Deriving the Lorentz Transformations | Special Relativity
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- เผยแพร่เมื่อ 21 ก.ค. 2024
- In this third video of the Special Relativity series, we derive the Lorentz transformations, which map events in one reference frame to another reference frame that moves at a constant relative velocity. We also demonstrate how these transformations can be used to derive the phenomena of time dilation and length contraction that we explored more informally in the last video.
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SPECIAL RELATIVITY SERIES
-----------------------------------------------
I. The Michelson-Morley Experiment ( • The Michelson-Morley E... )
II. Time Dilation and Length Contraction ( • Time Dilation and Leng... )
III. Deriving the Lorentz Transformations
IV. Deriving the General Lorentz Transformation ( • Deriving the General L... )
V. Spacetime ( • What is Spacetime? | S... )
VI. Relativistic Velocity Addition ( • Relativistic Velocity ... )
CHAPTERS
-----------------
Introduction 00:00
What are the Lorentz Transformations? 00:24
Hendrik Lorentz 01:00
Proof using Spherical Wavefronts of Light 01:43
Why Linearity? 04:09
Proof Continuation 07:53
The Lorentz Transformations 13:40
Time Dilation 14:00
Length Contraction 14:45
In simpler terms:
Length Contraction: The length of objects appears to "shrink" or contract when they are moving at speeds close to the speed of light, as observed from a stationary frame.
Time Dilation: Time appears to "slow down" or "elongate" for objects in motion compared to a stationary observer. Clocks on the moving object tick more slowly when viewed from the stationary frame.
awsome. you saved my time reading the papers
Thanks
what does special theory of relativity tells at 12:22 for both condition to be equal pls ellaborate it to me I am new with this stuff.
Super video. This channel will become one the the best educational channel. Mark my words. If u don't mind could u make video about the basics of algebra 1 2.most people struggle to learn it. It's a suggestion will help your youtube grow
Thank you for your comment! Are there any aspects of algebra (and difficulty level) that you think would be useful?
@@deepbean Infinite field speeds are possible, including the speed of nearfield light!! Fields like: nearfield gravity, magnetic field, electric field, and even nearfield light are all instantaneous, and they are completely incompatible with Relativity, which says nothing travels faster than light. The main problem is that it invalidates the Relativity of Simultaneity argument. This is because instantaneous fields propagate instantaneously to all inertial reference frames, thereby preserving simultaneity in all the frames. If you look at the Lorentz transforms and make c=infinity, then gamma equals one, and the Lorentz transforms becomes the Galilean transform, where space and time are independent and absolute, and space and time are the same in all inertial frames of reference.
Relativity is just an optical illusion, and because all of modern physics is based on Relativity, modern physics is fundamentally wrong and needs to be rethought. Relativity has a simple built in logical fallacy, and no theory based on a logical fallacy can be true, no matter how many experiments seem to prove it, or how many people say it is true. Below is a very simple logical argument highlighting the logical fallacy, using the same terminology Einstein used to derive Relativity.
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.
This argument is only the tip of the iceberg. There is much more evidence including both theoretical and experimental, so please keep reading. 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 1700s 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 has 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.
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
0:31 one question: Why would you use a left handed coordinate system?
at 8:07 why would the scale factor be different for light going in the opposite direction?
In 11:26
If we evaluate deep prime equal to 0 then we will get that x equals a c t over b and then the velocity will be AC over b because x equals v by t
At 3:28, we posit x = ct and x' = ct'. So, at 11:11, we have to say that at t = 0 x = 0 and so all the rest is moot. We are not allowed to draw conclusions about either x or x'.
Is there a Lorentz transformation for an inertial frame that moves with light speed ?
Yup! This would just be analogous with following the expansion of the light sphere
I got another question :
Suppose we have 3 relativity inertial frames X = (x,t) , Y = (y,t’), Z = (z,t”), where x = (x1,x2,x3), y = (y1,y2,y3), z = (z1,z2,z3).
Suppose that two frames X, Y have the same direction to each coordinate axis. At the initial time t = t’ = t” = 0, x and y coincide at the origin O = O’, while [z] = R[y]+ [u], where R is a rotation matrix and u is a fixed 3-vector.
Let X is stationary, while Y and Z move with the same velocity v = (v1,v2,v3). What I wonder is the coordinate of [z], is it still it still equal to R[y] + [u] over time ? Or is there a Lorentz transformer between Y and Z that make the equality [z] = R[y] + [u] no longer valid ?
Since Y and Z are moving at an equal velocity, if we are sitting in Y, it will be as if the Y/Z system is not moving at all, so your relation would remain satisfied.
I got 2 question : in this Lorentz transformation, suppose 2 frame coincide at t = t' = 0.
(1) Then, in that moment, all points in two frame should coincide. But from the equation x' = γ(x-vt), x and x' can't coincide exept the two origins. Is that the length contraction ?
(2) Next, from the equation of t', we have 0 = -γvx/c^2, which implies x = 0. It is not precise for the other points but only the orgin. So what is the problem here ?
Thank you..
Hi!
1) Yep, in a sense, it is length contraction, which, as we can see, is a natural outcome of the Lorentz transformations.
2) So here, the origin is defined as a spatiotemporal one, which means that x = 0 by definition when t = t' = 0. It is used as a convention, so it does not have to be defined this way, but then the equations would have to be changed.
no, jts easiear.You told Your start is by t=0,...so the term. vt=0 is also 0. and if we multiplay 0..with Gamma we became again 0.
It is start point and points are transfered into same space points.
Men showed tricky calculations for the known results.
for the second: again, Yot defined a startpoint, its a moment without movement A shot of event. So change of x was 0. You must let it go a while, then You get another x and t.
Light does not look constant relative to the observer until AFTER you use these transforms. That non-transformed reality does not disappear just because you changed the numbers with transform equations. It was a theory jump from ether to this. I don't know how people are comfortable with that. When you move your head, the entire Universe now has a different shape, and that makes sense to you?
Einstein's relativity is full of errors and is 100% wrong from the opening paragraphs of the hypothesis. That the simple truth, and we have been conned by big authoritative education institutions. They want us to be side tracked and dumb.
Gamma Ray Bursts, all of them, always arrive here in order of wavelength with radio being a month late sometimes. They don't come out and say it that way, because it's part of an afterglow theory, so they don't have to. If this GRB character were known in the year 1900, there is NO WAY Relativity would have been accepted by science with evidence that light may travel at differing speeds. Today, the paradigm is too deep, and there is and always has been 1 theory taught in schools, so it is not going to be anything else.
There is no "non-transformed reality" in special relativity because the transforms describe precisely what reality looks like in different reference frames.
@@deepbean Actual reality looks exactly the same in any frame, no transformations required. Because frames are imaginary and Special Relativity is a fantasy.
@@deepbean It CREATED a new reality for you, and you believe it. You do not actually see it. Time is in your head. What I say is also true.
I hope this isn't just the fog of memory, but I thought Einstein ascribed the linear aspect of the transformation to the isotropic property, the property that there is no preferred spatial direction. One obvious drawback is that now he's reaching beyond his two postulates. Aside from that, I'm not sure how the isotropic property implies linearity.
The most rigorous derivation of the Lorentz transformation that I have seen is in "The Theory of Fields" by Landau and Lifshitz.
Yeah, I think that makes a lot of sense. I suppose, when you don't favour any direction over the others, then you can't ascribe - like in my example here - which direction is x^2 and which is sqrt(x) etc; only a linear transform would preserve the isotropic property.
Landau and Lifshitz's proof is very compact and elegant. I've introduced Einstein's proof here primarily because it doesn't presuppose hyperbolic geometry and the invariance of the spacetime interval, but assuming those things, their working is far more brief!
(For anyone interested it's "The Classical Theory of Fields", Ch 1.4)
@@deepbean -- Your explanation is very intuitive!! Many books don't explain it all. They just say "clearly" it's linear and that's that. I like how you consider an x² term and clarify why it just isn't right. Then it's immediately easy to understand why an x³ term or an x⁴ will also lead to inconsistencies.
