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Hi Dave, I really enjoyed your course. Brought back good memories of the Chaos and dynamical systems course I did from Complexity Explorer years ago. I would have liked to try my hand at the homework problems for this relativity course, but couldn't find them in your github page

This video changed me as a person. When I first stumbled upon this video, I was intrigued by the thumbnail which propelled me to click on the title. The events that occured after clicking on this video was inexplicable. The method at which you carefully tackled topics of such complexity such as relativity really brought tears to my eyes. This was the only piece of media that brought me to tears after watching the re-enacment of macbeth by shakespeare. This video bolstered my knowledge and it is leading me to pursue physics in Harvard University. My life ambition has now transformed and when I become an adult (in a month), I want to make informational videos in order to educate the youth just like you do. Thank you my king, keep making videos!

Bullshit an experiment carried out once doesn't prove anything.

Good! but better use 'ct' instead of 't' as the time axis, to avoid any ambiguities.

I was wondering how Schutz claimed that the angle between x and x' is the same as the angle between t and t'. This whole argument was missing from his text -- it depends on some geometry resulting from sending out a beam of light from the origin. It's boggling that he printed a 3rd edition without including this argument. Surely SOMEBODY must have asked "How do you know those angles are equal?" in the past 20 or so years since his book was first published.

Do you have one that explains how "spacetime" tells matter how to move which includes an explanation of the actual physical process that would cause this physical motion?

you are amazing thank you

holy cow. i have been trying to figure out the proper time and have it actually stick for the past couple of days. the example with Anastasia and Baywolf really helped- I finally get it. thank you so much for providing a resource like this on TH-cam!

8:07 Isn't it rather that Ana is comparing the time on her watch to the time on Beowulf's watch?

So good. Thank you

Makes sense, thank you!

Saving lives in 2024! This was very good, thank you :)

Thank you kind sir for creating this course. My physics knowledge is almost non-existence and I was having hard times trying to understand relativity through TH-cam videos, but thanks to you and your course I can finally understand the importance and meaning of e=mc2. Thank you and may the force be with you.

Just being sure, Line C is positive 1/4 because it is a magnitude, right?

Nice Explanation!

I only clicked on this cos I saw the cat. love it

7:14 RIP

wonderful lecture.

why the angle between x' and t' is not 90°? is it three-dimensional?

Amazing relativity class ever!

Nearfield light has theoretically and experimentally been determined to be instantaneous, whereas farfield light is speed c. See papers below for details. Relativity is based on farfield light, yielding the Lorentz Transform. A derivation of Relativity using instantaneous nearfield light yields Galilean Relativity. This can be easily be seen by inserting c=infinity into the Lorentz Transform, yielding the Galilean Transform. So a moving object observed with farfield light will see Relativistic effects. But if the frequency of light is lowered such that instantaneous nearfield light is used, then no Relativistic effects will be observed. If time and space are real then they can not depend on the frequency of light used to measure its effects. So the effects of Relativity must be an optical illusion, and Galilean Relativity must be the correct theory of Relativity. *TH-cam presentation of above arguments: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html <th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html> *More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145 *pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1 Dr. William Walker

I still have a question about the projection, why is the projected t'A on the ct axis gamma t'A and why is the projected x'A on the x axis gamma x'A? Can I see it like this: The t'A is the proper time for the moving object, the time in the static frame runs faster, therefore it has the gamma factor. The x'A is the proper length or distance for the moving object, the length or the distance is longer in the static frame and therefore it has the gamma factor?

Would the signal travel faster than c if P and Q were entangled and the wave function collapsed at P? Could it be seen the the wave function collapsed at Q instead?

I calculated the transformation for event E using the Lorentz equations. The math result is that Event (3,5) in xt space converts to (1.1,4.1) in fair agreement with the graphical solution (0.8,4.2) demonstrated here. I am unsure about the need for the recalibration of the x't' axes units?

Very clear explanation of how to read the (x',t') values graphically from calibrated x' and t' axes. Well done. Thank you!

Very good course!

