Length contraction: the real explanation
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- Опубликовано: 4 окт 2024
- Relativity has many mind-bending consequences, but one of the weirdest is the idea that objects in motion get shorter. Bizarre or not, Fermilab’s Dr. Don Lincoln explains just how it works. You’ll be a believer.
One of the most gifted physics educators of our time!! Keep up the outstanding work Dr. Lincoln!
I finally understood the barn paradox. Math and animations were easy to understand. Thanks for another great video
I love this guy, because he is not afraid to give the derivations and you know you can trust every word he says.
I've been trying to understand special relativity all my life (I'm 65). Now, in just a dozen videos, Dr. Don has finally gotten it through my thick head. Thank you! TRIPLE the Fermilab budget, please.
I like how you put the equations in there while you're talking about it even if I don't understand the math I still get the principal excellent videos
All the math in this video is high school level, is just algebra.
hahahaha he's a con man and he got you.
Mate, why are you studying special relativity if you don't know high school Math?
@@cosmoscomputers4920 I think maybe he means that he does not know where the equations are coming from. Solving these two equations is easy... but the problem is.... they are hard to imagine.
@@dreamdiction TIME DILATION IS FULLY EXPLAINED, AS THE ULTIMATE MATHEMATICAL UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS CLEARLY PROVEN:
A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=MC2 IS F=MA. Gravity IS ELECTROMAGNETISM/energy. (The stars AND PLANETS are POINTS in the night sky.) Time DILATION ULTIMATELY proves ON BALANCE that electromagnetism/ENERGY IS GRAVITY, as C4 is a POINT that is ELECTROMAGNETIC/GRAVITATIONAL (ON BALANCE) as SPACE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Time DILATION proves that electromagnetism/ENERGY IS GRAVITY, AS E=mc2 is DIRECTLY and fundamentally derived from F=ma. E=mc2 IS F=ma. A planet AND a star thus constitute what is A POINT in the night sky. It ALL CLEARLY makes perfect sense. Gravity IS ELECTROMAGNETISM/ENERGY. ACCORDINGLY, I have ALSO fully explained the MATHEMATICAL UNIFICATION of Einstein's equations and Maxwell's equations (GIVEN THE ADDITION OF A FOURTH SPATIAL DIMENSION); AS E=mc2 IS F=ma. The Sun AND the Earth are F=ma AND E=mc2. Great. SO, ultimately and truly, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. AGAIN, time DILATION ULTIMATELY proves ON BALANCE that E=MC2 is F=ma; AS ELECTROMAGNETISM/energy is gravity. Great. Indeed, this NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. (E=mc2 IS F=ma.) Therefore, INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience; AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. SO, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Accordingly, the rotation of WHAT IS THE MOON matches it's revolution. MOREOVER, a given PLANET (including WHAT IS THE EARTH) sweeps out equal areas in equal times consistent WITH/AS E=MC2, F=MA, AND what is perpetual motion; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. GREAT !!! It ALL CLEARLY makes perfect sense. BALANCE and completeness go hand in hand. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. E=mc2 IS F=ma. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED ELECTROMAGNETIC/gravitational force/ENERGY, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE.) E=MC2 IS F=ma. Objects fall at the SAME RATE (neglecting air resistance, of course), AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. E=MC2 IS F=ma. It ALL CLEARLY makes perfect sense. Magnificent !!!
By Frank DiMeglio
Way cool, and the math isn't that tough. And you're definitely NOT wasting our time!
it was a rhetorical question buddy
I don't know, he's maybe wasting our time a little bit when he explains how to measure a stick a good two or three times before getting to the relativistic version.
He's not wasting our time, but some of this presentation is _false_ .
8:56 What you would actually _see_ of the basketball is a spherical ball, albeit with the seams strangely reconfigured.
This is Penrose-Terrell rotation, and he almost certainly would know of it, relativistic colliding nuclear particles notwithstanding.
math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html
@Kisa Vorobianinov if this was just optical effect you wouldn't be fittinv 20 meter stick in 10 metre.
Mr Lincoln, please keep these videos coming!!!!!!!!
constellationpegasus Dr. 😉👍
Please, Doctor Lincoln! (He deserves it.)
ScienceNinjaDude Then Zoltan it is.
