Login or e-mail Password   

Leibniz space-times

Can a cosmological theory be formulated in the same language we use for descriptions of subsystems of the universe, or does the extension of physics from local to cosmological require new principles or a new formulation of quantum theory?
Views: 4.825 Created 09/26/2006

More often than not, Lee Smolin’s essays are engaging and thought provoking. I specially appreciate his willingness to tackle conceptual issues, often dismissed as philosophical or uninteresting by a great deal of the physics community (which, in my opinion, should know better). Also of note are his efforts to convey to non-specialists the key ideas and problems faced by modern physics, without unduly over-simplifications or dishonest hype.

A case in point is his recent essay The Case for Background Independence, where the meaning, virtues and drawbacks of relationist theories of quantum gravity are explored in detail. More concretely, Smolin describes the close relationship between three key issues in fundamental physics, to wit:

  • Must a quantum theory of gravity be background independent, or can there can be a sensible and successful background dependent approach?
  • How are the parameters of the standard models of physics and cosmology to be determined?
  • Can a cosmological theory be formulated in the same language we use for descriptions of subsystems of the universe, or does the extension of physics from local to cosmological require new principles or a new formulation of quantum theory?

The article begins with a brief historical review of relationism, as understood by Leibniz and summarized in his principles of sufficient reason (there’s always a rational cause for Nature’s choices) and the identity of the indiscernible (entities with exactly the same properties are to be considered the same) [1]. These principles rule out absolute space-times (like Newton’s) or a fixed Minkowskian background (like perturbative string theory), since they single out a preferred structure ‘without reason’, as do theories posing any number of free parameters (think of the much debated landscape) [2]. As is well known, Newton won the day back in the seventeenth century, until Mach’s sharp criticism marked the resurgence of relationist ideas. Mach rejected Newtonian absolute space-time, favouring a purely relational definition of inertia [3], which ultimately would inspire Einstein in his quest for the general theory of relativity [4].

Smolin’s article continues with a careful definition, in modern terms, of relational space and time, and follows with a discussion of some current theories featuring background independence: general relativity, causal sets, loop quantum gravity, causal dynamical triangulation models and background independent approaches (by Smolin himself) to M-theory. In a nutshell, it is argued that any self-respecting relational theory should comply to three principles:

  • There is no background.
  • The fundamental properties of the elementary entities consist entirely in relationships between those elementary entities.
  • The relationships are not fixed, but evolve according to law. Time is nothing but changes in the relationships, and consists of nothing but their ordering.

None of the theories above passes without problems this litmus test of pure relationsm. Take for instance general relativity. To begin with the dimension, topology and differential structure of space-time are givens, and thus play the role of a background. And, on the other hand, only when we apply GR to a compact universe without boundary can we aspire to a relational view, since otherwise we would have arbitrary boundary conditions (partially) determining the structure of space-time. Once you abide to these preconditions, a proper interpretation of general covariance (in which you identify space-times related by arbitrary coordinate transformations) provides a relational description of space-time (for an in-depth discussion of the subtle interplay between gauge invariance and relationsm, see also this excellent article by Lusanna and Pari, and references therein). As a second example, loop quantum gravity is also background dependent: in this case, the topological space containing the spin-networks of the theory. Other than that, loops are an almost paradigmatic case of a relational description in terms of graphs, with nodes being the entities and edges representing their relationships.

