How Does Rotational Relativity Affect Particle Dynamics in a Two-Body System?

[Jonnyb42]

@Kynnath (#31)
Ok, I don't mean to pick at your post too much, but I think there are limitations to the examples.

A way to see it is, imagine that the universe is a play.

A play has a stage, which implies an absolute reference, and

Imagine you grab a wire frame, and put it in front of your screen.

same with the screen.
I know those seem like trivial things to point out, but they affect the way we think about the problem. If you rotated the wire frame synchronously with something on the screen, you might come up with similar problems in trying to describe motion in terms of that rotating wire frame.

Just a thought in general, how can we know anything is an inertial reference? It requires us to assume another frame of reference is inertial. I know this was pointed out earlier, but it makes it hard for me to imagine a reference frame as inertial or non-inertial.

Also, an argument against seeing a fictitious force and then concluding that the frame of reference must be a non-inertial reference frame is that when you do that it becomes circular. The fictitious force is due to a non-inertial frame of reference, and now the frame of reference is non-inertial because of the fictitious force.

In special relativity, for instance, the order of events may differ, but it’s difficult to find an example within special relativity where it does not apply.

I have not studied relativity, but if that were really the case, I think it would become arguable that the same [total] event is taking place.

Here is a picture to show the original problem:
[PLAIN]http://mynqa.com/Cargo/FIG1.bmp
The shown coordinate system is rotating along with particles A and B as seen from particle C, some gravitationally negligible distance away.
In this coordinate system, A and B have a gravitational attraction towards each other, but their distance is unchanging. With no other forces acting on the system, (besides the negligible pull from particle C), how do they not collide?

After many posts, it is apparent to me that it is a problem of inertia and "What makes some coordinate systems inertial and others not?"

 

[Kynnath]

A play has a stage, which implies an absolute reference

Not really. The stage can be considered another 'actor' in the play. The actors have to be at certain places on the stage at given time, but you can make the same considerations for other actors. You could describe the play in terms of how the stage and the other characters flow around a given character, and the description would be just as accurate, if a little more confusing to our minds.

Also, an argument against seeing a fictitious force and then concluding that the frame of reference must be a non-inertial reference frame is that when you do that it becomes circular. The fictitious force is due to a non-inertial frame of reference, and now the frame of reference is non-inertial because of the fictitious force.

That's not circular. That's a simple deduction. You're just wording it in a convoluted way.

*If a frame shows fictitious forces, it is non-inertial.
*This frame shows fictitious forces (forces that can't be explained from any other source).
-> Conclusion: this frame is non-inertial.

You can explain why non-inertial frames display fictitious forces, but that's a separate matter, and you don't need to know that to be able to determine if a particular frame is non-inertial.

Let's try coming from the other direction. What would you expect to happen, if things didn't work the way they did? If watching from the rotating frame, the particles collide, what would you see from a different reference frame?

In this coordinate system, A and B have a gravitational attraction towards each other, but their distance is unchanging. With no other forces acting on the system, (besides the negligible pull from particle C), how do they not collide?

See, here is your mistake. You're trying to work out things first, then trying to force the system to do what you thought it should do. It doesn't work that way. You observe the system first, then try to work out what forces are in play.

Your first observation is, "The bodies do not move towards each other." From that, you determine their accelerations are 0. So the sum of forces on them is 0. You then try to work out what forces those are. There is the force of gravity, for one. Those pull them together. So you take that out of the sum of forces, and are left with a force pulling outwards.

And that is the answer to your last question. You can tell you are inside a non-inertial reference frame because of that. You don't need to compare to another reference or anyhing like that, the information from the frame itself is sufficient to work it out. There is a force left over you can't justify. You can't make it go away, and then be shocked that the bodies don't collide after you ignored a force in the system.

 

[Cleonis]

Just a thought in general, how can we know anything is an inertial reference? It requires us to assume another frame of reference is inertial. I know this was pointed out earlier, but it makes it hard for me to imagine a reference frame as inertial or non-inertial.

Also, an argument against seeing a fictitious force and then concluding that the frame of reference must be a non-inertial reference frame is that when you do that it becomes circular. The fictitious force is due to a non-inertial frame of reference, and now the frame of reference is non-inertial because of the fictitious force.

