Quadratic Gravity is Possible

Quanta magazine has article on quadratic gravity.

I mentioned this before as an obvious alternative way to quantize gravity.

People have been saying for a long time that string theory is the only hope for quantizing gravity. It is completely false. For example, Brian Greene says in a new video:

0:00 String theory is the most potent and powerful approach that we have discovered as a species for blending general relativity and quantum mechanics.

He goes on to say that string theory is still viable as long as researchers want to work on it, and that is how science works.

Goedel Proved Hilbert Wrong

I wondered whether Goedel literally proved Hilbert wrong, as is commonly claimed. I doubted it.

David Hilbert didn’t leave a single, tidy quote where he explicitly says, “I demand completeness and consistency provable from within,” in those exact words. His vision for the formalization of mathematics, known as Hilbert’s Program, emerged through his lectures, papers, and talks—particularly in the 1920s — and is pieced together from these sources. I’ll show you where these demands are clearest, based on his own words and how contemporaries understood him, without inventing anything he didn’t say.

Completeness

Hilbert’s call for a complete axiomatic system — where all true statements in a mathematical domain (like arithmetic) can be derived from the axioms—shines through in his 1900 address to the International Congress of Mathematicians in Paris. There, he posed his famous 23 problems, and the second problem implicitly reflects this goal. He asked for a proof of the consistency of arithmetic’s axioms but tied it to a broader vision of a “definite system” that settles all questions. He wrote:

“By the solution of these problems, a definitive clarification of the foundations of analysis and arithmetic will be obtained, and the system of axioms will be so complete that all remaining questions can be decided by purely logical deduction from them.”

(From Hilbert’s 1900 address, as translated in various editions, e.g., Bulletin of the AMS, 1902). The term “complete” here doesn’t mean Gödel-style completeness yet (that formal definition came later), but Hilbert’s intent was a system where no mathematical truth escapes the axioms’ reach. In his 1922 lecture “The Logical Foundations of Mathematics” (published in From Kant to Hilbert, ed. Ewald), he’s more explicit:

“The chief requirement of the theory of axioms must be that it makes it possible to decide, by means of a finite number of logical inferences, whether any given statement formulated in the language of the theory is true or false.”

This is Hilbert pushing for what we’d now call decidability — every statement provable or disprovable within the system—which implies completeness. He wanted math to be a closed, self-sufficient machine.

Consistency Provable from Within

Hilbert’s demand that consistency be provable “from within” the system is trickier—he didn’t phrase it exactly that way, but it’s how his program was framed, and Gödel’s response hinges on this interpretation. In his 1925 paper “On the Infinite” (Über das Unendliche, Mathematische Annalen), Hilbert outlines his method, later dubbed “finitism,” to secure mathematics:

“We must establish the consistency of the axioms by means of a careful description and analysis of the methods actually used in mathematics… The goal is to establish certainty by finitary means.”

He proposed proving consistency using only “finitary” reasoning — simple, concrete logic he believed was unassailable. Crucially, in his 1928 book Grundzüge der theoretischen Logik (with Wilhelm Ackermann), he posed the “consistency problem” as:

“To prove by finite methods that the axioms do not lead to a contradiction.”

Hilbert didn’t say “from within” verbatim, but his finitist approach aimed to use tools internal to the system’s basic logic, avoiding infinite or external assumptions. He saw this as a proof that the system (e.g., for arithmetic) could vouch for itself. At the 1928 International Congress, he reiterated:

“The development of mathematical science must proceed in such a way that… its freedom from contradiction is proved by methods inherent in the nature of the science itself.”

How Gödel Saw It

Gödel’s 1931 paper (On Formally Undecidable Propositions, Monatshefte für Mathematik) directly engages Hilbert’s goals. He notes that Hilbert’s Program seeks a system where “all true mathematical statements can be derived” (completeness) and where “the freedom from contradiction can be proved by finitary means” (consistency). Gödel then shows this is impossible for arithmetic, citing Hilbert’s own framework as the target.

Why “From Within”?

Hilbert’s insistence on finitary methods — logic he thought was intrinsic to math — implied a self-contained proof. Later scholars (e.g., von Neumann, in letters from the 1930s, and modern texts like Gödel’s Theorem: An Incomplete Guide by Torkel Franzén) interpret this as “within the system” because Hilbert rejected leaning on stronger, external systems, which would undermine his foundationalist aim.

