Against Space

By Sean Carroll | November 10, 2010 6:59 am

The Philosophy of Science Association meeting in Montreal was great fun. For one thing it was in Montreal; for another I got to hang out with Doctor Free-Ride; and as a bonus there were some interesting and provocative talks about the nature of time. I chatted with Tim Maudlin, Huw Price, Craig Callender, Nick Huggett, Chris Wuttrich, David Wallace, John Norton, and other people I always learn from when I talk to. Philosophers always force you to think hard about things.

Here are the slides from my own talk, which was supposed to be about time but ended up being more about space. Not much in the way of original research, just some ruminations on what is and is not “fundamental” about spacetime (with the caveat that this might not be a sensible question to ask). I made two basic points, which happily blended into each other: first, that the distinction between “position” (space) and “momentum” is not a fundamental aspect of classical mechanics or quantum mechanics, but instead reflects the particular Hamiltonian of our world; and second that holography implies that space is emergent, but in a very subtle and non-local way. This latter point is one reason why many of us are skeptical of approaches like loop quantum gravity, causal set theory, or dynamical triangulations; these all start by assuming that there are independent degrees of freedom at each spacetime point, and quantum gravity doesn’t seem to work that way.

Sadly the slides aren’t likely to be very comprehensible. There’s a lot of math, and the equations don’t come out completely clearly — my first time using Slideshare, so perhaps they would look better if I uploaded a pdf file rather than PowerPoint. (Hint: the slides are much more clear if you click “Menu” at the bottom left, and switch to full-screen mode.) Also I didn’t make any attempt to have the slides stand by themselves without the accompanying words. But at least this will serve as documentation that I really did give a talk at the conference, no just hang out in restaurants in Montreal.

CATEGORIZED UNDER: Philosophy, Science, Time
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  • Valatan

    The phase space structure of Loop Quantum Gravity is pretty carefully set by boundary conditions (or, more properly, a total divergence in the action), which enables them to use K_{ab} as a canonical variable and h^{ab} as its conjugate momentum. So, I don’t think its entirely fair to say that LQG starts by talking about dynamical degrees of freedom at a point, and ignores boundaries.

    And has anyone worked out an AdS/CFT in the context of not-string theory? I don’t see how something that is a consequence of string theory should be taken to be a generic property of quantum gravity. Certainly, classically, gravity has two local degrees of freedom corresponding to gravitational wave polarizations (and then several of topological/boundary degrees of freedom)

  • James

    The holographic principle has a firm realisation in the form of the AdS/CFT correspondence, but it is independent of (and predates) it. Quantum gravity’s holographic nature was first suggested by Bekenstein entropy – ie, that the entropy of a black hole is proportional to the horizon area, not the volume contained within. This was way before string theory entered the frame (though Vafa and Strominger would later account for it with string theory).

  • http://guidetoreality.blogspot.com Steve Esser

    That was interesting, even if I’m missing alot. I like the highlighting of the linkage between position and local interaction.

  • Doug

    But LQG has a derivation of Bekenstein entropy also. So if Bekenstein entropy is why you believe in the holographic principle, the holographic principle should not be why you doubt LQG.

  • Ben Finney

    Yes, please use the open PDF document format instead of proprietary ones. Also, please put the slides somewhere we can download them; as it stands, we can’t download them without jumping through sign-up hoops.

  • Andrew

    As a humble suggestion, perhaps you should start using the beamer pdflatex package instead of powerpoint or clones? Nice PDFs straight from compilation with overlays, transitions, animations, etc, available.

  • Just Learning

    Space is relational database created by our brains. Distance and time are merely reflections of the relative processing effort needed to restructure the data call. People and other “thinking” objects seem to be manifestations of singularities (or topological defects) in the data structure, where data is restructered unpredictably.

  • Anders

    All this would be cool to see you talk about in a more simplified and/or pedagogical way for us people who just have this stuff as a hobby interest. Maybe a little audio to go with the slides? For what it’s worth i would personally enjoy that.

  • Anders

    Some smooth analogies from the smooth analogies master.

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  • James

    Looks like a v interesting talk, by the way – would’ve been good to hear what you said along with the slides.

  • uhmmm

    Is your first “Closing Rumination” bullet point (and really the thrust of your slides up to the AdS/CFT slide) essentially Einstein’s resolution of the hole argument, viz. coordinates are not physically meaningful in themselves but only emerge in the presence of objects with momentum?

    Or, quoting him:

    ‘All our spacetime verifications invariably amount to a determination of spacetime coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meeting of two or more of these points.’

