arXiv:1001.3538v1 [physics.pop-ph] 20 Jan 2010
At the Frontier of Knowledge
Nordita, Roslagstullsbacken 23, 106 91 Stockholm, Sweden
At any time, there are areas of science where we are standing at the frontier of
knowledge, and can wonder whether we have reached a fundamental limit to hu-
man understanding. What is ultimately possible in physics? I will argue here that
it is ultimately impossible to answer this question. For this, I will first distinguish
three different reasons why the possibility of progress is doubted and offer exam-
ples for these cases. Based on this, one can then identify three reasons for why
progress might indeed be impossible, and finally conclude that it is impossible to
decide which case we are facing.
There are three different reasons why scientists question whether progress in a
particular direction is possible at all.
D1) There exists a proof or no-go theorem for theoretical impossibility.
Modern theoretical physics is formulated in the language of mathematics,
and consequently subject to mathematical proof. Such proof can be in the
form of excluding particular scenarios due to inconsistency.
A basic example is that in Special Relativity it is not possible for massive
particles to travel faster than the speed of light. Other examples are the
Weinberg-Witten theorem that shows the incompatibility of massless gravi-
tons with any Lorentz covariant renormalizable quantum field theory and
with that constrains approaches to emergent gravity , or the no-go theo-
rems on gravitational theories with more than one interacting metric tensor
Physicists have a love-hate relationship with no-go theorems. They love
them for the power to sort out possible options and reduce the space of
theories that have to be considered. No-go theorems also clarify why a
particular direction is not promising. Physicists hate no-go theorems for the
D2) There exists an argument for practical impossibility.
Even though progress may not be impossible on theoretical grounds, it may
be impossible for all practical purposes. An example may be testing quan-
tum gravity. To present day we have no experimental evidence for quantum
gravity. And as if that wasn’t depressing enough already, it has been shown
 that even with a detector the size of Jupiter we would not be able to
measure a single graviton if we waited the lifetime of the universe, and any
improvement in the detector would let it collapse to a black hole. It is of
littlecomfort thatwecould testparticlescatteringin theregimewhere quan-
tum gravitational effects are expected to become important with a collider
the size of the Milky Way.
Another example for questioning practical possibility is the emergence of
structures on increasingly macroscopic levels. While most particle physi-
properties, and chemical reactions can in principle all be derived from the
Standard Model of Particle Physics, we are far off achieving such a deriva-
tion. Even more glaring gaps arise on higher levels. Can one derive all of
biology from fundamental physics? What about psychology? Sociology,
anybody? A hardcore believer in reductionism will think it possible.
It has been shown in a specific setting that more really is different  and a
derivation of emergent from fundamental properties impossible even theo-
retically. This specific setting is an infinitely extended, and thus unphysical,
system but nevertheless sharpens the question for practical possibility even
for finite systems. This example is still under debate, but it might turn out
to also represent a case in which for all practical purposes a derivation is
impossible to achieve.
D3) Despite long efforts, no progress has been made.
This situation is one that seems to bother physicists today more than ever
due to the lack of breakthroughs in fundamental physics that has lasted sev-
eral decades now. This is even more frustrating since meanwhile the world
around us seems to change in a faster pace every day.
As an example for doubt of this category may serve the understanding of
quantum mechanics, in particular its measurement process and interpreta-
tion. “Shut up and calculate” is a still prevalent pragmatic approach fre-
quently complemented by the attitude that there is nothing more to under-
stand than what our present theories describe, and all questioning of the
or a pastime for philosophers, or maybe both amounts to the same.
Another example is instead of attempting to explain the parameters of the
Standard Model to conjecture there is no explanation other than that we
just happen to live in a part of the “multiverse” – a structure containing
universes with all possible choices of parameters – in which the parameters
are suitablefor theexistenceoflife. After all, if lifewasn’t possiblewiththe
parameters we observe, then we wouldn’t be here to observe them. While
this is an expression of doubt of category 3, it is not to say invoking such
reasoning, known as the “anthropic principle,” is necessarily scientifically
empty. We have observational evidence that our universe allows for the
existence of life, and given a useful quantification of “existence of life,”
the requirement of its possibility constrains the parameters in the standard
model. The controversy remains though whether or not to give up searching
for a more satisfactory explanation  simply on the basis that none has
been found for many decades.
The previous section categorized causes to suspect fundamental limits to our
knowledge; the following categorizes actual reasons for impossibilities corre-
sponding to the above mentioned three reasons of doubt.
I1) Impossible because the laws of Nature do not allow it.
That is D1 is indeed true. This implies D2 is also true.
