Questioning the supremacy of mathematical formalism in understanding the universe

[wtf]

I completely disagree with Wigner. I see no miracle here. I see the human mind modelling the patterns of order which he observes in nature in whatever way which works the best for him. These models make no truth statements whatsoever about the universe and if the human mind figures out a better way of modelling his world then he can simply chuck all his fancy equations in the bin to join Ptolemy's epicycles. Wigner's is a Platonist doctrine which depends on the notion of transcendent cause and should thus be anathema to a philosopher.

Excellent answer, your post expressed my thinking on this subject far better than I could.

... it would also be unfair to suggest that Newton himself was unaware of this limitation imposed on his own methodology.

Newton directly addressed this issue in his famous quote, "I frame no hypothesis." In his own time Newton was challenged because his theory only said what gravity did. He didn't explain why. By contrast, Descartes had a theory that gravity was caused by energy vortices pushing the planets around. That was an explanatory theory, and Newton had no explanation.

Newton famously addressed this point, saying that making up explanations has no place in science. He said:

[quote="In 1713 Isaac Newton""]I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.[/quote]

I'm always struck by how modern Newton's thinking was. He could come back today and explain this same point to many scientists who don't understand the nature of their own enterprise.

[Obvious Leo]

Niels Bohr nailed the same point in a quote which I paraphrase from an approximate memory.

"It is NOT the role of the physicist to explain what the universe is but merely to determine what he can meaningfully say about the behaviour of matter and energy within it."

This later became known as the "physics is whatever works" approach, which I agree with, and even later was summed up as "shut up and calculate", which I agree with even more. I wish that some of the media sluts in modern physics would heed Bohr's wise advice.

[surreptitious57]

Now general relativity might have to go since it is very ineffective in dealing with the very large
or the very small. Spacetime itself may even have have to go for it might not be as uniform and
seamless at the quantum level as it is at the classical level as everything is predicated upon the
quantum. Without it the classical level which we observe would not exist which includes us also

[Obvious Leo]

Now general relativity might have to go since it is very ineffective in dealing with the very large
or the very small. Spacetime itself may even have have to go for it might not be as uniform and
seamless at the quantum level as it is at the classical level as everything is predicated upon the
quantum. Without it the classical level which we observe would not exist which includes us also

The spacetime narrative was metaphysically flawed from the outset but only in recent years have some of the most illustrious of the illuminati in theoretical physics been willing to acknowledge that this is in all likelihood why the current models used in physics contradict each other and describe a universe which makes no sense. The logical positivists decided that it would be more convenient to redefine what making sense means rather than consider the possibility that the models were not modelling the real world, but after a century in the conceptual wilderness it would be fair to say that this has not been a very successful policy.

[ittiandro]

"Obvious Leo" ,

The circularity of scientific thinking, to which both you and me refer, ( although I see it as a problem and not as an answer), seems to be broken, when, strangely, it yields scientific hypotheses that are empirically validated. How can a mathematically formulated scientific hypothesis have a predictive value and be empirically confirmed , as it often happens, if it is nothing more than an inner model of our mind? This is still my problem.

Man’s success in landing on the moon, hundreds of thousands of miles away or, more recently, the spectacular landing of the Rover vehicle on Mars, was made possible thanks to astronomy and other sciences, which were able, among other things, to calculate the positions of eventual asteroids, planets, stars, etc in the path of the spacecraft, with their trajectories, their gravitational interactions, their spectrographic signatures, their speeds and thus avoid collision. Isn't the knowledge of these elements also an explanation of how various parts of our universe work?

Can we really say that what we call external reality, in this case those celestial bodies, in their behaviours, do not have an “objective” external existence, but are only part of a pre-existing mind-created narrative, when, in fact, their supposed “ un-reality”, if ignored, can mean the difference between a spacecraft successfully landing on the moon or tragically smashing, instead, against an asteroid or simply getting lost in the immensity of space?
Dr Johnson’s famous kicking of the stone in response to Berkeley’s idealistic contentions, well expresses the difficulties inherent to an unalloyed idealism.

The human mind often shows an uncanny capability to explain away problems which it cannot( or does not want to) solve , This seems to vindicate William James’ idea that often, behind our beliefs, our “will to believe” ( no matter what) plays a more important role than the reasons against them. A believer will often, if not always, believe in God and similarly an an atheist will deny its existence, both ignoring the problems inherent to their respective views. .

