# Take on Length Contraction at relativistic speeds

• B
That's how you measure the rest length - that is, a measurement the distance between where the two ends are using a frame in which the object is at rest.
Since LET and SR are identical mathematically and experimentally, length contraction should be observed even when you're in the frame you intend to measure its length.

Ibix
I meant be in the frame as the frame you wish to measure the length of.
You mean, you want the measuring stick to be at rest with respect to the object being measured? If you are at rest with respect to an object then you measure its rest length, yes. No one debates that. But you can easily measure something other than the rest length by using a measuring stick that isn't at rest.

As @PeroK notes, if you can't measure this somehow then it's not meaningful to talk about length contraction (or indeed time dilation, to which the same arguments would apply). And we most definitely have made measurements of time dilation - see the cosmic ray muons, for example.

Ibix
Since LET and SR are identical mathematically and experimentally, length contraction should be observed even when you're in the frame you intend to measure its length.
You really need to do the maths. It's five minutes' work to show that measurements of the length of a moving object give a length contracted length.

PeroK
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You really need to do the maths. It's five minutes' work to show that measurements of the length of a moving object give a length contracted length.
And, also, that if there were no length contraction, there would be no relativity of simultaneity either. Both ends of the metre sticks would be coincident at the same time in both frames, as would clocks placed at the ends. And everything would be synchronised.

And then you would have Galilean relativity with an infinite invariant speed.

• Ibix
Remember, if there are ants that live on the rod, and think that the clocks at both ends are in synch, then any observer who finds the rod to be contracted will find those clocks to be out of synch. The distortion of length and the distortion of simultaneity happen together.

How does one measure a stick's rest length using time stamps?

PeroK
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How does one measure a stick's rest length using time stamps?
If an object is at rest, you don't need the measurements to be simultaneous - as long as it doesn't move you can measure the rest length more easily. But, if you want to, you can make sure that the actual position measurements of the front and back are simultaneous.

The issue with measuring a moving object is that you really do need to ensure that the measurements are simultaneous in your frame. If you do it properly, the only answer you can get is the "contracted" length. The measurement cannot result in the rest length of the object. So, you cannot directly measure an object's rest length while it is moving. If you also measure its speed, however, you can infer its rest length from this and your measurement of its length. Whether you can call this a measurement of its rest length is more semantics than physics. You can certainly calculate its rest length.

• Ibix

Dale
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At this point the rather long thread hijack and mistakes by @DJ_Juggernaut is ended. If he has follow-up questions he may ask them in a new thread. Further responses to him will be deleted from this thread. Hopefully we did not lose @Simi

So, on the 1st page I was arguing that the way the measurements are taken, probably would matter!
The way @PeroK setup the measurements is very convenient for what I was thinking.
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.
In case that the detectors are at a distance of 5 mm away from the object passing by them, wouldn't them register the length of the object as being actually the proper length of the object?

Wouldn't the distance between the detectors and the traveling object affect the measured length (or the length contraction for that matter)? Like in, the further away the detectors are from the traveling object, the grater the discrepancy between proper length and measured length would get?

Let's say that we have the following disposition for the detectors relative to the direction of motion:

Setup A: length contraction detectors field 1.1.png

Setup B: length contraction detectors field 1.2.png

Would those two different scenarios measure the same length for object O, traveling at .9c, relative to the detectors?

P.S. the distance between the detectors is equal, relative to direction of movement of object O.

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Ibix
Would those two different scenarios measure the same length for object O, traveling at .9c, relative to the detectors?
Yes. Setup B is simply a silly setup that may require calculation to derive what its rest frame calls the length of the object.

A.T.
Wouldn't the distance between the detectors and the traveling object affect the measured length ...
If you place the detectors at different distances from the objects path, you have to correct for that to get the correct length. That has nothing to do with length contraction and SR, as it would happen in classical Newtonian physics too.

No idea why you are making your life so difficult with this impractical setup though.

• PeroK
PeroK
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Wouldn't the distance between the detectors and the traveling object affect the measured length (or the length contraction for that matter)? Like in, the further away the detectors are from the traveling object, the grater the discrepancy between proper length and measured length would get?
That's why I had the clunky but effective setup where the object actually hits a switch.

The fundamental point is this. If you draw a diagram of where an object is in your reference frame, then it is length contracted. How you measure the length of a moving object is up to you. But, you must somehow identify where the front and rear are at the same time.

For example, an object with a rest/proper length of ##1m## travelling at ##0.8c## will be only ##0.6m## long in your frame. If you draw a diagram where (at time ##t=0##, say) the rear of the object is at the origin, then the front of the object is at distance of ##0.6m##.

There are lots of thought experiments, like a jet of paint is ejected at time ##t=0## (in your frame) at ##x=0## and ##x = 1m##. Leaving aside the finite speed of the paint, the jet at ##1m## really does miss the front of the train.

The point is that a contracted length is a contracted length. The front and rear of the object really are closer together in your frame.

