B Take on Length Contraction at relativistic speeds

[Janus]

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.

Thanks @PeroK . Going once more thorough the comments, I saw @Nugatory explanation:But, doesn't this contradict with the bellow statement?

I'm having troubles seeing those statements as non-mutually exclusive.

Well, but I guess @Ibix's last comment cleared things out for me.

This is what I was not understanding actually, the physical change of the object length. No I get it, it's not an actual physical length change but a measurement of length in a different system of coordinates. A transformation applied to the mathematical model which reads different values from a different points of view.

That's great, so the physical properties of the object remain unchanged no matter what the speed. This is perfectly acceptable.

Still, reverting back to what @Nugatory said earlier, shouldn't a real world array of detectors like the ones that he described, register the proper length for the moving object?
At least, I see no reason as to why the detectors would measure anything else but the proper length in any situation (since the physical properties of the object remain unchanged no matter what the speed).

Consider the following diagrams. The gap between the black objects is the distance between our "detectors" and the red line the object whose length you are measuring.
The top image is when the object is at rest with respect to the detectors. The detectors measure its length by noting how it lines up with the gap (the green dotted lines). It is obviously longer than the gap
The second image is for when the object has a significant speed relative to the detectors. It has It's proper length has not changed, But it is rotated such that its ends now fit between the green lines. By the detector's measurement of "length" is is shorter.
The trick here to realize that "up: and "down" in this diagram represents time and not spatial distance. A separation along the vertical direction is a measurement of a time interval. So if you think of length contraction as a rotation, it is a rotation in space-time and not just space. The only "length" the detectors can measure is the in the horizontal direction, to measure in the vertical direction, you would need to use clocks.

Think of it like trying to fit an object through a doorway. In the top image both ends try to go through at the same time and it won't fit. In the second image, it is rotated so that one end goes through the door first, and then the other, and it does fit through the doorway.

 

[Ebeb]

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[Simi]

Very nice explanations.

So, considering all that you have said, if there's no physical change of the object's properties/length in the real world, this means that Length Contraction represents object properties translated from the 3D model into the 4 dimensional space-time coordinates system, where you indeed will have different measurements.
In this case, having an array of detectors in the Atacama desert at a distance of 1 mm away from one-another, and an object passes over the detectors with 0.9c (the object has a switch at the end and one at front) activating with both of the switches, simultaneously (in the array frame of reference) two detectors, the distance between those two detectors will be the proper length of the object. Though, if translated in the 4D space-time model, this will measure a Length Contraction.
So you never lose Length Contraction, you don't lose SR, you just have to translate the experiment in the mathematical form of a space-time model to have different readings, which makes sense in my mind. I mean, it was never meant to convince that length changes at relativistic speeds rather it is a different reading in a 4D space.

 

[jbriggs444]

In this case, having an array of detectors in the Atacama desert at a distance of 1 mm away from one-another, and an object passes over the detectors with 0.9c (the object has a switch at the end and one at front) activating with both of the switches, simultaneously (in the array frame of reference) two detectors, the distance between those two detectors will be the proper length of the object.

Let me get this straight.

You have an array of detectors. You have an object with a front end and a back end. The object is in motion. We are taking the array of detectors to be at rest.

You have a switch at each end of the object. I take it that these switches are attached to high powered lasers. When switched on, the lasers trigger the adjacent detector.

You trigger both switches, simultaneously in the rest frame of the detectors. The result is to trigger two detectors simultaneously, again in the rest frame of the detectors. The distance between the two triggered detectors is the length measurement.

This procedure measures contracted length, not proper length.

 

[A.T.]

In this case, having an array of detectors in the Atacama desert at a distance of 1 mm away from one-another, and an object passes over the detectors with 0.9c (the object has a switch at the end and one at front) activating with both of the switches, simultaneously (in the array frame of reference) two detectors, the distance between those two detectors will be the proper length of the object.

You failed to specify in which frame you measure the distance between those two detectors. If you meant "distance between those two detectors in the rest frame of the detectors", then you are wrong: it will be the contracted distance of the object.

This has been explained many times in this thread.

 

[Simi]

I know that length contraction at relativistic speeds has been proven in the lab, experimentally, using subatomic particles and I guess nobody can argue the results. I for one, don't.
But, did we had any attempts of proving length contraction, experimentally, using macro objects (not quantum objects)? Did we actually observe this or it's an extrapolation from the quantum world and a deduction?

 

[jbriggs444]

But, did we had any attempts of proving length contraction, experimentally, using macro objects (not quantum objects)? Did we actually observe this or it's an extrapolation from the quantum world and a deduction?

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html. See section 7.

 

[1977ub]

I know that length contraction at relativistic speeds has been proven in the lab, experimentally, using subatomic particles and I guess nobody can argue the results. I for one, don't.
But, did we had any attempts of proving length contraction, experimentally, using macro objects (not quantum objects)? Did we actually observe this or it's an extrapolation from the quantum world and a deduction?