Unfortunately, the “new” views which we please to take in order to get out of a dead-end, like on the present issue, often entangle us in just as many problems as the original view, because they run counter a deeply rooted and to me justified expectation that there IS a reality to be explained and that it CAN, in varying degrees, be explained. Faced with the failure to explain how this interaction between our mind and the " external reality" works, we then say :“ well, there is no reality, therefore there is nothing to explain but the workings of our mind”.

Very easy and perhaps even convenient to recede into this sort of ..circular idealism, but have we really done more than shoving the problem in a drawer, so that we are not confronted with the embarrassing “ irrationality” of having to admit the existence of a mystery or the limits of our mind?

The ramblings of linguistic analysis, spearheaded by Logical Posivtism ,( from which even science today has increasingly disassociated itself, at least in certain areas, in the face of the weakening of the traditional empiricist paradigm, particularly in theoretical physics) have embarked some “ philosophical minds” ( see A,J. Ayer) on a blind dogmatic crusade under the banner of empiricism and empirical verifiability not only in science, but also in human discourse in general.

His statement that human discourse is meaningless when it is about entities which are not “empirically verifiable”,..is an example of this crude dogmatism, which, paradoxically, would make even the highest expressions of our civilization essentially meaningless, the ramblings of irrational minds..,

I wonder what he would have made of… Higgs’ bosons or curved space or .the .tensors, or notions like Entanglement in Quantum Mechanics, Heisenberg’s Uncertainty Principle, the Schrödinger cat, or other implications of Quantum Mechanics, leading even to the violation of the principle of non-contradiction, at least at the microscopic level.

I once read a scientist, I don’t remember if Sir John Eccles or other, stating that the conditions for the existence and the functioning of life as we know it are so incredibly complex and numerous, practically infinite, that the fact that they should all combine and coalesce, by hazard, in giving birth to life is nothing short of a miracle..
Believing in pure hazard would therefore be just as problematic, if not more, than believing in the argument from design and the existence of God..

Ittiandro.



.

[Obvious Leo]

The circularity of scientific thinking, to which both you and me refer, ( although I see it as a problem and not as an answer), seems to be broken, when, strangely, it yields scientific hypotheses that are empirically validated. How can a mathematically formulated scientific hypothesis have a predictive value and be empirically confirmed , as it often happens, if it is nothing more than an inner model of our mind? This is still my problem.

I agree that this is a problem but it is not a problem without an explanation. If you ever hear somebody use the phrase "the evidence speaks for itself" then you can be sure that you're dealing with a dickhead because evidence does not speak. It is the interpreter of the evidence who speaks. The main problem that physics has always had to confront has never varied and even though great conferences have been held to resolve it, it has never been resolved. I refer to the "observer problem", sometimes known as the "measurement problem", or even the "consciousness problem", a phrase which sails impressively close to the truth. An observation is an act of cognition and "collapsing a wave function" is just a fancy term for taking a look and interpreting what we see. If we design our models specifically to predict what we're going to observe then we should be unsurprised when we duly go ahead and observe what our models have predicted, the Higgs boson being an excellent example.

Man’s success in landing on the moon, hundreds of thousands of miles away or, more recently, the spectacular landing of the Rover vehicle on Mars, was made possible thanks to astronomy and other sciences, which were able, among other things, to calculate the positions of eventual asteroids, planets, stars, etc in the path of the spacecraft, with their trajectories, their gravitational interactions, their spectrographic signatures, their speeds and thus avoid collision. Isn't the knowledge of these elements also an explanation of how various parts of our universe work?

Absolutely not. There is no valid reason why we couldn't send a mission to Mars solely by using Ptolemy's geocentric cosmology, with a greatly embellished suite of epicycles. I shudder to think what the equations might look like but this is perfectly logically possible. If such a mission were successful have we then proven that the earth is at the centre of the solar system?

