Length Contraction

[zapatos]

1 hour ago, thomas reid said:

My question still is: is length contraction something that is viewed to happen or is it something that happens?

Length contraction is viewed to happen, and does happen, from the perspective of the proper frame. And by contrast, at the very same time you are seeing length contraction, there is another frame in which length contraction does not happen for that very same object.

[thomas reid]

Okay ... so length contraction physically occurs.  And if it physically occurs then it also "appears" that way because it is that way.  ("Appears" is the word used on my Sparknotes flash card.)

Cool.

I guess I just find the flash card misleading when it uses the word "appears" and does not mention that it does happen.  (It could "appear" to happen but not actually happen, or it could "appear" to happen because it happens.)

Thank you.

Cheers!

[Strange]

2 hours ago, thomas reid said:

I think length contraction is physically real in the rest frame.  I think the moving body becomes physically shorter in its direction of motion in the rest frame.

Obviously not. You are in your own rest frame, no? And you are seen as "physically shorter" by observers moving relative to you (and there are a near infinite number of those moving at different speeds and directions). But you are not contracted by all sorts of different amounts in different directions (in your own frame of reference) are you.

2 hours ago, thomas reid said:

Okay ... so length contraction physically occurs.  And if it physically occurs then it also "appears" that way because it is that way.  ("Appears" is the word used on my Sparknotes flash card.)

Cool.

I guess I just find the flash card misleading when it uses the word "appears" and does not mention that it does happen.  (It could "appear" to happen but not actually happen, or it could "appear" to happen because it happens.)

This is purely a matter of what you mean by "physically" or "appears". In other words, it is an issue of semantics (or ontology, if you insist) not physics.

[thomas reid]

" Obviously not. You are in your own rest frame, no? And you are seen as "physically shorter" by observers moving relative to you (and there are a near infinite number of those moving at different speeds and directions). But you are not contracted by all sorts of different amounts in different directions (in your own frame of reference) are you. "

Then what about time dilation?

I am in my own rest frame.  And time is moving forward normally for me in my rest frame.

I am also moving in other people's rest frames.  And in their rest frames I am getting older by slower amounts.

I don't just "appear" to be getting older by a slower amount in another rest frame, I am getting older by a slower amount.  And in different rest frames, where I am moving at different speeds, I am getting older more slowly in some and I am getting older less slowly in others.

Yes?

Time dilation and length contraction are the two most basic relativistic dynamics.  Perhaps it is the case that when it comes to time dilation I am really getting older by a lesser amount in another rest frame, but with length contraction I am not really getting shorter in that same other rest frame.  Perhaps time dilation is not about mere appearances, while length contract may be (depending on how the word "appear" is used).  I don't know.  I suppose that argument can be made.

I open to being wrong.

But I just thought of an example of why I think it's proper to say that length contraction is "physically real" and not just a matter of "appearance" or "measurement" (regardless of how these two terms are defined).

Think about the Ladder and Barn Paradox.

 

(Without going into the whole story of the paradox) at one point in the "paradox", in the inertial frame of reference of the barn at rest, the ladder is within the two closed barn doors.

And if the guy who is in control of these barn doors (differently from how the paradox is usually laid out) chooses to not reopen the barn doors, then the ladder will remain physically and really within the barn.  (In this case it will collide with the closed barn door and then expand, but it will remain within the barn, assuming the barn doors are made out of strong stuff.)

This is how I'm thinking about it.  At this point in the Ladder and Barn Paradox, the ladder does not just "appear" to be in the barn or is not just "measured" to be in the barn, it is, in fact, in the barn.

But ... maybe I'm wrong.

[Strange]

1 hour ago, thomas reid said:

I don't just "appear" to be getting older by a slower amount in another rest frame, I am getting older by a slower amount.  And in different rest frames, where I am moving at different speeds, I am getting older more slowly in some and I am getting older less slowly in others.

And they all also think you travelled different distances. So, to my mind, this is the problem with thinking it is a "physical" effect (depending, of course, what you think that word means): you can't be different ages at the same time.

It is probably more accurate to say it is a measurement effect. The change in measurements is real not just a matter of "appearance".

