Not a Very Big Bang About Genesis
By Mark Perakh
First posted on April 11, 1999. Updated in December 2001.
The arguments related to the beginning of the Bronze age.
The arguments related to archeological data about times earlier than 5760 years ago
Schroeder estimates probabilities
Some specific faults and errors in Schroeder's first book
Schroeder's second book
Change of dates in the second book compared to the first one
Zero time interval in a light beam
Diffraction of waves according to Schroeder
Diluted heat and masers
Schroeder's third book
this article I will discuss three books by Gerald L. Schroeder [1,2,3]. which
have gained a substantial popularity among readers and have often been acclaimed
as a very successful clarification of how to reconcile the biblical story with
The first book  titled Big Bang and
Genesis is subtitled "The discovery of harmony between modern science
and the Bible." This subtitle
is a concise expression of the main thrust of the book. Schroeder set out on an ambitious road aimed at demonstrating to both
believers and skeptics that the contradictions between the biblical revelations
and the claims of science simply stem from incorrect interpretations and that
every word of the Bible is really in complete agreement with the results of
Schroeder starts his book  with a rather lengthy
narrative about his participation in the underground tests of atomic bombs. This narrative has little to do with the book's subject, but was
apparently designed to demonstrate to the readers that Schroeder is eminently
qualified to do the job. We learn that Schroeder is not some ignoramus in science blindly defending the biblical stories,
but, on the contrary, an experienced physicist with a Ph.D. degree. Indeed, we find in his book multiple respectful references to facts
established by science, from archeological data to Einstein's theory of
relativity. Overall, Schroeder's
idea is that every word in the Bible is literally true and also absolutely
compatible with scientific data. No
contradiction whatsoever exists between the revelations of the Bible and the
results of modern science - or so says Dr. Schroeder.
Who could object to such a statement if it were proven
in a perfectly logical way without any distortion of known facts?
In Chapter 1 of his first book  Schroeder
tells us that this book was a result of his efforts to answer his children's
questions, particularly those of his
son Joshua, who had studied the Bible from the age of three, and at the age of
eight started discovering what seemed to be contradictions between the Bible and
Schroeder does not explicitly tell us if his explanations satisfied his eight-year old son,
but such a notion seems to be implied. What is of interest though, is whether or not Schroeder's explanation can
satisfy people of a more advanced age than eight.
The discussion of Schroeder's book  will include the following sections:
1) Schroeder's chronology
2) Schroeder's estimate of probabilities.
3) Some particular details and examples from Schroeder's
2. Schroeder's chronology
On page 12 of his book  Schroeder writes: "..the discord
between archeology and theology is neither necessary nor valid." A few lines later he continues: "My goal in this book is to explain
this compatibility to expert and layperson alike."
we see, Schroeder has formulated the ambitious intention of explaining to both
experts and laypersons, all of whom had wandered in dark until his book, the
actual meaning of both scientific data and biblical revelations. It is, surely, a very commendable goal. An important milestone on the road to his goal is Schroeder's analysis of
chronological data, which until his book seemed to be irreconcilably different
in the Bible and in science.
Schroeder's chronological exploration consists of two
parts. The first part deals with
the biblical account of the creation of the world in six days and the second
with the period of time between the end of those six days and our time. Let us consider each part of Schroeder's
chronology in the above order.
Creation of the world in six days
according to Schroeder
Since the general thrust of Schroeder's book was to prove that the biblical account and
scientific data do not contradict each other, one of his important tasks was to
reconcile the biblical story about the creation of the world in six days with
scientific evidence which asserts that the universe is about 15 billion years
Before his book, this contradiction between the Bible
and science had been discussed an uncounted number of times. A notion that was often suggested was that the word "day" in
the Bible was not meant to literally denote "day" as we understand it,
i.e. as approximately 1/365 of the duration of earth's revolution around the
sun. What is a billion years for us humans, may be one day for God - that is how
that interpretation went.
Despite Schroeder's assertions to the contrary, his
explanation is actually in the same vein, but with one difference. Schroeder turns to his background in physics, in particular to Einstein's
theory of relativity, in order to provide a specific clarification of the
six-day creation story, which, in his view, is compatible with science.
As Schroeder explains, the theory of relativity has established, among
other things, that there is no absolute time. Of course, this is true. In
different frames of reference, continues Schroeder, the time interval between
two events may be quite different. This, of course, is also true. What lasted six days in one frame of reference may very well last 15
billion years in some other frame of reference. This is true as well.
Schroeder proceeds to give an example of
"time dilation." This is
a well known experimental result regarding the behavior of mu-mesons (muons). As Schroeder tells the readers, while 200 microseconds elapse in the
frame of reference attached to the ground, only 4.5 microseconds elapse in the
frame of reference of the moving muon itself. Experts would gladly agree with that statement, while laypersons have to
rely on Schroeder's scientific background and accept his statements.
From this point on the paths of experts and of
laypersons necessarily will go in different directions. Laypersons, impressed by Schroeder's scientific credentials, may continue
accepting his further explanations. The
experts, however, would rather shrug off the next step in Schroeder's line of
thought. In that next step,
Schroeder makes a leap from the case of fast moving muons to the case of creation of the universe in six days. According to Schroeder, before creating the first man, Adam, God acted in
his own frame of reference, vastly different from the frame of reference which
would be chosen by him at the moment of Adam's creation. In the pre-Adam frame
of reference - the frame of the Creator - what would become billions of years on
the future post-Adam clock were just days. At the moment of Adam's creation, God
chose to switch to the post-Adam frame of reference, which then became the same
for God and men. What had been only
six days in the pre-Adam frame of reference, in the new frame of reference
common for both the Creator and the creation, would become billions of years. That is what Schroeder tells us.
Can we assert that the above idea is false? We can't. On the other hand, can we assert, based on rational
considerations, that the above idea is true? Again, we can't.
Schroeder's explanation requires a leap of faith. It is fine as long as it is not suggested to be an explanation based on
science. There is nothing
scientific in the notion that God's frame of reference may be vastly different
from men's frame of reference. As
far as faith is considered, the above assertion is not a new one, and is simply
beyond any discussion in rational, scientific terms. Schroeder, though, wants readers to believe that the described
explanation is somehow based on the theory of relativity. It is not.
