# Take on Length Contraction at relativistic speeds

• B
• Simi
In summary: Earth as being 0.9c shorter than it would on their home planet, even though the rod on Earth is the same length as the one on their home planet.
Simi
Hello everyone and apologize if my questions seem a bit off, please have patience with me.

I want to have the following, rather simple, thought experiment.

Let's say that we have a moving object O with the proper length L, when at rest. Let's say that object O starts moving at 0.9c (90% the speed of light).
I would like to know what's your take on the Length Contraction at the relativistic speed of object O? Is it a real length contraction which can be perceived and measured from two distinct frame of references, one from an observer A which is at rest relative to object O and second from an observer B, in a frame of reference which is in motion, traveling with the same speed with the moving object O.
Would both observer, A & B, measure the same length (a contracted length l smaller than the proper length L, l < L) for the moving object O? Or, would observer A measure the object's length as being l (contracted, l < L) while observer B, moving with object O, will measure the object as heaving its fully proper length, L.

My take is that while, observer A will measure the object O as having the length contracted, l, observer B will say that O will have its proper length, L.

"The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.

—Albert Einstein, 1911"

Please don't close my topic even if you find my questions a bit ... easy for you or on a different spectrum from the main stream opinions. I would just like to try a different perspective and conduct it as constructive topic to promote growth. I have no intent on trolling.

One never experiences length contraction in one's own reference frame.
That goes for anyone else in the same reference frame (i.e. stationary with respect to you).

So, observer A observes no length contraction in object O.

FactChecker and Simi
Simi said:
Let's say that we have a moving object O with the proper length L, when at rest. Let's say that object O starts moving at 0.9c (90% the speed of light).
I would like to know what's your take on the Length Contraction at the relativistic speed of object O? Is it a real length contraction which can be perceived and measured from two distinct frame of references, one from an observer A which is at rest relative to object O and second from an observer B, in a frame of reference which is in motion, traveling with the same speed with the moving object O.
You made a mess describing the reference frames of objects A and B because you never defined the starting rest frame. I suspect you intended object A to be at rest relative to the starting frame and B to be in motion relative to the starting frame. The way you described them, they are both comoving with (at rest relative to) object O.

As for whether length contraction is real: it is as real as the distance measured on the odometer of your car.

Simi said:
I would like to know what's your take on the Length Contraction at the relativistic speed of object O? Is it a real length contraction which can be perceived and measured from two distinct frame of references, one from an observer A which is at rest relative to object O and second from an observer B, in a frame of reference which is in motion, traveling with the same speed with the moving object O.
Would both observer, A & B, measure the same length (a contracted length l smaller than the proper length L, l < L) for the moving object O? Or, would observer A measure the object's length as being l (contracted, l < L) while observer B, moving with object O, will measure the object as heaving its fully proper length, L.
You said A was at rest with respect to O; thus it will measure the rest length. B is moving with respect to O (edit: I think - on a re-read, I'm not sure what you actually intend for B), so will measure the contracted length.
Simi said:
My take is that while, observer A will measure the object O as having the length contracted, l, observer B will say that O will have its proper length, L.
That's the wrong way round (edit: again, this statement depends on whether I've correctly interpreted your setup). I am at rest with respect to Earth as A is at rest with respect to O. An alien passing Earth in a rocket at 0.9c sees the Earth as moving at 0.9c as B sees O moving at 0.9c. I don't measure the Earth to be length contracted.
Simi said:
"The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.
"Really exists" is not a helpful term, since it implies that something could "not really exist". It either exists or it doesn't - "really" doesn't add anything. That's all Einstein's saying.
Simi said:
Please don't close my topic even if you find my questions a bit ... easy for you or on a different spectrum from the main stream opinions. I would just like to try a different perspective and conduct it as constructive topic to promote growth.
You might want to re-read the PF guidelines (see the Help link at the bottom of the page). We're not here to help you develop a "different perspective", especially as the two you've come up with so far have been obviously nonsensical. If you want to learn mainstream physics, we're happy to help.

Last edited:
Simi said:
two distinct frame of references, one from an observer A which is at rest relative to object O and second from an observer B, in a frame of reference which is in motion, traveling with the same speed with the moving object O.
This is confusing. As written A and B are both at rest relative to O and relative to each other. Is that what you intended?