Can we really say that what we call external reality, in this case those celestial bodies, in their behaviours, do not have an “objective” external existence, but are only part of a pre-existing mind-created narrative,

We can accept the existence of an objective reality but we can draw no conclusions about what form such an objective reality takes. This is basic Kant 101. Imagine the hypothetical extra-terrestrial civilisation of a similar intelligence to our own. We can imagine them modelling stars, planets and galaxies in much the same way as we do but surely we draw a long bow if we were to make the same assumption about atoms, quarks, electrons etc. There could be an almost infinite number of different ways of modelling the subatomic world so we indulge ourselves in a gigantic act of hubris if we somehow assume that we've stumbled on the "right" one. There is no "right" way of doing this and I'll be quite happy to bet that a hundred years from now these particles will have gone the way of phlogiston. We'll have figured out a better way of doing this because such is the way of science.

The human mind often shows an uncanny capability to explain away problems which it cannot( or does not want to) solve , This seems to vindicate William James’ idea that often, behind our beliefs, our “will to believe” ( no matter what) plays a more important role than the reasons against them. A believer will often, if not always, believe in God and similarly an an atheist will deny its existence, both ignoring the problems inherent to their respective views. .

And a clever mathematical physicist can always salvage his theory with a set of new equations and additional hypotheses. Dark energy, dark matter, eternal inflation, etc are the new Ptolemaic epicycles.

I once read a scientist, I don’t remember if Sir John Eccles or other, stating that the conditions for the existence and the functioning of life as we know it are so incredibly complex and numerous, practically infinite, that the fact that they should all combine and coalesce, by hazard, in giving birth to life is nothing short of a miracle..
Believing in pure hazard would therefore be just as problematic, if not more, than believing in the argument from design and the existence of God..

Do you regard it as a miracle that of all the possible human beings who your parents could have created in their long-ago act of love it was actually YOU that was brought into existence? Was this an event of such astonishing unlikelihood that either all the people who you are not must also exist or else the invisible hand of the supernatural must be at work. Such is the quality of the above logic.

[Obvious Leo]

Ittiandro. I need to fly interstate on business very shortly and I'll be absent from the forum for a few days but please don't go away. As a logician and philosopher of applied metaphysics the questions which you raise form the central plank of my ongoing work and I'm delighted to encounter somebody who recognises the profound significance of such questions. Until the science of physics abandons its logical positivist stance and acknowledges such questions as valid then its quest for a unification model will lie forever beyond its grasp. The problem of physics is not a physical problem but a metaphysical problem, and indeed a meta-mathematical problem.

[ittiandro]

Because they are two different ways of expressing the same thing gravity and time can be quantised equivalently but this interpretation can never be accommodated within the spacetime narrative because this narrative is founded on a fundamentally flawed a priori assumption, namely the constant speed of light.

Examine these two statements in terms of their logical consistency and thus their truth value.

1. the speed of light is a constant

2. the speed of light is only observed to be a constant because it is proportional to clock-speed.

Both of these statements will produce identical epistemic phenomena for the observer to observe but only one of them makes sense.

You may philosophize as much as you want, but you perhaps overlook the fundamental distinction between philosophy ( even philosophy of science!) and science. You can use logic to invalidate a statement about the invariance of the speed of light, but not the invariance itself.
This is the task of science, not philosophy or logic.The invariance of the speed of light is a mathematically tested and empirically validated property of the universe . Its truth is beyond the purview of logical arguments. It lies in the predictive success of scientific hypotheses like the Theory of Relativity, which take it as a fundamental assumption.

I have some difficulties with the statement that the invariance of the speed of light is a “fundamentally flawed A PRIORI assumption”, if anything because this “flawed” “assumption “is empirically validated so far by science and all the technological applications based on it.

For one thing, it is at the core of Relativity. If you challenge it, then we have to question the whole theory of Relativity, which is based upon it.
We would also fall back on something similar to the angst faced by physics in the light of the Michelson-Morley experiment.

I am not saying that scientific hypotheses or laws cannot be revised and even discarded, but it is not an easy task to challenge Maxwell’s equations. Indeed, challenging the validity of such a fundamental law requires, to me, none less than another Einstein, which is rather improbable, at least..statistically. I am not aware of any attempt being made by scientists at the moment.

WE are all welcome to try, but to question the principle of the invariance of the speed of light and the Maxwell equations, requires a rigorous scientific, mathematically backed methodology, not just a sweeping philosophical statement.
Furthermore, this is the task of science, not that of philosophy, unless the philosopher is also a scientist and shifts his/her language and methodology to those of science.