What the special theory of relativity (STR) has
established is indeed that time flows at different rate in different
"inertial frames of reference." What the STR meant by different
inertial frames of reference was quite rigorously defined. The rate of time flow is different in two such frames of reference which
mechanically move relative to each other with certain constant speeds. To make a period
of time that is billions of years long in one frame of reference, last only six
days in the other frame of reference, these two frames of reference must move
relative to each other with an extremely high speed.
course, to apply this rigorously defined situation to the creation of the
universe according to the Bible requires a considerable stretch of imagination. To satisfy the requirements of the special theory of
relativity, as per Schroeder's explanation, we have to accept that, first, God
is a physical body, second, that it is a body which occupies a certain localized
volume in space, and third, to imagine that, during the six days of creation,
the Creator was rushing at an enormous speed past the universe he was creating. What would then remain from the concept of the omnipresent non-material
God? God performing a marathon - this picture might have been
satisfactory for Schroeder's eight-year old son. For those over eight years of
age, a better choice seems to be relegating the six-days creation story back to
the realm of faith.
his second book  as well as in some more recent postings on the Internet, Schroeder has modified
his interpretation of the biblical story by referring, instead of the special
theory of relativity, to Einstein's general theory of relativity (GTR).
It has been shown in the GTR that gravitational fields also affect
the rate of time flow. In his
second book  and the above paper on the Internet, Schroeder builds his
alleged rational explanation of the six days of creation by calculating in
detail the duration of every of the six days in question in terms of the men's
calendar, using the concept of the time's dependence on gravitation.
The essence of the alleged explanation, given by Schroeder, is as
follows: At the moment of the big bang, a "fireball" was instantly created,
which was pure energy. This embryo
of the emerging universe did not yet contain any mass, and therefore, according
to Schroeder, there was no
gravitation. Along with the
expansion of the emerging universe, energy was transforming into mass (in
accordance with Einstein's famous equation E=mc2). Accompanying the emergence of masses, gravitational forces took hold,
increasing along with the appearance of the ever larger amount of mass. As the gravitational forces grew, the time flow slowed down. Schroeder suggests that the decrease of the rate of time flow followed a
certain mathematical law. What lasted just one (the first) day of creation, on
the scale of our conventional calendar is eight billion years. What lasted one more (the second) day of creation, on the scale of our
conventional calendar was four billion years, etc. The total duration of creation was exactly six days as per
the scale of time which corresponded to the levels of gravitational forces at
each step of the universe's expansion, whereas on our conventional time scale
it lasted about 15 billion years, in full agreement with the scientific data.
It is easy to see that we can represent Schroeder’s implicit calculation by the following formula:
Tn = 1.6 x 1010/2n,
where n =1 for the First day of creation, n=2 for the Second day, etc., and Tn is the duration of the "day" of creation number n on our time scale, expressed in the number of conventional years. Schroeder provides no reason why the rate of the time flow should have gradually decreased according to that rather than to any other regularity except for his desire to reconcile the biblical story with scientific data.
It is easy to imagine how laymen may be impressed by the above
explanation, which looks so elegant on its face. Let us avoid discussion of some minor dubious points in Schroeder's
exercise, concentrating instead on the most egregious misunderstanding of the
matter by Schroeder, which renders his alleged explanation meaningless.
While supposedly utilizing the concept of relativity of time, Schroeder
actually has based his discussion on the concept of an absolute time, thus
contradicting the very premise of his discourse.
To explain Schroeder's distortion of the theory of relativity, let us
first again recall certain concepts of the special theory of relativity using
them as an analogy. The STR had
established relativity of velocity. It
taught us that there is no such thing as absolute velocity. The concept of velocity has meaning only in terms of a
comparison between two (or more) frames of reference. If we considered the entire universe as a single frame of reference, the
concept of velocity would have no meaning. Consider an even simpler example. Imagine
that we are in a plane, which is flying with a constant velocity relative to the
ground. The windows of the plane
are curtained, so we cannot see the ground or clouds. In such a situation there is no way to assert whether the plane is moving
or is stationary. From the viewpoint of physics, there is no difference between
the states of motion with a constant velocity and of being at rest. No physical experiment performed inside that plane would allow us to
distinguish between the states of motion with a constant velocity and remaining
at rest. Therefore, within the
confines of that plane, the concept of its velocity has no meaning. It would acquire meaning though if we had a way to relate the motion of
that plane to some other body (i.e. to some other frame of reference) such as,
for example, the ground. If we
consider now the entire universe as a single frame of reference, there is no
meaning which can be attributed to the velocity of the universe's motion,
unless there is another universe, which could serve as a reference.
There is some analogy between the above situation and the model
suggested by Schroeder. The concept
of different rates of time flow depending on gravitation has a meaningful
interpretation only in terms of at least two different bodies subjected to
different gravitational forces. In
such two systems, clocks would tick at different rates. However, to discover the difference between the mentioned clocks, there
must be a way to compare them to each other.
Schroeder actually considers the universe as a whole, and suggests that
along with the increase in the amount of mass, and, hence, in the level of
gravitation all over the universe, the time flow is slowing down. This consideration has a number of serious flaws. I will discuss here only his most egregious
misinterpretation of the GTR.
As the amount of masses
increased, as postulated by Schroeder, this affected all clocks in the universe
equally. (There are differences
between the clocks located in various parts of the universe, which is though
irrelevant to Schroeder's model). The
universal clock suggested by Schroeder, namely the frequency of Penzias-Wilson radiation, is subjected to that effect as well as any
other imaginable clock. Since all the clocks are subjected to the same effect of
increasing gravitation, there is no way to discover the alleged deceleration of
time's flow. (The extrapolation of the red shift into the past can be
utilized to estimate the length of the universe's existence, but not to
discover or measure the time dilation, not any more than it could be possible to
lift oneself out of a pit by grabbing one's hair with one's own hand and
pulling it up, without any independent point of support). To reveal any
difference in the rate of time flow, one would need an independent clock, which
is not affected by the change of gravitation, and which could be used as a
reference. In other words, one
would need a reference clock, which would be nothing less than a clock showing
absolute time. Such a clock is not known. Since
the alleged deceleration of time's flow cannot be measured, or even
discovered, it has no physical meaning, and has no effect on any physical
processes, unless an absolute time, independent of frames of reference, is
Therefore, what lasted six
days 15 billions years ago, lasts exactly six days now. If there were available some other observable universe, which
could be utilized as an independent frame of reference, then it could be
possible to find out if one day in our century is different from one day 15
billion years ago. As it is, the length of a day in our century is to all
intents and purposes exactly the same as it was 15 billion years ago. This length of the day is necessarily measured in arbitrary units, and
has no definable absolute ("actual") magnitude.
In other words, again, the
difference in the rate of time flow between our time and that fifteen billions
years ago could be attributed some meaning only if there existed absolute time. Since GTR rejects the concept of absolute time, the idea of Schroeder
contradicts the very essence of the theory of relativity, on which he has
allegedly based his model.
