What space contracts in Special Relativity?

[dEdt]

This is what Lorentz was forced to assume, and why his viewpoint lost out to Einstein's. All Lorentz really had to go on was the fact that a moving Coulomb field appears contracted. But the world is made of other things besides electromagnetism. The shape of planetary orbits for example is determined by Newtonian gravity. How does Newtonian gravity transform under a velocity boost? We now know that gravity does NOT transform the same way as electromagnetism.

And the shape of nuclei (or neutron stars) must change exactly the same way too. But even without knowing of the existence or nature of the nuclear force, Lorentz had to hypothesize that all forces underwent an identical contraction. Einstein of course replaced this ad hoc assumption with the much simpler idea that space itself was responsible.

What clinched the argument in Einstein's favor was the realization that relativity applied to particle kinematics as well, which Lorentz's theory did not.

Yes, you're absolutely correct. Einstein's approach allowed people to calculate things like the length contraction of an atomic nucleus without having to know all the laws of physics, if the laws of physics are assumed to be Lorentz invariant. However, this doesn't mean that Lorentz was wrong to state the Lorentz contraction could in principle be explained by looking at the forces holding something together. As Pauli put it,

Should one, then, completely abandon any attempt to explain the Lorentz contraction
atomistically? We think that the answer to this question should be No. The contraction
of a measuring rod is not an elementary but a very complicated process. It would not take
place except for the covariance with respect to the Lorentz group of the basic equations
of electron theory, as well as of those laws, as yet unknown to us, which determine the
cohesion of the electron itself.

 

[dEdt]

All measurements are made when the 3 labs are moving inertially. Did the rod experience any strain or change in molecular configuration because the other two labs made a measurement ?

The molecular configuration of the rod did change (namely, the molecules compressed and got closer to each other), but not as a result of the measurement. It came about because of the rod's motion.

If you keep in mind that force is not a Lorentz invariant quantity, you'll see that there's no contradiction in having three observers reach different conclusions about the nature of the intermolecular forces acting in a rod.

 

[Mentz114]

Thank you for trying to explain my doubts. But ...

...
It came about because of the rod's motion.
..

But the motion is relative, so the rod must have a nearly infinite number of configurations simultaneously.

If you keep in mind that force is not a Lorentz invariant quantity, you'll see that there's no contradiction in having three observers reach different conclusions about the nature of the intermolecular forces acting in a rod.

But the motion is inertial so there are no forces involved. How does the motion change the molecular configuration ?

 

[dEdt]

But the motion is relative, so the rod must have a nearly infinite number of configurations simultaneously.

I think it's more accurate to say there there are an infinite number of different ways to describe the configuration of the rod, one for each reference frame.

Let's step away from something as complicated as a rod and look at something simpler, like a point charge. Figure 1 shows the electric field produced by a stationary point charge.

http://upload.wikimedia.org/wikipedia/commons/b/b9/Relativistic_electromagnetism_fig3.svg

Figure 2 shows the electric field produced by a moving charge.

http://upload.wikimedia.org/wikipedia/commons/b/b2/Relativistic_electromagnetism_fig4.svg

Clearly there's a difference between the two electric fields -- a difference that arises from the point charge's motion.

An observer at rest relative to the point charge will always see Figure 1, while an observer moving relative to the will always see Figure 2. Is it correct to say that there are two (or more) different configurations of the electric field? I don't think so. Better to say that there are two different descriptions of the electric field.

But the motion is inertial so there are no forces involved. How does the motion change the molecular configuration ?

There are no external forces on the rod, but there are plenty of internal forces.

 

[Mentz114]

I think it's more accurate to say there there are an infinite number of different ways to describe the configuration of the rod, one for each reference frame

(my emphasis)

Sure, from a moving POV the charge distribution/rod looks different. But nothing happened to the rod, because there's no physical difference between inertial motion and rest.

None of these arguments demonstrate more than the fact that things are different when measured (described ?) from a moving POV. Which we expect. But the rod is unchanged by this.

There are no external forces on the rod, but there are plenty of internal forces.

Which remain unchanged for the rod in any state of inertial motion.