The Evidence

Completeness: 1900 address, 1922 lecture—Hilbert wants all truths decidable from axioms.
Consistency from Within: 1925 paper, 1928 book/talk—proof via finitary, internal means.

Hilbert’s words don’t always use modern terms, but his intent, as read by peers and successors, aligns with these demands. Gödel’s theorems hit precisely because they showed these twin pillars — total coverage and self-proved safety — couldn’t stand together. I can’t paste a single smoking-gun quote, but the pattern across these works is what mathematicians like Gödel and historians like Constance Reid (Hilbert, 1970) point to as the program’s heart.

Okay, I guess Hilbert was wrong, but people wrongfully conclude that mathematical axiomatization does not work. In fact, mathematics can be axiomatized as ZFC, where ZFC is consistent and powerful enough to prove all the theorems of math. It just isn't strong enough to decide every question, or to prove consistency within ZFC.

It was not wrong to try to axiomatize mathematics, not wrong to demand finitary reasoning, and not wrong to want consistency. If he really wanted to prove consistency from within the system, that is not possible, and is not really desirable. Hilbert's real error was to think it is desirable, if he really thought that.

The reason is that an inconsistent system can prove anything. If a system has a contradiction then it can prove 1=2 or anything else. So it does not make any sense for a system to prove itself consistent. It is like asking someone if he is honest. A liar will say that he is honest, and you learn nothing. To assess someone's honesty, you have to ask someone else.

If it is true that Hilbert wanted a math system to prove itself consistent, then he was wrong because that is a nonsensical thing to want. That should have been obvious long before Goedel.

People hear all this and figure that our axiom systems are not strong enough to prove what we want. But actually, Harvey Friedman's grand conjecture says that all our big math theorems can be proved in much weak axiom systems than ZFC, which is what is usually used.

Explanation of Newtonian Time

Matt Farr posted a new paper on Time in Classical Physics:

Wigner (1995, 334) describes how Newton’s “most important” achievement was the division of the world into “Initial Conditions and Laws of Nature”, noting that “[b]efore Newton there was no sharp separation between the two concepts. […] After Newton’s time the sharp separation of initial conditions and laws of nature was taken for granted and rarely even mentioned.” This is the central feature of the Newtonian schema.

Some people are so locked into this view that they say that indeterminism and free will are inconceivable. When you make a choice at a restaurant menu, it has to be determined by the initial conditions, or else the laws of physics are violated. No, that is just the Newtonian schema.

For example, Sabine Hossenfelder argues:

And according to new scientist, the superdeterminist view 5:20 naturally raises the possibility that the laws of physics are at odds with unlimited free will. 5:26 What are we to make of this? For one thing, this free will assumption in quantum physics, despite 5:33 its name, has nothing to do with what we normally refer to as free will in none of the definitions 5:40 that philosophers like to use.

Regardless of what you think quantum physics exactly means, the laws 5:47 of physics are always at odds with unlimited free will. This is why they're called laws. If you jump 5:54 off a bridge, you'll fall down. And no amount of free will is going to make you fall up.

She is saying that the Newtonian schema leaves no room for free will. If your initial conditions have you jumping off a bridge, the laws of physics determine your fall, and free will cannot do anything.

I think she is alluding to philosophers who try to define free will as being compatible with all your choices being determined before you were born. To those philosophers, free will is just in your imagination, and has nothing to do with the laws of physics or any actual choices you make. Most philosophers have such a nihilist view.

Yes, the Newton schema assumes that the past determines the future. That is not a law of physics. It is just an assumption. It works well approximately in a great many cases. Not all cases, if you believe in free will.

Some people also argue that the future can determine the past, in the same way that the past determines the future.

The above paper looks at what Newton said about time, and contrasts it with relativity and Lagrangian mechanics. Everyone says Newtonian time is more intuitive than relativistic time, but I am not sure. I have no intuition for anything going faster than light, as Newtonian time allows.

Lagrangian mechanics is another story. Time is just another variable, and it is not so clear how causality works. The paper tries to make sense of it.

New Scientist just released a video:

What Is Reality? Does Quantum Physics Have The Answer?

Over the past century, quantum physics has transformed science and reshaped our understanding of reality. In this special compilation from the New Scientist archive, we trace that evolution, from the birth of quantum mechanics to today’s lab-made “mini universes.”

