Dr. Bee Revives Nonlocal gravity

Sabine Hossenfelder posts a new video:

0:38 The laws of physics that we have discovered have one thing in common: they are local. This means that objects in two different locations cannot interact with each other. They don’t know anything of each other. ...

A bit like theorists and experimentalists. 0:53 It is only by sending some sort of signal from one object to the other that they can react to each other’s presence. We have no idea why the laws of nature are this way. There’s no particular reason why they should be. It’s just that it corresponds to our experience.

I would say that there are reasons. Locality is the whole basis of scientific reductionism. It allows us to do controlled experiments. Without it, we could never make sense out of the world.

Also, it is all a consequence of the non-euclidean geometry of spacetime.

1:09 Newtonian gravity is not local, this bothered Newton a lot back then. You see if you take Newton’s law of gravity, with the gravitational force proportional to the mass divided by the square of the distance, then if you move the mass, the distance increases and the force changes instantaneously, everywhere. Newton was greatly bothered by this. He called it “action at a distance” and that’s also what Einstein meant by the phrase.

1:39 Einstein’s theory of general relativity, which we use now to describe gravity, doesn’t have this problem. In Einstein’s theory, gravity is described by the curvature of space and time. And that curvature is caused by the mass and energy in spacetime. If you move the mass that causes spacetime to curve, then the curvature changes, but not instantaneously. The change spreads outwards at the speed of light

Actually it was Poincare who figured out that gravity propagates at the speed of light. Einstein did not accept or believe it.

And this nonlocal gravity just seems to do it. 4:18 Better still the idea that gravity isn’t entirely local is something you’d expect to naturally occur in a theory of quantum gravity because we know that quantum physics isn’t local. I really like the idea.

No, this is crazy talk. Quantum physics is just as local as general relativity. In cosmology, you could have a couple of orbits that are correlated, so that knowledge of one tells you something about the other. That's all people mean by quantum nonlocality.

A reader will surely say that no, quantum nonlocality means that a correlation could be quantitatively greater that what a believer in an alternative theory might expect. Yes, that is true, but it does not have a bearing on whether a theory is local or nonlocal.

In another video, she endorses the Einstein block universe.

Maybe this video more than anything explains why I've always been a bad 11:30 fit for academia. Because what really is this? Is it philosophy? Is it physics? It's neither here nor there. Yet for me, questions like this are the reason I studied physics because I want to understand how the universe works.

Academia has no need for her twisted ideas about how the universe works.

Elsewhere she expreses a belief in superdeterminism, but that contradicts some of what she says here. Maybe she has abandoned superdeterminism, but she ought to explain it.

quantum 9:43 physics has an indeterministic unpredictable element which is what happens the moment one makes a measurement. ... There seems to be a difference between the past and the future in quantum mechanics.

Most of the video is an argument that Einstein's relativity requires us to believe in the block universe, where the future is as real as the past. She says different coordinates are allowed, and so the meaning of "now" can be different for different observers.

This is a misunderstanding of relativity. Einstein was a determinist, and did believe in the block universe, but most physicists do not.

Yes, relativity does allow different coordinates, but that does not mean you have to accept another "now", or that the future is determined. Most physicists accept that the CMB radiation defines a universal now, without contradicting relativity.

Even if I accepted that there is no universal "now", and that my future is already in a past coordinate system for some other observer, it would not follow that my future is determined. She defines "now" by coordinate lines, not light cones, so an observer does not even see what is now for him.

Dr. Bee talks about many science topics outside her expertise. These two videos are squarely within her expertise, so I expect better.

Cantor's Diagonal Argument

Cantor's diagonal argument is famous for proving the uncountability of the real numbers. It is not so well known that Cantor's first set theory article proved it differently.

Here is the proof. First of all, we need to assume the completeness of the reals, in some form.

Theorem. If { A_k } is a collection of compact nested subsets of R, the real numbers, then the intersection is nonempty.

Compact means closed and bounded, like the interval [0,1], including the endpoints. Nested means each contains the next. The proof depends on how you have defined R. For example, you could get an intersection point as the least upper bound of the left endpoints.

This is a way of expressing the completeness of the reals. If we used the rationals instead, then we could have nested intervals about √2, and the intersection would not include any rational numbers.

To prove uncountability, suppose we have an enumeration { x_k } of R, and we seek a contradiction. We define a collection { A_k } with x_k not in A_k, and apply the theorem to get a real number in all the sets, and hence not in the enumeration.

Start with [0,1]. Let A₁ be a closed interval subset excluding x₁. Eg, if x₁ = 0.4, then A₁ could be [0,.3] or [.5,1]. Likewise, let A₂ be a subset of A₁ that excludes x₂, and so on, and thus A_k excludes x₁,..., x_k. Applying the theorem gives at least one real in all of the intervals, and hence not part of the enumeration.

This is really a diagonalization argument, and maybe less intuitive, so what's the point?

I like it better. The usual diagonal argument is deceptively simple, as it assumes facts about the reals, such as every decimal expansion converging to a real, and reals having unique decimal expansions, with certain exceptions. This is still a diagonal argument, gets more directly to the heart of the matter, and explicitly uses the completeness of the reals, without the distracting decimal expansions.

Cantor gave a similar diagonal argument to show that the cardinality of a set A is less than the set P(A) of all its subsets.

Suppose not, so that there is some onto function f: A -> P(A). That is, where f(A) = P(A). Then let B = { a in A : a not in f(a) }. If B = f(b) for some b in A, then b is in f(b) if and only if b is not in f(b), a contradiction. Thus the image of f cannot be all of P(A).

This shows that taking all subsets always gives a set of larger cardinality.

Scott Aaronson recommends a video on Cantor's diagonal argument.

Wild Enthusiasm for Quantum Computing

This new interview makes a lot of big claims for quantum computing:

Q-Day — when quantum computers crack all encryption — is coming. Quantum eMotion COO John Young breaks down the pros and cons of what’s to come.

It is all ridiculous. I could not even bear to listen to the whole thing.

I have gotten used to this sort of enthusiasm for AI. But a 100 million people use AI everyday. Quantum computing has very little hope of ever accomplishing anything.