The Galilean transformation equations are correct. There have always been clocks that were slow or fast. Galileo and Isaac Newton could have calculated the mathematics of a slower or faster clock, which scientists of today cannot because their minds are so taken over by Einstein's illogical conclusions. To prove that slower clocks have always existed, I once bought a clock at Walgreen's drug store that lost ten minutes every day. The same thing could have happened back when Galileo was alive. Can the Galilean transformation equations describe the time of a slower or faster clock? Yes, surprisingly, they can. Here are the Galilean transformation equations. x'=x-vt y'=y z'=z t'=t Modern scientists say that the Galilean transformation equations can only describe Isaac Newton's concept of absolute time. This also is incorrect. The Galilean transformation equations can be used with any standard of time. If you want to describe time of a slower clock, such as the one described by Einstein in his Special Theory, all you have to do is use another set of Galilean transformation equations with different variables for velocity and time. So suppose we have a clock in a flying airplane. Einstein's Special Theory says that this clock will be slower than a clock on the ground. So to show the Galilean transformation equations according to the time of the slower clock in the airplane the inverse Galilean transformation equations would be x = x' - (-vt/n')n' y = y' z = z' n = n' n' is the time of the slower clock in the airplane. (-vt/n') is the velocity of the ground relative to the airplane according to the time of the slower clock in the airplane. n = n' shows that the time of the slower clock in the airplane is being used in both frames of reference. To show that this agrees with the original set of Galilean transformation equations, all we have to do is cancel out the (n')'s, and we have the original equations with the time of the clock on the ground. x = x' - (-vt/n')n' x = x' +vt t = t' Now we do what scientists claim cannot be done. We describe constant speed of light with the Galilean transformation equations. This is done by saying x = ct and x' = cn' instead of saying x=ct and x'=ct' the way Einstein did. x' cannot equal ct' in the Galilean transformation equations because t'=t. A different variable has to be used for time in the moving frame of reference. x' = x - vt cn' = ct - vt n' = t - vt/c This value for n' is actually the same as the expression in the numerator of Lorentz's equation for t'. t-vt/c = t' - vct/c^2 = t - vx/c^2 The x in this expression is not needed in the Galilean transformation equation n' = t-vt/c because there is no length contraction in the Galilean transformation equations.

The path you draw starting at 1:43 ends up going faster than light.

Since the t component is kinetic energy, wouldn’t that mean in cases where kinetic energy isn’t conserved, momentum isn’t conserved?

The effects of Relativity are just an optical illusion. Instantaneous fields are well known in physics, even though they are ignored by the scientific community. Nearfield gravity is known to be instantaneous and is used to calculate the orbits of planets, comets, rockets with incredible accuracy. Simone LaPlace was the 1st to notice this in the late 1700s, where he noticed that in order for the orbits of the planets to be stable, gravity had to act instantaneously. This can also be seen in that the formula for gravity is not a function of time, which means it acts instantaneously. This is not the only instantaneous known field, Coulombs law for the electric field, and Biot-Savart law for the magnetic field are also independent of time and are also instantaneous for slowly moving sources. Light itself turns out to be instantaneous in the nearfield and reduces to the speed of light about one wavelength from the source. A recent radio wave experiment, measured the time delay of signals transmitted between 2 dipole antennas as the antennas were separated from the nearfield to the farfield, showed that the radio waves (light) propagates instantaneously in the nearfield and reduces to the speed of light in the farfield after one wavelength. This corresponds to not only the phase speed and group speed, but also the information speed. These results are completely incompatible with Special Relativity, which is based on the speed of light being a constant c. Inserting c=infinity into the Lorentz transformation yields Galilean transformations, where space and time are absolute. This shows that if an inertial moving object is observed using instantaneous nearfield light, then no time dilation , length contraction, or simultaneity Relativistic effects will be observed. So if Relativistic effects are observed using farfield speed c light, then by simply flicking a switch, one can change the frequency of the light, such that instantaneous light used instead, and the effects of Relativity would go away. This shows that the effects of Relativity are just an optical illusion and that Galilean Relativity is the correct form of Relativity, and in Galilean Relativity there is no speed limit. Here is another very powerful argument that shows Relativity is based on a logical fallacy. According to Relativity, observers on a moving train and on a stationary train platform will disagree on the size of the ""Train"" and the passage of time on the ""Train"". This is a complete logical contradiction if the size and the passage of time of the train are real. If the size of the train is real, then the ""Train"" can not be both contracted and not contracted. The same goes for the observed passage of time on the ""Train"". If these effects are observed, then the only possible conclusion is that it is an optical illusion. Things that are real must appear to be same from all frames of reference. If not, then by definition it is an illusion. Again the argument is very simple and it is the argument Einstein used to derive Relativity, and no acceleration is used in the argument. A train with length (L) traveling at constant velocity (v) relative a stationary observer on a station platform. According to Relativity, the stationary observer will see the train contracted (L/r, where r is the Relativistic gamma), whereas an observer on the train will see it not contracted (L). So the train is both contracted (L/r) and not contracted (L) depending on the observer. This is a complete contradiction (L not equal L/r) and can not be true if length is real. The same argument applies to passage of time on the Train, where both observers will disagree on the passage of time. If time is real, it can not be both dilated and not dilated (T not equal rT). If space and time are observed to be both large and small simultaneously for one inertial reference frame, such as the ""Train"", then it must be an optical illusion. It should be noted that experiments proving Relativity can only give evidence that the theory may be true, but an experiment disproving Relativity, or a logical proof showing a logical fallacy in the theory can absolutely disprove the theory. I have provided both. Since General Relativity is based on Special Relativity, General Relativity must also be an optical illusion. Spacetime is flat and gravity must be a propagating field. Researchers have shown that in the weak field limit, which is what we only observe, General Relativity reduces to Gravitoelectromagnetism, which shows gravity can be modeled as 4 Maxwell equations similar in form to those for electromagnetic fields, yielding Electric and Magnetic components of gravity. This theory explains all gravitational effects as well as the instantaneous nearfield and speed of light farfield propagating fields. So gravity is a propagating field that can finally be quantized enabling the unification of gravity and quantum mechanics. The current interpretation of quantum mechanics makes no sense, involving particles that are not real until measured, and in a fuzzy superposition of states. On the other hand, the Pilot Wave interpretation of Quantum Mechanics makes makes much more sense, which says particles are always real with real positions and velocities. The particles also interact with an energetic quantum field that permeates all of space, forming a pilot wave that guides the particle. This simpler deterministic explanation explains all known quantum phenomena. The only problem is that the Pilot Wave is known to interact instantaneously with all other particles, and this is completely incompatible with Relativity, but is compatible with Galilean Relativity. But because of the evidence presented here, this is no longer a problem, and elevates the Pilot Interpretation to our best explanation of Quantum Mechanics. *TH-cam presentation of above argument: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html *Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145

