The Many-Worlds interpretation of quantum physics
From Absolute Indetermination to Relative
The idea is to dismiss the reality of the collapse, consider that
the deterministic evolution without collapse is all what happens,
and admit a persisting coexistence of all possibilities in
parallel worlds, in each of which things would only "look as if"
the collapse happened.
For this, the physical measurement process is analyzed as an
emergent macroscopic process called decoherence.
By applying the deterministic quantum evolution of physical states
(without measurement) to the case of the measurement apparatus, we
deduce that the systems, starting from a "clearly identified"
initial state, naturally evolves into a very complex state of
correlation with the environment. In an emergent manner, the
higher and higher complexity of this entanglement involving larger
and larger parts of the environment turns out to be irreversible,
so that for all practical purposes the quantum state of the whole
system (the measurement apparatus correlated with escaping parts
of the environment) behaves as a classically probabilistic
superposition of states expressing the possible measurement
results, whose probabilities are exactly those that the basic
axioms of quantum theory initially expressed on the system that
was to be measured.
For details, see my texts :
The trouble with probabilities
The trouble is that, while the result indeed has the right mathematical
structure of the expected probabilistic outcome, the ontological
meaning of probabilities is lost: the different possible
results keep coexisting, carrying weights corresponding to
their "probability of being real". But, in this interpretation,
there is no more such a thing as a fact of the matter, of which
possibility becomes real. All possibilities remain real, so that
the problem is to make sense of their "weights" and what can they
have to do with the intuitive idea, or the experience, of
These weights (values of the "probabilities" given by Born's rule)
need to make objective ontological sense, in order to account for
the objective experimental fact that measurement outcomes appear
to follow (at least roughly) these probability laws.
A naive idea would be to try identifying the probabilities as the
ratio of the numbers of resulting parallel worlds. This cannot
work at all. First, because in many cases there is just a small
number of possible elementary measurement results, while the
values of their probabilities are arbitrary real numbers that have
nothing to do with any counting of possibilities. Then, because
the only thing that the number of copies of a given possible world
really depends on, is the amount of time waited to let it split
into more and more divisions before counting them. Clearly, it
does not make any sense.
Another idea, followed by David Wallace, would be to develop a
concept of subjective probabilities and "rational decisions" to be
developed by individual minds in the worlds that split. Such
arguments are doomed to remain purely circular and missing the
point, as what is to be explained is not the process of a priori
guesses that "rational agents", or rather serious students, would
need to have correctly calculated in order to pass their exams of
theoretical physics, but a posteriori factual observations.
No. In fact, there is a unique mathematically correct solution to
this problem that remains faithful to the basic idea of the
many-worlds interpretation, and it is very simple. The solution is
to accept Born's rule as a postulate, reinterpreted in the absence
of measurement, taking weights to mean "amount of existence"
instead of "probability".
The problems to be discussed then, are purely philosophical:
Is the divisibility of existence an
acceptable ontology ?
If "physical existence" was all what needs to be accounted for,
and the heck knows what a concept of "physical existence" might
look like and why it should matter, then there would be no problem
to conceive physical existence as divisible like a quantity
The problem comes when trying to apply it to the case of
conscious existence as defined by the Artificial Intelligence
thesis of consciousness. This thesis says: "an individual has a
conscious existence, if the operations of his brain happen to be
The problem is, for the laws of physics operate, they must anyway
fully and correctly compute what happens in every world that got a
nonzero amount of existence, no matter how much this amount is.
Therefore, the strict application of the AI thesis of
consciousness would result in dismissing the role of the physical
amounts of existence, in favor of an equal distribution of
conscious existence to every different configuration of a mind
that happens to be computed in any world that got at least a bit
of physical existence. In this case the Born rule would break
down, and would not fit with what we experimentally (subjectively)
The logical solution, then, would be to modify the AI thesis in
this way : "The amount of conscious existence of an individual, is
defined as the amount of times that the operations of his brain
happen to be physically computed".
This way, if there are 2 individuals A and B far away from each
other, and if B makes any measure that splits his world into
parallel copies but without anyhow affecting (informing) A, then
A's total amount of conscious existence remains unaffected by this
split: it is the same whether the operations of A's brain are
analyzed as happening "once" with the initial total amount of
existence it had before B's measure, or as happening "many times",
once in each of the worlds resulting from B's measure, but each
receiving only a piece of this divided existence (as defined by
B's "measurement probabilities").
let us go further : should these "amounts of times" that a mind
is computed, be only considered additive when occurring between
parallel worlds, or can they also be counted as adding up in case
the same computation happened to be repeated in different parts of
the same world ?
