Length Contraction (Special Theory of Relativity)
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- Опубликовано: 12 июл 2024
- What is Length Contraction? How to obtain its formula from Lorentz transformations?
In this video I talk about one of the most surprising consequences of the two postulates of Special Theory of Relativity, i.e. Length Contraction, also known as Lorentz Contraction. When two observers are in relative motion, they measure the distance between two points to be different. As a result, moving objects appear to contract along the direction of motion, with respect to an observer at rest. This can be easily demonstrated via the lorentz transformation equations.
We will also compare the extent of Length contraction at various speeds, and I will also mention one experimental observation that is directly related to the concept of length contraction.
00:00 Introduction
02:04 What is Length Contraction?
04:51 Derivation using LT
13:43 Conclusions
#SpecialTheoryofRelativity #STR
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PLAYLIST ON Special Theory of Relativity
• Special Theory of Rela...
-----------------------------------------------------
1. History of Special Relativity ► • History of Special Rel...
2. Michelson Morley Experiment ► • Michelson Morley Exper...
3. Special Theory of Relativity ► • Special Theory of Rela...
4. Time Dilation (Thought Exp) ► • What is Time Dilation?...
5. Length Contraction (Thought Exp) ► • What is Length Contrac...
6. Lorentz Transormations ► • Derive Lorentz Transfo...
7. Relativity of Simultaneity ► • Relativity of Simultan...
8. Can you prove E=MC² ► • Can you PROVE the most...
-----------------------------------------------------
9. Special Theory of Relativity ► • Special Theory of Rela...
10. Length Contraction ► • Length Contraction (Sp...
11. Length Contraction of Inclined Rod ► • Length Contraction (& ...
12. Time Dilation ► • The Mind Bending Predi...
13. Muon Decay Experiment ► • The Mind-Blowing Proof...
14. Relativistic Velocity Transformations ► • Derivation of Relativi...
15. Speed of light in moving medium ► • Speed of Light in a mo...
16. Relativistic Doppler Effect ► • What is Relativistic D...
17. Relativistic Mass? ► • What is Relativistic m...
18. Relativistic Kinetic Energy ► • Relativistic Kinetic E...
19. Relativistic Force ► • Relativistic Force
20. Relativistic Energy & Momentum ► • Relativistic Energy an...
21. Magnetism arises from Relativity ► • The Hidden Connection ...
22. GATE Physics question ► • GATE Physics: Problem ...
23. TIFR Physics question ► • TIFR Physics: Problem ...
24. Question on Volume contraction ► • Volume Contraction in ...
25. JEST Physics question ► • JEST Physics: Solving ...
26. NET Physics question ► • CSIR-NET Physics Probl...
27. Spacetime Invariant Interval ► • SPACETIME Interval & i...
28. Minkowski Spacetime ► • Minkowski SPACETIME, H...
29. Eucledian Space & Minkowski Spacetime ► • 5 Main Differences b/w...
30. Spacetime Diagrams ► • Time Dilation, Length ...
31. Four Vectors in Relativity ► • What are FOUR VECTORS ...
32. Doppler Effect using 4-vectors ► • How to use 4 VECTORS t...
33. Compton Effect using 4-vectors ► • How to prove Compton e...
34. Particle Decay using 4-vectors ► • Particle Decay in Rela...
35. (SHORTS) Does Light experience time ► • Does light photon expe...
36. (SHORTS) Light for moving observer ► • What is the speed of L...
37. (SHORTS) Nothing can travel faster than light ► • Why nothing can travel...
38. (SHORTS) What is farther away ► • What is farther away, ...
Length Contraction of Inclined Rod ► ruclips.net/video/D53-VROc01A/видео.html
Relativity is just an optical illusion and Galilean Relativity is the correct form of Relativity. The proof is that instantaneous fields are known to exist: nearfield gravity, electric field, magnetic field, nearfield light, and quantum entanglement, which are completely incompatible with Relativity. Even light itself is instantaneous in the nearfield and reduces to the speed of light in the farfield. Inserting c=infinity into the Lorentz transformations, yields the Galilean transformations, where time and space are absolute and not interdependent, only the present exists, the past is gone, and the future is yet to be. Also in Galilean Relativity, time is synchronized in all inertial frames of reference. If a moving object is observed with speed c farfield light, Relativistic effects will be observed, but they are not real, and can be proven by changing the frequency of the light and observing the moving object with instantaneous nearfield light, where no relativistic effects will be seen.
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.
*RUclips presentation of above argument: ruclips.net/video/sePdJ7vSQvQ/видео.html
*Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145
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This is one of the best videos I have ever come across. The clarity and ease with which you explain these complicated topics is simply mind blowing.
