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Why the foundations of physics have not progressed for 40 years

Physicists face stagnation if they continue to treat the philosophy of science as a joke

Why Phsyics has made no progress in 50 years

In the foundations of physics, we have not seen progress since the mid 1970s when the standard model of particle physics was completed. Ever since then, the theories we use to describe observations have remained unchanged. Sure, some aspects of these theories have only been experimentally confirmed later. The last to-be-confirmed particle was the Higgs-boson, predicted in the 1960s, measured in 2012. But all shortcomings of these theories – the lacking quantization of gravity, dark matter, the quantum measurement problem, and more – have been known for more than 80 years. And they are as unsolved today as they were then.

The major cause of this stagnation is that physics has changed, but physicists have not changed their methods. As physics has progressed, the foundations have become increasingly harder to probe by experiment. Technological advances have not kept size and expenses manageable. This is why, in physics today, we have collaborations of thousands of people operating machines that cost billions of dollars.

With fewer experiments, serendipitous discoveries become increasingly unlikely. And lacking those discoveries, the technological progress that would be needed to keep experiments economically viable never materializes. It’s a vicious cycle: Costly experiments result in lack of progress. Lack of progress increases the costs of further experiment. This cycle must eventually lead into a dead end when experiments become simply too expensive to remain affordable. A $40 billion particle collider is such a dead end.

The only way to avoid being sucked into this vicious cycle is to choose carefully which hypothesis to put to the test. But physicists still operate by the “just look” idea like this was the 19th century. They do not think about which hypotheses are promising because their education has not taught them to do so. Such self-reflection would require knowledge of the philosophy and sociology of science, and those are subjects physicists merely make dismissive jokes about. They believe they are too intelligent to have to think about what they are doing.

The consequence has been that experiments in the foundations of physics past the 1970s have only confirmed the already existing theories. None found evidence of anything beyond what we already know.

But theoretical physicists did not learn the lesson and still ignore the philosophy and sociology of science. I encounter this dismissive behavior personally pretty much every time I try to explain to a cosmologist or particle physicists that we need smarter ways to share information and make decisions in large, like-minded communities. If they react at all, they are insulted if I point out that social reinforcement – aka group-think – befalls us all, unless we actively take measures to prevent it.

Instead of examining the way that they propose hypotheses and revising their methods, theoretical physicists have developed a habit of putting forward entirely baseless speculations. Over and over again I have heard them justifying their mindless production of mathematical fiction as “healthy speculation” – entirely ignoring that this type of speculation has demonstrably not worked for decades and continues to not work. There is nothing healthy about this. It’s sick science. And, embarrassingly enough, that’s plain to see for everyone who does not work in the field.

This behavior is based on the hopelessly naïve, not to mention ill-informed, belief that science always progresses somehow, and that sooner or later certainly someone will stumble over something interesting. But even if that happened – even if someone found a piece of the puzzle – at this point we wouldn’t notice, because today any drop of genuine theoretical progress would drown in an ocean of “healthy speculation”.

And so, what we have here in the foundation of physics is a plain failure of the scientific method. All these wrong predictions should have taught physicists that just because they can write down equations for something does not mean this math is a scientifically promising hypothesis. String theory, supersymmetry, multiverses. There’s math for it, alright. Pretty math, even. But that doesn’t mean this math describes reality.

Physicists need new methods. Better methods. Methods that are appropriate to the present century.

And please spare me the complaints that I supposedly do not have anything better to suggest, because that is a false accusation. I have said many times that looking at the history of physics teaches us that resolving inconsistencies has been a reliable path to breakthroughs, so that’s what we should focus on. I may be on the wrong track with this, of course. But for all I can tell at this moment in history I am the only physicist who has at least come up with an idea for what to do.

Why don’t physicists have a hard look at their history and learn from their failure? Because the existing scientific system does not encourage learning. Physicists today can happily make career by writing papers about things no one has ever observed, and never will observe. This continues to go on because there is nothing and no one that can stop it.

You may want to put this down as a minor worry because – $40 billion dollar collider aside – who really cares about the foundations of physics? Maybe all these string theorists have been wasting tax-money for decades, alright, but in the large scheme of things it’s not all that much money. I grant you that much. Theorists are not expensive.

