Absolutely fabulous, clear and concise big-picture summary of the *principles* of the maths behind GR, with no false analogies or hand-wavy glosses. I wish I had seen this *before* watching all the more detailed lecture series on tensor calculus, etc. The framework would have helped everything slot into place much more easily.
Professor Carroll's statement that "Everything is Waves" is perfectly correct, if not quite clear, only lacking acknowledgement of the i-reflection containment wave-packaging formation at Euler's e-Pi-i 1-0-infinity instantaneous Perspective. A Rose by any other name will smell as Sweet, and Students can verify the truth of the matter by analysing 3BLUE 1BROWN graphics of Euler's practical Intuition in terms of line-of-sight superposition density-intensity, rotation of orthogonal-normal axial-tangential alignments in superimposed 6D radially synchronised reflection combinations and permutations of 0-1-2-ness, GD&P parallel coexistence Flash recognition of self-defining Polar-Cartesian Orthographic time-timing.
If you can, listen to the Mindscape version of this talk. It's more detailed because its professor Carrols podcast and can take as long as he likes. Its brilliant and inspiring. For me, It was like a religious experience but real.
Sean needs to get a nobel prize for his services to popularizing science and helping us understand this incredibly deep concepts man. Human Treasure. THANK YOU PROF. CARROLL!
This space time alteration of the time interval is true at all speeds. The alterations of time interval is not only measureable at the speed of light. When you fly coast to coast the alteration's of the time interval is about 30 minutes greater than the stationary time.
Just pretend for a moment that it is the Higgs Field that limits the passage of energy through space to the observed speed of light, and that it is the Higgs Field that requires exponentially larger amounts of energy to accelerate larger quantities of energy towards the speed of light. It is possible that without the Higgs Field, then, that energy can operate at above light speed. The Higgs experiment demonstrated that if you hit the Higgs Field hard enough a particle will be produced. Now consider the nucleus of Protons and Neutrons. We believe that there is a concentration of energy there in the form of highly energetic quarks gyrating aggressively but never flying apart. To keep the quarks in place we’ve invented a strong Nuclear force to contain that energy, yet we know that there is some restraint that is powerful enough to limit the speed of all energy to a finite limit. Now consider for a moment that a universal restraint (Field) that can cause moving energy to require an exponentially large amount of energy to approach the speed of light, might also be able to restrain the Energy of Quarks and keep them contained as a particle. Regardless of what you choose to call that restraint (Field,Force) the effects is the exact same for the very same reason, except that the Higgs experiment acted on the Higgs Field from the outside crushing in, but with the nucleus of Protons and Neutrons the energy of the Quarks is acting outwards at the speed of light or even greater. If the Quark Energy operates at greater than the speed of light, something like a Higgs Shell should be produced, but not as a shell so much as a highly energized field reaction zone, the energy density of which dissipates exponentially as the square of the distance from the reaction zone. By this thinking it should be clear that the Higgs Field just might be all of the Strong Nuclear Force, the Weak Nuclear Force, and Gravity depending on the distance from the Nucleus of the Protons and Neutrons. In this thought model Gravity it is the Field Energy Intensity Gradient between empty Space and the highly energised space around the primary energy concentrations in the Universe, Protons and Neutrons. This would require that matter moves through space influenced by the Energy Density of the Universal Field (Higgs Field) and the Matter moves by its own Reaction with the Field against that Field towards the highest Energy Density (masses of Matter, Stars and Galaxies of Stars), away from the Lowest Energy Density.
What’s refreshing about this introduction to general relativity is that Einstein got a lot of help from others to derive his field equation. Einstein could not have worked out the theory without first adopting Minkowski’s spacetime formulation of special relativity and later learning Riemann’s differential geometry. The popular view is that Einstein predicted black holes and nuclear energy because of E = mc^2 but he did not. The important solutions to his field equation that are currently used to understand black holes and cosmology were made later by others. Einstein’s main contribution was the equivalence principle as the key to extending flat Minkowski spacetime of special relativity to include gravity as curved spacetime in general relativity. But Einstein was not always convinced that gravitational waves were real and he strongly doubted the existence of black holes even though his equation predicted both black holes and gravitational waves.
Fascinating as always, clear explanation, simple and enjoyable. Love the voice and looks of the good professor. At 79 years of age, I find it easy to understand and appreciate Einstein equation. Why didn’t I find inspiring Physicist like Sean Carroll when I was younger. I hope my grandchildren find you, and able to read, speak and write your mathematical language.
if proper time goes to 0 at event horizon, then how does it ever go back up if there is no rate of change, is this why people would appear smeared on the horizon falling inward
Proper time does _not_ go to zero at the event horizon. The ratio of proper time and _coordinate time_ goes to infinity. But this is a problem with the coordinates, not the proper time. The singularity at the event horizon is what is called a "coordinate singularity" and it simply goes away with a better choice of coordinates. Proper time is what the object measures for itself. And a feature of General Relativity is that spacetime is "locally flat". That means the object _never notices_ the curvature. The event horizon is no interesting place for an object crossing it. But these coordinates still represent something physically interesting. As you say, because the observer that is represented by them sees time slow down near the horizon, they will see objects slow down, light become redshifted, and the object smear over the horizon. Because this is what they can observe _from a distance_ . But locally this is not what happens. The falling object crosses the event horizon without issue.