Conclusion: Schroeder's attempt to reconcile the biblical tale
about six days of creation with scientific data which assert that the age of the
universe is about 15 billion years, failed. It was based on a misapplication of the theory of
Schroeder's chronology between
the first six days and our time
As Schroeder tells us, at the moment the first man was
created, God instantly switched from his previous frame of reference, in which
the creation took six days, to a new frame of reference, this time the same for
God and men. Since then that frame of reference is the one the mankind lives in. Hence, everything the Bible tells us about events that occurred starting
with Adam's appearance, is chronologically precise. If the Bible says, for example, that Adam was 130 years old when his son
Seth was born, then it is precisely 130 years as we understand them, i.e. the
period of time it took the Earth to make 130 revolutions about the sun. If the Bible says that Adam was created by God 5,750 years before the publication of his book , it means precisely that –
the time the earth circled the sun 5,750 times, counted in the same years we
conventionally mean. Schroeder tells us that the above number
– 5,750 years since Adam - is precisely compatible with the scientifically
established chronology of human history. Here
is the pertinent quote from Schroeder's book (page 31): "In the year 1990,
all the generations since Adam have a cumulative age of 5,750 years. This biblical date for the dawn of recorded history is closely matched by
the archeological finds of the last two centuries."
This is a very impressive statement. The
average reader would be eagerly waiting for proof based on scientific data. Schroeder proceeds to provide such a proof.
His argument in support of his thesis is
twofold. One part of his argument
deals with the beginning of the Bronze age and the other with the nature of those human-like creatures, who, according to archeological data, lived
already thousands years earlier than about 6,000 years ago.
Let us consider both parts of Schroeder's argumentation.
arguments related to the beginning of the Bronze age.
Schroeder juxtaposes the generations of the descendants of Adam's two sons, Seth and Cain. The Bible provides the ages of all the descendants of Seth, starting with
Seth's son Enosh, all the way to Noah, who, at the time of Flood, was 600 years
old. There were nine generations between Seth and Noah. Then Schroeder counts nine generations of descendants of Cain, ending
with Tuval-Cain. The ages of Cain's descendants are not provided in the Bible,
so Schroeder assumes that Tuval-Cain was a contemporary of Noah and from that he
concludes that the time interval between Adam and Tuval-Cain was the same as
between Adam and Noah, i.e. according to Schroeder's calculations, some 1350
years. Subtracting 1350 from 5750,
Schroeder concludes that Tuval-Cain lived about 4400 years ago.
The above calculation is however wrong, and, as we
will see later (when discussing Schroeder's second book ) he himself was
forced to change the above numbers. Schroeder
does not say a single word as to why he has changed the described data in his
second book. It is sufficient,
though, to read the pertinent verses (4:20 to 4:22) in the Book of Genesis to
see the source of Schroeder's error. While
counting generations between Cain and Tuval-Cain, Schroeder includes in his
count Iaval (the seventh generation) and Yuval (the eighth generation), although it is clearly said in those verses that
Yaval (also sometimes transliterated as Jabal) and Yuval (Jubal) were not the
grandfather and the father of Tuval-Cain, but rather his half-brothers, as they
all were sons of Lemach. Hence,
Tuval-Cain, according to the Bible, belonged to the seventh generation after
Cain rather than to the ninth. This
shifts Tuval-Cain's lifetime back several hundred years from Schroeder's
assertion in his first book.
However, since we are now discussing the first book where Schroeder has based important
and far-reaching conclusions on the above numbers, let us accept those numbers
for further discussion, especially since in his second book Schroeder did not
change his conclusions based on the above dates.
As the next step, Schroeder tells us that Tuval-Cain,
according to the Bible, was the inventor of bronze. Hence, according to Schroeder, the Bible informs us that the
Bronze age started about 4400 years ago. This,
asserts Schroeder, is precisely what the science tells us! What a proof of complete compatibility of the Bible and science!
Is it indeed?
Let us check precisely what the Bible says about
that. Schroeder refers to Genesis
4:22. Let us look at that
reference. Here is the literal
translation into English of the text of the book of Genesis, 4:22: "Also Zillah gave birth to Tuval-Cain, smith of all cutting tools of
copper and iron..."
Note that the last two words (copper and iron) are, in
the Hebrew text, "nekhoshet ubarzel." Schroeder tells us that in the early Hebrew the word "nekhoshet"
(which he transliterated as "nhoshet") meant both bronze and brass.
Of course, this can only be guessed, since the literal
meaning of that word is copper, whereas the Hebrew word for bronze is arad
and for brass it is pliz. However,
the words arad and pliz are absent in the text of the Torah, which
may indicate that these words appeared in the Hebrew vocabulary later than the
Torah was written. Therefore it is possible that the word nekhoshet (Nun-Khet-Shin-Tav) was indeed used in that context to denote not just
pure copper but also copper-based alloys like bronze and brass.
However, it is hard not to notice that Schroeder, in
his quest for the chronological coincidence between the Biblical account and
scientific data, conveniently pretends not to notice in the same passage about
Tuval-Cain the word "barzel," which means iron. If Tuval-Cain made tools not only of copper or bronze, but also of iron,
then we must place his lifetime at a much later date than Schroeder wants us to
believe. The use of iron started, roughly, some fifteen centuries after that of
bronze. Hence, just one word
omitted by Schroeder in his reference to the biblical text makes his
chronological exercise ingloriously collapse. Moreover, the glaring omission of that reference to iron, which obviously
could be only deliberate, undermines all of Schroeder's arguments, making his
attitude suspect of being not quite impartial. There goes all Schroeder's
As we will see, in his second book, where Schroeder
changes the dates (without any explanation for the reason) the described
discrepancy is only exacerbated.
arguments related to archeological data about times earlier than 5760 years ago
Having successfully, in his view, dealt with the
beginning of the Bronze age, Schroeder faced another controversy between
science and the Bible. According to
the Bible, the first man, Adam, was created less than 6,000 years ago. On the other hand, archeological data indicate that creatures possessing
many characteristics of humans lived at much earlier time. To reconcile these two viewpoints Schroeder advances some rather clever
explanations. According to his
suggestion, the human-like creatures that lived before Adam were not really
human. They were, Schroeder tells us, animals which had some characteristics in
common with post-Adam humans, but did not possess a human soul (in Hebrew - neshamah). Adam, according to that explanation. was the first real man, the first to
receive from God his neshamah, whereas pre-Adam humanlike animals did not
Before discussing in detail Schroeder's notion about
Adam being the first real human possessing the "neshamah" let
us make note of the following historical evidence. If we believe Schroeder, at a certain moment in the history of men, namely less than 6,000 years ego, a revolutionary event occurred
which radically changed the nature of the humanlike animals converting them into
real humans, who were given the "neshama," thus separating them in a crucial manner from all other animals. There is, though, historic evidence that, for example in the country of
Egypt, a well organized state existed earlier than 6,000 years ago. There is plenty of information about that state. If at a certain moment, about 6,000 years ago, a revolutionary change in
the nature of men took place, wouldn't we expect that such an event would be
somehow reflected in the records pertaining to that time? There is no evidence whatsoever in the scientifically established history
of Egypt which would indicate any radical change in the nature of men at the
above mentioned time.