Here is how I see it.

The laws of motion that we have formulated are not based on circular reasoning. If they would be merely the product of circular reasoning then they would be unconnected to our physical reality. But as we know the laws of motion do a fine job of describing the properties of motion.

However, to formulate the laws of motion in the first place a necessity was recognition of the significance of the equivalence class of inertial coordinate systems. That was what Galilei urged in his writings, presenting the thought experiment of tossing an object up inside the cabin of a boat, when sailing with uniform velocity on perfectly smooth water. Galilei argued: we know from experience that the motion relative to the cabin does not reveal the velocity of the boat.
If you have a number of boats, all sailing with uniform velocity on perfectly smooth water, then inside the cabin you cannot tell what the velocity of that boat is with respect to any other of the boats. Implicitly that reasoning asserts the existence of an equivalence class of inertial coordinate systems.

What then distinguishes the class of inertial coordinate systems from other classes? There is only one criterium: the laws of motion are valid if and only if a member of the class of inertial coordinate systems is used to reference the motion. It's the laws of motion that provide the criterium.

So really there are two mental structures:
- The laws of motion.
- The equivalence class of inertial coordinate systems.,
Those two are mutually dependent. Each defines the other, and each needs the other in order to be defined.

This mutual dependence has led some people to suggest that 'the idea of inertial coordinate systems is circular reasoning'.I think that accusation of "circular reasoning" doesn't add up. Clearly the laws of motion are not circular reasoning.

Try to imagine a Universe without inertia. All motion would be completely lawless then. (I think such a Universe cannot exist in the first place.)
The laws of motion do the following: they describe the properties of inertia.

Formulating laws of motion is possible because inertia is so uniform and has such definable properties. The physical properties of inertia give rise to the equivalence class of inertial coordanate systems.
Yet some people seem reluctant to acknowledge that inertia exists. That is like being a scuba-diver who is reluctant to acknowledge that buoyancy exists.

 

[JDługosz]

Jonnyb42,

Newton thought about a similar thing, being two balls and a string. Set it spinning, and the string gets tight to keep them from flying off in opposite directions.

You understand that position and linear motion are totally relative—there is no marked zero point (origin) in the universe, and no concept of linear motion except between objects. "Inertia" works with these concepts in particular, along with the idea that all directions are the same, and the rules don't change over time.

However, rotation is not like that. Rotation is absolute. Given the above relativeness of inertia, it emerges that rotation is not relative.

If you were keeping station with your test objects, you could not say what speed you were traveling at in any absolute sense. However, you can state that you are not rotating in an absolute sense.

 

[Jonnyb42]

However, rotation is not like that. Rotation is absolute.

Yeah I had come to this conclusion, but it is still not satisfying because then I wonder why rotation is absolute. It is just a motion which I can easily imagine putting a coordinate system on.

 

[Phrak]

Jonnyb42,

Newton thought about a similar thing, being two balls and a string. Set it spinning, and the string gets tight to keep them from flying off in opposite directions.

You understand that position and linear motion are totally relative—there is no marked zero point (origin) in the universe, and no concept of linear motion except between objects. "Inertia" works with these concepts in particular, along with the idea that all directions are the same, and the rules don't change over time.

However, rotation is not like that. Rotation is absolute. Given the above relativeness of inertia, it emerges that rotation is not relative.

I'm glade you put it like this. It helps clarify the question. The question is "Why is there a preferred coordinate system over others, in states of relative rotational motion, which we may call absolute? As yet, no one seems be arguing that this presumption is unjustified based upon theory or evidence, though I may have missed it.

 

[JDługosz]

Yeah I had come to this conclusion, but it is still not satisfying because then I wonder why rotation is absolute. It is just a motion which I can easily imagine putting a coordinate system on.

I'm glade you put it like this. It helps clarify the question. The question is "Why is there a preferred [sic] coordinate system over others, in states of relative rotational motion, which we may call absolute? As yet, no one seems be arguing that this presumption is unjustified based upon theory or evidence, though I may have missed it.