This is not the complete story. Setting the wave equation equal to zero is only valid in the farfield. To understand what goes on in the nearfield, the wave equation must be set equal to a source term. The mathematics is much more complicated, but the results show that the speed of light is instantaneous in the nearfield and reduces to speed of light in the farfield after about one wavelength. This matches well with Coulombs law for the electric field , and the Biot-Savart law for the magnetic field, which says these fields are instantaneous since they it independent of time. In the farfield setting the wave equation to zero shows that the fields propagate at speed c. A recent radio wave experiment, measured the time delay of signals transmitted between 2 dipole antennas as the antennas were separated from the nearfield to the farfield, showed that the radio waves (light) propagates instantaneously in the nearfield and reduces to the speed of light in the farfield after one wavelength. This corresponds to not only the phase speed and group speed, but also the information speed. These results are completely incompatible with Special Relativity, which is based on the speed of light being a constant c. Inserting c=infinity into the Lorentz transformation yields Galilean transformations, where space and time are absolute. This shows that if an inertial moving object is observed using instantaneous nearfield light, then no time dilation , length contraction, or simultaneity Relativistic effects will be observed. So if Relativistic effects are observed using farfield speed c light, then by simply flicking a switch, one can change the frequency of the light, such that instantaneous light used instead, and the effects of Relativity would go away. This shows that the effects of Relativity are just an optical illusion and that Galilean Relativity is the correct form of Relativity, and in Galilean Relativity there is no speed limit. Here is another very powerful argument that shows Relativity is based on a logical fallacy. According to Relativity, observers on a moving train and on a stationary train platform will disagree on the size of the ""Train"" and the passage of time on the ""Train"". This is a complete logical contradiction if the size and the passage of time of the train are real. If the size of the train is real, then the ""Train"" can not be both contracted and not contracted. The same goes for the observed passage of time on the ""Train"". If these effects are observed, then the only possible conclusion is that it is an optical illusion. Things that are real must appear to be same from all frames of reference. If not, then by definition it is an illusion. Again the argument is very simple and it is the argument Einstein used to derive Relativity, and no acceleration is used in the argument. A train with length (L) traveling at constant velocity (v) relative a stationary observer on a station platform. According to Relativity, the stationary observer will see the train contracted (L/r, where r is the Relativistic gamma), whereas an observer on the train will see it not contracted (L). So the train is both contracted (L/r) and not contracted (L) depending on the observer. This is a complete contradiction (L not equal L/r) and can not be true if length is real. The same argument applies to passage of time on the Train, where both observers will disagree on the passage of time. If time is real, it can not be both dilated and not dilated (T not equal rT). If space and time are observed to be both large and small simultaneously for one inertial reference frame, such as the ""Train"", then it must be an optical illusion. It should be noted that experiments proving Relativity can only give evidence that the theory may be true, but an experiment disproving Relativity, or a logical proof showing a logical fallacy in the theory can absolutely disprove the theory. I have provided both. Since General Relativity is based on Special Relativity, General Relativity must also be an optical illusion. Spacetime is flat and gravity must be a propagating field. Researchers have shown that in the weak field limit, which is what we only observe, General Relativity reduces to Gravitoelectromagnetism, which shows gravity can be modeled as 4 Maxwell equations similar in form to those for electromagnetic fields, yielding Electric and Magnetic components of gravity. This theory explains all gravitational effects as well as the instantaneous nearfield and speed of light farfield propagating fields. So gravity is a propagating field that can finally be quantized enabling the unification of gravity and quantum mechanics. The current interpretation of quantum mechanics makes no sense, involving particles that are not real until measured, and in a fuzzy superposition of states. On the other hand, the Pilot Wave interpretation of Quantum Mechanics makes makes much more sense, which says particles are always real with real positions and velocities. The particles also interact with an energetic quantum field that permeates all of space, forming a pilot wave that guides the particle. This simpler deterministic explanation explains all known quantum phenomena. The only problem is that the Pilot Wave is known to interact instantaneously with all other particles, and this is completely incompatible with Relativity, but is compatible with Galilean Relativity. But because of the evidence presented here, this is no longer a problem, and elevates the Pilot Interpretation to our best explanation of Quantum Mechanics. *TH-cam presentation of above argument: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html *Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145

Instantaneous fields are well known in physics, even though they are currently ignored by the scientific community. Nearfield gravity is known to be instantaneous and is used to calculate the orbits of planets, comets, rockets with incredible accuracy. Simone LaPlace was the 1st to notice this in the late 1700s, where he noticed that in order for the orbits of the planets to be stable, gravity had to act instantaneously. This can also be seen in that the formula for gravity is not a function of time, which means it acts instantaneously. This is not the only instantaneous known field, Coulombs law for the electric field, and Biot-Savart law for the magnetic field are also independent of time and are also instantaneous for slowly moving sources. Light itself turns out to be instantaneous in the nearfield and reduces to the speed of light about one wavelength from the source. A recent radio wave experiment, measured the time delay of signals transmitted between 2 dipole antennas as the antennas were separated from the nearfield to the farfield, showed that the radio waves (light) propagates instantaneously in the nearfield and reduces to the speed of light in the farfield after one wavelength. This corresponds to not only the phase speed and group speed, but also the information speed. These results are completely incompatible with Special Relativity, which is based on the speed of light being a constant c. Inserting c=infinity into the Lorentz transformation yields Galilean transformations, where space and time are absolute. This shows that if an inertial moving object is observed using instantaneous nearfield light, then no time dilation , length contraction, or simultaneity Relativistic effects will be observed. So if Relativistic effects are observed using farfield speed c light, then by simply flicking a switch, one can change the frequency of the light, such that instantaneous light used instead, and the effects of Relativity would go away. This shows that the effects of Relativity are just an optical illusion and that Galilean Relativity is the correct form of Relativity. Here is another very powerful argument that shows Relativity is based on a logical fallacy. According to Relativity, observers on a moving train and on a stationary train platform will disagree on the size of the ""Train"" and the passage of time on the ""Train"". This is a complete logical contradiction if the size and the passage of time of the train are real. If the size of the train is real, then the ""Train"" can not be both contracted and not contracted. The same goes for the observed passage of time on the ""Train"". If these effects are observed, then the only possible conclusion is that it is an optical illusion. Things that are real must appear to be same from all frames of reference. If not, then by definition it is an illusion. Again the argument is very simple and it is the argument Einstein used to derive Relativity, and no acceleration is used in the argument. A train with length (L) traveling at constant velocity (v) relative a stationary observer on a station platform. According to Relativity, the stationary observer will see the train contracted (L/r, where r is the Relativistic gamma), whereas an observer on the train will see it not contracted (L). So the train is both contracted (L/r) and not contracted (L) depending on the observer. This is a complete contradiction (L not equal L/r) and can not be true if length is real. The same argument applies to passage of time on the Train, where both observers will disagree on the passage of time. If time is real, it can not be both dilated and not dilated (T not equal rT). If space and time are observed to be both large and small simultaneously for one inertial reference frame, such as the ""Train"", then it must be an optical illusion. It should be noted that experiments proving Relativity can only give evidence that the theory may be true, but an experiment disproving Relativity, or a logical proof showing a logical fallacy in the theory can absolutely disprove the theory. I have provided both. Since General Relativity is based on Special Relativity, General Relativity must also be an optical illusion. Spacetime is flat and gravity must be a propagating field. Researchers have shown that in the weak field limit, which is what we only observe, General Relativity reduces to Gravitoelectromagnetism, which shows gravity can be modeled as 4 Maxwell equations similar in form to those for electromagnetic fields, yielding Electric and Magnetic components of gravity. This theory explains all gravitational effects as well as the instantaneous nearfield and speed of light farfield propagating fields. So gravity is a propagating field that can finally be quantized enabling the unification of gravity and quantum mechanics. The current interpretation of quantum mechanics makes no sense, involving particles that are not real until measured, and in a fuzzy superposition of states. On the other hand, the Pilot Wave interpretation of Quantum Mechanics makes makes much more sense, which says particles are always real with real positions and velocities. The particles also interact with an energetic quantum field that permeates all of space, forming a pilot wave that guides the particle. This simpler deterministic explanation explains all known quantum phenomena. The only problem is that the Pilot Wave is known to interact instantaneously with all other particles, and this is completely incompatible with Relativity, but is compatible with Galilean Relativity. But because of the evidence presented here, this is no longer a problem, and elevates the Pilot Interpretation to our best explanation of Quantum Mechanics. *TH-cam presentation of above argument: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html *Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145