Eschewing the law of the invariance of the speed of light falls within the broader, and to me questionable, tendency, in some quarters, to move away from realism, i.e. to relativize and subjectivize the “ reality” with which science deals, by reducing scientific discourse to no more than a circular process fed by the models we have chosen in advance as a given methodological perspective ( which could be different).

In the end, what science arrives at would no longer be a reality in its own right, neither an explanation of it , however partial or even wrong, but just a “ description”, whose TRUTH would be nothing more than the consistency with the a priori chosen models.

I may be wrong, but I am inclined to think that such a view is more akin to overzealous philosophical thinking than to true scientific thinking, because it has always been and it must be the fundamental assumption of science that 1) there is an external world 2) this world can be causally explained 3) the truth of the explanations is measured by the standard of empirical observation and the predictive capability of the hypotheses , rather than the mere conformity of the hypotheses with the a priori chosen models.

To deny reality to the world and to think that it cannot be known in itself, other than as a mere reflection of our a priori mental constructs, is an implicit return to the things in themselves and the epitome of a more serious circular thinking: things in themselves have been defined as not knowable, therefore outside the scope of philosophy and science, but then they are implicitly reintroduced as the standard by which we measure ( and in this case deny) the reality of the world we live in and the truth of the explanations provided by science.

Syllogistically, this can be expressed as follows:
1. Things in themselves do not exist, but even if they did, they would be unknowable
2. Whatever science claims to know, cannot be the things in themselves
3. Therefore science does not yield true knowledge.

What about if we ignored once for all the shadow of these darned unknowable noumena and we admitted as a working hypothesis that what we know of the external reality through science or sense perception IS or can be true knowledge, to the extent that it is validated by empirical observation, at least provisionally, until better hypotheses are found?

There is no need to submit the existence of reality to the “ probatio diabolica” of the things in themselves, which we know to be an impossible condition, precisely because we defined it as such. …

In the end, if we can walk on the moon or should we become able through stem- cells technology to re-regrow human limbs or organs,(which will become possible in not too distant a future ), is there any sense in asking such a question as : “ Yes, we do all this, but is the scientific knowledge behind it REAL knowledge of the external world?”

I don’t think many scientists will ask it, just as not too many of them are doubting the principle of the invariance of the speed of light, at least AS SCIENTISTS.

Personally I’d ban this type of questions from any meaningful philosophical discourse, in compliance with the all-too-forgotten principle known as the “ Ockam razor’ “, based on William of Ockam’s reminder that :
“Entia naturae non sunt multiplicanda praeter necessitatem ” ( conceptual distinctions in nature should not be multiplied beyond what is necessary)


Ittiandro

[Obvious Leo]

You may philosophize as much as you want, but you perhaps overlook the fundamental distinction between philosophy ( even philosophy of science!) and science. You cannot use logic to invalidate a law such as that of the invariance of the speed of of light, which is a mathematically tested and empirically validated property of the universe . Its truth is beyond the purview of logical arguments. It lies in the predictive success of scientific hypotheses like the Theory of Relativity, which take it as a fundamental assumption.

You overlook a couple of important points here. You forget that SR was published prior to GR and was not subsequently updated in the light of further knowledge. The constant speed of light was assumed to be invariant because it was not known that clocks ticks at different speeds in different gravitational environments. SR was formulated on the Newtonian assumption that clocks tick at the same speed regardless of whereabouts in the universe they are. However GR showed that clock-speed is inversely proportional to gravity in a precise mathematical relationship which is inversely logarithmic in its nature and that this inverse relationship must apply all the way down to the Planck scale. What this in fact proves is that the speed of light is the most inconstant speed in the universe. For example the speed of light on the moon is the same as the speed of light on earth but what this in fact proves is that the speed of light is NOT a constant because these two measurements are being made on clocks that tick at different speeds. A clock on the carpet ticks faster than one on the bare floorboards beside it and a clock on the electron ticks faster that a clock on the nucleus it orbits. In fact what GR shows us is that the speed of light and the speed at which time passes are one and the same thing, and this is the elephant in the room of physics because this brings gravity into the Standard Model, where it is conspicuous by its absence.

For one thing, it is at the core of Relativity. If you challenge it, then we have to question the whole theory of Relativity, which is based upon it.
We would also fall back on something similar to the angst faced by physics in the light of the Michelson-Morley experiment.

