Most theorists think they have the right theory but are wrong. So just because Einstein was right, that doesn't mean he had good reason to believe he was right. He could have been a lucky draw from the same process.

The Einstein field equation itself is actually extremely simple:

G = 8piT

Sure, if we don't mind that G and T take a full page to write out in terms of the derivatives of the metric tensor. By this logic every equation is extremely simple -- it simply asserts that A=B for some A,B. :-)

Hanson, that's why I picked Einstein - he'd already been "lucky" once at that point. Also, he would still need quite a lot of evidence just to get to the point of having a remote chance of being right.

McCabe, you're right, it's completely obvious, it makes you wonder why Einstein took ten years to figure it out.

"And remember that General Relativity was correct, from all the vast space of possibilities."

The Einstein field equation itself is actually extremely simple:

G = 8piT

where G is the Einstein tensor and T is the stress-energy tensor. Few serious competitors to GR have emerged for a very good reason; what sane modifications could you make to this equation? G and T have to be directly proportional, because everyone knows that the curvature of spacetime (and hence the effect of gravity) is directly proportional to the quantity of matter/energy. The constant of proportionality is fixed by direct measurement of g. G must vanish when T vanishes, as there must be no gravity in the absence of matter. T itself cannot be modified, because it's the only sane way to measure mass, energy, and momentum in the Lorentzian manifold framework. G cannot be modified, because it must be constructable from the metric tensor (a property of spacetime), it must be directly proportional to the amount of curvature, and it must be invariant with respect to the choice of coordinate system (the full derivation is left as an exercise to the reader in my textbook).

I agree with Tom that there isn't that much room to change the field equations once you have decided on the Riemannian tensor framework: gravity cannot be expressed as first-order differential equations and still fit with observation, while number of objects to build a set of second-order equations is very limited. The equations are the simplest possibility (with the cosmological constant as a slight uglification, but it is just a constant of integration).

But selecting the tensor framework, that is of course where all the bits had to go. It is not an obvious choice at all.

It is interesting to note that Einstein's last paper, "On the relativistic theory of the non-symmetric field" includes a discussion of the "strength" of different theories in terms of how many undetermined degrees of freedom they have. http://books.google.com/books?id=tB9Roi3YnAgC&pg=PA131&lpg=PA131&dq=%22relativistic+theory+of+the+non+symmetric+field%22&source=web&ots=EkMv5tudsI&sig=lkTQE94Ay1h2-qS0mcbGT3xa22M If I recall right, he finds his own theory to be rather flabby.

Once you assume:

1) the equations describing gravity are invariant under all coordinate transformations,

2) energy-momentum is not locally created or destroyed,

3) the equations describing gravity involve only the flow of energy-momentum and the curvature of the spacetime metric (and not powers or products or derivatives of these),

4) the equations reduce to ordinary Newtonian gravity in a suitable limit,

then Einstein's equations for general relativity are the only possible choice... except for one adjustable parameter, the cosmological constant.

(First Einstein said this constant was nonzero, then he said that was the "biggest mistake in his life", and then it turned out he was right in the first place. It's not zero, it's roughly 0.0000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000001. So, a bit of waffling on this issue is understandable.)

It took Einstein about 10 years of hard work to figure this out, with a lot of help from a mathematician Marcel Grossman who taught him the required math. But by the time he talked to that reporter he knew this stuff. That's what gave him his confidence.

His assumptions 1)-4) could have been wrong, of course. But he was playing a strong hand of cards - and he knew it.

By the way, he did write a paper where he got the equations wrong and predicted a wrong value for the deflection of starlight by the Earth's gravitational field. But luckily he caught his mistake before the experiment was done. If he'd caught his mistake afterwards, lots of people would have thought he was just retroactively fudging his theory to fit the data.

Tarleton, people do propose lots of complex wrong theories, but they don't propose literally quintillions of wrong complex theories for every right complex theory. If the ratio is even ten wrong to one right, you can tell the good guessers must have possessed massive evidence - survivorship bias is not remotely enough to account for it. As for the wrong guessers, they are more likely to have suffered from bad evidence or bad thinking, than from having almost exactly enough evidence processed correctly followed by a wrong guess.

"If only you had been around to solve the problem instead of Maxwell and Einstein, how much work could have been saved!"

Obvious != simple != easy to learn. You of all people should understand this. You seemed to understand it seven years ago, back during the days of your wild and reckless youth. To quote SitS:

"Let's take a concrete example, the story Flowers for Algernon (later the movie Charly), by Daniel Keyes. (I'm afraid I'll have to tell you how the story comes out, but it's a Character story, not an Idea story, so that shouldn't spoil it.) Flowers for Algernon is about a neurosurgical procedure for intelligence enhancement. This procedure was first tested on a mouse, Algernon, and later on a retarded human, Charlie Gordon. The enhanced Charlie has the standard science-fictional set of superhuman characteristics; he thinks fast, learns a lifetime of knowledge in a few weeks, and discusses arcane mathematics (not shown). Then the mouse, Algernon, gets sick and dies. Charlie analyzes the enhancement procedure (not shown) and concludes that the process is basically flawed. Later, Charlie dies.