To further discuss Schroeder's clever explanation we
have to define what distinguishes a man from an animal. In that endeavor I will not argue against Schroeder's contention that
pre-Adam humanlike creatures did not possess a neshamah, because this
notion cannot be either proven or rejected based on any rationally acceptable
evidence. It is a matter of faith, and in this article I do not argue either in
favor or against faith. We can, though, try to establish some verifiable
criteria which would enable us to distinguish between animals and men.
It seems reasonable to assume that the following
features are usual characteristics of humans while absent in animals:
Humans possess language, necessarily spoken and more
often than not also written. Each human language has a well defined grammatical
structure. No animals have a real language (unless the word language is
applied to the primitive systems of sounds used by some animals, like dolphins
or chimpanzees, which lack any
grammatical structure and have an extremely limited "vocabulary"). Of
course, no animal uses a written language.
Humans often form societies comprising thousands of
members, structured vertically with many layers of hierarchy. The closest form of a hierarchy in the animal world is that in a family,
say, of wolves, apes, or lions. The human society often forms a government and a
law system. There is no equivalent to a government in the animal world
(where the formations closest to a society are cattle herds and wolf packs).
Humans usually develop technologies aimed at improving
their standard of living. These
technologies involve building living quarters, making tools for acquiring food
and clothing, etc. Humans possess
an obvious capacity to improve the design of their creations and to invent new
forms of technology. Some animals
also build living quarters or even construct dams (beavers) and the like, but
they never change the scheme of those constructions and have no evident capacity
to improve and to invent.
Humans typically develop arts, including music, dance,
and art of images (like painting). No
animals are known to have any form of art.
Finally, humans often develop some form of religion,
whereas no animals are known to have any religious concepts or any notion of a
deity (unless you believe your dog considers you to be God). I assume the development of religion can very decisively distinguish real
man from any other humanlike or non-humanlike creature.
If we account for the above points, then, according to
Schroeder's concept, the humanlike predecessors of Adam who had not really been
humans, but just humanlike animals, did not have a written language, did not
have a law system, did not have any government, did not have any art and did not
have any religion.
Archeological data strongly contradict the above
In this article I do not try to prove either the
biblical or the scientific viewpoint, leaving it to each reader to decide for
him/herself whether to accept the biblical or the scientific side of the story. My goal in this article is only to test Schroeder's arguments in regard
to the absence of contradiction between the above two views. Since Schroeder accepts equally both world outlooks, we have no need to
judge the merits of either of the two views, but only to see if these two views
can be logically reconciled.
What is the Bible's story? It says that the first man
walked on the earth roughly 6,000 years ago.
What is the scientific story? It is rather different.
Archeological data indicate that humanlike creatures
made tools of stone as early as about 40,000 years ago. Is any animal known to shape stones into tools?
The color pictures of animals had been drawn on rocks
as early as about 27,000 years ago (for example, the image of a horse in Pech
Merle, France). What animal is
known to engage in art?
As archeological data indicate, as early as 23,000
years ago humanlike creatures used to embellish their looks by means of beads
attached to their clothing. Is
there any animal known to use artificially made clothing and, moreover, to
embellish them in any way?
Archeological data indicate that as early as 18,000
years ago humanlike creatures used needles made of bones to sew clothing. Is there any animal known to sew clothing?
Archeological data indicate that the bow and arrow was
already in use about 11,000 years ago. Is
there any animal capable of inventing and using sophisticated tools such as the
bow and arrow?
Archeological data indicate that as early as about
9,000 years ago humanlike creatures already used pottery. To make the pottery, those humanlike creatures used kilns
where the temperature reached about 1000 degrees. Is there any animal capable of
constructing kilns and, moreover, of making and utilizing pottery?
At about the same time, some 9,000 years ago, the
humanlike creatures built settlements occupying over two hectares each, where
buildings were used as living quarters and as storage sheds. About 8,000 years
ago, the size of such settlements was sometimes up to 15 hectares. The
inhabitants of those settlements used artificial irrigation and grew crops. They
used seals, which proves the existence of some form of a writing system and of
some form of documentation. Are there any animals known for building villages,
using artificial irrigation, growing crops, and using a writing system and a
Finally, one more thing archeology tells us about is
as follows: As early as about 8,000 years ago, that is some 2,000 years before
the date, when, according to the Bible, the first man, Adam, appeared, humanlike
creatures (as, for example, inhabitants of the Sumerian settlement at Tepe Gawra
in Mesopotamia) systematically built, in the centers of their villages,
religious shrines and temples. Is
there an animal, however intelligent, that is known to have any religious
What we can say with a reasonable confidence, is that
the arguments by Schroeder aimed at
proving the compatibility of the biblical and the scientific accounts, fall
apart at even a perfunctory glance.
3. Schroeder estimates probabilities
In the chapters dealing with probabilities,
Schroeder's attitude is different from that in the chapters dealing with
chronology. In the latter,
Schroeder fully accepted scientific data and tried to reconcile them with the
biblical story. That attitude was due to Schroeder's
opinion that the archeological data are so firmly established that refuting them
would be surely a losing proposition. Hence,
to salvage his belief in the biblical story Schroeder had no other resort but to
look for a way to reconcile the biblical and the archeological stories. As the previous sections of this paper have demonstrated, Schroeder failed in his attempt.
In the chapters dealing with probabilistic estimates
in regard to the origin of life, Schroeder
felt more comfortable in adhering to the biblical story because the origin of
life, as suggested in science, has not been proven scientifically to the same
irrefutable extent as the archeological data. Therefore, when dealing with the origin of life, Schroeder seems to be confident in his ability to refute the scientific
hypothesis in favor of the biblical story. There are no more attempts to reconcile the scientific and the biblical
views, but rather an unequivocal rejection of the scientific hypothesis, and an
equally unequivocal acceptance of the biblical story.
The scientific hypothesis is based on the assumption
that life emerged spontaneously as a result of chance interactions between
chemicals in the primeval atmosphere of the Earth several billions years ago. Another version of that hypothesis suggests that life could have been
brought to the Earth from some other worlds, where it originated spontaneously via
the above mentioned, largely stochastic process.
