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  1. Stephen Hawking thought an asteroid impact posed the greatest threat to life on Earth. Thanks to <deleted> for sponsoring this video. Any Discussions About This Topic Thread?
  2. Those images appear to be Kaleidoscopic (having complex patterns of colors; multicolored, made up of a complex mix of elements; multifaceted.) (ref. 1) Reference: Wikipedia - Kaleidoscope: (ref. 1) https://en.wikipedia.org/wiki/Kaleidoscope
  3. Those appear to be Moiré patterns. (ref. 1) The interference effect can be produced when two or more zone plates overlap and are rotated, or when an opaque ruled pattern with transparent gaps is overlaid on another similar pattern and are rotated. Reference: Wikipedia - Moiré pattern - rotated patterns: (ref. 1) https://en.wikipedia.org/wiki/Moiré_pattern#Rotated_patterns https://upload.wikimedia.org/wikipedia/commons/9/97/Moire_Lines.svg
  4. The parameters are identical for modelling any real physical object. (ref. 1) Note that all the interference patterns that you have pictured are formally called Fresnel zone plates, and informally just called zone plates. The results are identical, with the exception that the original object may be physical and the other object may be a virtual hologram. The mathematics in (ref. 1) are capable of modelling any Fresnel zone plate, including point source holograms (ref. 2). Can a physical Fresnel lens project a virtual hologram?....Affirmative. (ref. 3) Reference: Wikipedia - Fresnel Zone Plate: (ref. 1) https://en.wikipedia.org/wiki/Zone_plate Wikipedia - Hologram - point sources: (ref. 2) https://en.wikipedia.org/wiki/Holography#Point_sources Physical Fresnel Lens Hologram Test: (ref. 3) https://www.youtube.com/watch?v=f8wSabvv1xs
  5. As of 2018, the Supreme Court had overruled more than 300 of its own cases. (ref. 1) Negative, there are no legal mandates to "balance the courts" by partisan boundaries. There are only three legal mandates, one mandate is an Act, one mandate is a congressional statute, and the other mandate is a constitutional article. By "even split", I presume you mean an even partisan (a strong supporter of a party, cause, or person; prejudiced in favor of a particular cause) boundary for the total number of justices. It is constitutionally possible, though improbable based upon the partisan affiliation of the nominating president. Although nominating Supreme Court justices based upon suspected partisan affiliation is in my opinion, constitutionally repugnant due to the "apolitical" constitutional design for judicial selection. In my opinion it would have the opposite effect of splitting the court down partisan lines and decide cases more on partisan politics than on case precedent merits. Only if the federal district courts or the Supreme Court ruled that the legislative acts that constructed the judiciary structure were illegal or unconstitutional (not in accordance with a political constitution, especially the United States Constitution, or with procedural rules). Affirmative, if the Supreme Court ruled that the addition of a new justice office was illegal by Act, statute or unconstitutional by established boundaries or with procedural rules. For example, a majority of congressional partisans wanted to "stack" the court with more than nine justices, without a presidential nomination and based upon suspected partisan affiliation for generating judicial bias for political gain regarding any existent de jure (by Right; according to law) legal precedent, in violation of the Judiciary Act of 1869 and Title 28 U.S.C. § 1 and the United States Constitution, Article II, Section 2, Clause 2. Constitutionally, the alteration of the judiciary branch of government requires a Act of Congress, which creates a law, or modifies an existing law, with a simple majority of both the House of Representatives, and the Senate. (> = 51%), (51 of 100). However, if the structural judiciary branch of government is already bounded within the constitution and therefore requires a modification or constitutional amendment, then to become an operative part of the United States Constitution, an amendment, whether proposed by Congress or a national constitutional convention, must be ratified by either: The legislatures of three-fourths (> = 75%) (at present 38) of the states; or State ratifying conventions in three-fourths (> = 75%) (at present 38) of the states. (ref. 6) Negative, the court has evolved to the nine members only by congressional Acts and statute, a constitutional power and boundary entrusted only to Congress. Article III of the United States Constitution sets neither the size of the Supreme Court nor any specific positions on it, though the existence of the office of the chief justice is tacitly acknowledged in Article I, Section 3, Clause 6. Instead, these powers are entrusted to Congress, which initially established a six-member Supreme Court composed of a chief justice and five associate justices through the Judiciary Act of 1789. The Judiciary Act of 1869 also called the Circuit Judges Act, and Title 28 U.S.C. § 1, returned the number of justices to nine, where it has since