Dr. Leonard Susskind. Physicist. Will speak about the origin of the Universe. In a conference organized by the Skeptic magazine and Templeton foundation. What caught my attention reading Dr. Susskind’s bio was the first sentence: The discoverer of string theory.

I write down “definition is discovery” as yet another physics pun. A theory is not discovered. Susskind may have been one of the original researchers who defined a set of PQs for something that later came to be known as the string theory. But no one discovered string theory.

To say “I discovered the string theory” is the same as Al Gore’s claim that he discovered the Internet. Al Gore’s claim appears funny to many people but not Susskind’s. Why? We say that Internet was invented, not discovered. But Susskind is way ahead of the game. He is a scholastic Doctor of Philosophy. He knows how to define things. That’s his job. He says he discovered the String Theory because he assumes that the String Theory is the “language god wrote nature.” Susskind claims that he discovered something that already existed in nature. Just like Newton claiming that he discovered something called the universal force of gravity. Of course Newton did not discover any such force. He defined it.

There is nothing new under scholastic skies. Doctors of Philosophy have been using the same professional tricks for thousands of years. Yet another proof that physics is no different than politics and physicists are no different than politicians. They love doublespeak and they corrupt our language for personal profit.

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Dear Zeynel,

I disagree with you at some things. First, many mathematicians think that the mathematics are not invented but they are discovered. Mathematics are universals, no matter, if they are discovered by humans or are discovered by intelligence from other nature.

As the String Theory has generated a lot of excellent mathematic, we can say that the String Theory has been discovered. Moreover, the String Theory is a very serious candidate for Theory Of Everything (TOE). String Theory predicts the Gauge-gravity duality. This duality is one of the most important conceptual breakthroughs in theoretical physics of the 1990s. Thanks to this duality has been proved some surprising dualities between different branch of physics, for example:

- AdS/QCD –> Gravity – Theory of the strong interaction duality.

http://en.wikipedia.org/wiki/AdS/QCD

- AdS/CFT –> Gravity – Quantum Field Theory which is the mathematical background for Condensed Matter Physics.

http://motls.blogspot.com/2007/02/adscft-and-condensed-matter-physics.html

- AdS/CFT –> Gravity – Fluid Dynamics

http://arxiv.org/abs/0809.4272

- AdS/CFT –> Gravity – Atomic Physics

http://physics.aps.org/articles/v1/10

Therefore, Leonard Susskind is one of the discoverers of String Theory.

The Best.

Hi Alberto,

Thanks for your comment. I didn’t know this was such a contentious issue.

Google finds several discussions about math invented or discovered. I believe the same goes for the string theory.

I tend to agree with this view:

This is interesting too:

People who say that string theory was invented are Platonists.

Here Leonard Susskind’s name does not appear until the 1970s. And with Yoichiro Nambu and Holger Bech Nielsen. And what they did was to present “a physical interpretation of Euler’s formula by representing nuclear forces as vibrating one-dimensional strings.” To me this is like a definition. Did Ptolemy discover that the earth was stationary? Did Copernicus discover that the Earth move? No. They assumed those as axioms.

Very interesting bio of Susskind. Here he says that “it was during that time that I

co-discovered string theory.”Here it is stated that he discovered the string theory “independantly of two others.”

And does one discover or invent his offspring? Because here Susskind is called the father of string theory.

OK. In his bio above he says that he discoveed a new pattern. He thinks the pattern is there and he discovered it. It’s like when the computer fits the right curve to data it discovers the curve. I guess that makes sense.

The question,

Do Math depend of his creator? What do I want to say with this? If intelligent aliens (no human) exist and they could do math, would they do the same maths than humans? I think that if the answer is yes (in all cases) then Math are invented but If the answer is no then Math are discovered. And If only there was one intelligence able to do math? (namely human intelligence). Well, In this case we can wonder if the humans do the same mathematics when they don’t communicate their ideas. Well, Although many breakthroughs has been achieved in a independent way, the authors had been influenced by the same background. But there is a singular situation. I am referring to what happened at Kerala School:

http://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics

The mathematicians of this school discovered some concepts which belong to the realm of Calculus. And Calculus was discovered (inveted) later by Newton and Leibnitz. It’s not clear but it is believed that Newton and Leibnitz didn´t know the ideas that aroused from Kerala School.