The concept of "inertia" follows from the concept that an object follows its natural state of motion unless changed. "It doesn't change unless you change it". Why is a straight line of uniform speed "natural"? It follows from the idea that space is the same everywhere and has no hard zero point to measure against. That is, it emerges from starting with as little as possible and not adding special rules!

Given that uniform linear motion is all relative, it emerges that rotation is not. Just by tying two balls together with a string, you are preventing them from following their natural motion. If natural motion is to move in a line at uniform speed, making something move in a curved path is "doing something" to it. If you observe two balls tied together, if the string is under tension then you are rotating. You can indeed tell, in an absolute sense.

It's no different than noting that two balls are moving relative to each other. Just because you can't put absolute motion against space doesn't mean that all kinds of measurements of moving objects are meaningless.

--John

 

[Jonnyb42]

Well it appears we have a dissagreement, that perhaps needs to get sorted out?

I ask if General Relativity has the solution to my problem,

Cleonis told me

No.

(at post #25)

but Demystifier said

But in the relativity theory, this question can be answered: You accelerate with respect to the metric field (metric tensor).

(https://www.physicsforums.com/showthread.php?t=405216" on post #33)

 

[JDługosz]

Jonnyb42,
General Relativity adds in gravity. It does not do anything about rotation.

 

[Jano L.]

I agree with Jonny - in Newton's mechanics, one has to assume that there is a reference frame in which Newton's laws are valid. That means, we assume the law of inertia holds - a free body moves with constant velocity, as measured with respect to this special frame.

This clearly does not work for every frame (for example it does not work for a child on the roundabout), so the question arises, why certain frames are ok (law of inertia holds), but some of them are not?

There is a well known answer due to Mach, who says that these bad frames have no fixed orientation with respect to distant stars. So not all frames of reference are equivalent, at least in our experience - only the inertial ones, with fixed orientation with respect to stars.

However, from the global viewpoint, also the distant stars and their motion should be described and explained, because they do not form a rigid body. Imagine the stars moved much faster, so that it would be impossible to use them as a reference frame.
How to identify or construct the inertial frame then?

 

[Cleonis]

Well it appears we have a dissagreement, that perhaps needs to get sorted out?
I ask if General Relativity has the solution to my problem,

Well, I may have misinterpreted what for you the core of your question is. Let me get back to the start.

At the start you pointed out the case of two celestial bodies orbiting their common center of mass in perfectly circular orbits. That is a very uniform motion pattern. Yet this rotation is not relative.

You seem to yearn for an exhaustive explanation of why rotation is absolute.The thing is, while physics theories are good or even profound explanations, they are not exhaustive explanations. Don't get me wrong: theories can be deep; the deeper the better. In theoretical physics progress is made when a new description is found that moves the physics understanding to a deeper level. But this is not limitless.

In the case of theory of motion it's the properties of inertia that give rise to the fact that rotation is absolute. The current situation is that we have to assume the properties of inertia in order to formulate theories at all.

GR unifies the description of inertia and the description of gravitation in a single framework. But GR does not explain inertia exhaustively. In order to formulate GR the properties of inertia had to be assumed.

In GR math there is an apparatus, called the 'metric tensor' that is used for describing the inertia/gravitation properties of whatever is being examined. (What is being examined is a volume of space with sources of gravitation in it.) But it's not that this metric tensor is a window to deeper understanding of inertia. In order to formulate GR the properties of inertia had to be assumed.

Jonnyb42,
Over time I've been getting the impression that you yearn for an explanation of inertia itself. If that is the case then you're outta luck. That which has been presented in this thread is that which is available.

 

[lugita15]

No. An observer can certainly tell that he is in an non-inertial frame. Just check Newton's laws.

How can an observer tell that he is in a non-inertial frame? What if he assumes that the fictitious force he is experiencing are genuine forces?

 

[Kynnath]

Fictitious forces are already indistinguishable from real forces. They are as 'real' as genuine forces. They're fictitious because they don't have a reaction pair. In an inertial system, every force is balanced by an opposing reaction. Te fictitious force is the remainder from the acceleration of the reference frame.

 

[JDługosz]

Imagine the stars moved much faster, so that it would be impossible to use them as a reference frame.
How to identify or construct the inertial frame then?

Using the two balls connected by a string.

