Two scientists are completely isolated in two different boxes:

  1. First box moves uniformly straight (in a perfect space).

  2. Second box rotates uniformly (also in a perfect space).

The scientists have any instrument to detect his movement. Who makes? The second.

Why a type of motion is relative and another is not? Why not are both relative? Why not are both absolute?

(I do NOT mean the theory of relativity by Albert Einstein)

  • $\begingroup$ Re The scientists have any instrument to detect his movement. Relative to what? $\endgroup$ – David Hammen Aug 24 '15 at 23:27
  • $\begingroup$ Who makes? does not make sense. $\endgroup$ – Kyle Kanos Aug 25 '15 at 1:52
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    $\begingroup$ @DavidHammen The rotation movement it's easy to detect with a pendulum. $\endgroup$ – Stefan Aug 25 '15 at 7:47
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    $\begingroup$ Sorry for bad english, @KyleKanos .Who makes=Who can to detect his movement. $\endgroup$ – Stefan Aug 25 '15 at 7:49
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    $\begingroup$ The OP asks for the criteria to distinguish between relative and absolute motion, I think his question is clear, why put on hold? $\endgroup$ – Omar Nagib Aug 26 '15 at 16:49

This discussion is only in the context of newtonian mechnaics(since this is what the OP asked for).

The galilean principle of relativity states:

-The laws of physics hold in thier simplest form with respect to inertial frames of reference.

-Time intervals and distances between events are the same for all frames of reference.

The relativity of constant velocity motion is a direct consequence of the galilean relativiy:

Say you have two inertial frames of reference, $S$ and $S'$, with coordinates $(x,t)$ and $(x',t)$, where $S$ is at rest and $S'$ moves with velocity $v$ with respect to $S$.Then using galilean transformation which relates the coordinates of $S$ and $S'$, with the given information, we can deduce what $S'$ says about the motion of its frame and the motion of $S$ with respect to it:

$x'=x-vt$ .

The equation of motion of $S'$ with respect to $S$ is simply given by


Plugging in the transformation one gets: $x'=vt-vt=0$ .

Differentiating by $\dfrac{d}{dt}$ to obtain the velocity of $S'$ in his frame one gets:


So $S'$ claims that he's at rest and not moving.

In addition to that consider rearranging terms of the galilean transformation to look like this:


$S'$ can claim that actually he is at rest and it's $S$ that is moving with velocity $-v$.

But the ultimate reason why constant velocity motion is relative is the following argument :

In addition to the existence of $S$ and $S'$, consider a particle that is being acted upon by a force $F=m\dfrac{d^2x}{dt^2}$ in $S$.

how the laws of physics look like in $S'$?

Since we know that


Differentiating twice with time one gets:


So that we get $F=m\dfrac{d^2x'}{dt^2}$.

So the laws of physics look exactly the same in both $S$ and $S'$, satisfying the principle of relativity.

What implication does this result have on constant velocity motion? Well it implies that constant velocity is relative since:

-every observer can claim he's at rest and it's the other observer who's moving.

-since the laws of physics are the same in both the rest and the moving(with constant velocity) frame. If you locked both $S$ and $S'$ in a closed box, they won't be able to make an experiment to tell apart if they're moving or not. The world just behaves the same if you're at rest or moving with constant velocity.

What about motion that's not at constant velocity? It turns out that such frames are non-inertial frames of reference, in that the laws of physics don't hold true in them.

(To give you a fun task to do, consider two frames, $S$ at rest on the ground and $S''$ that is accelerating with $a$ with respect to $S$, thier coordinates are related by $x"=x-\dfrac{1}{2}at^2$, and say you have a particle that is acted upon by $F=m\dfrac{d^2x}{dt^2}$ in $S$, if the principle of relativity holds we should expect that in $S"$ $F=m\dfrac{d^2x"}{dt^2}$, check if this is true or not(it's not!) and since it's not true, $S"$ cannot claim rightly he's at rest and it's $S$ who's accelerating.)