 

[bahamagreen]

My old book says...

The Hamiltonian for the atom will have operators that only operate on the coordinates of the particular particles, but it also includes motion of the atom as a whole (the center of mass).

So the Schrödinger equation may be separated, and the eigenfunctions connected only through a common separation constant, which includes the kinetic energy of the center of mass of the atom.

So unless the atom is "in a box", the KE can assume any value, so the eigenfunctions are independent* of each other, and the internal state of the atom is independent of the motion of its center of mass.

*In the event that the separation constant, itself, is quantized; the factors of the eigenfunctions may be only conditionally independent.

 

[dEdt]

But nothing happened to the rod, because there's no physical difference between inertial motion and rest.

Not true. The laws of physics in any given reference frame make a clear distinction between objects at rest and objects in motion. Just take a look at the difference between a stationary point charge and a moving point charge. Don't confuse the this fact with the claim that the laws of physics are the same for observers moving with constant velocity relative to each other.

None of these arguments demonstrate more than the fact that things are different when measured (described ?) from a moving POV. Which we expect. But the rod is unchanged by this.

If the rod were unchanged by motion, it wouldn't shrink.

Which remain unchanged for the rod in any state of inertial motion.

Again, not true. Forces are not Lorentz covariant.

 

[dEdt]

My old book says...

The Hamiltonian for the atom will have operators that only operate on the coordinates of the particular particles, but it also includes motion of the atom as a whole (the center of mass).

So the Schrödinger equation may be separated, and the eigenfunctions connected only through a common separation constant, which includes the kinetic energy of the center of mass of the atom.

So unless the atom is "in a box", the KE can assume any value, so the eigenfunctions are independent* of each other, and the internal state of the atom is independent of the motion of its center of mass.

*In the event that the separation constant, itself, is quantized; the factors of the eigenfunctions may be only conditionally independent.

It sounds like you're using non-relativistic quantum mechanics. If you use QED, you'll see that your claim isn't true.

 

[Mentz114]

If the rod were unchanged by motion, it wouldn't shrink.

I'm asserting that the rod does not shrink. How can my motion affect some independent object ? Therefore I see no need to invoke any additional physics to 'explain' the relativistic effect, viz that measuring something in motion will give smaller number than the rest frame measurement.

But nothing happened to the rod, because there's no physical difference between inertial motion and rest.

Again, not true. Forces are not Lorentz covariant.

You misunderstand me because you are assuming the rod shrinks and trying to explain 'how' using an irrelevant and speculative mechanism.

 

[dEdt]

I'm asserting that the rod does not shrink. How can my motion affect some independent object ?

Well, your assertion is simply incorrect. That a moving object shrinks can be deduced from the Lorentz invariance of the laws of physics, and the Lorentz invariance of the laws of physics is an experimental fact built into all fundamental theories of physics since the 20th century. To deny the reality of Lorentz contraction is either to deny modern physics or to use a non-standard definition of the length of an object.

Presumably you also don't believe in time dilation ie that processes take longer when in motion than
when at rest. How exactly do you explain the experimental verifications of time dilation?

If you want to understand how motion "[can] affect some independent object", just look at Maxwell's equations. The equations contain a current density term, which depends on the motion of the charge distribution. Hence then laws of physics -- at least as expressed in a particular inertial coordinate system -- affect objects in different ways depending on their motion. If that seems unintuitive to you, then your intuition is simply wrong.

 

[Mentz114]

Well, your assertion is simply incorrect. That a moving object shrinks can be deduced from the Lorentz invariance of the laws of physics, and the Lorentz invariance of the laws of physics is an experimental fact built into all fundamental theories of physics since the 20th century. To deny the reality of Lorentz contraction is either to deny modern physics or to use a non-standard definition of the length of an object.

Obviously, I disagree. And for the record I define the length of an object as the result of the measurement in the objects rest frame.

Presumably you also don't believe in time dilation ie that processes take longer when in motion than when at rest. How exactly do you explain the experimental verifications of time dilation?