To clarify the other posts subsequent to yours, prepare the balls and string and identify that there are no other forces acting on them (e.g. you don't want one to be magnetic and the other not, with a big magnet near by; you don't want to be on the surface of a planet; you don't want to be in an accelerating spaceship). That is, you prepare what you suppose should illustrate the law of inertia. Does it?

If the balls don't stay put when released, but accelerate on their own, then there are either forces you have not identified (a student messed with your lab to make the experiment mess up in front of the class?), or you are not in an inertial reference frame.

Doing several experiments and mapping the results, you can probe the details of the observed forces. You may identify the source of the unknown force. Or you may discover that it follows what you expect of "centrifugal force" from a specific axis and rate of rotation, which you then determine.

--John

 

[Jonnyb42]

Today I have discovered a great thing. This principle that has bothered me for so long, turns out to be the exact motive for the General Theory of Relativity. This problem is described somewhat differently, but named the Principle of Equivalence. I know someone earlier in the thread said this, but I have found this out myself.

I would like to thank those who helped me with this, I still do not know the answer fully, but I am finally happy to know there is an answer, and I know where the answer is. From here on I will be studying GR. Thanks again

-Jonny

 

[Jonnyb42]

Ok so I haven't been as successful as I had hoped in solving this problem, as I thought from my previous post. I have a number of new questions:

This same exact question can be represented as follows: Two balls of water floating in space, one is spinning and one is not (as seen from a third observer.) The spinning one is flattened into an ellipsoid, while the still one is a perfect sphere.
(Then the questions follow similarly to the original problem.)

The problem is, it is the same problem even without gravity. This has mainly to do with rotation. General Relativity isn't required to answer the above scenario is it?

Also, about the original problem. I thought about it, and isn't it true that there are no detectable forces on either object due to the revolution about one another?

 

[e2m2a]

isn't it true that there are no detectable forces on either object due to the revolution about one another?

Consider this. Suppose your two orbiting objects are not particles, but purely homogenous planets of the same density made of one substance. Suppose neither planet is spinning on its own spin axis.

You are located on one of the planets. Now, you weigh yourself on an extremely sensitive scale on the side of the planet that is facing the other planet. You record your weight.

Then, you travel to the opposite side of the planet, 180 degrees from your initial position, and weigh yourself again. You then compare both weight measurements. Will they agree?

 

[Jonnyb42]

Suppose your two orbiting objects are not particles, but purely homogenous planets of the same density made of one substance. Suppose neither planet is spinning on its own spin axis.

You are located on one of the planets. Now, you weigh yourself on an extremely sensitive scale on the side of the planet that is facing the other planet. You record your weight.

Then, you travel to the opposite side of the planet, 180 degrees from your initial position, and weigh yourself again. You then compare both weight measurements. Will they agree?

If the diameter of the planets are negligible compared their seperation, then yes they should.
If the two planets were held together by some (rediculously stong) thick cable, and the cable were the only thing keeping them from flying apart, then the two measurements would not be the same.

 

[e2m2a]

If the diameter of the planets are negligible compared their seperation, then yes they should.

No, the diameter of the planets would not matter. The direction of the measurements is what is relevant. A sensitive enough scale would detect a difference. Imagine this.

The Earth is spinning on its axis. The shape of the Earth approximates that of an oblate spheroid, which means it is somewhat flattened at the poles and bulges at the equator.

If you were to measure your weight at one of the poles and compare it to your weight at the equator, it is a known fact of physics that your apparent weight would be less at the equator. Why is this?

This is due to a centrifugal effect with respect to the frame of the spinning earth. With respect to the frame of the earth, it would appear that some strange force is pulling you in a radial-outward direction, away from the center of mass of the earth, such that it causes your weight to decrease at the equator.

Now, imagine the Earth has plastic properties and we do a topological “morphing” of the earth. We stretch and redistribute the earth’s mass such that it is now shaped like two rotating balls, connected by a long infinitely strong string of earth-matter holding the balls of Earth mass in orbit around their common center of mass. This approximates your initial model if we assume the mass of the “string” is negligible and it has infinite tensile strength.

