I should like to arrive in Berlin on the evening of July 15th, if that is agreeable to you; i.e. if it can be so arranged that the train does not arrive much too late. I will have to study the very many different possibilities first, and then I will let you know definitely. In the meantime, my warmest thanks once again to you and your wife for your great kindness. Please do not put yourself out at all; the less trouble I give you the happier I will be!
With sincere respect, I am always
Yours,
E. Schrödinger
7. Planck to Schrödinger
Grunewald
15 June 1926
Dear Colleague,
Many thanks for your letter of the 11th which brought us your most welcome acceptance. Besides that it once again communicates news that will make the heart of every theoretical physicist leap for joy. But we will be able to talk more about that when you are here; there are always many questions to be asked, for the appetite increases with eating. Just take care not to overwork. And so I await the announcement of your arrival time on the 15th of July. The earlier, the better. You lecture to the Physical Society6 then on the 16th, and on the 17th to our Colloquium. On the evening of the 17th I hope to have several colleagues and you at our home. For all eventualities I repeat that I shall be in Bonn from the 5th to the 11th of July. My address, however, remains the usual one.
Warmest greetings.
Yours,
Planck
8. Schrödinger to Planck
Zürich
4 July 1927
My dear Professor,
. . . . . . .
May I talk a little physics yet? I should like so much to know how the quantum situation is judged in Berlin and especially by you yourself. Is what the matrix-physicists and q-number-physicists say true—that the wave equation describes only the behavior of a statistical ensemble, just like the so-called Fokker partial differential equation perhaps? I would willingly believe it since the interpretation is really much more convenient, if I could only pacify my conscience and convince it that it is not frivolous to get off so easily in overcoming the difficulties. I believe I am right that you yourself wrestled with the first and most basic assumption of discontinuity (i.e. precisely “the quantum theory”) in its day, wrestled a hard intellectual struggle with your whole soul, as the “second version”7 which followed so long afterwards shows most clearly. I believe that one is obliged to take up this struggle anew with the same seriousness among today’s newly emerged points of view. I do not have the feeling that this is really happening on the part of those who today already announce categorically: the discontinuous exchange of energy must be adhered to.
What seems most questionable to me in Born’s probability interpretation is that when it is carried out in more detail (by its adherents) the most remarkable things come forth naturally: the probabilities of events that a naive interpretation would consider to be independent do not simply multiply when combined, but instead “the probability amplitudes interfere” in a completely mysterious way (namely, just like my wave amplitudes, of course). In a brand new article by Heisenberg even my much smiled at wave packets are said to have finally found their suitable interpretation as “probability packets”. The first is especially comical. It can also be expressed this way: the Born probability (more correctly its square root) is a two dimensional vector; its addition is to be carried out vectorially. The multiplication is still more complicated, I believe.
Well, as God wills; I keep quiet. That is, if one really must, I too will become accustomed to such things.
With kindest regards to your wife, Professor Planck, I remain
Yours faithfully,
E. Schrödinger
9. Einstein to Schrödinger
16 April 1926
Dear Colleague,
Professor Planck pointed your theory out to me with well justified enthusiasm, and then I studied it too, with the greatest interest. In the process one doubt has arisen which I hope you can dispel for me. If I have two systems that are not coupled to each other at all, and if E1 is an allowed energy value of the first system and E2 an allowed energy value of the second, then E1 + E2 = E must be an allowed energy value of the total system consisting of both of them. I do not, however, understand how your equation
is to express this property.
So that you can see what I mean, I put down another equation that would satisfy this condition:
For, the two equations
(valid for the phase space of the first system)
(valid for the phase space of the second system) have as a consequence
(valid in the combined q- space).
As proof one need only multiply the equations by φ2 and φ1 respectively and add. φ1 φ2 would, therefore, be a solution of the equation for the combined system, belonging to the energy value E, + E2.
I have tried in vain to establish a relationship of this sort for your equation.
It also seems to me that the equation ought to have such a structure that the integration constant of the energy does not appear in it; this also holds for the equation I have constructed, but despite that I have not been able to assign a physical significance to it, a matter on which I have not reflected sufficiently.
With warmest greetings from
A. Einstein
The idea of your article shows real genius.8
10. Einstein to Schrödinger
22 April 1926
Dear Colleague,
I have just seen from your first article that you really based your considerations on the equation
div grad ψ + constant (E—Φ) ψ = 0
which satisfies the addition theorem for independent systems. So my letter was superfluous.
I see no basic difference between your work9 on the theory of the [ideal] gas and my own. For according to you, too, the state (of equal probability) is characterized by the values of the set of numbers n1, n2, n3, …, where the numbers n1, n2, etc. have the same meaning as they do for me.
