An experiment devised in Griffith University's Centre for Quantum Dynamics has for the first time demonstrated Albert Einstein's original conception of "spooky action at a distance" using a single particle.

In a paper published in the journal *Nature Communications*, CQD Director Professor Howard Wiseman and his experimental collaborators at the University of Tokyo report their use of homodyne measurements to show what Einstein did not believe to be real, namely the non-local collapse of a particle's wave function.

According to quantum mechanics, a single particle can be described by a wave function that spreads over arbitrarily large distances, but is never detected in two or more places.

This phenomenon is explained in quantum theory by what Einstein disparaged in 1927 as "spooky action at a distance", or the instantaneous non-local collapse of the wave function to wherever the particle is detected.

Almost 90 years later, by splitting a single photon between two laboratories, scientists have used homodyne detectors—which measure wave-like properties—to show the collapse of the wave function is a real effect.

This phenomenon is the strongest yet proof of the entanglement of a single particle, an unusual form of quantum entanglement that is being increasingly explored for quantum communication and computation.

"Einstein never accepted orthodox quantum mechanics and the original basis of his contention was this single-particle argument. This is why it is important to demonstrate non-local wave function collapse with a single particle," says Professor Wiseman.

"Einstein's view was that the detection of the particle only ever at one point could be much better explained by the hypothesis that the particle is only ever at one point, without invoking the instantaneous collapse of the wave function to nothing at all other points.

"However, rather than simply detecting the presence or absence of the particle, we used homodyne measurements enabling one party to make different measurements and the other, using quantum tomography, to test the effect of those choices."

"Through these different measurements, you see the wave function collapse in different ways, thus proving its existence and showing that Einstein was wrong."

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## Noumenon

Every article on the topic of quantum wavefunctions should at least point out that wavefunctions are not Real physical entities of itself, but rather a mathematical construct. Schrodinger's heart was broken. It's the same popularizing error made in general relativity with talk of curved space-time. Neither, are observable things of themselves.

## Anonym

## casualjoe

If you are not comfortable with this concept then you probably shouldn't be on a physics site, go outside and experience the world.

Wavefunctions work, and if they seem a bit weird to you it's because they 'are' weird.

## Noumenon

Why? What does stating what in fact the vast majority of physicists think, lead you to think that I shouldn't be at a physics site or that I do not myself find interest in quantum mechanics?

Max Born long ago ruined Schrodinger's hope that his wavefunction in his wave equation would represent an objective physical wave. This is a fact. It was Schrodinger then on that account who wished not to be involved in QM.

## casualjoe

The only relevant info I can think of is in this poll: http://arxiv.org/...69v1.pdf

Which shows a difference of opinion between physicists, if anything.

## Noumenon

It has been historically true, as a matter of fact. Perhaps today however, my use of "vast majority" may or may not have been an exaggeration. Let's say it's 50/50. Should the 50% who agree with me, not concern themselves with physics as you suggest that I shouldn't? Do you see how your (possibly valid) point even strengthens mine further?

The person who conducted that poll is Max Tegmark, a Realist to the extreme, in fact a metaphysician and entirely bias,... who admitted that that poll was "highly informal and unscientific," as "several people voted more than once, many abstained".

But yet you have not retracted your statement that I should not be at a physics site.

## Noumenon

All of that is correct and is not in conflict with my point above. That wavefunctions are useful mathematical constructs, does not of itself imply the reality of physical wavefunctions. It is not observable as such.

Einstein's own special theory of relativity made any reference to a physical substantive space, like the aether, redundant and meaningless. The general theory of relativity is not founded on any such physical "space-field" or "time-particle".

Einstein was careful to Define space and time, Operationally,... which is to say, they are defined, rather than observed, in terms of rods and clocks, .... physical systems themselves.

## shoebox22

## DarkLordKelvin

## DarkLordKelvin

## DarkLordKelvin

## Noumenon

Yes, ....cannot be assessed as it exists in itself, which is to say, prior to conforming the 'underlying reality' or 'state' to a conceptual structure that is defined by the macroscopic apparatus design and therefore a-priori, the mind.....

## Noumenon

...... the Hilbert space representation is supplied by the macroscopic experimental apparatus, in the sense that it defines the basis axis, one 'axis' for every possible observable value, to which the wavefunction is collapsed during a measurement.

Prior to measurement, the 'underlying quantum entity' simply has no conceptual value! There is no such conceptual form until the macro-scaled experimental apparatus defines one. The independent underlying reality (as it exists in itself), is conceptually formless. Knowledge is not possible except through concepts, so the 'state' is conformed to or projected into concepts.