My main quest is to debate and exchange ideas. I would like to develop intuition into the phenomena and maybe serve as edification for others having the same questions.

I apologize guys, indeed my question was poorly formed and caused confusion.
What I meant was that observer A was stationary relative to object O while observer B, in the same frame of reference as O.

@DaveC426913 answered my question, indeed I was expecting that the observer in the same frame of reference as O, would not register any length contraction. But, I have a question more to the point: Would the length measured by B, be equal to the proper length of O, meaning L?

In that case, would be appropriate to assume that, this is actually due to an optical effect caused by the Doppler effect of light? @Ibix, this would also answer to the "Really exists" formulation, in the sens that it is observable and measurable from a stationary point of reference but from the same frame of reference, it doesn't exists at all.

Simi said:
I apologize guys, indeed my question was poorly formed and caused confusion.
What I meant was that observer A was stationary relative to object O while observer B, in the same frame of reference as O.
This is the same redundancy you wrote before: your descriptions of the A and B are inadvertently identical. You need to learn about how to describe reference frames. Rule number 1: an object is stationary with respect to itself (a reference frame centered on itself). So when you describe an object to be in motion, it means you are describing it moving with respect to a different reference frame.

For your scenario, you didn't define/name that starting/stationary reference frame. So let's call it frame "S". Now, object "O" is moving at .9C as measured with respect to frame S. How are the other two objects moving with respect to frame S? One is stationary with respect to S and the other is moving at .9C (flying in formation with object O), right?
In that case, would be appropriate to assume that, this is actually due to an optical effect caused by the Doppler effect of light? @Ibix, this would also answer to the "Really exists" formulation, in the sens that it is observable and measurable from a stationary point of reference but from the same frame of reference, it doesn't exists at all.
This is a really bad way of thinking about it. If you are traveling in a car at 60 mph and you crash into a brick wall, you might argue that your car had no kinetic energy relative to you. But that won't prevent the brick wall from crushing the car. It's not an optical illusion any more than kinetic energy is.

Simi said:
What I meant was that observer A was stationary relative to object O while observer B, in the same frame of reference as O.
So then A is also stationary with respect to B.

Simi said:
My main quest is to debate and exchange ideas. I would like to develop intuition into the phenomena and maybe serve as edification for others having the same questions.

I apologize guys, indeed my question was poorly formed and caused confusion.
What I meant was that observer A was stationary relative to object O while observer B, in the same frame of reference as O.

@DaveC426913 answered my question, indeed I was expecting that the observer in the same frame of reference as O, would not register any length contraction. But, I have a question more to the point: Would the length measured by B, be equal to the proper length of O, meaning L?

In that case, would be appropriate to assume that, this is actually due to an optical effect caused by the Doppler effect of light? @Ibix, this would also answer to the "Really exists" formulation, in the sens that it is observable and measurable from a stationary point of reference but from the same frame of reference, it doesn't exists at all.

I think you have a number of issues.

I'm not sure you've accepted the principle of relativity that all motion is relative. Your questions are phrased in the context of an absolute motion. I suspect this is clouding all your questions on SR.

If you say "rest" length rather than "proper" length, then there is no question. An object has its proper length in its rest frame. Or, in other, an object has its proper length to observers who are at rest relative to the object.

Your questions avoiding the real issue, which is "how is length defined"? In other words, if something is moving in a certain reference frame, how does someone at rest in that frame define its length? The answer is that, since both ends are moving, you need a simultaneous measurement of the position of both ends.

If the object is at rest, then these simultaneous measurements are easy. But, if the object is moving, it's harder to organise these simultaneous measurements.

Simi
Yes @russ_watters. So. @Dale, observer A is on Earth. Object O is a rocket traveling away from Earth with 0.9c which has the proper length, L. Observer B is inside the rocket. Observer A from Earth, registers a length contraction of, l. Observer B, registers no length contraction and measures object O has having its proper length of, L.

PeroK
Simi said:
Yes @russ_watters. So. @Dale, observer A is on Earth. Object O is a rocket traveling away from Earth with 0.9c which has the proper length, L. Observer B is inside the rocket. Observer A from Earth, registers a length contraction of, l. Observer B, registers no length contraction and measures object O has having its proper length of, L.
Correct.

