Symmetry, structure, and spacetime

Philosophy of Space and Time
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But they should nonetheless be prominently listed among the early proposals assuming that some of the theories used in quantum-gravity research might be testable with currently-available experimental techniques. In particular, some of these studies, perhaps most notably the ones in Ref.

[] Deformed relativity symmetries and the local structure of spacetime

But, in spite of their objective significance, these studies did not manage to have an impact on the overall development of quantum-gravity research. It is true that this kind of dimensional-analysis reasoning does not amount to really establishing that the relevant candidate quantum-gravity effect is being probed with Planck-scale sensitivity, and this resulted in a perception that such studies, while deserving some interest, could not be described objectively as probes of the quantum-gravity realm. For some theorists a certain level of uneasiness also originated from the fact that the formalisms adopted in studies such as the ones in Ref.

Still, it did turn out that those earlier attempts to investigate the quantum-gravity problem experimentally were setting the stage for a wider acceptance of quantum-spacetime phenomenology. The situation started to evolve rather rapidly when in the span of just a few years, between and , several analyses were produced describing different physical contexts in which effects introduced genuinely at the Planck sale could be tested. It started with some analyses of observations of gamma-ray bursts at sub-MeV energies [ 66 , , ], then came some analyses of large laser-light interferometers [ 51 , 54 , 53 , ], quickly followed by the first discussions of Planck scale effects relevant for the analysis of ultra-high-energy cosmic rays [ , 38 , 73 ] and the first analyses relevant for observations of TeV gamma rays from blazars [ 38 , 73 , ] also see Ref.

In particular, the fact that some of these analyses as I discuss in detail later considered Planck-scale effects amounting to departures from classical Lorentz symmetry played a key role in their ability to have an impact on a significant portion of the overall quantum-gravity-research effort. And the idea of having some departure from Lorentz symmetry does not necessarily require violations of ordinary quantum mechanics.

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An example of this type is provided by Loop Quantum Gravity LQG [ , 96 , , , 93 ], where one is presently unable to even formulate many desirable physics questions, but at least some however tentative progress has been made [ , 33 , , 75 , ] in the exploration of the kinematics of the Minkowski limit. From a pure-phenomenology perspective, the lates transition is particularly significant, as I shall discuss in greater detail later, in as much as it marks a sharp transition toward falsifiability.

Some of the lates phenomenology proposals concern effects that one can imagine honestly deriving in a given quantum-gravity theory. Instead the effects described in studies such as the ones reported in Ref. This is a point that I am planning to convey strongly with some key parts of this review, together with another sign of maturity of this phenomenology: the ability to discriminate between different but similar Planck-scale physics scenarios. In order for a phenomenology to even get started one must find some instances in which the new-physics effects can be distinguished from the effects predicted by current theories, but a more mature phenomenology should also be able to discriminate between similar but somewhat different new-physics scenarios.

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And it is not uncommon for recent quantum-gravity reviews [ 91 , , , ], even when the primary focus is on developments on the mathematics side, to discuss in some detail and acknowledge the significance of the work done in quantum-gravity phenomenology. So far, my preliminary description of quantum-spacetime phenomenology has a rather abstract character. It may be useful to now provide a simple example of analysis that illustrates some of the concepts I have discussed and renders more explicit the fact that some of the sensitivity levels now available experimentally do correspond to effects introduced genuinely at the Planck scale.

Week 2: Newton on space and time (Oct 24)

If used wisely, I feel that the structure I gave is still preferable to some of the alternatives that could have been considered. That course left a great impression on me, and I thank him for that. Providing a description of such a quantum-black-hole regime is probably the most fascinating challenge for quantum-gravity research, but evidently it is not a promising avenue for actually discovering quantum-gravity effects experimentally. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. For some time the main challenge came in addition to the mentioned interpretational challenges connected with spacetime locality from arguments suggesting that one might well replace a given nonlinear setup for a DSR model with one obtained by redefining nonlinearly the coordinatization of momentum space see, e. Sign up using Email and Password. Returns must be postmarked within 4 business days of authorisation and must be in resellable condition.