Schroeder has based his refutation of the above
hypothesis on certain probabilistic considerations. For example, on page 111 of his book  he wrote about the
scientists who adhere to the above scientific hypothesis: "These scientists
were making assumptions without any attempt to rigorously investigate the
probability of such events." Obviously,
what Schroeder wants us to believe is that unlike those less-than-rigorous
scientists, he has rigorously investigated the probability of a spontaneous
emergence of life via chance occurrence of chemical interactions. The conclusion Schroeder extracted from his rigorous investigation was
that spontaneous emergence of life was impossible because the time needed for
such an event to occur is so immense as to exceed the entire duration of the
existence of the universe. This
conclusion is far from being new and has been advanced an uncounted number of
times by the defenders of the biblical story.
The above consideration in turn is based on a certain
interpretation of the concept of probability, which Schroeder shares and tries
to explain. The essence of the
interpretation in question can be best illustrated by quoting again from
Schroeder's book (page 113):
"The probability of duplicating, by chance, two identical protein chains,
each with 100 amino-acids, is 1 chance in 20100, which equals the
digit 1 followed by 130 zeroes..."
While the arithmetic in the quoted segment is not
exactly correct (the actual expression contains many digits other than zeroes),
in principle Schroeder's statement is correct in that the probability in
question is indeed an extremely small number. However, as Schroeder continues, his further reasoning becomes contrary
to the correct concept of probability.
This is what follows on page 113: "To reach the
probable condition that a single protein might have developed by chance, we
would need 10110 trials to have been completed each second since the
start of the time. To carry out these concurrent trials, the feed stock of the
reactions would require 1090 grams of carbon. But the entire mass of the Earth (all elements combined) is only 6x1027
What a triumph for the opponents of the hypothesis of
the spontaneous emergence of life! What a nice calculation! What an impressive
statement so categorically demolishing the hypothesis of the spontaneous
emergence of life! If only these
statements and arguments were correct beyond the sheer arithmetic!
In reality, the above argumentation is wrong. It misinterprets the meaning of probability. If that argumentation were correct, then we would have to accept that to
win big in a California lottery, where the chance of winning the jackpot is
about 1 in 16,000,000, one necessarily needs to play the lottery 16,000,000
times. We know, though, that some
people have won big, having bought just one ticket the first time in their life.
Such a smile by the Lady luck happened more than once, defying the 16
The concept of probability and its application is
discussed in detail in my article Improbable Probabilities. That discussion demonstrates the
lack of substantiation in Schroeder's position.
The value of probability does not provide any
information in regard to what will occur in any individual trial. If the probability of an event is one out of trillion of
trillions, there is nothing surprising if that event actually occurs in a
particular trial, since its appearance is as likely as of any other equally
probable event. From this
standpoint, the arguments by Schroeder based on the very small calculated
probability of life emerging as a result of random chemical reactions are
meaningless, since a small calculated probability in no way means the
impossibility of an event.
Moreover, there are many situations where the possible
event are not equally probable. As
it is shown in my article on probabilities, referred to above, the calculated probability in a
certain sense reflects the level of information available about the object whose
behavior is being guessed, rather
than the objective likelihood of the event in question.
In regard to the random chemical reactions in the
primordial atmosphere, the
assumption of equiprobability has no foundation. Some chemical interactions must have been much more likely than some
others. Certain conditions in the
primordial atmosphere could have been conducive to certain interactions while
inhibiting some other interactions. Under
certain conditions, powerful catalytic effects could have emerged, greatly
enhancing the likelihood of interactions which would become steps toward the
emergence of life. Schroeder's calculations of probabilities completely ignore
such alternatives and are therefore nowhere near a reasonable proof.
Furthermore, the theories of the life emergence do not suggest that it was a single act wherein all the components of the living matter came together at once by sheer chance. On the contrary, the scientific theories suggest that life emerged as a result of many small steps each requiring a chance combination of only a very few components and hence having a reasonably large probability. This consideration alone makes Shroeder's calculations irrelevant.
Moreover, even if the probability of a spontaneous life emergence is assumed to have been very low, it is not a valid argument against its possibility. Life emerged at some time in the past. Whatever the steps were this process included, it was just one among a very large number N of possible (but by no means equally probable) events. Its calculated probability, however small it happens to be, has by itself no cognitive value. Any other of N possible events could have occurred, but did not. Maybe some of those N-1 events which did not happen would be as complex and amazing as life is. We will never know the answer to that. Hence the argument by Schroeder based on the calculation of probabilities of life emerging through some sequence of randomly occurring chemical reactions is meaningless. Equally unfounded are his calculations of the time allegedly necessary for such reactions to take place. If certain interaction were catalytically enhanced, with each step increasing the likelihood of the next consecutive step toward the emergence of life, the time necessary for the emergence of proteins was actually shorter by many orders of magnitude than that calculated by Schroeder.
Can the above considerations serve as proof that life
emerged spontaneously rather than having been created by a divine design?
Admittedly, it cannot. However, it
shows that the hypothesis of the spontaneous emergence of life does not
contradict any probabilistic considerations. The consideration of probabilities
by Schroeder cannot serve as a proof to the contrary.
Contrary to his proclaimed intention, Schroeder failed to
demonstrate the compatibility of the biblical account with the scientific view
in regard to the origin of life, whereas his probabilistic considerations are
4. Some specific faults and errors in Schroeder's book
Besides the above discussed general weaknesses of Schroeder's case, his book
contains a plethora of small and not so small specific erroneous statements and
arguments. Some of those faults will be discussed in this section.
Bible code example.
On page 182 of Schroeder's book, we read: "I
offer here only two examples of the thousands of subtleties found in the
first example offered by Schroeder is that of the so-called Bible code. The
Bible code controversy is discussed in detail, for example, at B-Codes Page where the lack of substantiation of the claims of the Bible code
proponents is shown. Schroeder's discourse is limited to a few primitive
examples which lack any statistical significance and testify to Schroeder's
amateurish level of familiarity with the subject he endeavored to discuss
2) Is weight and mass the same? Is kinetic energy proportional to velocity? Are the
laws of physics "nothing more" than laws of nature?
The above questions sound silly if one discusses
statements by a physicist, especially one with a Ph.D. degree. Unfortunately, Schroeder provides reason to raise the above questions. For example, on page 40 of his book  Schroeder writes : "The mass
(or weight) of the object while at rest is called, in technical terms, its rest
mass." I find it hard to
believe that a Ph.D. in physics could indeed think that mass and weight are the
same. I prefer to interpret the above sentence as a display of sloppiness in
style rather than of ignorance. This interpretation is reinforced by the use of
the words "in technical terms" which do not seem to convey any
meaning. In which non-technical
terms is the mass "while at rest" called something else rather
then rest mass?