In fact, if we tried the experiment by cloning A into an
identical copy A' at some other place of the same world, then
quantum fluctuations would "most probably" soon make this A'
behave a little bit differently from A, in the exact same way as
another version of A's behavior in some other branch of this
continuously splitting world. Thus, since in each world A and A'
are actually different while A' is only exactly copying the A of a
parallel world, for which their existence had to add up, we
clearly have to conclude that conscious existences must add up
when they coexist in the same world too.
The shrinked neurons thought experiment
Now it is just a little step further to extend this to the times
when A and A' remain identical in the same world (as unlikely as
they might stay so any significant amount of time) : the amount
conscious existence of a mind has to be counted not only as
weighted by the existence of worlds containing him, but also as
multiplied by the "amount of material stuff" that operates this
computation in this world. And in the same way as a world's
existence is quantitative (able of non-rational ratios) rather
than counted by integers (numbers of occurrences), the amount of
material stuff that operates a mind's computation to give weight
to his conscious existence, should be counted as quantitative too.
Now, since distances between copies don't matter, it should not
matter either if their locations come to coincide, each neuron of
the one staying just aside its copy in the other. Now we get a
method to force their behaviors to coincide : oblige each neuron
of the one to follow its copy's behavior, as they stay aside each
other. Finally, since the amount should be able to be quantitative
rather than as a number of copies, we can simplify everything by
replacing "2 neurons made to behave the same one aside the other",
by "one bigger neuron behaving the same as if it had normal size".
This suggests to consider a new version of the quantum
suicide problem, as follows :
Imagine a drug was found with the effect of shrinking the size of
neurons, but without actually affecting their behavior. So if you
take it, then for sure you don't notice anything, and (unlike in
the original version of the quantum suicide problem), other people
around won't notice anything either (they will see you alive and
conscious just the same), except that, in fact, the size of your
neuron shrinks, therefore actually reducing your "amount of
conscious existence". For this reason, should this drug be labeled
as "dangerous" as much as the quantum suicide experiment (entering
the box with Schrödinger's cat) ?
Now, if you had to choose between going with Schrödinger's cat
with a 10% risk of death, or take that drug that would shrink your
neurons by 20% without any noticeable effect, what would be your
But, what if it does not shrink all neurons in the same
proportions, but, for example, it affects some parts of the brain
more than others ? You would need to study some scientific details
of which parts of your brain are affected and how before taking a
decision, would you ? But why did you never consider the need to
make such studies any time before, to find out what kind of mental
stimulations "really matter" as forms of happiness or sadness ?
Now, imagine the effect of this drug was temporary: your neurons
will resume normal size after a few of days. Would it still have
to be considered dangerous ? Or would it be just as safe as if you
went for quantum suicide with a 50% risk of dying but a guarantee
of being cloned a few days later otherwise ? Why not use it in
guise of a method of anesthesia ?
To try answering the oddness of dividing existence into
fractions, some proposed to reinterpret these
divisions as those of the infinite number of occurrences of each
possible local world in an infinite Universe, where anything
than can happen actually happens an infinity of times. This way,
the indivisibility of the existence of each individual occurrence
is formally preserved in principle, despite the effective
divisions of existence in practice. However it remains doubtful
whether it is any real improvement : while physical systems can
indeed exist in several identical copies in the same space
according to the rules of quantum mechanics, identical copies of
minds may still be considered philosophically problematic.
Moreover it creates 2 new problems :
- On the mathematical articulation between the structure of
quantum measurement and the frequencies of occurrences
throughout the universe : without reading their article (sorry)
I'm skeptical of the possibility to make it coherent, unless of
course real collapses are introduced, which drives us back to
the initial problem instead of resolving it;
- It does not fit with the properties of cardinals of infinite
sets in mathematics.
The Many-worlds interpretation of the EPR paradox
Imagine a pair of entangled particles, that will be simultaneously
measured, each in a specific way, by Alice and Bob, such that for
each, the probability is 1/2 to find heads or tails, but globally
there is only 10% probability that they get the same result.
