Krauss Explains Extra Dimensions

Lawrence Krauss is one of the best public expositors of Physics, but I was disappointed by this interview.

3:29 and it was Einstein's genius to realize 3:31 well they're both right. Maxwell's right 3:34 and Galileo's right. what can what gives 3:37 here and he said well maybe it's the way 3:40 we measure space and time. maybe space 3:43 and time are personal things and they 3:45 depend upon your motion and in order to 3:48 get a measurement so each person's space 3:50 is in some and time in some sense unique 3:52 to them and that was the The Genesis of 3:55 special relativity

No, that was not the genesis of special relativity. That describes what Lorentz published in 1895, and Einstein's paper was not until 1905. Lorentz used Maxwell's equations to show how space and time can change to make observations independent of velocity of the frame, such as with the Michelson-Morley experiment.

Perhaps Krauss would object that Lorentz did not say that the theory is about the way we measure space and time. But Einstein did not either. That was done by Poincare and Minkowski.

there's an 4:21 absolute in the sense that that if you 4:24 think of the world as 4:26 four-dimensional time being an extra 4:28 dimension 4:30 then when I'm moving with respect to you 4:32 what I'm really kind of doing is 4:34 rotating in this four-dimensional space 4:36 so my space is your time and your time 4:38 is my space a little bit and when those 4:40 get mixed up you explain the wonderful 4:43 results of Einstein and so we now say 4:46 that we live in a four-dimensional 4:47 melski space

That idea was Poincare's in 1905, and built on by Minkowski in 1907. Einstein did not have anything to do with it.

If instead of living in 6:34 a four-dimensional world we live in a 6:35 five-dimensional world and somehow 6:37 electromagnetism is related to the 6:38 curvature of that extra Dimension that 6:40 you can't perceive well two people uh 6:44 kuta a mathematician and Klein a 6:46 physicist independently in in 1919 to 6:50 1926 came up with the same idea and 6:52 showed that this idea actually worked 6:54 mathematically if you assumed we live in 6:57 a five-dimensional universe and this 6:58 extra Dimension was invisible I and in 7:00 fact curled up on a very small 7:02 scale it was Klein who wanted it curved 7:04 up in a very small scale by the way and 7:07 I don't know if you can figure out why 7:08 kuta didn't didn't care he was a 7:10 mathematician why did he care the clein 7:12 wanted to say if there's an extra 7:13 Dimension if you don't see it there has 7:15 to be a reason and if it's curled up on 7:17 a very small scale then you can't 7:18 measure it in in in in experiments and 7:20 we can talk about that but in any case 7:22 if there was that extra Dimension and 7:24 and you could discuss a curvature in 7:26 that extra Dimension that you couldn't 7:28 directly see it's Remnant in the 7:30 four-dimensional its projection on the 7:32 four-dimensional universe that we can 7:33 see would give the equations of 7:35 electromagnetism it was an remarkable 7:38 idea turned out to be wrong because it 7:41 it also gave a little change to gravity 7:43 which we don't see and it got left aside

It was only wrong because Kaluza and Klein botched it up. Hermann Weyl was ahead of them with a similar idea in 1918, and that idea was essentially the modern gauge theory of electromagnetism. It can be viewed as a fifth dimension of spacetime, and it is not wrong.

He then rambles about string thoery having 22 extra dimensions. That theory really is wrong, or as Peter Woit would say, not even wrong.

You could say that the Standard Model has a group structure U(1)xSU(2)xSU(3) with 12 extra dimensions. We do not see them as spatial dimensions, as they have symmetries such that we only see the curvature effects. In that sense, we do have extra dimensions that are mostly hidden because of symmetries.

Here is Krauss giving a similar explanation of extra dimensions. He describes the extra dimensions as something that theorists have liked since 1919, but which have always failed. Maybe new accelerator experiments will detect extra dimensions.

It baffles me that he can say all this without mentioning that our very best modern Physics theory, the Standard Model, is a theory of extra dimensions. He talks about extra dimensions that are too small or too big or obscured for some other reason. In the Standard Model, the extra dimensions are obscured by gauge symmetries.

A Century of Quantum Mechanics

Physicist Sean M. Carroll writes a high-profile Nature essay:

Why even physicists still don’t understand quantum theory 100 years on

Quantum mechanics depicts a counter-intuitive reality in which the act of observation influences what is observed — and few can agree on what that means.

