5 8 D O C U M E N T 5 9 J U N E 1 9 2 3
The problem of the zero-point energy for hydrogen and helium doesn’t seem so
unpromising to me, after
all.[5]
For it appears that the volume dependence of the
energy for liquids and gases is described pretty well by the Van der Waals expres-
sion
.[6]
The evaporation heat D would be described by the formula
(1),
the temperature-pressure coefficient of the liquids by
,
which yields the relation
..
(2)
From (1) and (2) one can eliminate a, which results in a verifiable relation that
to my knowledge fits nicely for a “normal liquid.” For thermally degenerated liq-
uids with zero-point energy, there has to be an energy component that increases as
V drops, hence it produces a negative contribution to . Perhaps this is the reason
for helium’s density maximum.[7] How otherwise should α be able to become zero?
I think that a quantitative pursuit of these relations could lead to a proof of the ex-
istence of zero-point energy. What do you think of this? We should check this on
the empirical material for “normal liquids,” on one hand, for hydrogen and helium,
on the other hand, whereby one could, of course, also quantitatively calculate the
thermal degeneration to some extent. I lack the data here at home and I won’t get
to it at all. Maybe we could examine this together, when we meet again. I have pub-
lished the relativity paper,[8] but it hasn’t appeared yet. I doubt that it’s the true
thing. But the Weyl-Eddington path does finally have to be thought through to the
end.[9] Ilse had a minor stomach operation and is still in the clinic. Margot is with
her.[10] I’m struggling desperately with all this paper.
Warm greetings to you with your dear, logical Tanyas and with the two little
fellows,[11] from your
Einstein.
I haven’t answered the forwarded letters yet.
a
V
---
D RT –
1
Vfl.
-------
1
Vgas¹
---------·
–
©
§
a =
pd
Td
-----¹
-·
©
§
V
1
T∂V
-- -
∂u
------ =
T---
α
κ
a
Vfl¹
2
------¸
©
¨
§ ·
=
α = thermische Ausdehnung
κ= Kompressibilität
--------------------------------------------------------------------·
-
© ¹
§
T---
α
κ