So, Alice seeing her measurement result evolves into a superposition
(or split) between 2 mental states : Alice-head and Alice-tail, with
the same weight of 1/2 each.
In the same way, Bob evolves into a superposition (or splits) into 2
copies : Bob-head and Bob-tail, each with weight 1/2.
Then, Alice and Bob meet again.
Alice-head sees Bob in a superposition of states, composed of 10% of
Bob-head and 90% of Bob-tail,
Alice-tail sees Bob in its remaining states, that is a combination
of 90% of Bob-head with 10% of Bob-tail.
Bob-head sees Alice as in a superposition of states, composed of 10%
of Alice-head and 90% of Alice-tail
Bob-tail sees Alice in a combination of 90% of Alice-head with 10%
Then, Alice tells Bob her measurement result.
For her this changes essentially nothing :
When Alice-head says "head" she sees Bob as deterministically
evolving from the mixture (10% of Bob-head + 90% of Bob-tail), into
the mixture (10% of Bob-head-head + 90% of Bob-tail-head) ; and
similarly for Alice-tail who says "Tail".
But bob's experience here is a bit different :
Bob-head sees Alice's state collapsing from the undetermined state
of (10% Alice-head + 90% Alice-tail), into either Alice-head (with
10% probability) or Alice-tail (with 90% probability); this splits
himself between Bob-head-head and Bob-head-tail with these
Meanwhile, Bob-tail sees Alice's state collapsing from the
undetermined state of (90% Alice-head + 10% Alice-tail) as he saw
her, into either Alice-head (with 90% probability) or Alice-tail
(with 10% probability).
The state of the universe at the big bang
and its minimal entropy
Let us describe in more details what is the form of the "reality"
defined by quantum theory in its many-worlds interpretation,
Basically, only one thing is absolutely real, that is the "universal
wavefunction". It comes from the state of the Universe at the time
of the Big Bang. In order for things to be mathematically
well-defined as needed, this state of the Big Bang needs to be a
"completely specific state", i.e. it must describe the contents of
the spatial extension of the whole Universe of that time (or at
least it must cover all our causal past, that is inside our past
light cone, including what is hidden by the opacity of the matter
that emitted the cosmological background radiation), in all details
in a sense that quantum theory still allows :
More details, and how the idea of objection by the conservation of
energy does not work, were moved to a separate page : Time orientation and
the big bang
- either only one elementary state specified in "full details",
with zero entropy
- or an exactly defined classical superposition of many possible
elementary states with definite probabilities, thus with a
definite nonzero entropy (but anyway the entropy at the big bang
is the lowest amount of universal entropy that ever happened).
Consequences of the absence of individuality of quantum systems
Let us remember one of the fundamental properties of quantum
mechanical systems (as proven necessary by the formalism of quantum
theory) : they have no individuality ! They are completely "defined"
by their state, that is, the configuration of molecules inside, and
there is only a finite number of possible states for all systems
with given limits of size and energy. If an individual is defined by
his body, then there are only a finite number of "possible
individuals" and they have no individual identity. Namely, if the
same body happens to be identically repeated in several parts of the
universe, then they are not "different individuals similar to each
other" but they are the same individual. If it happened to me then
the question "which of them am I ?" strictly would not make any
sense. Instead, it would only mean that the configuration of the
universe around me is undetermined and I am collapsing the state of
rest of the universe (or equivalently, splitting myself into my
different local copies) by looking at it. You might say that
human-sized bodies are so big, with so many molecules inside, that
the number of distinct possible bodily states is crazily huge,
something like 101027, which may be reduced
"only" to something, say, in between 101015
and 101020 states after adequate file
compression, neglecting all insignificant fluctuations to which the
body naturally "resists", and ignoring lots of "unrealistic body
configurations". Thus, even if the universe is much bigger than the
limits of our cosmological horizon, the chances for an individual to
identically exist in several place-time locations are quite small.
Remember that we are in the many-worlds interpretation. Even if the
chances of identical repetition of an individual seem quite
unrealistic inside "one universe" in the one-world sense because it
is "too small", they become much more significant when you multiply
this by the number of alternative histories that could take place in
parallel since the Big Bang, say, on a given planet (to not count an
individual on a planet as split by random events happening on
another planet). Concretely, no single brain can ever "remember" the
whole evolutionary history of life on his planet. Therefore, it must
be "compatible" with many such histories. Formally, the Many-worlds
interpretation of quantum physics says that the past
evolutionary history relatively to a given individual
(especially one who is not a paleontologist), is largely undetermined.