On the other hand. Are Math and Physics the same stuff. I think that they are, because rigorous Physics is completely based on Math. Math have developed Physics and Physics has developed Math.

http://en.wikipedia.org/wiki/Mathematical_physics

As Physics has predictive power on nature and is the most fundamental science (the Chemistry is the Physics of the valence electrons …) I think that Physics and Math are discovered. But what about the mathematics which does not have a physical interpretation. Well I also believe in the multiverse of Level 4.

http://en.wikipedia.org/wiki/Ultimate_ensemble

(sorry for my bad English).

I wanted to say:

… I think that if the answer is yes (in all cases) then Math are discovered but If the answer is no then Math are invented …

Hi Alberto,

Thanks for the comments.

Do Math depend of his creator?What about not math but this comment? Does what the writer writes depend on the writer? Berkeley said that to exist is to be perceived. I think that this is relevant here. For a cat mathematics does not exist. So this cat may be looking at a triangle but he will never see a triangle. The same is true for us. There are so many things in the world that we are looking at but not seeing. Do they exist?

If intelligent aliens (no human) exist and they could do math, would they do the same math as humans?I think there is no reason to introduce aliens. There are unhuman organisms here on earth that can communicate with humans through human writing. These are corporations. So if you create a corporation whose purpose is to create mathematics (maybe something like Bourbaki, then that corporation will not be human but will be creating mathematics, satisfying your requirement. Would that organism create math as humans? I think so.

And if only there was one intelligence able to do math? (namely human intelligence)But you don’t need human intelligence, that is, you don’t need to have human body to do mathematics as proved above.

Mathematicians in [Kerala] discovered some concepts which belong to the realm of Calculus. And Calculus was discovered (invented) later by Newton and Leibniz.Interesting. In this sense it feels right to say that they “discovered” some mathematical concepts rather than “invented.”

So it seems to me that this is an issue about existence. For something to exist it does not need to exist eternally. All existence appears to be rearrangement. Corporations are living organisms and they exist by contract.

Are Math and Physics the same stuff. I think that they are because rigorous Physics is completely based on Math.Mathematics used in physics is not mathematics in the sense that Galileo would have understood the mathematics of his time, that is, geometry.

The Cambridge Companion to Galileo – Page 65

I don’t think mathematics used in physics is rigorous. The unit of mathematics in physics is the equation. And the equation is formed with an equality sign. In physics the equality sign, the fundamental symbol of equations, has at least 4 meanings. Equality, proportionality, identity, and definition. A physicist will use his authority and parse the equation the way it suits his purpose best. This is more like what Peripatetic doctors did with Latin. They could prove anything they wanted with their doctoral authority applied to Latin. I think physicists’ mathematics is more like Latin or maybe it should be called Mathematin.

As physics has predictive power on nature . . .And mathematics does not? For thousands of years Ptolemaic model, a purely geometric model of the world, made exact predictions of astronomical observations. But I think you mean

the mathematics which does not have a physical interpretation.This is interesting because I object to the use of the word “physical” to mean “natural” as you do here. Physical is physics propaganda. This is how professional doctors called physicists own nature. By naming nature physical. And physical also means “Newtonian” because physical nature is a nature that obeys the atomic materialism of Newtonism. So Ptolemaic model is a purely geometric model and it explains nature but it is not physical. I know physicists would claim that Ptolemaic model fails because it does not account for physical forces of Newtonian kind.

A comment on maths.

Mathematics is the science of quantification of the physical laws. Other than this they have no meaning at all.

So yes any mathematic construction would be based on the observation of physical reality and would end up being the same math that we are taught in school.

Dear Zeynel,

The Physics is the most fundamental science and has predictive power. Physics doesn’t explain the reality’s cat or our reality. That is correct. Physics explains the Reality of the Nature. Otherwise It would be a theory without predictive power. We can see the triangle, because our intelligence had been adapted to understand the Reality. You shouldn’t to apply relativism to the Physics. It doesn’t work. Reality has to exist.

