Gravity Unveiled pinned «با سلام. جلسه‌ی اول در تاریخ ۲۹ام بهمن ماه برگزار خواهد شد. مواردی که در این جلسه بررسی خواهند شد: 1.Smooth manifold 2.Smooth maps»
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Post #42
774
در رابطه با این جلسه اگر سوالی داشتید حتما به من پیام دهید.
@Radmehr_miradi
@Radmehr_miradi
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Post #41
812
با سلام.
جلسه‌ی اول در تاریخ ۲۹ام بهمن ماه برگزار خواهد شد.
مواردی که در این جلسه بررسی خواهند شد:
1.Smooth manifold
2.Smooth maps
جلسه‌ی اول در تاریخ ۲۹ام بهمن ماه برگزار خواهد شد.
مواردی که در این جلسه بررسی خواهند شد:
1.Smooth manifold
2.Smooth maps
- 👍 11
Post #40
692
Post #39
1.11K
Post #38
931
Fall in love with some activity, and do it! Nobody ever figures out what life is all about, and it doesn't matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough. Work as hard and as much as you want to on the things you like to do the best. Don't think about what you want to be, but what you want to do. Keep up some kind of a minimum with other things so that society doesn't stop you from doing anything at all.
- RICHARD FEYNMAN
- RICHARD FEYNMAN
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Post #36
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Post #34
738
Post #33
768
Free-Falling Elevator
Imagine you are inside a closed elevator that is falling freely under the influence of gravity. Suppose there are no windows to see outside. Inside this elevator:
1. What Happens to Objects Inside?
If you release an object (say, a ball), it will appear to float beside you. The ball is in free fall, and so are you. Both are following geodesics in the curved spacetime created by the Earth's mass.
To an observer inside the elevator, it seems as though there is no gravitational force acting on the ball. It is as if gravity "disappears."
2. What Happens Outside?
To an external observer watching the elevator, they would say the ball and the elevator are accelerating downward due to gravity.
Why This Shows Gravity Is Not a Force
Force Perspective: If gravity were a force, you would feel it pulling you down inside the elevator. However, you feel nothing—no pull, no pressure.
Spacetime Perspective: In general relativity, the elevator and the ball are simply following the natural curvature of spacetime. There is no need to invoke a "force" to explain their motion.
Comparison:
Now imagine the elevator is far from any massive object (e.g., in deep space) but accelerating upward due to a rocket engine.
Inside the elevator, you would feel a force pushing you toward the floor, similar to the sensation of "gravity."
This demonstrates that what we perceive as the "force of gravity" is indistinguishable from acceleration, reinforcing the idea that gravity is not a true force but a result of curved spacetime.
Imagine you are inside a closed elevator that is falling freely under the influence of gravity. Suppose there are no windows to see outside. Inside this elevator:
1. What Happens to Objects Inside?
If you release an object (say, a ball), it will appear to float beside you. The ball is in free fall, and so are you. Both are following geodesics in the curved spacetime created by the Earth's mass.
To an observer inside the elevator, it seems as though there is no gravitational force acting on the ball. It is as if gravity "disappears."
2. What Happens Outside?
To an external observer watching the elevator, they would say the ball and the elevator are accelerating downward due to gravity.
Why This Shows Gravity Is Not a Force
Force Perspective: If gravity were a force, you would feel it pulling you down inside the elevator. However, you feel nothing—no pull, no pressure.
Spacetime Perspective: In general relativity, the elevator and the ball are simply following the natural curvature of spacetime. There is no need to invoke a "force" to explain their motion.
Comparison:
Now imagine the elevator is far from any massive object (e.g., in deep space) but accelerating upward due to a rocket engine.
Inside the elevator, you would feel a force pushing you toward the floor, similar to the sensation of "gravity."
This demonstrates that what we perceive as the "force of gravity" is indistinguishable from acceleration, reinforcing the idea that gravity is not a true force but a result of curved spacetime.
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Post #30
564
Gravity Unveiled Why Luminiferous Aether is Disproved ? The concept of luminiferous aether was once central to physics as an attempt to explain the propagation of light. This theoretical medium was believed to permeate space, allowing light waves to travel through it, much…YouTube Michelson–Morley Experiment introduction | Special relativity | Physics | Khan Academy Simple idea behind the Michelson‒Morley experiment to detect ether wind. Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces…
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Post #29
534
Why Luminiferous Aether is Disproved ?