Hello, I think this may interest you, a type of space-time diagram better than Minkowsky's because on both axes the scales are the same. th-cam.com/video/o4kKeG8PyyM/w-d-xo.html In Argentina we use it a lot, and I think its dissemination is well worth it. A big greeting and congratulations for the channel.

it works

Hello Dave, I think this may interest you, a type of space-time diagram better than Minkowsky's because on both axes the scales are the same. th-cam.com/video/o4kKeG8PyyM/w-d-xo.html In Argentina we use it a lot, and I think its dissemination is well worth it.

Legend.

thank you so much for these videos

it was a very pleasant journey . Thank you for this playlist , it helped a lot

Sir i watched your whole playlist, its very underrated, i think it deserves way more views. You have helped me enormously, thank you very much!

Relativity Crisis: Einstein has taken us down a wrong path, and 100 years later, physics has not recovered from the consequences. We need to look at the clear evidence and go back to working on real physics instead of science fiction! Theory and experiments show Special Relativity and General Relativity are optical illusions. Space and time are absolute as denoted by Galilean Relativity. Hi my name is Dr William Walker and I am a PhD physicist and have been investigating this topic for 30 years. It has been known since the late 1700's by Simone Laplace that nearfield Gravity is instantaneous by analyzing the stability of the orbits of the planets about the sun. This is actually predicted by General Relativity by analyzing the propagating fields generated by an oscillating mass. In addition, General Relativity predicts that in the farfield Gravity propagates at the speed of light. The farfield speed of gravity was recently confirmed by LIGO. Recently it has been shown that light behaves in the same way by using Maxwell's equations to analyze the propagating fields generated my an oscillating charge. For more information search: William Walker Superluminal. This was experimentally confirmed by measuring radio waves propagating between 2 antennas and separating the antennas from the nearfield to the farfield, which occurs about 1 wavelength from the source. This behavior of gravity and light occurs not only for the phase and group speed, but also the information speed. This instantaneous nature of light and gravity near the source and been kept from the public and is not commonly known. The reason is that it shows that both Special Relativity and General Relativity are wrong! It can be easily shown that Instantaneous nearfield light yields Galilean Relativity and farfield light yields Einstein Relativity. This is because in the nearfield, gamma=1since c= infinity, and in the farfield, gamma= the Relativistic gamma since c= farfield speed of light. Since time and space are real, they can not depend on the frequency of light used. This is because c=wavelength x frequency, and 1 wavelength=c/frequency defines the nearfield from the farfield. Consequently Relativity is an optical illusion. Objects moving near the speed of light appear to contract in length and time appears to slow down, but it is just what you see using farfield light. Using nearfield light you will see that the object has not contracted and time has not changed. For more information: Search William Walker Relativity. Since General Relativity is based on Special Relativity, General Relativity must also be an optical illusion. Spacetime is flat and gravity must be a propagating field. Researchers have shown that in the weak field limit, which is what we only observe, General Relativity reduces to Gravitoelectromagnetism, which shows gravity can be modeled as 4 Maxwell equations similar in form to those for electromagnetic fields, yielding Electric and Magnetic components of gravity. This theory explains all gravitational effects as well as the instantaneous nearfield and speed of light farfield propagating fields. So gravity is a propagating field that can finally be quantized enabling the unification of gravity and quantum mechanics. TH-cam presentation: th-cam.com/video/uTrrlpQTmIY/w-d-xo.htmlsi=Oig115T-UkSDHN8o References: -------------------- William D. Walker, PhD Thesis - Gravitational Studies, ETH Zurich, 1997 drive.google.com/file/d/10TfEEYIa7FyOAJAr2dwKCQKE7qnMfnNs/view?usp=drivesdk William D. Walker, Superluminal Electromagnetic and Gravitational Fields Generated in the Nearfield of Dipole Sources, 2006 arxiv.org/abs/physics/0603240 William D. Walker, Nearfield Electromagnetic Effects on Einstein Special Relativity, 2007 arxiv.org/pdf/physics/0702166 Z. Wang, ‘New Investigations on Superluminal Propagation of Electromagnetic Waves in Nondispersive Media’, Nov. (2003). arxiv.org/vc/physics/papers/0311/0311061v1.pdf J. C. Sten and A. Hujanen, ‘Aspects on the Phase Delay and Phase Velocity in the Electromagnetic Near-Field’, Progress In Electromagnetics Research, PIER 56, 67-80, (2006). www.researchgate.net/publication/254072994_Aspects_on_the_phase_delay_and_phase_velocity_in_the_electromagnetic_near-field Hans G. Shantz, "Near Field Phase Behavior", 2005 www.researchgate.net/publication/4199558_Near_field_phase_behavior