It is not relativity which is in question but the entire spacetime paradigm on which relativity is founded which is in question. The simple fact is that time is NOT a spatial dimension because spatial dimensions are mathematical objects and not physical ones. The simplest explanation for Michelson-Morley was simply overlooked. The Cartesian 3 dimensional space is a property of the consciousness of the observer and NOT a physical property of the universe. This has been mainstream philosophy for millennia and is regarded as canonical doctrine in cognitive neuroscience.

In the end, what science arrives at would no longer be a reality in its own right, neither an explanation of it , however partial or even wrong, but just a “ description”, whose TRUTH would be nothing more than the consistency with the a priori chosen models.

The sad fact is that mathematical physics is not designed to model reality. It can only model a particular narrative of reality which must first be specified by the observer and therefore it is inherently tautologous. However when the models devised in this process then define a universe which makes no sense we can safely conclude that our presumptive narrative is bollocks. Attempting to redefine what making sense means is a gesture of spectacular hubris which has kept physics in a conceptual cul-de-sac for a century. GR blatantly contradicts SR and until this issue is resolved no hope of reconciling GR with QM can ever be possible because QM is entirely predicated on SR.

Syllogistically, this can be expressed as follows:
1. Things in themselves do not exist, but even if they did, they would be unknowable
2. Whatever science claims to know, cannot be the things in themselves
3. Therefore science does not yield true knowledge.

This is basic Kant 101 which any philosophy undergraduate would be expected to understand.

What about if we ignored once for all the shadow of these darned unknowable noumena and we admitted as a working hypothesis that what we know of the external reality through science or sense perception IS or can be true knowledge, to the extent that it is validated by empirical observation, at least provisionally, until better hypotheses are found?

Better hypotheses can only be found if the flaws in the current hypotheses are acknowledged as such. As long as the spacetime bullshit is regarded as holy writ then physics will never progress. There are far simpler explanations for the observed phenomena which do not require us to attribute magical physical properties to mathematical abstractions.

“Entia naturae non sunt multiplicanda praeter necessitatem ”

The physicists should be taking a good hard look at this quote and themselves in a mirror.

"It should be possible to explain the universe to a barmaid"...Albert Einstein

"The universe will ultimately reveal itself to be an entity of the most sublime austerity"....John Archibald Wheeler.

Einstein and Wheeler were both right because reality is EXACTLY what it appears to be, a PROCESS.

[ittiandro]

You forget that SR was published prior to GR and was not subsequently updated in the light of further knowledge. The constant speed of light was assumed to be invariant because it was not known that clocks ticks at different speeds in different gravitational environments......


It is not relativity which is in question but the entire spacetime paradigm on which relativity is founded which is in question. The simple fact is that time is NOT a spatial dimension because spatial dimensions are mathematical objects and not physical ones......


The sad fact is that mathematical physics is not designed to model reality. It can only model a particular narrative of reality which must first be specified by the observer and therefore it is inherently tautologous. However when the models devised in this process then define a universe which makes no sense we can safely conclude that our presumptive narrative is bollocks.....


As long as the spacetime bullshit is regarded as holy writ then physics will never progress. There are far simpler explanations for the observed phenomena which do not require us to attribute magical physical properties to mathematical abstractions.



"It should be possible to explain the universe to a barmaid"...Albert Einstein

S.R. already acknowledged that “ moving” clocks tick at different speeds for observers in different inertial frames. Here the explanation was that the speed at which they and/or the observer move causes space and time to contract.
G.R. simply added gravity as another element affecting the time-keeping speed of clocks, but, in this regard, it didn’t signify any fundamentally new perspective which could justify the questioning of the invariance of c.

If there were any reasons to question it, they already existed at the time of S.R. and I am sure that A. Einstein would have picked them up.

Indeed, just like you, I’m myself puzzled at theoretical constructs of a mathematical nature not having a physical reality, such as curved space and the like, but I think it is a bit of philosophical hubris to dispose of these seemingly problematic notions with the magic wand, as it were, of philosophical and/or logical arguments, ignoring the equally puzzling fact that these “flawed” metaphysical assumptions are the foundation stones of hypotheses having high predictive value and empirical validity.