Accelerated/non-inertial frames of reference are marked by the fact that Newton's laws like his second law and the law of conservation of momentum are violated. Or in other words, they're marked by the exsistence of ficticious forces, that are proprtional to mass in thier frames.

This brings us to your second question: is rotation relative or not?

This is the reason why rotation(and other forms of acceleration) are not relative:

-the laws of physics break down in such frames(that is, they don't hold in their simplest form as they do in inertial frames), so that even one is confined in a box, one can detect his absolute motion(rotation) through the existence of fictitious forces like the coriolis and centrifugal forces.

Now let's turn to the totally empty space case that you asked for:

There's an important point to tell. Newton regarded accelerated motion absolute in the sense that it moves with respect to absolute space, a structure whose exsistence he postulated to explain why acceleration is absolute and all observers agree on whether a body is accelerating or not. In modern formulations however, absolute space is not necessary and so it's discarded , it's said a frame's acceleration is absolute in the sense that it's accelerating to all inertial frames of reference.

Now let's answer your question(this is my understanding, and I'm ready to be corrected if I got something wrong):

-if you have totally empty space, and one observer in it, It makes no sense to tell if he's moving with constant velocity at all(that is if he's at rest or moving uniformly) or if he's accelerating or not. Since the concept of constant velocity motion makes sense only between two inertial frames of reference. Since there's only one frame, and the concept of acceleration in modern formulation only makes sense when one speaks of acceleration with respect to other inertial frames, It makes no sense to speak of any motion(be it uniform or rotation or whatever) in otherwise totally empty universe.

-Newton would agree upon my answer on uniform motion. But amazingly, he'd disagree regarding acceleration. For Newton who defines acceleration relative to absolute space, it makes total sense to speak of rotation of an object in an empty space, since it's rotating with respect to space itself.

So who is right? We don't know for these reasons: -the modern definition of acceleration(with respect to all inertial frames) vs newton's notion of acceleration against absolute space give the same experimental results in a universe that is populated by matter. To tell apart which is right, one has to do the experiment of rotating an object in a totally empty universe(which is impossible).

-Newtonian mechanics does not even hold in our universe,they're GR and QM that do(or more precisely, the to be found theory of quantum gravity).

I will leave others to talk about mach's principle.

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In Newtonian mechanics a particle will continue to move in a straight line, unless a force is acting on it.

Inside a rotating box, the particles are not moving in a straight line - they are rotating. In order to do this, they must have forces acting on them. In this case, the force is created by the inter-atomic or inter-molecular forces which hold stuff together. If you spin the box fast enough, the forces required would exceed the strength of the materials and everything would fly apart (in a straight line, at least until it hit something).

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Essentially, we don't know. Or in other words, that's how the universe is. It's like asking why the speed of light is independent of your reference frame, or why there are four fundamental forces. It has been found experimentally that this is how nature works. This is the complete answer; what follows is what some other people have thought about this issue.

Some people thought that this distinction between uniform and nonuniform motion was nonsense, and that all motion should be relative. If the universe as a whole was rotating, they said, how could you tell? What would it even mean to say that the whole universe is rotating? This idea was held very firmly by Mach (and Einstein was in the same camp too for a while!), and is enunciated in Mach's principle: All motion is relative to the matter content of the universe. If, as experiments show, we can detect absolute rotation, it's because we are really rotating with respect to all the galaxies and stars, and they are exerting some sort of influence. If they were rotating with us, we wouldn't be able to detect rotation.

Our current theories (General Relativity, in particular) say that this is false, and that uniform motion is the only one that is relative. But of course, this isn't really something we can test. We would have to either place a rotating lab in an empty universe, or put all the galaxies into rotation and see if we can detect something. Both things are essentially impossible, and so my opinion is that Mach's principle as it stands is irrelevant for physics. Unless someone postulates a specific way in which all the matter in the universe affects each other, it's not something that can be verified experimentally.

