Einstein's Greatest Blunder

The Cosmological Constant

Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder of his life.
 -- George Gamow, My World Line, 1970 [1]
Einstein's remark has become part of the folklore of physics, but was he right?  He certainly had cause to feel rueful about the cosmological constant; he had introduced it into his general theory of relativity in 1917,  as a last resort, to force the equations to yield a static universe. Even at the time, he apologized for doing so, because it spoiled the elegant simplicity of the field equations that he had struggled so hard to find.  Of course the universe is not static, just as his original equations were trying to tell him; his blindness lost him the chance to make one of the great predictions in physics. Even worse, a little more analysis would have shown that his static universe was not stable, and would have started to expand or contract if its perfect equilibrium was disturbed in any way.

The most banal reason for Einstein's blunder might have been a simple failure to think through the consequences of his own ideas (in itself, very unusual for Einstein, but he was mentally and physically exhausted at this time).  His 1917 paper finishes with the following:

It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [cosmological constant] is not introduced.  That term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of the stars.
So Einstein was aware that his equations had non-static solutions, but he had convinced himself they were irrelevant because the stars were known to move very slowly compared to the speed of light.   He seems to have missed the possibility of a coherent large-scale expansion or contraction, in which the motions of the stars near any observer would be negligible.  If we can make this excuse in 1917, it fails in the 1920s when Einstein read and commented on the work by both Friedman and Lemaître which explicitly demonstrated the expanding solutions. Although Einstein originally thought there was an error in Friedman's paper, he was soon convinced that it was mathematically correct; but his comments on both papers were that the physics was "tout à fait abominable" (as he told Lemaître in person!).

It is surprising that Einstein was so convinced that the universe was unchanging.  It is often said that this was assumed by everyone at this time, but there were plenty of currents of thought which went against the idea. Einstein was perfectly aware of the biblical claim of a finite age for the universe; in fact he had gone through a brief religious patch as a boy, which ended when he realized the Bible could not be literally true.  Perhaps he decided, as others have done, that any origin to the universe would effectively be a return to mythology.  It is also true that even those who believed in creation assumed that the universe was created in its present form, rather than evolving over time.  Another strong argument against an eternal universe was the second law of thermodynamics, which implied that in a finite time, entropy would increase to a maximum and all processes in the universe would grind to a halt: the so-called "heat death of the universe".  Einstein, a master of thermodynamic and statistical physics, can hardly have ignored this problem.  Just at this time,  there was a great deal of debate about the age of the Earth, and overwhelming evidence that it was finite.  Of course many astronomers believed that solar systems continually formed throughout an infinitely old universe, but the age of the Earth debate must have suggested to some that the universe itself had a finite age. [2]

From this history, Einstein's assessment of his "blunder" may seen justified.  On the other hand, it has been claimed that the history of cosmology in the twentieth century could be written as a history of the cosmological constant. As Gamow complained,  "Lambda" keeps coming back, and at present the evidence for it is stronger than ever before. So was it really a blunder to propose a concept so useful to cosmology?   On balance, it probably was.  Einstein saw the constant as a sort of irreducible curvature left over in space-time when all matter was removed.  This destroys the beauty of the field equations, which attribute the source of curvature entirely to matter as represented by the stress-energy tensor.  And in fact the constant is not even necessary, because it is perfectly possible to include an equivalent term as part of the stress-energy tensor, representing the vacuum value of some quantum field; this is the basis of inflationary cosmology.

But really, this won't do.  Blunder it was, but one far too minor to matter much to a towering figure like Einstein.  It is the sort of bourgeois mistake that might be appropriate for a Bohr, but Einstein is too sophisticated, too heroic, to make his defining error a missed opportunity that would have hardly changed his reputation.  Heroes need tragic flaws which lead to their downfall, and yet are so much part of their make-up that without the flaw, they would not have been heroes.  Now, it is not easy to paint Einstein's life as a tragedy.  He lived long, died famous and respected throughout the world, was held in affection by all who knew him, and gave every indication of having enjoyed the whole business.  Nevertheless, if it was no tragedy for Einstein, it was certainly a tragedy for physics that for the last twenty-five years of his life he was estranged from the active research community by his doubts about quantum mechanics.  And a major part of Einstein's irritation with quantum theory must have been the knowledge that the features in it that he most objected to were his own fault.  Einstein's contributions to quantum theory were of course enormous: his explanation of the photo-electric effect, his work on stimulated emission, Bose-Einstein statistics, and several other lesser topics.  But these were not the problem.  The problem was that quantum mechanics took its defining philosophy, its propaganda, straight out of Einstein's earliest work on relativity, and Einstein was appalled at the results.