[DimaMazin]

If distance between particles of S' frame is uncontracted in S frame then is it increased in S' frame?

[swansont]

On 9/22/2017 at 3:05 PM, Strange said:

And they all also think you travelled different distances. So, to my mind, this is the problem with thinking it is a "physical" effect (depending, of course, what you think that word means): you can't be different ages at the same time.

I'd say it's a matter of the last phrase simply not making sense in light of relativity. You have a variable, t. People will disagree on the value t they measure in their frame, when describing some event. There is no "same time" you can describe that makes sense for objects/observers, except under specific situations (in the same frame, for instance)

Relativity does not lend itself to the relevant colloquial expressions that made sense in Galilean systems.

[phyti]

On 9/19/2017 at 6:59 PM, thomas reid said:

In Relativity when something is moving does it become actually physically shorter or does it only appear shorter in the rest frame?

Chemistry teaches us that matter exists in lumps and can be deformed. Measure a metal rod, heat it and remeasure it. There are no rigid objects.

The attached file explains why length contraction is necessary to resolve the MMX. 

reflecting circle.pdf

[Strange]

5 minutes ago, phyti said:

Chemistry teaches us that matter exists in lumps and can be deformed. Measure a metal rod, heat it and remeasure it. There are no rigid objects.

That is not exactly relevant, though, is it.

5 minutes ago, phyti said:

The attached file explains why length contraction is necessary to resolve the MMX. 

And what is the source of this document?

[phyti]

19 hours ago, Strange said:

That is not exactly relevant, though, is it.

And what is the source of this document?

As Supernerd, why do you ask, you should know.

Did you find an error in the paper?

 

[Strange]

6 minutes ago, phyti said:

As Supernerd, why do you ask, you should know.

How should I know where a random PDF file comes from? That is why I asked.

[geordief]

Suppose  an observer in a stationary FoR  takes measurements of  an object or a group of objects  , and another non-stationary  observer takes the  measurements of the same object or group of objects.

 

Their measurements will differ.

 

Now  suppose that both pairs of observers  continue to make observations of the objects or group of objects  but  change their relative speeds so that they are now stationary wrt each other.

 

Will the measurements they  now make of the object or group of objects (as they have developed over the intervening time) be identical?

 

Taking into account  the twin paradox , this seems unlikely to me as in that scenario  the returning twin will view the evolved initial scenario (the parting) differently from the remaining twin (albeit dead) and so the change in measurements is real in that case and not apparent.

 

Does the twin paradox result also apply to the length contraction question  so that the length contraction has lasting and irreversible consequences in the way  interactions play out after the event and never "return to the status quo"?

Edited September 28, 2017 by geordief

[Endy0816]

10 hours ago, geordief said:

Does the twin paradox result also apply to the length contraction question  so that the length contraction has lasting and irreversible consequences in the way  interactions play out after the event and never "return to the status quo"?

Been talked about before here, but an Odometer(mileometer) readout would disagree with what the homebody twin considers the distance to be.

If something can serve as a record for how long in terms of time or distance the trip was, that record will remain after coming back.

There may be a natural equivalent to an odometer, not sure on that one.

Edited September 29, 2017 by Endy0816
clarity

[Strange]

Exactly.

Length contraction is equivalent to the different rate at which a cook ticks seen from a different frame of reference. Both of these will disappear when the two frames of reference are brought back together.

Ageing is equivalent to distance travelled. This will remain different even after the frames are brought back together.

[geordief]

3 hours ago, Strange said:

Exactly.

Length contraction is equivalent to the different rate at which a cook ticks seen from a different frame of reference. Both of these will disappear when the two frames of reference are brought back together.

Ageing is equivalent to distance travelled. This will remain different even after the frames are brought back together.

When two protons collide at relativistic speeds and are length contracted how is the bounce ** affected?

 

** perhaps   "bounce" is the wrong word  

 

 

Edited September 29, 2017 by geordief

[Strange]

39 minutes ago, geordief said:

When two protons collide at relativistic speeds and are length contracted how is the bounce ** affected?