The concept of luminiferous aether was once central to physics as an attempt to explain the propagation of light. This theoretical medium was believed to permeate space, allowing light waves to travel through it, much like sound waves travel through air. However, advancements in science, particularly in the late 19th and early 20th centuries, led to its disproof. This essay will explore the historical context, key experiments, and the rise of modern theories that rendered the luminiferous aether obsolete.
The Birth of the Aether Hypothesis
The concept of luminiferous aether emerged in the 17th and 18th centuries when scientists sought to explain how light propagated through the vacuum of space. Since sound and water waves required a medium, it seemed logical to propose that light waves also required one. The aether was conceived as an invisible, all-pervasive substance with no mass but capable of supporting electromagnetic waves.
In the early 19th century, James Clerk Maxwell's equations for electromagnetism further solidified the need for a medium. These equations described light as an electromagnetic wave, leading physicists to assume the existence of the aether as the medium for these waves.
The Michelson-Morley Experiment
The downfall of the aether theory began with the groundbreaking Michelson-Morley experiment in 1887. Albert A. Michelson and Edward W. Morley designed an experiment to detect the "aether wind," which was expected to result from the Earth's movement through the aether.
Using an interferometer, they aimed to measure differences in the speed of light in directions parallel and perpendicular to the Earth's motion. If the aether existed, the speed of light should vary depending on the direction relative to the aether wind. However, the experiment produced a null result—no significant difference was detected.
This result was one of the first major blows to the aether hypothesis, as it suggested that light's speed was constant regardless of the observer's motion.
Einstein's Special Theory of Relativity
The final nail in the coffin for the luminiferous aether came with Albert Einstein's special theory of relativity in 1905. Einstein proposed that the speed of light is constant in all inertial reference frames, eliminating the need for a medium like the aether.
In Einstein's framework, the laws of physics are the same for all observers in uniform motion, and time and space are not absolute but relative to the observer. These principles directly contradicted the idea of a stationary aether through which light travels.
Further Developments and Experimental Evidence
Subsequent experiments and theoretical advancements reinforced the rejection of the aether. Hendrik Lorentz's transformation equations, initially designed to preserve the concept of aether, were reinterpreted within Einstein's relativity as describing the relativistic effects of time dilation and length contraction.
Moreover, the advent of quantum mechanics and the wave-particle duality of light provided a new understanding of light propagation, making the aether entirely unnecessary. Photons, the quantum particles of light, do not require a medium to travel through space.
Modern Physics and the Aether
In modern physics, the luminiferous aether is considered a historical concept, replaced by the relativistic and quantum frameworks. The vacuum of space is no longer seen as an empty void but as a dynamic entity filled with quantum fields and virtual particles. These fields do not serve as a medium for light in the classical sense but represent the modern understanding of space-time and energy.
Conclusion
The luminiferous aether was an elegant yet ultimately flawed hypothesis born out of the need to explain light propagation. Groundbreaking experiments like the Michelson-Morley experiment and revolutionary theories like Einstein's special relativity dismantled the aether theory, replacing it with a deeper understanding of space, time, and light.
The concept of luminiferous aether was once central to physics as an attempt to explain the propagation of light. This theoretical medium was believed to permeate space, allowing light waves to travel through it, much like sound waves travel through air. However, advancements in science, particularly in the late 19th and early 20th centuries, led to its disproof. This essay will explore the historical context, key experiments, and the rise of modern theories that rendered the luminiferous aether obsolete.
The Birth of the Aether Hypothesis
The concept of luminiferous aether emerged in the 17th and 18th centuries when scientists sought to explain how light propagated through the vacuum of space. Since sound and water waves required a medium, it seemed logical to propose that light waves also required one. The aether was conceived as an invisible, all-pervasive substance with no mass but capable of supporting electromagnetic waves.
In the early 19th century, James Clerk Maxwell's equations for electromagnetism further solidified the need for a medium. These equations described light as an electromagnetic wave, leading physicists to assume the existence of the aether as the medium for these waves.
The Michelson-Morley Experiment
The downfall of the aether theory began with the groundbreaking Michelson-Morley experiment in 1887. Albert A. Michelson and Edward W. Morley designed an experiment to detect the "aether wind," which was expected to result from the Earth's movement through the aether.
