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

[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.