remained. (ref. 3, 4) Year - justice number, Congressional Act: 1789 - 6, Judiciary Act of 1789 1807 - 7, Seventh Circuit Act of 1807 1837 - 9, Eighth and Ninth Circuits Act of 1837 1863 - 10, Tenth Circuit Act of 1863 1866 - 9, Judicial Circuits Act of 1866 1869 - 9, Judiciary Act of 1869 1948 - 9, Title 28 U.S.C. § 1 2020 - 9, remained. U.S. Citizens do not have the Right to vote for a president, registered voters only have the constitutional Right to vote for an elector, under the United States Constitution Twelfth Amendment. (ref. 7) When people cast their vote, they are not actually voting for president, but for a group of people called electors. The number of electors each state gets is equal to its total number of Senators and Representatives in Congress. A total of 538 electors form the Electoral College. Each elector casts one vote following the general election. Only an elector has the constitutional Right to vote for a president. (ref. 7) In the United States, federal and state courts at all levels, both appellate and trial are able to review and declare the "constitutionality", or agreement with the Constitution, or unconstitutionality of legislation by a process of judicial interpretation that is relevant to any case properly within their jurisdiction. In American legal language, "judicial review" refers primarily to the adjudication of constitutionality of statutes, especially by the Supreme Court of the United States. This is commonly held to have been established in the case of Marbury v. Madison, which was argued before the Supreme Court in 1803. (ref. 8) Reference: Wikipedia - SCOTUS overruled decisions: (ref. 1) https://en.wikipedia.org/wiki/List_of_overruled_United_States_Supreme_Court_decisions Wikipedia - SCOTUS Nomination, confirmation, and appointment: (ref. 2) https://en.wikipedia.org/wiki/Supreme_Court_of_the_United_States#Nomination,_confirmation,_and_appointment Wikipedia - SCOTUS size: (ref. 3) https://en.wikipedia.org/wiki/Supreme_Court_of_the_United_States#Size_of_the_court Cornell University - 28 U.S.C. § 1: (ref. 4) https://www.law.cornell.edu/uscode/text/28/1 Wikipedia - Act of Congress: (ref. 5) https://en.wikipedia.org/wiki/Act_of_Congress Wikipedia - United States constitutional amendment - federal constitution: (ref. 6) https://en.wikipedia.org/wiki/Constitutional_amendment#Federal_constitution Wikipedia - United States Constitution - Twelfth Amendment: (ref. 7) https://en.wikipedia.org/wiki/Twelfth_Amendment_to_the_United_States_Constitution Wikipedia - United States - Judicial Review: (ref. 8) https://en.wikipedia.org/wiki/Judicial_review#Review_by_general_courts Wikipedia - United States - Marbury v. Madison (1803): (ref. 9) https://en.wikipedia.org/wiki/Marbury_v._Madison
  6. More to the point of OP's topic title "Constitutional laws" and OP's questions. In order for any form of human government to be "constitutional", it must be founded upon a "constitution" that establishes the parameters that such a form of government must be founded within by constitutional boundaries established within its constitution. If such a constitutional form of government be a Constitutional Democracy or a Constitutional Republic, is an experimental a priori (relating to or denoting reasoning or knowledge which proceeds from theoretical deduction rather than from observation or experience) political science expression, based upon pre-existant knowledge of philosophical and scientific constitutional principles regarding forms of governments. Ideally, in the United States constitution, the political scientists "founders" constitutionally intended Supreme Court justices to be unbiased and "apolitcal" (not interested or involved in politics), hence the reasoning for the lifetime tenure for Supreme Court justices that are not directly elected public officials and selected and installed only by the most representative areas in such a government. In the United States constitution, it is not numerated as to how many Supreme Court judges are required to make a constitutional ruling, the court has evolved to the nine members only by statute. Because the number is bound by statute, it would be federally illegal to "stack" the court to higher numbers solely for generating judicial bias for political gain regarding any existent de jure (by Right; according to law) legal precedent. Legal interpretation of legislative acts or laws, is one of the corner stones of any legal or justice system within any form of government. Fundamentally, any law derived by any state or federal level of government really falls within two categories, "constitutional" and "unconstitutional". In the United States, the constitutional validity of a legislative act derived by any state or federal form of government may be challenged by a process called "judicial review" or through a "writ of certiorari". The United States constitution is not "written in stone", it is in fact alterable and amendable, possibly although improbably even abolishable by its own intrinsic constitutional design. The constitution is intrinsically designed to be difficult to alter for any governing body without a representative majority.