I don't think so. The Parallel Postulate (parallel lines don't diverge) has been proved mathematically to be necessary for Euclidean Geometry (so assuming Euclidean geometry then it's true and so not a subject of the Incompleteness Theorem). If you set it up so parallel lines get further away from each other, you get negative curvature (Lobachesky), or they get closer to each other (spherical surfaces) you get positive curvature. This all provable, and proved, and so not really anything to do with Incompleteness.
@@ghytredstillghytred7617 So the subtlety that Euclid couldn't prove it using HIS axioms has no real bearing, because it is possible to prove it within the larger sphere of mathematics, within which the world of geometry lives? That makes sense. I sort of thought that was the answer all along, but figured "Why not ask someone?" Cool.
@@abcde_fz No - the parallel postulate was one of Euclid's axioms. However over the centuries many mathematicians thought it might not be needed, but could never prove it wasn't required. Eventually, someone proved that it was required (i.e. Euclid was correct). So all 5 of Euclid's axioms were required to prove all his theorems, and not just the 4 some mathematicians thought might do. As for 'Ask someone', it was the people who you (or I) would ask who were arguing, and eventually one of them proved that Euclid was right and it was needed just as Euclid had it. (To be clear. |Euclid never thought it wasn't needed and nobody questioned it for centuries.) Anyway, whether it is required or not is subject to proof within the standard rules of arithmetic (even as Euclid understood them back then), so Godel's Incompleteness theorem has nothing to say about it.
@@ghytredstillghytred7617 Thanx for some clarification. I may study logic, but I'm no expert in the particulars of, well, quite a few things! So I throw out some questions, and see what comes back. Have a great day!
18:56 - Not true! You are talking about the Equivalence principle. You can do an experiment which would easily discriminate if you are in a gravitational field, or if you are instead accelerating in a rocket. In the case of gravity, you could also measure the tidal force, which wouldn't be present in the case of an accelerating object. I frankly don't understand why everybody repats that the Equivalnce principle is so fundamental. The equivalence principle holds only locally, i.e. on a infinitesimaly small scale.
The equivalence principle being an infinitesimal statement is exactly what makes it so fundamental. It means spacetime can be treated as locally flat. This is the entire basis of General Relativity.
Not in modern physics. Time, like space, is a tool to locate events in the universe. And how, in space, would you even define motion without time? It is a change of position _over time_ .
@@johnsongibbs6567 You can't define motion without time, but you can define time without motion. Time is required for motion, not the other way around.
@@johnsongibbs6567Motion happens regardless of time , it is independent of time , where time is an abstract human convention that we use to express moments of the motion in the human reference of time , whether you define motion or not it is still an event that happens .
We have understood gravity partly wrong, which is why it struggles to fit into QT. Our universe is composed of two omnipresent hyperfields: electromagnetic- and gravitational hyperfield, where gravitational consists both gravity and antigravity as each others polarities. These hyperfields are interlocked and interact with each other and materializing on interaction. All matter in the universe is materialized hyperfields and all the more complex forces are created by their interaction through matter. An example of this would be creating electricity through friction: interaction of physical objects disturbs the EM-hyperfield, which creates a local electric charge, materializing into electrons in the center. this is exactly why we see "spontaneous emergenge and disappearance of particles: they materialize from the hyperfields and dematerialize back in to them. Compress the hyperfields into a singularity and you will see a very rapid emergence of particles and forces of nature. The principle of antigravity engine is to disturb the gravitational hyperfield with two strong vibrating electric magnetic fields, which are created and pressed next to each other, which interferes with the gravitational hyperfield, causing the polarities of gravity collapse into and past each other locally, creating a negative gravitational sphere. The movement is created by creating two antigravity spheres next to each other, which creates a flow in the hyperfield around the antigravity system.
Much as I respect Dr Carroll and enjoy his presentations, there is a problem with the vocal track on this. It sounds as if processed through Auto tune or some other audio filter. I find it irritates and prevents enjoyment of the interesting material. Sorry if anyone is offended.
