Mach space in The Fabric of the Cosmos

[nightcleaner]

I have been reading about Mach space in Dr. Brian Greene's recent book, "The Fabric of the Cosmos", and must admit I am somewhat confused. This is not Dr. Greene's fault, I am sure. I was hoping for some clarification here. I will try to summarize what I found in Dr. Greene's book.

Mach proposed that in free empty space, with no uneven field or distant object to be related, a spinning object will not feel the centripetal forces. In common language, in totally empty space, how could it know it was spinning, without any distant object to relate itself?

My understanding is that objects are composed of parts. Did Mach neglect the fact that the parts are related to each other? An astronaut spinning in free space still feels his hands pulled outward, because his hands are accelerated in relation to his body. He doesn't need distant stars to know this. What am I missing?

Thanks,

nc

 

[turbo]

Mach proposed that in free empty space, with no uneven field or distant object to be related, a spinning object will not feel the centripetal forces. In common language, in totally empty space, how could it know it was spinning, without any distant object to relate itself?

My understanding is that objects are composed of parts. Did Mach neglect the fact that the parts are related to each other? An astronaut spinning in free space still feels his hands pulled outward, because his hands are accelerated in relation to his body. He doesn't need distant stars to know this. What am I missing?

Here is a thought-experiment that may confuse things even more:

Suppose you have a space station made of two parallel wheels connected by a common axle. The "tires" of the wheels are toroidal, and they contain crew quarters, labs, control rooms, etc. To provide about 1/2 G of "artificial gravity" for the folks working in each half of the station, you counter-rotate the wheels. Now the crew members can walk on the "floors" formed by the inside walls of the torii. The crew members can look out the windows at the opposite torus and see it spinning past them, and they feel the "artificial gravity" pulling them to the "floor" of their torus. They also notice that the background stars are moving at half the rotational speed of the neighboring torus. So far, so good. Now place that same station in Machian space with NO external masses - no stars and galaxies by which one can gauge one's movement. How are inertial forces expressed and measured in each torus?

Let's now go back to the beginning, and after we set up our space station, we do our best to keep one torus stationary so we can use all the great zero-G labs we set up in it, and we spin the other torus twice as fast as in the previous example, so the crew quarters will have normal-feeling one-G "gravitation", allowing the crew can walk, run, exercise, etc. The people floating around at their stations in the "stationary" zero-G toroid will see that the background stars remain fixed, while the other toroid rotates at the same speed as in the previous example. Now, let's pop this space station into that special Machian space that has no stars, galaxies, etc. Again, how are inertial forces expressed and measured in each torus?

In both examples (in real space), the people in one torus module will see the other torus rotating at equivalent rates - the only difference will be in the apparent rotation rate of the background universe. In both examples that we transported into empty (Machian) space, the people in each torus will see exactly the same rotation rate in the opposite torus, but they will see NO rotation of the background of space with which to determine their own rotation or lack thereof.

 

[Garth]

Now place that same station in Machian space with NO external masses - no stars and galaxies by which one can gauge one's movement. How are inertial forces expressed and measured in each torus?

The movement of one torus is measured against the movement of the other, if they are of equal mass then the two torii have equal and opposite motion.

It is similar to the question of whether a single body in an empty universe can experience inertial force, what would its acceleration be measured against? In order to produce such a force one would have to create a reaction of some kind. Say split the body exactly in half and use some force (magnetic repulsion say) to propel them apart. As soon as the split happens the motion of one half can be measured against the other, and it will be found to be equal and opposite.

Let's now go back to the beginning, and after we set up our space station, we do our best to keep one torus stationary so we can use all the great zero-G labs we set up in it, and we spin the other torus twice as fast as in the previous example, so the crew quarters will have normal-feeling one-G "gravitation"

The centripetal virtual force is proportional to $$\omega^2$$ so in that torus the crew will feel 2-G. In the Machian empty universe in the same example there is no 'absolute non-rotating frame, so both torii rotate at the orginal rate in opposite directions and their crews would feel 1/2 G as before.
We cannot find out which scenario is correct as we cannot do this experiment.
Garth

 

[nightcleaner]

Thank you for the replies, but perhaps my question was misunderstood.

In Mach space, there is no background. Will water in the bucket or people in the spacestation or two rocks on a string experience centripetel force in a background free environment?