  7. Affirmative. I have located the official "Extended Baryon Oscillation Spectroscopic Survey (eBOSS)" website, listed in reference. The eBOSS team is using a universal time coordinate scale as the domain axis on their map, however, I am also interested in examining the CMBR photon surface of last scattering radial metric distance used on this map, the metric correspondence between space and time, called space-time. If anyone is able to cite a reference to that eBOSS CMBR radial metric data, please post a reference link. This is the YouTube "visualization of the data" video linked from their website: Reference: The Extended Baryon Oscillation Spectroscopic Survey (eBOSS) website: https://www.sdss.org/surveys/eboss/ The full list of publications from eBOSS: https://ui.adsabs.harvard.edu/public-libraries/zjBkevkvQoCBUhWbnd38qg
  8. Astrophysicists unveil biggest-ever 3D map of Universe: The map is very isotropic and homogeneous, the large scale galactic filaments are not as apparent on this scale. Discussion? Isotropic: .(of an object or substance) having a physical property which has the same value when measured in different directions. .(of a property or phenomenon) not varying in magnitude according to the direction of measurement. Homogeneous: .of uniform structure or composition throughout. Reference: https://www.ctvnews.ca/sci-tech/astrophysicists-unveil-biggest-ever-3d-map-of-universe-1.5030682
  9. Affirmative, during the inflationary epoch, the universe was homogeneous and isotropic, every particle point location in space-time was inflating and expanding from every other particle point location in space-time faster than invariant luminous velocity. Any primordial quantum black holes generated as bosonic radiation when the strong force broke symmetry from gravity, would have evaporated instantly from Hawking blackbody radiation. [math]\;[/math] Hawking blackbody radiation evaporation time for a Planck mass quantum black hole: [math]t_{ev} = \frac{5120 \pi G^{2} m_{P}^{3}}{\hbar c^{4}} = 5120 \pi t_{P} = 5120 \pi \sqrt{\frac{\hbar G}{c^{5}}} = 8.671 \cdot 10^{-40} \; \text{s}[/math] [math]\;[/math] [math]\boxed{t_{ev} = 5120 \pi \sqrt{\frac{\hbar G}{c^{5}}}}[/math] [math]\boxed{t_{ev} = 8.671 \cdot 10^{-40} \; \text{s}}[/math] [math]\;[/math] This next presented Hawking blackbody radiation model is based on quantum physics and classical Newtonian gravitation. [math]\;[/math] Surface radius gravitational acceleration: [math]g = \frac{G M}{r^{2}}[/math] [math]\;[/math] Surface radius gravitational escape velocity: [math]v_{e} = \sqrt{\frac{2 G M}{r}}[/math] [math]\;[/math] Hawking blackbody radiation peak radiation energy initial model condition: [math]\boxed{\frac{2 \pi E}{\hbar} = \frac{g}{v_{e}}}[/math] [math]\;[/math] Hawking blackbody radiation peak radiation energy initial model condition integration via substitution: [math]\frac{2 \pi E}{\hbar} = \frac{g}{v_{e}} = \left(\frac{G M}{r^{2}} \right)\left(\sqrt{\frac{r}{2 G M}} \right) = \sqrt{\frac{G M}{2 r^{3}}}[/math] [math]\;[/math] Surface radius Hawking blackbody radiation peak radiation energy initial model