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  • $\begingroup$ You might take another look at frame dragging in GR. At least some people have interpreted it as giving Mach's principle a bit of a reprieve. $\endgroup$ – dmckee --- ex-moderator kitten Aug 25 '15 at 3:58
  • $\begingroup$ There's also laser gyros running on the Sagnac effect. That's a purely relativistic device that detects rotations. I was unclear about what @Javier was saying in his last paragraph, but it seems like that's some experimental confirmation that the rotating frame really is different. $\endgroup$ – Brick Aug 25 '15 at 7:15
  • $\begingroup$ @dmckee: I've never heard anyone formulate that quantitatively. To me it sounds like it can't be done; one problem is that the gravitational effects of far away matter decrease with distance. Also frame dragging is extremely weak. It would be interesting to attempt a detailed calculation, though. $\endgroup$ – Javier Aug 25 '15 at 10:47

I think a very neat answer to your question may come from this simulation of a rotating cylindrical spaceship (not mine!). The simulation itself is a Java applet. Below I am citing from the description of the problem it addresses, because it outlines the answer you are looking for, namely the difference between what one guy (Ralph) sees inside the rotating lab compared to another guy (Paul) who is outside the lab in an inertial frame.

"Ralph is traveling in his spaceship in interplanetary space on his way to Mars. The interior of the ship is cylindrical with radius 10 metres. The ship is rotating with the angular velocity 1 radian per second, which gives a centripetal acceleration of 10 m/s2 on the inner wall. So Ralph can walk around on the inner wall, always feeling that the gravitation is 1 g. Since there are no portholes in the ship, Ralph isn't aware that the spaceship is rotating; he thinks there is some form of artificial gravity made with Star Trek technology.

To pass the time on his long journey, Ralph is sometimes playing with a ball. He is puzzled by the weird behaviour of the ball. When he drops the ball, it falls towards the inner wall, as expected, but it is also veering a little to the left. If he hold the ball 2 metres above the wall, and throws it to the left with the initial velocity 8 m/s, the ball doesn't fall at all, it moves around the spaceship at 2 metres height above the wall, with the constant speed 8 m/s. If he on the other hand throws it to the right with the same speed, the ball falls much faster to the wall than expected.

But Ralph is a smart guy, so he his determined to figure out how the strange artificial gravity works. He throws the ball in many different directions and with different speeds, carefully measuring the trajectory of the ball with his camcorder. He finds that there must be two different forces acting on the ball, one that is acting radially out from the centre of the ship. This force gives the ball an acceleration which is equal to R per second squared, where R is the distance the ball is from the centre. The other force is proportional to the speed of the ball, and is always acting perpendicular to the velocity, to the right of the direction of the velocity. This force gives the ball an acceleration which is 2v per second, where v is the speed of the ball.

Ralph is of course convinced that these forces must be real, how else could the ball behave as it does ?

Paul, wearing a spacesuit, is outside the ship peeping in through a hidden porthole in the nose of the ship. Paul is not rotating. When Ralph is throwing the ball, Paul can see that no forces whatsoever are acting on the ball; the ball is always moving along straight trajectories with constant speed. This is as expected, the ball is after all weightless in space free of gravity.

The simulation shows two views of the ship's interior, one from the rotating frame where the ship is stationary (Ralph's frame), and one from the non rotating frame where the ship is rotating (Paul's frame). You can let Ralph throw his ball, and see the trajectory of the ball in the two views. The real point with the simulation is to demonstrate the fictitious forces in a rotating frame.

The simulation shows two views of the ship's interior, one from the rotating frame where the ship is stationary (Ralph's frame), and one from the non rotating frame where the ship is rotating (Paul's frame). You can let Ralph throw his ball, and see the trajectory of the ball in the two views. The real point with the simulation is to demonstrate the fictitious forces in a rotating frame."

Hope it helps.

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You are not the first how thinks about this. Rotating a water bucket the water inside will form a curved surface. This was the argument for Newton, that there is an absolute space. Later Ernst Mach pointed out, that the surrounding masses are responsible for the centrifugal forces. Indeed an astronaut in a big enough spaceship will observe the rotation. Having during rotation in an object in his hand and let it out, the object will fly straight away.