Time dilation has never been directly experimentally verified which gives it the same ontological status as length contraction. What has been verified is that the elapsed time on a clock is the proper interval of its worldline between events.

If you want to understand how motion "[can] affect some independent object", just look at Maxwell's equations. The equations contain a current density term, which depends on the motion of the charge distribution. Hence then laws of physics -- at least as expressed in a particular inertial coordinate system -- affect objects in different ways depending on their motion. If that seems unintuitive to you, then your intuition is simply wrong.

I think this is irrelevant. Also, I don't rely on intuition.

I'll make two more points

1. the outcome of the barn-pole paradox ( viz, that the pole which is slightly longer then the barn when they are measured at rest) is as if both the pole and barn did not shrink or expand. So no direct evidence for length contraction ( but lots for relativity of simultaneity ).

2. If the distance ( space ) between two objects at rest wrt each other is measured from a moving platform, it will give a result smaller than the rest frame measurement. What made the empty space shrink ?

I'm tired so I won't be able to reply ( should you persist ) until tomorrow on my clock.

 

[stevendaryl]

Obviously, I disagree. And for the record I define the length of an object as the result of the measurement in the objects rest frame.

Some of the disagreement here may simply be a clash of definitions. If you define length in a frame to be the distance between two ends measured simultaneously, then a rod does shrink when you accelerate it from rest. If you define it your way, it doesn't shrink.

 

[dEdt]

And for the record I define the length of an object as the result of the measurement in the objects rest frame.

Well then it's practically a tautology to say that the length of an object isn't affected by motion. However, if you define length as the distance between the endpoints of an object measured simultaneously -- which is how almost everyone defines it -- then you are forced to the conclusion that objects compress under motion.

Time dilation has never been directly experimentally verified

No. Muons in cosmic rays decay more slowly than muons at rest in the laboratory.

2. If the distance ( space ) between two objects at rest wrt each other is measured from a moving platform, it will give a result smaller than the rest frame measurement. What made the empty space shrink ?

The question is not, what made the empty space shrink, but rather, why do the two observers disagree about the distance between the two objects. To the observer on the moving platform, the reason an observer at rest wrt the object measures a greater distance is because he is using measuring rods which are contracted.

 

[Mentz114]

Well then it's practically a tautology to say that the length of an object isn't affected by motion. However, if you define length as the distance between the endpoints of an object measured simultaneously -- which is how almost everyone defines it -- then you are forced to the conclusion that objects compress under motion.

No, your point below allows me to say that there is no compression - only that my rulers are different.

I think this contradicts what you say here

The question is not, what made the empty space shrink, but rather, why do the two observers disagree about the distance between the two objects. To the observer on the moving platform, the reason an observer at rest wrt the object measures a greater distance is because he is using measuring rods which are contracted.

Again I assert that length contraction is a relativistic effect which makes any measurement on a moving object give a smaller number that the rest-frame measurement. It does not imply that the object is compressed, only that different 'rulers' ( coordinates) are being used. The Lorentz transformation gives the relationship between the clocks and rulers in the two frames, it does not imply that the object has changed.

You have to choose between 'object compresses' or 'rulers are different'. You don't need both and the second requires no additional physics.

 

[Mentz114]

Some of the disagreement here may simply be a clash of definitions. If you define length in a frame to be the distance between two ends measured simultaneously, then a rod does shrink when you accelerate it from rest. If you define it your way, it doesn't shrink.

Sure. But a property of an object has the value that the object itself assigns. Suppose you measured yourself to be x meters from head to toe. I make a remote moving measure and tell you that you are actually y meters from head to toe. Who are you going to believe ?
Put the 'proper' back in 'property'.

 

[stevendaryl]

Sure. But a property of an object has the value that the object itself assigns.

Who says? I don't think that's a consistent approach. For instance, light certainly has properties--frequency, wavelength, momentum--but it doesn't make sense to ask what properties the light assigns itself, because there is no such thing as the rest frame of light.

 

[Mentz114]

Who says? I don't think that's a consistent approach. For instance, light certainly has properties--frequency, wavelength, momentum--but it doesn't make sense to ask what properties the light assigns itself, because there is no such thing as the rest frame of light.