Raffiniert ist der Herrgott aber boshaft ist er nicht  -- Albert Einstein
No other physicist is as quotable or as widely quoted as Einstein. Every physicist knows his famous dictum, at least in translation: "Subtle is the Lord, but malicious He is not'' (although I prefer Einstein's own translation: ``God is slick, but He ain't mean'' [3]).  This particular saying is worth unpacking in detail.  It was made in response to a claim in 1927 that a tiny "ether drift" had finally been detected.  Einstein rejected this out of hand: to have an ether which was almost undetectable (requiring special relativity to be almost correct), but yet present (undermining the foundation of relativity) seemed absurd to Einstein, and indeed his intuition proved right.  But the comment can be taken more generally as an emotionally powerful justification for the central idea of relativity theory: that what cannot be measured, does not exist.  God would not be malicious enough to hide an important part of reality in a way that we cannot reach;  if no experiment can reveal the true rest frame of the ether, then there is no ether, and no frame of absolute rest.  Although Einstein phrases this as an ex cathedra statement, one that apparently tolerates no contradiction, the very fact that he invokes God implies that he is not entirely serious [4], or to put it another way,  it identifies this as a statement of belief rather than logic.  The sentiment is the core of positivism, which, via the work of Ernst Mach and others, had deeply impressed Einstein in his student days. One could say that Einstein's main achievement in 1905 was to use this positivistic rejection of purely theoretical entities to weld together the mish-mash of ideas that already existed (Lorentz-Fitzgerald contraction, Larmor time dilation, etc.) into a coherent and well-justified whole.  Lorentz had published his full transform in 1904 (unknown to Einstein at the time), which contains essentially all of the mathematics of special relativity, but Einstein gets the main credit because of the importance of his metaphysical input to the theory (or rather, subtraction from it).

The impact of relativity on young physicists at the time was enormous.  Einstein was the hero to be emulated and, if possible, surpassed.  The founders of quantum mechanics quite consciously and explicitly followed Einstein's positivistic lead in developing their new science.  Heisenberg systematically eliminated all elements from his picture of the atomic world that could not be directly observed, until in fact there was so little left that no "picture" was possible in the sense of traditional physics.  In 1928, Neils Bohr presented his principle of complementarity, the core of the Copenhagen interpretation,  as a new relativity: no statement about the micro-world could be made at all, except in relation to some particular experimental set-up.  Bohr's subtle (some would say impenetrable) arguments for complementarity, gained him a reputation as a philosopher, but in fact he was not widely read in philosophy; he took his lead from Einstein.  Heisenberg recalled that in his one serious discussion of science with Einstein,  he argued that quantum mechanics was following in the footsteps of relativity.  He was astounded when Einstein replied "Perhaps I did use such philosophy earlier, and also wrote it, but it is nonsense all the same."

Complementarity crossed a line that Einstein would not pass. Among the unobservable inessentials that Bohr jettisoned was the very notion that there was a real world of atoms in any meaningful sense.  Einstein, like most physicists, remained committed to the idea that our everyday world was made of atoms; unlike most physicists, he fully understood what Bohr was saying and could not accept the retreat from realism.  It is worth recalling that Einstein's own Ph.D. research had aimed to remove the last doubts about the reality of atoms.  By the late 1920s, Einstein's philosophy had been changed in important ways by his work on general relativity.  He had started out with the aim of constructing a theory of gravity that conformed not just to the local truths of special relativity, but to Mach's principle, the idea that motion, even accelerated motion, is not absolute but always relative to the background of matter in the universe, the "fixed stars" in the old-fashioned phrase.  Although at first Einstein thought he had succeeded, it soon became apparent that general relativity did not conform to Mach's principle much better than did Newtonian dynamics. Applying general relativity to Newton's crucial thought experiment, water in a spinning bucket would feel a centrifugal force whether or not there were any distant stars to act as a reference (the stars do have a weak effect, but it does not dominate).

One can argue that Mach's principle fails in general relativity because space-time becomes too real a thing in its own right. Space itself can act as an adequate reference because all places in "empty" space are not equivalent: the curvature can change from point to point, even in the absence of matter, as demonstrated most clearly by gravitational waves.  But this "reality" of space-time led Einstein away from his former positivism, towards a new respect, in effect, for metaphysics. Much of his later career was devoted to trying to reduce all reality to pure geometry, so that particles were seen as just wrinkles in the continuum.  This new perspective made Einstein highly critical of quantum mechanics, whereas the younger physicists like Heisenberg and Pauli were impatient to escape philosophical wrangling and get on with applying what was clearly a spectacularly fruitful theory.  The inevitable result was that Bohr's paradoxical sayings were deemed to be the last word on the subject, and quantum mechanics became the archetype of anti-realist science.  Einstein wrote to his fellow dissenter Schrödinger:

The Heisenberg-Bohr tranquillizing philosophy - or religion? - is so delicately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused.
During the cold war this attitude was cemented in the West by its opposition to communism,  with its agressively materialist and realist philosophy.  One of Einstein's most significant post-war achievements was to convince the young David Bohm that the Copenhagen interpretation was unsustainable.  But when Bohm produced a completely realist "hidden variable" interpretation of quantum mechanics, incidentally demolishing "proofs" that the Copenhagen interpretation was the only one possible, his achievement was dismissed out of hand as "ideological" because of Bohm's known Marxist sympathies; shortly afterwards the McCarthy committee effectively forced him to emigrate from the USA.