That's a science-fictional enhanced human. A real enhanced human would not have been taken by surprise. A real enhanced human would realize that any simple intelligence enhancement will be a net evolutionary disadvantage - if enhancing intelligence were a matter of a simple surgical procedure, it would have long ago occurred as a natural mutation. This goes double for a procedure that works on rats! (As far as I know, this never occurred to Keyes. I selected Flowers, out of all the famous stories of intelligence enhancement, because, for reasons of dramatic unity, this story shows what happens to be the correct outcome.)

Note that I didn't dazzle you with an abstruse technobabble explanation for Charlie's death; my explanation is two sentences long and can be understood by someone who isn't an expert in the field. It's the simplicity of smartness that's so impossible to convey in fiction, and so shocking when we encounter it in person. All that science fiction can do to show intelligence is jargon and gadgetry. A truly ultrasmart Charlie Gordon wouldn't have been taken by surprise; he would have deduced his probable fate using the above, very simple, line of reasoning. He would have accepted that probability, rearranged his priorities, and acted accordingly until his time ran out - or, more probably, figured out an equally simple and obvious-in-retrospect way to avoid his fate. If Charlie Gordon had really been ultrasmart, there would have been no story. "

We know that Newton's theory of gravity was hard to invent; it must not have been obvious, because nobody had solved it until Newton, and he was lauded as a hero for his great theory. And yet, it is so simple that we teach it to high school students, and some of them actually understand it. Newton's equation is also a unique solution; the constant of proportionality is fixed by experiment, the m/r^2 term is fixed by the need to include Kepler's laws (which were well known at the time), and extra terms are excluded, because F must vanish when M2 vanishes, or else you violate the laws of motion which Newton had just discovered.

"McCabe, you're right, it's completely obvious, it makes you wonder why Einstein took ten years to figure it out."

I never said it was obvious; I said that the equations were a unique solution imposed by various constraints. Proving that the equations are a unique solution is quite difficult; I can't do it, even with a ready-made textbook in front of me. There are many examples of simple, unique-solution equations being very hard to derive- Newton's law of gravity and Maxwell's laws of electromagnetism come to mind.

"But selecting the tensor framework, that is of course where all the bits had to go. It is not an obvious choice at all."

I agree that it is not at all obvious, but the search space doesn't seem to be all that large- how many mathematical toys are there which could form a viable framework for gravity? The difficulty seems to be in understanding the math well enough to determine whether it can represent real-world phenomena. Differential geometry is not a simple Bayesian hypothesis like "the cat is blue"; to figure out whether piece of evidence Q supports a geometric theory of gravity, you have to understand what a geometric theory of gravity would look like (in Bayesian terms, which outcomes it would predict), which is quite difficult.

"Tom, is that an elaborate joke?"

No. What makes you think that?

Um, guys, there are an infinite number of possible hypotheses. Any evidence that corroborates one theory also corroborates (or fails to refute) an infinite number of alternative specifiable accounts of the world.

What evidence does is allow us to say "Whatever the truth is, it must coexist in the same universe with the true nature of this evidence I have accepted. Theory X and its infinite number of variants seems to be ruled out by this evidence (although I may have misinterpreted the theory or the nature of the evidence), whereas Theory Y and its infinite number of variants seems not yet to be ruled out."

Yeah, I realize this is a complicated way to phrase it. The reason I like to phrase it this way is to point out that Einstein did not have merely 29 "bits" of evidence, he had VAST evidence, based on an entire lifetime of neuron-level programming, that automatically focused his mind on a productive way of thinking about the universe. He was imagining and eliminating vast swaths of potential theories of the universe, as are we all, from his earliest days in the womb. This is hardly surprising, considering that humans are the result of an evolutionary process that systematically killed the creatures who couldn't map the universe sufficiently well.

We can never know if we are getting to the right hypothesis. What we can say is that we have arrived at a hypothesis that is isomorphic with the truth, as we understand that hypothesis, over the span of evidence we think we have and think we understand. Always the next bit of evidence we discover may turn what we think we knew upside down. All knowledge is defeasible.

"Fixed by evidence" != "simple". There are few alternatives to Newton's Laws, perhaps, once you (a) invent calculus as the language of description, the interpreter to run the code; (b) observe Kepler's laws; (c) realize that objects in motion remain in motion unless a force acts upon them, as opposed to Aristotle's view, and therefore the law should be written in second derivatives as opposed to third or first derivatives; etc. etc.