Indeed, the math are not created by an only human intellect but by a group of them which are connected to each other. For the existence of the corporations, which you have referred, it is a necessary condition that there were human intelligence. Bourbaki was not more than a one of these groups. The alien intelligence, what I was referring, doesn’t need human intellect at all.

The Geometry has a capital importance in the modern Physics. The General Relativity is a geometric theory and describes the gravity like a curved space-time and not like a force. The rest of interactions arises thanks to the symmetry of gauge fields (the theory involves fiber bundles, i.e. Geometry) and this can be explained using the framework of Quantum Field Theory. String Theory is pure Geometry, too. Namely, the Quantum Geometry. The equations (and numbers) appear only when we have put into a reference of frame . The central concept is the symmetry.

If you pick the adequate reference of frame, the mathematical background of the Ptolemaic model is only an approximate solution of the Universal Gravitation for Solar System. But Ptolemy did a wrong physical interpretation of these mathematics. My opinion: Mathematics + Correct Physical Interpretation = Nature.

“The central concept is the symmetry.”

And if i may add, symmetry and the way it breaks.

I almost totally agree with the views of Alberto GP above. I have nonetheless one objection on your last equation. My objection is that this equation is static and can be misunderstood. For instance someone might think that if we get a perfect mathematical theory we could explain once and for all all physicall phenomena, sth which is not true. Mathematics and physics are in a never-ending process of developement in conjuction with our understanding and observing of the physical world.

Hi Alberto,

The Physics is the most fundamental science and has predictive power.Maybe you would agree that physics is a vast field. It’s so vast that it takes over two decades to study and even then a physicist must specialize in a narrow field within physics. No one physicist knows all of physics. Physics has no boundaries.

Physics is the name of a vast academic field. Or physics is a system of legal physical quantities. Physics studies physical quantities. And physics is a legal sytem because it allows contradictions. As you mention, physics models nature. But it models nature in a legal way, in other words, physics legislates nature. For example, physics allows in nature both force and no-force. Also physics defines a nature made of particles and then also without particles but fields and also not particles, not fields but probabilities. I believe that nature is not legal but rational.

To say that “physics is science” does not mean much. Science is another word for knowledge and physics surely includes knowledge. But this does not describe physics.

Here’s another contradiction in physics. You say that physics has predictive power. String theory is physics but it does not have predictive power. So physics allows non-predictive theories.

Physics is best described as “physics is what physicists do.”

And you say that physics is fundamental. I disagree with this too. Physics is based on conventional units and constants. This makes physics engineering. And physics does not allow questioning of fundamental questions. One of the most fundamental questions is the divisibility of matter. Physics does not allow a scientific investigation of the question “Is matter infinitely divisible?” Or even “Is there matter?” Physics is based on the dogma of atomic materialism. This dogma cannot be questioned within physics.

Sorry to interupt. As a physicist i would like to comment on some of the things you say above, and i would also like to hear Alberto’s views.

- “For example, physics allows in nature both force and no-force. Also physics defines a nature made of particles and then also without particles but fields and also not particles, not fields but probabilities.”

This is not correct. Actually physics is a science that continuously evolves and so our understanding of the world and hence the physical descriptions that we use evolve also. The modern view of elementary interactions states that the fundamental entities are quantum fields. Physical particles are a series of infinite quantum excitations of these fields. Then the way these fields couple together (interact) determines potential energy. Then force is the negative gradient of this potential energy. This is the modern view of force. I don’t know where you read that physics accept force and no-force and all the rest, but they are wrong. And probabilites are not physical entities, they are mathematical constructions.

- Science is another word for knowledge.

Not exactly. For example, you know that if you touch an ice-cube you will feel cold. This is knowledge but not science. Science collects all empirical knowledge that we get from experiments and observations, tries to understand why and how these observations are the way they are and finally constructs general laws that have the ability to predict the outcome of similar experiments.

- String theory is physics but it does not have predictive power.