Unfortunately for the above relatively benign
interpretation, Schroeder expresses himself in the same way more than once. The same expression "mass (or weight)" appears, for example, on
page 37, giving rise to suspicion that Schroeder may actually believe that mass
is the same as weight. Such a statement made by an undergraduate student on an
exam in general physics would result in an immediate F grade. The rest mass is a
body's property, a constant independent of the frame of reference, whereas the
total (or relativistic) mass is a function of velocity, and, as such, depends on
the choice of frame of reference. The
body's weight is a completely different quantity, reflecting the interaction of
the body in question with a planet. It
depends on both the mass of the body in question and the mass of the planet and,
in the first approximation, on the squared distance from that planet's center
(assuming the body in question is much smaller than the planet or has spherical
shape itself). I am sure Schroeder had studied these facts as a student.
On the same page Schroeder writes: "It acquires velocity and in so doing acquires kinetic energy
proportional to the velocity." Come
on, Dr. Schroeder! Don't you know
that kinetic energy is proportional to squared velocity? Is it sloppiness
On page 41 we find one more expression which, to put
it mildly, sounds strange from a Ph.D. in physics. I quote: "...laws of
Physics (which are no more than laws of nature)...." Are they indeed? Schroeder seems to be unaware that laws of physics are postulates based
on interpretation of experimental evidence. At the best, the laws of physics can be considered our guesses as to what
the reasonable approximation of laws of nature can be. Laws of nature supposedly
did not change from, say, the 17th to the 20th century, whereas the laws of
physics have gone through drastic modifications and many amendments.
There are more examples of very dubious statements by
Schroeder, and it is immaterial whether they stemmed from a lack of knowledge or a lack of meticulousness in writing a book which supposedly
sheds light on important matters.
Just a couple more of examples of less than
accurate ways Dr. Schroeder expresses himself. On page 100 we read: "We see randomness of entropy increase in every
observable system." This
is gobbledygook. Entropy itself is a measure of disorder, i.e. of randomness. The expression "randomness of entropy" is devoid of any
Page 117: "The centrifugal force of the spin
flattened the cloud into a disk." This is one more display of either a lack of sufficient understanding or
of stylistic sloppiness. Centrifugal
force is what is called in physics force of inertia. It is considered to be a
fictional force. The real force in
this case is centripetal force, caused by gravitation. It is convenient in certain cases to use the concept of
centrifugal force when writing certain equations. (It is sometimes referred to as D'Alembert's principle). However, saying that centrifugal force "flattened the cloud"
means veiling the essence of the matter in a cloud of a meaningless phraseology.
Further examples of less than reliable statements
could be given.
5. Schroeder's second book
Now let us discuss the second book by Schroeder,
The Science of God, subtitled "The Convergence of Scientific
and Biblical Wisdom" . It
is considerably larger than the first book. Judging by the size and the title, one might expect that the second book
would continue and expand on the subject of the first book. Indeed, to some extent it turns out to be true, as Schroeder repeats in
his second book a number of points discussed in the first book, partially
modifying and adding to them.
On the other hand, the second book differs rather
substantially from the first one. One
difference is that in the first book Schroeder limited himself to a relatively
narrow circle of topics, while in the second book he tries to cover a much
larger scope of problems. One of
the results is a loss of the sharpness of the book's focus. Various chapters discuss questions sometimes little related to each
other, hence, instead of the relatively clear plan in the first book, in the
second one we see a farrago of topics and subjects, each discussed separately. This situation dictates as well the form of my review. Unlike with the first book, this time I will discuss various aspects of
Schroeder's second book one by one, without subordinating the discussion to any
Another peculiarity of Schroeder's second book
is its uneven character. One can
indicate some well written passages in that book, where the subject is explained
correctly and in an easily comprehensible form. On the other hand, many sections contain factual errors,
sometimes of an elementary nature and sounding quite odd, if we remember that
the writer claims to be an experienced physicist with a Ph.D. degree. We will discuss examples of both types.
Finally, one more feature of the book in question: in this book Schroeder provides data which contradict the data given in
his own first book, without a word of explanation. We start with the discussion of precisely this feature.
6. Change of dates in the second book compared to the first one
One of the differences between the first and the
second books by Schroeder relates to the chronological data in regard to Noah,
the Flood, Tuval-Cain, and the onset of the Bronze age.
In his first book, Schroeder calculated that the
interval of time between Adam and Tuval-Cain was about 1350 years, that Tuval-Cain
was a contemporary of Noah, and that the Bronze age started some 4400 years ago
(pages 31-32 and Table 2 in the first book ). In the second book  the
onset of the Bronze age is said to have happened about 5000 years ago, i.e.
about 600 years earlier than in the first book (see, for example, page 131 in
). Furthermore, on page 130 of
 Schroeder maintains that the time interval between Adam and Tuval-Cain was
700 years, instead of the 1350 years he indicated in . On the other hand, in  (page
131) the date of the Flood is said to be about 4100 years ago, which is about 900 years
later than that date of the advent of Bronze which is given in that book. According to these altered dates, Tuval-Cain is no longer
considered to be Noah's contemporary, since the invention of bronze, attributed
by Schroeder to Tuval-Cain, is now said to have happened 900 years earlier than in . Schroeder does not provide a single word of explanation as
to why he changed the dates after his first book.
As was indicated in the
previous sections of this article, the above alteration of dates was apparently
done because somebody had shown to Schroeder the error in his count of
generations between Cain and Tuval-Cain in his first book.
If a writer changes his views, are the readers not
entitled to at least some explanation?
Despite the change of dates, Schroeder still asserts
in his second book that the advent of the Bronze age, according to the
archeological data, precisely coincides with the biblical story (as per his
calculations). Like in his
first book, Schroeder again pretends not to notice the statement in Genesis 4.22
indicating that Tuval-Cain also made tools
of iron. Since in the second book
the lifetime of Tuval-Cain is shifted back by some 900 years, it makes it even
farther in time from the iron age as determined by archeology. This completely undermines Schroeder's chronological exercise.
Zero time interval in frames of reference moving with the speed of light?
The section in question (pages 161-164) describes the "shrinking of time" in fast moving frames of reference according to the theory of relativity. As that theory asserts, the time interval between two events which occur at the same location within some frame of reference and measured in that frame of reference is always shorter than the time interval between the same events, measured in another frame of reference which moves with a certain speed relative to the first frame of reference, so in that second frame of reference the events in question occur at different locations. The larger the speed of motion of one frame of reference relative to the other one, the larger the difference between the time intervals. If the speed approaches speed of light, the "local" time interval approaches zero.