Using an interferometer, they aimed to measure differences in the speed of light in directions parallel and perpendicular to the Earth's motion. If the aether existed, the speed of light should vary depending on the direction relative to the aether wind. However, the experiment produced a null result—no significant difference was detected.
This result was one of the first major blows to the aether hypothesis, as it suggested that light's speed was constant regardless of the observer's motion.
Einstein's Special Theory of Relativity
The final nail in the coffin for the luminiferous aether came with Albert Einstein's special theory of relativity in 1905. Einstein proposed that the speed of light is constant in all inertial reference frames, eliminating the need for a medium like the aether.
In Einstein's framework, the laws of physics are the same for all observers in uniform motion, and time and space are not absolute but relative to the observer. These principles directly contradicted the idea of a stationary aether through which light travels.
Further Developments and Experimental Evidence
Subsequent experiments and theoretical advancements reinforced the rejection of the aether. Hendrik Lorentz's transformation equations, initially designed to preserve the concept of aether, were reinterpreted within Einstein's relativity as describing the relativistic effects of time dilation and length contraction.
Moreover, the advent of quantum mechanics and the wave-particle duality of light provided a new understanding of light propagation, making the aether entirely unnecessary. Photons, the quantum particles of light, do not require a medium to travel through space.
Modern Physics and the Aether
In modern physics, the luminiferous aether is considered a historical concept, replaced by the relativistic and quantum frameworks. The vacuum of space is no longer seen as an empty void but as a dynamic entity filled with quantum fields and virtual particles. These fields do not serve as a medium for light in the classical sense but represent the modern understanding of space-time and energy.
Conclusion
The luminiferous aether was an elegant yet ultimately flawed hypothesis born out of the need to explain light propagation. Groundbreaking experiments like the Michelson-Morley experiment and revolutionary theories like Einstein's special relativity dismantled the aether theory, replacing it with a deeper understanding of space, time, and light.
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Post #28
468
Gravity Unveiled In a four-dimensional Minkowski spacetime with the metric signature , the Minkowski metric tensor can describe the curvature of spacetime caused by a massive object.
Explanation: The Minkowski metric is the metric tensor of flat spacetime in special relativity and does not account for spacetime curvature caused by massive objects. Curved spacetime, as described in general relativity, requires a general metric , which incorporates the effects of the energy-momentum tensor via Einstein's field equations. The Minkowski metric is only valid in the absence of gravitational fields.
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Post #27
491
Gravity Unveiled In a four-dimensional Minkowski spacetime with the metric signature , the Minkowski metric tensor can describe the curvature of spacetime caused by a massive object.
The metric signature is (- + + +)
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Post #26
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Post #25
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Post #24
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Post #23
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باسلام.
جلسه‌ی اول از ابتدای ترم بعدی آغاز خواهد شد.
مواردی که در جلسه‌ی اول بررسی خواهند شد:
1.Smooth manifold
2.Smooth maps
مفاهیم مورد نیاز از توپولوژی و معادلات دیفرانسیل نیز بررسی خواهد شد تا پیش نیازی برای جلسه نباشد.
جلسه‌ی اول از ابتدای ترم بعدی آغاز خواهد شد.
مواردی که در جلسه‌ی اول بررسی خواهند شد:
1.Smooth manifold
2.Smooth maps
مفاهیم مورد نیاز از توپولوژی و معادلات دیفرانسیل نیز بررسی خواهد شد تا پیش نیازی برای جلسه نباشد.
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Post #22
508
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Post #21
544
با سلام
دوستانی که میخواهند از دانشگاه های دیگر تشریف بیارند، از درب خیابان ۱۶ آذر وارد شوند.
دوستانی که میخواهند از دانشگاه های دیگر تشریف بیارند، از درب خیابان ۱۶ آذر وارد شوند.
Post #20
568
Gravity Unveiled با سلام. جلسه‌ی صفر همین دوشنبه (۱۷ام) برگزار خواهد شد. کلیات کارگاه و برخی مفاهیم ساده‌ی اولیه در این جلسه گفته خواهند شد.
جلسه‌ی صفر ساعت ۱۷ در کلاس ۲۰۷ دانشکده‌ی ریاضی برگزار خواهد شد.
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