If I take Nugatory detectors array setup (garage door example) further, to perform the measurements:
So, the object (traveling at 0.9c relative to the sensors array) has detectors on both ends. In that case, we measure the distance between two sensors which detect both object's end at the same time. In this case, should I expect the distance between those two sensors to be, the proper length of the object (the length of the object in its own frame of reference)?

Last edited:
I'm trying another view, let's say that I am in a medium which alters greatly the speed of light and it is lowered to

c = 100 m/s

I have an object (with the length of one meter) traveling with 99 m/s through that medium. I setup an array of sensors in that medium which are meant to measure the length of the object.
Using Lorentz formula (L = L_0 * Sqrt(1 - v^2/c^2)) to measure the length of the moving object, I get the following measurement: ~0.141 m.
Is it safe to assume that the object's length in this medium is actually ~0.141 m? Or am I missing something and this thought experiment is not valid?

PeroK
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I'm trying another view, let's say that I am in a medium which alters greatly the speed of light and it is lowered to

c = 100 m/s

I have an object (with the length of one meter) traveling with 99 m/s through that medium. I setup an array of sensors in that medium which are meant to measure the length of the object.
Using Lorentz formula (L = L_0 * Sqrt(1 - v^2/c^2)) to measure the length of the moving object, I get the following measurement: ~0.141 m.
Is it safe to assume that the object's length in this medium is actually ~0.141 m? Or am I missing something and this thought experiment is not valid?
##c## is a universal constant. The speed of light in a medium (other than vacuum) is of no relevance to SR.

Also, the speed of light (or any signal) is not relevant to the measurement result you will get. You could set up an experiment where local observations are communicated to you by carrier pigeon. But, the speed of the carrier pigeon has no relevance to the information than the pigeon is carrying.

SR is a theory about the nature of time and space. The theory predicts certain things. E.g. length contraction. That needs to be confirmed by measurement.

You need, somehow, to get rid of the idea that the travel time of light signals has something to do with SR. It does not. Try to imagine experiments in a darkened room, where all the events are recorded by collisions, switches and time stamps. That information is sent to you electronically, where you can look at it. That way, you take all this irrelevance about the time travel of light signals out of the equation.

I see!
In that case, do we know the reason why length contraction (actual physical modification of length) occurs only in the direction of motion? Should not the whole object attempt to undergo the same transformation?
Having the contraction in the direction of motion might be interpreted as an optical / electromagnetic effect along the motion axis due to the fact that information is read by the detectors electromagnetically, at the speed of light.
That was actually the reason why I envisioned the thought experiment in a different medium.

A.T.
Should not the whole object attempt to undergo the same transformation?
Consider an object flying fast trough a narrow hole, from different frames. All frames must agree whether it fits through or not.

Having the contraction in the direction of motion might be interpreted as an optical / electromagnetic effect along the motion axis due to the fact that information is read by the detectors electromagnetically, at the speed of light.
No, length contraction is what you get after you already accounted for signal delays.

jbriggs444
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actual physical modification of length
It is not a modification of length at all. It is a modification in the coordinate system you are using to assess the length. Just as there is no physical modification of a 1 inch by 12 inch ruler when you measure it crosswise (and measure 1 inch in perpendicular width) and when you then re-measure it (and measure 1.5 inch in diagonal width). The ruler really physically is both 1 inch wide and 1.5 inches wide.

• m4r35n357
Just to add for the benefit of the OP, the "contracted length" consists of a "smeared over time" perspective of the moving object, not a snapshot!

A.T.
Just to add for the benefit of the OP, the "contracted length" consists of a "smeared over time" perspective of the moving object, not a snapshot!
What do you mean by "smeared over time"? To determine the contracted length in some frame F, you use the positions of the object's ends at the same time according to F.

@A.T. , I'm thinking that height contraction would still allow the object to fit through the narrow hole.

@jbriggs444 , so you say it's not a physical modification. Here I was a bit confused since reading some of the posts I thought it implied an actual physical change. An idea which I'm not very comfortable with, either. If I understand correctly you say that this implies a mathematical transformation, a change of basis from one coordinate system to another. So, you are talking about a mathematical model to described the phenomena.

Somehow I get the sense that you and @PeroK don't agree on this either or is just my fracture here?

@m4r35n357 in that case, considering the following experiment I stated above:

If I take @Nugatory detectors array setup (garage door example) further, to perform the measurements:
So, the object (traveling at 0.9c relative to the sensors array) has detectors on both ends. In that case, we measure the distance between two sensors which detect both object's ends at the same time. In this case, should I expect the distance between those two sensors to be, the proper length of the object ?
- because, this would be more of a snapshot than a "smear over time"? (length contraction detectors field 1.3.png)

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A.T.
@A.T. , I'm thinking that height contraction would still allow the object to fit through the narrow hole.
What about the frame of the object, where the hole is contracted, not the object?

- because, this would be more of a snapshot than a "smear over time"? (length contraction detectors field 1.3.png)
If it is not a "smear over time", then there is no "length contraction".

[EDIT] and that is as good a definition of "loss of simultaneity" as I can give!

jbriggs444
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