My understanding is that Mach said they would not feel any centripetel force because without a background they cannot be said to rotate. I am suggesting that the water itself, or the station or the rocks on a string, are systems in themselves and therefore provide their own internal background. One rock is accelerated compared to the other, so the string pulls taut. The astronauts are part of the station, which is their background, so the idea that there are no background stars is not to the point. The water in the bucket curls, because the molocules and atoms in the water form a system of parts, and the parts are related to each other, and so one part may move in an accelerated fashion compared to another part.

If we are to make progress on this question, I suggest we use Occam's razor to remove any non-essential details. I think I remember that the rocks on a string idea was of Einstein. It seems the simplest system to me which may illustrate the point.

Mach would say that in a background free condition, (Mach space, no stars, no uneven fields) the two rocks cannot be related to anything to determine that they are in a condition of rotation. I would say that they are still related to each other, and so the idea of background stars or no background stars is irrelevant. The rocks form their own spacetime lattice and so can be made to feel centripetel force.

What I wish to resolve by this line of thought is that the argument of Mach is mis-stated. Macroscopic objects like space stations and astronauts and rocks on a string form their own background. If we wish to use Mach's argument, the object to be rotated or not rotated must not be an object in space as we know it, but instead must be a point particle in an otherwise empty spacetime. Can such a fundamental indivisible particle be said to rotate? If so, what does this tell us about quantum spin?

I hope to engage someone in discussion on this point.

Thanks for being here.

nc

 

[Garth]

That was the same concept of Mach space as I was using. Take the bucket. If the whole bucket and its contents revolve in an otherwise empty universe then according to Mach the water should be flat. The whole system rotates together, but as there is nothing that it is rotating with respect to there can be (according to MP) no rotation and no centrifugal force on the water molecules.

How this relates to quantum effects is indeed an interesting question, but we must remember that quantum spin is not rotation as we normally know it to be!

Garth

 

[turbo]

In the Machian empty universe in the same example there is no 'absolute non-rotating frame, so both torii rotate at the orginal rate in opposite directions and their crews would feel 1/2 G as before.
We cannot find out which scenario is correct as we cannot do this experiment.
Garth

Unfortunately, I came up with a similar result using Mach's terms. Perhaps we have to substitute the local "ground state of the universe" for Mach's "all matter in all of the universe" to make sense of his insistence that movement relative to the cosmological background is intrinsic to inertia. If inertia is conferred by movement relative to objects that are many light-years away, we have a HUGE "action at a distance" problem.

 

[Chronos]

Doesn't classical mechanics work in this example? Even in an otherwise empty universe, there is still me, the rock and the string. Do we not have inertial mass?

 

[Garth]

Chronos - If it is you, a rock, and (for the sake of argument), a massless string then the universe is not empty! To spin the rock you would need some kind of reaction force that would spin the rock one way and yourself the other.

turbo-1 - Yes there is action at a distance, just as with gravitation. I don't know whether you have followed the thread on the Cosmological Twin Paradox?here. But the inference is if the universe is closed and circumnavigation were possible then locally a preferred frame is defined (the one belonging to the stationary twin) by the global topology of the universe. An action-at-a-distance indeed!

Just a thought.

Garth

 

[nightcleaner]

That was the same concept of Mach space as I was using. Take the bucket. If the whole bucket and its contents revolve in an otherwise empty universe then according to Mach the water should be flat. The whole system rotates together, but as there is nothing that it is rotating with respect to there can be (according to MP) no rotation and no centrifugal force on the water molecules.

How this relates to quantum effects is indeed an interesting question, but we must remember that quantum spin is not rotation as we normally know it to be!

Garth

Thanks, Garth. I am not sure what MP is. My question to Mach would be, why have you neglected that the water itself is made up of many molecules, all related to each other? If the water is turning on an axis, then the molecules in and near the axis will have different motions compared to the molecules near the edge of the water. The curvature of the surface of the water has nothing to do with distant stars, everything to do with different motions of the water molecules compared to each other. I would therefore agree with Chronos that classical mechanics should still work in Mach space.

Then if we redesign Mach's experiment to occur on the Planck spacetime scale, where quantum effects become important, perhaps we can deduce something about the geometry of quarks. Events on the Planck scale are largely isolated from background by the extremely short times and distances involved, which make the local region of the quark environment unperturbed, as fits the description of Mach space. Then how should we expect simple two and three object systems in rotation to behave in such an environment? Do we get the restricted spin states found in quantum effects?