But even if you don’t care what’s up with strings and multiverses, you should worry about what is happening here. The foundations of physics are the canary in the coal mine. It’s an old discipline and the first to run into this problem. But the same problem will sooner or later surface in other disciplines if experiments become increasingly expensive and recruit large fractions of the scientific community.

Indeed, we see this beginning to happen in medicine and in ecology, too.

Small-scale drug trials have pretty much run their course. These are good only to find in-your-face correlations that are universal across most people. Medicine, therefore, will increasingly have to rely on data collected from large groups over long periods of time to find increasingly personalized diagnoses and prescriptions. The studies which are necessary for this are extremely costly. They must be chosen carefully for not many of them can be made. The study of ecosystems faces a similar challenge, where small, isolated investigations are about to reach their limits.

How physicists handle their crisis will give an example to other disciplines. So watch this space.


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robert ansley 20 June 2020

This was a very enlightening article for me. My field is saturated with amateurs that have no concept of scientific method, they simply throw everything at a wall to see what sticks. I was surprised to see similar human behavior in physics, such as not understanding the history of successes and more importantly the failures. I’m talking about psychical research and specifically the phenomenon of voices appearing in recordings that currently cannot be explained. Because of the noise created by the wildly popular culture of “ghost hunters,” results from serious research is completely drowned out. They announce “discoveries” almost daily that have been known for over 100 years, repeat failure after failure, and apply non-sequitur logic to develop useless theories. Of course there are highly credentialed scientists investigating psychical phenomenon such as at the London Society for Psychical Research of which I am a member. But most people have never heard of them because the SPR doesn’t have a show on the Travel Channel. It’s Psychical Research battling Paranormal Entertainment. I expected ro find this behavior in my field of study, but not in Physics. I was surprised to read an article where I could replace every mention of “physics” with “psychical research” and still have a valid opinion piece. This human behavior will evidently impede progress and innovation in every discipline.

I was recording myself one night to determine the severity of my sleep apnea when three voices appeared loud and clear on the recording that I cannot explain. Was my own mind projecting thought waves? Were there discarnate entities in the room with me? Was my digital recorder picking up stray radio or television waves? I can repeat the results in tightly controlled conditions and have eliminated stray radio waves as the source through the use of a Faraday Cage, but I’ll probably never find an answer for the origin of the voices. Even if I could, what would the value of that information be? Restricted by lack of funding and the social distancing I experience when telling friends and family about it I have become discouraged. I expected the behavior in my eclectic field, how much more discouraging must it be for physicists?

David Harness 11 May 2020

In any event, the global complex system COVID19 shutdown has cast the standard model of physics-supersymmetry (SM-SUSY) zero-sized material particle hidden dimensional physics multi-body problem in its final falsified state at LHC energy levels – since the sovereign-corporate bankruptcies will not entertain any further funding of the Future Circular Collider (FCC) or Circular Electron Proton Collider (CEPC) next generation of electromagnetic turbulence. The multi-body problem is proven to be computationally intractable starting with the 3-body problem let alone the entire freaking universe. Computationally intractable means no hidden dimensional unknown string-membrane-lattice material mechanisms can be described or operate in machine language logic. Hence: Contradiction by AI failure.

After 70 years standard model cosmologists famously claim to "understand" only 5% of the universe, which zero-sized particle zoo model they are trying to apply to the unknown 95% of the universe attributed to dark energy and matter – with zero results.

As Prof. Hossenfelder describes the particle zoo keepers haven't found the superpartner critters they need to make the standard model of physics SM-SUSY particle-sparticle foundations of physics model work.

Clearly the foundations of physics trend has arrived at verification of the immaterialism of Plato, Planck, Bohr, Heisenberg, Born, Schrodinger, and Wheeler is taking place – verifying at both the high-energy physics and low-energy physics spooky NPR Bell inequality entanglement freedom of choice experimental levels – the last theory standing of quantum information theory psychophysical parallelism.

Clearly the falsification at LHC energy levels of Aristotle's classical materialism in modern form Randall, Krauss, Greene, Tyson, Higgs of the SM-SUSY particle-sparticle zoo – of zero-sized imaginary-invisible mathematical point particle unknown string-membrane-lattice classical materialism mechanisms which occupy no space having the 4D spacetime measurements of nothingness – is apparent in having all the self-definition and explanatory attributes of immaterialism – except for the logical conclusion.