I don't think this is relevant because light is not an object. Length contraction is a kinematic effect between timelike worldlines.

If it is merely a convention how one defines length, then I choose the rest frame measurement. The point I'm trying to make is that there's nothing in SR that requires 'the rod' to become compressed. There is only one rod, yes ?

 

[FactChecker]

Hi. I know that space for an object in motion will contract, relative to an observer. We generally read that space contracts for the object in the direction of motion. But doesn't space around the object also contract? Can someone clarify this? Thanks.

"around the object" -- If you are asking about distances measured perpendicular to the direction of motion, then no. Those measurements do not change. Both reference frames agree about distances in those directions.

If you are asking about measuring the rocket compared to the space that it is in, then yes. Everything apparently shrinks in that direction. So the moving person cannot detect any change in his own rocket size. The change in length is only apparent to the people in the "stationary" reference frame. Suppose I am stationary and you are in the rocket. Before you start moving, we have identical length rulers and agree that your rocket is 100 ft long. When you are traveling, you still measure your rocket as 100 ft long using your (shrunken) ruler. I think that your rocket is shorter. I understand why you still think it is 100 ft because your ruler has shrunk the exact same amount. So your ruler is wrong and your 100 ft measurement has become wrong.

 

[stevendaryl]

I don't think this is relevant because light is not an object.

That reinforces my point--that it isn't a consistent approach to talk about properties with respect to objects. If you take an extended object, such as a train, and start accelerating it, there IS no such thing as "the rest frame of the object" because in general, different parts of the object are traveling at different speeds.

If you pick an inertial Cartesian coordinate system to describe motion and distance and so forth, then it will be the case that:

1. Take a "rigid" rod that initially has length L when at rest. Gently accelerate it in the direction of its length to a new speed v. Allow it to come to an equilibrium length at the new speed. Then that length will be L \sqrt{1-\frac{v^2}{c^2}}.
2. Take a metronome, or windup clock, or something that regularly emits a "tick" at an interval of time T when at rest. Gently accelerate it to a new speed v. Afterward, it will tick with an interval given by \dfrac{T}{\sqrt{1-\frac{v^2}{c^2}}}

These are facts. Now, it is the case that Minkowsky spacetime allows these facts to be given a "geometric" interpretation: There is an intrinsic length for rods and an intrinsic tick rate for metronomes, and the measured length and rate is computed by a kind of geometric projection. But the fact that it has a geometric explanation doesn't negate the length contraction and time dilation, it just explains it.

 

[WannabeNewton]

But the fact that it has a geometric explanation doesn't negate the length contraction and time dilation, it just explains it.

I agree wholeheartedly with the rest of your post but I'm going to have to just slightly disagree here. Length contraction isn't explained in SR in the constructive sense if you use the relativity of simultaneity (i.e. a relativized chronogeometric structure of space-time) as the basis of the derivation whereas it is explained in Lorentz ether theory in terms of the microscopic Maxwell equations in the constructive sense. In other words the former falls out of chronogeometric assumptions of SR whereas the latter is a consequence of dynamics.

That being said, dEdt you should stop arguing your position as if it's a black and white issue in your favor because it isn't. While length contraction being explained dynamically by the microscopic Maxwell equations is an uncontentious part of Lorentz ether theory, the same doesn't go for SR. There is a profuse of literature in the philosophy of physics still debating whether the same constructive dynamical explanation of length contraction can be extended to the framework of SR in place of Einstein's non-constructive chronogeometric derivation of length contraction. You should probably read up on the literature first before trying to act as if you're 100% in the right.

 

[Mentz114]

That reinforces my point--that it isn't a consistent approach to talk about properties with respect to objects. If you take an extended object, such as a train, and start accelerating it, there IS no such thing as "the rest frame of the object" because in general, different parts of the object are traveling at different speeds.

Irrelevant. I'm talking about inertial motion.

Take a "rigid" rod that initially has length L when at rest. Gently acceleratBut the fact that it has a geometric explanation doesn't negate the length contraction and time dilation, it just explains it.