After his review of quantum gravity theories, Smolin takes issue with string theory. His subsequent train of thought heavily relies on the fact that relationism, or, more concretely, Leibniz’s principle of the indiscernible, rules out space-times with global symmetries. For if we cannot distinguish this universe from one moved 10 feet to the left, we must identify the two situations, i.e., deny any meaning or reality to the underlying, symmetric structure. But, as is happens, the M-theory programme consists, broadly speaking, in maximizing the symmetry groups of the theories embodied in the desired unified description. More concretely, in background-dependent theories, the properties of elemental entities are described in terms of representations of symmetries of the background’s vacuum state. Each of the five string theories embodied by M-string (should it exist!) has its own vacuum, related with each other via duality transformations (basically, compactifying spatial dimensions one way or the other one is able to jump from one string theory to the next). Thus, M-theory should be background independent (i.e., encompass different backgrounds), but, on the other hand, one expects that the unique unified theory will have the largest possible symmetry group consistent with the basic principles of physics, such as quantum theory and relativity. Smolin discusses some possible solutions this contradiction (which a lack, er, background to comment intelligently), including some sort of (as yet unknown) dynamical mechanism for spontaneous symmetry breaking (which would result in a Leibniz-compliant explanation for the actual properties–such as masses and coupling constants–that we find in our universe).

After all the fuss, there is disappointingly little to be said about relationist unified theories [5]. Invoking again the principle of the indiscernible, Smolin rules out symmetries that would make (unified) identities undistinguishable (if two entities have the same relationships with the rest, they are the same entity). By the same token, a universe in thermal equilibrium is out of the question. Reassuringly, our universe is not, and the negative specific heat of gravitationally bound systems precludes its evolution to such an state. The case is then made (after casting evolution theory as a relationist one, which is OK by me) for Smolin’s peculiar idea of cosmological natural selection. To my view, it is an overly speculative idea, if only for the fact that it depends on black holes giving rise to new universes when they collapse [6]. If that were the case, and provided that each new universe is created with random values for the free parameters of our theories, one would expect that a process similar to natural selection would lead to universes with its parameters tuned to favour a higher and higher number of black-holes (which seems to be the case in our universe). Nice as the idea is, i think we’re a little far from real physics here.

The article closes with a short section on the cosmological constant problem (with the interesting observation than only casual set theory has predicted so far a realistic value) and relational approaches to (cosmological) quantum theory. Again, the author adheres to non-orthodox ideas. This time, to recent proposals (see here and here) of hidden-variable theories, albeit they have far better grounds than the reproducing universes idea. The possibility of a relational hidden-variable theory is argued for with a simple and somewhat compelling line of thought. In classical physics, the phase space of a system of N particles is described by a 6N variables, while a quantum mechanical state vector would depend on 3N variables. On the other hand, in a purely relational theory one would need to use N^2 variables, as these are the number of possible relations between N particles. These would be the hidden-variables completely (and non-locally) describing our particles, which would need statistical laws when using just 3N parameters.

An amazing journey, by all accounts.


[1] See here for excellent (and free) editions of all relevant Leibniz works, including his Monadology, and here for commented excerpts of the Leibniz-Clarke correspondence.

[2] See also here for an interesting take on Leibniz’s principle under the light of Gödel’s and Turing’s incompleteness theorems as further developed by Gregory Chaitin.

[3] Julian Barbour’s “The Discovery of Dynamics: A Study from a Machian Point of View of the Discovery and the Structure of Dynamical Theories” is the definitive reference to know more about the history of the absolute/relative divide. (Another amazing book by Barbour on these issues is “The End of Time : The Next Revolution in Physics”, thoroughly reviewed by Soshichi Uchii here. Smolin himself has many an interesting thing to say about Barbour’s timeless Platonia.)

[4] Barbour argues in his book that Einstein seems to have misunderstood Mach’s discussions on the concept of inertia, taking it for the dynamical quantity entering Newton’s second law instead of the inertial motion caused by space-time according to Newton’s first law.

[5] I’m also a bit surprised by Smolin’s uncritical acceptance of reductionism, which he simply considers, “to a certain degree”, as common-sense.

[6] Tellingly, the only reference where this theory is developed is Smolin’s popular science book “The Life of the Cosmos”.