Again, if you challenge the spacetime paradigm, which is at the core of G.R., you must challenge the validity of Relativity. The only problem is how can Relativity be invalidated on theoretical or philosophical grounds, if its predictions are validated empirically. I have already raised this point, but I don’t think you have responded.

Besides, even more down-to-earth disciplines such as Euclidean geometry, having wide-spread practical use, are based on notions like points, lines, angles, tangents, sine, cosine, etc, which do not have a physical reality. So where do we draw the line?

You call ( rather expeditiously) “bollocks” and “ bullshit” what is endorsed by the most brilliant scientific minds, beginning with A. Einstein.
I am aware that the “ argumentum ad auctoritatem” is a formal logic fallacy, but I think in this case, given the name and the prestige of such “ bullshit-mongering” scientists, appealing to their authority is justified.

Personally, not being a scientist, I don’t know how to replace this” bollocks” with any other viable hypotheses. Neither do I think that my philosophical background allows me to make meaningful comments on the validity of one of the most fundamental laws of physics: the invariance of c.

There are certainly more nebulous areas in science, especially, in cosmology, where the paths of philosophy and science cross and the philosopher’s contributions can be just as meaningful as scientific speculation. I do not think we are at the crossroads on this issue, because what you call “ flawed” or, worse”, bullshit” metaphysical presuppositions have yielded highly successful scientific hypotheses and technological applications.

The links between these “ bullshit” presuppositions and the hypotheses that feed on them may be tenuous or utterly incomprehensible, but we shouldn’t reject as “ bollocks” all that we don’t understand and for which we cannot offer an alternative solution.…

If I were a scientist and I had problems with some of the prevailing views, I’d lay them out in scientific terms and try to propose alternatives, rather then accusing my peers of spreading “ bollocks” and “ bullshit”.

AS to Einstein’s statement "It should be possible to explain the universe to a barmaid"... Well he probably assumed that all the barmaids have the same intelligence that he and other few selected had or have . The truth is that for most of us what we don’t understand vastly exceeds what we understand, especially in science and even more so when we are not scientists.

Ittiandro

[Obvious Leo]

Here the explanation was that the speed at which they and/or the observer move causes space and time to contract.

This is not a physical explanation because the Cartesian space has no physical properties, as Leibniz pointed out. Therefore to speak of the contraction of space is to make a mathematical statement and nor a physical one. It was subsequently shown, however, that time does not pass at a constant speed because of gravity so the speed at which time passes is clearly a real and measurable effect of gravity. This is ignored in SR which is nowadays regarded as a "special case" of GR in the so-called "flat space" which is patently absurd since GR clearly shows that there is no such thing as a "flat space" in the physical universe. This means that the Lorentz-Fitzgerald contraction is nothing more than a mathematical abstraction with no real physical analogue. In their logical positivist zeal the physicists are conflating their map with the territory and since QM is entirely predicated on SR and not GR this explains why QM is riddled with paradoxes and metaphysical absurdities. I make no apology for describing as bullshit any model which requires a particle to be in an infinite number of places at the same time and allows for effects to precede their causes. QM is nothing more than a mathematical procedure for codifying a particular class of observations, the nature of which must be specified in advance. Physic continues to ignore the fact that an observation is an act of cognition.

G.R. simply added gravity as another element affecting the time-keeping speed of clocks, but, in this regard, it didn’t signify any fundamentally new perspective which could justify the questioning of the invariance of c.

This is the elephant in the room of physics. Because the speed of light was observed to be a constant it was therefore assumed that the speed of light actually IS a constant but after GR this assumption was falsified. GR shows that the speed of light is proportional to clockspeed and that clockspeed is variable all the way down to the Planck scale in an inversely logarithmic relationship with gravity. Since this interpretation can more easily explain the so-called "expanding space" it must be preferred on the grounds of Occam economy.

If there were any reasons to question it, they already existed at the time of S.R. and I am sure that A. Einstein would have picked them up.

He did, and he referred to it constantly throughout his life. He knew that EPR falsified the spacetime paradigm and he also knew why. It is because spacetime is still an aether theory, despite its embellishments on the Newtonian model.