I misunderstood length contraction until your caveat about the time of measurement in the primed frame. That, and the fact that if you take away the stick, you still have coordinates doing their thing, was super illuminating. Thank you for such a crispy clear explanation! I’m learning how current densities transform from one inertial frame to another and this was the missing piece. Many thanks! 😁☺️🙌🏽🎊
hey i am also confused about that , can you help me ? As of now I am confused why current densities
remain constant in primed frame but not in the moving elctron's frame , since in the rest/prime frame the current densities should also be changed
@@zhinkunakur4751 In understanding SPACE, what is gravity, TIME, AND time dilation (ON BALANCE), it is important is it to understand what is a BALANCED displacement of what is SPACE. ELECTROMAGNETISM/energy is gravity ON/IN BALANCE.
Consider what is E=MC2. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Consider TIME AND time dilation ON BALANCE. (c squared CLEARLY represents a dimension of SPACE ON BALANCE.) Indeed, the stars are POINTS in the night sky ON BALANCE. The rotation of WHAT IS THE MOON matches the revolution. Consider what is THE EYE, AND notice what is the TRANSLUCENT AND BLUE sky ON BALANCE. NOW, consider what is the BALANCED MIDDLE DISTANCE in/of SPACE. CLEARLY, BALANCED inertia/INERTIAL RESISTANCE is fundamental (ON BALANCE). “Mass"/ENERGY IS GRAVITY. ON BALANCE, consider what is the orange (AND setting) Sun. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE) consistent WITH E=MC2, F=ma, TIME, AND time dilation ON BALANCE. This CLEARLY AND NECESSARILY represents, DESCRIBES, AND INVOLVES what is possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE). Notice what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE. Great. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Indeed, inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/AS) GRAVITATIONAL force/ENERGY; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). This CLEARLY explains what is E=MC2 AND F=ma ON BALANCE, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !! (Consider TIME AND time dilation ON BALANCE.) Great. Indeed, consider WHAT IS THE EARTH/ground ON BALANCE. I have mathematically proven why the rotation of WHAT IS THE MOON matches the revolution, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE). Consider TIME AND time dilation ON BALANCE, AS the stars AND PLANETS are POINTS in the night sky ON BALANCE; AS c squared CLEARLY represents a dimension of SPACE ON BALANCE. (Consider what is THE EYE ON BALANCE.) I have mathematically proven what is the fourth dimension, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! I have explained why what are OBJECTS may fall at the SAME RATE.
By Frank Martin DiMeglio
I think you are not considering the observer who Co-moves with the electron can't perceive that.
The phenomenon in particle lab and acceleration of electrons is.. 🤔 Well. You get wavefronts, and the measurements at the first one, has more electric charge density, similar to the ambulance which has Doppler effect.
Now, this is an effect that happens for real. It's odd of course. And the reference frames do work. I repeat. These phenomena occur, weird but real
This channel has a strong PBS Space Time vibe and I love it, great video.
Omfg I understood everything and I'm an idiot! Dropped out of high school and lost memory of most my childhood and schooling This guy is a science/maths god! I whole heartedly believe in the adage "The only good is knowledge and the only evil is ignorance" -Socrates. You sir are a champion of good! Thank you so much! Thanks to you I actually think I could do physics! Me of all people! Your so great at teaching! ❤
💟
So..... the earth could be flat at high speed..... mmmhhhhhmmmmmmmmm.........
Oh - Don't you start with that. (-:
(But it does kind of make sense though)
Gaspar Albertengo Not for the people ON the earth, for the observer. It's like saying a siren sounds distorted for the people in the car.
@@satunnainenkatselija4478 r u indian or Russia
We are not outside that frame of reference though.
@@DoctorRocker66 the Reptilians from Nibiru think the Earth is flat... :)
Thank you, Dr. Don Fermi of Lincoln Labs!
Great explanation! The basic math really helps a lot in understanding the relations there. Just please keep up making those awesome physics videos, I really love those.
I like that Lincoln often sticks to the appropriate equation in his explanations, which is helpful in the education sector. But, for seasoned pros, we know that length is actually defined by the distance a beam of light travels. So, you have had enough of education already, you don't even need the equations any more. You know when someone is moving, the time he/she spent on moving while measuring the stick needs to be added to the equation of calculating the stick's length. Then, of course, the length of the stick will vary depending on the speed he/she travels.
Mind blown yet again. Thank you Dr. Lincoln for another great video explanation!!!!
Answer: This happens when a man enters into a cold pool of water.
Question: What is Length Contraction?
I understood that reference!
