A theoretical physics FAQ [Archive]

Arnold Neumaier

Oct19-04, 03:29 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n-------------------------\nA theoretical physics FAQ\n-------------------------\n\n\nhttp://www.mat.univie.ac.at/~neum/physics-faq.txt\n\n\nThis site contains answers to some frequently asked questions from\ntheoretical physics. They were edited from my answers to\npostings to the newsgroup sci.physics.research, and first posted\nthere on April 28, 2004. The 21 topics in the initial version\nhave grown to 62 topics by October 18, 2004, and are likely to\ngrow further.\n\nOf course, the FAQ refers only to a tiny part of theoretical physics,\nand the answers are only as good as my understanding of the matter.\nThis doesn\'t mean that they are poor but probably that they are\nnot perfect, and sometimes controversial.\n\nIf you spot errors or have suggestions for improvements,\nplease write me (at Arnold.Neumaier@univie.ac.at).\n\nIf you have questions, please post them to the moderated newsgroup\nsci.physics.research (http://www.lns.cornell.edu/spr)!\n\n\nHappy Reading!\n\nArnold Neumaier\nUniversity of Vienna\nhttp://www.mat.univie.ac.at/~neum/\nI like to see people grow\n\n\n-----------------\nTable of Contents\n-----------------\n\n1a. What are \'bare\' and \'dressed\' particles?\n1b. How meaningful are single Feynman diagrams?\n1c. How real are \'virtual particles\'?\n1d. What is the meaning of \'on-shell\' and \'off-shell\'?\n1e. Virtual particles and Coulomb interaction\n1f. Are virtual particles and decaying particles (resonances) the same?\n1g. Can particles go backward in time?\n1h. What about particles faster than light (tachyons)?\n1i. How real is the wave function?\n1j. Are electrons pointlike/structureless?\n\n2a. Summing divergent series\n2b. What about relativistic QFT at finite times?\n2c. Nonperturbative computations in QFT\n2d. Functional integrals, Wightman functions, and rigorous QFT\n2e. The formal functional integral approach to QFT\n2f. Is there a rigorous interacting QFT in 4 dimensions?\n2g. Is QED consistent?\n2h. The classical limit of relativistic QFT\n2i. Bound states in relativistic QFT\n2j. Why normal ordering?\n2k. Why is QFT based on a classical action?\n2l. Renormalization without infinities\n\n3a. Is there a multiparticle relativistic quantum mechanics?\n3b. Localization and position operators\n3c. Lie groups and Lie algebras\n3d. Representations of the Poincare group, spin and gauge invariance\n3e. The Galilei group as contraction of the Poincare group\n\n4a What are bras and kets?\n4b. What is the meaning of the entries of a density matrix?\n4c. Can all quantum states be realized in nature?\n4d. A concise formulation of the measurement problem of QM\n4e. The double slit experiment\n4f. The Stern-Gerlach experiment\n4g. The minimal interpretation\n4h. The preferred basis problem\n4i. Does decoherence solve the measurement problem?\n4j. Stochastic quantum mechanics\n4k. Which interpretation of quantum mechanics is most consistent?\n4l. Is there a relativistic measurement theory?\n\n5a. Random numbers and other random objects\n5b. What is the meaning of probabilities?\n5c. What about the subjective interpretation of probabilities?\n5d. Are probabilities limits of relative frequencies?\n5e. How meaningful are probabilities of single events?\n5f. How probable are realizations of stochastic processes?\n5g. How do probabilities apply in practice?\n5h. Incomplete knowledge and statistics\n5i. Priors and entropy in probability theory\n\n6a. Energy in general relativity\n6b. What is the tetrad formalism?\n6c. Difficulties in quantizing gravity\n6d. What is canonical quantum gravity?\n6e. Is quantum mechanics compatible with general relativity?\n6f. Why do gravitons have spin 2?\n\n7a. On progress in science\n7b. Can good theories be falsified?\n7c. Theoretical challenges close to experimental data\n7d. Why bother about rigor in physics?\n7e. How precise can physical language be?\n\n8a. Useful background for theoretical physics\n8b. Other physics FAQs\n\n9a. Acknowledgments\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>-------------------------
A theoretical physics FAQ
-------------------------

http://www.mat.univie.ac.at/~neum/physics-faq.txt

This site contains answers to some frequently asked questions from
theoretical physics. They were edited from my answers to
postings to the newsgroup sci.physics.research, and first posted
there on April 28, 2004. The 21 topics in the initial version
have grown to 62 topics by October 18, 2004, and are likely to
grow further.

Of course, the FAQ refers only to a tiny part of theoretical physics,
and the answers are only as good as my understanding of the matter.
This doesn't mean that they are poor but probably that they are
not perfect, and sometimes controversial.

If you spot errors or have suggestions for improvements,
please write me (at Arnold.Neumaier@univie.ac.at).

If you have questions, please post them to the moderated newsgroup
sci.physics.research (http://www.lns.cornell.edu/spr)!