I do not understand how you are allowed to use the last form of (4), in your article, since this is not consistent with the condition Σn4 = const.
Best wishes from
A. Einstein
11. Schrödinger to Einstein
Zürich
23 April 1926
My dear Professor,
My hearty thanks for your extremely kind letter of the 16th. Your approval and Planck’s mean more to me than that of half the world. Besides, the whole thing would certainly not have originated yet, and perhaps never would have, (I mean, not from me), if I had not had the importance of de Broglie’s ideas really brought home to me by your second paper on gas degeneracy.10
The objection in your last letter makes me even happier. It is based on an error in memory. The equation
is not mine, as a matter of fact, but my equation really runs exactly like the one that you constructed free hand from the two requirements of the “additivity” of the quantum levels and the non-appearance of the absolute value of the energy:
Your very basic requirements are therefore fulfilled. I am, moreover, very grateful for this error in memory because it was through your remark that I first became consciously aware of an important property of the formal apparatus. Besides, one’s confidence in a formulation always increases if one—and especially if you—construct the same thing afresh from a few fundamental requirements.
Just recently I read with the greatest interest your proposal in Naturwissenschaften for a new coherence experiment.11 I have not yet finished thinking it over. That always takes me rather long. I am not completely sure how you conceive of the arrangement behind the grating. (“Behind the grating the light will be made parallel by means of another lens …”) I imagine the wire grating at the focus of this farther lens and then perhaps a Fabry-Perot interferometer (plane parallel layer of air, rings of equal inclination). Then one would usually say: each point of the light source corresponds to a point of the circular image. The gra
ting is the light source. Then the light beams from different slits of the grating would really not interfere with one another. But, according to the classical theory, we have here the unique situation that different points of the light source vibrate coherently in a legitimate way. I have not yet made clear to myself how that works out. But maybe the arrangement, as I continue to think about it, is also stupid.
I very much enjoyed your delightful explanation of the formation of meanders.12 It just happens that my wife had asked me about the “teacup phenomenon”13 a few days earlier, but I did not know a rational explanation. She says that she will never stir her tea again without thinking of you.
Kindest regards from
Yours faithfully,
E. Schrödinger
12. Einstein to Schrödinger
26 April 1926
Dear Colleague,
Many thanks for your letter. I am convinced that you have made a decisive advance with your formulation of the quantum condition, just as I am equally convinced that the Heisenberg-Born route is off the track. The same condition of system additivity is not satisfied in their method.
I have now discovered considerations that nearly rule out the existence of elementary spherical waves, so that I am pretty well convinced that the experiment I proposed will turn out negatively. Its simplest realization is, in principle:
A direction of emission R corresponds to a point in the focal plane of the telescope. Rays emitted in the direction R by a particle reach, or do not reach, the telescope (alternately); for a suitable relationship between the particle velocity and the path difference the interference would have to be destroyed, which, however, I do not believe. Diffraction at the grating acts as a disturbance, but not so strongly as to destroy the demonstrative power of the experiment.
Friendly greetings.
A. Einstein
13. Schrödinger to Einstein
Cunostrasse 44
Berlin—Grunewald
30 May 1928
My dear Professor Einstein,
Enclosed is a letter from Niels Bohr14 who, at the end, expresses the wish that you and Planck might also be made aware of its contents. I also enclose the carbon copy of my letter just so that you can see what set off the discussion. The remark about the uncertainty relation in the ideal gas runs as follows, when worked out: if we quantize a molecule that is reflected back and forth on the segment l , then we have
Neighboring quantized values of the momentum therefore differ from each other by so little, (namely by only h2l), that even with the largest possible uncertainty in the coordinate (Δx = l), I cannot buy enough accuracy in the momentum to allow me to distinguish between neighboring quantum states. What Bohr says about this case at the end of the third page, I do not understand at all.*
If it is agreeable to you, I would be glad to come over sometime to talk about the letter, but perhaps you do not have much time now, before your departure, and you need to be sparing with it.
With greetings and best regards to the whole family,
Yours sincerely,
Schrödinger
_______________
* Everything that I have just said is surely terribly trivial!
14. Einstein to Schrödinger
31 May 1928
Dear Schrödinger,
I think that you have hit the nail on the head. It is true that the evasion using the arbitrarily large domain of cyclic variables to limit the value of Δ p is very ingenious.15 But an uncertainty relation interpreted that way does not appear to be very illuminating. The thing was invented for free particles, and it fits only that case in a natural way. Your claim that the concepts p,q will have to be given up, if they can only claim such a “shaky” meaning, seems to me to be fully justified. The Heisenberg-Bohr16 tranquilizing 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. So let him lie there.