We explore how quantum ideas revolutionised technology, how they continue to inspire new forms of creativity, and how recent breakthroughs are pushing the limits of what we can understand.

Most of it is not too bad, but it presents an expert physicist saying, about interpretations of quantum mechanics:

I think the 5:02 one that is probably most compelling to 5:04 the majority of physicists is called the 5:06 many worlds interpretation. It's 5:08 compelling because it says that 5:09 fundamentally we are also in superposition. Every possibility has a 5:14 realization in different worlds.

No, this is crazy stuff. I hope it is not true that a majority of physicists find this nuttiness compelling.

The Schroedinger Cat was once an example of silly thinking. Now this man is compelled to believe in many-worlds because he wants to believe that he is just like a Schroeding cat.

Quantum Computing Skepticism

I gave an online presentation on my quantum computing skepticism, and it is now posted. Thanks to the sponsors for making this happen, and persisting in the face of criticism from enthusiasts.

Why Einstein's Dishonesty was Tolerated

I wrote a book on Einstein, but I was never able to explain why everyone overcredits him for relativity and other wisdom.

One explanation is that most people do not know the history of relativity. Yes, that's true, but the history is well-documented for all the scholars who bother to look.

Another possible explanation is that his reputation was being propped up by friends or Jews or Leftists or others who were partial to him for some reason. But he gets plenty of exaggerated support from non-Jews and others with no obvious ties.

Galina Weinstein is an Israeli philosopher, and Einstein scholar and worshipper, and she suggests another possibility. Because the Nazis denigrated Einstein in the 1930s, an Einstein critic might get labeled a Nazi.

What is not acceptable is ... to frame the [relativity priority] debate in terms that echo long-standing prejudicial tropes.

As I commented:

Apparently this is a veiled reference to a stereotype of Jews being dishonest plagiarists, and as being parasitic, unoriginal, morally corrupt, and eager to appropriate the achievements and culture of others.

That seems rude, but Weinstein is essentially saying that Einstein must be credited to avoid those stereotypes. Just to be sure, I conferred with an AI, and it confirmed the interpretation.

A 1931 German book was titled, A Hundred Authors Against Einstein. According to Wikipedia, Einstein said the authors were Nazi professors, but that was not true. Maybe a couple of them were Nazis. He emigrated from Germany a couple of years later.

Sabine Hossenfelder says the book's main objection was that "Einstein’s theory is merely a philosophical construction." But that is how Einstein's biggest admirers credit him. He cannot be credited with any of the mathematical or physical elements of the theory, and they all predate him.

All this gave the impression that criticizing Einstein was something that ignorant and anti-Jewish Nazis would do.

To me, the history of relativity seems far removed from Jewish issues. But then Weinstein argues that certain Einstein criticisms are unacceptable, if they echo Jewish stereotypes.

If she is right, then maybe that is why almost everyone credits Einstein for relativity, and idolizes him as a great genius. They will be called Nazi and prejudiced, if they do not.

Then there is the issue of Deutsche Physik versus Jewish science. I cannot find a clear explanation of the difference. Wikipedia says that some Germans questioned Einstein's notion of the aether, and some experimental results.

Any analysis of how Einstein's relativity work might be Jewish science must be based on what Einstein actually contributed to special relativity. The consensus among historians is that Einstein ignored experiments like Michelson-Morley, and that he had no new formulas or testable ideas. Einstein is usually praised for obscure terminological differences that have no physical significance. Is there something Talmudic about that? I don't know.

This all seems foolish to me. Einstein was a brilliant physicist. There are lots of other brilliant Jewish physicists. Just credit them for what they did. Those who artificially inflate his reputation are the ones echoing those long-standing tropes.

The Fitzgerald-Lorentz Contraction is not Real

Sabine Hossenfelder's latest physics video:

Over a century ago, Einstein wrote his theories of special relativity and general relativity. Within those theories, he predicted that, as an object moves faster, it slightly contracts in length. However, 50 years later Penrose and Terrell predicted that what one would see is instead that the object is rotated. In a recent experiment, physicists proved that this Penrose-Terrell effect is actually real. Let’s take a look.

She is a big Einstein idolizer. Her favorite prop is an Einstein bobblehead.

Let me review the basic facts.

