big brother. Particles whose mass tends to zero will basically never sit still. This also applies when, say, electric force is applied instead of gravitational force, which is the reason I called the second kind of mass more general.

Zero mass particles, like photons, don’t move infinitely fast, even though that is suggested by F = m a. It turns out that they move with a fixed speed. And when I say fixed, I really mean fixed. If you carry a flashlight, flip it on so that photons will start leaving the lamp with speed of light c and then decide to run after the emitted photons, the photons will still be moving with the speed of light with respect to you. Not just in a practical sense, although compared to the speed of light (299 792 458 m / s) you’re practically standing still when running at, say 10 m / s (assuming you’re Guinness book of records material). The speed of light with respect to a moving observer stays exactly c. Where normally you’d just subtract velocities (i.e. c minus 10 m / s) to get the relative velocity, this simple subtraction rule ceases to be valid when one of the velocities approaches the speed of light. Instead, it gets replaced by relativity theory. We will not go into that here, but just note that this aspect of nature yields us a second universal constant in the speed of light c

The quantum uncertainty

We now have G and c, both combinations in the dimensions of mass, length and time (although mass only occurs in G). A third constant would give us as many constants as dimensions (which will turn out to be just what we need). In quantum mechanics we can find our third ingredient, the uncertainty constant h. At 6.626068 × 10^-34 m^2 kg / s, this constant sets the uncertainty between a particles position and momentum, as well as the minimum energy for a photon. The former means that we can only measure a particle’s position at the cost of complete ignorance of its momentum and vice versa. The latter means that photons come in quanta, and indeed the development of theory of quantum mechanics was triggered by scientists discovering (almost accidentally) the existence of h. I discuss quantum uncertainty a little bit here as well. For now we have what we need in the existence of h.

God-given units

The set of G, c and h, provides us with what have been called god-given units, which must please Abdel-Baset al-Sayyed (or followers of other monotheistic religions), as long as they ignore that this is meant in the proverbial sense. Much like Einstein’s famous phrase God does not play dice is a statement about (assumed) aspects of the laws of nature, rather than an expression of religious sentiment.

So what then is a natural unit for time? Since G is m^3 kg^-1 s^-2, c is m / s and h is m^2 kg / s, it follows that the square root of h G / c^5 has the dimension of time. To be precise, we’d get:

1 natural time unit = sqrt(h G / c^5) = 1.35138 x 10^-32 seconds

Mass and distance units can be calculated in the same way. As can energy (for Joule is after all equivalent to kg m^2 / s^2, just think of kinetic energy from high-school physics, 1/2 m v^2) and momentum:

1 natural distance unit = sqrt( h G / c^3) = 4.05134 x 10^-24 meters
1 natural mass unit = sqrt( h c / G) = 5.45552 x 10^-19 kilogram
1 natural energy unit = sqrt( h c / G) x c^2 = 0.04903 Joule

The translations of these natural units into our own units is, of course, as arbitrary as our definition of what constitutes a meter or a kilogram. But that is not the point, which is rather that we now have a unique and universal way of expressing our arbitrary choices, even to aliens from beyond the galaxy. And one of the most profound questions about nature one can ask is, is there any reason for this system to exist?. Or in other words, knowing only about G and h, could we reasonably expect a third fundamental constant to exist in order that we can make combinations to express quantities we measure directly? Or, in yet other words, should we expect that the number of fundamental constants in nature equals the number of truly independent dimensions of measurement? Or is the whole thing just a trivial coincidence?

Advertisements

Another mosque in Manhattan

August 27, 2010

While back in the Netherlands the adults are busy negotiating a government coalition, PVV (‘Freedom Party’) political leader and big time winner at the latest Dutch elections Geert Wilders has been booking a trip to New York -To protest the mosque that is planned two blocks from ground zero and has become one of the most successful recent fabricated controversies. Although the PVV doesn’t do facts (see also my previous post on their proposed environmental policy), a lot of context has surfaced over the past weeks, for example in a number of excellent pieces in the New York Times.

The building

Park place, another busy street in lower Manhattan. On this picture some are protesting for freedom of religion immediately in front of nr. 51. Most people are on the picture coincidentally and going about their business. To the immediate left of the building is the Amish market, to the immediate right is a bar. Outside the picture, to the back of photographer are a church and a number of very tall buildings.

When you actually live in Manhattan like I do, it is easy to stroll downtown and see for yourself that, no, the building is not planned on ground zero, but two blocks away. At a planned 15 levels it will be about as high as its direct neighbours. The building between the planned center and the WTC site is at least as high, so the center will not overlook the site either. Only a few paces away, nearby buildings can be found that are a lot higher. Park 51 will not be conspicuous or stand out in any way. What’s more (NY times again):

There have been mosques in that part of Lower Manhattan for many years, one 12 blocks from the trade center, another a mere 4 blocks away. No one got in a lather over those places. Might, then, a four-block gap instead of a two-block gap be acceptable?