Thus, as the role of the "absolute reality" of the universal
wave-function (in its way of defining or "creating" specific
realities), is ultimately reducible to its way of distributing
respective weights ("amounts of existence") to all possible states
(configurations) of biological systems as measured by their "total
amount of connection" to the initial state of the universe (the big
bang), we can notice that its computation of this distribution is
quite strange and indirect : the weight it gives to each individual
comes by adding up the weights of all possible evolutionary
histories that may lead to it !
The same thing happens for the astronomical data relatively to an
individual who is not an astronomer: the rest of the universe is in
a state of indeterminacy, between many possibilities obtained by
adding up the weights of all possible histories of the Universe
corresponding to the different possible outcomes of quantum
fluctuations that could occur shortly after the Big Bang, and that
could lead to the same planet (or at least the same given individual
no matter his planet) but with different "rests of the Universe".
How the universal wavefunction defines and distributes reality
Then, this universal wavefunction distributes partial "amounts of
existence" between all possible individuals. The mathematical
operation defining the measure of this existence, is a tensorial operation, that
is a sort of dot product, bilinear with respect to these 2 data :
But apart from this necessary difference between the full
definiteness of the state of the big bang and the partial
definiteness of the state of the individual (and of course that
these states look very different), the product operation between
them looks perfectly symmetric (by time-reversal).
- The state of the big bang (which defines the universal
- The state of the individual. But it only needs to be conceived
as a partial information, that is, some information about one's
own body that needs not be exhaustive, and ignoring all what is
outside the body.
- Just like in any dot product operation, the product operation
itself, which connects together both things to be multiplied,
can be seen as a third object in the list of things that are
multiplied. Here, this third object that multiplies both above
states (the state of the universe at the big bang and the state
of the individual), represents the shape of all the space-time
between the big bang and the individual. This would make clear
sense in the formalism of quantum field theory, where it can be
summed up as the data of the space-time location of the
individual inside the universe (with respect to the big bang),
that is defined in the absolute independently of all the
material content of the rest of the universe (leaving unclear,
however, the question of its invariance with respect to a global
shift of the whole content of the universe; at least this
operation depends on the age of the universe). It looks less
clear how things can be defined if this portion of space-time is
curved by gravity in an undetermined way depending on the
material content in between : quantum gravity may be required to
make sense of this. The simplest approximate guess we can make
here (the classical limit), is that the total thing we need to
insert as making up the whole operation of probability
computation, looks like the sum of all contributions from the
different possible space-time shapes between the big bang and
the individual (thus including a sum over all possible ages of
the universe), with of course the risk for this to diverge
(after all, the occurrence of an infinity of copies of an
individual, gives him an infinite amount of existence !).
Let us point out the natural ontological meaning of tensorial
operations : the multiplication means the coexistence of
things in different places of same universe, while the addition
means the list of alternative possibilities for the same
object, that exclude each other ("existing" in parallel bits of
universe excluding each other, to be alternatively glued at the same
place of the universe). Concretely, this appears in probability
operations : we have 2 individuals, A that may be in state A1 or A2;
and B that may be either in state B1 or B2. The total probability
for A to be in state (A1 or A2) is the sum of their probabilities,
while the probability to have ((A in state A1) with (B in state B1))
is the product of their probabilities, if they are not correlated
(if they are correlated it also comes from a tensorial product but
involving vector spaces with more dimensions than the simple product
Correlations between experiences or parts of memory
If I exist, then I have the same feeling of existence no matter what
"amount of existence" the universe gave me, so, what difference does
it make for me ? Directly, not much. However, the laws of physics
have 2 effects on me : one for my past which I could verify, and the
other for my future, which I can predict.
As for the past, it concerns the correlations between my past
perceptions. This can be equivalently expressed in 2 ways :
- The immediate correlation that I can find now between the
different parts of my memory, assumed to be a material memory.
It is is computed exactly as above, where the state of my brain
(thus my memory) contains all this information, thus contains
the tensor product between these bits of memory.
