# John Bell actually misunderstood relativity, too

Luboš Motl, May 16, 2015

*For the sake of unity, I adopt Bell’s spelling «Fitzgerald». The physicist’s name was FitzGerald.*

John Bell is one of the ultimate darlings of the chronic interpreters and the anti-quantum zealots in particular. They like to maintain a widespread myth that Bell has found something important about Nature – or about quantum mechanics. He didn’t. He only found something moderately important – but not completely unknown – about a class of *wrong* candidate theories of Nature, the local «realist» hidden-variable theories. The word «realist» is a euphemism for «classical» and it is synonymous with «non-quantum».

While this theorem has often been discussed in the debates about the foundations of quantum mechanics, Bell himself is responsible for much of the anti-quantum fog that is omnipresent these days. He said – and it was completely unbacked by any of his «solid» work – that the resolution is that Nature is realist but it is not local. The truth is the opposite, of course. Nature is quantum – i.e. non-realist – but it is local. It has to be local because the special theory of relativity demands that.

Just a few hours ago, I believed that Bell was simply ready to abandon special relativity because «realism» (i.e. the faith that quantum mechanics must ultimately be wrong) was a more important dogma than relativity for him. But only today in the afternoon, I was led to a text that shows that it was just a part of the story. He was actually ready to abandon relativity because he was a relativity denier. To say the least, he denied that Einstein has changed anything about the *content of physics*. In his opinion, the previous theories based on the aether were already OK and Einstein has only changed the style, philosophy, and pedagogy!

I was led to these insights through two papers critical of Bell’s opinions on relativity, one by Petkov and another one by Nerlich. There exist several other papers like that, I learned later.

More importantly, I found the full text by Bell that shows his deep misunderstanding of the special theory of relativity:

It was written in 1976 and it is actually included in his «Speakable And Unspeakable In Quantum Mechanics» which is so popular among armchair physicists.

Bell’s paper on relativity claims that relativity should be taught totally differently – not according to Einstein but according to Fitzgerald, Larmor, Lorentz, and Poincaré – who clearly *didn’t* understand the spacetime and the behavior of physical objects at higher speeds correctly up to 1905 when Einstein taught them better.

At the beginning, he says:

I have for long thought that if I had the opportunity to teach this subject, I would emphasize the continuity with earlier ideas. Usually it is the discontinuity which is stressed, the radical break with more primitive notions of space and time. Often the result is to destroy completely the confidence of the student in perfectly sound and useful concepts already acquired.

So far it’s pretty innocent but problems are hiding in these claims from the very beginning. The reason why relativity – and quantum mechanics – are taught as a «discontinuity» is that they *are* a «discontinuity», a radical conceptual change within the basic assumptions of physics. If nothing radical had changed in 1905 and 1915 and 1925, we wouldn’t need to spend much time with teaching it. 😉 The confidence of a student – and everyone else – in non-relativistic and non-quantum physics has to be «destroyed» because they’re wrong, not «perfectly sound». Up to some level (speed of small size), the novelties are negligible and the old theories are «useful». But if one wants to study fundamental laws or high speeds or the microscopic world etc., he simply needs to abandon the old way of thinking completely.

He is frequently repeating the thesis that what Fitzgerald and the other people believed was physically *equivalent* to Einstein’s special relativity – it only differed in «style, pedagogy, and philosophy». Those claims are clearly wrong, as I will discuss. I think that he said such things about the «equivalence» because he wanted to mask that he was just another full-fledged crank who has «proven Einstein wrong». But everything else he wrote about his solution to the physics problems makes it spectacularly clear that he hasn’t embraced the relativist thinking about the phenomena.

His persistent obsession with words such as «style, pedagogy, and philosophy» makes it clear that already many decades ago, the broader physics community suffered from the presence of shallow bullšitters who are much more interested in P.R. and ways to impress the stupid people than about the scientific truth. Physics just doesn’t care about «style, pedagogy, and philosophy». Physics cares about physics and what Bell said about relativistic phenomena was just totally wrong.

**Two spaceships and a rope**

At the beginning, he talks about the problem of 2 uniformly accelerating rockets connected by a thin rope. Will the rope break? The rockets start at distance \(D\) from each other at \(t=0\), according to their initially shared rest frame, and that’s the moment when they begin to accelerate. (He uses a redundant third rocket in between to synchronize them to make you sure that he isn’t quite sure what he is doing.)

He said that the rope will break. Everyone at CERN would tell him that the rope won’t break. Well, the rope will break – if the accelerations are the same – but for completely different reasons than he suggested. The relativistic solution of this problem is trivial.