Calling it a mosque is also an oversimplification, it is envisioned as a center that includes a prayer room. From the Washington Post:

The stated goal behind building the Muslim center in lower Manhattan is to recapture the spirit of mutual respect between Judaism, Christianity and Islam that existed in Cordoba, Spain, from 700 – 1200 AD. While Europe was trapped in the Dark Ages, marked by bloody religious repression, Cordoba thrived as a commercial and cultural center with what was, for the time, a high level of religious freedom. For example, in the 10th Century, Cordoba became the intellectual capital for Jews worldwide. The stated point of the project is creating a world where Jews, Christians and Muslims connect again in a way that builds mutual understanding and respect.

This stated intent can be found on the website of the Park 51 project:

New York deserves its reputation as a peerless center of arts, culture and ideas. Park51 honors and furthers that tradition, envisioning a community center for all of us, bringing the best of the world to New York City, and New York City’s energy, diversity and aspirations to the world. Park51 will become a model for future institutions, with its inclusive focus, outstanding facilities and dedication to social needs. To realize this mission, Park51 will:

* Uphold respect for the diversity of expression and ideas between all people
* Cultivate and embrace neighborly relations between all New Yorkers, fostering a spirit of civic participation and an awareness of common needs and opportunities
* Encourage open discussion and dialogue on issues of relevance to New Yorkers, Americans and the international reality of our interconnected planet
* Revive the historic Muslim tradition of education, engagement and service, becoming a resource for empowerment and advancement
* Connect New York’s communities to global ideas and trends
* Commit to social justice, dignified human development and spiritual growth for all
* Pursue the development of American Muslim identities, engaging New York’s many and diverse Muslim communities and promoting empowerment and compassion for all
* Build partnerships and relationships with key actors and institutions who share our values, to address shared needs and solve common problems
* Establish a state-of-the-art green facility that will serve as a model and inspiration for sustainable space, helping to advance sustainable living in urban contexts
* Empower our communities with the skills and knowledge they need to advance in their various life stages
* Provide financial assistance for those in need, offering subsidies for our programming and scholarships to reach new audiences and further our vision

The imam

The imam in the middle of the muslim center furor, has been heavily criticized for the following statement he made during an interview in Sept. 2001, shortly after the twin towers were struck:

I wouldn’t say that the United States deserved what happened, but the United States policies were an accessory to the crime that happened,

But for those with an outside view and sober understanding of 20th century American foreign policy (which I am neither condemning nor endorsing here) this is merely stating the obvious. I don’t personally recall similar statements generating much outrage in Europe, at least, and in the rest of the interview Abdul Faisel Rauf actually provides a thoughtful analysis about what happened:

MR. BRADLEY (voiceover): And throughout the Muslim world, there is also strong opposition to America’s foreign policy, particularly in the Middle East, because of its support of Israel and economic sanctions against Iraq.

MR. ABDUL RAUF: It is a reaction against the policies of the U.S. government, politically, where we espouse principles of democracy and human rights and where we ally ourselves with oppressive regimes in many of these countries.

MR. BRADLEY: Are — are — are you in any way suggesting that we in the United States deserved what happened?

MR. ABDUL RAUF: I wouldn’t say that the United States deserved what happened, but the United States policies were an accessory to the crime that happened.

MR. BRADLEY: O.K. You say that we’re an accessory?

MR. ABDUL RAUF: Yes.

MR. BRADLEY: How?

MR. ABDUL RAUF: Because we have been an accessory to a lot of — of innocent lives dying in the world. In fact, it — in the most direct sense, Osama bin Laden is made in the U.S.A.

To which I would like to add the neutral observation that an act of terrorism is also the only war strategy available to a side that does not have the resources to buy their own Daisy Cutters or MOAB’s. Ugly and despicable, yes, but it is a collective failure of humanity that in the 21st century the world still is ugly and despicable.

The two links provided in the beginning of this section provide a lot of information about imam Rauf and his all-American personal history. Ironically, at the moment Rauf is away on a trip to Bahrain with the explicit intent to improve cross-cultural relations and understanding. And not for the first time either:

If one were to hearken back to the halcyon days of the Bush Administration, one would remember that, when Bush adviser Karen Hughes was appointed Undersecretary of State for Public Diplomacy, the Bush Administration saw improving America’s standing among Muslims abroad as a part of its national security strategy. And, as such, Hughes set up listening tours, attended meetings and worked with interfaith groups that — shocking, by today’s Republican standards — included actual Muslims.
One of those people was Imam Feisal Abdul Rauf.

