Introduction to Loop Quantum Gravity - Lecture 2: Space
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- Опубліковано 5 чер 2024
- This course was given at the CPT in Marseille in February and March 2018. Lecture 2 is on the different notions of "space" and their role in quantum gravity.
A latex transcript of the lectures is available here: arxiv.org/abs/2305.12215
(thanks to Pietropaolo Frisoni) - Наука та технологія
I have never seen a professor who dedicates such an amount of time for the historical development of human thought. Grande Carlone nazionale!
I mean, teaching a physics course...
A general discussion about the notion of spacetime: Aristotle, Newton, Einstein, Rovelli.
No maths involved, enjoyable also for the general public. Recommended to philosophers.
Dear Francesca I am new to physics and studying the philosophy of science. Do I have to know higher maths if I wanted to study quantum mechanics or your subject of interest. I love this subject but I am always terrified that it will launch into higher abstract maths of which I know nothing. Thank you. I just bought your book .
A question about the role of topology and continuity vs granular spacetime may be a very important one with respect to the notion of the dynamical entity, called "quantum gravitational field" that we called space time.
That is a great question. It is possible to get quantum mechanics from non-trivial spacetime topology keeping spacetime a smooth continuum, which has discrete structure (the closed timelike curve homotopy), and then one does not need to discretize spacetime.
Lecture 1 was very enjoyable. It is indeed suitable for a general audience, eg those who have read one of Prof Rovelli's popular books. The suggestion by an audience member that Thermodynamics is one of the models of the world which we want to accomodate in a theory of quantum gravity is spot on, in my opinion. Thermodynamics speaks of processes, not physical structure. Thanks to Prof Rovelli for making these lectures and course materials available.
Very nice introduction
despite I have no in-depth knowledge of this advanced field of physics, i’m being interested in path integral. I knew that these are not well defined from a mathematical point of view, but rather as a limit. in the interpretation of PI, a particle moves in the empty space between A and B as if it interacts with infinite screens and infinite slits. But if spacetime is not a continuum then there is a physical meaning in the fact that the integral is not well defined and maybe, the particle rather than interpreting it as if it were scattering with slites, could be scattering with the quanta of space time.
I'd like to know what you think of this speculation
Consider (a) If spacetime is not a continuum there are no paths, a path is a continuous topological concept. (b) The path integral is well-defined if there is a cut-off, and/or by employing the use of a regularizer and not being tempted to use the cheap unphysical trick of Wick rotation, so you can use something like Picard-Lefschetz theory to compute Lorentzian path integrals. The physics puzzle is what cut-off is physical and how to use it? Most would say the Planck scale, but few know how to make this a proper QG theory. I believe the answer is not to doubly quantize gravity. Gravity is already a quantum theory once closed timelike curves are admitted at the Planck scale. I'd be surprised if this were not true. But sadly I doubt experiments will show us this in my lifetime.
If true, or something like this, then it would mean there is no need to incorporate superposition of spacetime. The quantum theory is the theory of ordinary spacetime but with non-trivial topology. The superpositions are restricted to the local structures (aka. elementary particles).
What does this discussion tell us about Mach’s principle?
The movement of the water Is a cause of interactional communications Between the bucket and the water
Love these but its a pity the sound is blurred.
@23:00 is Carlo saying this correctly? Spacetime is not the field, it is mathematically a field with a multivector algebra structure. But that is not a _physical field_ --- a physical field is a quantity that takes a value at every point in a space or a spacetime. The coordinates of spacetime are not a physical field because, as Galileo and Einstein taught us, the labels are not physically relevant. Gravity is different to spacetime. The physical quantity corresponding to the gravity field (physical) is the mass and curvature, both, you cannot just say it is "spacetime", since that neglects matter-energy and the theory of gravity concerns both, both matter _and_ spacetime curvature. You cannot separate them. Computing just one side of the Einstein equations gets you nowhere (except for having found a vacuum solution if you compute the metric side).
Even in topological 4-geon theory the masses are not really _the spacetime_ --- the masses are localized regions of non-trivial spacetime topology, it is a subtle issue whether you can claim these geons _are_ spacetime or rather are proper subsets, or structures "living on" the spacetime. But that's the type of subtlety I don't really care about, provided someone else knows what you mean the categorical distinctions are just definitional.
@38:00 Democritus does not make sense, but you can always make sense of Democritus. A dualism works fine for this. Just take his "non-being" as meaning "where there is no mass", and "being" to be "where there is mass". Both refer to space (the "where"). Quantum mechanics does not change this an awful lot, it just spreads out mass in terms of non-Kolmogorov generalized probability, "here is where we might detect mass" --- which makes vacuum versus matter fuzzy, but not necessarily ontologically fuzzy, only fuzzy with respect to our measurements, hence also with respect to what physics we can effectively model. Dualism is not a bad metaphysics, I'd argue pretty much everything we know has dual aspects, and of course mathematics is riddled with duality, just take the spacetime algebra duality transforms for starters, or vectors and linear transforms more specifically. I don't like Tegmark's MUH nonsense (it ain't science), but if you do take the mathematical models for physics half-seriously, doesn't this tell you something about duals in physics? They are all around us.
28:00 can hear guy heavily breathing down the mic
@25:00 sure, but he is violating his own principles laid out in Lecture-1 here. If we take nature at face value and strive for a bit of minimalism, then for damn sure we "know" spacetime itself is not quantum mechanical. The matter fields are "quantum mechanical" but the spacetime itself is not, not as far as any empirical evidence shows. The Feynman-Aharonov experiments are the best bet for detecting superposition of the spacetime manifold, but they are extremely subtle experiments. I'd be lucky to learn of definitive Feynman-Aharonov experiments in my lifetime I reckon. Until such a time it is useful if some people continue working under the assumption gravity is already a quantum theory, but not because of spacetime superposition, rather because matter can traverse closed timelike curves. Note it is wrong to say the "matter fields" traverse CTCs, because the field concept is specifically an auxiliary accounting trick to avoid CTCs. So it is completely balmy to go reinserting CTCs in a field theory when the whole idea of field theory is to avoid CTCs --- as Feynman taught everyone (everyone who was listening & reading).
This makes me uncomfortable. If we accept space as an entity, then we must also accept another entity- that of 'not space'. You cannot know there is light unless there is darkness. And this 'anti-space' is a funny thing , this 'non-being' of Democritus- it has no dimension but only location defined by the location of the quanta of space.And the only quality we can ascribe to this anti-space is how many 'cells of space' it contains - which we interpret as gravity. So if gravity is a phenomenon of multiple quanta of space, we cannot talk about quantum gravity any more than we can talk about a flock of sheep if we only have 1 sheep.