## Noumenon

Exactly correct, ....or it may be that various a-priori concepts that the mind uses to synthesize and order experience are at the QM scale, exposed as artificial, in the sense that they are "forms of thought" we evolved with at the macro-realm , and therefore have no intrinsic reality themselves,... locality, causality, separability, space, time, counter-factuality, wave, particle, place,.. ?

"The doctrine that the world is made up of objects whose existence is independent of human consciousness [mind] turns out to be in conflict with quantum mechanics and with facts established by experiment." - B d'Espagnat

## Noumenon

Immanuel Kant, the first great epistemologist, justified an objective reality also, and termed this underlying reality, "Noumenon". It is unknowable in itself,.... that is, until it is subjected and made to conform to our a-priori forms of thought, i.e. dressed in concepts.

Now, mentioning a philosopher from 1790 (Kant) may seem like an irrelevant distraction, but in fact, N. Bohr and d'Espagnat drew similar conclusions through an analysis of QM. Abraham Pais once referred to Bohr as the natural successor to Kant.

## Mimath224

## theon

## Dethe

## andrewoliver

There have been many minds wondering about the so-called wave particle duality for the best part of a century.

Not really having studied any advanced physics myself, but with a mathematics degree, and having studied a little philosophy, and undertaken a lot of reading of popular science journalism, may I say that the theory a non physicist such as myself likes is that these 'elementary particles' travel as waves and interact at points: that the four forces we know well seem to have spacelike pointlike points of interaction events and spacetimelike wavelike movement as wave functions mediated by some form of arrow of time causality from the particle creation event towards wheresoever the wave-particle interacts the next event(s).

That is counterintuitive but not non-realist.

If the contemplation of an observer and the observer's expectations could be demonstrated to affect the experimental statistics, that would show the truth of idealism ...

## mogmich

But if you say that, you cannot say also, that quantum waves are not real!

(Or else you are actually saying, that "Reality is not real", which is meaningless).

If this "Universal Quantum Wave" is not in itself real, then it cannot be a complete description of Reality. There is neccessarily something else, which is not explained.

## Mimath224

## andrewoliver

The computational nature of reality science fiction crowd argue interestingly that there are information bit stings of finite or countable extensible length that pervade the universe embedded in a finite dimensional Euclidian algebraic hyperspace our dense curved three spacelike, one timelike dimension universe is a subspace of. If integrating over the surface of the light cone of possible causality, or integrating over the surface light cone of causality/consequence, or integrating through the solid light cone of causality the preceding possible message-communicators subspace, that 'a force' is an integral with some kernel function that generates pseudo-random bit strings that then determine what the quantum mechanical servo-mechanisms the little computers at each point of spacetime do, occasionally erupt into eventhood.

I watch too much Star Trek Lost In Space Blake's Seven Dr Who perhaps?

## Noumenon

Positivism or rejection of Realism, does not necessarily imply Idealism. Kant avoided that progression by drawing the Noumenon / Phenomenon distinction, and d'Espagnat also recognized an (unknowable in itself) Objective reality,... and they were positivists.

The wavefunction is not observable like a physical wave would be. It is an artificial form, a mathematical means of representing the "something else".

Interestingly locally, QM IS complete, in the sense that there is nothing missing! The Bell inequalities proved this in a way that is independent of any particular theory (based only on experiment)!

## Noumenon

Good question. I don't know. At present GR and QFT are not compatible theories.

An 'Observer' manifestly implies a-priori conditions of thought, given the nature of mind. This means scaling the micro to the macro so that these conditions are met.

The problem is that this causes decoherence (loss of off diagonal terms of the quantum density matrix), in other words loss of quantum behaviour. Further experiments with meso-scaled objects may allow a quantitative observation of decoherence,... however at present it can not be said to solve the measurement problem.

## DarkLordKelvin

Nope, not in this case, because the experiment uses a single photon that is spatially entangled, so each detection event measures either "photon" or "no photon", rather than "spin up" or "spin down", BUT at the same time, Bob's results are correlated by choices made by Alice at her end. Thus the wavefunction of the photon must be extended non-locally so that it is sensitive to the apparatus at the locations of both Bob and Alice at the time of the measurement that collapses the photon.