Indeed, just like you, I’m myself puzzled at theoretical constructs of a mathematical nature not having a physical reality, such as curved space and the like, but I think it is a bit of philosophical hubris to dispose of these seemingly problematic notions with the magic wand, as it were, of philosophical and/or logical arguments, ignoring the equally puzzling fact that these “flawed” metaphysical assumptions are the foundation stones of hypotheses having high predictive value and empirical validity.

The predictive value of these models is routinely overstated. Despite the extremely precise nature of the predictions which QM and GR can generate they remain statistical models only. They cannot predict the future, even in principle, but only the probability of a particular future, and this has very important metaphysical consequences. It means that the notion of "laws of physics" is a myth. Nature does not conform to a suite of laws at all but is self-determining and it is the observer who constructs this self-determining behaviour of matter and energy into a system of laws.

Again, if you challenge the spacetime paradigm, which is at the core of G.R., you must challenge the validity of Relativity.

This is not true. Relativity is open to a vastly simpler interpretation if the physical world is regarded as a continuum of gravity and time which the observer constructs within his consciousness into a continuum of space and time. Such an interpretation is also consistent with millennia of philosophy dating back to the pre-Socratics. The universe is not a collection of objects moving in space but a sequence of events occurring in time which the observer constructs into a personal narrative of objects moving in space. This narrative simply MUST be bogus because the speed of light is finite and thus the observer only has information about events which no longer exist. The cognitive map of the observer is a holographic representation of his own past and it is this very hologram which the models of physics are modelling.

Besides, even more down-to-earth disciplines such as Euclidean geometry, having wide-spread practical use, are based on notions like points, lines, angles, tangents, sine, cosine, etc, which do not have a physical reality. So where do we draw the line?

We don't. Mathematics was never designed to model the real world. It was only ever designed to model the mind of he who observes it and then seeks to explain his observation in this way. It is inherently tautologous, which is why Ptolemy's geocentric cosmology survived for 1400 years.

"It is the THEORY which determines what the observer will observe".....Albert Einstein

If somebody were to make the attempt all of modern cosmology could be mathematically expressed in terms of Ptolemy's geocentric assumption with a vastly more sophisticated suite of epicycles. The sums would be horrendous but there is no logical reason why this couldn't be done and such a model would have the same predictive authority as any which are currently being used. However this would not prove that the earth is at the centre of the solar system. It would only prove that humans are very clever at modelling their assumptions in such a way that these assumptions confirm themselves. Any new empirical data can simply be appended to the model with brute mathematical force so that the new data will conform to the theory.

'Mathematics can be used to prove ANYTHING"....Albert Einstein.

I am aware that the “ argumentum ad auctoritatem” is a formal logic fallacy, but I think in this case, given the name and the prestige of such “ bullshit-mongering” scientists, appealing to their authority is justified.

You're not alone. Many people think the same but this won't alter the fact that the models which physics is using are mutually exclusive and collectively describe a universe which makes no sense. Physicists may grant themselves the privilege of redefining what making sense means that this doesn't mean that the philosophers should stand meekly by and allow them to get away with it. In any event I'm just a simple country lad who was brought up to accept that if it looks like bullshit then it probably is and thus far the physicist's attempts to persuade me to the contrary have been unpersuasive. I reckon a cat can be either dead OR alive but not both simultaneously and if anybody wants to suggest otherwise then the convention in philosophy is that extraordinary claims require extraordinary proof. Such a proof has never been forthcoming and it'll take a lot more than a collection of fancy equations to satisfy the proof burden.

Personally, not being a scientist, I don’t know how to replace this” bollocks” with any other viable hypotheses.

For a hundred years no other hypothesis has even been considered. The spacetime paradigm has been adopted as canonical doctrine and all new evidence has simply been interpreted in such a way that it accords with it. Not only was Einstein aware of this problem but so were Planck and Bohr. However it was Thomas Kuhn who laid the problem the most clearly. The problem of physics is not a problem of physics but a problem of the way we think about the world.

AS to Einstein’s statement "It should be possible to explain the universe to a barmaid"...

In all his writings Einstein was very clear in his mind about what a true unification model would be able to achieve. He was adamant throughout his life that the real universe is something which a child could understand and I reckon he was right. I reckon reality is exactly what it appears to be and if you ask any child he'll tell you exactly what reality is. To a child reality is simply what's happening all around him and to a physicist this can and should mean only one thing. The universe is that which is continuously coming into existence at the speed of light.