Similar articles


11
comments: 9 | views: 7334
9
comments: 3 | views: 3459
9
comments: 50 | views: 23649
9
comments: 5 | views: 2871
8
comments: 2 | views: 22213
8
comments: 3 | views: 9758
8
comments: 28 | views: 42113
8
comments: 21 | views: 5263
7
comments: 11 | views: 3681
7
comments: 38 | views: 11855
 
Author
Added by: tor
Article

Related topics





  Usman,  08/20/2016

Someone Sometimes with visits your blog regularly and recommended it in my experience to read as well. The way of writing is excellent and also the content is top-notch. Thanks for that insight you provide the readers!
girlsdoporn
https://www.slideshare.net/girlsdoporn

  Usman,  09/20/2016

It is brilliant blog. I like the way you express information to us.
Check out this Vaporize Review
http://www.smokingblendreviews(...)review/

  Usman,  09/21/2016

The post is really interesting and I think from this post I am able to know something valuable about . I am so glad to get this opportunity. Keep sharing!

news
http://www.bestjuicerpicks.com/

  Usman,  09/27/2016

I would like to suggest you that please keep on sharing such type of information with us. I really found it to much informative.
breast enhancement treatment
http://biggerbreastsin30days.c(...)s-work/

  Usman,  09/27/2016

Hello! This post couldn’t be written any better! Reading this post reminds me of my previous room mate! He always kept chatting about this.
atomic clock
http://www.worldclock.com/atomic-clock/

  Usman,  09/27/2016

This article was composed by a genuine speculation essayist. I concur a considerable lot of the with the strong focuses made by the essayist. I'll be back.
farmville 2 cheats online
https://farmvillecheatstwo.com/

  Usman,  09/27/2016

A great website with interesting and unique material what else would you need.
http://kingofcracks.com/overwa(...)-crack/

  Usman,  10/01/2016

Articles are very informative and hope again I’ll find more like that.
cheap waist trainer
https://nomadeyes.com/collecti(...)trainer

  Usman,  10/02/2016

I don't generally commentary on blogs but as I see this blog I completely motivated to make one praise that I understand that not enough for the significant context on your writing as one that could understand easily.

have a peek at these guys
http://www.gliesegames.com/lat(...)points/

  Usman,  10/02/2016

This content is written very well. Your use of formatting when making your points makes your observations very clear and easy to understand. Thank you.

have a peek at these guys
http://www.folkd.com/user/glas(...)classau

  Usman,  10/02/2016

Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work.

dog adoption
http://dogtrainingmobile.com/

  Usman,  10/03/2016

I got so involved in this material that I couldn’t stop reading. I am impressed with your work and skill.
Salvia divinorum
http://aplus.com/a/davidfourni(...)medicin

  Usman,  10/03/2016

Wow i can say this is another extraordinary article of course of this blog.Bookmarked this website..

INTERIOR DESIGN IN ABU DHABI
http://www.antonovich-design.a(...)bi.html

  Usman,  10/04/2016

Also operate a site and if you are ever interested in doing some visitor writing for me if possible feel free to let me know, im always look for people to check out my web site.

game apps
http://mobilegamesonly.com

  Usman,  10/05/2016

This article was composed by a genuine speculation essayist. I concur a considerable lot of the with the strong focuses made by the essayist. I'll be back.
check my source
http://lattenrosttest.soup.io/

  Usman,  10/06/2016

Hello! This post couldn’t be written any better! Reading this post reminds me of my previous room mate! He always kept chatting about this.
check my blog
http://www.cocktaildressesforj(...)resses/

  Usman,  10/08/2016

I like how you think and the way you represent your views in this article. I agree with your way of thinking.
saving money even though sustaining high quality in business
http://www.shopsalaam.com/savi(...)siness/

  Usman,  10/15/2016

Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work.
jeff
http://jeffstern.com/index.php(...)ptions/

  Usman,  10/15/2016

The information you have posted is very useful. The sites you have referred was good. Thanks for sharing..
pregnancy
https://www.duringpregnancy.us

  Usman,  10/16/2016

The post is really interesting and I think from this post I am able to know something valuable about . I am so glad to get this opportunity. Keep sharing!
Pokemon Go hack Generator
http://hackday.tv/