The relativity length contraction was discovered by Fitzgerald in 1889 and Lorentz in 1892. Lorentz also discovered time dilation in 1895. Both of them used these to explain the 1887 Michelson-Morley experiment.

Poincare in 1905 and Minkowski in 1907 explained these as a new geometry of spacetime. In their interpretation, the spacetime distortions are not real, but an artifact of choosing a frame in the 4D non-euclidean geometry. This interpretation was quickly accepted, and is the dominant one today.

Dr. Bee starts:

0:00 Albert Einstein totally changed our understanding of space and time. ...

Einstein’s theory of 0:46 special relativity makes two most remarkable predictions. The first is time dilation, 0:52 the other one is length contraction. Time dilation means that if an object moves faster 0:58 than its internal time passes slower. Length contraction means that the same fast-moving 1:05 object will also be shorter. It’s not that it appears shorter, it actually is shorter.

No, Lorentz and others made those remarkable predictions 10+ years ahead of Einstein. They said that the motion actually actually made the Michelson apparatus shorter. I think most physicists today would say that it only appears shorter.

In 1931, a group of scientists went so far 1:24 as to publish a book called “100 authors against Einstein.” It’s an interesting historical summary 1:31 of why people rejected Einstein’s insights, more than 2 decades after he had put them forward.

1:38 Some of them claimed Einstein’s maths is wrong. Some said the maths is right, 1:44 but they did it earlier.

The most frequent objection though was that they thought 1:49 Einstein’s theory is merely a philosophical construction. They thought that special 1:55 relativity tells us something about the way we see things. Not about how they really are. 2:01 Well, they were wrong. We know that length contraction is real. A moving object really is 2:08 shorter.

Her opinion is very strange. Lorentz and Poincare had all the equations and predictions before Einstein. The only way to credit Einstein for relativity is to say that he had a superior philosophical construction. If the Lorentz contraction is real and the 1931 book was wrong to say that Einstein had a philosophical construction, then Lorentz had it all before Einstein.

Here is what Poincare wrote in 1905, before Einstein:

But the question can still be seen form another point of view, which could be better understood by analogy. Let us suppose an astronomer before Copernicus who reflects on the system of Ptolemy; ...

Or this part which would be, so to speak, common to all the physical phenomena, would be only apparent, something which would be due to our methods of measurement. ...

so that the theory of Lorentz is as completely rejected as it was the system of Ptolemy by the intervention of Copernicus.

He says his view is like Copernicus rejecting Ptolemy, putting a new view on the same data. The relativity contraction is only apparent, due to our methods of measurement.

This is the modern view of relativity. It was popularized by Minkowski in 1907-8, and accepted ever since. Einstein is only credited because of a mistaken belief that he contributed to this modern view. In fact, the view was published before Einstein, and Einstein rejected it when he learned about it.

Most of Dr. Bee's video is about a new paper confirming a visual illusion that Penrose discovered.

Whatever Happened to String Theory?

Gizmodo reports:

Whatever Happened to String Theory?

At the turn of the century, it sounded as if string theory could give us big answers about the universe. Well… has it?

Believe it or not, physicists want to keep it simple. That’s why many scientists, including Albert Einstein, believe physics could eventually converge into a single, overarching paradigm that describes the universe — a theory of everything.

It was always a foolish belief. Especially Einstein's version of it. Anyone looking for a "paradigm" is not doing science.

Enter string theory. Very broadly speaking, string theory is a mathematical framework that replaces point-like particles with one-dimensional “strings” as the fundamental building blocks of matter. It was initially proposed as an explanation for a different phenomenon but quickly caught the attention of physicists working to unify quantum mechanics and general relativity—two extremely successful, equally valid theories that notoriously don’t get along.

Everybody says those theories conflict, but there is no problem as they apply to anything observable.

Then followed two “superstring revolutions,” which saw impressive strides in mapping out the details of how string theory could capture the complexity of our universe. The fervor of string theory naturally leaked over to popular conversations—science enthusiasts of the 1990s and 2000s, I’m looking at you—producing famous documentaries such as PBS’s The Elegant Universe and a trove of popular and academic books.

The word "revolution" is another tipoff that science is not being done.

The article requested comments from experts, and got a variety of opinions.

I say that string theory was trying to solve a problem that did not exist. It was a mathematical exercise with no relation to science.

In twenty years, I look forward to articles on what happened to quantum computing, quantum cryptography, teleportation, and other trendy topics of today.