And so “Time is running out for supersymmetry and string theory – Are physicists giving up?”

Well if anyone here hasn't abandoned ye all faith in SM-SUSY, including Prof. Hossenfelder or anyone else anywhere with half her honesty, intelligence, and courage – falsification of immaterialism could be shown by introducing material substance at some point to repair the PhD answers to the question posted on Quora: “If the CERN LHC proton-proton beam collisions actually consist of quarks of zero size why don't the quark-gluon-quark beams just pass through one another without colliding?”

The virtually immaterial explanations of standard materialism – indicate a nonstandard foundation of physics is starting to seem more likely all the time, especially since there is a 4D computational mathematical physics quantum information theory formalization one can just read – or better yet just click through the Maplesoft or Mathematica 4D electromagnetic energy-momentum density tensor integration equations:

Sanjeev Aaryabhatt 2 May 2020

I'll reply in below points-
1- this article is good. Suggest me if I can use in my upcoming book.
2- let's come to your article- actually the story was different. The science witnessed the tallest building in the city. They took the direction which seems aligned to the science. The science reached to a hill, where from the city was looking too small along with the tallest building. Bent with loads of responsibility, the science lost its free mind and declared that tallest building in the city is very tiny.
3- you are trying to find the truth. No different way of experimenting is required. Science is actually very easy. You just need to know the right logic with logical source of information.
4- you do not need any experiment, if you don't need mathematical calculations. Your brain is wise enough to confirm you the correctness of logical information.
5- are you really looking for the right information, the truth Nd the logic behind it? How long you will dare to go to find the truth?
You just need the right path. After lock down, I'll try to help you. You may remind me.

Juris Bogdanovs 14 April 2020

For approach like this I like Professor Sabine Hossenfelder! And yet, when other people say virtually the same about some of the existing theories, she becomes angry and somewhat takes an insult herself... I wrote an article on Quora about the true pattern of Magnetic field that is revealed in that book titled 'Blunders of Science and Religions", and no scientist finds it inspiring or even worth looking at. The general feeling about the world of science today is that it is more like the Emperor's New Clothes tale...
That article can be found here -

That book I was quoting previously describes how the idea about the Big Bang itself has derived from mathematical model and the idea is absolutely contradicting real life observations. That book explains many claims from this theory as being absolutely false and impossible. And the same is with the magnetic field and its mechanics.

Big Bang claims that the universe was smaller up to the point of Singularity. And, the smaller it was, the hotter it was. Real life observations and experiments say that this is impossoble. The hotter something is, the more it expands. No exceptions apart from few gases in a small range of temperatures, and even that might be a misinterpretation of the reality.

Also, the Big Bang declares that whole Matter of Universe was billions and trillions and zillions (etc...) times smaller. But that is also impossible according to real life observations. The most iconic example of that is the pressure of air in our tyres. The more we squeeze them, the more they push back. And this correlation, as we know it, never stops. So, to get the Universe 100 times smaller would request unimaginable force, let alone to keep going in this direction for trillions of times... There is absolutely no evidence that anything of that could be possible.

Nevertheless, science declared that the Big Bang theory is the best theory we have as Einstein's mathematics allowed it... Since when mathematical models replaced reality? And you see this all over theoretical physics today. It creates and teaches impossible models all over the place. And that String theory or Multiverses are only the best known of them. The subatomic zoo is made up following identical approach - it was absolutely invented and there is no shred of proof for it.

The whole science right now is more like a joke.

Where does Universe/Existence come from? Once again, this is spectacularly addressed in that book I quoted previously - Blunders of Science and Religions. It suggests a theory that explains everything in respect to origins of Universe and doesn't leave any open questions. But who cares, as we are in love with the least possible of all theories addressing Origins of the universe, namely, the Big Bang madness...

And Big Bang fails on all claims of it, including CMB and Emergence of chemical elements and how it started etc... So, who and why is pedalling this Big Bang???

Uncle Al 20 February 2020

The sum of all the positive integers beginning with 1 is famously demonstrable to being -1/12 (regularization). This is essential to number theory and to string theory. It is also silly at face value - but that does not matter. So stipulated!

What is the sum of all positive integers beginning with zero? Is it an "uh-oh?"