condition: [math]\boxed{\frac{2 \pi E}{\hbar} = \sqrt{\frac{G M}{2 r^{3}}}}[/math] [math]\;[/math] Surface radius Hawking blackbody radiation peak radiation temperature: [math]E = k_{B} T_{H} = \frac{\hbar}{2 \pi} \sqrt{\frac{G M}{2 r^{3}}}[/math] [math]\;[/math] [math]\boxed{T_{H} = \frac{\hbar}{2 \pi k_{B}} \sqrt{\frac{G M}{2 r^{3}}}}[/math] [math]\;[/math] Stellar model radiation source is a perfect blackbody: [math]\boxed{\epsilon = 1}[/math] [math]\;[/math] Stefan-Boltzmann Hawking blackbody radiation power law derivation integration via substitution: [math]P_{H} = A_{s} \epsilon \sigma T_{H}^{4} = \left(4 \pi r^{2} \right) \left(\frac{\pi^{2} k_{B}^{4}}{60 c^{2} \hbar^{3}} \right) \left(\frac{\hbar}{2 \pi k_{B}} \sqrt{\frac{G M}{2 r^{3}}} \right)^{4} = \frac{\hbar G^{2} M^{2}}{960 \pi c^{2} r^{4}}[/math] [math]\;[/math] Stefan-Boltzmann Hawking blackbody radiation power law: [math]\boxed{P_{H} = \frac{\hbar G^{2} M^{2}}{960 \pi c^{2} r^{4}}}[/math] [math]\;[/math] One solar mass neutron star model total stellar radius: (ref. 1) [math]\boxed{R_{ns} = 1 \cdot 10^{4} \; \text{m}}[/math] [math]\;[/math] One solar mass neutron star model Hawking blackbody radiation peak radiation temperature: [math]T_{H} = \frac{\hbar}{2 \pi k_{B}} \sqrt{\frac{G M_{\odot}}{2 R_{ns}^{3}}} = 9.903 \cdot 10^{-9} \; \text{K}[/math] [math]\boxed{T_{H} = \frac{\hbar}{2 \pi k_{B}} \sqrt{\frac{G M_{\odot}}{2 R_{ns}^{3}}}}[/math] [math]\boxed{T_{H} = 9.903 \cdot 10^{-9} \; \text{K}}[/math] [math]\;[/math] One solar mass neutron star model Hawking blackbody radiation power law: [math]P_{H} = \frac{\hbar G^{2} M_{\odot}^{2}}{960 \pi c^{2} R_{ns}^{4}} = 6.852 \cdot 10^{-31} \; \text{W}[/math] [math]\boxed{P_{H} = \frac{\hbar G^{2} M_{\odot}^{2}}{960 \pi c^{2} R_{ns}^{4}}}[/math] [math]\boxed{P_{H} = 6.852 \cdot 10^{-31} \; \text{W}}[/math] [math]\;[/math] Can thermodynamic neutron stars generate Hawking blackbody radiation? [math]\;[/math] Any discussions and/or peer reviews about this specific topic thread? [math]\;[/math] Reference: Wikipedia - neutron star: (ref. 1) https://en.wikipedia.org/wiki/Neutron_star Wikipedia - Hawking radiation: (ref. 2) https://en.wikipedia.org/wiki/Hawking_radiation
  10. According to this model, a result which occurs during Schwarzschild black hole Hawking radiation evaporation, when Hawking radiation evaporation lifetime is set at one second remaining. [math]\;[/math] Schwarzschild black hole total Hawking evaporation time with one second lifetime remaining: [math]\boxed{t_{1} = 1 \; \text{s}}[/math] [math]\;[/math] Schwarzschild black hole total Hawking evaporation mass with one second lifetime remaining: [math]\boxed{M_{1} = \left(\frac{t_{1} \hbar c^{4}}{5120 \pi G^{2}} \right)^{\frac{1}{3}} }[/math] [math]\;[/math] [math]\boxed{M_{1} = 2.282 \cdot 10^{5} \; \text{kg}}[/math] [math]\;[/math] Schwarzschild black hole Bekenstein-Hawking total power luminosity integration via substitution: [math]P_{1} = \frac{\hbar c^{6}}{15360 \pi G^{2} M_{1}^{2}} = \frac{\hbar c^{6}}{15360 \pi G^{2}} \left[\left(\frac{5120 \pi G^{2}}{t_{1} \hbar c^{4}} \right)^{\frac{1}{3}} \right]^{2} = \frac{}{24} \left(\frac{\hbar