But this religion has so damned little effect on me that, in spite of everything, I say
not: E and ν
but rather: E or ν;
and indeed: not ν, but rather E (it is ultimately real). But I cannot make head or tail of it mathematically. My brain is also too worn out by this time. If you would give me the pleasure of a visit from you again sometime it would be good of you and very fine for me.
Best regards from
A. Einstein
15. Schrödinger to Einstein
7, Sentier des Lapins
LaPanne, Belgium
19 July 1939
Dear Einstein,
. . . . . . .
A few months ago a Dutch newspaper carried a report which sounded comparatively intelligent that you have discovered something important about the connection between gravitation and matter waves. I would be terribly interested in that because I have really believed for a long time that the ψ-waves are to be identified with waves representing disturbances of the gravitational potential; not, of course, with those you studied first, but rather with ones that transport real mass, i.e. a non-vanishing Tik. That is, I believe that one has to introduce matter into the abstract general theory of relativity, which contains the Tik only as “asylum ignorantiae” (to use your own expression), not as mass points or something like that, but rather, shall we say, as quantized gravitational waves. I have done a good many calculations on this point but have found out very little, except that § 13.7 of Eddington’s book “Protons and Electrons”, which had fascinated me very much, is false. But it is unfortunately not very hard to find major errors in this ingenious book.
It’s a shame that I had to fill so much of this letter with uninteresting personal things about myself, but it is really so terribly hard to write, (I mean about such things as those just above).
If this letter reaches you on your sailboat I wish you much rest and enjoyment there. I am wonderfully well off here on the charming Belgian shore with these delightful people, happy as children. If one could only be somewhat more light-hearted and could think less about what is to become of oneself. Vacations are fine, but a vacation for which one cannot perceive a definite end is a peculiar thing.
Best regards from
Yours sincerely,
Schrödinger
16. Einstein to Schrödinger
Peconic,17 9 VIII 1939
Dear Schrödinger,
. . . . . . .
Now to physics. I am as convinced as ever that the wave representation of matter is an incomplete representation of the state of affairs, no matter how practically useful it has proved itself to be. The prettiest way to show this is by your example with the cat18 (radioactive decay with an explosion coupled to it.) At a fixed time parts of the ψ-function correspond to the cat being alive and other parts to the cat being pulverized.
If one attempts to interpret the ψ-function as a complete description of a state, independent of whether or not it is observed, then this means that at the time in question the cat is neither alive nor pulverized. But one or the other situation would be realized by making an observation.
If one rejects this interpretation then one must assume that the ψ-function does not express the real situation but rather that it expresses the contents of our knowledge of the situation. This is Born’s interpretation19 which most theorists today probably share. But then the laws of nature that one can formulate do not apply to the change with time of something that exists, but rather to the time variation of the content of our legitimate expectations.
Both points of view are logically unobjectionable; but I cannot believe that either of these viewpoints will finally be established.
There is also the mystic, who forbids, as being unscientific, an inquiry about something that exists independently of whether or not it is observed, i.e. the question as to whether or not the cat is alive at a particular instant before an observation is made (Bohr). Then both interpretations fuse into a gentle fog, in which I feel no better than I do i
n either of the previously mentioned interpretations, which do take a position with respect to the concept of reality.
I am as convinced as ever that this most remarkable situation has come about because we have not yet achieved a complete description of the actual state of affairs.
Of course I admit that such a complete description would not be observable in its entirety in the individual case, but from a rational point of view one also could not require this.
I write this to you, not with any illusions that I will convince you, but with the sole intention of letting you understand my point of view, which has driven me into deep solitude. I have also brought it to the point of a real mathematical theory, whose testing, however, is naturally very difficult.
Best regards from
Yours,
A. Einstein
17. Schrödinger to Einstein
Innsbruck, Innrain 55
18 November 1950
Dear Einstein,
It seems to me that the concept of probability is terribly mishandled these days. Probability surely has as its substance a statement as to whether something is or is not the case—an uncertain statement, to be sure. But nevertheless it has meaning only if one is indeed convinced that the something in question quite definitely either is or is not the case. A probabilistic assertion presupposes the full reality of its subject. No reasonable person would express a conjecture as to whether Caesar rolled a five with his dice at the Rubicon. But the quantum mechanics people sometimes act as if probabilistic statements were to be applied just to events whose reality is vague.
Letters on Wave Mechanics: Correspondence with H. A. Lorentz, Max Planck, and Erwin Schrodinger Page 3