Greald Henstra 27 January 2020

Ever since Popper, exactly one hundred years ago now, true science is a cycle of inventing and trying to falsify hypotheses. Hypotheses are nothing but speculations, healthy or not, until having past at least one falsification test. Math has been shown to be an excellent tool to make up new hypotheses. But when they can no longer be tested i's reached its scientific limits. Too bad for the scientific industry. Let me add a drop in the ocean with a suggestion to clean up science. See for that.

Vadim Golub 23 January 2020

It seems that all science and information related industries suffer from the same malady - inability to communicate constructively. It will only grow further as volume of information grows and, unfortunately, most of it is garbage (even filtering takes time and it certainly takes time to learn, to distinguish one from another).
Inability to communicate is not only scientific and informational staple. Those industries are just facing it most acutely, as they require high flexibility and constructive action. At the same time, it is only here where we have any chance at all to approach the question intelligently, discover and test a new way of approaching problems and consequently education.

Sabine noticed the urgent need for us to find more constructive strategies and better ways to communicate them. It is exactly the crux of the issue. However, if I understood it correctly (not a physicist), I do not think looking at history would be of much help here. Not that it is useless, it is just now we are facing completely different models, not sure anyone is yet fully aware of how the Internet changed and continue to change the game. But the intuition is spot on here. Lacking communication is a systematic behavior and it can be approached more sanely. Ironically, math or scientific thinking plays a key function here.

Usually, when we think about math, we think about some abstract conception, a reduction which is distant from life. We forget about the main strength of math - thinking in relations. For simplicity and further elaboration let's mark them thinking A - thinking in terms, definitions - and thinking B - thinking in relations. When we think about math, we mostly stress thinking A, that is a reduction of process to a thing and operating over this thing without any connection to anything else. That is a prevalent mode of thinking overall, not only in scientific circles. It necessarily leads to missing connection with the real processes and miscommunication as a result. However, in reality math or scientific thinking is successful exactly because of prevalence of thinking in relations, or thinking B. Why is it ironic? Many scientists, mathematicians, programmers, etc. develop that kind of thinking in their work but cannot transfer it to other areas (e.g. personal communication). Although, feel it instinctively in communication with others (e.g. family members), just unable to share it, as it is often misunderstood and leads to irritation (due to lack of concentration, interest, or both).

How is it all connected? When we function in A thinking, we don't feel the connection toward anything, we cannot share. We communicate starting from a concept. That part is important. On the other hand, when we feel the deep connection toward something we generally tend to find the language and communicate it. Connection is relation. It only comes from understanding. It reveals what relates to what and how. Therefore, it cannot be drilled, coerced, forced. It can only be discovered through observation, experimentation, and dare one say... play (scientific method). In that case communication is catalyzed by connection, or through relation. That is important. A: concept - first, prove it to life - second. B: life - first, concept - later. So it is not history as such which is crucial (albeit, intuition behind it is), but connection, or seeing the relations first. What relates to what and how. Otherwise, everything becomes artificial, dull, without any sense, mere intellection.

Sabine, if you read this commentary, think about Max Born's "Einstein's Theory of Relativity" and how well he approaches it, presenting all the required for understanding structure of science (even from a layman's perspective) from Galilei to Newton to Lorentz, and managing to make it terse and meaningful, so it becomes alive and kicking. Or Faraday's brilliant "The Chemical History of a Candle" which doesn't even require any previous knowledge. Or a good example can be seen in Feynman's case (e.g. even his entertainment piece "Fun to Imagine" presents this well). What happens there? After watching/reading any of those one may not remember definitions, formulas alright (thinking A) but one will certainly develop some understanding, some 'feeling' for a topic, that is, relation (thinking B).

And there even was a man who due to the same very concern (search for methodology to develop proper communication) attempted to come up with general enough approach, so that anyone can benefit from it, not only a scientist. He attempted to come up with the theory of sanity through communication. The man is Alfred Korzybski and the book is "Science and Sanity". Some claim that he started the wave of NLP (not natural language processing, another one, stupid one), it is a common misconception of those who did not read the book. It can be of value if one is seriously enquiring into the question of relations.

Mike Ivsin 21 January 2020

The earth is flat and stationary. Start there.
Light at reflection produces no momentum (no force).
These are but two true statements. Physicists don't test because they do not follow the scientific method. Cannot wait until they roll over and wake up irrelevant.