Please recall that my original contention was that Einstein must have had enough observational evidence to fix the information inherent in General Relativity as a solution. If you describe ways that the information in General Relativity can be fixed by evidence, you are not contradicting this.

You are also falling prey to hindsight by not making an equal effort to consider how you could have justified alternatives as unique obvious solutions using subsets of other knowledge known at the time, rather than the particular aspects that now obviously seem so prominent.

Many popular reports of Eddington's test mislead people into thinking it provided significant evidence. See these two Wikipedia pages for reports that the raw evidence was nearly worthless. Einstein may have known how little evidence that test would provide.

I guess a defense of old Albert would go something like this; the route he took to establish his theory didn't rely upon empirical evidence of the sort Eddington was trying to discover but rather was an elegant way to explain certain unusual properties of light and energy which, once he had formulated his theory, it seemed obvious to him could not be explained any other way. The kind of empirical validation which Eddington was carrying out was a laudable and necessary step in the process of theory confirmation/falstification but nevertheless it is entirely reasonable for Einstein to believe that no such confirmation was necessary as, relative to the theoretical status quo prior to the theory of relativity, the theory of relativity had vastly greater explanatory power and so any theory which might supplant it would have to incorporate elements of the theory, or postulates very similar to the theory, to explain the same things. Einstein had a sense of humour and was, I take it, simply relaying the idea that he thought it much more likely that any negative result from Eddington's expedition would turn out to be due to poor expedition data rather than a problem with the theory; I don't think he was every claiming (non-sensical) 100% certainty. The man may have been a genius, but he wasn't an idiot.

Maybe we should also consider that Einstein fully understood the irony in his statement, and was in a humorous mood. After all, what he would do if the attempt to verify did not succeed was not of any import whatever. It was a typical "sell newspaper" question.

Something doesn't feel right. Don't people frequently propose complex theories that turn out to be wrong?

Abraham Pais, one of Einstein's many friends, has said that Einstein loved to joke. Are you sure his "sorry for the good Lord" wasn't a bit of humor?

That waste of three minutes wasn't your fault. But the decision to sink more time into posting a comment that obviously won't do any good (not least because it's completely unspecific) was.

"Please recall that my original contention was that Einstein must have had enough observational evidence to fix the information inherent in General Relativity as a solution. If you describe ways that the information in General Relativity can be fixed by evidence, you are not contradicting this."

True; why do you have to contradict the main point of a post to comment on it? My point was that the space of possibilities was not vast; it was quite small, given the common-sense rules of gravity and math which were known at the time. Developing GR took years, not because Einstein has to sort through ten million different versions of the theory, but because developing a single version of the theory is difficult.

"You are also falling prey to hindsight by not making an equal effort to consider how you could have justified alternatives as unique obvious solutions using subsets of other knowledge known at the time, rather than the particular aspects that now obviously seem so prominent."

This is mathematically impossible unless you assume false knowledge. If equations (A, B, C, D, E) are known at the time of Newton, and Newton's theory of gravity is unique if you assume A, C and D, then any alternative theory of gravity must contradict A, C, or D. Suppose that you can construct an alternative theory of gravity, which is unique assuming equations B and E. If you assume that both B and E are true, then the alternative theory of gravity must be true, hence Newton's theory must be false, hence either A, C, or D must be false. We know now that A, C, and D are all true, therefore, either B or E must be false.

In other words: Einstein also said that God does not play dice with the universe. However, not only does God play dice, but sometimes he ignores the result and just says it worked.

"Sure, if we don't mind that G and T take a full page to write out in terms of the derivatives of the metric tensor."

The Riemann tensor is a more natural measure of curvature than the metric tensor, and even in that language it's still pretty simple:

8piT = R (tensor) - .5gR (scalar)

where R (tensor) (subscript) ab = Riemann tensor (superscript) c (subscript) acb and R (scalar) = g (superscript) ab * R (tensor) (subscript) ab

You can make any theory seem complicated by writing it out in some nonstandard format. Take Maxwell's equations of electromagnetism in tensor form:

dF = 0 dF = 4pi*J

Now differential form:

(divergence) E = p (divergence) B = 0 (curl) E = -dB/dt (curl) B = J + dE/dt

Now integral form:

(flux E over closed surface A) = q (flux B over closed surface A) = 0 (line integral of E over closed loop l) = - d (flux of B over surface enclosed by l)/dt (line integral of B over closed loop l) = (current I passing through surface enclosed by l) + d (flux of E over surface enclosed by l)/dt

Now in action-at-a-distance form:

E = (sum q) -q/4/pi ((r' unit vector from q)/r'/r' + r' d/dt ((r' unit vector from q)/r'/r') + d^2/dt^2 (r' unit vector from q)) B = (sum q) E x -(r' unit vector from q)

Tom, is that an elaborate joke?