c^{10}}{10 \pi \left(G t_{1} \right)^{2}} \right)^{\frac{1}{3}}[/math] [math]\;[/math] Schwarzschild black hole Bekenstein-Hawking total power luminosity at one second lifetime remaining: [math]\boxed{P_{1} = \frac{}{24} \left(\frac{\hbar c^{10}}{10 \pi \left(G t_{1} \right)^{2}} \right)^{\frac{1}{3}}}[/math] [math]\;[/math] [math]\boxed{P_{1} = 6.838 \cdot 10^{21} \; \text{W}}[/math] [math]\;[/math] [math]1 \; \text{megaton TNT} = 4.184 \cdot 10^{15} \; \text{j}[/math] [math]\;[/math] [math]\boxed{P_{1} = 1.634 \cdot 10^{6} \; \frac{\text{megatons TNT}}{\text{s}}}[/math] [math]\;[/math] Schwarzschild black hole peak Hawking radiation temperature at one second lifetime remaining integration via substitution: [math]T_{1} = \frac{\hbar c^{3}}{8 \pi G M_{1} k_{B}} = \frac{\hbar c^{3}}{8 \pi G k_{B}} \left(\frac{5120 \pi G^{2}}{t_{1} \hbar c^{4}} \right)^{\frac{1}{3}} = \frac{}{k_{B}} \left(\frac{10 \hbar^{2} c^{5}}{G t_{1} \pi^{2}} \right)^{\frac{1}{3}}[/math] [math]\;[/math] Schwarzschild black hole peak Hawking radiation temperature at one second lifetime remaining: [math]\boxed{T_{1} = \frac{}{k_{B}} \left(\frac{10 \hbar^{2} c^{5}}{G t_{1} \pi^{2}} \right)^{\frac{1}{3}}}[/math] [math]\;[/math] [math]\boxed{T_{1} = 5.376 \cdot 10^{17} \; \text{K}}[/math] [math]\;[/math] Schwarzschild black hole total Hawking energy radiation emission after one second lifetime remaining integration via substitution: [math]M_{1} = \frac{E_{1}}{c^{2}} = \left(\frac{t_{1} \hbar c^{4}}{5120 \pi G^{2}} \right)^{\frac{1}{3}} \rightarrow E_{1} = c^{2} \left(\frac{t_{1} \hbar c^{4}}{5120 \pi G^{2}} \right)^{\frac{1}{3}} = \left(\frac{t_{1} \hbar c^{10}}{5120 \pi G^{2}} \right)^{\frac{1}{3}}[/math] [math]\;[/math] Schwarzschild black hole total Hawking energy radiation emission after one second lifetime remaining: [math]\boxed{E_{1} = \left(\frac{t_{1} \hbar c^{10}}{5120 \pi G^{2}} \right)^{\frac{1}{3}}}[/math] [math]\;[/math] [math]\boxed{E_{1} = 2.051 \cdot 10^{22} \; \text{j}}[/math] [math]\;[/math] [math]1 \; \text{megaton TNT} = 4.184 \cdot 10^{15} \; \text{j}[/math] [math]\;[/math] [math]\boxed{E_{1} = 4.903 \cdot 10^{6} \; \text{megatons TNT}}[/math] [math]\;[/math] Is this the eventual fate for every black hole in the entire universe? [math]\;[/math] Any discussions and/or peer reviews about this specific topic thread? [math]\;[/math]
  11. Orion1

    Latex test

    [math]F(x) = \int_{a}^{b} f(x)dx[/math] [math]\boxed{F(x) = \int_{a}^{b} f(x) dx}[/math]
  12. Orion1

    Latex test

    [math]\dashbox{F(x) = \int_{a}^{b} f(x)dx }[/math] [math]\boxed{F(x) = \int_{a}^{b} f(x)dx}[/math]
  13. Affirmative, stellar black hole masses typically range between 2.27 to 16 solar masses, and are generated from stellar supernovas. (ref. 1) [math]2.27 \cdot M_{\odot} \leq M_{bh} \leq 16 \cdot M_{\odot}[/math] [math]\;[/math] According to this model, any Schwarzschild black hole capable of evaporating completely from Hawking radiation within the universe age, the Schwarzschild black hole must have an initial primordial mass less than or equal to this Hawking evaporation