The people who we consider to be moving along with the object find there to be no contraction. We find their clocks to not be synchronized with each other.

 

[Ibix]

But, did we had any attempts of proving length contraction, experimentally, using macro objects (not quantum objects)?

Consider the cosmic ray muons. From our perspective they survive to reach sea level because their time is dilated. From their perspective there must be a reason that they can get through the atmosphere - its rest depth is too deep for them to cross given their short lifetimes. So what's happened?

Basically you have two options. The first is that the atmosphere is length contracted in this frame. The second is that the principle of relativity is wrong, and the muons are time dilated in an absolute sense, and see Earthbound clocks ticking fast.

But we test the principle of relativity every day, and there is no evidence of it being wrong. If you don't want to believe length contraction you need to come up with a coherent explanation for gross violation of relativity at high speeds while approximating it absurdly well at low speed.

 

[Nugatory]

But, did we had any attempts of proving length contraction, experimentally, using macro objects (not quantum objects)? Did we actually observe this or it's an extrapolation from the quantum world and a deduction?

It's not practical to measure length contraction with macroscopic objects. To see why, try calculating the kinetic energy of a 1 kilogram object moving fast enough to contract by 1% and compare with total annual worldwide energy production.
(Time dilation in macroscopic clocks is much easier to observe because we can work with slower speeds over a longer time and because our best clocks are many orders of magnitude more accurate than our best instruments for measuring the length of moving objects.)

However, we can and do measure length contraction of distances: measurements of the distance traveled by subatomic particles before they decay show that, in the frame in which the particle is at rest and the detector is moving towards the particle, the distance between the particle source and the detector is length contracted compared with the distance in the frame in which the particle is moving and the lab, particle source, and particle detector are all at rest.

In any case time dilation, relativity of simultaneity, and length contraction all follow from the same proven-correct equations (the Lorentz transforms) so any consistent theory has to include all three. If any two of them are experimentally confirmed then the third must be present even if we lack the tools to measure it directly.

 

[Janus]

Very nice explanations.

So, considering all that you have said, if there's no physical change of the object's properties/length in the real world, this means that Length Contraction represents object properties translated from the 3D model into the 4 dimensional space-time coordinates system, where you indeed will have different measurements.

It's more the other way around. The 4D model is actually a better representation of the "real world" object, and it is the projection of that object onto our 3D perception of the universe that results in our measuring length contraction. Our three 3D world is just a "shadow play" of the 4D reality. We can only directly measure the shadows cast, and must infer the 4D model from that.

In this case, having an array of detectors in the Atacama desert at a distance of 1 mm away from one-another, and an object passes over the detectors with 0.9c (the object has a switch at the end and one at front) activating with both of the switches, simultaneously (in the array frame of reference) two detectors, the distance between those two detectors will be the proper length of the object. Though, if translated in the 4D space-time model, this will measure a Length Contraction.
So you never lose Length Contraction, you don't lose SR, you just have to translate the experiment in the mathematical form of a space-time model to have different readings, which makes sense in my mind. I mean, it was never meant to convince that length changes at relativistic speeds rather it is a different reading in a 4D space.

With the red arrows being the detectors and the green line the object with the switches at the ends, then if the switches of the object are detected simultaneously in rest frame of the desert, then the top image shows the length measurement you get for the object in the desert frame. (object shown moving left to right) This will be the length contracted length of the object.
However, in the rest frame of the object, it is the detectors that are moving (right to left) and are length contracted while the object is its proper length. Thus you get the two bottom images with the object triggering one detector and then the other.

So, you will directly measure the contracted length, and if you know the relative speed you can use this to work out what the proper length is.

I

 

[A.T.]

I know that length contraction at relativistic speeds has been proven in the lab, experimentally, using subatomic particle...But, did we had any attempts of proving length contraction, experimentally, using macro objects

Yes, as noted above, the observations imply a contracted macroscopic environment in the frame of the particles.

Also, the macroscopic objects are made of subatomic particles. Accepting the bricks being contracted, but not the whole house makes no sense.

 

[Ebeb]

Our three 3D world is just a "shadow play" of the 4D reality. We can only directly measure the shadows cast, and must infer the 4D model from that.

I don't understand your 'shadow'. 4D world contains far more events than one 3D world. Hence a 3D world cannot be a projection nor shadow of such a vast 4D world. A 3D world is a section through 4D world.

 

[DaveC426913]

I don't understand your 'shadow'. 4D world contains far more events than one 3D world.

He didn't say 'a shadow'; he said 'shadow-play'.

Hence a 3D world cannot be a projection nor shadow of such a vast 4D world.

You are taking his words too literally.

 

[David Lewis]

… 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...

Not sure about the "two distinct frames of reference" part, but length contraction is real -- even at non-relativistic speeds -- just as time dilation is real. Things will happen more slowly (from your standpoint) for objects in motion with respect to you.

 

[A.T.]

No I get it, it's not an actual physical length change but a measurement of length in a different system of coordinates.

