Fermat's Library | The Evolution of the Physicist's Picture of Nature annotated/explained version.

### TL;DR In this paper Dirac discusses: - how our view of spa...

Paul Adrien Maurice Dirac is one of the most influential physicists...

Evolution of our notion of space: - Flat space, before Newton - N...

> ### I think there is a moral to this story, namely that it is mor...

Newtonian physics depicts a deterministic Universe in which objects...

The two types difficulties in Quantum Theory: - **Class One:** How...

### Renormalization: Renormalization is a collection of techniques...

Dirac believes that we should not be bothered if the state of Quant...

Great silent video demonstration by the Royal Institute describing ...

> #### It seems to be one of the fundamental features of nature tha...



  

  

   

 



 

    in    

   

     

       

 

 



       

     

       



       



     

    



    

     

   





     



     



    



 

     

     

     

     

 

      

      

    

 

    

       

   

    

 

    

      

     

       



     

     

     

 

    



     

   







 



 50].

  

    

    

      

     

    

     

   





     

  

  

     



        

   

      



      

      

     

    

    

    



      

    

    

      

    

   



     

        

 

       

    

   

    

    

      







    

 

     

       

     



 

    

      

    

      

  

      

   

      

  

   

     

 

       

       

       

    







        

       

       

   

    





      

      

      

    

      

       

      

      

      

     







     

  

 

       

   

   

     

    

     

    



  

      

   

      



         

  

    



     

 





     

    

       

    

    

      

      

       

    

     

     



      

    



     

     

      

      

  

       

     

     

     

      

 

      



     

 



     

     

       

       

        

     



      

     

    

    

     

   

    



    

    



     



    

    

       

    

    





    

     

 



     



      



    

    

     



   



      





      



 

      

       

    



      

     



     

        

     

     

     

     

      

     

    

    



    

    

  

    

   



       

       

      

  



     

      

 

     



  

  

    

 



    

      

  

      

     

     

      

     

      

 



         

     

         

    

      

      

      

 

      





 

     

     

      

     











      

      





      

     



     

     

      

     

      

     

      

   





        

 



    



  

        



   

       



        







  

    

       

        

        

      



       



     

 

 

       

     

      

   



     

       



     

     



       



      

       

      

     

      



 



    

     

      

        





       

     

       

     



      

     

 

 



    

     

 

     

      



     



      

       

      

     

     





    



      

      

     

   

     

      

     

     

       

     

     

     

        

     

  



    

      

     

 

      

  

   

      

  

     

    

    

  )    

   

      

     

      

      

       

      

    

      

      

      

     

      



      

   

 

      

  



      

 



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

     



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      

      



     

 

 

       

   

        

       

       

     

        

    

        

    

       

   

     



  



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 

 

   

 

      

 

 

      

      

     

    

      





      

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   

    

      

       

      

 

       

     

     

     

    



        



       

       



     

    

      

     

 

      

       

     





    

      

      

       

      

        



 

    

       





   

    

      







      

 

      

       

       



     

       

     

 



    

 

      







     



     

    

 



      



     

      

     

        

     

      

     

 

         

     

       

    

     



   

             

              



      



     



    (   

 



      

     

         

   

   



      

      

       

   

   

      

      

    

     

     

      

      

      

     



  

     





 

     

     

      

      

      

     

     

     

      



     

    

      

     

      

    



     

        

      

   



       

    



   

 

     

       

         

       

           

         

               

            





          

              

        

      





    ,    

          





         

    



 



  



     

      

  

      

    

     

 

      

      

 



    

     

      

     

       



     



     

       

       

    

     



   

   

     



       

       

   

  

       

      

     



       

      

       

     

       



     

     

       

      

 

        

       

       

 

     

       

      

      

 

       



      

  



   



     

         

        

 





      

        

        

       

   

   

    



   

       

    

      

  

     

    

      

    

      

      





      

 

       



    

     



        

  

     



 

 

     

     

      



   

       



    

      

     



 



      

      

       

       

      

    

      

       



     

  

      

      

 O  





            

         



 

      

    

 

     









      



     

      



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

    



     

      

      

     

  

       

      

     



  

      

     

      



       

      

       

      

      

 

  

      

      

  



       

        



 

     

 

       



  

         

        

        

      

  

     

     

   

     

         

        



      



     

     

  

     

      

      

    

      

    

       

      



      

     

     

  

    

       

 

  

   

       



      

     

      

 

       

       



       

         

    

  

     

       

    

     

   



    

       







     

    

    





       

       



    

 

     

    



       

     

       

    

        

      

   

     

      

 





        







 

      



      

      

     

       

     

      

       

     

       

     

 

      

      

     

    

      

       

       

    

     

   

    

      



      

    

   

      

      

     

      

     



      

     

   