Explanation, can get shaped by mathematical formulas, and become a science which is important, time’s is a local phenomenon, and it doesn’t exists at spaces and universes, and the ends of space time’s arrived
I begin to understand why my High School Teacher Wife abhorred the dreaded marking of papers and homework. What can you say? Gravity is acceleration, as explained by Einsteinian Curvatures based in instantaneous real-time and logarithmic time-timing sync-duration uncertainty relative-timing, ie Relativity in Form following e-Pi-i Fusion Function continuous i-reflection containment. If you were marking a paper, this is like I was told once, "There appears to be gaps in the Student's knowledge", which I could show applied equally to the Lecturer.., well it did take 50 years to begin to find appropriate words to say. That is why I cannot exceed my TA qualifications, and Students are required to use "bootstrapping" and consulting with anyone who hasn't worked it out themselves, but they know what is wrong with the Disproof Methodology, the uncertain Modulation Mechanism, as applicable to examples.
I don't understand mathematics. I need a calculator for anything more complex than the times table. And so I'd appreciate some help with Euclid's fifth postulate. Namely, *how can you start two parallel lines running from right angles if you are **_already_** on a curved surface?* i.e If you start with a line segment on a curved surface, then won't any two right angles create lines that _aren't parallel to begin with?_ The degree to which they are not initially parallel may be infinitesimally small, but if you are on a sphere, saddle, or torus then how can they begin parallel? Moreover, given that curves exist within our 3D world, why didn't anybody realise earlier that two parallel lines on a tabletop would cease being such as soon as they hit the fruit bowl? Obviously there must be sensible answers here. And, as stated, any help would be much appreciated!
This is best described by the mention he made about using calculus to "zoom in." If you get "close enough" to the intersections of the lines on the surface of the sphere, it "appears" that you are on a flat surface. On a flat surface, there's no contradiction: the 2 lines intersecting the first line are parallel, right? So if you imagine yourself being a super-tiny spectator and standing at the intersections of those lines, as you slowly turn in a circle and look along all the lines as they move away from you, they will always APPEAR perfectly straight to you. Does that help?
Ok for starters. 3 dimensions or vector for space are faulty and should not be used. We need better fundamental vectors . I.e radians and length. Spheres are more fundamental than cubes an describe our world better. So why do we use cube math. We also can fit more degrees of freedom into a sphere and hence can do better math with less complexity. I'm sure aliens would not use our silly math principles. We need to change our fundamental view on our world..
We don't use "cube math". We can represent any vector in rectangular coordinates or in spherical coordinates. A sphere is just as three dimensional as a cube. We can either use "up, front, left" as our dimensions or a radius and two angles. That is the great thing about vectors. It doesn't matter how you represent them. So we are free to choose useful coordinates. The object itself doesn't change.
F = G(Mm/r^2) is contradictory to human-invented concept of light or photons because mass of photons is considered to be nought = 0 . Let m= mass of light / photons---> F= G( M X 0)/ r^2) = 0, whereas light / photons are factually the most attracted form of matter in the universe to every other single form of matter in the universe due to the intrinsic properties of light field, and according to the formula of the magnitude of the gravitational force F = G(Mm/r^2), the gravitational force acting on light or photons from stars, including the Sun, and the Moon is obviously false What does my simple example above shows all of you, who are either scientists, physicists, astronomers or PhD students of quantum mechanics, particle physics, chemistry and astronomy? It obviously shows you that there have been a lot of flaws and defective holes in all branches of physics, mathematics and astronomy due to human too much reliance on defective concepts of mathematics, with severe lack of logical reasoning totally based on objective and undeniable facts known or verifiable to all human beings All what you guys have been doing for centuries is to copy old ideas of scientists of the previous centuries , and manipulating the flaws and defective holes of mathematical concepts to derive new formula and interpret such formulas as new and netter theories without even checking whether there is any contradictions between your subjective interpretations based on such defective mathematical formulas and objective and undeniable facts. None of you guys still has not yet been able to see that the concept of time invented by human limited knowledge never ever exists anywhere in the universe, and that it actually is the same as space plus emotion because it is not the symbolic mathematical units on your clocks and calendars, it it actually represents the continuous sequence of changes of physical structures and positions in space of all form of matter in the universe Time = continuous changes of physical structure + positions in space That formula is inevitably applicable to every single form of matter in the universe., but it is not the number of hours on human-invented clocks, nor days , weeks, months, years on human -invented calendars, nor even the distances in space which the Earth travels along its orbit around the Sun, while continuously and endlessly rotating about its shifting axis. The distances in space which the Earth travels along its orbit around the Sun has been used as the frame of reference for human limited knowledge to evaluate the differences among the changes of physical structures and positions in space