Special Relativity: Length Contraction

In this video, I use the equation for time dilation that I derived in that video to derive the equation for length contraction. There is also a more qualitative explanation for why moving objects experience length contraction.

[NEO-zy]

The only video which clearly explained length contraction intuitively

[dixieflatline]

Thank you very much for the videos on the special relativity, they are much clearer than the explanations of my physics teacher!

[peternolan]

Hello Maxwell,

Excellent video including your video on time dilation.

All the best and many thanks,

Peter Nolan. Ph.D.(physics). Dublin. Ireland. I'm nearly 68.

[chenweizhi]

Haha... Finally found a simple derivation of length contraction from time dilation, thank you!

[paulg]

Best explanation of length contraction, only suggestion, use Lo, to for one frame L, t for other.

[michaelhill]

4:53 Why are we assuming the speeds are the same but not the lengths? I mean, I know this has all long been established as reflecting reality but I'm not sure what the justification for this assumption is in this derivation.

[googotygame]

Why is delta t the time for the stationary observer in the first scenario? I thought t_0 is the one for the stationary observer

[Nilcha-]

I think all problems arise due to the fact that we use light to measure distance. It's like using sound to measure distance, and not a ruler.

Now, a ruler is not possible in the universe world, so we are stuck with light.

It becomes clearer if you use sound as an example to explain this concept and avoid any math or formulas.

[syedabbas]

Tell me if I am wrong. T and L should be the measurements for the same observation. I.e at rest. T dsh and L dash are the measurements of skateboard

[rbwinn]

Here is how to figure length contraction.
x'=x-vt
y'=y
z'=z
t'=t
Einstein says there is a slower clock in the moving frame of reference.
x = x' - (-vt/n')n'
y = y'
z = z'
n = n'
n' is the time of the slower clock in S'(x', y', z', n'). (-vt/n') is the velocity of frame of reference S(x, y, z, n) relative to S'(x', y', z', n'). n = n' shows that the time of Einstein's slower clock is being used in both frames of reference, just as a clock in S that shows t is being used in the first set of Galilean transformation equations. So now we show light to be traveling at c=186, 000 ni/sec in both frames of reference according to the times of clocks in each frame of reference.
x = x', x' = cn'
x'=x-vt
cn' = ct - vt
n' = t-vt/c
The clock in S' is slower than the clock in S, and there is no length contraction.

[lovelyfairy]

thnks a lot helped me a lot....the way you explained the whole concept with simple example is jst outstanding....

[riraldi]

Relativity is a very difficult theory to be explained because we don't have a good notion of time. I have adopted a notion of time on a block universe as a sweep at constant velocity of this universe and Lorentz equation are direct consequences. See in my social f

[lalsenarath]

No need for time dilation since both observers see different set of photons!

[bontlelerato]

In your next video can you please explain Lorentz transformation

[morten]

So i'm having some trouble understanding length contraction and i'm hoping for someone to explain my issue in this video.
First of all i do understand time dilation.

Second: it makes perfectly sense when the equation is presented when speed/v is agreed is the same for both observers and the time they meassure is different hence the length would also appear different.
My issue is following.

So due to the principle of relativity both observers should see the others observers clock tic slower than it's own clock.
Let me try to elaborate by this thought experiment.
lets say that the person on the skateboard is measuring his time between point a and b, but then he ALSO take a reading on the clock on the observer he believe is moving and than he will conclude that his(the skateboard guy) clock is moving faster than the observer on the grounds clock.
So now the skateboard guy has two readings, his own clock which is moving faster and the observer on the grounds clock which is running slower due to he believes it is the person on the ground thats moving. Thats his conclusion when they meet.
And again due to principle of relativity the person on the ground also takes two measurement of his own clock and the skateboard observers clock and conclude that the skateboards guy clock is moving slower than his own.
So when they meet they cannot agree that it is ONLY the skateboards guys clock that was running slower. They should now both say that it is the opposite observers clock that ran slower.
So can someone explain why it is ONLY the skateboards clock that ran slower when they meet and compare? they should come to the conclusion that their own clock ran faster than the other observer.

Is there an actual measure of the length contraction?

[dr.junaidhassan]

Dear Maxwell, thank you so much for this excellent video!

I’m struggling big time with the length contraction explanation here:


I'll really appreciate if you might be able to help.

She says that length contraction would occur for Jane, standing at the platform. She actually used the time dilation formula and calculated that for the train to rush past Jane, it would take less time (=5.77E-07 sec) compared to that for Bob (=6.66E-07 sec) on the train. She then put this number into the distance (length) formula and said that a 100 m long train would seem to be 86.6 m long to Jane.
That is problematic because we solve the twin paradox saying that, objectively speaking, the person on a fast-moving ride would experience less (slow) passing of time than the one on the earth. But then, in the above example, why did the physicist assign less time to the stationary Jane (rather than to the moving Bob)? I understand that Bob would claim that Jane is moving and that her time would pass slowly; hence, he would assign shorter time-span (=5.77E-07 sec) to her and claim that her measurement of length would subsequently contract. But that claim is in fact wrong in light of our objective solution to the twin paradox that it is Bob, rather than Jane, who would experience lesser time.
How to solve this one? Am I missing something?

[williamwalker]

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.

*YouTube presentation of above argument: