## Physicists Clarify Exotic Force 86

Posted
by
timothy

from the gravity-is-pretty-exotic-stuff dept.

from the gravity-is-pretty-exotic-stuff dept.

Azazel writes

*"A research group, including Purdue University physicist Ephraim Fischbach, has completed an experiment which shows that gravity behaves exactly as Isaac Newton predicted, even at small scales. Unfortunately for those in search of the so-called "Theory of Everything," the finding would seem to rule out the exceptions to his time-honored theories that physicists believe might occur when objects are tiny enough."*
## Did I miss something? (Score:1)

## Re:Did I miss something? (Score:4, Interesting)

Well, this is the first time I've heard of the "Casimir force" force, but reading the article linked to in the article (how's that for RTFM) explains that pretty well. Now, the prevailing "ToE" is to the best of my knowledge, string theory. This theory was developed to explain the inconsistancies with Newton's and Einstein's laws when you got down to a sub-atomic level. This study is basically saying that string theory is wrong, and that Newton and Einstein (for the most part) were right.

Now, the interesting there here is the "Casimir force" which basically, is the force of photons striking an object. We touched on this actually in high school physics. We were experimenting to find out if light was a wave of a particle. (its a wave of particles). I started to ask questions like, if that's true, wouldn't most stationary objects eventually gain mass due to a build up of photons. We never quite got into that... probably a little advanced for most people in high school physics. Sorry, back on topic. This force, becomes very powerful (comparatively) at sub-atomic levels. The force of a particle travelling at the speed of light can become very significant. In fact, it becomes more significant than gravity. So, everything as usualy, I'm not sure I'd agree, but it hopefully does get us one step closer to the ToE.

## Accumulation of photons (Score:5, Interesting)

Particle/wave duality is not fully explained by thinking of light as a wave of particles, as this conflicts with observations of diffraction gratings at extremely low light intensities. It is my understanding that a "refinement" is to describe light as a single photon that exists with varying probabilities across the wave. (The wave is then a probability wave.)

QM allows objects to exist at multiple points or in multiple states simultaneously, until directly observed. If you do try to directly observe a photon, you do indeed see a single packet of energy. But if you look only at the results, you see a wave.

By looking at light as a probability wave, a lot of apparent paradoxes don't "go away" but do fit a lot better with other known apparent paradoxes, which (to me) indicates the phenomena are related and not distinct.

Getting back to gravity, we could be in for an interesting dilema here. With no variations so far detected, the theory of gravity being an exchange of particles seems less likely. Einstein's model of a distorted space/time would seem to be the more probable, at this point.

This is important, as the predicted QM model for gravity could not be compatible with Enstein's model of gravity. They could not coexist, one had to be wrong. At this point, it seems likely that the particle-exchange model is the one that is wrong, which means QM in its eventual form will likely not be 100% particle based. It may need to be a heterogenius model.

As an aside, let us assume gravity does bend space/time. Since information cannot travel infinitely fast, and as no two events can occur simultaneously, when a massive object moves, space cannot restore itself the moment the object has left. Thus, there must be something analogous to a restoring force within space/time, and therefore some parallel to Hooke's Law.

By implication, an object moving fast enough should leave a trail, where the effect of gravity on space/time is apparent, even though there is no longer any source of that gravity present. A massive-enough object may even leave some sort of "wake", similar to that of a boat, only in gravity rather than in water.

Hooke predicts an upper limit to expansion, though. Something stretched beyond a certain point cannot be restored to its original dimensions, but will rather be restored to some other state, with a much lower restoring force existing.

By implication, a sufficiently massive black hole should result in a region of permanently deformed space/time, as the expansion would exceed the Universe's ability to restore.

As far as I know, no such "massless holes" have been found, but the more the Einstinian model is verified, the more certain I am that such a thing must exist.

## Re:Accumulation of photons (Score:2, Interesting)

Wow, loved that comment. I had never thought of the "wake" effect of a massive object moving (or disappearing) and space/time not being able to completely restore itself afterwards. Even though my understanding of physics is quite limited (high school level plus some reading and disucssions since then), I do tend to grasp most concepts, and the idea that gravity was a force travelling as a particle never quite felt right. However, the idea that a massive object could bend space/time did.