Robert Callaghan 18 January 2020

Elizabeth Warren is Harvard's first professor of color, if that is not academic fraud, what is?
Dozens of peer reviewed literature on academic fraud and gender bending chemical emasculation.

All your climate and energy charts on one single page

Bing Laher 15 January 2020

This is written like someone who has absolutely no knowledge of how experimental physics works nowadays. I'm assuming that the author isn't as ignorant on the subject matter as that, and this is just a very manipulative way to spread (while not exactly outright lies) misinformation about *how everyone else is wrong*. I'm sorry, but until I see some due diligence, I'll give the argument here no weight. Or more accurately, I'll give it the weight it deserves: mediocre troll, kinda boring. I'm sad my view gave you money for this trash meant to elicit reactionary, knee-jerk reactions.

Nicole Tedesco 15 January 2020

I cannot agree with the author. The basic epistemological principles of science are very much intact, thank you. In the end, perhaps I am simply confused over what the author means by "philosphy".

The author, Dr. Sabine Hossenfelder, whic is a research fellow at the Frankfurt Institute for Advanced Studies, argues that somehow the both philosophy and sociology of science are broken in some way. Experiments in physics are becoming increasingly expensive with little return, and that is a fair complaint. However, this does not mean basic scientific epistemology is at risk? Perhaps she is not proposing it is, but the article is written in such as way as to be just vague enough to imply this conclusion.

Dr. Hossenfelder suggests that "pretty math" is not reality, but merely models reality. This is a fair observation. The modeling of reality by math can result in a great deal of idle speculation. I agree with that. History is full of this kind of idle speculation which can become ever more idle and more speculative when data is scarce or even non-existent. Without data nothing stands to counter empty speculation. In the end this problem--as it always has--calls for more data to match the mathematical speculations and eliminate those that simply do not work. This is how science works when it is successful. I am not sure if Dr. Hossenfelder is suggesting anything different other than to urge increased caution with experimental choice. This, however, does not imply fundamental problems with the philosophy of science. There may be sociological problems, political problems in particular, but not problems of basic epistemology. Of course, this begs the question as to what Dr. Hossenfelder means by "philosophy". Does she mean, as I have speculated, epistemology, or perhaps ethics, morality, metaphysics, logic, or aesthetics? Perhaps this is where I find myself confused. I should be confused, because Dr. Hossenfelder has not defined "philosphy" enough for this article to make sense enough to interpret it properly.

As Thomas Kuhn pointed out decades ago, what generally needs to change is the worldview, or paradigm in which all models and data are conceptualized within. This is a cognitive problem, more in line with Piaget than with Karl Popper for instance. Language will expand to embody completely new concepts that only make sense in the new worldview. Meanwhile, as we see in engineering worldviews, dimishing returns are to be had as one continually improves upon existing technologies to the point of maximum optimization. The top of the innovation S-curve yields decreasing improvements for the money spent. This only stops when a new revolution takes place in the innovation cycle. Pocket and wrist watches became thinner, increasingly feature laden over time. At some point the market became saturated as no new features for pocket or wrist watches made sense in the worldview of pocket or wrist watches of the era. One day came the smartphone and everything changed. Science is no different. I am not sure Dr. Hossenfelder understands this.

Sok Puppette 15 January 2020

OK, maybe I'm missing something, but doesn't saying "I am the only physicist who has at least come up with an idea for what to do" kind of beg the question of exactly what that idea may be? If you're not going to explain it here, shouldn't you at least point us to where you DO explain it? As it stands, this rant seems to be a content-free waste of time. If you don't want to be accused of having no suggestions, you need to say what your suggestions are.

I sure hope you don't think "resolving inconsistencies" counts, because that is a pointless prescription unless you can say how to do it.

Do you propose some specific experiment? What is it? Do you have a particular "scientifically promising hypothesis"? What is it? Do you have some succinct, useful criterion for distinguishing promising from unpromising hypotheses, or some specific course of action that could be expected to generating promising hypotheses? What are those, and why are they good? Can you describe how, specifically, to apply the "philosophy and sociology of science" to get anywhere closer to any of those things?