  Usman,  10/16/2016

Nice looking site.really appreciate for it and It is also useful for me.Thank you for sharing.
NBA 2K17 Codes
http://nba2k17-locker-codes.com

  Usman,  10/17/2016

Articles are very informative and hope again I’ll find more like that.
try this for tuber simulator tricks
http://arduin-delos.com/tuber-(...)nd-bux/

  Usman,  10/17/2016

I would like to suggest you that please keep on sharing such type of information with us. I really found it to much informative.
buy youtube likes safe
http://www.rebelmouse.com/buyy(...)88.html

  Usman,  10/18/2016

This article was composed by a genuine speculation essayist. I concur a considerable lot of the with the strong focuses made by the essayist. I'll be back.
click here
http://www.spycoupon.in/paytm-(...)shback/

  Usman,  10/19/2016

I would like to suggest you that please keep on sharing such type of information with us. I really found it to much informative.
Clean to Bright
http://www.cleantobright.com/

  Usman,  10/19/2016

i will visit your website routinely for some most recent post. I will visit your website frequently for Some most recent post.
buy twitter followers http://followersbiz.com/buy-tw(...)lowers/

  Usman,  10/20/2016

I need to say you did a especially professional process in every details you described get the basic reality
chalk markers
https://www.amazon.com/dp/B00PM473TK

  Usman,  10/22/2016

I like how you think and the way you represent your views in this article. I agree with your way of thinking.
FIFA Mobile Hack
http://www.osonslafrance.com

  aftabak,  10/27/2016

With Candy Camera’s beautifying filters and silent mode you can take beautiful selfies anywhere and anytime It has the diverse range of filters designed specifically for selfies You can also create collage through with this app. <a href="http://mysocialimage.co.uk/201(...)ndroid/">Best selfie apps</a>

  Usman,  10/28/2016

Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work.
Instagram account real followers https://toofame.com

  aftabak,  10/29/2016

The procedure accomplishes this by redistributing the skin and soft tissues to their natural position in an up and back direction This is done by tightening and repairing the underlying muscle and fascia as well as removing excess skin. Beverly Hills Skin Care Products http://www.didblog.com/2016/09(...)re.html

  Usman,  10/29/2016

Hello! This post couldn’t be written any better! Reading this post reminds me of my previous room mate! He always kept chatting about this.
midtown by deyaar
http://midtown.ae/gallery

  Usman,  10/29/2016

Articles are very informative and hope again I’ll find more like that.
vladimir ribakov forex
http://www.forexwatchdog.us/p/(...)de.html

  Usman,  10/30/2016

This is my first time i visit here. I discovered such a large number of fascinating stuff in your web journal particularly its discourse.
ultrasonic pest repellers reviews
http://termitedroppings.org/ul(...)eviews/

  Usman,  11/10/2016

Articles are very informative and hope again I’ll find more like that.
video spin blaster pro plus
https://www.samplesite.com/vid(...)review/

  Usman,  11/12/2016

The post is really interesting and I think from this post I am able to know something valuable about . I am so glad to get this opportunity. Keep sharing!
James
http://besttumbledryers.com

  Usman,  11/14/2016

I wanted to thank you for this great read!! I definitely enjoying every little bit of it I have you bookmarked to check out new stuff you post.
The Homebase
http://www.thehomebase.ca

  Usman,  11/14/2016

I would like to suggest you that please keep on sharing such type of information with us. I really found it to much informative.
dmca takedown
http://www.offshoredmca.com/ho(...)otices/

  Usman,  11/15/2016

Im moving forward and may apply to my current job as a pet sitter, which is very enjoyable, but I need to additional expand. Regards.
click this
https://multimeditation.com/wh(...)tation/

  Usman,  11/16/2016

This is my first time i visit here. I discovered such a large number of fascinating stuff in your web journal particularly its discourse.
war thunder free golden eagles
http://hackscentral.com/war-th(...)s-hack/