You should tell about the laplace transformation
Laplace
Man I learnt so much about relativity from you than any other youtuber! Thank you 🙏
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Thank you so much. Your lecture helps me so much to comprehend this phenomenon.
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🎉 sensational. Explained so well ( or as Dirac would say “ very satisfactory “.
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Length contraction and time dilation both are 2 v imp topic for us...so wr should know about this and you made it easy and simplefor us
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Well explained. I noticed only a few mistakes and one confusing formulation:
• At 0:34, you should not speak of “high velocity”, but high _speed_. (It does not make sense to speak of a vector as being “high”/“large”.)
• At 2:10: Spacetime does NOT “[stretch] and [distort]” here (and it is/has not a “fabric”). Instead, the constancy of the speed of light (in vacuum) leads to the model of spacetime (the Minkowski metric and other, curved spacetime metrics) in the first place.
• From 16:42, the label of the vertical axis of the diagram (“L₀/L”) is wrong. As L₀ is the proper length, which does not change, and the shown value *decreases* as the speed (given in units of c) *increases*, the vertical axis, where the values increase upwards, should be labeled “L/L₀”.
Finally, at 11:20, the statement along the lines “If I am at rest relative to the rod, I can measure its length by measuring the coordinates [of its end points] at different times. No problem.” was confusing at first. We may only do that if we assume that the proper length of the rod does not change in-between (which it certainly could, e.g. by thermal expansion). So (it is better to say that) in *all* situations a length is defined by the difference of the coordinates of the end points at the same time, and that it is the relativity of simultaneity that leads to "length contraction" instead. (This can be easily demonstrated in a Minkowski diagram.)
13:51 sir if we use inverse Lorentz transformation (x=x'-vt') gamma then the result comes opposite that is length Dialiation ... Why? Or
Why dont you solve it from ∆L=xb -xa... And put the value of xa, xb (from inverse Lorentz transformation) in ∆L
Love u sir
Epic
Sir thank you so much.before your lecturer I have a doubt that the frame is in motion then the length measured by observer in the moving frame is not rest length.but now I clear.thank you sir.
Hi, great work as usual, did you read about that muon particle example in Richard Feynman's book: Six Not So Easy Pieces ? I had recently read this example there.
Thanks a lot sir for making topic clear in my mind
at 11:28 the best explanation why the observer has to measure the moving things simultaneously, not measuring today then measuring the leftover a month later, or the rod will be too long.
No it isn't. It's obvious that you can't measure one end now and the other a bit later. You dont need relativity to tell you that. The length contraction is not real.
Could you explain pole and barn paradox?
Sir, which books you are using for STR?
Sir, এটা একটু clear করবেন যখন object Rest এ আছে আর Observer v velocity নিয়ে moving Frame এ object এর থেকে দূরে সরে যাচ্ছে? তখনও কি formula L= L০ √{1-(v/c)^2} হবে?
Hi sir..!
Can gravity also cause length contraction..?
its answer would be very relevant for me.. 😊
So nicely explained, but I didn't understand the example u gave, is the particle is "rod" or the distance between atmosphere and sea? Obviously the particle must be the "rod" as it's traveling 98% of C so the length of the particle should've contracted!? Isn't it or m I wrong please someone explain it to me as I m so dumb to understand it very well on this particular example
will length contraction and time dilation occur in radiation(EM wave) free space?
My answers is "No"
as there is no need to maintain the speed of EM wave(C) inside a radiation free space by stretching space-time fabric.
You are basically saying that the frame 2 containing the rod and observer 2 is at rest and the lab frame 1 containing the observer 1 is moving relative to frame2. Hence observer 1 (thinking that he himself is at rest) will see the rod as being shorter than how observer 2 sees it. My question on this model is: in practice, how will observer 1 of frame 1 measure the rod of frame2? It seems like observer2 will do the measurements and calculate the contraction using your equation and give the result to observer 1.
Also, I am not sure if it is viable to use Lorentz Transformation equations for proving length contraction because length contraction is built into these equations.
That's what I was getting at This is just circular logic. Without telling us /how/ these measurements are made, the whole video tells us nothing. If I make a measurement of a vehicle traveling past my house, then I will get a shorter or longer length, depending of the order in which I make the measurements. This is obvious. If I make the measurements simultaneously, I'll get the /right length/. At close to light speed, the light travel time has to be borne in mind. Compensating for this, I will get the real length again. If I didn't compensate for light travel time, then my experiment would be invalid.
I can't see anything non obvious here
13:51 sir if we use inverse Lorentz transformation (x=x'-vt') gamma then the result comes opposite that is length Dialiation ... Why? Or
Why dont you solve it from ∆L=xb -xa... And put the value of xa, xb (from inverse Lorentz transformation) in ∆L
Im in the 11th grade going into algebra 2 and I was able to sort of understand this, Im trying to discover more about black holes lol.