## Mimath224

x+ ≡ 1/ √ 2 (x º +x ¹ ) and a corresponding coordinate for x-. But for strings these may under go compactification thus ceating a 'subspace'(?). But I haven't read/don't know how to apply a Loop Integration on said compactification part of which I suspect would be in the spacelike/lightlike surface-surface/D-brane/3D interphase.

Coincidence you should mention Star Trek etc Ha!

## DarkLordKelvin

Well, special relativity would definitely be "there" .. there are several relativistic corrections that need to be applied when calculating electronic structure of atoms, such as spin-orbit coupling, and corrections to the kinetic energies of core electrons in heavy atoms. The whole concept of intrinsic angular momentum or "spin" (added by Pauli as a phenomenological "hack" in non-relativistic QM), can only be derived a priori from the relativistic Dirac equation. My understanding of GR is far from complete, but with that caveat, I think it only produces observable effects over macroscopic scales, for macroscopic energies and momenta.

## DarkLordKelvin

Well, we've learned just a bit more about quantum mechanics since the time of Planck. How does the concept of intrinsic angular momentum arise in the context of "electromagnetic wave theory"? What is the "mechanical analog" for intrinsic angular momentum of spin 1/2 particles?

## Dethe

## calibrowns

## Protoplasmix

heh, I'm a tool, hardly the sharpest. When you observe signs like +,-,*,/, etc. in the literature they're a very real part of the physics.

## DarkLordKelvin

Yes, "collapse" is an aspect of the Copenhagen interpretation (aka standard QM) that is essentially shorthand for "the measurement problem" that is known to afflict the CI. In a nutshell, the issue is that the mathematical theory of QM allows for arbitrary "mixtures" (superpositions, including entangled states) of quantum states with different eigenvalues, but when a measurement is performed on such a state, only one of the eigenvalues will be observed. This is one of the fundamental postulates of the theory and applies for all superposition states, no matter their spatial extent. Einstein & others thought this "non-locality" was paradoxical & possibly violated SR, because it implied that all parts of the wavefunction (i.e. with space-like separations) had to "know" simultaneously when the measurement was performed.

## DarkLordKelvin

Along these lines, the famous Einstein-Podolsky-Rosen (EPR) paradox was a gedanken experiment that they used to illustrate that QM had to provide an incomplete description of physical reality, since it did not provide a mechanism whereby the wavefunction collapse could always give the "right" answer (e.g. that a pair of appropriately entangled particles would always be found to have opposite spins, assuming "perfectly efficient" measurement apparatus). Various "hidden-variable" theories have been proposed that involve the entangled particles being imbued with their ultimate measurement values when they are produced, but a brilliant guy named Bell showed that all such theories are inadequate to reproduce the results predicted by QM. His famous "Bell-inequalities" have since been used by experimentalists (c.f. Aspect, Zellinger) to show that the QM predictions are verified to within many, many standard deviations. The experiment described above is that latest such result.

## DarkLordKelvin

So anyway, to get back to your question. There are other QM interpretations that don't require the notion of "collapse". For example, Everett's "Many-Worlds" interpretation postulates that the universe "splits" at the moment of every measurement on a QM system, with two or more "new realities" being spawned, one for each possible experimental result. It sounds wacky, and has its own set of issues re:measurement, but it reproduces the results of standard QM, and is therefore generally held to be an equally "valid" interpretation.

Another "no-collapse" theory is Bohmian-mechanics, which eschews the wave-particle duality aspect of standard QM, saying that massive particles (e.g. electrons) follow deterministic trajectories, but they are also acted upon by a "quantum force" that arises from the identical "wavefunction" from standard QM, thus ensuring that the predictions/observations of standard QM are reproduced. BM avoids collapse by being explicitly non-local.

## DarkLordKelvin

Much like the "measurement problem" in standard QM, the explicit non-locality of BM gets it into trouble with relativity, and it is also an explicitly a deterministic theory, holding that the probabilistic appearance of measurements on quantum systems is a consequence of the fundamental "unpredictability" of the "quantum force".

There are other interpretations, but those are the major ones ... well there is big one left, which happens to be the one I tend to favor (as did Feynman .. perhaps the only thing we have in common) .. the instrumentalist interpretation, aka "shut up and calculate". This is more of a point of view than a formal interpretation, but the essential character is that while all of these "behind the scenes" aspects of wavefunction collapse, splitting of universes, and quantum-forces may be fun to think about (and argue about), but that the only thing that really matters is their utility in predicting/explaining experimental observations.

## Protoplasmix

Whatever philosophical essence the laws of science may have, when some aspect occurs repeatedly in experiments and observations, it gains the status of "law".