In these discussions people often argue whether something is "physical" or "real", but often mean different things by these terms or don't even have a precise definition of them in their own mind.

Consider a circular train track and an unlimited supply of train engines, entering that circle from an tangential side track. The number of engines you can fit on that circle, depends on their contracted length. The faster they go, the more of them you can fit in.

Whether you consider that "real" or "physical" is semantics.

 

[David Lewis]

The number of engines you can fit on that circle, depends on their contracted length. The faster they go, the more of them you can fit in.

Will the track be length contracted in the reference frame of the engine?

 

[Ibix]

Will the track be length contracted in the reference frame of the engine?

The engine is not inertial, so length contraction does not apply to its frame. It's an acceptable approximation to consider any short section of a train as inertial, and deduce that it must be length contracted, but you cannot think of the whole track this way from the engine frame.

 

[A.T.]

Will the track be length contracted in the reference frame of the engine?

As @Ibix wrote, you can consider an instantaneous inertial co-moving frame, where the usual Lorentz transformation applies, but an engine is only at rest for an instant.

Alternatively you can consider a rotating frame, where all the engines filling the circle are permanently stationary. So they are non-contracted and thus have a total length greater than 2πr, but still fit onto a circumference of radius r. You can interpret this as an non-Euclidean spatial geometry in the rotating frame. But note that the usual simultaneity convention doesn't work continuously along the circumference, so you cannot use simple Lorentz transformations to analyse this globally.

The point I was making with this example is that for storing moving stuff in a loop, the contracted length is the relevant one. So regardless if you call length contraction "real" or "physical", you have to account for it because it has concrete practical consequences.

 

[Ebeb]

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He didn't say 'a shadow'; he said 'shadow-play'.

That's even worse.

You are taking his words too literally.

I thought the goal of communication in science was to be as specific as possible?

The 'projection' and 'shadow' wording follows from looking at a stick from a non-90 degree angle, resulting in a shorter view of the stick. This misleading analogy blocks the interested layman's mind from really understanding how it works .

Consider two trains moving relative to each other. The dots represent wagons of the train. In a train frame the wagons are simultaneously of the same color. But every split second the wagons change color, simultaneousely in their respective frame.
A contracted train is a collection of wagons of a different color: a 3D section through a collection of (in time) successive 3D trains of the 4D train object.

The contracted train is not a projection or shadow of a length of the proper train. It's the actual length of the moving 3D train (made of wagons of a different color and changing colors in time), present in the observers 3D space/world.

I leave it to the reader to philosophy about what is phyically real or not, but keeping the following in mind: if an observer considers a train at rest relative to him being a "physically real" object present in a "physically really existing 3D space/world", then the contracted train is also a "physically real" object present in that 3D space/world.

 

[DaveC426913]

A contracted train is a collection of wagons of a different color

I haven't processed your post fully yet, but I have to say, you really missed an opportunity here: instead of wagons, you really should have used horses.

 

[Viopia]

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.

Hi. I am not a physicist but I watched an interesting video on YouTube regarding time dilation and length contraction. If the formula for length contraction shown in the video is correct, something traveling at the speed of light, ie: a photon, would experience an infinite length contraction. This would mean that the photon would pass the start and finish line of any distance instantaneously. Would this also mean that an entangled photon would be at the same point in spacetime as its entangled partner and so there would be no "spooky action" at a distance from the photons frame of reference?

 

[jbriggs444]

the photons frame of reference?

There is no such thing as the rest frame for a photon.

It would be self-contradictory to have an inertial rest frame for light in a theory where light moves at c in all inertial frames.

 

[1977ub]

For some interesting imagery regarding null intervals you might enjoy working your way through this:

https://www.mathpages.com/rr/s9-09/9-09.htm

 

[Janus]

I watched an interesting video on YouTube regarding time dilation and length contraction.

At the start of the video he quotes the expert as saying "The photon experiences no time", he then goes on to say that zero time exists for the photon between the moment it is emitted and received. However, this second statement doesn't really follow the first according to Relativity. To see why, you have to look at the actual time dilation equation:
$$ T = \frac{t}{\sqrt{1-\frac{v^2}{c^2}}}$$
here T is time as measured by our observer, and t is time as measured by the clock that is moving relative to the observer.
So for example is v=.0866c, then T= t/0.5) = 2t, which equates to our observer measuring every tick of the moving clock as equally 2 ticks of his own clock.
But what happens if we make v=c? then we get T= t/0. But division by zero is undefined and has no answer. So for a photon, time is undefined. It has no physical meaning. It does not "experience time" because the whole concept has no meaning for it. This is not the same as it experiencing zero time. Zero time, even if it has no duration is still a defined duration, and there is no defined duration of time that light measures.
And thus if you go on to say that " the photon doesn't experience length either" this means that length is equally undefined for a photon. This is just another way of saying that a photon has no valid reference frame from which to measure time or space.

 

[PeterDonis]

This thread has run its course and is now closed.

Edit: A thread hijack has also been cleaned up.