 

** perhaps   "bounce" is the wrong word  

This is one of the best examples of length contraction. The results can only be explained in terms of flattened disks colliding: https://en.wikipedia.org/wiki/Length_contraction#Experimental_verifications

[phyti]

On 9/28/2017 at 10:54 PM, Endy0816 said:

Been talked about before here, but an Odometer(mileometer) readout would disagree with what the homebody twin considers the distance to be.

If something can serve as a record for how long in terms of time or distance the trip was, that record will remain after coming back.

There may be a natural equivalent to an odometer, not sure on that one.

There is, it's called a clock.

[Endy0816]

11 hours ago, phyti said:

There is, it's called a clock.

Could you clarify?

[Dubbelosix]

On 20/09/2017 at 4:23 PM, thomas reid said:

In the "Jouster's Paradox" two jousters with lances of equal lengths when at rest are moving towards one another.

And so in the one inertial frame of reference the one jouster gets knocked over first.

And in the other inertial frame of reference the other jouster gets knocked over first.

And the resolution of the "paradox" is that no body is a perfectly rigid body.  And so after colliding the shortened lance (one or the other depending on which frame of reference is being considered) then stretches out on then knocks over the other jouster.

If this is a correct statement of the Jouster's Paradox then, to me, it seems that length contraction must be real (there must be a real physical contraction of the length of the moving body in the resting body's frame of reference) for the moving jouster to get knocked off first (in the resting frame of reference) before the resting jouster gets knocked off (in the resting frame of reference).

This is why the "appearance" reference on my flash card confused me.

No?

 

 

 

 

 

 

 

Hadn't heard of this either, but Born rigid has a long history - and a very interesting one. I've took the liberty of finding this history for you:

 

''1909: Max Born introduces a notion of rigid motion in special relativity.^[6]

• 1909: After studying Born's notion of rigidity, Paul Ehrenfest demonstrated by means of a paradox about a cylinder that goes from rest to rotation, that most motions of extended bodies cannot be Born rigid.^[1]
• 1910: Gustav Herglotz and Fritz Noether independently elaborated on Born's model and showed (Herglotz-Noether theorem) that Born rigidity only allows of three degrees of freedom for bodies in motion. For instance, it's possible that a rigid body is executing uniform rotation, yet accelerated rotation is impossible. So a Born rigid body cannot be brought from a state of rest into rotation, confirming Ehrenfest's result.^[7][8]
• 1910: Max Planck calls attention to the fact that one should not confuse the problem of the contraction of a disc due to spinning it up, with that of what disk-riding observers will measure as compared to stationary observers. He suggests that resolving the first problem will require introducing some material model and employing the theory of elasticity.^[9]
• 1910: Theodor Kaluza points out that there is nothing inherently paradoxical about the static and disk-riding observers obtaining different results for the circumference. This does however imply, Kaluza argues, that "the geometry of the rotating disk" is non-euclidean. He asserts without proof that this geometry is in fact essentially just the geometry of the hyperbolic plane.^[10]
• 1911: Max von Laue shows, that an accelerated body has an infinite amount of degrees of freedom, thus no rigid bodies can exist in special relativity.^[11]
• 1916: While writing up his new general theory of relativity, Albert Einstein notices that disk-riding observers measure a longer circumference, C′ = 2π r √(1−v²)⁻¹. That is, because rulers moving parallel to their length axis appear shorter as measured by static observers, the disk-riding observers can fit more smaller rulers of a given length around the circumference than stationary observers could.
• 1922: In his seminal book "The Mathematical Theory of Relativity" (p. 113), A.S.Eddington calculates a contraction of the radius of the rotating disc (compared to stationary scales) of one quarter of the 'Lorentz contraction' factor applied to the circumference.
• 1935: Paul Langevin essentially introduces a moving frame (or frame field in modern language) corresponding to the family of disk-riding observers, now called Langevin observers. (See the figure.) He also shows that distances measured by nearby Langevin observers correspond to a certain Riemannian metric, now called the Langevin-Landau-Lifschitz metric. (See Born coordinates for details.)^[12]
• 1937: Jan Weyssenhoff (now perhaps best known for his work on Cartan connections with zero curvature and nonzero torsion) notices that the Langevin observers are not hypersurface orthogonal. Therefore, the Langevin-Landau-Lifschitz metric is defined, not on some hyperslice of Minkowski spacetime, but on the quotient space obtained by replacing each world line with a point. This gives a three-dimensional smooth manifold which becomes a Riemannian manifold when we add the metric structure.
• 1946: Nathan Rosen shows that inertial observers instantaneously comoving with Langevin observers also measure small distances given by Langevin-Landau-Lifschitz metric.
• 1946: E. L. Hill analyzes relativistic stresses in a material in which (roughly speaking) the speed of sound equals the speed of light and shows these just cancel the radial expansion due to centrifugal force (in any physically realistic material, the relativistic effects lessen but do not cancel the radial expansion). Hill explains errors in earlier analyses by Arthur Eddington and others.^[13]
• 1952: C. Møller attempts to study null geodesics from the point of view of rotating observers (but incorrectly tries to use slices rather than the appropriate quotient space)
• 1968: V. Cantoni provides a straightforward, purely kinematical explanation of the paradox.
• 1975: Øyvind Grøn writes a classic review paper about solutions of the "paradox"
• 1977: Grünbaum and Janis introduce a notion of physically realizable "non-rigidity" which can be applied to the spin-up of an initially non-rotating disk (this notion is not physically realistic for real materials from which one might make a disk, but it is useful for thought experiments).^[14]
• 1981: Grøn notices that Hooke's law is not consistent with Lorentz transformations and introduces a relativistic generalization.
• 1997: T. A. Weber explicitly introduces the frame field associated with Langevin observers.
• 2000: Hrvoje Nikolić points out that the paradox disappears when (in accordance with general theory of relativity) each piece of the rotating disk is treated separately, as living in its own local non-inertial frame.''