among the observable different forms of matter in the universe. The reason why human beings use the Earth's rotational motion and the effects of sunlight on the surface of this planet as the frame of reference is that the speed or velocity the Earth's rotational motion is almost constant, and endless or infinite. It is just similar to using all human-invented measuring instruments, such as a ruler, a metre stick, a scale to measure lengths in space, and weights of different forms of matter. All such measurement instruments are divided into smaller parts, all those smaller parts are equal, which means that the changes in length and weight are always constant. Ex, from 1 cm to 2cm , and 2 cm to 3 cm and so forth. You can easily and clearly see that the continuous sequence of changes of position in space is constant ,, and always equal to 1cm, no matter how far you will go. Why is it constant? The answer is because the changes are continuous , or there is not any hole or disruption from 1cm to infinity, like there is not any cessation of your life from the time you were born to the time your physical body is transformed into other forms of matter or different chemical compounds. Such continuous sequences of changes of physical structures and positions in space are what the concept of time actually represents You guys will have a chance to read my official unquestionable or indisputable research paper with objective and undeniable facts which will topple all the current theories, concepts of mathematics, physics, and astronomy irreversibly in a few years
You admit to not knowing what Time is, Sean. Yet you make countless (unattested) assertions about Time. How does that work, Sean?? And you apparently believe is it 'real'. Where is the evidence? And as Time is the dimension of change (rates and events...for what other evidence of 'time passing' is there but quintillions of quantum change events?) Change is reference-frame (e.g. quantum) specific. i.e. quintillions of Arrows of Change, not one universal Arrow of Time. How do the Tensors relate to this? Because if Space is the (abstract) dimension of position (hence xyz axis) and time the (abstract) dimension of change-rate (hence 'per hour') surely Space-Time is the abstract dimension of changing position i.e. Motion?? In reality there is no 'fabric' of space-time, for its an abstract dimension - there is motion...motion is real. Why not talk about the underlying reality i.e. relative motion rather than the abstract space-time?
That would be real science and involve actual work. Science only deals in the fantasies that can't be disproven, like whether or not there is a God. This way they can always be right, even though they are always wrong.
This is fun imagining-imaging to reduce concept to symbols, the same reason for perception paradox is why "The biggest idea in the Universe" is the Singularity-point, no size, no difference in pure-math relative-timing motion forever.., because Euler's e-Pi-i sync-duration in/of Newton's axial-tangential Polar-Cartesian Fluxion-Integral @.dt, Superspin Modulation 1-0-infinity that is Absolute Zero Kelvin i-reflection Timing-spacing.., all-ways all-at-once instantaneous ONE-INFINITY=> Eternity-now Observational realization-recognition, and is WYSIWYG without the inside-outside misunderstanding of Reciproction-recirculation superposition, ie we see the Holographic Principle for what it is, making 0-1-2-ness GD&P temporal logarithmic superposition-cross-sectional picture-plane in Perspective.., the Unzicker Flash perception that is equivalent to real-time recognition at the Centre of Time, here-now-forever. And the consequence of nothing floating in No-thing ONE-INFINITY singularity positioning integration with the sizeless-wordless Apature of entangled e-Pi-i infinitesimal-gravitational off resonance sync-duration receeding-vanishing into-no-thing Perspective Principle is enough to justify Professor Carroll's teaching methods to Students in conscious awareness.
In the beginning was the Word, and the Word was with God, and the Word was God. 2He was with God in the beginning. 3Through him all things were made; without him nothing was made that has been made. (John 1:1-3)
Jesus Christ loves you! Put your trust in him today before it's too late. He promises to transform you and make you new. Christ awaits for you to put your trust in Him.
Absolutely fabulous, clear and concise big-picture summary of the *principles* of the maths behind GR, with no false analogies or hand-wavy glosses. I wish I had seen this *before* watching all the more detailed lecture series on tensor calculus, etc. The framework would have helped everything slot into place much more easily.
Professor Carroll's statement that "Everything is Waves" is perfectly correct, if not quite clear, only lacking acknowledgement of the i-reflection containment wave-packaging formation at Euler's e-Pi-i 1-0-infinity instantaneous Perspective.
A Rose by any other name will smell as Sweet, and Students can verify the truth of the matter by analysing 3BLUE 1BROWN graphics of Euler's practical Intuition in terms of line-of-sight superposition density-intensity, rotation of orthogonal-normal axial-tangential alignments in superimposed 6D radially synchronised reflection combinations and permutations of 0-1-2-ness, GD&P parallel coexistence Flash recognition of self-defining Polar-Cartesian Orthographic time-timing.
If you can, listen to the Mindscape version of this talk. It's more detailed because its professor Carrols podcast and can take as long as he likes. Its brilliant and inspiring. For me, It was like a religious experience but real.
Sean is a FABULOUS communicator
"These pretzels are making me thirsty!"
Sean needs to get a nobel prize for his services to popularizing science and helping us understand this incredibly deep concepts man. Human Treasure. THANK YOU PROF. CARROLL!
2 of my favorite channels collide! I love listening to Sean Carroll! 💙
As usual, Sean is absolutely inspiring. Great connection with CCC.
Excellent Sean!!