Since mathematics is the very basis (or language) of such fundamental principles as symmetry and conservation of energy, it therefore constrains the range of resolution of possible QM wavefunctions along with the physical dynamics of their interactions and their eventual macroscopic expression, as though the nature of maths' abstract laws constitute a real physical "law" for both QM and GR.

## DarkLordKelvin

Well, from a philosophical point of view, you seem to be describing something that is epistemic, not "real" (ontic). Our understanding of the world is not the world.

## Protoplasmix

## Protoplasmix

## Noumenon

I would only say that one should regard the Copenhagen Interpretation itself as a "shut up and calculate" point of view, since epistemic considerations as expressed by Bohr argue for a positivist point of view that de facto limits theoretical constructions to the role of simply providing a means of making predictions of observables, and invalidating the supposed role of physics of explaining how reality "is" independent of observation.

Another reason is that since the "collapse of the wavefunction" was never intended (in C.I.) as collapse of a dynamical physical wave, is was never actually an added element, but rather the actual way in which QM experience occurs (as projected into the macro apparatus),... and indeed the notion of "collapse" turned out to be intrinsic to the Von Neumann / Dirac Hilbert space mathematical foundation of QM.

## Noumenon

So in a sense, personally I never quite understood why historically C.I. is even regarded as "an interpretation". To me it seems that "an interpretation" implies adding some conceptual layer that is in addition to the core mathematical foundation,... as indeed the pilot wave and many-worlds interpretation do by proposing non-observable entities (metaphysical) in order to arbitrarily satisfy bias intuition.

## Mimath224

I disagree but do appreciate it depends on 'the school of thought' one subscribes to. Definition of maths varies;'The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.' American Heritage Dict;'The abstract science of number, quantity, and space, either as abstract concepts ( pure mathematics), or as applied to other disciplines such as physics and engineering ( applied mathematics)' Oxford Dict; B. Russell defined maths as symbolic logic...and the list goes on.

I see maths as absract entities that obey certain rules, used in the measurement of science but are inventions. f can represent a function, frequency, force etc. One say's 'x represents 1 orange' rarely the other way round. The actual orange is real but 'x' and '1' are abstract. (cont.)

## Mimath224

Not going to stop us trying eh?

## Protoplasmix

The same can be said about the rules of maths -- we invent the symbols but the rest is discovery and derivation. Can you think of any reason, other than the rules of maths, that explains why the laws of physics should be the same in your lab as they are in my lab?

Nope, not at all :)

We still don't know for sure if the nontrivial zeros of Riemann's zeta function all have real part one-half...

## Noumenon

I had an interesting debate with DaSchnieb [whom seems to have capitulated or fallen off the edge of the earth],.. Here, in which I suggested that Wigner's mystery is merely illusionary......

The core elements of mathematics must be a-priori judgments of intuition, a la Kant, hard-wired in the mind via evolution in order to synthesize experience. These conceptual forms of thought or a-priori intuitions, give only the illusion that they are intrinsic features of independent reality, or that there is an unreasonable effectiveness of mathematics to the natural sciences, because rationalization of empirical experience itself must necessarily be in terms of those conceptual forms, given the nature of mind.

## Noumenon

## Noumenon

This is not correct. I must have conflated two points. The Schrodinger equation is deterministic and entirely incompatible with wavefunction "collapse". It should be related as "in order to get collapse, in line with experiment, one must add a term to the Schrodinger equation". I would have to include the Born rule (an aspect of C.I.) as part of the mathematical foundation to save my "2nd reason" above.

## Noumenon

Every measurement in fact confirms "collapse", which is why I don't think it should be considered a layer of interpretation. That's the essence of the "problem". The unitary evolution of the state vector (the Schrodinger/Dirac equation) is deterministic and so there is no collapse [except by modifying the equation], ...but experiment always results in state reduction "collapse"...

That's were the Born rule comes into play. Is the Born rule "the added layer of interpretation" or is that the "Schrodinger/Dirac equation is a physical wave" an added layer of interpretation? Imo, since there is no observational basis for the latter, while there is for the former, it is the latter which is an added layer of interpretation.

## DarkLordKelvin

## Noumenon

But it isn't. It only "should" be a consequence of the Schrödinger equation if one a-priori presumes or interprets ψ as a physical wave. There is no observational evidence for that presumptive interpretation.

If one is a-priori agnostic and allows empirical evidence to decide the ontological status of ψ, then a physical wave interpretation is untenable, and the Born rule (or law) is manifest.

