1. How Hume and Mach Helped Einstein Find Special Relativity
John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh

2. “…a special kinship.”
“He [the student Einstein] approached the broader aspects of thought through philosophical studies,
chiefly through his readings in Kant and Schopenhauer,
and later through his study of Hume, with whom he felt a special kinship.”
Anton Reiser = Rudolf Kayser,
Einstein’s step son-in-law,
married to Ilse Einstein.
Anton Reiser, Albert Einstein: A Biographical Portrait. Albert & Charles Boni, New York, 1930.

3. “…obscure stuff….”
“If one reads Hume’s books, one is amazed that many and sometimes even highly esteemed philosophers after him have been able to write so much obscure stuff
and even find grateful readers.”
“Remarks on Bertrand Russell’s Theory of Knowledge” in The Philosophy of Bertrand Russell, Vol V. of The Library of Living Philosophers. P. A. Schlipp, ed., Tudor

4. Was Einstein’s reading of Hume any practical use?
“Today everyone knows, of course, that all attempts to clarify this paradox [of chasing the beam of light] satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem. The type of critical reasoning required for the discovery of this central point was decisively furthered, in my case, especially by the reading of David Hume’s and Ernst Mach’s philosophical writings.”
Albert Einstein, Autobiographical Notes

5. This Talk
How Einstein’s reading of Hume and Mach played a decisive role at the crucial moment in Einstein’s 1905 discovery of special relativity.
The help did not come from Hume and Mach’s analysis of the notions of space and time specifically…

6. How to Use Concepts in Physical Theories
Concepts must be properly grounded in experience, else they fail to represent the physically real and are fictional. (From Hume and Mach)
Concepts without proper physical grounding need not be abjured (contrary to Mach and Hume?). They can be retained in a physical theory as long as their arbitrary character is recognized and in a way that does not unwittingly introduce false presumptions.
The breakthrough in Einstein’s 1905 discovery of special relativity came when he applied this view to the traditional concept of the simultaneity of distant events.

7. The Special Theory of Relativity of 1905

8. “On the electrodynamics of moving bodies”
Thought experiment with a magnet and conductor
I. Principle of relativity.
Equivalence of all inertial states of motion.
II. Light postulate.
Same speed c for light for all inertial observers.
Moving rods shrink.
Moving clocks slow.
Speed of light as an upper limit to motion.
And much more.

9. Its Origins in 19th Century Theories of Electricity and Magnetism

10. The Electromagnetic Ether
Electric and magnetic fields are states of an all-pervading electromagnetic ether.
The theory of electric and magnetic fields is the theory of this medium.

11. Our Moving Earth
Is this motion through the ether detectible?

12. Einstein’s Electrodynamical Pathway to Special Relativity

13. Einstein’s Early Fascination with the Ether
In 1895, a 16 year old Einstein wrote his first scientific manuscript: “On the examination of the state of the ether in a magnetic field.”
c.1901, Einstein was devising simple experiments intended to reveal the motion of the earth through the ether.

14. The magnet and conductor thought experiment (1901
The magnet and conductor thought experiment (1901?) A device that reveals motion through the ether?
IMPROVED
VERSION
conductor moves
with magnet
A magnet at rest in the ether is surrounded by a pure magnetic field H, but no electric field E. H H E
A magnet moving through the ether creates in addition an induced magnetic field.
Is this induced magnetic field the detectible mark of motion through the ether?

15. What is observable? no current current due to electric field
exactly balanced by
current due to motion of conductor in magnetic field
no current
conductor
Observables obey principle of relativity. Theoretical account should as well.
Einstein 1905

16. Einstein’s 1920 recollection of his reaction:
“The idea, however, that these were two, in principle different cases was unbearable for me.
The difference between the two, I was convinced, could only be a difference in choice of viewpoint and not a real difference.
Judged from the magnet, there was certainly no electric field present. Judged from the [resting observer], there certainly was one present.
Thus the existence of the electric field was a relative one, according to the state of motion of the coordinate system used, and only the electric and magnetic field together could be ascribed a kind of objective reality, apart from the state of motion of the observer or the coordinate system.
The phenomenon of magneto-electric induction compelled me to postulate the (special) principle of relativity.”