And finally, according to the State Department:

His work on tolerance and religious diversity is well-known and he brings a moderate perspective to foreign audiences on what it’s like to be a practicing Muslim in the United States,” State Department spokesman P. J. Crowley said Tuesday. He added that the department’s public-diplomacy offices “have a long-term relationship with” Rauf – including during the past Bush administration, when the religious leader undertook a similar speaking tour.

The Koran

If you’re interested in (having an opinion about) the Islam you could of course always read the Koran. It’s just a click away because it’s available for free from project Gutenberg in various translations. A search for the word “kill” in one of the Gutenberg texts then yields, for example, among other (more neutral) passages, the following:

And fight for the cause of God against those who fight against you: but commit not the injustice of attacking them first: God loveth not such injustice: And kill them wherever ye shall find them, and eject them from whatever place
they have ejected you; for civil discord is worse than carnage: yet attack them not at the sacred Mosque, unless they attack you therein; but if they attack you, slay them. Such the reward of the infidels.

But if they desist, then verily God is Gracious, Merciful. Fight therefore against them until there be no more civil discord, and the only worship be that of God: but if they desist, then let there be no hostility, save against the wicked.

That doesn’t appear to allow for a first strike against the infidels. That is nice. In Sura VIII.-THE SPOILS1 [XCV.], we find

And call to mind when the unbelievers plotted against thee, to detain thee prisoner, or to kill thee, or to banish thee: They plotted-but God plotted: and of plotters is God the best!

which seems to state that the actual killing is best left to God. And earlier in the same Sura it can be read that God has a mob of bloodthirsty angels on hand, whom he has instructed to

Strike off their heads then, and strike off from them every finger-tip.

So by not striking first and by staying clear of wrathful angels, bloodshed can be avoided? Alas, there is no such luck, for according to Sura IX.1-IMMUNITY [CXIII.]:

Make war upon such of those to whom the Scriptures have been given as believe not in God, or in the last day, and who forbid not that which God and His Apostle have forbidden, and who profess not the profession of the truth, until they pay tribute out of hand, and they be humbled. The Jews say, “Ezra (Ozair) is a son of God”; and the Christians say, “The Messiah is a son of God.” Such the sayings in their mouths! They resemble the saying of the Infidels of old! God do battle with them! How are they misguided!
[..]
Believers! wage war against such of the infidels as are your neighbours, and let them find you rigorous: and know that God is with those who fear him.

It’s a no-win situation. Keeping the zealots out of the city by denying them their center will only add fuel to the fire, for it is also written

But into whatsoever city ye enter, and they receive you not, go your ways out into the streets of the same, and say, Even the very dust of your city, which cleaveth on us, we do wipe off against you: notwithstanding be ye sure of this, that the kingdom of God is come nigh unto you. But I say unto you, that it shall be more tolerable in that day for Sodom, than for that city.

Whoops… That one is actually Jesus sending forth his followers in Luke 10:10-12. It is easy to confuse such passages in the Koran and the new testament (or the old testament, which is even more violent), such as this new testament passage from John 15:6 suggesting infidels be burned:

If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned.

There’s even a similarly scary mob of homicidal angels (Thessalonians 1:7-9):

And to you who are troubled rest with us, when the Lord Jesus shall be revealed from heaven with his mighty angels, In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ: Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power;

and ambiguous mixed messages, like those found in Luke 9:54-56, closely before the quoted Luke 10 passage, where Jesus disappoints his followers who are eager for destruction.

Which is it going to be? Don’t start fighting unless in defence, or kill all infidels? Both Koran and new testament are schizophrenic on this account, although the aforementioned Geert Wilders has made up his mind. After all, he only saw fit to compare the former book to Mein Kampf, and not the latter.

[update Oct 6, 2010 Some architect’s renderings of the planned building have become available here, see also the picture below:

It may turn out that I was wrong when I stated Park 51 will not be conspicuous or stand out in any way, although (depending on your taste in architecture) this looks an improvement over my expectations. The building is now scheduled to have sixteen floors, not fifteen, and judging from the image it will probably be slightly larger than the building opposite it. Also from the article:

The largest part of the building — four of 16 floors — would be taken up by a sports, fitness and swimming center. Another full floor would be occupied by a child care center and playground. Much of the rest of the building would be occupied by a restaurant, culinary school, artist studios, exhibition space and an auditorium for cultural events. El-Gamal said the idea was to build a facility that will attract neighborhood residents looking for a place to work out, as well as suburban Muslim couples spending “date night” in the city.

And the mosque part?

The building’s prayer space for Muslims — the part of the center that has caused some critics to derisively brand the center the “ground zero mega mosque” — would be located on two levels in the basement.

]