I'm part way thr

## Re:Accumulation of photons (Score:1)

## What? (Score:5, Informative)

isthe warping of space-time.So, no, you will not see a "wake" of gravity because you are an observer, you will be affected by the gravity of the object at a point. Since the object itself cannot move faster than the speed of light, the gravity well will always be able to restore faster than the object moves.

You may be thinking of frame-dragging, which is a different phenomenon.

BTW, what moderator decided that this comment was "Interesting"? What I wouldn't give for a "-1, Uninformed" mod.

## Re:What? (Score:3, Informative)

## Re:What? (Score:3, Informative)

## Re:What? (Score:5, Interesting)

Now onto the rest of my post: The physicists at Warwick University, for the Einstein Celebration, considered my theories on relativity to actually be pretty good. :) I had produced a summary of the derivation of relativity and from that derived what overall physical phenomena must underpin the entire theory.

The quantization of space/time is guaranteed. Why? Because matter is quantized, and matter and energy are simply different facets of the same thing, energy must be quantized. (Matter is merely condensed energy, it is therefore the same stuff, just in a different state.)

If energy is quantized, then fields must be quantized, as fields define energy. If fields are quantized, then space and time are quantized, as fields are defined over these.

The scale of quantization is extremely small. A Higg's Particle is the smallest unit of matter definable, but in order to have energy to condense, the scale on which a photon itself exists must be smaller still. There may well be smaller particles in the "quantum foam", which is fine as they don't have to be stable. The Higg's Particle is stable and is likely the smallest object that can be stable.

What does that give us for scale, though? Without knowing even the theoretical mass of the Higg's Particle, that is hard to even guess at, but a guesstimate based on existing data would imply quantization of space at around about 10^-50 m, and something comparable for time.

No, you do not perceive gravity as a point source, because you are not a point. That is why objects in a gravity well will stretch. EACH point of you will experience gravity differently and not from "one source" but rather from the composite value.

(If you are between Earth and the moon, you will experience gravity from each. At the right point, you will be held stationary because the interference will produce no net force. If that were not the case, the Universe would be in serious trouble. As would most of physics, as a lot depends on overlapping fields.)

We are talking about energy differentials. It is a grave mistake of the first order to distinguish between phenomena that are, in fact, the same thing. All objects travel at the speed of light, at different angles to space/time. It is the angle that produces relativistic mass, reliativistic length and relativistic time.

This can be proved by simple trigonometry, and is likely where Einstein got the equations in the first place. Relativity is just a restating of Pythagoras, as all equations are based on the same formula: R' = sqrt(1 - v^2/c^2), where R' is the relativistic version of the variable of interest.

When re-written, this becomes R'^2 + V^2 = C^2, which is basically Pythagoras.

However, the consequence of this is both simple and profound. If all objects indeed travel at the speed of light, at different angles to space/time, and indeed relativity is nothing more than the projection onto the plane of interest, then gravity is a direct consequence of this motion through space/time.

(Relativistic mass, by this logic, is simply a force exerted at 90' to space. The distortion of space is the result of this. This means tha

## Re:What? (Score:1, Flamebait)

Starting with some algebra. If R'=sqrt(1-v^2/c^2), then (R'^2)*c^2+v^2=c^2. You forgot a term. Remember this sequence: simple math FIRST, then general relativity. The other way around just needlessly complicates things.

Second, your formula doesn't even support your statement that all objects travel at the speed of lig

## Re:What? (Score:2, Interesting)

If you are stationary in space, then you are "moving" at the speed of light through time. Any motion through space reduces your velocity through time - but it always adds up to the speed of light.

I must admit, that idea made me stop and re-read that section of the book a couple of tim

## Re:What? (Score:2, Insightful)

If you are stationary in space, then you are "moving" at the speed of light through time. Any motion through space reduces your velocity through time - but it always adds up to the speed of light.That's more or less what relativity says. It's not so much that your velocity always adds up to the speed of light, however, as it is that we are travelling on a four dimensional vector. i.e. Just as a car traveling in a diagonal path has a slower southward velocity than a car travelling at the same speed but hea

## Re:What? (Score:2)

Second, your formula doesn't even support your statement that all objects travel at the speed of light. This is a nonsensical statement and I suppose it only figures that it needs nonsensical math to back it up, but wow you take it to extremes.Actually, this has become a fairly standard and accepted way of formulating SR from a simple geometric viewpoint.

It's okay to criticize people's theories, but if you're going to insult them and call them a "crank", at least make sure you're completely correct first

## Re:What? (Score:2)

30 second version.

Einstein postulated that the speed of light is the same for all oberservers. With this and the Pythagorean formula you can find the time dialation.

Dude sits in a box that has a device that emits a single photon from the floor towards the top. From his perspective the box is C*Tdude in height. Speed-o-light times the time it took for a single photon to travel from the bottom to the top of the box as mesured by the dudes cloc

## Re:What? (Score:4, Interesting)

BTW, what moderator decided that this comment was "Interesting"?"What deity bestowed the ultimate truth and power to judge the value of opinions upon you? I found the comment interesting. This is a great forum for discussion of news items, and that is what I come here for.

What I wouldn't give for a "-5, Callous Pedantism" mod.

## Re:What? (Score:2)

## Re:What? (Score:2)

## Photons have mass? (Score:5, Informative)

Photons have massNo! Photons have momentum. This does not imply that they have mass.

## Re:Photons have mass? (Score:1, Informative)

Actually, it more than simply implies that they have mass. You cannot have momentum without mass. You can have velocity without mass (in the case of neutrinos, I think), but not momentum. In fact, this is how you calculate momentum:

p = mv

p = momentum

m = mass

v = velocity

## Re:Photons have mass? (Score:2)

## Re:Photons have mass? (Score:2)

See Ask A Scientist [anl.gov].

## Re:Photons have mass? (Score:5, Informative)

In fact, this is how you calculate momentum...Not for photons.

This is how you calculate momentum for photons:

p = h / lambda, where lambda is wavelength.

Alternatively:

p = hf / c, where E is energy, and f is frequency.

More info here:

http://scienceworld.wolfram.com/physics/Photon.ht

And here:

http://scienceworld.wolfram.com/physics/Energy.ht

You can "back-calculate" a supposed mass for a photon, once you know its momentum, by using the p = mv equation. But this often called a "fictional" mass, because it is purely relativistic. If you took away a photon's speed, it would have neither mass nor momentum, and would essentially cease to exist. Mass as an fundamental physical quantity exists even in the absence of velocity. This cannot happen with a photon...

Unless you subscribe to the view that photons do not always travel at c in vacuum. But I will not argue that here. Not enough space, and I don't want to be in a flamewar.

## Re:Photons have mass? (Score:2)

## Re:Photons have mass? (Score:1)

And it would take an infinite amount of energy if you could. So it's not absurd to say it would end up with an infinite mass...that energy would have to end up somewhere. ;)

(No, I'm not talking about outside of a vacuum. That isn't really taking away their speed.)

## Re:Photons have mass? (Score:1)

## Re:Photons have mass? (Score:1)

## Re:Photons have mass? (Score:3, Informative)

The bending of light around large objects is not due to the planet excerting a force due to gravity on the photon, but instead the presence of the planet bending the space-time around the planet, then the photon travels in a straight line through this curved space-time.

This means that the photon does not need to have mass to be bent by light.

## Don't photons have energy? (Score:2)

## Re:Don't photons have energy? (Score:2)

## Re:Don't photons have energy? (Score:1)

The mass defined here is the effective mass, the full equation is E^2=(pc)^2 + mc^2. Where m = m_0 {sqrt[1-(v/c)^2]}^(-1), and m_0 is the rest mass, the mass a particle has when it is not moving. So for a particle with mass, at rest, then the equation is E=m_0 c^2. But for a photon, which doesn't have mass, m_0=0, and the second term is zero, all its energy comes from the first term, so E=pc, momentum times the speed of light.

If a photon had mass

## Re:Don't photons have energy? (Score:1)

E^2=(pc)^2 + (mc^2)^2

## Re:Photons have mass? (Score:3, Informative)

Unless I'm mistaken, the general belief is that a photon does have mass.No offense intended, but you are mistaken.