Now, as for whether or not the length contraction is "real". Let's say the ship is traveling to Alpha Centauri. How far away from Earth is Alpha Centauri? Hint: it's a trick question.

Simi said:
Yes @russ_watters. So. @Dale, observer A is on Earth. Object O is a rocket traveling away from Earth with 0.9c which has the proper length, L. Observer B is inside the rocket. Observer A from Earth, registers a length contraction of, l. Observer B, registers no length contraction and measures object O has having its proper length of, L.
Yes. That is right.

I'll get back guys, I have to ponder more, further on this topic. I want to extend this thought experiment a bit more.

Simi said:
I want to extend this thought experiment a bit more.
Before you do, be sure that you can properly handle this one:

You are holding a meter stick; it is at rest relative to you.
I am holding a meter stick; it is at rest relative to me.
You and I are moving relative one another, with speed .8c
We are both holding our meter sticks parallel to the direction of motion.

Using the frame in which I am rest, how long is my meter stick and how long is yours?
Using the frame in which you are at rest, how long is my meter stick and how long is yours?
Both of us will find that our own meter sticks are one meter long and the one that is moving relative to us is length-contracted to .6 meters.

Nugatory said:
Using the frame in which I am rest, how long is my meter stick and how long is yours?
Using the frame in which you are at rest, how long is my meter stick and how long is yours?
This sounds like a game 10-year-old boys used to play in the treehouse.

Or so I've heard...

phinds, Simi and PeroK
lol @DaveC426913

@Nugatory, I completely agree with your statement. Now, let's add some twist to your scenario. I argue (maybe wrongly, but this will be probably clarified in the end) that the way the measurements are conducted from each point of view, matters. How do you observe? What is the method by which you establish, from your point of view/frame of reference, the length of my stick (@DaveC426913 , please, just shut-up)? What instruments are you using? I'm taking this experiment out of the thought-experiment area into a real scenario.

Simi said:
lol @DaveC426913

@Nugatory, I completely agree with your statement. Now, let's add some twist to your scenario. I argue (maybe wrongly, but this will be probably clarified in the end) that the way the measurements are conducted from each point of view, matters. How do you observe? What is the method by which you establish, from your point of view/frame of reference, the length of my stick (@DaveC426913 , please, just shut-up)? What instruments are you using? I'm taking this experiment out of the thought-experiment area into a real scenario.

I would have a series of detectors that would record the time the front of the object and the rear of the object pass. We could assume that the detectors are ##0.1m## apart, say.

This would tell us a) the speed of the moving object (and confirm it is moving at constant speed); and b) The length of the object.

PeroK said:
This would tell us a) the speed of the moving object (and confirm it is moving at constant speed); and b) The length of the object.
Erm, not to be nit-picky, but I don't think you can get all three with your setup.
In fact, I think to get even one you must assume the other two.

DaveC426913 said:
Erm, not to be nit-picky, but I don't think you can get all three with your setup.
In fact, I think to get even one you must assume the other two.

A position against time graph gives you the velocity and acceleration. The length follows from the simultaneous relative position of the front and rear of the object; so actually you get the changing length even for an accelerating object. Surely?

PeroK said:
A position against time graph gives you the velocity and acceleration. The length follows from the simultaneous relative position of the front and rear of the object; so actually you get the changing length even for an accelerating object. Surely?
Fair enough. From your description I envisioned only two detectors. I think you'd need more to be able to distinguish, say, speed from length.

DaveC426913 said:
Fair enough. From your description I envisioned only two detectors. I think you'd need more to be able to distinguish, say, speed from length.

I'd want loadsa detectors. As many as possible!

Simi said:
I argue that the way the measurements are conducted from each point of view, matters.
Just have each observer use the same instruments in his rest frame, then the situation is symmetrical.

Simi said:
How do you observe? What is the method by which you establish, from your point of view/frame of reference, the length of my stick
The length of an object is the distance between two points where its two ends are at the same time. Because of the relativity of simultaneity, "where its two ends are at the same time" will generally identify different points when we use different frames, hence produce different lengths.