This space time alteration of the time interval is true at all speeds. The alterations of time interval is not only measureable at the speed of light. When you fly coast to coast the alteration's of the time interval is about 30 minutes greater than the stationary time.
I DON'T BELIEVE ALBERT EINSTEIN WAS A CLASSICAL PHYSICIST ONLY.
Great explanation, Thank you
I wish I had this video when I was teaching at Cornell before going to Stanford
Just pretend for a moment that it is the Higgs Field that limits the passage of energy through space to the observed speed of light, and that it is the Higgs Field that requires exponentially larger amounts of energy to accelerate larger quantities of energy towards the speed of light. It is possible that without the Higgs Field, then, that energy can operate at above light speed. The Higgs experiment demonstrated that if you hit the Higgs Field hard enough a particle will be produced.
Now consider the nucleus of Protons and Neutrons. We believe that there is a concentration of energy there in the form of highly energetic quarks gyrating aggressively but never flying apart. To keep the quarks in place we’ve invented a strong Nuclear force to contain that energy, yet we know that there is some restraint that is powerful enough to limit the speed of all energy to a finite limit.
Now consider for a moment that a universal restraint (Field) that can cause moving energy to require an exponentially large amount of energy to approach the speed of light, might also be able to restrain the Energy of Quarks and keep them contained as a particle. Regardless of what you choose to call that restraint (Field,Force) the effects is the exact same for the very same reason, except that the Higgs experiment acted on the Higgs Field from the outside crushing in, but with the nucleus of Protons and Neutrons the energy of the Quarks is acting outwards at the speed of light or even greater. If the Quark Energy operates at greater than the speed of light, something like a Higgs Shell should be produced, but not as a shell so much as a highly energized field reaction zone, the energy density of which dissipates exponentially as the square of the distance from the reaction zone.
By this thinking it should be clear that the Higgs Field just might be all of the Strong Nuclear Force, the Weak Nuclear Force, and Gravity depending on the distance from the Nucleus of the Protons and Neutrons. In this thought model Gravity it is the Field Energy Intensity Gradient between empty Space and the highly energised space around the primary energy concentrations in the Universe, Protons and Neutrons. This would require that matter moves through space influenced by the Energy Density of the Universal Field (Higgs Field) and the Matter moves by its own Reaction with the Field against that Field towards the highest Energy Density (masses of Matter, Stars and Galaxies of Stars), away from the Lowest Energy Density.
What’s refreshing about this introduction to general relativity is that Einstein got a lot of help from others to derive his field equation. Einstein could not have worked out the theory without first adopting Minkowski’s spacetime formulation of special relativity and later learning Riemann’s differential geometry. The popular view is that Einstein predicted black holes and nuclear energy because of E = mc^2 but he did not. The important solutions to his field equation that are currently used to understand black holes and cosmology were made later by others. Einstein’s main contribution was the equivalence principle as the key to extending flat Minkowski spacetime of special relativity to include gravity as curved spacetime in general relativity. But Einstein was not always convinced that gravitational waves were real and he strongly doubted the existence of black holes even though his equation predicted both black holes and gravitational waves.
A great summary. Looking forward to the next 2 volumes.
Love Professor Carroll.
Sean carool is a fantastic teacher
Excellent lecture!
Wonderfully clear.
Music to my ears.. 🎼🎶🎸
thank you so much for offering such high level to laymen in an understandable way. It's an amazing talk, and shows a deep respect for the listeners
Brilliant presentation. I'm reading the book.
Fascinating as always, clear explanation, simple and enjoyable. Love the voice and looks of the good professor. At 79 years of age, I find it easy to understand and appreciate Einstein equation. Why didn’t I find inspiring Physicist like Sean Carroll when I was younger. I hope my grandchildren find you, and able to read, speak and write your mathematical language.
Ludwig Lange is the person who introduced the inertial reference frame, and abandoned the notion of absolute rest.
So good!
Question:
Is the flow of time fundamental in the creation of consciousness?
What does the word creation mean in this context?
Such exciting information, presented in a way that cajoles every brain particle to consider new possibilities
I love that the Riemann tensor indices are rho, mu, and nu, the consonants of 'Riemann'. If that's a coincidence, I don't want to know about it.
Great stuff
Thank you
Im not much into books honestly but im very tempted on buying this one. I wonder if its something i can get in a physical bookstore in Argentina
Talk about a goof troop interviewer at the end.
“Durrr I hear there’s 3 books!”
if proper time goes to 0 at event horizon, then how does it ever go back up if there is no rate of change, is this why people would appear smeared on the horizon falling inward
Proper time does _not_ go to zero at the event horizon. The ratio of proper time and _coordinate time_ goes to infinity. But this is a problem with the coordinates, not the proper time. The singularity at the event horizon is what is called a "coordinate singularity" and it simply goes away with a better choice of coordinates.