If photons do not have mass, why are they affected by gravity?According to relativity, gravity bends space. It doesn't act directly on other mass. Rather space acts on mass, by telling "how to move", which is along paths called "geodesics". A geodesic is a path demarking the "shape" of spacetime in a region. Light moves along geodesics, which is basically a way of saying that it perc

## Re:Photons have mass? (Score:2, Interesting)

## Re:Did I miss something? (Score:2)

Casimir force has nothing, let me repeat,

nothingto do with the force of photons striking an object. You are undoubtedly confused and I can't even begin to guess from where you gleaned this information. The Casimir force arises from the relative density of quantum vacuum fluctuations of the space between two## Re:Did I miss something? (Score:3, Informative)

You are undoubtedly confused and I can't even begin to guess from where you gleaned this informationWell, as I said, I read the article about Casimir force linked to in the original article ( [purdue.edu] http://news.uns.purdue.edu/UNS/html4ever/030811.F ischbach.casimir.html [purdue.edu]) which contains this paragraph:

The Casimir force has to do with the minute pressure that real and virtual photons of light exert when they bump against an object. High quantities of photons are constantly striking you from all directions, emitt## Re:Did I miss something? (Score:2)

## Re:Did I miss something? (Score:2)

c.## Re:Did I miss something? (Score:4, Insightful)

Yes and no...what's noteworthy about this experiment is what they

didn'tfind. Much like the Michelson-Morley experiment [wikipedia.org] in 1887, which set out measure the 'aether', and instead failed utterly to detect any such thing, this experiment was devised to detect exceptions to the behavior of gravity on a quantum scale, and found no such exceptions.Ephraim's not giving up yet, though...he plans on developing another experimental apparatus that is a million times more sensitive than the one that was used in this experiment. Also, even though this experiment was nominally a 'failure', the fringe benefit of clarifying the Casmir force is a big success.

## Common sence (Score:2)

## Re:Common sence (Score:2)

The problem is there are two different common senses in effect. One the one hand we know gravity exists, so common sense says it should exists everywhere. On the other hand there is no explination to account for gravity (We can measure it, but cannot explain it), and the some theories that when looked at alone seem to imply that gravity doesn't apply.

So they have proved one side right, but only at the expense of making some otherwise well tested theories fail.

Gravity is easy for the uneducated masse

## Gravity at small length scales (Score:5, Informative)

There are suggestions out there that one way to test for the existence of extra "compactified" spatial dimensions (the kind of stuff needed in string theories) is to look for deviations from Newton's 1/r^2 gravity at small distance scales. See, for example, here [lanl.gov].

The problem is, it's very hard to measure

justthe gravitational interaction between two objects separated at micron scales. Gravity is incredibly weak compared to common forces like electrostatics and magnetic interactions, and even more exotic things like Casimir forces (related to the van der Waals interaction).The Purdue team has shown that the measured Casimir force in their experiment acts just as expected, setting a new limit on how screwy gravity can be at these distance scales.

For what it's worth, there are two other big efforts in this area. The one at Stanford [stanford.edu] is led by Aharon Kapitulnik, and is so sensitive that their apparatus can detect the different forces on Au and Si in the earth's magnetic field due to diamagnetism (!). The one at Washington [washington.edu] is reportedly even more sensitive, and there are rumors [blogspot.com]circulating that they

mayhave seen something exciting.The really cool thing here is how table-top solid state experiments may have something profound to say about high energy physics, without any big accelerators.

## Re:Gravity at small length scales (Score:3, Interesting)

arerelated and that this has been known since 1955. On the one hand I've studied quantum field theory and read papers on the Casimir force, and on the other hand I've worked with computational chemists who put the vdW force into their models all the time. But I had no clue these things were related. I had merely assumed that the vdW for## Re:Gravity at small length scales (Score:3, Informative)

In short, when you assume "action at a distance" and calculate the instantaneous forces between fluctuating dipoles, you get the van der Waals interaction. When you do full local treatment of the quantum EM fields, including retardation effects, you get the Casimir force.

## Correction to the above.... (Score:5, Informative)

independentof the Casimir force - basically it's a background-free measurement. Very slick.## Free Link (Score:1, Informative)

## Re:Gravity at small length scales (Score:2)

Or am I all wet?

## Re:Gravity at small length scales (Score:5, Informative)

Physicists have a really, really hard time explaining *why* gravity is 10^42 times weaker than all other forces. (If you really want to split hairs, it's about 10^38 times weaker than the Weak Force, but what's an order of magnitude among friends?) Gravity appears to be a completely different manifestation than the electromagnetic, weak, and strong forces of nature. This irks many, and they try to rectify that by a Grand Unifying Theory (GUT).