This is a very long discussion. In fact many prominent physicists argue that string theory is not a scientific theory, just because it can’t be falsified experimentally. So this is not a case against physics but a case against string theory.

- Physics is based on conventional units and constants.

Obviously you refer to physical constants, right? Well these are not conventions, they are just some constants that we get from observations (this is how the world is). Then physics tries to understand why these constants exist and why they have these exact values.

- “Is matter infinitely divisible?” Or even “Is there matter?”

I will repeat this for a millionth time more. These are not scientific questions. They are purely philosophical, so physics cannot give definite answers about them.

- dogma of atomic materialism

What is this? It’s the first time i hear about it. And as the dominant ideology is idealism, i can assure you that physics is basically interpreted in an idealistic or positivist manner. Thera are very few physicists who accept the materialistic views (among them are your favourite ones who combat BB cosmology).

In fact many prominent physicists argue that string theory is not a scientific theory just because it can’t be falsified experimentally.Physics does not have a written constitution. Maybe it should. And as far as I know there is no law in physics profession that requires that a theory must be “scientific.” The word science, as understood by physicists, already means physics. Therefore, a physics theory must be a physical theory but what does that mean? It means that a theory must contain legal physical quantities and conform to the rest of physics.

Yes, there are self-regulatory rules that professional physicists invented to stop each other from gaining unfair professional points, such as the requirement that all experiments must be duplicated by hostile parties so that physicists do not cheat and report something they did not observe. It doesn’t happen. Academic physics experiments are not replicated. But the myth that physics is an experimental science remains.

So this is not a case against physics but a case against string theory.But string theory is a legal part of physics. I don’t know how you can deny this. Just yesterday the Nobel prize for physics were given to String theorists. And according to Reference Frame

When general relativity was invented (discovered?) it was not a part of legal physics either. Now it is. There is a cycle to the invention of new theories within the profession of physics. Once a theory becomes “mechanics” and it enters textbooks, active research on it closes. The new generation of physicists need their own new framework so that they can make their careers. String theory was invented to be that framework. And it is a perfectly designed framework because it is infinitely commentable. You can almost write string theory papers authomatically by a recipe. The critics of string theory are part of the legalization of the string theory into physics. There are too many PhDs in string theory for it not to be mainstream and legal physics.

“It means that a theory must contain legal physical quantities and conform to the rest of physics.”

This is not correct. For a theory to be scientific it must be experimentally falsificable. For a theory to be a correct physical theory it must have the ability to explain and predict the results of physical phenomena.

“But the myth that physics is an experimental science remains.”

Physics is indeed an experimental science. Why do you say it isn’t?

“But string theory is a legal part of physics.”

Who says so? As a matter of fact, i wrote above that this is disputed.

“Yoichiro Nambu joins a long sequence of string theorists who have won the prestigious award”

If you are referring to Nobel prize, Nambu did not win it for his work in string theory. No string theorist has won a Nobel prize. Nambu won it for his work in symmetry breaking in quantum field theory.

“Once a theory becomes “mechanics” and it enters textbooks, active research on it closes”

No it doesn’t. Quantum electrodynamics has been in textbooks several decades now. However there is still active scientific interest on the field.

“And it is a perfectly designed framework because it is infinitely commentable”

That’s exactly what’s not perfect about it.

“Once a theory becomes “mechanics” and it enters textbooks, active research on it closes”No it doesn’t. Quantum electrodynamics has been in textbooks several decades now. However there is still active scientific interest on the field.Thanks for correcting. Can we amend it to read “Once a theory enters

first-yeartextbooks active research on itmostlycloses?”“Can we amend it to read “Once a theory enters first-year textbooks active research on it mostly closes?””

OK, let’s talk about 1st-year textbooks. In an undergraduate course 1st-year physics usually includes Newtonian mechanics and possibly some classical electromagnetism and thermodynamics. These branches have a “scientific life” of more than 200 years. So it is very logical that most problems that belong to these branches have been solved. However, as far as i am aware there are still open problems for mechanics and electromagnetism, although (i think) of not fundamental importance.