## Mimath224

The laws of 'nature' do not favour magic which would be required to make 'a orrange plus another orange produces a orange plus a orange plus a orange'. "nature' prefers a deterministic setup which allows us to make predictions about given environment (you lab, my lab). We see the patterns and we invent a system to model those patterns and we are then able to classify. If we cannot classify 'something' or experiment with it then we either 'debunk' it or leave it alone.

## Protoplasmix

In the above experiment it appears that the researchers have succeeded in splitting a fundamental particle, which isn't supposed to be possible. When Einstein looked at the maths of QM, he and Podolsky and Rosen used it to predict 'spooky action' -- turns out when you crack open a photon and look inside, what you observe is possibility-squared governed by maths, i.e., objects, states and a set of postulates whose dynamics follow the abstract rules of maths as far as we can measure. And that's admitting that our knowledge of maths and QM both is still less than complete.

## DarkLordKelvin

## Dethe

## Protoplasmix

Cont'd >

## Protoplasmix

I'm hardly the first person to point out deep connections between math and physics. If invariance appears backwards to you, I suggest boosting it to a proper coordinate system, so to speak, to one where you can consider the efficacy of a quantum computation wherein the reality of the system (nature itself), at the most fundamental level (or scale), is observed to be a computer crunching the data with unparalleled speed and accuracy. If that isn't helpful, I'll keep working on it :)

## antialias_physorg

Not sure if this is a good philosophical concept. Throughout the ages people have likened nature to that which was currently the state of the (technical) art. e.g. fire-earth-water-air for the ancient Greeks or being some kind of mechanism in victorian/industrial times. And now everyone is likening it to computers.

But each of those views make some tenuous (and up until now always wrong) assumptions.

For the greeks it was a 'doctrine of signatures' type of thinking. For the industrial times people it was determinism. And in our times it seems to be the conservation of information (which has not been disproven, yet. But given the historic trend I would not be surprised if that, too, would fall at some point)

Just a thought.

## Noumenon

The wavefunction description of that singular photon is a linear superposition of all possible paths, given the experimental setup. The wavefunction description is what splits in two, self interferes constructively of destructively , ...not what we ultimate observe as a discrete photon, E = vh.

Only a single wavefunction description is used for a quantum system consisting of several particles. So you see the wavefunction description is a mathematical construct and is itself not an observable entity,.... yet it allows predictions to be made of the system of particles or the singular photon.

## DarkLordKelvin

[ctd]

## DarkLordKelvin

However, energetic splitting of the photon is NOT what was predicted or observed in the experiment described above. Similar to what Noumenon described, what happened here was that the interaction with the first beamsplitter after the source caused the photon to become entangled with both measurement apparatus at the ends of the optical path. This is an almost perfect analog of the famous Schrodinger's cat gedanken, in the sense that following the measurement, the (unmodified) photon will be detected in a well defined "state" (i.e. at ONLY one end of the optical path), but prior to detection there is no way to know or predict which of the two possible states will be measured. Therefore, in the Copenhagen interpretation, we say that the photon has been placed in a mixed "superposition" of the two possible outcomes. Other interpretations choose a different phrasing for what happens, but predict the same experimental results. That is why the math is epistemic and not ontic.

## Noumenon

Constructing conceptual analogies, ...whether they be in transposing one system into the form of another or in constructing a mathematical model as representative of reality,... can only lead one further away, not closer, to the Original.

Understanding of Reality is not possible except through conceptual forms of thought, .... so it is and always has been, a presumption that any conceptual analogy such as a mathematical model could in principle obtain an exact one-to-one correspondence with Independent Reality (as it exists in itself).

It is not even verifiable since observation itself necessarily presupposes the same elements of conceptual form that the mathematical analogy takes, and so we can't get out of our own way to verify the correspondence,... iow, it is a self fulfilling prophecy that mathematics is applicable to description of observables ; Wigner's above "mystery" is rather a necessity.

.....

## Noumenon

So we can not obtain an understanding of Independent Reality as the Realists would have it,... we are limited only to predictive knowledge of experience.

## Protoplasmix

AA, the one constant since earth, air, fire, water has been maths. The postulates and interpretations may change, but never the veracity of logic/maths.

DLK, Nn, I'm not completely ignorant of QM, because maths. Thanks for the clarification about the energy, I'll refrain from using words like crack or break to describe splitting.