    ‘People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter.’

    or am I misunderstanding the line of thought expressed in your slides?

    Also, doubly unwarranted speculative question: at the *other* boundary condition in the limit of one object in (the? each?) Hubble volume, are there features we can think about that might illuminate (pardon the pun) space and time?

  • Anders

    According to my brain there has never been any experimental proof of hawking radiation existing. Another thing i don’t get is the correlation between the information content of a black hole and its event horizon. There are apparently a lot of interesting things that can be drawn from this correlation, like the holographic universe theory, but the whole “increased entropy leads to increased area” thing is also entirely theoretical unless it’s been possible to watch how black holes actually behave when they get more energy from surrounding space.

  • Paul Stankus

    Sean — I’m glad to be reading you here at CV regularly again. Your “fundamentalism” talk was fun to look at! but what stood out for me was the lack of reference to causality. When you ask “What is fundamental?” it seems to me that causality is the most basic answer, more basic even than time. Cause follows effect; we only need to talk about time in order to describe causality — or, to put it the other way, if there were no causality then it would be senseless/impossible to talk about time.

    My intuitive, back-of-the-back-of-the-mind feeling is that both space and time should both emerge from causality. At my Bear of Little Brain level this fits right in with relativity: from any small patch that is local in space and time, the patches that are causally connected to it are in separated in the “time” direction, and those not causally connected are separated in the “space” direction. It’s sort of a matter of taste as to which of these you want to call “privileged,” but it’s a basic reason to expect two different kinds of separations before making any claims about geometry or even continuity. In Lee Smolin’s book he describes one of the approaches to quantum gravity taking this view, that the fundamental descriptor of the universe is the causality network between different points/events; though at the time of that writing, IIRC, he said they hadn’t made much progress. Know anything about it? (sorry if this is already gone over in your book, I’ve only recently been able to afford a copy and haven’t gotten that far yet)

  • George Musser

    Great talk! Holography is also often said to rule out condensed-matter-analogue theories, but doesn’t Horava, for one, argue that it is a low-energy phenomenon — that, at high energies, there are more degrees of freedom than the holographic bound would imply?
    George

  • João Gil

    I think you are all nuts.. if I want time I´ll buy it and if i want space I´ll think of time. Time is an entity under which all thinkin entity needs to be in reference to. If the thinking entity refers its energetic power to a non referable entity it goes into void and dismisses its abiltity to comunicate the reference it refered to. This means the leg was bigger than the step. This does not imply that the energic power to think non referable entities proves a natural understanding of the means by which the thinking entity thinks itself in time-space. It just proves that the spiral in which a theory is proven is decayed in along with the energetic power to think of reference and non reference by time itself. ultimately and AHHHhhhhhhh I WAS KILLED BY ALIENS

  • Aiya-Oba

    Time is changeless (absolute) Space.

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  • Daniel Tung

    My view on the last is exactly the opposite.
    Only a new understanding of space (and time) will help us understand the beginning of universe. :)

  • Anchor

    Anders (#9, 10, 14) can speak freely as anyone else and supply contrary opinion. In this case, Anders eventually resolves his problems (#14) with things his brain doesn’t get:

    1. “…there has never been any experimental proof of hawking radiation existing.”

    and

    2. “Another thing i don’t get is the correlation between the information content of a black hole and its event horizon.”

    3. Concluding that, “There are apparently a lot of interesting things that can be drawn from this correlation, like the holographic universe theory, but the whole “increased entropy leads to increased area” thing is also entirely theoretical unless it’s been possible to watch how black holes actually behave when they get more energy from surrounding space.”

    AFTER he said this (#9 and #10):

    4. “All this would be cool to see you talk about in a more simplified and/or pedagogical way for us people who just have this stuff as a hobby interest. Maybe a little audio to go with the slides? For what it’s worth i would personally enjoy that.”

    …not to mention a backhanded sleight in the form of this:

    5. “Some smooth analogies from the smooth analogies master.”

    It is no wonder that physicists automatically spurn the likes of Anders, who might understandably tend to figure that every person who examines “this stuff as a hobby interest” is most probably a crackpot.

    It is quite evident you also “don’t get” that you find no reason to understand why it is crucial that YOU understand. Any barking from your kind is nothing more than a contest. You serve no actual purpose but to diminish the authentic amateur theorist that is actually out there that may have something of substance to contribute.

    Wouldn’t you think so Anders, “according to [your] brain”?

    Feeling obnoxiously clever is not the same as being even slightly let alone fully informed.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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