One recent shot at explaining all this was well laid out in this article in Physics Today [physicstoday.org] (subscription required, sorry) from 2002. In short, it theorized that gravity exists in 11 dimensions, not just 3, over short distances. Over some distance, the force known as gravity would "collapse" back down to our traditional 3. The fact that it acted over 11 dimensions, not 3, made gravity drop off as something like 1/r^10. This could help explain the apparent weakness of gravity.

IIRC, the authors predicted that gravity would get measurably stronger at small distances, as it was acting in many dimensions at once. Towards the upper end of their estimates, they predicted that gravity could be measurably stronger at distances around 3-5 millimeters.

As I read this latest discovery, it appears to throw water on that attempt to unify gravity with everything else. Back to the drawing board.

## Re:Gravity at small length scales (Score:2)

"they predicted that gravity could be measurably stronger at distances around 3-5 millimeters"Wouldn't gravity changing at 3-5 millimeters mean that people would notice its effects in everyday life?

## Re:Gravity at small length scales (Score:1, Interesting)

## Re:Gravity at small length scales (Score:1)

Can anyone familiar with this experiment elaborate?

## Yes. . .everythings normal BUT. . . (Score:3, Insightful)

But what's eating all the theorists is that they have absolutely no idea why. The venerable laws of gravitation are empirical, in the sense that noone knows where it comes from other than the fact that it is associated with mass. All the other forces of nature have a quantum explanation, and have a particle that transmits them (most notably electromagnetism and photons). Noone has been able to satisfactorily reconcile gravity with any fundamental (quantum mechanical) nature of a particle.

It's almost scary that we know more about what binds subatomic particles together than what keeps the moon orbiting the earth. It's also ironic that most people's only introduction to physics is newtonian physics which is presented in textbooks as complete and understood. It's true we have the math to predict the effect of gravity to arbitrary precision, but I'm sure engineers can back me up that just because something has a robust empirical law doesn't mean anyone really understands how it works.

## Re:Yes. . .everythings normal BUT. . . (Score:2)

That's my non-insightful insight for the day...

## Re:Yes. . .everythings normal BUT. . . (Score:1)

unknown, I'd like to point out the following strangeness about Time:1) Between 8am and 5pm, Time is slower than between 5pm and 8am.

2) Friday, 5m - Monday 8am goes by a lightning speed compared to "Normal Time"

3) One year passes faster than 365.4 days

4) Right now, it's 9:30pm, and I'm wasting precious Time on this useless post.

4a) So I *seriously* hope you are too!

## Re:Yes. . .everythings normal BUT. . . (Score:1)

## Re:Yes. . .everythings normal BUT. . . (Score:1)

don'tknow instead of giving the impression that everything's been worked out and it's all unimportant minutiae you could always look up in the encyclopedia if you were really desperate. . .I was floored on my first day of intro physics when the professor told us it's

## Re:Yes. . .everythings normal BUT. . . (Score:1)

## Re:Yes. . .everythings normal BUT. . . (Score:1)

I guess my problem is that physicists, especially in academia, are encouraged to pursue things with no obvious practical use. Excessive attention to practicality is viewed as pandering for funding. Engineers, on the other hand, are taught the complete opposite. . .practicality is k

## Re:Yes. . .everythings normal BUT. . . (Score:1)

Obviously any school worth your money is going to try and place the right professors for the right job. Look at the factulty that the my school has for biomedical physics. Doctors in addition to

## Re:Yes. . .everythings normal BUT. . . (Score:2)

## Re:Yes. . .everythings normal BUT. . . (Score:1)

It's almost scary that we know more about what binds subatomic particles together than what keeps the moon orbiting the earth.If you find that almost scary then do you almost cream your pants considering that we know more about what binds subatomic particles together than the nature of our own mind? I mean we do "know" that there is a certain relationship between physical phenomena and psychical events, but yet we don't know what thoughts are and how it is even possible that the "I" can create them.

I

## Business as usual; gotta keep looking closer (Score:1)

So no big breakthrough, but it is nice that they narrowed down the field of search a bit.

## Re:Business as usual; gotta keep looking closer (Score:2, Informative)

The experiment is looking for evidence that gravity does not follow Newton's law at very small scales. This is predicted by some theories (notably string theory). Confirmation that gravity behaves "normally" up to these atomic scales rules out some t

## Explaining Gravity (Score:3, Interesting)

So they still haven't observed the graviton and are still having trouble explaining why.