But sir plz need an answer
Sir at the initiation of vedio u explained that length contraction APPEARS and doesn't actually happen, so how can atmosphere shrink for so called meons?
Sir plz answer
It does not "appears" but actually happens but it's different for different observers
Like for muon it's stationary but it's surrounding is moving so the length of surrounding contracts
@@furious7346But if they are 'observing' and not interacting with it, then all that is being described is an optical effect If it 'really' happens to an observer, then what is it, beyond observation that actually happens.
There is nothing to write home about here.
Sir what about the observer who is in the state of rest w.r.t S' , what he is going to observe -
1.The length of rod remains same (i.e. proper length) or
2. The increase in the length
( Due to obtained relation).
Pls tell..., because mathematically the length w.r.t. S' increases.
The observer in s' frame will measure proper length because in its own frame length is not changing.i hope I am correct
when object moving on angle ∆ than then what is the Lorentz Transformation please make a video sir
Next video - will upload tomorrow :)
Sir aap bhot aacha content provided karva rahe ho pen English mein hi kyo .....
Please 🙏 hindi mein bhi kuch toh provided karvaeye
I have some doubt in identifying proper length and relative length plz someone help me to clear it
C is constant but not the same for all observer.in our earth gravity frame that is 3×10^8 but not other different frame
No, it's still 3e8 m/s in any frame. It's just the the two definitions of metre and second will be different if these two frames share two events in common.
The correct equations for relativity are these.
x' = x - vt
y' = y
z' = z
t' = t
The reason why scientists could not reconcile these equations with the results of the Michelson-Morley experiment can be seen in the last equation, t'=t. If t represents GPs time on the surface of the earth, then t' cannot be the time of a slower clock because scientists were representing the transmission of light by x = ct and x'=ct'. Since x was a longer length than x', x' could not equal ct' if t'=t. What the equations are saying is that the time of a clock on the surface of the earth is being used in both frames of reference. If there is a slower clock in the moving frame of reference, as Einstein theorizes, then these equations say nothing about the time of that clock. So scientists began to use Lorentz"s equations because they showed x=ct and x'=ct'. But scientists had not considered the axioms of algebra which show that the time of the slower clock can be shown by the Galilean transformation equations. What is required is another set of Galilean transformation equations with different variables for velocity and time as shown by the time of the slower clock. The inverse equations then would be
x = x' - (-vt/n')n'
y = y'
z = z'
n = n'
n' is the time of the slower clock. (-vt/n') is the velocity of frame of reference S relative to frame of reference S' according to the time of the slower clock that shows n'. The equation n = n' shows that the time of the clock that shows n' is being used in both frames of reference. So now instead of x=ct and x'=ct', we have x=ct and x'=cn'.
x'=x-vt
cn' = ct -vt
n' = t-vt/c = t-vct/c^2 = t - vx/c^2, which is the numerator of Lorentz's equation for t'. This part of Lorentz's equation is why n' is less than t. The denominator of Lorentz's equation causes the length contraction and is unnecessary if we are using the Galilean transformation equations because the Galilean transformation equations have no length contraction.
So, considering the orbit of the planet Mercury, which was one of the first proofs that Einstein's equations were correct, if we compare the value for n' from the Galilean transformation equations with t' from the Lorentz equations at 30 mi/sec, the speed of Mercury in its orbit, we get a result that agrees with Lorentz's result for t' to several decimal places, but differs from the result obtained from t' in the Galilean transformation equations, which Isaac Newton used in his calculation of Mercury's orbit. We can also apply this principle to the other planets of the solar system. Earth has a speed of 20 mi/sec in its orbit, which gives it a faster time for a clock on earth than for a clock on Mercury. In like manner the outer planets will have faster rates of clock time than Mercury and earth because they are slower in their orbits than the inner planets. We could also apply this principle to atoms and molecules, but scientists will not consider it. So we are stuck with an explanation of relativity that is a great deal like Ptolemy's explanation of the orbits of planets, which he described as epicyclical orbits around the earth instead of elliptical orbits around the sun. Scientists were slow to abandon Ptolemaic astronomy because Ptolemy's complicated equations were fairly accurate in predicting the positions of the planets in the sky. Scientists will also be slow to use the correct equations for relativity again, even though it has been explained to them for the last fifty years. I first thought of the beginnings of this idea when I was in physics class in high school. I have attempted to discuss it with scientists without success since that time. Their responses to this information are usually insults and profanity.
Believe me sir, No one can explain physics like you. Can I get your mail id sir?
It is not clear whether this is a complement or not.