These objectives motivate me to invite the reader to contemplate the possibility of a discretization of spacetime on a lattice with lattice spacing and a free particle propagating on such a spacetime. It is well established that in these hypotheses there are corrections to the energy-momentum on-shell relation, which in general are of the type 5.

I should stress that the idea of a rigid-lattice description of spacetime is not really one of the most advanced for quantum-gravity research but see the recent related study in Ref. Moreover, while it is easy to describe a free particle on such a lattice, the more realistic case of interacting fields is very different, and its implications for the form of the on-shell relation are expected to be significantly more complex than assumed in Eq.

In particular, if described within effective field theory, the implications for interacting theories of such a lattice description of spacetime include departures from special-relativistic on-shellness for which there is no Planck-scale suppression, and are therefore unacceptable.

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This is due to loop corrections, through a mechanism of the type discussed in Refs. I feel it is nonetheless very significant that the, however, unrealistic case of a free particle propagating in a lattice with Planck-scale lattice spacing leads to features of the type shown in Eq. It shows that features of the type shown in Eq. So, in spite of the idealizations involved, the smallness of the effects discussed in this Section is plausibly representative of the type of magnitude that quantum-spacetime effects could have, even though any realistic model of the Standard Model of particle physics in a quantum spacetime, should evidently remove those idealizations.

One finds that in most contexts corrections to the energy-momentum relation of the type in Eq. However at least if such a modified dispersion relation is part of a framework with standard laws of energy-momentum conservation , one easily finds [ , 38 , , 73 ] significant implications for the cosmic-ray spectrum. As I shall discuss in greater detail in Section 3. The Planck-scale correction terms in Eq.

This observation is one of the core ingredients of the quantum-spacetime phenomenology that has been done [ , 38 , , 73 ] analyzing GZK-scale cosmic rays. Another key ingredient of those analyses is the quality of cosmicray data, which has improved very significantly over these last few years, especially as a result of observations performed at the Pierre Auger Observatory. It is easy to figure out [ 52 , 73 ] that the large ordinary-physics number that acts as amplifier of the Planck-scale effect in this case is provided by the ratio between a cosmic-ray proton ultra-high energy, which can be of order 10 20 eV, and the mass rest energy of the proton.

And this is not surprising since the relevant Planck-scale effect is an effect of Lorentz symmetry violation, so that large boosts i.

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There are a strikingly large number of arguments pointing to the Planck scale as the characteristic scale of quantum-gravity effects. Although clearly these arguments are not all independent, their overall weight must certainly be judged as substantial. I shall not review them here since they can easily be found in several quantum-gravity reviews, and there are even some dedicated review papers see, e. While gravity usually is not involved in arguments that provide support for unification of the nongravitational couplings, it is striking from a quantum-gravity perspective that, even just using the little information we presently have mostly at scales below the TeV scale , our present best extrapolation of the available data on the running of these coupling constants rather robustly indicates that there will indeed be a unification and that this unification will occur at a scale that is not very far from the Planck scale.

In spite of the fact that we are not in a position to exclude that it is just a quantitative accident, this correspondence between otherwise completely unrelated scales must presently be treated as the clearest hint of new physics that is available to us. Even setting aside this coupling-unification argument, there are other compelling reasons for attributing to the Planck scale the role of characteristic sale of quantum-gravity effects. In particular, if one adopts the perspective of the effective-quantum-field-theory description of gravitational phenomena the case for the Planck scale can be made rather precisely.

A particularly compelling argument in this respect is found in Ref. Unitarity has been a successful criterion for determining the scale at which other effective quantum field theories break down, such as the Fermi theory of weak interactions. And it does turn out that the scale at which unitarity is violated for the effective-quantum-field-theory description of gravitational phenomena is within an order of magnitude of the Planck scale [ ].

Symmetry, Structure, and Spacetime

But it appears legitimate to consider alternatives to such estimates. For example, some authors see, e. And I find that, in relation to this issue, the recent mini- burst of interest in the role of gravity in unification is particularly exciting.

