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This video discusses the various concepts involved in quantum mechanics, such as spacetime, quantum field theory, and the conformal bootstrap. The author also reviews the difficulties of time, and how these difficulties are avoided in Euclidean space.

**00:00:00**In this lecture, N. Arkani-Hamed discusses spacetime and quantum mechanics, highlighting the importance of total positivity and motives. He also discusses the development of this field over the past several decades, and notes that a graduate-level introduction is still needed.**00:05:00**This lecture discusses how space and time are approximate in quantum mechanics, and how this affects our understanding of physics. It also discusses how gravity plays a role in these concepts, and how it can lead to black holes.**00:10:00**N. Arkani-Hamed discusses the two infinities that are important in quantum mechanics- the first infinity, which concerns probabilities, and the second infinity, which concerns the size of the apparatus. He explains that, although the second infinity is practically irrelevant, it is conceptually important because it means that measurements can never be exact within a fixed size room.**00:15:00**Quantum mechanics allows us to talk about observable phenomena, but we lose information by doing so. In anti-de-sitter space, the experiment starts and ends at infinity, so there is no gravity on the boundary. By fixing the geometry, we are able to solve the problems associated with quantum gravity near the Planck length.**00:20:00**This lecture discusses the idea that time may be emergent, meaning that it does not exist in a vacuum but emerges from physical laws. It also discusses how this could affect our understanding of physics, particularly quantum mechanics.**00:25:00**The author discusses the two main problems with quantum mechanics: the finitude of the number of degrees of freedom that are available to us, and the inability to predict precise events. He argues that the best way to think about quantum mechanics at the moment is to view it as a theory of space-time related to a single, unified underlying theory.**00:30:00**This lecture discusses the potential for new physics that does not rely on classical physics, specifically quantum mechanics. It explains how this new physics might be manifested in the real world, and the course is designed to show examples of this in practice.**00:35:00**In this lecture, N. Arkani-Hamed discusses how the physical laws governing spacetime and quantum mechanics are universal, and how the concept of scattering amplitudes can be used to understand this. He also discusses why time is important in this context, and how the boundary of flat space might be conceptualized as a normal place in anti-de Sitter space. Arkani-Hamed reviews why series expansions are important in quantum field theory, and how the concept of locality can be used to understand the behavior of particles at the boundary of flat space. He concludes the lecture by discussing how a local quantum field theory might be applicable to the physical laws governing spacetime and quantum mechanics.**00:40:00**In this lecture, N. Arkani-Hamed discusses the various concepts involved in quantum mechanics, such as spacetime, quantum field theory, and the conformal bootstrap. He also discusses the difficulties of time, and how these difficulties are avoided in Euclidean space.**00:45:00**This video discusses the problem of understanding how causal evolution works in the interior of space-time, and how current theories do not provide a clear answer. One possible solution is to look at the scattering amplitudes as functions of energies and momenta, which would allow for more detailed analysis of the structure of the amplitudes. However, this approach is far from being fully developed and is currently subject to many unanswered questions.**00:50:00**This lecture begins by introducing the concepts of locality and causality, and how they are tightly linked in a Lorentz-invariant theory. The talk then goes on to discuss the origins of the s matrix program, and how it ultimately failed because its practitioners could not figure out what the analytic properties of the scattering amplitudes were. This is followed by a discussion of the conformal bootstrap, which is a method for dealing with problems that are too hard for traditional math methods.**00:55:00**The video discusses how physicists hope to interpret singularities in Lorentzian kinematics by studying the amplitude and Lorentz invariants. However, they soon discovered that this is impossible, as every consistent quantum field theory will give you a consistent scattering matrix.

In this video, N. Arkani-Hamed discusses how total positivity and motives can help explain spacetime and quantum mechanics. He also provides problem sets for those who would like to continue their learning.

**01:00:00**In this lecture, N. Arkani-Hamed discusses how we need to find new principles to explain causality, unitarity, and locality in quantum mechanics. He also mentions how people working on quantum mechanics in the 1960s discovered that the kinematic space can be used to represent the scattering process.**01:05:00**The goal of this lecture is to explore the principle behind the discovery of simplicity in complex physical systems. The lecture goes into detail about how calculations in quantum field theory can reveal hidden symmetries and simplifications in complex systems. The lecture ends with a prediction for future research.**01:10:00**N. Arkani-Hamed discusses the structure of spacetime and quantum mechanics. He discusses the elimination of virtual particles, and how this leads to the theory of strings. He also discusses the nature of the Final Aim of quantum mechanics, which involves the inversion of the 1960s program.**01:15:00**The speaker in this video introduces the idea of total positivity and its various manifestations in mathematics and physics. He notes that while many of these interactions are esoteric, they are nevertheless fundamental to our understanding of the physical world. He provides some resources for those interested in further reading.**01:20:00**N. Arkani-Hamed discusses the concepts of spacetime and quantum mechanics, explaining how total positivity and motives can help explain these phenomena. He also provides problem sets for those who would like to continue their learning.

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