This is very reasonable, since a scientific theory has a limited domain of validity. Once the fundamental problems of such a theory have been solved, new problems arise that usually need a broader theory in order for them to be addressed. In a way it is impossible to solve every single problem in classical mechanics for example. And for me it has no sense (except for specific applications) once all fundamental problems have been elucidated. What does make sense indeed is to turn your attention to deeper, more fundamental problems that arise from the evolution of our physical theories.

Dear Zeinel,

You should read the Spyros’s comments and think slowly about them because I think that he knows very well this matter. I like Physics very much but I am not a professional physicist and I know very little about Physics and about math, too. Because of this many of things that I write could be wrong.

Dear Spyros,

I absolutely agree. The breaking of symmetry is a very important concept. For example, one of the LHC main goals is to find the Higgs bosson. The last particle predicted by the Standard Model what has not be discovered yet. This particle (field) has provided us a mechanism to explain how the rest of the particles obtain their masses and how the electroweak interaction is broken down at a certain energy scale. Precisely, the 2008 Nobel Prize has been awarded for elucidating this concept (in the context of high energy physics ). One of the things that I have never understood is why the T-symmetry is not considered the way to connect microscopic models with macroscopic models (with friction). I wonder if there would be a some mechanism of T-symmetry breaking to obtain macroscopic physics from microscopic physics without to use statistical mechanics.

‘Mathematics and physics are in a never-ending process of development in conjunction with our understanding and observing of the physical world.’

I think that you have the same point of view than S. Hawking about this issue. If you think that there is a unique Universe (

with a single system of physical laws) then Gödel’s incompleteness theorems can be interpreted in the following way

(Lim (n –> infinite) (Math Theory)n) + correct physical interpretation = Nature

where (Math Theory)n ‘is a consistent math theory that includes’ (Math Theory)n-1

But I prefer the theory of Tegmark (albeit it’s a very polemic theory)

About the general discussion:

I think that String Theory is not a scientific theory if we use the Popper’s philosophy, because, String Theory can’t be falsified with the current technology. But, String Theory makes predictions and, in principle, it can be falsified. For example, String Theory predicts hidden dimensions and, in this model, the elemental particles are objects with one dimension (namely strings, not points).If we would have got a particle accelerator able to accelerate the particles at Planck scale, then, String Theory would be a scientific theory in a Popper sense.

I disagree with the following statement:

“String theory is physics but it does not have predictive power”

because String Theory make the following ‘postdictions’

- General Relativity

- Gauge Theory (MSSM by means of certain copactifications of the hidden dimensions in the Heterotic Model, F-Theory (IIB), IIA model)

http://indico.cern.ch/getFile.py/access?contribId=8&resId=0&materialId=slides&confId=21917

and the following predictions:

- Supersymmetry

- String Landscaspe (Supersymmetry is break and it can be described our Universe among many others)

- Dirac neutrino mass (F model)

http://arxiv.org/abs/0806.0102

Dear Zeinel,

You should read the Spyros’s comments and think slowly about them because I think that he knows very well this matter. I like Physics very much but I am not a professional physicist and I know very little about Physics and about Math, too. Because of this, many of things that I write could be wrong.

Dear Spyros,

I absolutely agree. The breaking of symmetry is a very important concept. For example, one of the LHC main goals is to find the Higgs bosson. The last particle predicted by the Standard Model what has not been discovered yet. This particle (field) has provided us a mechanism to explain how the rest of the particles obtain their masses and how the electroweak interaction is broken down at a certain energy scale. Precisely, the 2008 Nobel Prize has been awarded for elucidating this concept (in the context of high energy Physics ). One of the things that I have never understood is why the T-symmetry is not considered the way to connect microscopic models with macroscopic models (with friction). I wonder if there would be a some mechanism of T-symmetry breaking to obtain macroscopic Physics from microscopic Physics without to use statistical mechanics.

‘Mathematics and physics are in a never-ending process of development in conjunction with our understanding and observing of the physical world.’