I2) Possible in theory, but impossible in practice.
That is though D1 is not true, D2 is true.
I3) Possible both in theory and in practice, but not yet possible
Though progress is not excluded neither in theory nor practice, it might not
be possibleat a given time because theoretical knowledge is still missing, or
necessary data has not yet been obtained. Scientific insight builds upon pre-
vious knowledge. Progress is thus gradual and can stagnate if an essential
building block is missing.
Since impossibility of the type I3 can be overcome, we will not consider it to
be a fundamental impossibility.
Though physicists do not usually include this in discussions about fundamen-
tal limits, any question for what is possible should take into account constraints
set by the human brain. It is in our nature to overestimate the human capability
to understand the world and to exert control about it. However, the capacity and
ability of our brains is finite. It is limited in the processes it can perform, and it
is limited in speed. There will thus be problems the human brain in its present
form will not be able to solve at all, or not in a limited amount of time. And since
solving a problem might be necessary to sustain an environment in which solving
of problems can be pursued, a problem that cannot be solved in a limited amount
of time might turn into one that cannot be solved at all.
This limitcould beovercomewith improvementsofthehuman brain, eitherby
evolution or design. It is far from clear though whether such an improvement can
be limitless. Though not in the realm of physics, the possibility of enhancements
of human cognition is another question at the frontier of knowledge to which we
presently have no answer. The above cases I2 and I3 both should be understood as
including this potential limit to human ingenuity: An experiment that we cannot
think of cannot be realized, and a problem whose solution takes more time than
has passed will not yet be solved.
Where are we?
Let us now investigate whether from any of the three doubts one can conclude a
fundamental impossibility of type I1 or I2.
First, we note that proofs are only about the mathematical properties of cer-
tain objects in their assumptions. A physical theory that describes the real world
necessarily also needs a connection between these mathematical objects and the
corresponding objects of the real world. While evidence might be abundant that a
particular mathematical description of reality is excellent, it can never be verified
and shown to be true. Consequently, it is impossible to know whether a particular
mathematical representationis indeed a truedescriptionof reality, and it cannot be
concluded a mathematical proof based on it must necessarily apply to the physical
world. We can thus never know whether D1 is caused by an actual fundamental
Another way to put this is that no proof is ever better than its assumptions. A
industrycalled Supersymmetry, and bi-metrictheories maybe non-interacting.
Turning to doubt D2, no argument for practical impossibility can be obtained
without a theoretical basis quantifying this practicability. Since the theoretical
basis can never be verified, neither can the practical impossibility. Thus, I2 cannot
be followed from D2, and neither of the both fundamental impossibilitiescan ever
be identified with certainty.
Coming back to our earlier D2 examples, despite all ridicule about “Chao-
plexity”  scientists still investigate emergence in complex systems with the
hope to achieve a coherent understanding, and during the last decade an increas-
ing amount of tests of quantum gravity has been proposed. These proposals have
in common a modification in the assumptions that lead to the conclusion quantum
gravity might be practically untestable. Two scenarios that have obtained par-
ticularly much attention are higher dimensional gravity, in which case quantum
gravity might become testable at the Large Hadron Collider , and deviations
from Lorentz invariance resulting in modified dispersion relations , poten-
tially observable in gamma ray bursts . Depending on your attitude you might
call thesestudies interestingor a folly, but what they are for certain is possibilities.
Finally, let us discuss doubt D3. If we assumeknowledgediscovery is pursued
as a desirable activity then doubt D3 is equivalent to impossibility I3, since in this
case the only reason for lacking progress can be that it has not been possible. With
hindsight one often wonders why a particular conclusion was not drawn earlier,
even though the pieces were all there already. But since we included limitations
of the human brain, slow insights represent imperfections in scientists’ thought
processes that are part of I3. So long as increasing the understanding of Nature
continues to be part of our societies’ pursuits, it can then never be concluded from
D3 that an impossibility is fundamental.
What wecan thusstatewithcertaintyat anytimeismerely“Toourbestcurrent
knowledge...” To our best current knowledge it is not possible to travel faster than
the speed of light. To our best current knowledge we cannot see beyond the black
hole horizon. To our best current knowledgethe measurement process in quantum
mechanics is non-deterministic.
It remains to be said howeverthat progress on fundamental questions becomes
impossibleindeed ifwe do not pursue it. And onereason for not pursuingit would Download full-text
be the mistaken conviction that it is impossible.
Scientific progress is driven by curiosity, and the desire to contribute a piece
to mankind’s increasing body of knowledge. It lives from creativity, from stub-
bornness, and from hope. What I have shown here is that there is always reason
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