Schroeder considers the example of a light signal which carries information about the explosion of a supernova that occurred 170 thousand years ago (measured in the earth's time). Since the supernova (1978A) is located 170 thousand light years from the earth, the light signal took exactly that long to reach the earth. Since, though, the light signal moves with the speed of light, the flow of time in the frame of reference attached to the signal "stopped." If there existed an observer "living" in the frame of reference of the signal, (which is impossible as no physical body can move with the speed of light) for "him" the explosion of the supernova and the arrival of the signal on Earth would have happened simultaneously.
Schroeder's explanation entails a serious flaw. A frame of reference which can be attached to photons simply does not exist. If it existed, the photons would be at rest in such a system. However, photons cannot be at rest. According to the special theory of relativity, photons always move with the same speed (in vacuum) in every frame of reference. If a frame of reference wherein photons are at rest existed, time would stop in such a frame. Since, though, no such frames of reference are possible, Schroeder's concept is meaningless.
Of course, in accordance with his agenda, Schroeder tries to prove the analogy between the described alleged "paradox" of the theory of relativity and the concept of God being "outside time." The concept of God being "outside time" belongs to the realm of faith and has nothing in common with the non-existing effect of "time stopping" in systems moving with the speed of light. Schroeder's attempt, inadvertently invoking the image of God running with speed of light past stars and planets in order to satisfy the conditions of the theory of relativity, can only discredit Schroeder's approach, and, with it, the concepts of faith themselves.
8. Diffraction of waves according to Schroeder
On pages 150-151 in  Schroeder explains the
diffraction of waves. Like his example about the light signal from a supernova, these paragraphs have been well written. Up to a certain point,
Schroeder's explanations are correct and explain the diffraction, using the
example of sea waves, in an easily comprehensible form. Unfortunately, in this case too, Schroeder failed to maintain the
competent level of discourse throughout his presentation. As long as Schroeder considers diffraction on an opening whose size is
close to the wavelength, his explanation is correct. However, it becomes wrong when he talks about openings whose size exceeds
the wavelength. Indeed, on page 150
he asserts that diffraction does not take place if the opening's size is larger
than the wavelength.
If that assertion were correct, it would make it
possible to build optical microscopes with an unlimited magnification. The ingress aperture of a microscope is much larger than the wavelength
of visible light. If
there were no diffraction on that aperture, then, utilizing a large number of
consecutive lenses, one could reach a magnification of many millions without
resorting to electron microscopy. Alas,
diffraction puts a limit on the resolving power of any optical device, and with
it on the useful magnification.
In the simplest case of diffraction on a single
opening, increasing the opening's size does not eliminate diffraction but rather
widens the central diffraction maximum, pushing the maxima of higher order to
the opening's edges, and squeezing them closer to each other. Diffraction is inevitable even if one of the opening's edges lies
infinitely far, so actually rather than to speak about an opening, in this case
one has to consider the wave's motion past the corner of an opaque wall. Diffraction
always takes place if there is any constraint imposed on the free propagation of
The above is one of many examples of imprecision typical
of Schroeder's style, casting shadow on all of his arguments.
9. Diluted heat and masers
In this section I will discuss a number of the
particular errors which are abundant in Schroeder's second book.
page 152, at the beginning of a section titled "The discovery of
wave-particle duality" Schroeder tells the story of the discovery and
interpretation of the photoelectric effect. Here, within a half-page, he manages to accumulate a long list of errors.
Schroeder starts with the statement that in 1905 Einstein published the results of experiments that demonstrated what has become
known as the "photoelectric effect." In fact, Einstein did not publish any experimental data
on photo effect because he never performed any such experiments. The photoelectric effect was discovered and partially studied by Heinrich
Hertz more than 25 years earlier. Einstein
offered in his paper a theory of that effect.
Schroeder writes further:
"Light, shining on certain metals, knocks free a stream of
electrons..." In fact,
not "certain metals," but every metal or semiconductor.
Schroeder continues: "Einstein demonstrated that
the rate at which electrons are emitted from metal is related not only to the
intensity of the light beam but also to the color of the light." This is an incorrect statement. The rate of electron emission, i.e. the
number of electrons emitted per second, does
depend on the light intensity but does not depend on the "color" of the light. What indeed
depends on the "color" of the light, i.e. on the wavelength, is the
kinetic energy of the emitted electrons. Also,
Einstein did not demonstrate this, as the dependence of electron's kinetic
energy, measured via the so- called "stopping
voltage, " on the wavelength of light, had already been discovered by
2) On page 154 Schroeder describes experiments with a
beam of atoms directed toward a plate with slits in it. He wrote: "Here we use a maser, a gun that can fire one atom at a
A reader familiar at least with some rudimentary
information in physics or electronics, must wonder whether Schroeder has less understanding of atoms or of masers. It is known that word
"maser" is the abbreviation for the expression "Microwave
Amplification by Stimulated Emission of Radiation." No maser is capable of firing atoms, either one by one or in groups. Most commonly masers are used as sources of coherent electromagnetic radiation in the microwave range. A version of a maser
that works in the range of visible light is sometimes called the optical maser,
but more often, laser, which has by now become a ubiquitous component of many
appliances, including, for example, CD players. Schroeder could acquire that information from any technical handbook or
It would be possible to continue a discussion of many
erroneous and unsubstantiated statements in Schroeder's second book.I feel, however, that I have already spent much more time and effort on
the analysis of that opus than it deserves.
Therefore I will make only one more comment.
On page 180 we read: "The cooling effect of an
expansion is logical. It is the
dilution of a given amount of heat in an ever larger volume."
From the viewpoint of elementary thermodynamics,
Schroeder's statement is nothing short of a bad joke. If Schroeder opened a textbook on physics, the chapter on
thermodynamics, he would learn or recall that heat cannot be "diluted"
in whatever volume. The expression
used by Schroeder gives rise to an impression that, however hard it is to
believe, he still adheres to the theory of caloric fluid, abandoned by science
as erroneous since Rumford (1796). It
is a trivial knowledge in physics that heat is not a substance which is
contained within a volume.
On page 183
Schroeder repeats his meaningless statement about "heat dilution."