I think that you have the same point of view than S. Hawking about this issue. If you think that there is a unique Universe (

with a single system of physical laws) then Gödel’s incompleteness theorems can be interpreted in the following way

(Lim (n –> infinite) (Math Theory)n) + correct physical interpretation = Nature

where (Math Theory)n ‘is a consistent Math theory that includes’ (Math Theory)n-1

But I prefer the theory of Tegmark (albeit it’s a very polemic theory)

About the general discussion:

I think that String Theory is not a scientific theory if we use the Popper’s philosophy, because, String Theory can’t be falsified with the current technology. But, String Theory makes predictions and, in principle, it can be falsified. For example, String Theory predicts hidden dimensions and, in this model, the elemental particles are objects with one dimension (namely strings, not points).If we would have got a particle accelerator able to accelerate the particles at Planck scale, then, String Theory would be a scientific theory in a Popper sense.

I disagree with the following statement:

“String theory is Physics but it does not have predictive power”

because String Theory make the following ‘postdictions’

- General Relativity

- Gauge Theory (MSSM by means of certain copactifications of the hidden dimensions in the Heterotic Model, F-Theory (IIB), IIA model)

http://indico.cern.ch/getFile.py/access?contribId=8&resId=0&materialId=slides&confId=21917

and the following predictions:

- Supersymmetry

- String Landscaspe (When Supersymmetry is broken, the solutions of String Theory can describe our Universe among many others)

- Dirac neutrino mass (F model)

http://arxiv.org/abs/0806.0102

Dear Alberto,

i am trully fascinated by the fact that you can follow and obviously recreate scientific literature without being a professional physicist. You must have spent years studying physics and maths to do this and i think it is very remarkable.

A thing that immediately caught my interest was your reference to the T-symmetry and its possibility of serving as a link for microscopic and macroscopic dynamics. Do you have any specific reference in mind?

S. Hawking (except of his abilities as a theoretical physicist) is on a wrong philosophical track, i think. He always likes to make predictions about when physics will end (he thinks that a Theory of Everything will be the end of physics). In response i have to remark that back in 1900 Lord Kelvin said that physics was complete, except for 2 potholes (“dark clouds” as he named them). The ultraviolet catastrophe in Rayleigh-Jeans law and the negative result of Michelson-Morley experiment. You must have heard that these 2 dark clouds led to quantum mechanics and special relativity.

As for string theory, i am in no position to judge its scientific faults as i have not yet had any serious involvement in the field. Many people say that because of the toughness of string theory, you need to devote decades in order to understand it and once you get a grasp, you don’t want to get rid of it (and possibly end up doing mathematics and not physics). I am mostly interested in the AdS/CFT part, since my specialization lies in the field of elementary particles.

Thanks Spyros,

But, many times I misunderstand the concepts and mix the things in random ways. Unfortunately, I have very little time to study this issues. I am only a crackpot, but I’m not worried for that. What really matters is that I am happy with this hobby.

‘A thing that immediately caught my interest was your reference to the T-symmetry and its possibility of serving as a link for microscopic and macroscopic dynamics. Do you have any specific reference in mind?’

Let’s set the stage with a bit more of detail:

I always have thought that the reductionism is the spirit of Physics, and we can explain the whole nature with this philosophy. I think that the phenomenological theories like Maxwell’s theory of electromagnetism, classical mechanics and thermodynamics can be described by means of the elementary particles plus the dynamics among this particles plus the dynamics of the spacetime where the elementary particles are placed. For example, the Ehrenfest theorem shows that Newton’s laws of motion can be derived from Schrödinger equation, as long as, the forces are conservatives. In solid state Physics is shown that the quantum harmonic crystal is a better model than the classical harmonic crystal. We can derive the classical model from the quantum model and we can derive either, the motions equations and the constitutive equations of the theory of elasticity, from the classical harmonic crystal.