What I'd like to know is, why aren't physicists trying harder to explain gravity as a "pseudo-force" like the centrifugal "force" and the Coriolis effect? That's not just a rhetorical question. What makes physicists so sure that the graviton even exists? I trust that there must be some deep reasoning involved -- what is it?

## Re:Explaining Gravity (Score:1, Informative)

The minimum observed limit on the speed of gravity is >= 2*10^10c.

http://www.ldolphin.org/vanFlandern/gravityspeed.

Yes, 20 billion times the speed of light.

## Re:Explaining Gravity (Score:5, Informative)

shouldn'thave seen quantum gravity yet.What you describe (gravity as pseudoforce) is actually something like the way gravity works in general relativity. In that theory, mass warps the fabric of spacetime. Objects travel in the straightest lines they can in this curved space, and we perceive the bends in those paths as being because of a "force" between masses. This theory has been extremely successful in explaining all sorts of large-scale phenomena (not to mention the fact that it is very theoretically beautiful).

The problem is that general relativity and quantum field theory (the theoretical framework of "particles" being exchanged that works so well for the other forces) seem to be fundamentally incompatible. General relativity is fundamentally a theory of the way the geometry of spacetime changes. Field theory is formulated on a pre-existing, static background spacetime. You get into mathematical trouble however you try to get these together.

You can continue in (at least) two ways. Particle physicists are usually more inclined to think that the field theory point of view is fundamental, and that whole geometry thing is just the way things look on large scales. This leads to string theory and the usual discussion of gravitons. If you treat the geometric point of view as more fundamental, you try quantizing spacetime and get loop quantum gravity. String theory is more popular, but no one knows what the right answer is (both may even be different points of view on the same thing!).

## Re:Explaining Gravity (Score:2)

## String theory (Score:3, Interesting)

Nobody has ever adequately explained to me

whystring theory is popular. It isn't actually a "theory", since it hasn't made any testable predictions. There is no problem which it has (yet) solved. Its desirable features (e.g. supersymmetry) are not known to be useful in the first place. Even its motivating examples don't seem to fit the theory. (Hadrons look like strings, but no known string models look anything like hadrons.)As far as I can tell, the argument seems to be that high-energy physicists n

## Re:String theory (Score:3, Interesting)

I think the thing that really got people excited about string theory was the fact that it's a quantum theory of gravity that works at all. That's pretty powerful, since people had been trying crazy t

## Re:Explaining Gravity Clarified (Score:1)

Centrifugal "force" and the Coriolis "force" are not real forces because in both cases you would see it's just inertia and nothing more

if you were observing from the proper inertial frame. It just looks like an extra force when we make the assumption that our rotating Earth is an inertial frame or that the merry-go-round we are on is an inertial frame (both cases are rotating which means they are being accellerated and are therefore improper frames). So the## exotic force? (Score:1, Offtopic)

## Re:exotic force? (Score:1)

## Re:exotic force? (Score:1)

"social life. . heh. . .women. ..heh. . .a physicist craves not these things.. ."

I think he went on to say econ majors were the dark side of the force but he was usually drowned out by hysteric laughter at this point.

I have to tell you, though, it doesn't help that most of the women in physics I knew were completely asexual. Except for the one diamond in the rough that was an avid

## Cavendish: It takes Big Balls to measure Gravity! (Score:2)

http://www.fourmilab.com/gravitation/ [fourmilab.com]

## Everytime gravity stops sucking... (Score:2, Funny)

http://en.wikipedia.org/wiki/Brian_Greene [wikipedia.org]

## $\alpha \leq 10^{12}$? Why so large? (Score:3, Insightful)

So, as I see it, they've shown that this "other" interaction is less than a million million times stronger than Newtonian gravity, right? Until $\alpha \approx 1$, I wouldn't say they've "shown that gravity behaves exactly as Isaac Newton predicted". This is interesting, of course, but there's a long way to go. Fortunately they conclude their Letter by saying they expect to be able to get limits on $\alpha$ down to 10^6 with $\lambda\approx 100nm$. We'll be looking forward to it.

As a side note, it'd be really nice if /. learned to render TeX for any non-physicists who might be reading this.

## Re:$\alpha \leq 10^{12}$? Why so large? (Score:2)

You're right about TeX. I suppose we can wait for

## Theory of Everything (Score:1)