Take the two part quark-antiquark pair in an electron. Without external references, the only information about the spin condition of the pair is whether you are looking at it from the top or the bottom. It can only be said to rotate plus or rotate minus, which, if I have gotten all this down correctly, is the definition of a spin 1/2 particle.

If I have achieved communication here, I would like to extend this reasoning to see how the three quark particles might be seen to behave in the unperturbed space-time environment near the Planck scale.

Please help me with some feedback. I do respect and honor your opinions, and hope through this dialog to be able to improve my descriptions.

THanks,

nc

 

[jcsd]

MP is Mach's principle, which basically states that inertia (the resistance to the chnage of motion) is caused by movement relative to the background created by all the matter in the universe and therefore if we remove this matter then acceleration would be relative too and the 'fictious' inertial forces would not be present in any frames.

Mach's principle is not actually a feature of any of our currnetly accpeted theories, though it did influence Albert Einstein (which does include the relativity of accelartion, though not in the Machian sense).

 

[Garth]

nc - It is good to respond your posts.
Mach's Principle: There is no absolute frame that defines inertial frames of reference, inertial mass is determined by the distribution of mass and energy in the rest of the universe.

Consider your bucket in an otherwise empty unverse: If you say, "If the water is turning on an axis, then the molecules in and near the axis will have different motions compared to the molecules near the edge of the water." the question is 'turning' and 'motions' with respect to what?

Although I am not competent to extend MP to quantum physics, it would seem to me that if you had a sole electron in an otherwise empty universe you would not be able to determine its spin. Not only would you need an observer to "collapse the probability wave function", but also the direction of spin would be dependent on the orientation of that observer - but which way is 'up' in that empty universe?

Apart from that I am concerned that quantum spin does not infer motion or rotation and acceleration as classical spin does, therefore it may be completely independent of any Machian-type considerations.

Garth

 

[nightcleaner]

MP is Mach's principle, which basically states that inertia (the resistance to the chnage of motion) is caused by movement relative to the background created by all the matter in the universe and therefore if we remove this matter then acceleration would be relative too and the 'fictious' inertial forces would not be present in any frames.
Hi jcsd
Thanks for the very clear and concise definition. This helps.
So inertia is resistance to change in motion, and change in motion is acceleration, so we could just say that inertia is resistance to acceleration.
MP then states the proposition that inertia, or resistance to acceleration, is caused by motion relative to the background. I have replaced your word "movement" with the word "motion," for reasons of economy of idea. {If you have no objection?)

To recap, Resistance to acceleration is caused by motion relative to the background. I have an immediate concern with the apparent lack of parity between motion, represented in physics by distance per time, and acceleration, represented by distance per (time squared). But perhaps we will return to that later.

It is the notion of background which remains to be investigated. MP, if I have it correctly, places the background at a distance from the object, as a hollow sphere surrounding the space in which the object is found, marked by certain stars of reference. Then if the marks are removed, even though the sphere might remain in place, acceleration effects disappear? This seems unsatisfactory to me. Perhaps Mach would say that it is the sphere itself which must be removed, and not merely the marked stars. Very well. Let us make it so.

Now we have an object in unmarked space. The object however has a geometry of its own, assuming it is a macroscopic agglomeration of definable points, such as an astronaut or a body of water or even two rocks on a string (or two quarks and their gluons?). Mach says it has the quality of rotation, which he says results in no accelerative forces internal to the body. His argument then seems to self-conflict, since he first says there can be no rotation in unmarked space, and then says that the body is in rotation. However, perhaps that can be overlooked, and still get some meaning from the ideas.

We have one remaining part of this problem to investigate. We have considered the object, and the space that it is in, but any observation requires a third part. That is the observer. The observer in Mach's space is an undefined entity, except that as part of Mach space, it can be assumed to be disembodied, possessing no mass or fixed position. The point of observation may be moved with no physical effect on the body or the space, as we can investigate the astronauts hand or his intestines as we will. We can recede until the object is no more than a single quantum point from our view, or we can enlarge the object and move our point of view within it until it constitutes a universe in itself.