But, To obtain the internal energy and the specific heat for the classical model, we must use the Boltzmann distribution. For the quantum model, we can start with the density matrix and derive the partition function for the Gibbs canonical ensemble. If we average the hamiltonian using this ensemble we obtain the internal energy for the crystal, moreover, the entropy can be derived from the density matrix. With the entropy function, we can explain the irreversible phenomenon at the macroscopic scale. The S matrix lets us compute the expectation values of observables, too. The density matrix is a linear combination of the ket-bra (operators). Each ket is a pure state. The pure states are vectors that belong to a basis of the Hilbert Space of the system. Each particle that constitute the whole system has a individual Hilbert space, but the Hilbert Space of the physical system is the tensor product of all individual Hilbert Spaces. I think that the Hilbert Space of the system has T-Symmetry (by means of the antiunitary operators) but I don’t know. My question; Is there some mechanism to obtain another Hilbert Space of the same system without T-Symmetry and that lets us to explain the expectation values of the operators, internal energy, entropy … without to use the density matrix, namely, by means of the vectors what are solutions of the Schrödinger equation?

I have no idea.

Alberto,

i will try to write general comments here.

First of all, reductionism is not the spirit of Physics. Reductionism in physics started from Laplace’s thoughts that if we knew the motion of every single atom (or elementary particle) in the universe, we could determine the future of all physical phenomena. Today we know that this can’t be the case. And i will explain why.

The laws that govern the different levels of organization of matter are not only quantitatively different but also qualitatively. For instance, QM is not the microscopic version of Newtonian mechanics, it is a qualitatively different theory. It is true though, that through the correspondence principle, QM must tend to the classical results at large scales. However, you can’t use QM to find the motion of a golf ball hitting a wall, for example.

And this is also obvious in Ehrenfest’s theorem, which you seem to have misunderstood. Newton’s laws of motion cannot be derived by Schroedinger’s equation or by QM. If you check more closely, you will see that in classical mechanics, the analogue of Ehrenfest’s theorem is Liouville’s theorem, which uses Poisson brackets instead of commutators.

So, every level has its own laws that are qualitatively different from the other levels’ laws and reductionism does not apply.

Now T-symmetry is a very deep problem in physics. We know that T-symmetry is violated in nature. This can be examined in 2 levels: microscopic and macroscopic. At the 2nd, we know that T must not be a symmetry, from the 2nd law of thermodynamics, since entropy is increasing in the universe. At the first, we know that since CP is violated, then from CPT theorem must also be violated in microscopic scales (weak interaction). Now at this level, the correct physical theory that describes these phenomena is QFT and this uses Fock and not Hilbert spaces.

I think that the problem is quite diffucult to be addressed in its complete generality. I think that the works about T-symmetry are restricted to QM and not QFT. You must search this out yourself.

However, i know, that in QCD for example there has been extensive work that involves the relation of time reversal with the production of spin asymmetries (see the works of Dennis Sivers).

However, considering what i wrote above, i think it is impossible to connect friction and macroscopic phenomena to microscopic dynamics.

PS. You must know that this kind of problem (a complete, self-consistent and definite proof) needs a great deal of mathematics. And QFT does not still have a solid mathematic description (although it recreate results with unprecedented accuracy).

Spyros, Thanks you for your response!,

I going to read it quietly to see what I can learn. But I am sad, because now I feel that it is not possible to understand the nature (as a whole) by mean of a few mathematical axioms. Since some time ago, I was looking for the proof that would indicate how to obtain the Maxwell equations from the QED. I thought just the opposite of what really happens.

I can’t understand the mathematical background of the quantum field theory. What is necessary?

Functional Analysis + Group Theory + Differential Geometry

What books are good to learn QFT (at introductory level)?

Well, most physicists (even Nobel laureates) will tell you that noone understands QFT perfectly. And what makes it more difficult is that the bibliography is so vast, that you can say that there is no standard way of learning QFT (unlike quantum mechanics for example).

In the last years, most graduate QFT courses are taught according to Peskin and Schroeder’s book “Introduction to QFT”. This is a huge one, includes QED,QCD and renormalization according to Wilson’s prescription.

Another book which tends to become a standard reference is Itzykson and Zuber’s “QFT”. This includes almost every topic in QFT but it is pedagogically unacceptable.

From these 2 i would recommend the 1st, although i think that most people (even physics undergraduates) will find it difficult.

If you just want to get a feel (and only a feel) of QFT, read A.Zee’s “QFT in a nutshell”. Then there is Lahiri and Pal’s “A first book of QFT” that follows a more down-to-earth (with less mathematical proofs etc) approach.