So I love Mach's principle. From the above mentioned article in Wikipedia: "In some of his later papers (especially in 1920 and 1924), Einstein gave a new definition of the aether by identifying it with "properties of space". Einstein also said that in general relativity the "aether" is not absolute anymore, as the gravitational field and therefore the structure of spacetime depends on the presence of matter. (It also must be said that Einstein's terminology (i.e. aether = properties of space) was not accepted by the scientific community.)"

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Only one engineer is needed, on Earth, but better on space.

With a microwave antenna tuned to the CMB frequency we can sense, and in fact we do, both the daily rotation motion of the Earth around the axis, the annual motion of Earth around the Sun (elliptic path) and the motion of the entire Solar System at 369 km/s in direction to Leo constellation (unmeasurable acceleration).

To measure the rotation motion a Foucault pendulum can be used, or a Sagnac interferometer.

All of the above motions can be considered absolute because nothing else but one observer is needed. To be considered relative you need two objects and describe the motion of one irt the other.

Consider one observer in the Moon and other at Earth each sensing the CMB photons:
They can use their absolute motions to describe their relative motions, ignoring an initial offset.

They have to assume a 3 fixed axis, given 3 fixed points in distant space, or better derived by the analysis of the common description around the Sun, same annual period and the similar change of the acceleration. In short, comparing their data, they will deduce that both are orbiting a common star, and that the Moon is orbiting the Earth.

Then when I read that, according to Relativity, there are no privileged references, I do not believe. As you see the CMB reference is special because the CMB photons provide a time base, a length unit and a reference frame common to all objects. This knowledge was not accessible to Einstein.

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    $\begingroup$ The principle of relativity doesn't say that two observers can't measure their relative motions. It says that if you're in uniform motion, you (a single observer) can't measure your velocity without looking outside your lab. In this case, measuring the CMB counts as looking outside. You would just be measuring your velocity with respect to the CMB. $\endgroup$ – Javier Aug 24 '15 at 23:13
  • $\begingroup$ @Javier Of course: "The principle of relativity doesn't say that two observers can't measure their relative motions". Using only the CMB reference each observer can synchronize the clock and length units without resorting to Einstein procedure. $\endgroup$ – Helder Velez Aug 25 '15 at 1:15
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    $\begingroup$ I'm sorry, I don't understand what you're saying. The CMB is not special. For example, if you know what the Sun's spectrum looks like in the Sun's rest frame, if later you want to know your velocity you can measure the Sun's Doppler shift to figure out your velocity with respect to the Sun. This doesn't contradict relativity. And I think your last paragraph could use a little humility; Einstein might not have known about the CMB, but every physicist for the last 50 years has, and relativity hasn't gone anywhere. $\endgroup$ – Javier Aug 25 '15 at 1:47
  • $\begingroup$ @Javier I understand your worry: in Motion Mountain book (online) page 149 to the question: Is velocity absolute?, it says "We do not feel translational, unaccelerated motions because this is impossible in principle." But is contradicted by WMAP experiment arxiv.org/pdf/1303.5087.pdf Planck 2013 results. XXVII .. Eppur si muove $\endgroup$ – Helder Velez Aug 25 '15 at 2:08
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    $\begingroup$ This answer may clear up some confusion for you. The key point is, "The only difference is that in the CMB rest frame you measure no velocity with respect to the CMB photons, but that does not imply any fundamental difference in the laws of physics." $\endgroup$ – 2012rcampion Aug 25 '15 at 2:54

This is by the mechanical theory of Newton, which postulates that moving straightly and uniformly is equivalent to rest, but does not state a similar statement about rotation. (And stating a similar statement about rotation would contradict to the rest of the Newtonian theory.)


Well, the laws of Newton are an approximation of special relativity, which in turn is an approximation of general relativity, which is an approximation of some other theory, which may probably be an approximation of another theory, maybe so infinitely.

Why, we don't know. It is because God created mechanics in this way.

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