Do you have a twin paradox video? I have yet to see a correct explanation of it.
@@user-lb8qx8yl8k I'm glad you found it useful! I also felt the same when reading other proofs of this; they just represented linearity as a fact, so I thought it was important to justify it here.
Also, I am indeed planning a Twin Paradox one 2-3 videos ahead! I've found a ton of confusion circulating on the Internet about it as well.
Me again, and I would also like to tell you about the Lorentz Transformations
... I would like to explain my opinion to you by talking about " the correspondence principle ".
The correspondence principle is related to Lorentz Transformations. (and to Galileo's Transformations)
Maybe you know it, but there is something strange.
The two main Lorentz transformations are::
a) x '= gamma * (x - v * t)
b) x = gamma * (x '+ v * t ' )
The other two Lorentz Transformations:
c) t '= gamma * (t - vx/c^2)
and
d) t = gamma * (t '+ vx '/c^2)
are obtained from a) and b)
In this case it is enough to consider the two Transformations a) and b), because c) and d) depend on a) and b)
At low speeds the Lorentz factor (gamma) is a number very close to 1,
and so the two Lorentz transformations a) and b) become:
a_1) x '= x - v * t
b_1) x = x ' + v * t '
Substituting a_1 in b_1 we obtain:
x = x - v * t + v * t '
v * t ' = v * t
t ' = t
" THE CORRESPONDENCE PRINCIPLE " IS SATISFIED:
x '= x - v * t
t ' = t
(At low speeds, Galileo's Transformations are obtained)
And it is not the same, if we consider the two Lorentz Transformations a) and c)
a) x '= gamma * ( x - v * t )
c) t '= gamma * (t - vx/c^2)
At low speeds, the two Lorentz transformations a) and c) become:
a_1) x ' = x - v * t
c_1) t ' = t - vx/c^2
But if we consider large values of x, then t ' is not equal to t. (and Galileo's Transformations are not obtained)
- And the strange is that in this case it is enough to consider the two Transformations a) and c),
because b) and d) depend on a) and c)
If you are interested in this topic, here is the link to a video by Roger Anderton:
th-cam.com/video/Ew2o8KezEAw/w-d-xo.html
Thanks again for your comment Massimiliano; yes that's right, in the limit of low velocities, relativistic behaviour closely approximates "Newtonian" behaviour (I.e. the Galilean transforms).
Microphone volume levels - you have it too loud which is causing distortion and makes the video horrible to listen to. When you're quieter there's no distortion, it's only when you're louder. So turn the volume down.
You should see Green, Yellow or Red for volume levels on your recording app. For sure you're in the red.
Re edit the video with the volume reduced.
I can't re-upload this, but will keep in mind for future videos.
Infinite field speeds are possible, including the speed of nearfield light!! Fields like: nearfield gravity, magnetic field, electric field, and even nearfield light are all instantaneous, and they are completely incompatible with Relativity, which says nothing travels faster than light. The main problem is that it invalidates the Relativity of Simultaneity argument. This is because instantaneous fields propagate instantaneously to all inertial reference frames, thereby preserving simultaneity in all the frames. If you look at the Lorentz transforms and make c=infinity, then gamma equals one, and the Lorentz transforms becomes the Galilean transform, where space and time are independent and absolute, and space and time are the same in all inertial frames of reference.
Relativity is just an optical illusion, and because all of modern physics is based on Relativity, modern physics is fundamentally wrong and needs to be rethought. Relativity has a simple built in logical fallacy, and no theory based on a logical fallacy can be true, no matter how many experiments seem to prove it, or how many people say it is true. Below is a very simple logical argument highlighting the logical fallacy, using the same terminology Einstein used to derive Relativity.
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.
This argument is only the tip of the iceberg. There is much more evidence including both theoretical and experimental, so please keep reading. 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 1700s 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 has 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.
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
My brain hurts😢
A quadratic relationship does exist. I'll let you figure that one out. It isn't that hard.