If you find any popularized books (such as Feynman’s “QED: a strange theory of light and matter”) i suggest that you take it from there and then slowly start learning the formalism of QFT (if you feel the need to).

As far as the mathematical background is concerned you will need real and complex analysis. If you want to tackle the topics on unification, then you will need some group theory. (this is for an introductory level).

Keep in mind, that unlike most instructors suggest, it is not necessary to have mastered completely the lower levels of mathematics or physics in order to understand more advanced topics. This can be done simultaneously. As a matter of fact, tackling a more advanced topic might sometimes help you understand better a simpler one.

Hi Alberto,

# I like physics very much but

# I am not a professional physicist

# and I know very little about Physics

# and about Math, too.

My opinion is that this is an advantage, not a handicap, for studying nature. An ignorance of legal physics will give an amateur researcher a tremendous advantage in investigations of nature for several reasons. Consider Galileo. Initially he was a professional doctor of philosophy, the profession practiced by physicists today, but he realized that if he stayed within the system he could only write yet another De Motu on the impetus theory by using legal physics concepts. Today the academic buzzword is not impetus but gravity and it has many species and physicists are required to publish books no longer on motion but on gravity. Names may have changed but the legal system is the same. In other words, the more physics you study the more physics you learn and that takes the researcher away from nature. How can academic physics take one away from nature? Well, consider the question you were asking about Quantum Field Theory. QFT is at least three levels away from nature: Quantum, field and theory.

What is the question that QFT is trying to answer? Can the same question be answered without QFT? You say that you need to know functional analysis, group theory and differential geometry. Does the punishment match the crime in this case? No.

And physics education continuously delays a direct investigation of nature and wastes the most productive years of students by teaching them how to pass standard physics tests and methods of how to advance in physics hierarchy. How much of her overall physics education do you think this physicist working at LHC tying cables uses in her daily work? And also there are strict professional rules on the kind of research that students can do until they get tenure. Maybe Spyros can answer if this is true? And only a few get tenure.

Consider this summary of QFT from Wikipedia:

So physicists negotiated among themselves to call particles “excited states of a field” . . . for now. This tells me that QFT is an academic physics problem trying to solve earlier problems that were created by previous generations of physicists. So it is a legal problem. It is a semantic problem. It assumes force. It assumes that force is mediated by other particles . . . I think these assumptions come before mathematics that are used to manipulate these assumed objects.

There is nothing mysterious about mathematics used in physics. The way they define arbitrary legal physical quantities physicists define arbitrary rules for mathematics too, to make everything work. Incidentally, I don’t see anything wrong with this method. But physicists must admit that this is what’s going on.

Physicists have every right to work on QFT and try to fit collider observations into mathematical models. I am sure that’s a good professional pursuit for them, most Nobel prizes are given in this field, I believe. To me, it looks more like engineering. In any case, it is the same problem that astronomers faced two thousand years ago. The result was the Ptolemaic theory. And that was a beautiful mathematical theory. My interest lies in the assumptions that physicists make rather than their mathematical models. Because mathematics cannot prove or disprove their assumptions.

“What is the question that QFT is trying to answer? Can the same question be answered without QFT? You say that you need to know functional analysis, group theory and differential geometry. Does the punishment match the crime in this case? No.”

If you know any way to reconstruct the exterme precision with which QED and QCD describe natural phenomena, without having to use all this tedious mathematics, i would be very glad to hear it.

“This tells me that QFT is an academic physics problem trying to solve earlier problems that were created by previous generations of physicists”

QFT was constructed to fulfill the need to reconciliate relativity with quantum mechanics. However it is not just an academic problem, since this need was not invented academically but was posed by the phenomena that we studied and needed both relativity and QM to be explained. Hence, QFT is not an academic problem but a theory which describes certain natural phenomena.

“It assumes force. ”

Where did you read that? This is wrong.

“physicists define arbitrary rules for mathematics too, to make everything work”

This is also wrong. Mathematics (and physics) need to be self-consistent, to say the least. Did you find any inconcistency in a given mathematical or physical theory?