If you want to talk about unproductive paths, people have been working on "smarter ways to share information and make decisions in large, like-minded communities" thousands of years of which we have records, and probably hundreds of thousands of which we do not. There's been very little meaningful progress over the centuries... but there have been innumerable highflown unsupported theories and not a few expensive experiments. Do you believe that that sort of project always progresses somehow? 'Cuz there's lots of evidence that it does NOT.

John Wilson 14 January 2020

I totally agree that many physicists have lost their way. I experienced this effect myself in grad school physics at Georgia Tech. There were the core classes that taught solid physics, based on actual experimental results and real science. Then there were the speculative classes. Like many others at the time, I was drawn to some of the more "mystical" aspects of QM since it was not well understood. The big push of course was to "Quantize Gravity". It has been years since that time, and I have watched the flow of events as everyone still states that "General Relativity and Quantum Mechanics are not compatible." This is incorrect, and it is the basis of the mistake that has caused the stagnation of physics for decades.

General Relativity (GR) has passed every test that has been made on it. There are no violations of Lorentz Invariance. Special Relativity (SR) is simply the approximate limiting-case of GR for when masses are small (i.e. low curvature = "flat" spacetime). Now here is the part that has been missed. One can derive Relativisitic Quantum Mechanics (RQM) from principles of Special Relativity and just a few empirical observations. Standard Quantum Mechanics (QM) is just the low-velocity ( |v| << c ) limiting-case of RQM. That means that QM is *not* fundamental. No one will be "quantizing gravity" because it doesn't work that way. GR --> SR --> RQM --> QM --> CM. That is the path from General Relativity to everyday Classical Mechanics (CM).

Here is the tensor mathematics (well-examined and known to describe correct physics, based on actually experimental physics) and the pieces of the puzzle that can lead physics out of the hole that Sabine mentions. Just because the quantum pieces are little doesn't mean that you build everything else out of them. GR gives the general rules for how one "measures" things.

John Wilson

Uncle Al 14 January 2020

Physics' empirically sterile 50 years may be a demonstrable wavefunction conceptual defect. Matter wave interference[1] is QM’s beating heart, including 25,000 Da molecules[2]. Schrödinger's box superposition of states applied to slit grating input of optically resolved chiral molecules: (±x,±y,±z) + (∓x,∓y,∓z) = zero, or [ket(left-handed)] + ket(right-handed)]/[sqrt(2)] = zero must output observable 1:1 mixture of hands, a racemate, Hund's paradox. Input[3] a robust single enantiomer molecular beam[4], racemization energy greater than 1414 kJ/mol. Examine the output enantiomer ratio[5]. No diffraction pattern emerges (one may not "shut up and calculate), a racemate emerges (classical thermodynamics is shattered), or the universe uncreates. Any of the three is better than what physics has now. In QFT veritas, in Pyrex sanitas. Look.

[1] DOI:10.1002/prop.201600025; DOI:10.1038/nnano.2015.179, arXiv:1602.07578
[2] DOI:10.1038/s41567-019-0663-9, DOI:10.1039/c3cp51500a, arXiv:1703.02129
[3] DOI:10.1002/anie.201704221
[4] 2-trifluoromethyl-D_3-trishomocubane, MW = 214 Da

D Gillies 13 January 2020

I was quite shocked to notice that so many of the big efforts in science in the 2010s were to confirm things that were already known (gravity waves, higgs boson, etc.). Unfortunate, since that is a very low-impact pursuit ...

David Samson 13 January 2020

The primary limitation in any of the sciences is that any meaningful hypothesis is limited by our ability to make measurements. If you can't put a "ruler" next to it, any comments you make amount to little more than conjecture. The issues regarding "dark matter" & "dark energy" highlight this limitation. We can measure a gravitational effect but otherwise, we have no way of interacting with the ~93% of the universe that falls under this rubric. There's probably some good science to be found in that portion of the universe but if we can't make decent measurements, we aren't doing science.

Владимир Хомяков 13 January 2020

S.V. Siparov. Metric dynamics.

arXiv:1506.03304v1 General Physics (physics.gen-ph) [v1] Fri, 17 Apr 2015

The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems’ dynamics is equivalent to the choice of the corresponding metric of an anisotropic space, which is used for the modeling of physical reality and the processes that take place. The examples from hydrodynamics, electrodynamics, quantum mechanics and theory of gravitation are discussed. This approach makes it possible to get rid of some known paradoxes; it can be also used for the further development of the theory.