🤣🤣🤣🤣🤣🤣🤣🤣
Primed and unprimed both in the cold pool have length contraction
@@kseriousr I understood that reference
typical comment coming from the back rank of basically any classes all around the world!😅
One of the oldest but underrated channel , tho it has quality content 😟
It was an amazing,I hope it gets more views,it made it really clear
You like a real serious professor one would expect in a university talking about dry topics, but your t-shirts and the prefessional nature of your presentation reveal someone with a superior sense of humor who mastered the true art of subtly delivering the punchlines. Keep those videos comming!
i bet no other video on youtube descibes relativity like this series here.congradulations.
The way you shown things makes the math raiser. You get it to say what is needed for your explanation.
Professor Don I like your every videos it helps me a lot to understand physics again in an interesting manner. Thank you Sir. Sir kindly make a video on why scientists are facing difficulties in achieving superconductivity at room temperature.
I still got the principles while I completely didn’t understand the equation. Thanks, that’s very friendly for someone like me who doesn’t quite into Math😊
This was the best explanation of this I have seen using pre high school math!
I wish there was something similar available way back when I was at University. When we got in to tensor algebra of relativity we had probably still a rather foggy picture of what was going on as explained here. Which is evidently still true since people still promote non existent paradoxes. Many courses on advanced subjects would benefit from starting with a simple explanation like this. Quite the opposite I remember the professor talk about achieving mathematical maturity first and then getting into applications later. I think this is the wrong approach, at least for applied math and physics. In my view math is a simplified language to describe reality, so it helps to have an idea of the what You try to describe in the physical world.It is like skimming a book helps to get an overview before getting into the details.
This sounds like the basis of most arguments, one person sees/perceives one thing that the other doesn't, all the while the truth is actually perpendicular to them. Lol. Thank you, Dr. Lincoln, for your insight as always, these are a pleasure to watch.
2:18 Actually, I tried to do that a few hours ago.....
But somewhat, my derivation was:
d’=t’•√(c²-v²)
Your derivation is correct!
I have to give to you. If I don't fully get the explanation of a physical phenomenon, I always turn to Fermilab to clear it out. Many thanks!
As always, Doc, spot on! I am re-teaching myself relativity from my university physics days, and your videos are always a great addition to my studies!
for me it is the best of Dr Lincoln so far (and I've seen them all) but what strikes me is the supreme role of algebra in reaching the conclusion and how Dr Lincoln surrendered his problem to it. you might think this is obvious and simple but i still see algebra as being on top of even Relativity. sheer magic.
What would happen if you put a length contracted stick into a barn, closed the doors, then it hits the door and decelerates (assume very strong door)
The stick is longer than the barn, yet it is inside the barn and no longer subject to length contraction?
The observer who sees the stick moving but the barn stationary, sees that the stick has shrunk and can fit in the barn. Then, the stick hits the right door.
Assuming the observer could see inside the barn, of course (maybe there is a window or a larger door facing the observer that is open), then they would be amazed as they watched the stick suddenly grow rapidly and kick the other door back open. That's the primed observer.
The unprimed observer would see that the barn is shrunk initially and moving, but that the stick was stationary and longer. But remember, events that are simultaneous for one observer are not simultaneous for another.
So the unprimed observer would see the stick enter the barn, and then hit the right door. Immediately the unprimed observer would see that the stick is starting to shrink because it is now moving relative to the unprimed observer, since it is being accelerated to the left (hits the door and decelerates). The unprimed observer would then see the back door try to close but it would hit the stick and be pushed back.
So both observers would agree that the back (left) door tried to close but hit the trailing end of the stick before it could close all the way, resulting in it being kicked back open.
Well, a stick hitting a barn door at 85% of the speed of light would be pretty spectacular as teh energy released would vaporise everything in a considerable radius.
Love the barn example. Also, saying that these effects are measured during {X} experiment is really helpful. These series of videos are great!
This might explain something I have observed on Grindr...
I simply used the thought experiment from your Lorentz factor derivation.
The equations in my derivation were:
L₀=c•∆t
L=∆t•√(c²-v²)
So:
∆t=L₀/c
And now if we do some simple algebra, we get:
L=L₀•√[1-(v/c)²]
L=L₀/γ
01:19 I'm a musician, Don... I have to trust you! 🤯
Everything just clicked in the last minute of this video. What an amazing explanation!