Bohm's version of quantum mechanics was no more acceptable to Einstein than was Bohr's.  Its very clarity and unambiguity brought into the open the non-locality of quantum mechanics, a feature that was vehemently opposed in Einstein's last really influential paper: the Einstein-Podolsky-Rosen article of 1935.  EPR showed that the quantum mechanical description of the world leaves out concepts that are required for "local realism",  the idea that the entities it describes are real (in a rather minimalist sense), and interact purely locally, as relativity seems to demand (so there is no instantaneous communication between widely separated events).  The history of this article is well known: Bohr produced a characteristically opaque reply, which boiled down to "So what?", and the busy quantum mechanicians deemed him to have won the argument, in most cases without bothering to read either article.  Years later, David Bohm tried to work out his worries about quantum mechanics by writing a textbook, and in the process re-phrased the EPR argument in a much more straightforward way. For a while, he convinced himself of the Copenhagen interpretation, but in trying to convert Einstein, as we have seen, Einstein converted him instead.  Bohm's textbook, and his later hidden variable theory, came as a revelation to an Irish graduate student called John Bell, tempting him to work on the foundations of quantum mechanics as something of a hobby, beside his official work on particle accelerator design. Bell came to see that Bohm's version of the EPR thought experiment could be converted into one which gave measurably different results between quantum mechanics and any local realist theory: the famous Bell inequalities, first published in 1964, and tested rather definitively in 1982 by Aspect et al..  Nobody was greatly surprised that Aspect et al. confirmed the prediction of quantum mechanics and decisively ruled out local realist theories; what was surprising was Bell's discovery that the apparently metaphysical criterion of local realism implied quantitatively different predictions from quantum mechanics.

Einstein died a decade before Bell's work was published, but I can't resist speculating about how he would have chosen between the two principles which defined his life in science: realism and locality.  It is  difficult to imagine that with his commitment to understanding nature, and his deep reverence for its mystery, Einstein could have been satisfied with the concept of physics as a mere machine for predicting the results of experiments, with an explicit denial that there was any deeper reality than our everyday world, and with a rejection of the possibility that the success of physical theories could be explained in any coherent way.  There seems little point in retaining locality while at the same time denying that the particles and fields which act "locally" have any existence except as elements in a calculation. But how could one have a realistic, non-local theory that is also consistent with all the results of relativity?  David Bohm's theory gives no answer, as it is constructed only in the non-relativistic approximation.  The fundamental problem is causality: if two events with a space-like separation are non-locally linked, as in EPR experiments, which comes first? What one needs is a privileged frame, whether defined by the presence of God (as Newton thought) or of the ether (as the Maxwellians thought) or in a more abstract way. The crucial subtlety is that no experiment in either classical or quantum physics can show which frame is the fundamental one: both theories are Lorentz-invarient in this sense.  Such an "ether frame" is analogous to Newton's absolute space; impossible to find, but  providing a sort of metaphysical guarantee of the system.  As Bell pointed out, in his lecture "How to teach special relativity", such a frame is not incompatible with the physical content of relativity; on the contrary, it was fundamental to electrodynamics in 1904, with an ether unlocatable because matter and fields obeyed the Lorentz transforms.  Doubtless this scheme would still be taught today, had not the world been dazzled by a brilliant analysis from an unknown Zurich patent clerk, who swept away such unobservable concepts as the ether with an inspiring but ultimately naive faith that the innermost workings of nature must be detectable by experiment.  Knowing that his analysis has made it virtually impossible for most physicists to conceive of a realistic interpretation of the laws of nature, as we now understand them, would not Einstein have been forced to admit that the special theory of relativity, the springboard for his career, his escape ticket from the patent office, the foundation for so much of his achievement, was the biggest blunder of his life?

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[1] It is just as well that Einstein made this remark to Gamow, otherwise Gamow would have been severely tempted to make it up.

[2] Einstein didn't know much astronomy, or he might have heard yet another argument for a finite-age universe: Olbers' paradox.  A known solution was a universe of finite age, although the more popular one was that the stars only occupied a finite volume (our Galaxy).  Neither solution was consistent with Einstein's static universe; but very probably no-one pointed this out to Einstein, as Olbers' paradox was not widely discussed until popularized by Hermann Bondi in the late 1950s.

[3] "Best 1930s gangster American", according to Phillip Helbig, who, being bilingual, should know.

[4] Einstein repeatedly denied that he believed in a personal God.  His religious feelings consisted in a profound sense of awe in the face of the mystery of nature.  Many of Einstein's statements on his beliefs are gathered here.

Last modified: 2001 February 16
J. P. Leahy

University of Manchester
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