Happy Reading!

Arnold Neumaier
University of Vienna
http://www.mat.univie.ac.at/~neum/
I like to see people grow

-----------------
Table of Contents
-----------------

1a. What are 'bare' and 'dressed' particles?
1b. How meaningful are single Feynman diagrams?
1c. How real are 'virtual particles'?
1d. What is the meaning of 'on-shell' and 'off-shell'?
1e. Virtual particles and Coulomb interaction
1f. Are virtual particles and decaying particles (resonances) the same?
1g. Can particles go backward in time?
1h. What about particles faster than light (tachyons)?
1i. How real is the wave function?
1j. Are electrons pointlike/structureless?

2a. Summing divergent series
2b. What about relativistic QFT at finite times?
2c. Nonperturbative computations in QFT
2d. Functional integrals, Wightman functions, and rigorous QFT
2e. The formal functional integral approach to QFT
2f. Is there a rigorous interacting QFT in 4 dimensions?
2g. Is QED consistent?
2h. The classical limit of relativistic QFT
2i. Bound states in relativistic QFT
2j. Why normal ordering?
2k. Why is QFT based on a classical action?
2l. Renormalization without infinities

3a. Is there a multiparticle relativistic quantum mechanics?
3b. Localization and position operators
3c. Lie groups and Lie algebras
3d. Representations of the Poincare group, spin and gauge invariance
3e. The Galilei group as contraction of the Poincare group

4a What are bras and kets?
4b. What is the meaning of the entries of a density matrix?
4c. Can all quantum states be realized in nature?
4d. A concise formulation of the measurement problem of QM
4e. The double slit experiment
4f. The Stern-Gerlach experiment
4g. The minimal interpretation
4h. The preferred basis problem
4i. Does decoherence solve the measurement problem?
4j. Stochastic quantum mechanics
4k. Which interpretation of quantum mechanics is most consistent?
4l. Is there a relativistic measurement theory?

5a. Random numbers and other random objects
5b. What is the meaning of probabilities?
5c. What about the subjective interpretation of probabilities?
5d. Are probabilities limits of relative frequencies?
5e. How meaningful are probabilities of single events?
5f. How probable are realizations of stochastic processes?
5g. How do probabilities apply in practice?
5h. Incomplete knowledge and statistics
5i. Priors and entropy in probability theory

6a. Energy in general relativity
6b. What is the tetrad formalism?
6c. Difficulties in quantizing gravity
6d. What is canonical quantum gravity?
6e. Is quantum mechanics compatible with general relativity?
6f. Why do gravitons have spin 2?

7a. On progress in science
7b. Can good theories be falsified?
7c. Theoretical challenges close to experimental data
7d. Why bother about rigor in physics?
7e. How precise can physical language be?

8a. Useful background for theoretical physics
8b. Other physics FAQs

9a. Acknowledgments

Aage Andersen

Oct20-04, 03:18 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nThank you for a very readable FAQ.\n\n> 7b. Can good theories be falsified?\n\nYou state that "Newton\'s theory will never be falsified", but isn\'t the\nobserved advance of Mercury\'s perihelion a falsification of the theory and a\nverification of GR?\n\nI agree with you that "a correct theory is not falsifiable".\n\nregards\n\nAage\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Thank you for a very readable FAQ.

> 7b. Can good theories be falsified?

You state that "Newton's theory will never be falsified", but isn't the
observed advance of Mercury's perihelion a falsification of the theory and a
verification of GR?

I agree with you that "a correct theory is not falsifiable".

regards

Aage

Arnold Neumaier

Oct20-04, 10:48 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nAage Andersen wrote:\n\n>> 7b. Can good theories be falsified?\n>\n> You state that "Newton\'s theory will never be falsified", but isn\'t the\n> observed advance of Mercury\'s perihelion a falsification of the theory and a\n> verification of GR?\n\nNewton\'s theory in the version of the 2th century (after 1919)\ncontains the qualification \'at speeds <<c\', as (should be) taught in\nelementary physics courses. I had qualified my statement accordingly.\n\nNewton himself stated the theory for objects and accuracies with which\nhe was familiar, such as apples and moons. As far as I know he had not\nclaimed that the theory was valid without restriction. (Otherwise\nmagnetism, a phenomenon already known to Newton, would have disproved\nhis theory already.)\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aage Andersen wrote:

>> 7b. Can good theories be falsified?
>
> You state that "Newton's theory will never be falsified", but isn't the
> observed advance of Mercury's perihelion a falsification of the theory and a
> verification of GR?

Newton's theory in the version of the 2th century (after 1919)
contains the qualification 'at speeds <<c', as (should be) taught in
elementary physics courses. I had qualified my statement accordingly.

Newton himself stated the theory for objects and accuracies with which
he was familiar, such as apples and moons. As far as I know he had not
claimed that the theory was valid without restriction. (Otherwise
magnetism, a phenomenon already known to Newton, would have disproved
his theory already.)

Arnold Neumaier