😂😂😂😂😂😂😂🤦‍♂️🤦‍♂️🤦‍♂️ Wrong.

How do you equate delta t and delta s? No.

Bravo!!

Your Lorentz equations are wrong, I fear. The Galilean transformation is always embedded in Lorentz: x‘ = gamma ( x - vt). You always write betha for speed, regardless if the speed of light is involved or not. Betha actually is v/c. So out of Galilean Trafo you get, with c = x/t: x‘ = gamma ( x - v x/c) = g ( 1 - betha) x. If you define v = betha as you always do things get messed up: x‘ = g ( x - betha t) with c = x/t gives x‘ = g ( x - v/c x/c) = g ( x - vx/ cc). The second term in the bracket is the correct term for t‘ which goes t‘ = g ( t - vx/cc) giving t‘ = g( 1- betha) t. Analoguesly for x‘: x‘ = g (x - vt), t = x/c, x‘ = g ( x - vx/c) = g ( 1 - betha) t.

I‘m late but I would just say I like your vids quite a lot. I‘m into that stuff seriously for some weeks now and its a fun thing. No overwhelming mathematics which you have no clue of but intellectually a bit demanding nevertheless. All the best and cheers.

Stephen Hawking book explaination ,a brief history of time ,great explaination ,I had confusion in this while reading the book

I don't expect an answer since it has been a couple years now since this video was put up. My question is that 4-momentum is by definition dR/dtau where tau is the proper time of the object in question, however, here there are four different objects, object 1, 2 (before collision) and 3 and 4 (after collision), and you said "rest frame" ... but the "rest frame" of which of the 4 objects? Each of the 4 objects have (potentially) different times since they could be moving at different relative velocities. I'll be grateful if you could answer my question.

if the planes are moving at the same speeds relative to earth, then due to v^2 in the time dilation equation it does not matter if they are moving in the same direction or in opposite directions, relative to earth, since (+v)^2 = (-v)^2.

Excellent Job! Please keep up the good work. I have been into special relativity for some months. I got a good start with Brian Green and his 11 hour video on SR but did not feel satisfied with the "photon clock." I went through some of his math for the Lorentz Factor which was good. But I still could not follow some other teachers who got into the hyperbola discussion for understanding time dilation. Your explanation is excellent and you go slow enough and use good video, moving diagrams, etc. I will stay with you if you keep his excellent presentation going. Will get to your other videos soon. thanks again.

Point B is being chosen arbitrarily here. Not good. Does not explain X axis rotation in moving frame which is crucial.