So wierd, it says 100+ comments but I can only see about 10 and no replies to comments. My internet speed must be approaching the speed of light and I am experiencing information contraction...
I can give you a heads up, if you’re lost.
Basically, I own the Universe, now.
Dr Lincoln, you have a geology based doppelganger in Nick Zentner. You make incredibly complex subjects very accessible to laymen. AND, you have a way of communicating that is very enjoyable to watch and hear. You and Mr Zenter should be required subjects for people studying to become teachers.
Great video, great explanation. Relativity is the second most weird thing in the universe. Guess what is the first.
Boaz Augusto Matos The solution to the Teleportation noncloning theorem ,which for now, has been hidden from human knowledge by our Creator, thats truly brilliant thinking !
ScienceNinjaDude it was meant to be Quantum Mechanics.... but I forgot women...
English food ...
Belly button fluff?
My mother
8:15 ... and what we find is that the length of the stick in the primed frame is the length in the umprimed frame, divided by gamma. 8:38 And, using the fact that both observers can claim that they are stationary, this means that a moving stick is shorter than an stationary one. Now, there's one important thing to remember and that is that the shrinking only occurs in the direction of motion. There is no shrinking side to side. 8:52 This means if you start with a basketball and accelerate i to high speeds, it will look like a pancake- still round in the direction perpendicular to the motion, but flat parallel to the direction of motion. 9:05
so whats the physics of length contraction? proving it mathematically isn't saying why space time contracts. I get it mathematically ,but I still fail to see how space time contracts when a mass is moving at high speeds. how does space time contract? is it because the mass going at such speeds warps space time? if so does that mean it has a greater gravitational pull as there is more energy from the object.
Spacetime doesn't contract at all in these examples. It's just that different observers might have different perspectives on spacetime based on their relative speeds. In fact, near the end of the video, it's mentioned that you don't need a stick to derive the same effect, so mass is completely not involved. Remember: special relativity shares a lot in common with the idea that the world looks upside down if you stand on your head; it's just that instead of normal rotation, you need the math for hyperbolic rotations, which is pretty unintuitive.
As for the why question, rephrased to "why do observer's perspectives on spacetime change with speed": well, that's just the way it looks if you look closely enough. I suppose it's a fruitful philosophical or religious question, but not a particularly scientific one.
I believe that all this is intimately connected with the relativity of simultaneity. I think that having a firm grasp of that helps to understand spacetime.
The stick is made of particles. When a force acts on one end of the stick to begin moving it, the force can only be transmitted through each particle, at most, at the speed of light.
If the stick is moving near the speed of light, the particles can still only interact with each other at the speed of light. This means it still takes time for one end to affect the other.
Since the stick is going nearly the same speed as the particles can transmit the force, this means the particles will need more time to "catch up" with the particles ahead of them. Due to the fact they're moving, this also means the transmission of the force will need to happen over a greater distance in space, compared to the stationary stick.
This is why time slows down as you move faster through space. It's also why you appear to turn into spaghetti to people who aren't moving; the particles literally need to cover more space to transmit the fact you're moving so fast.
You can really think of time as being how fast your particles can interact with each other. That's why time isn't the same for everyone.
It all boils down to the fact that since photons cannot slow down, the universe must compensate for that.
I can't even see the replies
I'm so glad I found out about this channel. One should never judge a channel by its number of subscribers, or should do it the opposite way : the more subscribers, the more likely the content is for everyday people 😂
When an object travels at a high speed,does the plank length contract ?
Hamani Maka no
@@fool5541 why?
Hamani Maka because universal constants don t change no matter what happens, the object’s length contracts, but it will never be shorter than Planck length.
I really don't know but I would think it would have to otherwise you would start changing the physics observed between different inertial frames of reference. I think that Planck length is inextricably tie two things like electromagnetic force and gravitational force
@@hotelmike7722 Yes. You'd basically have "different" plank lengths for each observer. But it doesn't change physics, objects themselves are different when they're moving, and that cancels the change.
Great explanation. I have a slight issue with saying this is what you would "see" rather than this is what you would "measure". In fact a moving sphere does not look flattened. When we talk about seeing we are talking about the light rays entering the eye. Roger Penrose showed in the1950s that a sphere does not look contracted (See the wikipedia page for the Terrel rotation - also from the 1950s). What happens is that the celestial sphere centred at the observer is transformed by a Möbius map (when considered as the Riemann sphere using stereographic projection) (Note that the proper orthochronous Lorentz transformations are isomorphic to the Möbius group). Möbius maps preserve circles-and-straight-lines and stereographic projection also preserves circles, so the sphere does not seem distorted.