If a rocket is moving at a constant acceleration measured in its instantaneous rest frame, it is moving along a hyperbola in the spacetime. The hyperbola \(c^2 t^2 — x^2 = — R^2\) is the Minkowski-signature counterpart of a circle: the hyperbola (and the left hand side of the equation that just defined it) is Lorentz-invariant just like a circle is rotationally invariant. So at every moment, after any boost, it looks the same. The acceleration is linked to the curvature of the hyperbola which immediately tells you that \(R=c^2/a\). The lower the acceleration is, the longer the radius \(R\) of the hyperbola is.

If you want two rockets with a time-dependent acceleration measured at rest and you want the situation not to change as you speed them up (increase the boost), it’s clear that they have to move along two *concentric hyperbolae*. The first rocket has \(R_1=c^2/a_1\), the second rocket has \(R_2=c^2/a_2\), and the difference between them has to be the proper distance \(D\) we started with. So the two accelerations have to obey

\[ \frac{c^2}{a_1} — \frac{c^2}{a_2} = D \]

That’s it! The sign is such that the rocket on the «rear» side that seemingly «chases» the other one has to accelerate at a higher rate (because it’s the rocket that is closer to the center of the hyperbola).

If this condition is satisfied, the rope won’t tear apart because the situation at every moment – in every boosted frame with the origin at \((0,0)\) – will look just like at \(t=0\). If the accelerations don’t obey the condition above, the rope will ultimately tear apart. Note that if \(D\) is much smaller than \(c^2/a_1\) and/or \(c^2/a_2\), the required accelerations will be very similar to each other, \(a_1\sim a_2\), and if you choose them exactly equal, it will take a very long time for the rope to be cut.

Maybe it was fast for you but if you think about it, it is a trivial problem about the geometry of the two-dimensional Minkowskian spacetime.

Instead of this correct solution, Bell wrote several long – and not really correct – pages where he was transforming the electric fields in the atoms of the rope! This is just so stupid. The point of relativity is that physics of moving objects may be (locally in time) transformed to physics of objects at rest. They’re the same. And the behavior of everything, not just Maxwell’s equations of electromagnetism but also mechanics, is Lorentz-covariant. It obeys the principle of relativity.

So we don’t need to know whether the rope is composed of atoms or has electric fields in it. The essence of the problem has nothing whatsoever to do with these particular examples of laws of physics that may operate inside the rope. The problem is all about a simple relativistic geometry and symmetries.

Fitzgerald and others believed in the aether – in fact, I think that he did so even after 1905 because this guy didn’t understand relativity. Relativity has killed the aether. The aether predicts the unobserved aether wind but many other wrong things, too. How could Bell claim that the difference was only in «philosophy, style, and pedagogy»? One may consider three possible classes of theories when it comes to the influence of the uniform motion:

- theories invariant under the Galilean transformations, like Newton’s mechanics
- theories invariant under the Lorentz transformations, like Einstein’s special relativity
- theories not required to obey the relativity principle, i.e. theories allowing preferred reference frames

Because I wrote the three groups in this way, you may see that (1) as well as (2) are subgroups of (3). If you don’t *require* the principle of relativity – all mutually moving observers may describe the laws of Nature in an equally simple way – it may still *happen* that your particular laws will respect the Lorentz symmetry or the Galilean symmetry. The principle of relativity implies that either (1) or (2) are correct because they’re based on the only two mathematically possible groups that respect the relativity principle; the Galilean group is a deformation of the Lorentz group, the Lorentz group is a deformation of the Galilean group. At low enough speeds, it was impossible to distinguish (1) and (2) experimentally. Once you have access to high speeds and/or high enough accuracy, (1) and (2) are totally inequivalent and experimentally distinguishable.

You could replace (3) by (3′) which is (3) with (1) and (2) removed. Then they would be disjoint, OK?

Now, everyone who was working in Newton’s framework was really believing in (1), the Galilean theories. Mechanics «self-evidently» obeyed that, they thought. And then they needed to explain the electromagnetic phenomena. But they believed that they were due to the aether. The aether was a material that was filling the space and was picking a preferred reference frame. Fundamentally, it was assumed to obey the Galilean symmetry of Newton’s physics. But waves etc. could have been propagating in the aether, and the equations governing these waves (Maxwell’s equations) happened to be Lorentz-symmetric. It was believed to be a kind of an accidental symmetry. (They didn’t like to talk about symmetries at all, but that doesn’t change the main point that they believed that there was nothing too deep or universal about the Lorentz’s «coordinate redefinition».)

If you consider the class of theories (3), it is compatible both with (1) and (2) which are special examples of (3). But this fact makes (3) much less predictive, too. In a theory in (3), you just can’t determine what the objects are doing at speed \(\vec v\) if you know what they are doing at rest! In both (1) and (2), you *may* determine that – because via the Galilean or Lorentz transformation, you may transform the situation to the rest. But in (3), you can’t determine that.