Now we just need to position enough detectors - all at rest in whatever frame we're using and all equipped with synchronized clocks (note that the clocks can be synchronized because they are at rest in that frame) - that one detector will record "front of object here" at the same time that another detector records "back of object here". The distance between these two detectors is the length of the object.

Simi
russ_watters said:
Correct.

Now, as for whether or not the length contraction is "real". Let's say the ship is traveling to Alpha Centauri. How far away from Earth is Alpha Centauri? Hint: it's a trick question.
Isn't Alpha Centauri 4.37 light-years from Earth? I don't see any "trick," unless you meant to ask how far Alpha Centauri is from the ship. An observer on the ship will measure a contracted distance, correct?

russ_watters
Freonpsandoz said:
Isn't Alpha Centauri 4.37 light-years from Earth? I don't see any "trick," unless you meant to ask how far Alpha Centauri is from the ship. An observer on the ship will measure a contracted distance, correct?
Yes, exactly.

russ_watters
Freonpsandoz said:
Isn't Alpha Centauri 4.37 light-years from Earth? I don't see any "trick," unless you meant to ask how far Alpha Centauri is from the ship. An observer on the ship will measure a contracted distance, correct?
Furthermore, neither 4.37ly nor the contracted distance is any more correct than the other. They are just measures of different things.

russ_watters
Simi said:
How do you observe? What is the method by which you establish, from your point of view/frame of reference, the length of my stick
To observe, you have to take a picture. But it won't appear contracted due to simultaneity. See here: https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.1041

DJ_Juggernaut said:
It won't. Length contraction is invisible to detectors due to simultaneity. A picture of a moving object will not appear contracted to any detector(s).
https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.1041 (Invisibility of length contraction)
That paper is talking about a different measurement and a different effect. The measurement described above will indeed show length contraction

DJ_Juggernaut said:
It won't. Length contraction is invisible to detectors due to simultaneity. A picture of a moving object will not appear contracted to any detector(s).
https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.1041 (Invisibility of length contraction)

We are talking about measurements of length, not the optical effects when an object is traveling at near light speed. The arrangement of a linear series of detectors in this thread does not lead to the Terrell effects you have linked to.

Length contraction is also invisbile if you are in a darkened room and you detect the movement of an object by physical contact with detectors. So, you can measure length contraction, even if you never see the object.

DJ_Juggernaut said:
It won't. Length contraction is invisible to detectors due to simultaneity. A picture of a moving object will not appear contracted to any detector.
https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.1041 (Invisibility of length contraction)
Right, a picture won't show anything That's why we need multiple detectors, one at the event "nose was here at at time T" and the other at the event "tail was here at that time T". Now we don't have a picture but we do have two points where the two ends of the object were at the same; the distance between these points is the ocntracted length.

DJ_Juggernaut said:
To observe, you have to take a picture.
You do not need to take a picture.

Much of the discussion above about multiple detectors is based on an idea in one of the early chapters of Taylor and Wheeler's "Spacetime Physics": A reference frame is modeled as as an infinite lattice of detectors with synchronized clocks, each recording only what happens at the point where they are. Measurements are carried out by collecting these recordings at our leisure and then analyzing them after the fact; there are no light travel delays to correct for.

Simi
Nugatory said:
You do not need to take a picture.
You may not need a picture but you need some EM signal to activate a measurement. How do you initiate a measurement?

DJ_Juggernaut said:
You may not need a picture but you need some EM signal to activate a measurement. How do you initiate a measurement?

You could do it with sound. You could do it with a physical probe: measuring the oil in your car. Something could flick a switch. In fact, the detectors in this thread could be switches that the object collides with and stops a clock.

Also, in physics, a measurement generally (as opposed to a "raw observation") takes into account factors such as travel time of the signal. If you say: event X took place at time ##t##. you do not mean that you received a signal about event X at time t. That's actually fundamental to classical physics. Although a lot of people believe that it's the basis of SR!

PeroK said:
You could do it with a physical probe:
Say you have two probes at each end of a moving stick, the flick will be simultaneous in the stick frame. Non-simultaneous for someone not on the stick. Therefore, the lengths are the same in both frames. Ergo you can't detect length contraction.

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