You are right, I called it Lorentz rotation, and it is obvious. As the ball passes, you still see a round ball, but it is rotated so you see its backside. consider th e light entering your eyes as forming what you see, not what is.
the term "simultaneous" should not be used to explain relativity
Isn't it that every observer can define and use the concept of simultaneously for events, but it may not be simultaneously for another observer?
Why? It's a relative notion.
That was totally worth the price of admission
And this person is Matt from PBS Space Time :D
It all boils down to the fact that by the time the moving object reaches the point in space where you begin your measurement, it will take the light a certain amount of time to reach your eyes or measuring device. Additionally, the object will have moved further along its trajectory by the time you measure the light coming off the tail end of it. The consequences of this differential delay in the leading and trailing ends of the measured light rays coming from the object causes a perceived distortion along the length of the object's path of motion. But like time contraction, length contraction is a function of the relativity of simultaneity and comes about only from perspectives of frame reference rather than actually altering the object's physical size characteristics.
Now when I see pancake I always ask myself - is it really flat or it is just moving on speed of light relative to me?
As they say, everything is relative from the perspective of the observer. A perfect example is when you're standing on Earth you feel no motion at all while an observer from the space station can actually see the movement. Then of course things start getting weird at near the speed of light which is what this video is trying to tackle (among other things).
This is the third video I see about this topic and this one is the most comprehensive! Thank you!
I hope you take care of your gym time.
A muon approching earth at almost speed of light, sees a flat earth. So , is earth flat ? According to the muon it is. Is length contraction a real effect, or a perspective effect? If 2 persons move away from each other, they see the other getting smaller and smaller. Nobody is getting realy smaller.
Yves Bulté a muon would decay faster than light is able to travel from the Earth to it's positon if It wants to see the whole Earth
Yves Bulté a muon can't even travel at the speed of light because it has masa
Yves Bulté Yes, someone IS really getting contracted. Who is getting contracted is relative. Each observer is correct in his own inertial frame of reference.
High-speed particles with short half-lives travel farther than they would be able to in their short lifetimes without relativistic effects. From an outside perspective, time is running slow for the particle. From the particle's perspective, the universe is "flattened", so the travel distance is shorter.
"From a certain point of view" yes, the Earth is flat. :) Vsauce has a video about it.
The math is easy enough that any high schooler who does their homework could keep up with this video. Please keep doing videos with math in it like this. People need to understand that math allows us to understand things even if we can't directly observe them.
“Physics is Everything”
Lol it feels like Trump is screaming this from his balcony. Instead of the world "everything" he prefers the world sh*t.
...Don’t know about that, but Solomon said “Vanity of vanities, saith the Preacher, vanity of vanities; all is vanity.”
Ecclesiastes 1:2 - www.biblegateway.com/passage?search=Ecclesiastes%201:2&version=KJV
A sphere will never flattened to an ellipsoid.... Terrell Penrose effect... the misconception of length contraction must be removed from the vido.
For the lazy~
Link: en.wikipedia.org/wiki/Terrell_rotation
Relevant quote: "A previously popular description of special relativity's predictions, in which an observer sees a passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong."
The Terrel Penrose effect was revisited by Robert J. Deissler in the 2005 paper "The appearance, apparent speed, and removal of optical effects for relativistically moving objects"
I do like how this all makes sense in a nerdy kind of way, and if I study it enough I may end up thinking I understand it. At least I will be confident enough so Dunning Kruger will get the best of me ;)
I wish too there would be such a person. But not found yet... jk
A lot of math for something very simple. The moving stick shrinks in all respects due to the pressure of the aether, the quantum fields, through which it moves. The aether presses on matter and the matter shortens. The observer inside the space craft also becomes shorter, everything does, proportional to the speed and the pressure the aether exerts. The inside observer still sees the yard stick as being one 6:37 yard long. The outside observer sees the space ship go by and observes that the yard stick is marked off in 36 inches but all dimensions are shorter.
Next weak: "Length contraction: the imaginary explanation"
There's a powerful analogy here between Lorentz transformations ("boosts"), and rotations in space. The latter use circular trig functions, the former use hyperbolic trig fns.
And the angle, θ (for rotations), is analogous to a boost parameter, α.