From what I understand of this, it re-inforces my point that length contraction does not need to be explained any further. The object does not need to be contracted. Where does it say in SR that the object contracts ?

Can you come up with an experiment that shows that the object contracted ? Say the pole in the barn-pole scenario ?

 

[WannabeNewton]

Where does it say in SR that the object contracts ?

Such a statement only has meaning relative to a choice of frame. In the inertial frame (modulo spatial rotations) in which the rod is initially at rest before being Born rigidly accelerated, it certainly does contract continuously during the acceleration phase and remains at a single contracted length after being brought to a constant velocity. On the other hand, in the rest frame of any given particle in the rod the spatial distances to neighboring particles in the rod will remain constant for all time because the entire time-like congruence of particles in the rod is Born rigid.

 

[dEdt]

WannabeNetwon

I won't pretend that my interpretation of SR isn't contentious -- in fact, I'd go as far as to say that it's a minority position. However, I will continue to passionately advocate for it because it is the correct interpretation. (Incidentally, it was in poor taste that you accused me of being ignorant of the literature in the philosophy of relativity. I've read most of Harvey Brown's work on the matter, including his book Physical Relativity, and have been thoroughly convinced by his arguments. On the other hand the papers countering his position, such as John Norton's "Why Constructive Relativity Fails", have been very feeble replies in my opinion.)

You begin by asserting that

In other words [length contraction] falls out of chronogeometric assumptions of SR whereas [in the Lorentz ether theory it] is a consequence of dynamics.

It's worth noting that, despite how confidently you state it, this interpretation of length contraction appears nowhere in Einstein's writings (at least that I'm aware of), even after he was introduced to Minkowski's work and even after his formulation of General Relativity. To the contrary, after Pauli wrote his review article on relativity, which contained the passage

Should one, then, completely abandon any attempt to explain the Lorentz contraction atomistically? We think that the answer to this question should be No. The contraction of a measuring rod is not an elementary but a very complicated process. It would not take place except for the covariance with respect to the Lorentz group of the basic equations of electron theory, as well as of those laws, as yet unknown to us, which determine the cohesion of the electron itself.

, Einstein enthusiastically praised it, writing that

Whoever studies this mature and grandly conceived work might not believe that its author is a twenty-one year old man. One wonders what to admire most, the psychological understanding for the development of ideas, the sureness of mathematical deduction, the profound physical insight, the capacity for lucid, systematical presentation, the knowledge of the literature, the complete treatment of the subject matter, or the sureness of critical appraisal.

For what it's worth, Eddington, who was responsible for introducing relativity to the English-speaking world, wrote that

There is really nothing mysterious about the FitzGerald contraction. It would be an unnatural property of a rod pictured in the old way as continuous substance occupying space in virtue of its substantiality; but it is an entirely natural property of a swarm of particles held in delicate balance by electromagnetic forces, and occupying space by buffeting away anything that tries to enter.

I hope these quotes convince you that the interpretation of length contraction, time dilation etc. as "geometric phenomena" is quite recent.

It's also an unsatisfactory interpretation in my opinion. To see why, we first have to ask ourselves, what is geometry? Without going into the level of rigor that would satisfy a mathematician, a geometry is a collection of things called points, obeying certain axioms, along with a way of assigning a number for every pair of points, this function being called the metric. Special Relativity gives us a way of creating a spacetime geometry, with events serving as the geometry's points, because the quantity $\eta_{\alpha\beta}\Delta x^\alpha\Delta x^\beta$ serves as a useful metric due to the fact that this quantity takes the same form in all inertial coordinate systems.

But here's the key point: the only reason we assign a such a metric to the set of events is because the laws of physics are Lorentz invariant. Otherwise, the quantity $\eta_{\alpha\beta}\Delta x^\alpha\Delta x^\beta$ would play no role in the laws of physics and hence would be completely useless. In other words, it is the symmetry properties of the dynamical laws of physics that create a spacetime geometry, not the other way around. So to explain length contraction in geometric terms is an indirect way of explaining it in terms of the dynamical laws of nature.

