Showing posts with label Nima Arkani-Hamed. Show all posts
Showing posts with label Nima Arkani-Hamed. Show all posts

Tuesday, November 18, 2014

Nima Arkani-Hamed Public Lecture: Quantum Mechanics and Spacetime in the 21st Century



Dr. Nima Arkani-Hamed (Perimeter Institute and Institute for Advanced Study) delivers the second lecture of the 2014/15 Perimeter Institute Public Lecture Series, in Waterloo, Ontario, Canada. Held at Perimeter Institute and webcast live worldwide on Nov. 6, 2014, Arkani-Hamed's lecture explores the exciting concepts of quantum mechanics and spacetime, and how our evolving understanding of their importance in fundamental physics will shape the field in the 21st Century. Perimeter Institute Public Lectures are held in the first week of each month. More information on Perimeter Public Lectures: http://ow.ly/DCYPc

Friday, January 03, 2014

Nima Arkani-Hamed Speaks with Ian McEwan



You Might like to move ahead to 12:45 on sliding scale....somewhat of an improvement from 15:45 of about 3:00 seconds. Nima acknowledges in speaking,  about the introduction of this video,  of a metaphor considering the Higg's Boson,  and of course speaks to the metaphors limitations.  So along with 3 seconds savings,  you also get to enjoy that introduction.

I could not help but think of Leonard Susskind,  Raphael Bousso, Juan Maldacena  and  Joseph Polchinski when talking about Falling into a Blackhole, when Nima was speaking. What Nima is saying is important to me. I understand what he is saying about what drives people to that wonder, and how to science people,  this is a fundamental feeling which is expressed across many of those who have had this mystery about the world at heart. Creatively expressed,  as to get to the source of things whether by the science, or,  with regard to the creation of artistic endeavor whether it be music or writing.

Nima speaks about Truth and that's with a capital "T,"  so I am not lost on the importance of this meaning, but like things of wonder and creativity,  the message of Truth is fundamental as well to people.

When Nima spoke about Stephen Weinberg's first three minutes this sent me back to the ideas regarding how our views have changed,  to ask, what the microseconds might have in store for us.  This becomes fundamental when we learn to see what models can apply them self too,  what we may be looking at the universe. This disturb me somewhat as some spoke ill of conceptual fundamentals of model theories when they did not understand this simple fact and were chorusing. Beauty and deep take on their true meaning.

Ian McEwan at 29:55 approximately spoke about the types of maths, and with his list I believe he failed to see the significance of what was sitting before him as Nima the mathematician. One has to see that the Theoretical was an accomplishment above all the maths to which included,  all these rigid structures Nima was talking about. It is not as if you can take a step and make an pronouncement without leveling the structure in some way without regarding the maths involved. This is what I have learn as a researcher within the subject of the sciences being spoken too, as I have come to know it. A White rectangle was simple in its description but we know what he meant right(LHC)?

Ian started to lose me when the significance of the conversation about commonality now became the race to become a known scientist.  Of course thoughts about publishing in the Arxiv as to the substance and work to establish credibility crossed my mind. But that timing was ill supported to the movement of this conversation to me. While Nima did professed to not understanding the creativity aspect of the work involved he was very aware of the structure ability to get to results being explained in science as his job done well. There could not have been a better discription of the creative process to me then how Nima logically explained it.

See Also:

Nima Arkani-Hamed debates a novelist

Friday, September 20, 2013

Nima Arkani-Hamed Lectures



Nima Arkani-Hamed on developments in Physics and future vision






The Salam Lecture Series 2012, with a week-long series of lectures by renowned theoretical physicist Nima Arkani-Hamed. Giving his audience a panoramic view of 400 years of physics in his first lecture, Arkani-Hamed provided insights into the various concepts that have dominated the world of fundamental physics at different points in history. "Everything that we have learned [over the past 400 years] can be subsumed with a basic slogan, and the slogan is that of unification," he said. "More and more disparate phenomena turn out to be different aspects of the same thing." "Physics," he stressed "forces you to remove artificial distinction between disciplines.





See Also:

Sunday, July 01, 2012

Nima Arkani-Hamed on Maximally Supersymmetric Theories

Could Nature, LHC prefer N=2 supersymmetry?

 SW: Can you explain to us some of the places where supersymmetry shows up in these various theories, and what it does for you when it does show up? 
 