Both these parameters are unlimited; the limitation to below-light-speed comes in because the speed (β = v/c) is tanh(α), and because -1 < tanh < 1.
The speed then, is analogous to slope (= tan θ) in the rotation case. And just as slopes don't add when two rotations are combined, so speeds don't add when two boosts are combined. Instead, it is θ and α that add.
Furthermore, the length of a moving stick is analogous to a single spatial component of a rotated object.
When you rotate a cube, you don't expect the "sideways" view of one edge to remain the same length; rather, that apparent length, x, of the edge, "mixes" with another, perpendicular component, y, in such a way that √(x² + y²), the true length of the edge, remains constant.
In the boost case, you can't expect the length component, x, to stay the same; rather, √(x² - c²t²), the true length of the stick, remains constant.
For a rotation, the invariant length follows from the identity, cos² + sin² = 1.
For a boost, the invariant 'interval' follows from the identity, cosh² - sinh² = 1.
Thus we get the metric for spacetime.
The above analogy, and the mathematics that flows from it, are, AFAIK, due to the late John Archibald Wheeler.
I post them here for those who want to delve a little more into said mathematics.
Thanks for a careful, detailed, easy-to-understand look at how this works!
Fred
I think it's β = i*v/c. And those hyperbolic trig functions are from cos(arctan(i*y/x))+sin(arctan(i*y/x)). If you get a sum or a difference in there it's because you did cos(arctan(i*y/x))+i*sin(arctan(i*y/x)). Which probably means you gotta tan(pi/4-arctan(y/x)/2). Since c is m/s, I suppose it can also be m/(i*s). Which might imply a real time in velocity and an imaginary time in the speed of light.
@@thomasolson7447 No, it actually *is* β = v/c.
There's no physical meaning to "imaginary" time or space; rather, the difference between Lorentz transformations in spacetime and orthogonal transformations in Euclidean n-space, is fundamentally that the former relies on hyperbolic trig functions, while the latter relies on circular trig functions. Those two classes of trig function are mathematically related in complex analysis, but that fact tells us nothing about the underlying physics.
@@ffggddss I haven't really thought it out completely. My thoughts are that if you freeze a reference frame (with respect to time), the gamma part is the real part. The 'v' part runs perpendicular to the plane of the frozen reference frame. It also comes with its own quadratic polynomial built in. If you take a moment and go through the hyperbolic identities with 'e' expansion, you'll see that they are almost the same thing. The imaginary value is also consistent with vector addition. It is just tangent addition with an 'i.'
(i*v/c-i*m/n)/(1+i^2*(v/c)*(m/n))
No calculus needed.
(v/(i*c)-m/(i*n))/(1+(v/c)*(m/n)/i^2), also works if i is a factor of imaginary time.
There is a mistake in the derivision of the formula. The lorentz transformation of space from a stationary frame to a motion frame should be x' = gamma(x - vt), but in the video it is x' = gamma(x - vt). Also, the lorentz transformation of time from a stationary frame to a motion frame should be t' = gamma(-vx/c^2 + t), but in the video it is t' = gamma(vx/c^2 + t). However, due to the counteract of the two wrong negative signs, the eventual conclusion is correct. To sum up, the mistake here is to use the lorentz transformation formula from a motion frame to a stationary frame to wrongly calculate the transformation from a stationary frame to a motion frame. It's just some personal thoughts, feel free to argue.
Great explanation, Thanks! Imagine the accretion disk of a black hole. Incoming matter moving faster and faster, getting flatter and flatter, packing immeasurable density into the disk.
You sir, you are that such a person! We study time dilation and length contraction in my modern physics course. I find this concept fascinating. You have explained it very well! Thank you.
I always think of it this way. Distance per unit time = speed. If we both agree that light travels at the same speed, then we must disagree on how long something took or how much distance was covered in order to get the same answer for the speed of light. The very definition of speed connects time and space and Relativity show us how.
The Math and Lorentz transformation is not a problem. It's the interpretaion of this effect and the reality of contraction. I see this as a perspective outlook put into Mathematics. Once the moving stik stops, one cannot see it shrunk; it strangely (not really!) goes back to its original size. This is the key issue people want to undresatand Dr.
It makes sense that velocity would effect size because the EM fields that give us our dimensions cannot speed up. They propagate from electrons and quarks at a speed that cannot add on the velocity of the molecules. The hard part for me is that each observer only sees the other having field propagating less far.