Proper time is what the object measures for itself. And a feature of General Relativity is that spacetime is "locally flat". That means the object _never notices_ the curvature. The event horizon is no interesting place for an object crossing it.
But these coordinates still represent something physically interesting. As you say, because the observer that is represented by them sees time slow down near the horizon, they will see objects slow down, light become redshifted, and the object smear over the horizon. Because this is what they can observe _from a distance_ .
But locally this is not what happens. The falling object crosses the event horizon without issue.
Is the "parallel postulate" an example of the Godel Incompleteness Theorem in ANY way?
I don't think so. The Parallel Postulate (parallel lines don't diverge) has been proved mathematically to be necessary for Euclidean Geometry (so assuming Euclidean geometry then it's true and so not a subject of the Incompleteness Theorem). If you set it up so parallel lines get further away from each other, you get negative curvature (Lobachesky), or they get closer to each other (spherical surfaces) you get positive curvature. This all provable, and proved, and so not really anything to do with Incompleteness.
@@ghytredstillghytred7617 So the subtlety that Euclid couldn't prove it using HIS axioms has no real bearing, because it is possible to prove it within the larger sphere of mathematics, within which the world of geometry lives? That makes sense. I sort of thought that was the answer all along, but figured "Why not ask someone?"
Cool.
@@abcde_fz No - the parallel postulate was one of Euclid's axioms. However over the centuries many mathematicians thought it might not be needed, but could never prove it wasn't required. Eventually, someone proved that it was required (i.e. Euclid was correct). So all 5 of Euclid's axioms were required to prove all his theorems, and not just the 4 some mathematicians thought might do. As for 'Ask someone', it was the people who you (or I) would ask who were arguing, and eventually one of them proved that Euclid was right and it was needed just as Euclid had it. (To be clear. |Euclid never thought it wasn't needed and nobody questioned it for centuries.)
Anyway, whether it is required or not is subject to proof within the standard rules of arithmetic (even as Euclid understood them back then), so Godel's Incompleteness theorem has nothing to say about it.
@@ghytredstillghytred7617 Thanx for some clarification. I may study logic, but I'm no expert in the particulars of, well, quite a few things! So I throw out some questions, and see what comes back.
Have a great day!
18:56 - Not true! You are talking about the Equivalence principle. You can do an experiment which would easily discriminate if you are in a gravitational field, or if you are instead accelerating in a rocket. In the case of gravity, you could also measure the tidal force, which wouldn't be present in the case of an accelerating object. I frankly don't understand why everybody repats that the Equivalnce principle is so fundamental. The equivalence principle holds only locally, i.e. on a infinitesimaly small scale.
The equivalence principle being an infinitesimal statement is exactly what makes it so fundamental. It means spacetime can be treated as locally flat. This is the entire basis of General Relativity.
Unbelievable that this guy doesn't have Kardashian (1a) amount of thumbs ups
Thank you for the great talk. I was wondering, is it accurate to think of time as the product of motion?
Not in modern physics. Time, like space, is a tool to locate events in the universe.
And how, in space, would you even define motion without time? It is a change of position _over time_ .
@@narfwhals7843 You can not define motion without time. That is why I see them as equivalents. Time is motion.
@@johnsongibbs6567 You can't define motion without time, but you can define time without motion.
Time is required for motion, not the other way around.
@@johnsongibbs6567Motion happens regardless of time , it is independent of time , where time is an abstract human convention that we use to express moments of the motion in the human reference of time , whether you define motion or not it is still an event that happens .
We have understood gravity partly wrong, which is why it struggles to fit into QT. Our universe is composed of two omnipresent hyperfields: electromagnetic- and gravitational hyperfield, where gravitational consists both gravity and antigravity as each others polarities. These hyperfields are interlocked and interact with each other and materializing on interaction. All matter in the universe is materialized hyperfields and all the more complex forces are created by their interaction through matter. An example of this would be creating electricity through friction: interaction of physical objects disturbs the EM-hyperfield, which creates a local electric charge, materializing into electrons in the center. this is exactly why we see "spontaneous emergenge and disappearance of particles: they materialize from the hyperfields and dematerialize back in to them. Compress the hyperfields into a singularity and you will see a very rapid emergence of particles and forces of nature.
The principle of antigravity engine is to disturb the gravitational hyperfield with two strong vibrating electric magnetic fields, which are created and pressed next to each other, which interferes with the gravitational hyperfield, causing the polarities of gravity collapse into and past each other locally, creating a negative gravitational sphere. The movement is created by creating two antigravity spheres next to each other, which creates a flow in the hyperfield around the antigravity system.
🙏🙏🙏
You could have at least spelled the name of the school correctly. FYI, it's Johns Hopkins
Much as I respect Dr Carroll and enjoy his presentations, there is a problem with the vocal track on this. It sounds as if processed through Auto tune or some other audio filter. I find it irritates and prevents enjoyment of the interesting material. Sorry if anyone is offended.
