You're asking for a list of existing known observations and facts that directly contradict the assertions of the previously discussed named entities, thereby falsifying them. Here's a breakdown based on the sources: - **Standard Model of Particle Physics (Higgs hierarchy problem):** While the hierarchy problem itself is a theoretical inconsistency, the continued **lack of direct experimental evidence for many Beyond the Standard Model (BSM) particles** predicted by theories aiming to solve it (like supersymmetric particles at expected energy scales) can be seen as a contradiction to the expectations of those specific extensions. - **ΛCDM model of cosmology (dark matter):** A significant challenge is the **persistent absence of direct, non-gravitational detection of any dark matter particle candidate** despite numerous and varied experimental efforts. Furthermore, the success of **Modified Newtonian Dynamics (MOND) in explaining galaxy rotation curves and other galactic-scale phenomena without invoking dark matter** directly contradicts the assertion that dark matter is necessary to explain these observations at these scales. - **ΛCDM model of cosmology (dark energy):** The most stark contradiction is the **cosmological constant problem**, the enormous disparity between the theoretically predicted quantum vacuum energy density and the observed value of the cosmological constant. This vast difference suggests a fundamental flaw in our understanding or calculations. Additionally, discrepancies like the **Hubble tension**, where different methods of measuring the Hubble constant yield inconsistent results, may indicate a fundamental issue with the ΛCDM model. - **Big Bang theory (Horizon Problem):** The observed **uniformity of the Cosmic Microwave Background (CMB) temperature across the entire sky** is a fact that the standard Big Bang theory without an inflationary epoch struggles to explain, as regions now far apart would not have been in causal contact to reach thermal equilibrium. - **Big Bang theory (Flatness Problem):** The highly precise measurements indicating that the **universe's spatial geometry is remarkably flat** require an extremely fine-tuned initial density in the standard Big Bang model, which is seen as an unnatural and problematic aspect. - **Newtonian gravity (failure to predict Mercury's precession):** The **anomalous precession of the perihelion of Mercury's orbit**, an observed fact that could not be accurately predicted by Newtonian gravity alone, was a key piece of evidence supporting Einstein's theory of General Relativity. - **WIMP miracle (lack of direct detection):** The **ongoing failure to conclusively detect WIMP (Weakly Interacting Massive Particle) dark matter through direct or indirect detection experiments** [8, 11, 15, 21, 43, 2403.15860, 7] despite significant experimental efforts contradicts the simplest and most elegant scenarios of the "WIMP miracle." - **Naturalness arguments in BSM physics (failure to find expected low-mass particles):** The **lack of discovery of many low-mass particles predicted by naturalness arguments**, such as supersymmetric partners expected to be within the reach of the Large Hadron Collider (LHC), challenges these specific theoretical motivations for BSM physics. It's important to note that for some of the other entities mentioned previously: - For the **Singularity Problem** in the Big Bang theory, it's a theoretical issue (a point where current physics breaks down) rather than a contradiction with a specific observation. - For **Λ’s Role (arbitrary tuning)** in the Big Bang theory, the issue is the lack of a natural explanation for the observed value, not a direct contradiction of an observation. - For the **Klein-Gordon and Dirac equations**, the initial issues like superluminal velocities and negative probabilities were resolved through the development of Quantum Field Theory and the Feynman-Stueckelberg interpretation; there are no current experimental facts contradicting their core relativistic quantum descriptions within their domain of applicability. - For the **Standard interpretation of quantum mechanics**, the issues are more about conceptual ambiguities and alternative interpretations rather than direct falsification by experimental facts. - Defining **reality solely in terms of information** is more of a philosophical stance than a scientific theory currently subject to direct falsification by known facts. - The **naive QFT calculation of quantum vacuum energy** is contradicted by the observed cosmological constant, as mentioned under dark energy. - For **Lorentz invariance** and the **CPT theorem**, current experimental evidence overwhelmingly supports these principles; no known facts contradict them at a fundamental level. - The **probability interpretation in the Many-Worlds Interpretation (MWI)** faces theoretical challenges in deriving the Born rule but isn't directly contradicted by current experimental facts. - **Classical cosmology's inability to describe the Planck era** is a theoretical limitation, not a contradiction with an observation. - **Inflationary models** lack direct empirical confirmation of the inflaton field, but successfully explain some key cosmological observations like CMB anisotropies. The scientific landscape is constantly evolving, and these points of tension and contradiction drive further research and the development of new theories.