Take on Length Contraction at relativistic speeds

[PeroK]

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.

There are a lot of ways to do it. A simple, if slightly clunky approach is:

The object has something at the front and back that flicks a series of switches. The switches record the time they are impacted by the front and the rear. Two time measurements for each switch.

That is then an elementary record of time that the front and rear pass each switch/detector.

If two switches are hit simultaneously in the lab frame, then that represents a simultaneous measurement in that frame, hence a measurement of length in the frame. The non-simultaneity in the object's frame is not an issue in the lab frame.

If two switches are hit simultaneously in the object's frame, then that represents a measurement of the distance between the detectors in the object's frame.

 

[Nugatory]

You may not need a picture but you need some EM signal to activate a measurement.

Not necessarily, although most practical detector designs will have some electronics in them somewhere. However, this is all besides the point because the essential thing is that we are using different detectors at the nose and at the tail so are not relying on any transmission between the two.

How do you initiate a measurement?

Here's one way of going about it.
Both detectors are standard interrupted-beam obstacle sensors, similar to the one that I installed myself on my automatic garage door. The detectors are constructed identically and placed across the path of the moving object: a light source on one side of the path of the moving object sends a narrow light beam perpendicular to that path. A photodetector on the other side of the path will receive that signal as long as the object is not in the way; and whenever the light appears or disappears will print out a slip of paper with a timestamp and either the word "ON" or "OFF" according to whether the light appeared or disappeared. We can gather up these slips of paper after the object has passed and see what they tell us.

To measure the length of the object I position my detectors in such a way that one detector records an OFF event with the same timestamp as an ON event recorded by the other detector. That gives me my simultaneous measurement of the position of the two ends of the object, and the distance between the detectors is the measured length of the moving object in the frame in which the detectors are at rest.

(It's actually possible to do this measurement with a single detector, but that involves calculating where the front of the object is at the same time that the back of the object is detected. This two-detector setup makes it very clear that we are directly measuring the distance between where the ends of the object are at the same time).

(The light delay for the signal moving between the path of the object and the detector is irrelevant for two reasons: first, in principle it can be made arbitrarily small; and second, the delay is the same at both detectors and independent of the speed or length of the measured object. It certainly does not involve any of the complexities discussed in the APS article you cited above).

 

[PeroK]

PS everyone is going to agree that you don't see "raw" time dilation if a clock is moving away from you or towards you. This is simply because you have the Doppler effect in addition to time dilation. But, you can measure the dilation of a moving clock with two observers - or by taking the light travel time into account.

Likewise, what one observer sees directly of a fast moving object is complicated by light signal travel times. In that respect, no one observer will ever "see" pure length contraction.

But, experimental physics and the concept of measuremnt goes far beyond the raw observations from a single source.

 

[Nugatory]

Mentors' note: An off-topic digression on exactly what counts as a "measurement" or "observation" of time dilation and lebgth contraction has been removed from this thread. Please don't reopen that particular rathole - it's unhelpful and unwinding it makes unnecessary work for the mentors.

 

[DJ_Juggernaut]

That gives me my simultaneous measurement of the position of the two ends of the object, and the distance between the detectors is the measured length of the moving object in the frame in which the detectors are at rest.

A simultaneous measurement is not simultaneous to a moving frame. The length measured will be the same. You cannot detect length contraction due to relativity of simultaneity.

 

[Nugatory]

A simultaneous measurement is not simultaneous to a moving frame. The length measured will be the same. You cannot detect length contraction due to relativity of simultaneity.

It is precisely because of the relativity of simultaneity that the technique I describe yields the contracted length. The two measurements are simultaneous in the frame in which the detectors are at rest, and therefore identify where the ends of the object are at the same time in that frame. The two measurements are not simultaneous in the frame in which the object is at rest and the detectors are moving (in that frame the nose detector is not unmasked until after the tail detector is masked).

 

[Ibix]

A simultaneous measurement is not simultaneous to a moving frame.

True, but irrelevant. If I want to measure the rest length of the rod, this is relevant. But we're deliberately measuring a non-rest length.

The length measured will be the same.

Can I suggest that you actually do the maths for an array of interrupted-beam sensors as Nugatory describes? Actually, a plane light source at y=+δ that emits a flash of light at t=-δ/c and a large photographic film at y=-δ, where δ is very very small, is easiest to model. The length measured this way will, indeed, be length contracted.

You cannot detect length contraction due to relativity of simultaneity.

In the rod's rest frame, no you can't. In any other frame, yes you can.

 

[DJ_Juggernaut]

It is precisely because of the relativity of simultaneity that the technique I describe yields the contracted length.

Your technique is omitting something. I will take some time to think about it.

 

[PeroK]

Your technique is omitting something. I will take some time to think about it.

There is a fundamental flaw with your argument. If you really could never measure length contraction, then it literally would not exist. Physics and SR in particular deal with what you can and do measure. The theory predicts it and a measurement must support it and show the predicted result.

Length contraction in SR is not some abstract mathematical function in the background that has no direct bearing on reality. The contracted length is literally what you measure in that frame.

If you measure the same length as in the rest frame, then there is no length contraction - by definition. Length is what you measure. It's not only an abstract concept in the theory.

Either, therefore, you are claiming that length contraction is wrong; or you are claiming that physics generally does not have a direct relation between the theory and the experiment?

Can you confirm your stated position?

 

[DJ_Juggernaut]

Can you confirm your stated position?

My position is that to measure the length of an object you need your detector to be on the object you intend to measure. I am still thinking about his technique. I will respond to it later.

 

[Ibix]

My position is that to measure the length of an object you need your detector to be on the object you intend to measure.

Huh? Why on Earth would you need that? How could you even define the length of a gap between two objects (possibly in motion with respect to each other) if that were the case?

 

[DJ_Juggernaut]

Why on Earth would you need that?

For it to be a direct measurement.

 

[Ibix]

For it to be a direct measurement.

Would you mind answering the other question in my post:

How could you even define the length of a gap between two objects (possibly in motion with respect to each other) if that were the case?

 

[DJ_Juggernaut]

Would you mind answering the other question in my post:

I meant be in the frame as the frame you wish to measure the length of.

 

[Nugatory]

My position is that to measure the length of an object you need your detector to be on the object you intend to measure.

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.

 

[DJ_Juggernaut]

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]

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.

 

[1977ub]

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.

 

[DJ_Juggernaut]

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

 

[PeroK]

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.

 

[m4r35n357]

See here: https://journals.aps.org/pr/abstract/10.1103/PhysRev.116.1041

Needs an account to read.

 

[Dale]

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

 

[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.

 

[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]

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 $1m$ traveling 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.

 

[Simi]

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)?

 

[Simi]

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]

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.

 

[Simi]

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]

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!