Has anything changed? Yes, the initial distribution of the Earth mass has changed. But has the dynamic effects of rotation changed? No. You would still see differences in weight measurements, regardless of the diameter of the balls. What is relevant is the direction in which you take the measurements.

Now here is the kicker to demonstrate this. Take two springs. Place one on the surface of one of the balls such that it is pointing toward the other ball. Take the other spring and place it on the opposite side of the ball. Measure the lengths of the two springs and compare.

The length of the spring facing the other ball will be slightly less(compressed) than its equilibrium length, and the length of the other spring on the opposite side of the ball will be slightly longer(stretched) than its equilibrium length. The difference is due to where you placed the springs with respect to the rotation of the two balls.

 

[Jonnyb42]

I know what you are saying, but your examples are based on equilibrium set by electromagnetism. Two planets revolving about each other are in equilibrium by gravity, and you would not be able to measure differences like that.

It's like astronauts orbiting earth; they do not feel centrifugal forces.

 

[Dale]

You may want to open a new thread in the relativity section for this.

 

[e2m2a]

You may want to open a new thread in the relativity section for this.

I agree with DaleSpam. Your initial question inevitably leads to discussions about inertia and general relativity.

Einstein tackled the question of the origin of inertia by trying to include the Mach's principle in his formulation of general relativity. However, later on in his life, he was dissatisfied with the attempt, and reportedly abandoned Mach's principle. Some physicists still maintain that the principle is still implied in his equations.

Presently, there is no general consensus in the main-stream scientific community of what causes inertia. It is truly one of the great mysteries of modern science, still with us in the 21st century.

Others in the relativity forum may give you some interesting insights and ideas, however, that touch on inertia as it relates to general relativity.

From my research I think there are two main "camps" on the explanation of the origin of inertia. I am not going to go into it, so as not to risk being censored for talking about "speculative theories." However, I will venture this and you can do your own research on the topic by searching the web.

One camp uses a Machian explanation on the origin of inertia, more the "main-stream" explanation. The other camp uses the vacuum energy as the origin of inertia, considered an out-on-the-fringe explanation. Both explanations share one common defect. Neither one can be absolutely proven or disproven.

To prove or disprove the Machian explanation, you would have to remove all of the cosmic mass in the universe, except for the test objects you were experimenting with, to see if inertia still would exist. Obviously, that can't be done.

To prove or disprove the vacuum energy explanation, you would have to remove all of the putative vacuum energy that exists in space. Obviously, that can't be done either.

I do lean toward one explanation over the other, but as I said, I will not risk being censored by talking about it.

Good luck in your search for an answer. Your curiosity and questioning about these things should be commended. It is what drives the advancement of science-- the willingness to search and question. Be brave enough to look at all sides of the issue with an open mind.

 

[Jonnyb42]

Good luck in your search for an answer.

Thanks, I concluded earlier to stop thinking about it as it is giving me a headache and distracting me from grades, and that I should only go back to it after studying general relativity. However, then I realized I have the same question for something small that rotates, it stretches and changes shape slightly, and how that should have nothing to do with general relativity (of course how would I really know that,) but anyways:

I am now thinking about this last discussion of ours, which very much relates to the original problem, but is more in the General Relativity realm, I will start a new thread here:
https://www.physicsforums.com/showthread.php?t=485975"

 

[Jonnyb42]

However, later on in his life, he was dissatisfied with the attempt, and reportedly abandoned Mach's principle.

I have read this as well elsewhere but don't remember where, can you or someone else show me some evidence of this?

 

[e2m2a]

I have read this as well elsewhere but don't remember where, can you or someone else show me some evidence of this?

Someone in the forum in your new thread may be able to give more information about this. I am not qualified to discuss this.

My understanding is one of the reasons Einstein became dissastified with Mach's Principle is because his field equations showed that inertia could exist in space devoid of matter. Also, Mach's Principle assumes a certain cosmological model of the universe must exist.

That is, some physicists have argued that Mach's Principle is not just a direct statement about the origin of inertia, but the principle implies the existence of a specific structure of the universe itself, a very grand and sweeping hypothesis.

I am not sure how the cosmological and astronomical community relates Mach's Principle to the apparent ever-accelerating state of the universe.