Let me back up for one second here: Supersymmetry is an extension of the symmetries of space-time, and it has this really interesting character. On the one hand, supersymmetric theories are examples of ordinary quantum field theories. They’re not radically outside the framework of the rubric handed down to us by our ancestors by the 1930s. But on the other hand, while being ordinary quantum field theories, they have extraordinary properties; they extend the symmetries of space-time. And so they fit at a nexus between two worlds. Considering this deep, central idea, it’s not surprising that it’s going to show up in a host of places.
One of the places it shows up is in attempts to extend, very pragmatically, the standard model of particle physics and to solve a variety of its problems. So there are these famous fine-tuning problems and other difficulties we have, which can be summarized as attempts to understand the following major puzzle: Because of quantum fluctuations—violent vacuum fluctuations that get more and more violent as you go to shorter and shorter distances—it seems to be impossible to have any macroscopic order in the universe at all. The universe is big, gravity is weak; there is a very big macroscopic universe, but that seems almost impossible given that there are these gigantic quantum fluctuations.

Supersymmetry is one attempt to solve these problems by coming up with an explanation for why the quantum fluctuations disappear at short distances. This isn’t a small problem, a details thing. If you’re going to fix it, it’s going to need a big fix. The way supersymmetry does it is by extending the idea of space-time, and it does it in a way that you can’t fluctuate at all in these quantum dimensions. There’s a perfect symmetry between the quantum dimensions and the ordinary dimensions, and so the gigantic quantum fluctuations have to cancel out. That’s why it showed up and people care about it a lot in particle physics and in finding extensions of the standard model. 

It also shows up all over the place in string theory, because if you’re going to have a quantum mechanical theory of gravity, which is what string theory is about, one of the first things it should do is give you a nice big macroscopic universe to play with—even a toy universe. Any other attempt to talk about quantum gravity just fails at this starting point, because of exactly the same violent quantum fluctuation problem. So supersymmetry shows up because it allows us to get going and even talk about it. It also shows up for other reasons.

It turns out that just the structure of quantum field theories—how to calculate with them, and see what the consequences are—is very rich, very complicated, and difficult to calculate with. When the couplings between quarks and gluons get strong, it’s impossible to calculate anything analytically, and for a long time people had no idea how to make progress. Supersymmetric theories have so many theoretical properties that you can really make wonderfully significant progress studying the dynamics of quantum field theories. And you do it by studying them in their most supersymmetric aspect first.
See:Nima Arkani-Hamed on Maximally Supersymmetric Theories- ScienceWatch.com correspondent Gary Taubes.


See Also:

Tuesday, May 15, 2012

Where is LHC Headed?

The speakers are: Michael Peskin (author of the famous QFT textbook) Nima Arkani-Hamed, Riccardo Rattazzi, Gavin Salam, Matt Strassler and Raman Sundrum (or Randall-Sundrum fame).

Monday, November 28, 2011

History of Supersymmetry to Today

Special Topic of Supersymmetry

by Science Watch


Since the 1980s, if not earlier, supersymmetry has reigned as the best available candidate for physics beyond the standard model. But experimental searches for supersymmetric particles have so far come up empty, only reconfirming the standard model again and again. This leaves supersymmetry a theory of infinite promise and ever more questionable reality. See Link above.

Also: What's Inside ScienceWatch.com This Month - ScienceWatch.com - Thomson Reuters



 Update-

See Also :

Tuesday, October 09, 2007

The Landscape Again and again....




Of course I am not qualified to have an opinion about whether the landscape is of value or not. That there are people on two sides that have differing opinions, and based on what they have as proof to the contrary, of one or another, is whether the issue is ready for a forgone conclusion? Whether the person in association is a forgone conclusion.

Topography of Energy?

7. dorigo - October 8, 2007
Hi anomalous,

I will take your word for it - I must admit I was not aware of the breadth of his works. However, Nima’s position on the anthropic landscape of ST is enough for me to warn any student about his views.
Cheers,
T.


Stanley Mandelstam Professor Emeritus Research: Particle Physics
My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.



So by looking at a statement of a person, I wondered, has such a conclusion been reached and support by documentation that will help me decide?