mass. This Hawking evaporation mass is similar to the mass of a small asteroid. [math]\;[/math] Schwarzschild black hole Bekenstein-Hawking total power luminosity: [math]\boxed{P_{H} = \frac{\hbar c^{6}}{15360 \pi G^{2} M^{2}}}[/math] [math]\;[/math] Universe age: [math]t_{u} = 13.799 \cdot 10^{9} \; \text{years} = 4.355 \cdot 10^{17} \; \text{s}[/math] [math]\;[/math] Schwarzschild black hole total Hawking evaporation mass in universe lifetime integration: [math]P_{H} = - \frac{dE}{dt} = -\left(\frac{d}{dt} \right) M c^2 = -c^2 \frac{dM}{dt} = \frac{\hbar c^{6}}{15360 \pi G^{2} M^{2}}[/math] [math]\;[/math] The differential variables are seperable, and the integrals can be written as: [math]- \int_{M_{ev}}^{0} M^{2} dM = \frac{\hbar c^{4}}{15360 \pi G^{2}} \; \int_{0}^{t_{u}} dt = \frac{M_{ev}^{3}}{3} = \frac{t_{u} \hbar c^{4}}{15360 \pi G^{2}}[/math] [math]\;[/math] Schwarzschild black hole total Hawking evaporation mass in universe lifetime: [math]\boxed{M_{ev} \leq \left(\frac{t_{u} \hbar c^{4}}{5120 \pi G^{2}} \right)^{\frac{1}{3}}}[/math] [math]\;[/math] [math]\boxed{M_{ev} \leq 1.730 \cdot 10^{11} \; \text{kg}}[/math] [math]\;[/math] Asteroid Castalia mass: (ref. 2) [math]M = 5.000 \cdot 10^{11} \; \text{kg}[/math] [math]\;[/math] Any discussions and/or peer reviews about this specific topic thread? [math]\;[/math] Reference: Science Forums - toy model black holes per galaxy average number - Orion1: (ref. 1) https://www.scienceforums.net/topic/120012-toy-model-black-holes-per-galaxy-average-number/ Asteroid Fact Sheet - NASA: (ref. 2) https://nssdc.gsfc.nasa.gov/planetary/factsheet/asteroidfact.html
  14. Translated from Google translate: The page appears to be modelling a classical harmonic oscillator for a mass m fixed to a special spring. This formula appears to be attempting to utilize Leibniz's notation for Newtons second law of motion: [math]m \frac{d^2 x}{dt^2} + F \cdot x = 0[/math] However, Newtons second law of motion in Leibniz's notation is: [math]F = m \frac{d^2 x}{dt^2}[/math] Subtracting force from both the equation left hand side and right hand side results in: [math]m \frac{d^2 x}{dt^2} - F = 0[/math] However, note the equation definition for the potential force on line 5: [math]F(x) = -\frac{dE_p}{dx}[/math] And the resulting potential energy: [math]E_p = -F(x) \cdot dx[/math] So, The equation on line 11 is mixing systeme internationale units of force (newtons) and energy (joules), which is mathematically incorrect. Kartazion, I recommend purchasing a university level physics textbook and study the section on Newtonian mechanics for classical harmonic oscillators. University level physics textbooks already provide the required level mathematics in Leibniz's notation, as well as numerical integration for models such as these, instead of landing in the middle of other online models that display crude and incorrect formulas and with insufficient modeling experience. Some experience in Latex modelling would be beneficial also. Reference: Anharmonic oscillator - Lemans university: https://bit.ly/2SKdIJX
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