Seems like rules of a simulation to me 😅
Sir aap ka sb pdhaya hua samajh me aa gaya lekin ek jagah abhi bhi doubt hai gama ka value me -1/2power hai aap to sirf 1/2ka power lekar baitha die. Or sabhi teacher yahi padha rahe hai galat salat
Beta, power me -1/2 hi use kiya h
@@FortheLoveofPhysics thank you sir mai ye topic chor dia tha samajh me nhi aane ke karan lekin aapke reply karne par mai video phir se dekha or samjhme aa gya. Thanks again sir
23 000 vues and only 900 likes #conclusion too many dump students watching a good teacher
Your conclusion. My conclusion is that lots of people came here looking for answers but found out nothing. This video explains nothing that needs relativity. It says it's not an optical illusion, but then goes on to talk if what observers will :see:.
@FTFE brought me here..
I'm not following this at all. I've known the Lorentz formula since forever but I can't understand what it's actually measuring.
Every explanation I ever watch has people saying 'blah..blah observer in reference frame sees length shortening in moving frame'.
What exactly do we mean by 'see' here ? If we're talking about literally seeing both ends of the rod in the moving frame, then the light travel time is obviously going to be longer for the distant point. That's obvious. You don't need relativity for that !
If the usage of 'see' is not lizeral, then how is the stationary observer supposed to make these measurements anyway ?
This seems to me to be the perfect definition of an 'optical illusion' but this guy insists it isn't.
If it's only an artefact of measurement, then why are we even interested in it ?
I am still confused and this video doesn't help.
What +is+ it that contracts and for whom?. Talking about 'seeing' things at near light speed doesn't help.
Length contraction is a very difficult subject and you have attempted to explain it. Unfortunately you resort to mathematics and everyone looses their feeling for it. You make a very big mistake in your video though. You mix up two words 'APPEAR' and 'MEASURE'. Length contraction according to special relativity is not due to 'appearance': it is due rather to CALCULATION. Why? you may ask, well I shall tell you. If an object has a component of velocity toward you it will appear ELONGATED because the light you receive from the front of the object is more recent in time that the light you receive from the back of the object (which is further in the past). When an object passes you then the converse will be the case and the object will appear compressed (such as if you were to take a photo of it). Length contraction only occurs if you work out the length taking into account the speed of light and the speed of the object. In other words: it is a result of a calculation NOT the result of a direct observation.
The underlying physical phenomena of length contraction is quite interesting. Those of you who know a little physics will have heard of the inverse square law for most forces, including gravity and electrostatic forces. The force between two electrons, for example, relies on the distance between A and B and the distance between B and A. You might say " wait a minute, these two distances are the same. But here is the crucial point: A actually sees B as it was some time in the past and B sees A as it was some time in the past. If A is one end of the stick and B is the other end of the stick then A and B CANNOT begin moving at the same time since A and B cannot communicate instantly. So A is zooming toward B and B does not realize it. It is only after light reaches B with the message "A has started moving" that B begins to move. BUT there is a subtle thing that I left out. B is also giving of signals. So as A approaches B it realised that it is too close to B. Eventually a sort of equilibrium is established that results in a length that is predicted by the length contraction formula. The only way to appreciate this is to spend a few weeks drawing diagrams and puzzling over it.
Now THAT is a more tangible explanation. Like me, you get the confusion between 'see', 'appear', and 'measure'.
Ate you therefore saying that length contraction is 'real' simply because the end doing the pushing hasn't managed to communicate this fact to the other atoms in the stick yet ?
Whenever I see any explanation of this phenomenona, I just suppose the whole thing is an ideal solid, and I'm not supposed to be thinking of forces etc.
Yours is the first time I gave heard it explained that way. It now makes sense to me how that 'two rockets connected by a string will snap' experiment: because they can't move as one homogenous unit: even a hyper stiff material will take a finite time for one end to know what the other is doing ?
Respected sir,
I request to you,Please make a video series on 𝔾𝕖𝕟𝕖𝕣𝕒𝕝 𝕥𝕙𝕖𝕠𝕣𝕪 𝕠𝕗 𝕣𝕖𝕝𝕒𝕥𝕚𝕧𝕚𝕥𝕪
That topic is too difficult for a you tube video. It took 10 years for Albert Einstein to get from special relativity to general relativity and I really don't think a video will help at all. You might well be fooled that you understand it - but honestly you won't. You probably require at least 4 years of university education in mathematical physics to understand it.
@@SK-ow4vw no you think tooo much about physics it's just simple subject (without any mathematical theories)
@@SK-ow4vw and above 2 topics are easy to understand
@@SK-ow4vw with very simple logic
@@SK-ow4vw I think you have been fooled by someone
Thank you very much sir ❤❤