Outrageous Fortune

There’s an article in this week’s Nature by Geoff Brumfiel entitled Outrageous Fortune about the anthropic Landscape debate. The particle physicists quoted are ones whose views are well-known: Susskind, Weinberg, Polchinski, Arkani-Hamed and Maldacena all line up in favor of the anthropic Landscape (with a caveat from Maldacena: “I really hope we have a better idea in the future”). Lisa Randall thinks accepting it is premature, that a better understanding of string theory will get rid of the Landscape, saying “You really need to explore alternatives before taking such radical leaps of faith.” All in all, Brumfiel finds “… in the overlapping circles of cosmology and string theory, the concept of a landscape of universes is becoming the dominant view.”

The only physicist quoted who recognizes that the Landscape is pseudo-science is David Gross. “It’s impossible to disprove” he says, and notes that because we can’t falsify the idea it’s not science. He sees the origin of this nonsense in string theorist’s inability to predict anything despite huge efforts over more than 20 years: “‘People in string theory are very frustrated, as am I, by our inability to be more predictive after all these years,’ he says. But that’s no excuse for using such ‘bizarre science’, he warns. ‘It is a dangerous business.’”

I continue to find it shocking that the many journalists who have been writing stories like this don’t seem to be able to locate any leading particle theorist other than Gross willing to publicly say that this is just not science.

For more about this controversy, take a look at the talks by Nima Arkani-Hamed given today at the Jerusalem Winter School on the topic of “The Landscape and the LHC”. The first of these was nearly an hour and a half of general anthropic landscape philosophy without any real content. It was repeatedly interrupted by challenges from a couple people in the audience, I think David Gross and Nati Seiberg. Unfortunately one couldn’t really hear the questions they were asking, just Arkani-Hamed’s responses. I only had time today to look at the beginning part of the second talk, which was about the idea of split supersymmetry.

Update: One of the more unusual aspects of this story is that, while much of the particle theory establishment is giving in to irrationality, Lubos Motl is here the voice of reason. I completely agree with his recent comments on this article. For some discussion of the relation of this to the Intelligent Design debate, see remarks by David Heddle and by Jonathan Witt of the Discovery Institute.


A sphere with three handles (and three holes), i.e., a genus-3 torus.

Jacques Distler :

This is false. The proof of finiteness, to all orders, is in quite solid shape. Explicit formulæ are currently known only up to 3-loop order, and the methods used to write down those formulæ clearly don’t generalize beyond 3 loops.

What’s certainly not clear (since you asked a very technical question, you will forgive me if my response is rather technical) is that, beyond 3 loops, the superstring measure over supermoduli space can be “pushed forward” to a measure over the moduli space of ordinary Riemann surfaces. It was a nontrivial (and, to many of us, somewhat surprising) result of d’Hoker and Phong that this does hold true at genus-2 and -3.


So by following the conversation I meet up with was offered as evidence, this then, leads me to follow up in even greater depth. How can one give a person such a title of "in question," based on what another posts, as to their characrter of study?

The equations of string theory specify the arrangement of the manifold configuration, along with their associated branes (green) and lines of force known as flux lines (orange). The physics that is observed in the three large dimensions depends on the size and the structure of the manifold: how many doughnut-like "handles" it has, the length and circumference of each handle, the number and locations of its branes, and the number of flux lines wrapped around each doughnut.

11. Plato - October 9, 2007
Tammaso:However, Nima’s position on the anthropic landscape of ST is enough for me to warn any student about his views.
So is this support for what you think is relevant. I have followed the discussions between Lee Smolin, Jacques Distler, Clifford of Asymptotia and Peter Woit of “Not Event Wrong.”

I wonder if you had “more information,” if this might change your statement above, and conclusion, you may have drawn from seeing another view? One you might not of seen before?

Is mathematical consistency of value to you when it is developing?


So with a certain knowledge already gain from following other discussions I am quick to ask if such a link to another is good enough for assigning credibility to another person. Especially one who holds a "view point" other then one held by Peter Woit. After all is Peter Woit not a mathematics man? I am really asking.



So based on this assumption(what I ask others not to do) about Peter Woit or string theorist while having a basis in mathematics. I am asking, that if such a development that is, "current and consistent in mathematics" why would this contradict and qualify any individual "to other then" what mathematics requires to move forward. To try and attempt too, "connect to reality" in a phenomenological way?