 

[Mentz114]

Such a statement only has meaning relative to a choice of frame. In the inertial frame (modulo spatial rotations) in which the rod is initially at rest before being Born rigidly accelerated, it certainly does contract continuously during the acceleration phase and remains at a single contracted length after being brought to a constant velocity. On the other hand, in the rest frame of any given particle in the rod the spatial distances to neighboring particles in the rod will remain constant for all time because the entire time-like congruence of particles in the rod is Born rigid.

Yes, but I've already said I'm talking about an effect that happens between inertial timelike worldlines. I don't see how rigidity affects the measurement of a moving rod between inertal frames.

 

[WannabeNewton]

(Incidentally, it was in poor taste that you accused me of being ignorant of the literature in the philosophy of relativity. I've read most of Harvey Brown's work on the matter, including his book Physical Relativity, and have been thoroughly convinced by his arguments. On the other hand the papers countering his position, such as John Norton's "Why Constructive Relativity Fails", have been very feeble replies in my opinion.)

While I apologize for my presumption, I would think a person who is aware of the contention would pay more caution in advocating the (as you put it) "minority position" as if it was unequivocally established in current literature. In other words, your previous posts give off the impression that said position is incontestable whereas the philosophical literature says otherwise so you should have elucidated that disclaimer. A fruitful discussion would entail both the pitfalls and the advantages of a constructive, dynamical explanation of length contraction by means of microscopic interactions.

It's also an unsatisfactory interpretation in my opinion.

This, on the other hand, I would say is not a minority view. Unfortunately the chronogeometric framework of SR provides such an elegant derivation (not explanation) of length contraction that a constructive, dynamical explanation is often eschewed.

Thanks for the historical quotes! I had seen Pauli's quote before but never the other two, and they are definitely on the convincing side.

 

[Mentz114]

WannabeNetwon

I won't pretend that my interpretation of SR isn't contentious --
...
...
...
But here's the key point: the only reason we assign a such a metric to the set of events is because the laws of physics are Lorentz invariant. Otherwise, the quantity $\eta_{\alpha\beta}\Delta x^\alpha\Delta x^beta$ would play no role in the laws of physics and hence would be completely useless. In other words, it is the symmetry properties of the dynamical laws of physics that create a spacetime geometry, not the other way around. So to explain length contraction in geometric terms is an indirect way of explaining it in terms of the dynamical laws of nature.

What you are talking about is not an interpretation of SR but some other theory. I wish you'd said this at the beginning instead of claiming a lot of false stuff about SR.

 

[dEdt]

What you are talking about is not an interpretation of SR but some other theory. I wish you'd said this at the beginning instead of claiming a lot of false stuff about SR.

You can disagree with this interpretation, but it is an interpretation of special relativity. What would make you say otherwise?

 

[stevendaryl]

Irrelevant. I'm talking about inertial motion.

You said:

But a property of an object has the value that the object itself assigns.

That didn't sound like it was restricted to objects moving inertially. But if you do restrict it to objects moving inertially, does that mean that objects that are accelerating don't have properties?

Where does it say in SR that the object contracts ?

Well, if you assume that an object is gently accelerated in the direction of its length in such a way that it always has the same length L in its instantaneous rest frame, then it follows that its length in any single rest frame contracts continuously. (Where, as I said, "length in a frame" means the distance between endpoints measured simultaneously in that frame.)

 

[Mentz114]

You can disagree with this interpretation, but it is an interpretation of special relativity. What would make you say otherwise?

Because SR does not try to explain the geometric effects. They are easily deduced from the geometry.

That has to be left to another theory.

 

[Mentz114]

You said:
That didn't sound like it was restricted to objects moving inertially. But if you do restrict it to objects moving inertially, does that mean that objects that are accelerating don't have properties?

It was meant so. If something is accelerating, does that mean it can never be or have been inertial ?

Well, if you assume that an object is gently accelerated in the direction of its length in such a way that it always has the same length L in its instantaneous rest frame, then it follows that its length in any single rest frame contracts continuously. (Where, as I said, "length in a frame" means the distance between endpoints measured simultaneously in that frame.)

With respect to you, I don't think this is a useful discussion.