17. The device of field transformations.
For the experts…
The device of field transformations.
“Judged from the magnet, there was certainly no electric field present.” H H’
E’ = - (1/c)vxH
“Judged from the [resting observer], there certainly was one present.”
Pure magnetic field H
Magnetic field H’ = H and Electric field E’ = - (1/c)vxH
change observer’s velocity by v

18. Which transformation for the general case?
For the experts…
Which transformation for the general case?
Lorentz transformation (First order)
Unusable without Lorentz’s local time. Einstein is still years from “the step.”
E = E’ + (1/c) uxH’
H = H’ - (1/c) uxE’
Simplified transformation
Unique, linear field transformation law under which Lorentz force law
f/e = E + (1/c) uxH
is covariant
E = E’ + (1/c) uxH’
H = H’

19. Maxwell’s electrodynamics splits into two partial theories
(“two charges partial theory”)
is covariant under
t=t’ r=r’-ut
E = E’ H = H’ - (1/c) uxE’
Full theory of Föppl’s (1894) two charges thought experiment, which violates the principle of relativity.
BUT
A moving magnet does not induce an electric field.
Lorentz force law not included.
(“magnet and conductor partial theory”)
is covariant under
t=t’ r=r’-ut
E = E’ + (1/c) uxH’ H = H’
Full theory of the magnet and conductor thought experiment.
BUT
A moving charge does not induce a magnetic field
(M1) ∇.E = 4πρ
(M3) ∇xH = (4π/c)j + (1/c)(∂E/∂t)
(M2) ∇.H = 4πρ
(M4) ∇xE = - (1/c)(∂H/∂t)
(L) f/e = E + (1/c) uxH

20. Einstein’s response “The difficulty to be overcome lay in the
constancy of the velocity of light in a vacuum,
which I first believed had to be given up.”
A consequence of Maxwell’s electrodynamics
Modify Maxwell’s electrodynamics
Footnote to Einstein’s 1920 recollection of the magnet conductor thought experiment

21. Ritz’s 1908 Emission “Theory” of light
A modified electrodynamics in which the velocity of the emitter is added vectorially to the velocity of light and electrodynamic action.
The new theory conforms to the principle of relativity without modifying Newtonian notions of space and time.
The constancy of the speed of light is abandoned. All speeds are possible.
Einstein later reported that he had given long and serious consideration to a Ritz-like electrodynamics during the seven years prior to 1905 in which he struggled to reconcile electrodynamics and the principle of relativity.
“…Ritz’s conception, which incidentally was also mine before rel. theory.”
Einstein to Ehrenfest,
June, 1912 and elsewhere

22. Propagation versus Projection (Maxwell) (Ritz) Light and
electromagnetic action propagates from fixed point in space that is left behind by a moving source.
The apparent source of light and electromagnetic action is boosted, and moves with uniformly moving source.
Ritz imagined that charges emit fictitious particles that are projected by ordinary rules of Galilean kinematics.

23. Propagation versus Projection (Maxwell) (Ritz) Light and
electromagnetic action propagates from fixed point in space that is left behind by a moving source.
The apparent source of light and electromagnetic action is boosted, and moves with uniformly moving source.

24. Einstein’s Objections to All Emission Theories of Light.
Collected from remarks in many places.
The physical state of a light ray is determined completely by its intensity and color [and polarization].
“ I decided [against an emission theory], since I was convinced that each light [ray] should be defined by frequency and intensity alone, quite independently of whether it comes from a moving or a resting light source.” Einstein to Ehrenfest, mid June 1912
The theory cannot be formulated in terms of differential equations.
Different velocities entail that light can back up on itself (later parts overtakes earlier).
e.g. Einstein to Shankland, 1950s
e.g. Einstein to Shankland, 1950s; to Hines Feb. 1952
Problems with shadow formation by a moving screen.
e.g. To Mario Viscardini, April 1922

25. Crisis and Breakthrough

26. Reconcile the “Apparently Incompatible” …
Principle of Relativity
From ether drift experiments, observables in electrodynamics, classical mechanics. Magnet and conductor.
with
Light Postulate
From Maxwell’s electrodynamics. All efforts to alter it had failed. Emission theories of light are untenable.