The basis of my insight is in fact current collider technologies, and the relationship I see to bulk production gravitons. If Gr is an outcome of String theory then, any pocket universe that demonstrates some mathematical consistency should, be of relevances in one's decision?

It is always a work in progress that such questions continue to push me forward. In that process I "vaguely recall" that Jacques did not think the association to modular form in terms of the genus figure could ever be related to that pocket universe?

I must say to you that in my case I am asking of Calabi Yau's, can have some predictability to how universe selection is accomplished and thus any steady development in mathematics pushing that landscape to credibility?

Wednesday, April 06, 2005

Symmetry: Dimensions of Particle Physics

I thought it important that I present the infomrtaion that was tied to John Ellis's article in previous thread below and what was happening in regards to Microstate blackhole recognition.


Let it Rain
The most energetic particles in the universe have a message for us. The gigantic Pierre Auger Southern Observatory, still under construction in Argentina, is already trying to decipher it.
By Davide Castelvecchi


Most people I have read reveal the silence of common information, as a realization of Blackholes as the cosmological design, we like to play with. But when it comes to testing these extra dimensions, imagine indeed, that such length's we go too, helps us to adjust to what happens around us everyday.

From this conceptualization, much has changed in the propspective views? Staunch supportors of rejection, do not realize what could be implied of the extra energy dissappearing and how you would measure it, in our everyday surroundings?.

I give a philospohical explanation to help explain the realization of how we see in these extra dimensions The earlyhsiory of extending these ideas, calls for more educative functions with those who do not understand this extension and theoretics going out on this limb. Should it be so easily dismissed?


If you do not follow this history, you will never understand what Nima Arkani-Hamed, Sava Dimopoulos, and Gia Dvali been doing with extra dimensions. There is a conceptual feature here that I have spoken too in regards to gravity that few understand.


So as we see Einstein's Bubble, we come to recognize the consistancy with which we would engage information that arises from such bubbles being burst. They give us information about the contents of these spaces, and from such light, we wonder what has been revealled? Cosmologiclaly the whole universe is teaming with the understanding that there can never be this zero function? To have realize it is a very dynamcial process that is continous and cyclical in nature?

Underlying this view of a cyclical nature, is the realization that such events are geometrically/topologically driven and schematically express the whole frame work of this discussion. How suttle it is sometimes, that we would be dismayed by physicists who are speaking about the geometrics/topological functions, to realize they are incorporating the realizations of this contraction/expansive feature, not only in the cosmo, but in how we see into the nature around us now.

Of course this is from a junior mind on these things in terms of education, but hopefully the vsion and eyesight, is well enough that such discriptions displayed, has viable perspectives to share?

Monday, November 01, 2004

Quantum Gravity

I've put together links for reference on the particular subject titled. If someone has others that they would like to add, please do. I will be placing a permanent link on the sidebar for reference. Hope its useful.

List of quantum gravity researchers

List of loop quantum gravity researchers

String Theorist People


Quantum Gravity quote

A pessimist might say that combining string theory and loop quantum gravity is like combining epicycles and aether.
(John Baez, TWF281)



What is Quantum Gravity?

Moderator: Stephen Shenker, Panelists: Abhay Ashtekar, Juan Maldacena, Leonard Susskind, Gerard 't Hooft, Cumrun Vafa





  • Jan Ambjørn








  • Kostas  Anagnostopoulos






  • John Baez






  • Julian Barbour







  • Chris  Isham







  • Ted  Jacobson







  • Renate  Loll







  • Fotini Markopoulou Kalamara at Penn
    State University
    and Albert
    Einstein Institute







  • Carlo  Rovelli






  • CGPG: Center  for Gravitational Physics and Geometry







  • High-Energy Theory  Group at The Niels Bohr Institute







  • Imperial College  Theoretical Physics Group







  • The Max Planck Institute for Gravitational Physics (Albert  Einstein Institute)







  • Penn State Physics Department







  • Perimeter Institute for Theoretical Physics






  • String theory







  • Loop quantum gravity of Smolin and Rovelli







  • Noncommutative geometry of Alain Connes








  • Twistor theory of Roger Penrose







  • Abhay Ashtekar -- Author of Ashtekar variables, he is one of the founders of loop quantum gravity.







  • John Baez -- Mathematical physicist.