In 1967, I read the following in a book of scientific enjoyments (published around 1900) that belonged to my great-grandmother [translation follows]:
"Érase una vez un joven llamado Frisco
Que tiraba a esgrima con gran rapidez
Y tan rápida fué su acción
Que de Fitzgerald la contracción
Redujo su florete a un disco".
Translation:
"This youngman called Frisk
Drew swords very rapidly
And so fast his action was
That Fitzgerald's contraction
Reduced his sword to a disk"
That was the first time that I met a reference to the Lorentz-Fitzgerald contraction.
I watched Professor Dave Explains and Minute Physics and still didn't understand this. They always omit the simplest part: Observers don't agree on what is "Simultaneous!" The barn analogy really made it click. Thank you!
Did it?
So, why does door 2 close before door 1 and not door 1 before door 2? That is always unexplained. That the stick would go through in one case and crash in the other is no explanation but a "make it fit to my expectation"-solution.
Shouldn't the stick be contracted when it moves towards you but expanded when it moves away from you?
You know like blue and red shift of light, like the sound of an ambulance passing you.
@@user-ut2mk6fm4y This stuff I watched 2 months ago buddy, I can't say I remember what I was able to understand then. Watch the Professor Dave Explains on Special Relativity, then General Relativity, then this video. I think I was able to grasp it after I watched those back to back.
i thought this guy was bs, but now, he has cleared my misconceptions. this guy is better than pbs.
Your explanation is so cool! Thanks! Many textbooks contain mistakes and confusion! Thanks for this wonderful video!
Well done. A good follow-on would be exploring how this is related to what happens to coordinate and proper distance in Schwarzschild geometry.
Hi Dr. Lincoln-- I know this video is from some time ago, but I just watched it hoping for a bit more insight about relativity. Good explanation of how we can use math to anticipate what we'll experience, and I followed all the math - much like the equation juggling in college physics, math, and chemistry, but at the same time I was hoping in the end for an explanation of what one might actually experience. If you could wrap up such math derivations/explanations with what it would mean to a human observer, that would be great.
To be more confusing, length is measured as distance light travels in a vacuum in 1/XXXXXX fraction of a second. It’s not a “distance” between points.
Another awesome vid. Thanks, Dr Lincoln!
I accelerated a 40 foot stick to 86% of the speed of light, put it in a 20 foot barn, and closed the doors. It really does work! Unfortunately, though, the thermal shockwave from the stick passing through the atmosphere obliterated the barn and also a 30km surrounding area was slightly vaporized.
Tetsujin: I accelerated a 40 foot stick to 86% of the speed of light, put it in a 20 foot barn, and closed the doors. It really does work! Unfortunately, though, the thermal shockwave from the stick passing through the atmosphere obliterated the barn and also a 30km surrounding area was slightly vaporized.
You should have accelerated the stick faster so that the length of the mass could have slipped below its swartzchild radius and collapsed itself and the barn into a black hole.
Sir, I really love your videos. Thank you so much for sharing and please continue.
I love the way you teach. Thank you
I had never heard it expressly said that events being simultaneous isn't preserved when you change inertial reference frames. That explains a lot.
Thank u Dr Don I certainly enjoy your demonstration ofknowledge
Great video professor Don. I had to rewind it like 10 times but it was worth the effort. I still need to watch it a couple times. But now I understand for the first time the math it's all about.
Thank you Don and team! You are awesome!
Nice explanation ! To understand, everyone must start somewhere.
there's nothing faster than the speed of light, with the exception of my finger hitting the like button when i learn that this is a USONIAN-made channel using METRIC
Inspite of being in 6th grade i understood the equations and the concept! Thank you sir
Thank you for such a nice explanation.I always had a nagging feeling about "bookish" explanation of length contraction and knew that, there is a better explanation.Thanks for making it clear.
From the unprimed perspective, the moving objects are scrunched together. If those moving objects had an electric charge, then the charges would also be scrunched. Measuring a fixed (from the unprimed perspective) area of moving charges would read a higher charge per area than that of stationary charges. This can make an electrically neutral object feel a charge imbalance when those charges are moving.
This is called magnetism.
I finally understand how Ludicrous Speed goes plaid.