More precisely, for the theories in (3′), you can’t do that because they strictly break the relativity principle. But if you only have a theory that is in (3) and you don’t know whether it belongs to (1) or (2), you must treat this theory as a generic theory in (3) i.e. as a theory in (3′). And the theories in (3′) are much less constrained i.e. much less predictive than those in (1) and especially (2).

But it was unbelievably stupid for Bell to say that the theories envisioning a fundamentally Galilean-invariant aether – whose vibrations manifested an accidental Lorentz symmetry – only differed from the fundamentally Lorentz-invariant theories by their «philosophies». This is a huge and totally material, tangible, testable, and fundamental physical difference! The global symmetry group of a physical theory is one of its most characteristic properties (one that is exactly the same for all mutually dual theories in string/M-theory, too) and the two groups, Galilean and Lorentz, are simply not isomorphic to one another!

Bell has never explicitly «endorsed» the aether but everything about his «solutions» to the problem make it clear that he believed exactly the same crap as e.g. Fitzgerald did. That’s also why he consistently talks about the «Fitzgerald contraction» – even though a sane modern physicist would talk about the «Lorentz contraction». But if he believed his claim that the Fitzgerald’s and Einstein’s treatments were physically equivalent, then the Fitzgerald contraction and the (relativistic) Lorentz contraction would have to be the same thing, too, right?

He seems totally unaware of this waterproof logic. Also, he never actually explains what is the difference between the effect he calls the «Fitzgerald contraction» and the actual relativistic «Lorentz contraction». Once again, my clear conclusion is that all his verbal approvals of relativity, Einstein, and the Lorentz contraction are just diplomatic clichés but at every point, he believes the pre-relativistic notions of Fitzgerald instead. Nerlich converged to the same conclusion.

This opinion of mine is also strengthened by many sentences – even in the very description of his two-rocket problem – that expose his belief that only the ropes contract at higher speeds, but the space itself doesn’t. So he always interprets the contraction of the rope at a higher speed as a consequence of some unnatural «stress». But relativity makes it clear that there is no «stress» in the sense of an «unnatural stress» when an object moves with a constant nonzero velocity. To move with a uniform velocity feels exactly the same as to be at rest! His comments about the «stress» make it totally clear that he didn’t get any of these points of relativity.

His comments about the specific solutions to the relativistic problem place him squarely to the category of the full-fledged anti-Einstein cranks. But at the same time, he was repeatedly obfuscating this fact by lots of inconsistent words that sound as approvals of relativity. This tension between his being a complete moron and his efforts to totally hide this fact culminate on the last page where he describes why «Fitzgerald+Lorentz and Einstein differ in the philosophy and the style». The «difference in philosophy» is, Bell ludicrously believed, that «whether there is a preferred frame is just a philosophy». Well, it’s surely not. And what is the «difference in style»?

The difference of style is that instead [sic] of inferring the experience of moving observers from known and conjectured laws of physics. Einstein starts from the

hypothesis[italicization by Bell] that the laws will look the same to all observers in uniform motion. This permits a very concise and elegant formulation of the theory, as often happens when one big assumption can be made to cover several less big ones. There is no intention here to make any reservation whatever about the power and precision of Einstein’s approach. But in my opinion there is also something to be said for taking students along the road made by Fitzgerald, Larmor, Lorentz, and Poincaré. The longer road sometimes gives more familiarity with the country.

Again, you see the fabricated diplomacy concerning relativity, along with the ludicrous claims that relativity and non-relativity are equivalent.

But what I want to emphasize is his criticism of Einstein for the fact that his theory – or its postulates – are a *hypothesis*, and that’s a disadvantage relatively to the pre-relativistic discussion of the phenomena that he preferred which are rooted in «known laws of physics». This is really a yummy statement because it makes it unequivocal that he thought that the non-relativistic physics was *more than just a hypothesis* – it was something he really believed or «knew» to be true, it was a set of facts.

For this reason, he misunderstood not only relativity. He misunderstood the very scientific method. In science, all sets of ideas, concepts, and equations designed to talk about the phenomena are always *hypotheses*. They have to be tested. They may be falsified. We don’t really «know» anything, especially not what the obsolete theories are saying. Newton’s and Fitzgerald’s opinions and frameworks to discuss phenomena at higher speeds were *hypotheses* just like Einstein’s special theory of relativity was a *hypothesis*. The only important difference between these hypotheses was that Einstein’s hypotheses apparently remain correct when \(v\to c\) while Newton’s, Fitzgerald’s, and Bell’s don’t! So no one would call special relativity a hypothesis anymore. It’s an important theory. Because it has passed so many tests and is so rigid, it’s really a fact by now.

So after having read this «article», I am much more shocked by the apologists of this crappy stinky superficial pseudo-scientific poseur and posera than I was previously.

By the way, David Bohm – who was one of Einstein’s last students – did understand the point of relativity, as shown in his neat textbook on the subject.