  • Julian Barbour -- Author of The End of Time, Absolute or Relative Motion? and The Discovery of Dynamics.







  • Martin Bojowald --






  • Louis Crane -- Theorist.







  • Rodolfo Gambini -- Author of Loops, Knots, Gauge Theories and Quantum Gravity.







  • Brian Greene -- Physicist who is considered one of the world's foremost string theorists.







  • Stephen Hawking -- Leading theoretical physicists.







  • Peter Higgs -- Proposed the 1960's theory of broken symmetry in electroweak theory,







  • Christopher Isham -- Theoretical physicist.










  • Michio Kaku -- Theoretical physicist with significant contribution to the string field theory.









  • Fotini Markopoulou-Kalamara -- Theoretical physicist interested in foundational mathematics and quantum mechanics







  • Roger Penrose -- Mathematical physicist and imade the invention of spin networks.







  • Jorge Pullin -- Theoretical physicist.







  • Carlo Rovelli -- Obtained, with Lee Smolin, an explicit basis of states of quantum geometry.







  • Lee Smolin -- Theoretical physicist who has made major contributions to loop quantum gravity.







  • Andrew Strominger -- Theoretical physicist who works on string theory







  • Thomas Thiemann -- Researcher.







  • Edward Witten -- Mathematical physicist who does research in M-theory







  • Centauro event







  • String theory







  • M-theory







  • Loop Quantum Gravity by Carlo Rovelli







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  • http://www.ap.univie.ac.at/users/fe/qg/













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  • What is Quantum Gravity

    Finally, string theory started out as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background. Although string theory had its origins in the study of quark confinement and not of quantum gravity, it was soon discovered that the string spectrum contains the graviton, and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background.

    LQG does not have this feature to describe point particles, where a one dimensional string includes gravity.


    According to Wikipedia:

    1.loop quantum gravity makes too many assumptions
    2. according to the logic of the renormalization group, the Einstein-Hilbert action is just an effective description at long distances

    3. loop quantum gravity is not a predictive theory

    4. loop quantum gravity has not offered any non-trivial self-consistency checks

    5. loop quantum gravity is isolated from particle physics

    6. loop quantum gravity does not guarantee that smooth space as we know it will emerge as the correct approximation of the theory at long distances

    7. loop quantum gravity violates the rules of special relativity

    8. the discrete area spectrum is not a consequence, but an assumption of loop quantum gravity

    9. the discrete area spectrum is not testable

    10. loop quantum gravity provides us with no tools to calculate the S-matrix

    11. loop quantum gravity does not really solve any UV problems

    12. loop quantum gravity is not able to calculate the black hole entropy, unlike string theory

    13. loop quantum gravity has no tools to answer other important questions of quantum gravity

    14. the criticisms of loop quantum gravity regarding other fields of physics are completely misguided

    15.loop quantum gravity calls for "background independence" are misguided

    16.loop quantum gravity is not science


    The numbered points are connected to deeper explanations.

    Criticisms of string theory can follow in someone else's post. With the group in favor of LQG they should be able together their heads and come up with lots of things

    Current theories of gravity are based on the geometric curvature of space.

    Current theories of other fundamental forces in the universe are 'quantum field theories', where particles pass other particles back and forth among themselves to interact.
    We know that geometric gravity theories conflict with quantum field theories, and that this conflict means that we don't know what happens under extreme conditions.

    A quantum theory of gravity would involve particles passing 'gravitons' back and forth among themselves. This quantum theory would probably be a more accurate description of gravity, and might be accurate enough to describe the extreme conditions found at the center of a black hole.

    David Palmer
    for Ask a High-Energy Astronomer


    Quantum Gravity

    Quantum gravity is the field of theoretical physics attempting to unify the subjects of Quantum mechanics and General relativity.

    Much of the difficulty in merging these theories comes from the radically different assumptions that these theories have on how the universe works. Quantum mechanics depends on particle fields embedded in the flat space-time of either Newtonian mechanics or special relativity. Einstein's theory of general relativity models gravity as a curvature within space-time that changes as mass moves. The most obvious ways of combining the two (such as treating gravity as simply another particle field) run quickly into what is known as the renormalization problem. Gravity particles would attract each other and if you add together all of the interactions you end up with many infinite results which can not easily be cancelled out. This is in contrast with quantum electrodynamics where the interactions do result in some infinite results, but those are few enough in number to be removable via renormalization.