- The correlation between my past experiences themselves, that
is, the states of sensorial perceptions I had at the different
times of the past, provided that I remember them (I have the
information about them in memory). Again the operation is
multilinear with respect to these different perceptions, but
taken as inserted in the space-time locations where they
So, the laws of physics define a probability law between
all possible combinations of perceptions, that is, a distribution
of amounts of existences between them.
The effect of this, which I can verify, is that my experience is
"not too untypical" with respect to this law.
The relative existence between objects or individuals, and
The next thing of interest I can get from the laws of physics, is
the state of the universe, or more concretely, the state of some
specific object A (in the sense of the "probability distribution"
between the possible states of this object), no more in the absolute
as above but relatively to me. It is defined as follows:
|(Probability for A
to be in state x relatively to me) =
||Amount of existence of (me with (A in
my amount of
existence, ignoring anything else
Indeed the mathematical structure from which the amounts of
existence are calculated from the universal wavefunction, as defined
above, ensures that the sum of the "probabilities" so defined for
all possible states of A, equals to 1 (i.e. the sum of amounts of
existence of me with each possible state of A, equals my amount of
existence ignoring A).
Now the question is, how can these quantities so defined, be of any
interest to me, so that I can meaningfully call them "probabilities"
event though the Many-Worlds has no true probabilities but only a
distribution of amounts of existence ?
Answer : Insofar as I'm going to measure A, the next versions of
myself with the additional memory content expressing each possible
result of this measurement, are going to get the respective shares
of my current amount of existence, as defined by these
"probabilities" of states of A relatively to me.
However, the real amounts of existence of these possible future
states of myself, might still differ from these shares (namely,
exceed them), in case I would lose a part of my memory in between,
letting me coincide with other versions of myself where the state of
this lost part of memory was different (thus adding up the amounts
of existence of the initally different versions of myself, in a
common pot). Anyway I won't notice any effect from this fusion :)
and, rationally speaking, I don't have to care.
Where is time gone ?
However, this leaves a big unknown : what is time, finally ? Is
time anything else than a space dimension among others ? If there
is "going to be" a next version of myself, that is, with some more
experiences and that will receive "some amount of existence", in
which meaningful sense can it be said that : "that will still be
me" and "that is my future" ? Or equivalently, how can the past
experiences that I remember, be said to be "my experiences" and
"past to me", if all there is, is... just different possible
states of people getting diverse amounts of existence, all in bulk
The notion of "how are things relatively to me", actually
constitutes another wavefunction of the universe, aside the
universal wavefunction that was mentioned above.
Let us call it "my universal wavefunction". It is defined
as follows (where "me" means more precisely "me now", i.e. without
To every object A (space-time location defined relatively to me)
that is outside my past cone (i.e. it is either in the future or
independent of me), it gives the state that is "the state of A
relatively to me" which we defined above.
This indeed has all the properties of a wavefunction, in the sense
that it satisfies the same law of evolution (Schrödinger equation)
as the universal wavefunction that was mentioned above. In
order for this to be the case, the above definition had to be
restricted to the A that are outside my past light cone, so that
the operation involves A only by its past light cone and not by
its future light cone. Precisely, it is operated by (only depends
on) the region of space-time that is the union of both past light
cones of me and A, by which these 3 things are connected: me and A
at the future ends of the region ; the Big Bang at the past end of
But then I can also extend my universal wavefunction to
my space-time neighborhood including my past, by taking the part
we just defined and applying the Schrödinger equation to rebuild
the rest; even if it does not coincide with some more directly
definable and meaningful result. For example, if I measured an
object (such as a spin) successively in 2 ways, and from the first
measure I deduced that the second measure necessarily had
probabilities 50% to give either result, and I got one of these
result, then (due to the time-symmetry of the Schrödinger
equation) my universal wavefunction gives 50% chance for the first
measurement result to have been what it was, which is absurd since
I know what it was. However such reasonings are dubious anyway,
since it can be absurd to claim applying the Schrödinger equation
backwards when describing processes that are seen at the same time
as thermodynamically irreversible, such as measurement processes.