 

 

This was extracted from the Ehrenfest problem of rotating bodies that should experience a length contraction. As Swansont has pointed out, and other posters have hinted at, there are no preferred frames in existence and asymptotic time is not a universal feature - that is we cannot always agree on what time it is, and for moving observers, this translates into we cannot always agree on when things happen!

[studiot]

Thanks for that excellent  list, dubbelosix. +1

 

You are now officially dubbeloseven

 

[Mordred]

I agree lol (to both statementsm now that the latter is stuck in my mind

Edited October 1, 2017 by Mordred

[phyti]

On 9/30/2017 at 11:52 PM, Endy0816 said:

Could you clarify?

There is a device called an integrator, with a wheel that follows a curve and totals the incremental lengths. A clock performs the same function. It accumulates time along any spacetime curve. It can't move any slower than zero, thus there is no opportunity to gain time. In the 'twin' scenario, the clock that loses the lesser amount of time belongs to the younger twin.

For distance, x=vt. For time, t=x/v, Inversely proportional to v. Given x, the greater the speed, the LESS the time (without relativity). It should be no surprise that time is less for high velocities in SR.

Edited October 2, 2017 by phyti

[J.C.MacSwell]

25 minutes ago, phyti said:

There is a device called an integrator, with a wheel that follows a curve and totals the incremental lengths. A clock performs the same function. It accumulates time along any spacetime curve. It can't move any slower than zero, thus there is no opportunity to gain time. In the 'twin' scenario, the clock that loses the lesser amount of time belongs to the younger twin.

For distance, x=vt. For time, t=x/v, Inversely proportional to v. Given x, the greater the speed, the LESS the time (without relativity). It should be no surprise that time is less for high velocities in SR.

Are you sure that is what you meant to say?

[Strange]

Yes: younger = less time elapsed.

But this doesn't seem to answer the question which was about a natural equivalent of an odometer. (Sore feet, maybe. :))

[J.C.MacSwell]

16 minutes ago, Strange said:

Yes: younger = less time elapsed.

But this doesn't seem to answer the question which was about a natural equivalent of an odometer. (Sore feet, maybe. :))

Right, but less time lost on a clock should equate to more time elapsed.