    Another difficulty comes from the success of both quantum mechanics and general relativity. Both have been highly successful and there are no
    known phenomenon that contradict the two. The energies and conditions at which quantum gravity are likely to be important are inaccessible to laboratory experiments. The result of this is that there are no experimental
    observations which would provide any hints as to how to combine the two.

    The general approach taken in deriving a theory of quantum gravity is to
    assume that the underlying theory will be simple and elegant and then to
    look at current theories for symmetries and hints for how to combine them
    elegantly into a overarching theory. One problem with this approach is
    that it is not known if quantum gravity will be a simple and elegant theory.

    Such a theory is required in order to understand those problems involving the combination of very large mass or energy and very small dimensions of space, such as the behaviour of black holes, and the origin of the universe.

    There are a number of proposed quantum gravity theories and proto-theories, including (for example) string theory and the loop quantum gravity of Smolin and Rovelli - see http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/
    The Noncommutative geometry of Alain Connes, and Twistor theory, of Roger Penrose, are also theories of quantum gravity


    The Quantum Gravity Concept Map is a highly experimental work: it's goals are to help the author organize his own understanding of the subject, and to test the hypothesis that html is a natural language for the construction of a concept map.

    Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. The ultimate goal is a unified framework for all fundamental forces—a theory of everything


    A history of the Planck values provides interesting material for reflections on timely and premature discoveries in the history of science. Today, the Planck values are more a part of physics itself than of its history. They are mentioned in connection with the cosmology of the early universe as well as in connection with particle physics. In considering certain problems associated with a unified theory (including the question of the stability of the proton), theorists discovered a characteristic mass ~ 1016mp (mpis the proton mass). To ground such a great value, one first refers to the still greater mass 1019mp. In the words of Steven Weinberg:

    This is known as the Planck mass, after Max Planck, who noted in 1900 that some such mass would appear naturally in any attempt to combine his quantum theory with the theory of gravitation. The Planck mass is roughly the energy at which the gravitational force between particles becomes stronger than the electroweak or the strong forces. In order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics at some energy at or below 1019 proton masses. (Weinberg 1981, p. 71).

    The fact that Weinberg takes such liberties with history in this quotation is evidence of the need to describe the real historical circumstances in which the Planck mass arose. As we saw, when Planck introduced the mass (ch/G)1/2 (~ 1019mp) in 1899, he did not intend to combine the theory of gravitation with quantum theory; he did not even suppose that his new constant would result in a new physical theory. The first "attempt to combine the quantum theory with the theory of gravitation," which demonstrated that "in order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics," was made by Bronstein in 1935. That the Planck mass may be regarded as a quantum-gravitational scale was pointed out explicitly by Klein and Wheeler twenty years later. At the same time, Landau also noted that the Planck energy (mass) corresponds to an equality of gravitational and electromagnetic interactions.

    Theoretical physicists are now confident that the role of the Planck values in quantum gravity, cosmology, and elementary particle theory will emerge from a unified theory of all fundamental interactions and that the Planck scales characterize the region in which the intensities of all fundamental interactions become comparable. If these expectations come true, the present report might become useful as the historical introduction for the book that it is currently impossible to write, The Small-Scale Structure of Space-Time.


    The struggle to free ourselves from background structures began long before Einstein developed general relativity, and is still not complete. The conflict between [B]Ptolemaic and Copernican cosmologies[/B], the dispute between Newton and Leibniz concerning absolute and relative motion, and the modern arguments concerning the `problem of time' in quantum gravity -- all are but chapters in the story of this struggle. I do not have room to sketch this story here, nor even to make more precise the all-important notion of `geometrical structure'. I can only point the reader towards the literature, starting perhaps with the books by Barbour [9] and Earman [15], various papers by Rovelli [25,26,27], and the many references therein.

    String theory has not gone far in this direction. This theory is usually formulated with the help of a metric on spacetime, which is treated as a background structure rather than a local degree of freedom like the rest. Most string theorists recognize that this is an unsatisfactory situation, and by now many are struggling towards a background-free formulation of the theory. However, in the words of two experts [18], ``it seems that a still more radical departure from conventional ideas about space and time may be required in order to arrive at a truly background independent formulation.