He did not write those titles. He does not deliver on the titled promises.

PHysicists understand quantum mechanics just fine, and there is broad agreement on what it means. There is a faction of philosopher wannabes like him who believe in many-worlds or some other goofy variant, but the real work is being done by those who follow Copenhagen or say shut up and calculate.

Most of what he writes is reasonable:

It was the German physicist Werner Heisenberg who, in 1925, first put forward a comprehensive version of quantum mechanics. ... So it is fair to celebrate 2025 as the true centenary of quantum theory. ...

Whereas in classical physics, a particle such as an electron has a real, objective position and momentum at any given moment, in quantum mechanics, those quantities don’t, in general, ‘exist’ in any objective way before that measurement. Position and momentum are things that can be observed, but they are not pre-existing facts. That is quite a distinction. The most vivid implication of this situation is Heisenberg’s uncertainty principle, introduced in 1927, which says that there is no state an electron can be in for which we can perfectly predict both its position and its momentum ahead of time2.

This is because position and momentum are non-commuting operators.

He starts to go off the rails:

As a result, the probability of observing one particle to be somewhere can depend on where we observe another particle to be, and this remains true no matter how far apart they are.

Actually, classical probabilities work the same way. Probabilities nearly always depend on other observations.

Bohr, along with Heisenberg, was willing to forgo any talk about what was ‘really happening’, focusing instead on making predictions for what will happen when something is measured.

The bizarre logic of the many-worlds theory

The latter perspective gave rise to ‘epistemic’ interpretations of quantum theory. The views of Bohr and Heisenberg came to be known as the Copenhagen interpretation, which is very close to what physicists teach in textbooks today.

Yes, that is the mainstream view. Science is all about what can be observed, not speculations about imaginary parallel universes.

Mercifully, the paywall blocked me from reading the rest, which presumably rambles into many-worlds nonsense. I can only get the above link to a 2019 essay:

At the beginning of Something Deeply Hidden, Sean Carroll cites the tale of the fox and the grapes from Aesop’s Fables. A hungry fox tries to reach a bunch of grapes dangling from a vine. Finding them beyond his grasp, but refusing to admit failure, the fox declares the grapes to be inedible and turns away. That, Carroll declares, encapsulates how physicists treat the wacky implications of quantum mechanics.

Carroll wants that to stop. The fox can reach the grapes, he argues, with the many-worlds theory.

That is where we get the term "sour grapes". In this case, the many-worlds theory really is inedible. Carroll is misleading everyone.

Update: Nature magazine also has an essay on Two-Eyed Seeing:

This Perspective focuses on the integration of traditional Indigenous views with biomedical approaches to research and care for brain and mental health, and both the breadth of knowledge and intellectual humility that can result when the two are combined.

It means mixing science with voodoo.

Three Geometrizations in History

Juliano C. S. Neves writes a New paper:

There have been three geometrizations in history. The first one is historically due to the Pythagorean school and Plato, the second one comes from Galileo, Kepler, Descartes and Newton, and the third geometrization of nature begins with Einstein's general relativity. Here the term geometrization of nature means the conception according to which nature (with its different meanings) is largely described by using geometry. ...

Undoubtedly, the history of the geometrized nature begins in the ancient Greek period. ...

Then the third movement into the geometrization of nature begins with Einstein (1916) and general relativity, which I call geometrization 3.0. However, following Lehmkuhl (2014), contrary to the common opinion in physics, it is worth emphasizing that Einstein did not consider general relativity as the theory that geometrizes gravity. But, as we will see, general relativity brings a lot of geometrical concepts to describe the phenomena.

For attempts to take geometry out of general relativity, see Anderson 1999 and Brown 2009.

So if Einstein did not geometrize gravity, who did? Everyone else accepted relativity as a geometric theory.

Brown explains that Einstein took decades to come around to the geometric view that Poincare and Minkowski had in 1905-8.

Why this lapse on Einstein’s part? I wonder if it was not because of the misgivings he had about the way he formulated his 1905 paper, misgivings which grew throughout his life. First, there is little doubt that right from the beginning he was aware of the limited explanatory power of what he called “principle theories” like thermodynamics. Secondly, when he confessed in 1949 to having committed in 1905 the “sin” of treating rods and clocks as primitive entities, and not as “moving atomic configurations” subject to dynamical analysis, he was merely repeating a point of self-correction he made in 1921. Finally, it is fairly clear that Einstein was increasingly unhappy with the central role that electrodynamics, and in particular the behaviour of light, played in his 1905 paper.