DLK, there can't be any putting a cart before a horse with invariance, because no such arrangement is invariant. The observed and quite precisely measured laws of physics are the same everywhere because the veracity of logic/math is invariant irrespective of physical circumstances and frames of reference. Symmetry breaks, because invariance.

## antialias_physorg

I agree. Maths is a tool based on (chosen) axioms. The axioms were chosen based on observations from physics (if I take one rock and another rock I have two rocks, etc. ). So there is definitely a connection there.

Maths can be adapted to describe anything - and if the current set of math is not adequate then another set can be added (like the adding of rational, irrational, complex, hypercomplex, etc. numbers and various forms of transformations).

Physics must be true. Maths must only be true within the bounds of math (self consistency). Not everything that is demonstrable with math must have a physical representation, though (easiest examples are the concepts of zero or infinity).

## antialias_physorg

So taking a mathematical approach (at it's extreme the "shut up and calculate" approach) IS valid as a successful strategy.

Because we must always factor the third thing into it besides physics and math: our brains. While math may easily describe an n dimensional space (and physics may well contain such a space if string theory pans out) then it's often just our brains that are lacking in the capacity to grok what the math (and hence the physics) says.

Math is the map. Physics is the territory. The map is not the territory. But not following the map is an idiotic way to find your way around..

## DarkLordKelvin

## PhysicsMatter

Kindred spirit Noumenon. I think that value of a type of quest for knowledge we call science is more to point out ways to engineer or harness something for peoples utilization rather then explaining reality of the Universe. In such context science provide narrative about universe as side show to justify what we conceptualize as causal or random relationships between phenomena. It's not about knowing how it is done in nature but more about how to simulate observed behavior via concepts of our mind.

You may be interested in something like that:

https://questforn...-quanta/

## Dethe

## Noumenon

Your link is interesting but seems generally "anti-scientific theory" in tone. Modern Physics theories are absolutely successful to incredible accuracy in predictive knowledge of experience... which is to say of 'phenomenal reality'.

It is just that 'phenomenal reality' includes a component that is mind dependent, and so cannot represent Independent Reality or Noumenon,... as scientific Realists believe. IOW, there are plenty of scientific Positivists who contribute to physics theories.

## Noumenon

It's not clear what your objection is, even though I agree with the rest of your post.

As I posted above somewhere, "there must be an underlying objective reality that says "no" to arbitrary [mathematical] constructions of experience."

## Protoplasmix

## Dethe

## Protoplasmix

My assertion remains, to the contrary, that math is a fundamental, inseparable part of physics. A hypothesis on any microscopic quantum mechanical causality one way or the other is where the dogma comes from and is the root of various objections, so I'll keep the dogma to a minimum until I can properly express the hypothesis using the terms of the art. Thanks, DLK, the objections are invaluable in that endeavor.

## DarkLordKelvin

"In fact none of micro-particles such as electron, proton, photon, neutron not to mention zoo of more exotic animals (quarks, neutrinos, tau, muon etc.) were ever directly observed and all are more or less products of unintelligible narratives, figments of scientific imagination. Their mass, charge and size are all inferred supposedly from experiments dealing with trillions of such "particles" measured not as individual particles but as mass densities, ... etc., all creations of mathematical field theory which QM adopted."

Is laughably wrong and points to the general ignorance of the author re: physics, chemistry, math and even history.

## DarkLordKelvin

There's no evidence Einstein ever actually said that, and even if he did, the context has been lost so it's not clear if he was just poking fun at people who hew to a theory even after it has been disproved, or poking fun at himself, since he had often quipped that if GR was ever found to be wrong, it would be "a bad day for God, since the theory is right." It also might have been intended to mean something like, "if you can't find evidence to support a theory, then you should keep looking".

## Accata

## antialias_physorg

I meant physics as in "the physical world" (i.e. reality) is consistent. There are no 'breaks' in reality where stuff suddenly behaves in a way that cannot be modelled via math.

That current theories aren't perfect isn't news - and there are good philosophical arguments that they never can be. Not least of which the map-territory argument.

But concluding from this that we should ditch math (and hence: logic) from inquiry into physical reality makes no sense at all.

Yes. Math is the language of logic, and logic seems to be universal (at the very least universal to the human brain*)

*However a word of caution: Logic makes a few assumptions that do not map unto the universe (e.g. that one can have two _absolutely_ separate/independent objects). I don't think that's a problem. But it's worth keeping in mind.

## Returners

## Protoplasmix

So I think invariance is more than just a principle. I think it's an entire branch of physics - and the study of the physics of invariance is what we call math. It's all physics, I think :)