31:40 are the indicies of the first column of the metric a typo? First column and first row are the same.
Explanation, can get shaped by mathematical formulas, and become a science which is important, time’s is a local phenomenon, and it doesn’t exists at spaces and universes, and the ends of space time’s arrived
I begin to understand why my High School Teacher Wife abhorred the dreaded marking of papers and homework. What can you say?
Gravity is acceleration, as explained by Einsteinian Curvatures based in instantaneous real-time and logarithmic time-timing sync-duration uncertainty relative-timing, ie Relativity in Form following e-Pi-i Fusion Function continuous i-reflection containment.
If you were marking a paper, this is like I was told once, "There appears to be gaps in the Student's knowledge", which I could show applied equally to the Lecturer.., well it did take 50 years to begin to find appropriate words to say.
That is why I cannot exceed my TA qualifications, and Students are required to use "bootstrapping" and consulting with anyone who hasn't worked it out themselves, but they know what is wrong with the Disproof Methodology, the uncertain Modulation Mechanism, as applicable to examples.
I don't understand mathematics. I need a calculator for anything more complex than the times table. And so I'd appreciate some help with Euclid's fifth postulate. Namely, *how can you start two parallel lines running from right angles if you are **_already_** on a curved surface?* i.e If you start with a line segment on a curved surface, then won't any two right angles create lines that _aren't parallel to begin with?_ The degree to which they are not initially parallel may be infinitesimally small, but if you are on a sphere, saddle, or torus then how can they begin parallel? Moreover, given that curves exist within our 3D world, why didn't anybody realise earlier that two parallel lines on a tabletop would cease being such as soon as they hit the fruit bowl? Obviously there must be sensible answers here. And, as stated, any help would be much appreciated!
This is best described by the mention he made about using calculus to "zoom in."
If you get "close enough" to the intersections of the lines on the surface of the sphere, it "appears" that you are on a flat surface.
On a flat surface, there's no contradiction: the 2 lines intersecting the first line are parallel, right?
So if you imagine yourself being a super-tiny spectator and standing at the intersections of those lines, as you slowly turn in a circle and look along all the lines as they move away from you, they will always APPEAR perfectly straight to you.
Does that help?
THAT'S RIGHT!🙂👋🖖👌🤙👍
I don't get it. Though I keep trying... I wonder what percentage of interested listeners get it... And how many are open about it....
Lost me when he said Hello !
Good
My dog has never tried to eat any of my fingers, even though they look like sausages.
Discuss.
Ok for starters. 3 dimensions or vector for space are faulty and should not be used. We need better fundamental vectors . I.e radians and length. Spheres are more fundamental than cubes an describe our world better. So why do we use cube math. We also can fit more degrees of freedom into a sphere and hence can do better math with less complexity. I'm sure aliens would not use our silly math principles. We need to change our fundamental view on our world..
We don't use "cube math". We can represent any vector in rectangular coordinates or in spherical coordinates.
A sphere is just as three dimensional as a cube.
We can either use "up, front, left" as our dimensions or a radius and two angles.
That is the great thing about vectors. It doesn't matter how you represent them. So we are free to choose useful coordinates. The object itself doesn't change.
Curvature, of earth 🌍 is also local phenomenon and doesn’t mean anything to change the local time’s
F = G(Mm/r^2) is contradictory to human-invented concept of light or photons because mass of photons is considered to be nought = 0 . Let m= mass of light / photons---> F= G( M X 0)/ r^2) = 0, whereas light / photons are factually the most attracted form of matter in the universe to every other single form of matter in the universe due to the intrinsic properties of light field, and according to the formula of the magnitude of the gravitational force F = G(Mm/r^2), the gravitational force acting on light or photons from stars, including the Sun, and the Moon is obviously false
What does my simple example above shows all of you, who are either scientists, physicists, astronomers or PhD students of quantum mechanics, particle physics, chemistry and astronomy?
It obviously shows you that there have been a lot of flaws and defective holes in all branches of physics, mathematics and astronomy due to human too much reliance on defective concepts of mathematics, with severe lack of logical reasoning totally based on objective and undeniable facts known or verifiable to all human beings
All what you guys have been doing for centuries is to copy old ideas of scientists of the previous centuries , and manipulating the flaws and defective holes of mathematical concepts to derive new formula and interpret such formulas as new and netter theories without even checking whether there is any contradictions between your subjective interpretations based on such defective mathematical formulas and objective and undeniable facts.