Precisely, my universal wavefunction differs from the
universal wavefunction, as it replaces its initial definition (the state of the
Big Bang that was taken as origin of space-time)
to be extended to its future by the Schrödinger equation, by the
Integral for all possible intermediate shapes and
contents of space-time with all possible
relative positions and speeds
(or possible space-time shapes) between me and the Big
(The wavefunction of me here now at rest, multiplied by the state of the Big Bang
regardless "however long ago at whatever speed")/(my amount of existence)
- While I can afford to leave the time of the Big Bang (age
of the universe) and its speed (relatively to me) in that state of
indetermination, I still cannot ignore it altogether,
otherwise (without assuming the past to have had lower entropy
than the present) it would not let me define any wavefunction at
all (attributions of probability distributions to states of
things relatively to me).
- My universal wavefunction differs from The universal
wavefunction, by these properties:
- According to My universal wavefunction, almost everything is
undetermined, except Me; and there is a nonzero probability
for the universe to have started by some big bang (as
certainty here would be incompatible with the definiteness of
my own state).
- According to The universal wavefunction, everything
except the big bang was in an even much worse state of
Where is Reality gone ?
Finally, the many-worlds interpretation itself suffers the exact
same problem as the Bohm
interpretation, only with a different choice of "physical
Any temptation to see a theological interpretation in the structures
of the above reasonings (that naturally came, let us remember, as
logical consequences of trying to interpret the physical world in
the absence of any fundamental role of consciousness), may be, after
all, not a purely fortuitous coincidence. Indeed the Mind makes
collapse interpretation will give this "coincidence" all its
- Bohmian mechanics takes the hidden variables as the pointer
(arbitrarily given from nowhere) that defines which world
"physically exists" inside the many-worlds landscape, but this
specific world (given by the values of hidden variables) still
depends on the structure of the many-worlds (that is, the
wavefunction, that "contains" all its other possible worlds) for
expressing its law of evolution.
- Everett's many-worlds takes the universal wavefunction
as the arbitrary pointer that defines the "physical existence"
of a specific many-worlds (a specific distribution of amounts of
existence between all possible worlds or organisms) inside the
Hilbert space, but the law of behavior (Schrödinger equation) of
this specific wavefunction, still depends on the structure of
the whole Hilbert space, with all its other elements (that are
other wavefunctions) implicitly required to somehow also exist.
There is no objective reason to consider some specific
wavefunction in that space to be more real than other
wavefunctions, such as, for example, my universal
Related texts by other authors
Not explicitly about many-worlds but about very related metaphysical concepts:
References about many-worlds
Interpretation of Quantum Mechanics: Many Worlds or Many Words ?
(with a small poll of opinions from University
of Maryland Baltimore County, 1997)
Emergent Multiverse: Quantum Theory according to the Everett
Interpretation by David Wallace (2012)
Worlds? Everett, Quantum Theory and Reality’, edited by
Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace
(2010) (see reviews on the site).
Function: Essays on the Metaphysics of Quantum Mechanics
quantum theory and reality? review by Iñaki San Pedro
Review by Jeremy
in the Stanford Encyclopedia of Philosophy
Coleman: Quantum mechanics in your face
The Many-Worlds Interpretation
of Quantum Mechanics by Douglas S. Jones, with many (broken)
Everett FAQ by Michael Clive Price (February 1995)
role does memory robots play in the many worlds interpretation?
list of links
An old list of links
series of articles
Carroll, Why the Many-Worlds Formulation of Quantum Mechanics Is
Interpretation Of Quantum Theory
Jeremy. “Some Worlds of Quantum Theory." - Review
of The Quantum Mechanics of Minds and Worlds
On the related concept of mathematical monism
It's Full of Clones: Living in a Mathematical Universe by Marc
Quora thread of questions
References more critical about many-worlds
for and against many worlds at Physics Stackexchange
philosophical discussion on interpretations, focused on the
Interpretations (Adrian Kent, 1997), answered
Nothing happens in the
Universe of the Everett Interpretation by Jan-Markus Schwindt
Against the Empirical Viability of the Deutsch Wallace Approach to
Decoherent or Incoherent?
many-worlds interpretation of quantum mechanics, in R. F.
Streater's list of lost causes
of the cosmological interpretation
Why is many-worlds winning the foundations debate?
Does it Make Sense to
Speak of Self-Locating Uncertainty in the Universal Wave
Function? Remarks on Sebens and Carroll
quantum physics (notions of states and measurements)
quantum physics main page (list)
Foundations of physics table of contents