This last aspect of Einstein’s reasoning brings us to the main point of this subsection. Einstein wrote in 1935:

The special theory of relativity grew out of the Maxwell electromagnetic equations. ... [but] the Lorentz transformation, the real basis of special-relativity theory, in itself has nothing to do with Maxwell theory. (Einstein 1935).

Similarly, in a 1955 letter to Born, Einstein would write that the “Lorentz transformation tran- scended its connection with Maxwell’s equations and has to do with the nature of space and time in general”. He went on to stress that “the Lorentz-invariance is a general condition for any physical theory.” (Born et al. 1971, p. 248). What is clear is that for the mature Einstein, the principle of Lorentz covariance, which applies to all the non-gravitational interactions, not just electrody- namics, is the heart of special relativity.8 In stressing this point, Einstein was distancing himself from his formulation of 1905 with its emphasis on fundamental phenomenological postulates (one of which being the “constancy” of the speed of light relative to the “rest” frame).

So Einstein finally adopted in 1935 the geometric view of relativity that Poincare published in 1905 and Minkowski improved and popularized in 1908. In that view, the Lorentz transformation is a symmetry of spacetime. It is a symmetry for any physical theory, and not just the Maxwell theory.

My theory is that the third geometrization occurred with Poincare and Minkowski in 1905-8. They both described it as a radical break from existing thinking. Poincare said that the new geometry was like Copernicus replacing Ptolemy, and Minkowski said that henceforth space and time will be united. The essence of special relativity is that there is a non-euclidean geometry on spacetime. Einstein missed it, but it is what make special relativity so popular with others.

Here is Sean M. Carroll describing the geometry of relativity, in his recent book:

But he didn’t go quite so far as to advocate joining space and time into a single unified space-time. That step was left to his former university professor, Hermann Minkowski, in the early 20th century. The arena of special relativity is today known as Minkowski space-time. ...

But, says relativity, just as the distance as the crow flies is generally different from the distance you actually travel between two points in space, the duration of time that you experience generally won’t be the same as the universal coordinate time. You experience an amount of time that can be measured by a clock that you carry with you on the journey. This is the proper time along the path. And the duration measured by a clock, just like the distance traveled as measured by the odometer on your car, will depend on the path you take. ...

The difference is this: In space, a straight line describes the shortest distance between two points. In space-time, by contrast, a straight path yields the longest elapsed time between two events. It’s that flip from shortest distance to longest time that distinguishes time from space.

Euclidean geometry has the shortest distance between two points is given by the Pythagorean theorem. Distances in the non-euclidean geometry of spacetime work differently.

Of course he does have to give some goofy reason to credit Einstein, as everyone else does:

The development of relativity is usually attributed to Albert Einstein, but ...

Einstein’s contribution in 1905 was to point out that the ether had become completely unnecessary, and that we could better understand the laws of physics without it.

No, this is a myth. What Einstein said about the aether was nearly identical to what Lorentz said ten years earlier. That is, they both rejected theories that depended on aether motion or motion against the aether, and their theories avoided mentioning the aether. Einstein could never explain how his theory was different from Lorentz's. Poincare and Minkowski did explain how their relativity theory was different, and the difference was non-euclidean geometry, not aether.

Professor has Trump Derangement Syndrome

Scott Aaronson is going nuts again, and posting crazy anti-Trump rants.

I cannot even figure out what he is complaining about. I expect him to complain for four years, no matter what.

He is entitled to his political views, but he cannot explain how Kamala Harris would have been better than Donald Trump on anything.

He believes in many-worlds theory, so I should not expect him to be rational about anything.

Update: Here is a physicist trying to reason with his fellow academic leftists:

The thoughtlessness of guilt by association

We cannot judge ideas on the basis of the people who happen to hold them

I am surprised that this needs to be said. You would think that professors would be trained to judge ideas on their merit. No, he says the leftists are engaged in an ideological war, where leftists favor transgendering children in order to maintain an opposition to right-wingers like Trump.