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A convincing case is being built concerning the possibility that gravity might affect the running of the Standard-Model coupling constants, and this too could have significant effects for the estimate of the unification scale see, e. And in turn there is a rather robust argument see, e. My personal perspective on the overall balance of this limited insight that is available to us is summarized by the attitude I adopted for this review in relation to the expectations for the value of the quantum-spacetime scale.

But at the same time imposes upon us at least a certain level of prudence: we cannot assume that the quantum-spacetime scale is exactly the Planck length, but we have some encouragement for assuming that it is within a few orders of magnitude of the Planck length. It is in my opinion the most natural working assumption in light of the information presently available to us, but we should be fully aware of the fact that our naive estimates might be off by more than a few orders of magnitude. Following the line of reasoning adopted here this would take the shape of a solution for that unexpectedly turned out to be wildly different form the Planck length.

As stressed earlier in this section, we cannot place much hope of experimental breakthroughs in the full quantum-black-hole regime. Our best chances are for studies of contexts amenable to a description in terms of the properties of particles in a background quantum spacetime. And, as also already stressed, these effects will be minute, with magnitude governed by some power of the ratio between the Planck length and the wavelength of the particles involved.

Symmetries I: Continuous spacetime symmetry: why we need Lagrangians in field theory

The presence of these suppression factors on the one hand reduces sharply our chances of actually discovering quantum-spacetime effects, but on the other hand simplifies the problem of figuring out what are the most promising experimental contexts, since these experimental contexts must enjoy very special properties that would not easily go unnoticed.

It is mostly as a result of this type of consideration that traditional quantum-gravity reviews considered the possibility of experimental studies with unmitigated pessimism.

Week 3: Leibniz on space and time (Oct 31)

1 Interpretation and Formalism 2 Space and Time in the Leibniz-Clarke Debate 3 The Interpretation of Gauge Symmetries 4 Spacetime in General Relativity 5. Buy Symmetry, Structure, and Spacetime (Volume 3) on ✓ FREE SHIPPING on qualified orders.

However, the presence of these large suppression factors surely cannot suffice for drawing any conclusions. Even just looking within the subject of particle physics we know that certain types of small effects can be studied, as illustrated by the example of the remarkable limits obtained on proton instability. The prediction of proton decay within certain grand unified theories of particle physics is really a small effect, suppressed by the fourth power of the ratio between the mass of the proton and grand-unification scale, which is only three orders of magnitude smaller than the Planck scale.

Symmetry in QFT and Gravity - Hirosi Ooguri

Outside of particle physics more success stories of this type are easily found: think for example of the Brownian-motion studies conducted a century ago. Within the Einstein description one uses Brownian-motion measurements on macroscopic scales as evidence for the atomic structure of matter. For the Brownian-motion case the needed amplifier is provided by the fact that a very large number of microscopic processes intervenes in each single macroscopic effect that is being measured.

It is hard but clearly not impossible to find experimental contexts in which there is effectively a large amplification of some small effects of interest. And this is the strategy that is adopted [ 52 ] in the attempts to gain access to the Planck-scale realm. Something else that characterizes the work attitude of the community, whose results I am here reviewing, is the expectation that the solution of the quantum-gravity problem will require a significant change of theory paradigm. Members of this community find in the structure of the quantum-gravity problem sufficient elements for expecting that the transition from our current theories to a successful theory of quantum gravity should be no less probably more significant then the transition from classical mechanics to quantum mechanics, the prototypical example of a change of theory paradigm.

This marks a strong difference in intuition and methodology with respect to other areas of quantum-gravity research, which do not assume the need of a paradigm change. If the string theory program turned out to be successful then quantum gravity should take the shape of just one more particularly complex but nonetheless consequential step in the exploitation of the current theory paradigm, the one that took us all the way from QED to the Standard Model of particle physics.

This difference of intuitions even affects the nature of the sort of questions the different communities ask. The expectation of those not preparing for a change of theory paradigm is that one day some brilliant mind will wake up with the correct full quantum-gravity theory, with a single big conceptual jump.