27. Einstein Recalls the Decisive Moment
“The Step”
“Why are these two things inconsistent with each other? I felt that I was facing an extremely difficult problem. I suspected that Lorentz’s ideas had to be modified somehow, but spent almost a year on fruitless thoughts. And I felt that was puzzle not to be easily solved.
But a friend of mine living in living in Bern (Switzerland) [Michele Besso] helped me by chance. One beautiful day, I visited him and said to him: ‘I presently have a problem that I have been totally unable to solve. Today I have brought this “struggle” with me.’ We then had extensive discussions, and suddenly I realized the solution. The very next day, I visited him again and immediately said to him: ‘Thanks to you, I have completely solved my problem.”
My solution actually concerned the concept of time. Namely, time cannot be absolutely defined by itself, and there is an unbreakable connection between time and signal velocity. Using this idea, I could now resolve the great difficulty that I previously felt.
After I had this inspiration, it took only five weeks to complete what is now known as the special theory of relativity.”
From a lecture given in Kyoto, Dec. 14, Notes by Jun Ishiwara; translation Akira Ukawa; revised John Stachel.

28. Einstein’s analysis in his 1905 “On the Electrodynamics of Moving Bodies” (simplified):
The platform observer judges the two flashes to be simultaneous and the two clocks to be properly synchronized.
The moving observer judges the A flash to happen earlier and the two clocks not to be properly synchronized.

29. Relativity of simultaneity
Inertial observers in relative motion may disagree on the time order of spatially separated events.
What the thought experiment shows
Principle of relativity +
Light postulate
Relativity of simultaneity
The deduction reversed
Is there empirical content in the theory? Is the compatibility of the two principles just an artifact of our conventional decision to proclaim simultaneity in an idiosyncratic way? NO. That Einstein’s definition works is a contingent matter, requiring the truth of the facts that underpin special relativity.
--It would fail in a Galilean covariant theory of light. In the latter, in one frame, light will have many speeds according to the speed of the emitter. No single resynchronization of clocks will be able to bring all these different speeds to the same constant c.
--It would fail in an ether theory in which light moves at c with respect to the ether. On observer moving at c would see frozen light and no clock resynchronization protocol would set it into motion at any speed, let alone c.
Principle of relativity +
Relativity of simultaneity
Same speed of light for all inertial observers
…the two principles are compatible if we revise our notions of space and time.

30. The central insight A view about how concepts should be used in physical theories.

31. Concepts must be properly grounded in experience...
“After seven years of reflection in vain ( ), the solution came to me suddenly with the thought that our concepts and laws of space and time can only claim validity insofar as they stand in a clear relation to experiences; and that experience could very well lead to the alteration of the concepts and laws. By a revision of the concept of simultaneity into a more malleable form, I thus arrived at the special theory of relativity.”
From a 1924 recording transcribed by Herneck in 1966.
“The concept [of simultaneity] does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case.”
A. Einstein, Relativity, §8
“…an illustration which Einstein offered in discussion. Suppose somebody uses the word ‘hunchback.’ If this concept is to have any clear meaning, there must be some way of finding out whether or not a man has a hunched back. If I could conceive of no possibility of reaching such a decision, the word would have no real meaning for me.”
To Wertheimer in a 1916 interview.