      

 

       

       

      

 

    



 





   



 

      

     

    

       

      



     

     

       



    

     

  

 



      

      

      

 

 

      

     

     

     

     

     

   

      

      

     

      

   



 

      

   



   

     

       

     

      

 

     

      

     

      

      

       

           



   



   

      

 





 

    

     



      

 

       



    

     

     

      

    

    

   

  





     

    

 

       

     

      

       



 

         

 





       

    

    

 

  

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Discussion

> ### I think there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment. Great quote by Dirac, who believed in the beauty of Nature and this beauty would naturally appear in the equations of physics and mathematics describing it. very deep very deep Great silent video demonstration by the Royal Institute describing Michael Faraday's discovery of lines of force. [![](https://i.imgur.com/3FcYYcP.png)](https://www.youtube.com/watch?v=-FMEV3UxI4A) Paul Adrien Maurice Dirac is one of the most influential physicists of the 20th century. He made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics and **predicted the existence of antimatter when he formulated the Dirac equation.** Dirac was awarded the **1933 Nobel Prize in Physics** with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". ![Dirac](https://i.imgur.com/vBLnZto.jpg) ***"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."*** \- P. A. M. Dirac ### TL;DR In this paper Dirac discusses: - how our view of space evolved from flat space to 4-dimensional space-time and finally General Relativity introduced the notion of curved 4-dimensional space-time - how the discovery of Quantum Mechanics (QM) changed our view of the Universe from a deterministic (Newton) to probabilistic view (QM) - the problems and difficulties in the new description of the Universe given by QM ### Renormalization: Renormalization is a collection of techniques developed by physicists to treat infinities arising in calculated quantities. They alter the values of quantities to compensate for effects of their self-interactions. ### Regularization: In Quantum Field Theory, regularization is a method to turn singularities into finite values by the introduction of a suitable parameter called regulator. The regulator introduces the possibility of "new physics" and models our lack of knowledge about physics at with the present theory. This method allows the theory to discard infinite and give accurate predictions within its intended scale of use, i.e. Quantum Mechanics and Electrodynamics Learn more here: - [Wikipedia: Renormalization](https://en.wikipedia.org/wiki/Renormalization) - [Wikipedia: Regularization](https://en.wikipedia.org/wiki/Regularization_(physics)) Newtonian physics depicts a deterministic Universe in which objects move in perfectly determined ways. At the macroscopic scale Newtonian physics gives accurate predictions of observations. When we start studying the infinitesimally small we enter the real of Quantum Mechanics and new previously hidden properties start to appear. Observations are no longer deterministic but become probabilistic. One of the most interesting experiments depicting the probabilistic aspect of Quantum Mechanics is the **double-slit experiment.** Photons are fired one-by-one through a double-slit apparatus at a distant screen. Curiously, they do not arrive at any single point, nor even the two points lined up with the slits. See image below. ![slit experiement](https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Double-slit_experiment_results_Tanamura_2.jpg/800px-Double-slit_experiment_results_Tanamura_2.jpg) *Patterns created by photons (white) in the double-slit experiment* The two types difficulties in Quantum Theory: - **Class One:** How can we get a consistent picture of reality with Quantum Theory? This type of difficulties do not concern the physicists, they concern the philosophers who seeks a satisfying picture of nature. - **Class Two:** The present laws are not always adequate to describe reality, and the theory shows limitations. These are the difficulties that concern the physicist and that are worth worrying about. Dirac believes that we should not be bothered if the state of Quantum Mechanics (QM) cannot give us a complete view of the Universe. He believes that there is still a lot to be discovered and as we learn more about QM we will have better models to describe and interpret our observations. *See quote below.* > #### Evolution does not go backward. It will have to go forward. There will have to be some new development that is quite unexpected, that we cannot make a guess about, which will take us still further from Classical ideas but which will alter completely the discussion of uncertainty relations. And when this new development occurs, people will find it all rather futile to have had so much of a discussion on the role of observation in the theory, because they will have then a much better point of view from which to look at things. So I shall say that if we can find a way to describe the uncertainty relations and the indeterminacy of present quantum mechanics that is satisfying to our philosophical ideas, we can count ourselves lucky. But if we cannot find such a way, it is nothing to be really disturbed about. We simply have to take into account that we are at a transitional stage and that perhaps it is quite impossible to get a satisfactory picture for this stage. *- P. A. M. Dirac* Evolution of our notion of space: - Flat space, before Newton - Newton introduced was the first to introduce a 3-dimensional notion of space (x, y, z) - Einstein was the first to introduce the idea of 4-dimensional space-time (x, y, z, t) with his theory of Special Relativity - Einstein's General Relativity introduced the notion of **curved 4-dimensional space** > #### It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better. - *P. A. M. Dirac*

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