  Usman,  11/20/2016

I really appreciate the kind of topics you post here. Thanks for sharing us a great information that is actually helpful. Good day!
find more
http://itoeye.co.uk/

  raj,  11/23/2016

I would like to thank this wonderful reading for your time !!!
fund raising companies in india
http://enablersinvestment.com/

  raj,  11/23/2016

San Diego Moving Company
http://wemove247.com/

  Thomas Wilson,  11/24/2016

This is an informative post review. I am so pleased to get this post article and nice information. I was looking forward to get such a post which is very helpful to us. A big thank for posting this article in this website. Keep it up.
http://happywheels3demo.com

  Usman,  11/27/2016

I really loved reading your blog. It was very well authored and easy to understand.
information
http://www.thesilverbird.com/

  Usman,  11/29/2016

The details about the searchdaimon are well explained along with some pictures and I hope that other readers will also experience how I feel after reading your article.
anti aging creams
http://www.nssusa.org/blossom-(...)-young/

  Usman,  12/04/2016

Hello! I just wish to give an enormous thumbs up for the nice info you've got right here on this post. I will probably be coming back to your weblog for more soon!
Kawaii shop
http://www.kawaiitoko.com/

  Tien Ban  (www),  12/12/2016

Mình tuân thủ đúng cách dùng thuốc và chỉ định đi khám lại, đến khi bác sĩ bảo ok rồi mình mới yên tâm. bạn xem thêm để biết http://dongyhuynhtantrieu.com/(...)t-nhat/

  Usman,  01/09/2017

I am very enjoyed for this blog. Its an informative topic. It help me very much to solve some problems. Its opportunity are so fantastic and working style so speedy.
http://www.flowerdeliverywiz.com

  Thomas Wilson,  01/13/2017

I needed to send you the tiny remark so as to say thank you over again over the amazing things you’ve shared at this time.
http://colorswitchaz.com ,
http://robloxaz.com ,
http://a10games.xyz,

  Usman,  01/22/2017

aaaa

  Usman,  01/22/2017

it's really cool blog. Linking is very useful thing.you have really helped
http://2011rsme.com/chester-ta(...)hiring/

  Usman,  01/22/2017

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it..
http://www.mk-watch.com/exciti(...)atures/

  Usman,  01/22/2017

You completely match our expectation and the variety of our information.
http://www.asamilwaukee.org/co(...)ements/

  David Green,  06/27/2017

I just want to say thanks for your wonderful post, it is contain a lot of knowledge and information that i needed right now. I wanna tell you that if you want to get more fun and enjoyment then visit my site and get more fun.
http://colour-switch.com

  femto,  06/28/2017

Se você deseja descobrir maneiras de ganhar um como ser mais atraente para as garotas coração coronário feminino simplesmente porque quer dormir junto com ela, ela vai saber exatamente o que está fazendo e se afastar de você como a praga. É a garota que coloca seu coração em primeiro lugar que o intriga, a mulher que como ser mais atraente ele respeita. Se assim for, lembre-se de que, para fazer c ...  show more

  narinder,  07/30/2017

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it..

http://myussdcodes.com/ussd-co(...)tworks/

  narinder,  07/30/2017

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it..

http://easyrechargetricks.com/(...)r-code/

  sadiyajaan,  08/22/2017

There are so many great information on this post and i like to share this post with my friends, so thanks for sharing this post.
http://www.mahipalpurcallgirls.com
http://www.bangalorehotcallgirls.in
http://www.thebangaloreescort.com

  narinder,  08/23/2017

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it..

http://www.customercaretollfre(...)number/



Add your opinion
You must be logged in to write a comment. If you're not a registered member, please register. It takes only few seconds, and you get an access to additional functions .
 


About EIOBA
Articles
Explore
Publish
Community
Statistics
Users online: 224
Registered: 93.979
Comments: 3.293
Articles: 7.790
© 2005-2017 EIOBA group.