32. …so we may purge a priori (absoluteness of simultaneity) from our concepts.
“The illusion which prevailed prior to the enunciation of the theory of relativity--that, from the point of view of experience the meaning of simultaneity in relation to spatially distant events and, consequently, that the meaning of physical time is a priori clear--this illusion had its origin in the fact that in our everyday experience we can neglect the time of propagation of light. We are accustomed on this account to fail to differentiate between "simultaneously seen" and "simultaneously happening"; and, as a result, the difference between time and local time is blurred.
The lack of definiteness which, from the point of view of its empirical significance, adheres to the notion of time in classical mechanics was veiled by the axiomatic representation of space and time as given independently of our sense experiences. Such a use of notions--independent of the empirical basis
to which they owe their existence--does not necessarily damage science. One may, however, easily be led into the error of believing that these
notions, whose origin is forgotten, are logically necessary and therefore unalterable, and this error may constitute a serious danger to the progress of science.”
Einstein, “Physics and Reality,” 1936.

33. …and Einstein credits Hume and Mach
“Today everyone knows, of course, that all attempts to clarify this paradox [of chasing the beam of light] satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem. The type of critical reasoning required for the discovery of this central point was decisively furthered, in my case, especially by the reading of David Hume’s and Ernst Mach’s philosophical writings.”
Albert Einstein, Autobiographical Notes

34. Mach

35. Einstein attributes this view of concepts to Mach
from Einstein’s obituary
for Mach, 1916
“Science is, according to Mach, nothing but the comparison and orderly arrangement of factually given contents of consciousness, in accord with certain gradually acquired points of view and methods….
…concepts have meaning only in so far as they can be found in things, just as they are the points of view according to which these things are organized. (Analysis of concepts)”
Empirical grounding of concepts
“Concepts that have proven useful in ordering things can easily gain authority over us such that we forget their worldly origin and take them as immutably given. They are then rather rubber-stamped as a ‘necessity of thought’ and an ‘a priori given,’ etc. Such errors often make the path of scientific progress impassable for a long time…”
Dangers of a priori

36. Einstein attributes this view of concepts to Mach
from Einstein’s obituary
for Mach, 1916
Quotes of Mach’s reanalysis of judgments of time
(as expressions of dependence upon pendulum oscillations or the Earth’s position);
of motion; Newton’s bucket.
Illustration
It is not improbable that Mach would have hit upon relativity theory if, in the time that he was of young and fresh spirit, physicists would already have been moved by the question of the meaning of the constancy of the speed of light. In this absence of this stimulation, which follows from Maxwell-Lorentz electrodynamics, even Mach’s critical urge did not suffice to arouse a feeling for the necessity of a definition of simultaneity for spatially distant events.
Einstein sees link to simultaneity

37. Hume

38. “…and still much more Hume…”
“Your exposition is also quite right that positivism suggested rel. theory, without requiring it. Also you have correctly seen that this line of thought was of great influence on my efforts and indeed E. Mach and still much more Hume, whose treatise on understanding I studied with eagerness and admiration shortly before finding relativity theory.”
Einstein to Moritz Schlick, Dec
Editors, Einstein Papers, Vol. 2
• On the known reading list of “Einstein’s Olympia Academy”
• First part then available in new German translation (and Einstein recalled reading Hume in German)
“treatise on understanding” =
“A Treatise of Human Nature”?
or “An Enquiry concerning Human Understanding”?

39. David Hume, A Treatise of Human Nature
Dependence of concepts on experience
“…all our simple ideas proceed either mediately or immediately, from their correspondent impressions.
This then is the first principle I establish in the science of human nature…”
Book 1, Part 1, Section 1.
Application to time
“As ‘tis from the disposition of visible and tangible objects we receive the idea of space, so from the succession of ideas and impressions we form the idea of time, nor is it possible for time alone ever to make its appearance, or be taken notice of by the mind.
…time cannot make its appearance to the mind either alone, or attended with a steady unchangeable object, but is always discover’d by some perceivable succession of changeable objects.”
Book 1, Part II, Section III.