True, but there is one problem which is the epistemic unkown of the one way speed of light casting doubt on our vision and our measuring equipment. On the other hand, particle accelerators seem to be the greatest evidence for the objective, physical, existence of length contraction -- since it seemingly does not require knowing one way speeds of light in order to make measurements to lengths of particle decay. And that vindicates the inductively verified nature of actual length contraction in the real world in my opinion. And perhaps it supports the idea that the speed of light might actually be constant in both directions, since predictions in the theory formulated that way match observations in the particle accelerator.
That was the best intro of Fermilab
The length contraction can be compared to an optical illusion. An analogy on a time scale easier to deal with is a variation of the ambulance siren with higher pitch approaching then lower pitch when it continue pass us and is driving away.
This is the Dopler effect. It is working even if the listener is moving. The ambulance frequency will go from high to low when it pass us on the highway.
Replace the siren with a loudspeaker. The moving vehicle is transmitting important informations about a nuclear plant which could explode if we don't follow precisely every steps.
The message is so important that any drivers on the opposite lane which cross that moving vehicle is tasked to relay what their cell phone catch to the authorities.
The voice pitch is different depending on the relative speed of the vehicles that drive on the same highway and the actual instruction that are given on the loudspeaker also arrive with different timing.
The analogy with length contraction is related to a perception. The objects do not really contracts while moving close to the speed of light. But we may never know for sure the real length if we don't have enough information about our own motion.
Good clear video as always.
Dr Lincoln, please make video about general relativity. I think you are good at explaining complicated things
The more you look at these Lorentz transformations, the more they appear to describe projections back and forth, so the Lorentz factor
gamma = sqrt ( 1 - v^2 / c^2 ) =
sqrt ( 1 - ( v / c ) ^2 )
looks suspiciously like a cosine, if you just interpret this geometrically.
So in this interpretation it's not really the length of on object that shrinks ( is contracted ), but rather the length (!) of its projection ( or its presence rather ) along the length axis that gets shorter the faster the object moves relative to the observer in that direction - i.e. the faster an object moves relative to an observer, the more it is "out of" his (length) dimension in the direction of motion.
It could also be of interest to think of time dilation instead as the result of their time arrows (!, vectors ) pointing in different directions (rotated) in a complex (2D) time plane (!) - the faster an object moves relative to an observer, the more their time arrows point away from each others - approaching 90 degress, as the speed approaches the speed of light.
Ron's outbound and return inbound time dilation from Don's point of view explains the age difference.
But, at near light speed (Ron) is red shifted into Don's past on the outbound, but blue shifted into Don's future
(Con'd) on Don's inbound trip. How does this square with the final result that Don is younger than Ron ?
I remember years ago reading Einstein's little book "The Meaning of Relativity". In the beginning he gives a thought experiment to demonstrate that Special Relativity is incomplete. It blew my mind, such a simple example. Imagine that you have a very large number of 1 meter sticks and you place them in orbit around the sun so that each one touches the next, forming the circumference of a circle of length 2 * PI * R. Now spin the ring of meter sticks to close to the speed of light. From the vantage point of the sun (or similar) the meter sticks all contract, but the distance to the ring is the same, each stick is still in contact with the others. So it is no longer 2*PI*R but it must be. What has happened to space?
frame jumping requires acceleration, but the magnitude of the time-shift depends on the delta velocity and position where the change in velocity happened.
A question from all who talk about length contraction - will we be able to observe the things around us when we are at the high speed? No, we will not see a single things, then how will we observe that length is contracted?
We will have all the thinghs to see which occupies in 3,00,000 km in a single second.... Imagine what will we see???
Great video! First video on length contraction I actually understood
This doesn't have anything specifically to do with the topic so please bear with me. A long time ago before the PC was developed, I was in science classes in junior high and high school. I was fascinated to find out that the reason for the colors in a soap film was that the waves of certain colors would cancel each other. The result was various colors all due to the interaction of photons with each other in the soap bubble. Then later we were told that energy is neither created or destroyed but only changed form. Fast forward some 40-45 years and I finally asked myself the question: What happened to the energy in the soap bubble cancellations? I know this isn't relativity, but...would you mind explaining that?
It's all nicely explained except at the end. Space does not change, the stick is shrinking in space. Distance doesnt contract body does.Just look for Bell paradox (2 rockets conected with a rope) and you will see that distance between rockets doesnt shrink.
Glad we have you, doc!
I usually gets lost, but I doesn't give up. I want something to takeaway every time I watch a Dr. Lincoln video, and I got it. "Shrinking only occurs in the direction of motion, not side to side". Ha, I'm smarter than I was 5 minutes ago!