Heat is defined in thermodynamics as a quantity
analogous to work and serving as a measure of energy transformation, provided
such a transformation occurs via random molecular interactions. This quantity cannot experience a dilution either at expansion or in any
other process. Of course, it is
possible that Schroeder improperly used the term heat, actually having in mind a component of the internal energy which is
actually the kinetic energy of molecular motion, and which often is referred to
as thermal energy. If this is the
case, it still does not make Schroeder's notion about the reason for a
temperature drop at expansion correct. According to the first law of
thermodynamics, the temperature drop at expansion occurs because the work of
expansion is done at the expense of the internal energy, and the temperature is
the measure of that energy. Expansion
causes not a "dilution"
of thermal energy, but the decrease of the root-mean-square speed of molecular
example, expansion into vacuum is an isothermal process. This means that if a system expands into vacuum, its temperature remains
constant (because no work is done in such a process). Expansion itself cannot cause a system's temperature drop, which occurs
only if, in the course of expansion, some work is done by the system.
It should be noted that the application of thermodynamics to the universe as a whole is uncertain (which
in no way justifies the ridiculous invention of a "heat dilution" by
Schroeder). The theory of
universe's expansion after the big bang does not explain where the universe
was expanding to. Actually this
theory seems to imply that the expansion occurred into "nothing," whatever
the meaning of that word can be. This "nothing" is of course not what within
the universe is referred to as vacuum.
above uncertainty calls for a question, why the temperature of the universe
dropped along with its expansion? Thermodynamics
per se cannot provide a direct and
detailed answer to that question. However,
we may reasonably expect that at least the most fundamental laws of physics,
including the energy conservation law, retain validity when we discuss the
expansion of the universe. In view
of that, the cooling down of the universe can be hypothesized as the result of
the endothermic nature of the
processes in which stars, galaxies, chemical elements, etc, had been created out
of the primordial "hot soup," postulated by the theory. Enormous amounts of thermal energy of the primordial "fireball"
converted into other forms of energy, including the energy potentially contained
in the created masses, as per Einstein's equation (E=mc2).
to address the complex question of the universe's cooling by inventing the
meaningless "dilution of heat in ever increasing volume" tells much more
about Schroeder's scientific competence than about the subject of the
10. Schroeder's third book
his latest book  Schroeder mainly discusses various aspects of molecular
biology, while the sections dealing with physics occupy only a small part of the
book. Since I am not an expert in
molecular biology, I will not argue against Schroeder's excursion into that
marvelous science. Schroeder is a
physicist by education hence he is as much a dilettante in biology as I am. Any
dispute between him and me in regard to biology would therefore be like a
dispute between two blind men regarding the quality of a beautiful landscape
painted by a famous artist. However,
I am qualified to argue against Schroeder's errors when he endeavors to
discuss physics. Given the sad fact
that he was awarded a PhD degree in physics by a prestigious institution, the
elementary errors in Schroeder's discourse are simply stunning.
Here is an example.
page 38 of his book Schroeder suggested the following equation:
where h is Planck's constant, f
is the frequency of deBroglie's wave for a particle, m is the
particle's mass and c is speed of light.
Whereas equation (1) is absurd, it is easy to
figure out how Schroeder derived it. He read somewhere about the following correct equations :
and 2) E=mc2.......................(3)
Equation (2) was originally suggested by Planck
(in 1900) for the quantum of energy emitted by a black body. In 1905, Einstein
applied that equation to the energy of photons regardless of whether they are
emitted, traveling or absorbed by a material. In 1923 de Broglie suggested to expand the application of that
equation to all particles, either massless as a photon or having a rest mass
m. As to equation (3), it is
probably the most widely known equation of science derived by Einstein in 1905 as
a part of his special theory of relativity.
In both equations (2) and (3) E denotes energy of a particle. Obviously lacking proper
understanding of these two equations, and seeing the same letter E on the
left side of both, Schroeder mechanically combined the equations (2) and (3)
into one equation (1).
for Schroeder, he obviously did not know that E in equation (2) and E
in equation (3), while both denoting the energy of a particle, actually denote
two different energies. E in
equation (2) denotes the variable energy of a moving particle, related to
that particle's momentum. E
in equation (3) is a constant for a given particle, which denotes the
so-called rest energy. These two types of particle's energy have little to do
with each other. The absurdity of
Schroeder's equation (1) is immediately obvious when we notice that it
equalizes a variable quantity to a constant. Indeed, the frequency f
of de Broglie wave for a particle is not a fixed constant but depends on
the particle's momentum, i.e. on its velocity.
Schroeder could have easily realized the senselessness of his equation
(1) if he thought for a minute what are the values of the quantities in that
constant equals about h=6.626.10-34 J.s while the speed of light
equals c=2.997.108 m/s. Let
us apply Schroeder's equation (1), for example, to the electron. The mass of an electron is close to 9.1x10-31kg. Then the right side of equation (1), i.e. the electron's rest energy is
about 8.17x10-14 Joule, or about 5.1x105 eV (electron-volt). Hence, if Schroeder's equation (1) were correct, all
electrons in the world would always have the same energy of about 5.1x105 eV.
To have such level of energy, free electrons must be accelerated by a voltage a
little more than half a million volt. Of
course, different electrons (as well as any other particles) actually possess
different levels of energy in a wide range rather than all having the same
energy of about half a million electron-volt.
In fact, an
equation formally looking like equation (1) can be legitimately written for the
process of particle-antiparticle annihilation. For example, for an electron-positron annihilation an
equation looking like (1) would be correct if m denoted the electron's (or,
equally, the positron's) mass and hf
the energy of one of the two gamma-photons emerging as a result of those
particles' mutual annihilation. The imprecision would in this case be only due
to neglecting those constituents of the particle's energy which do not
originate from its rest mass (such as kinetic energy of the particle's motion
etc). Anyway, though, this case has
nothing to do with Schroeder's discourse and with de Broglie's wave.
The equation (1) is not the only error in Schroeder's new book.
However, it seems sufficient to limit the demonstration of the inaccuracies in
Schroeder's literary production to the above examples.
Since Schroeder's insufficient competence in physics, which is
his professional field, is obvious, what credibility can be given to his lengthy
discourse on molecular biology which is not his professional field? Moreover, what credibility can be given to his general thesis asserting
the alleged harmony between the Bible and science?
 Gerald L. Schroeder, Genesis and the Big
Bang, The discovery of the harmony between modern science and the Bible.
Bantam Books, 1992.
 Gerald L. Schroeder,
The Science of God. The Convergence of Scientific and Biblical Wisdom, The
Free Press, 1997.
 Gerald L. Schroeder,
The Hidden Face of God, How Science Reveals the Ultimate Truth, The Free
 David Halliday,
Robert Resnick and Jearl Walker, Fundamentals of Physics, John Wiley
& Son, Inc., 1993.
Mark Perakh's home page.