40. David Hume, A Treatise of Human Nature
Inapplicability of concept without corresponding experience
“I know there are some who pretend, that the idea of duration is applicable in a proper sense to objects, which are perfectly unchangeable…But to be convinced of its falsehood we need but reflect on the foregoing conclusion, that the idea of duration is always deriv’d from a succession of changeable objects, and can never be convey’d to the mind by any thing stedfast and unchangeable…
…Ideas always represent the objects or impressions from which they are deriv’d, and can never without a fiction represent or be appl’d to any other…”
Book 1, Part II, Section III.
Substance discussed in Book 1, Part I. Section VI.
Causation discussed in Book I, Part III.
We have no idea of substance beyond the collection of particular qualities. We have no idea of causation beyond contiguity and succession--no necessary connection.
This mode of analysis is applied throughout the Treatise.

41. “Olympia Academy” 1902+
“Together we read, after Pearson, Mach’s Analysis of Sensations and Mechanics, Mill’s Logic, Hume’s Treatise on Human Nature (sic), … [much more]…
We devoted weeks to the discussion of David Hume’s eminently penetrating criticism of conceptions of substance and causality.”
Solovine, “Introduction” to Albert Einstein, Letters to Solovine: New York Citadel, 1993.
Maurice Solovine
Albert Einstein
Conrad Habicht

42. Why Hume more than Mach?

43. Why Hume more than Mach?
A conjecture: Einstein thought that Mach (but not Hume) denied the freedom of creation of concepts exercised by Einstein when he introduced a new definition of distant simultaneity in 1905?
“I see [Mach’s] weakness in this, that he more or less believed science to consist in a mere “ordering” of empirical “material”; that is to say, he did not recognize the freely constructive element in the formation of concepts. In a way he thought that theories arose through discoveries and not through inventions. He even went so far that he regarded “sensations” not only as material which has to be investigated, but, as it were, as the building blocks of the real world…”
Einstein to Besso on 6. Jan. 1948
“Hume saw clearly that certain concepts, as for example that of causality, cannot be deduced from the material of experience by logical methods.”
Einstein, Autobiographical Notes

44. Einstein absolves Hume of Machian Guilt
“…the concepts which arise in our thought in our linguistic expressions are all--when viewed logically--the free creations of thought which cannot inductively be gained from sense experiences…
As soon as one is at home in Hume’s critique one is easily led to believe that all those concepts and proposition which cannot be deduced from the sensory raw material are, on account of their ‘metaphysical’ character, to be removed from thinking…
…by his clear critique Hume did not only advance philosophy in a decisive way but also--through no fault of his--created a danger for philosophy in that, following his critique, a fateful ‘fear of metaphysics’ arose which has come to be a malady of contemporary empiricistic philosophy…”
“Remarks on Bertrand Russell’s Theory of Knowledge” in The Philosophy of Bertrand Russell, Vol V. of The Library of Living Philosophers. P. A. Schlipp, ed., Tudor

45. Winding Up

46. This Talk What did Einstein learn from Hume and Mach?
The requirement that concepts must be properly grounded in experience.
The warning that use of concepts not so grounded may unwittingly introduce false presumptions.
The courage to mount his own account of how concepts not properly grounded in experience may be introduced via definitions.
Einstein’s opportunism
He drew on Hume and Mach selectively just as it suited his purposes in physical theorizing. Einstein did not effectively address the systematic problems of the view.
How can experience of particulars yield universally applicable concepts?
Hume: Missing shade of blue.
Mach: It cannot. “No one is warranted in extending these principles beyond the boundaries of experience.”
Einstein: It is a “miracle”; “leaves us in awe”; “we shall never understand [it]”.
Missing shade of blue in Bk 1, Pt. 1, Sec 1. See also sec VII
Mach. Science of Mechanics p. 280
Einstein. Physics and Reality.

47. Finis

48. Einstein’s Definition of Simultaneity
Events “0” at places A and B are simultaneous.

49. Relativity of Simultaneity
The same process viewed by an observer who moves with respect to the platform.
Events “0” at places A and B are simultaneous.
Observers in relative motion disagree on the simultaneity of spatially separated events.