None of you guys still has not yet been able to see that the concept of time invented by human limited knowledge never ever exists anywhere in the universe, and that it actually is the same as space plus emotion because it is not the symbolic mathematical units on your clocks and calendars, it it actually represents the continuous sequence of changes of physical structures and positions in space of all form of matter in the universe
Time = continuous changes of physical structure + positions in space
That formula is inevitably applicable to every single form of matter in the universe., but it is not the number of hours on human-invented clocks, nor days , weeks, months, years on human -invented calendars, nor even the distances in space which the Earth travels along its orbit around the Sun, while continuously and endlessly rotating about its shifting axis. The distances in space which the Earth travels along its orbit around the Sun has been used as the frame of reference for human limited knowledge to evaluate the differences among the changes of physical structures and positions in space among the observable different forms of matter in the universe. The reason why human beings use the Earth's rotational motion and the effects of sunlight on the surface of this planet as the frame of reference is that the speed or velocity the Earth's rotational motion is almost constant, and endless or infinite. It is just similar to using all human-invented measuring instruments, such as a ruler, a metre stick, a scale to measure lengths in space, and weights of different forms of matter. All such measurement instruments are divided into smaller parts, all those smaller parts are equal, which means that the changes in length and weight are always constant. Ex, from 1 cm to 2cm , and 2 cm to 3 cm and so forth. You can easily and clearly see that the continuous sequence of changes of position in space is constant ,, and always equal to 1cm, no matter how far you will go.
Why is it constant?
The answer is because the changes are continuous , or there is not any hole or disruption from 1cm to infinity, like there is not any cessation of your life from the time you were born to the time your physical body is transformed into other forms of matter or different chemical compounds. Such continuous sequences of changes of physical structures and positions in space are what the concept of time actually represents
You guys will have a chance to read my official unquestionable or indisputable research paper with objective and undeniable facts which will topple all the current theories, concepts of mathematics, physics, and astronomy irreversibly in a few years
Ok Terrance Howard
The introduction was so long winded I didn’t even watch the video. I think you need to readjust your ideas about a proper introduction.
Gee moo knew, math from "the far side"..... 🐮
The Professor is out of touch with reality if he thinks his mathematical explanations can be understood by the average reader.
You admit to not knowing what Time is, Sean. Yet you make countless (unattested) assertions about Time. How does that work, Sean?? And you apparently believe is it 'real'. Where is the evidence?
And as Time is the dimension of change (rates and events...for what other evidence of 'time passing' is there but quintillions of quantum change events?) Change is reference-frame (e.g. quantum) specific. i.e. quintillions of Arrows of Change, not one universal Arrow of Time. How do the Tensors relate to this?
Because if Space is the (abstract) dimension of position (hence xyz axis) and time the (abstract) dimension of change-rate (hence 'per hour') surely Space-Time is the abstract dimension of changing position i.e. Motion?? In reality there is no 'fabric' of space-time, for its an abstract dimension - there is motion...motion is real. Why not talk about the underlying reality i.e. relative motion rather than the abstract space-time?
That would be real science and involve actual work. Science only deals in the fantasies that can't be disproven, like whether or not there is a God. This way they can always be right, even though they are always wrong.
Physics does not "know" what ANYTHING is. It just describes observed behavior. You probably need clergy or gurus for whatever you're asking about.
This is fun imagining-imaging to reduce concept to symbols, the same reason for perception paradox is why "The biggest idea in the Universe" is the Singularity-point, no size, no difference in pure-math relative-timing motion forever.., because Euler's e-Pi-i sync-duration in/of Newton's axial-tangential Polar-Cartesian Fluxion-Integral @.dt, Superspin Modulation 1-0-infinity that is Absolute Zero Kelvin i-reflection Timing-spacing.., all-ways all-at-once instantaneous ONE-INFINITY=> Eternity-now Observational realization-recognition, and is WYSIWYG without the inside-outside misunderstanding of Reciproction-recirculation superposition, ie we see the Holographic Principle for what it is, making 0-1-2-ness GD&P temporal logarithmic superposition-cross-sectional picture-plane in Perspective.., the Unzicker Flash perception that is equivalent to real-time recognition at the Centre of Time, here-now-forever.
And the consequence of nothing floating in No-thing ONE-INFINITY singularity positioning integration with the sizeless-wordless Apature of entangled e-Pi-i infinitesimal-gravitational off resonance sync-duration receeding-vanishing into-no-thing Perspective Principle is enough to justify Professor Carroll's teaching methods to Students in conscious awareness.
In the beginning was the Word, and the Word was with God, and the Word was God. 2He was with God in the beginning. 3Through him all things were made; without him nothing was made that has been made. (John 1:1-3)
You can't put a man on the moon with that bullshit, no matter how zealous you are.
Jesus Christ loves you! Put your trust in him today before it's too late. He promises to transform you and make you new. Christ awaits for you to put your trust in Him.
i dont see here Ancient Greek Cosmology bye bye
Eww. Did not like this at all! Ed Witten puts this guy to shame 👎🏻👎🏻.