Mach says this universe is rotating. What can that mean? Notice that he does not say that the notion of rotation is meaningless, he says that rotation produces no acceleration. Do I have this right? I am afraid I must admit I have not seen Mach's original papers, but know of these arguments only through summations by other thinkers.

If the universe is said to be rotating, I assume we must say that our observation point may take a resting position, in which its location may not have to be adjusted, and from which the various parts of the astronaut's body are seen to change in relation to each other. This change is rather specific. The astronaut is not torn apart by the motion, but remains an astronaut. Yet as we watch, we see first one side of the astronaut, then another side, and this motion repeats as the astronaut turns. We may notice that the various parts of the astronauts body move in different ways, compared to each other. There is an axis which does not seem to move, and there is a left and a right, one of which seems to move toward us, and the other away from us. If we give ourselves a sort of x-ray vision, we may see that the front side of the astronaut is moving in the opposite direction from the back side of the astronaut.

There is one other way we could see this same scene, and that is if we do not assume our point of view is in a rest position, but that our position is rotating around the astronaut, providing a series of movements and their associated viewpoints, as if we were in orbit around the astronaut's apparent axis. This is, however, not what Mach has stated. Or. perhaps, Mach would say that the two ideas of motion are equivalent.

However, I would have to disagree. The two motions, one in which we are orbiting, and the other in which the astronaut is rotating, are not the same, even in an otherwise unmarked universe. The difference has to do with the condition that our observer has to be massless and chargeless and have no effect on the object or on the universe it inhabits. The only quality our observer has is a sense of position and of direction. Maintaining a position identical to an orbital requires that our point of view take on a series of highly specific changes. This is highly complicated, requiring not only adjustments in position, but also in attitude, since we require to be looking toward the astronaut throughout our pseudo-orbit. In order to maintain such a position, we would have to do a series of extremely complicated calculations and adjustments. Fortunately for our discussion, we can just pretend that the calculations and adjustments have already been made, and we can merely state that we are in orbit around the astronaut. But if we were to actually try to simulate this motion, as in a computer animation, we would have a great deal of work cut out for us.

No, we must stick with the program given to us. We are not in motion around the astronaut. The astronaut is said to be rotating and so we must make it so, and not the other way around.

Now given that the astronaut is rotating, and the hand is moving in relation to the intestines, and the other hand is moving in a contrary direction in relation to the intestines, and yet the astronaut retains his form, is there any necessary centripetal acceleration?

We must return to the physical definition of motion and of acceleration. Motion is a change in coordinate x with respect to time. Acceleration is a change in coordinate x in relation to (time squared). I think I know what change in x is. So we must think in terms of what is meant by the difference between time and the square of time. Or more exactly, the difference between the inverse of time and the inverse of the square of time.

If an object is in simple motion, we can plot its position in the dimension x against a position in time t. The time t and the position in dimension x can be laid out on an orthogonal chart in two dimensions, with equal intervals being given to the respective time and space. Then we will see that simple motion results in a plot of a straight line.

If an object in simple motion is plotted in space against time squared, that is if the time interval is not equal but is given an exponential notation, so that the interval changes along the time line in a continuous adiabatic fashion, then we will see that the plot is not a straight line, but is curved. If the plot is a straight line on the time squared chart, we must assume that the object in motion is under some forced acceleration.

The astronaut or other macroscopic object carries with it its own referential system. We can call the length of the astronauts thumb joint an inch and the length of the astronauts foot a foot and so on, and so set up our metric for x. Then we can see if changes in x per t result in a straight line or a line that is curved. Carrying out this operation, we will find that the astronaut's hands are accelerated compared to each other, without reference to any outside conditions.

To see this, consider the position of the hands of the astronaut in a dimension x placed so that it is orthogonal, that is at ninety degrees, from the axis of rotation. When the hands are in line with the middle of the astronaut, they are moving relative to x at some velocity. However, when they are at their fullest extension in x, they are instantaneously not moving with relation to the axis at all. If we follow one hand as it moves in x, we will see that it starts out in the middle with a direction in x, reaches its extrema and stops moving instantaneously in x (we may say that it is still moving in y) and then changes direction and moves backward in x until it reaches the opposite extreme. This change in motion in x is by definition acceleration.

Have I missed anything?

I would go on from here to consider the case of a single quantum particle, because I think Mach's brilliant idea does apply to systems that are entirely local, such as may be found below the quantum foam. Quantum foam begins at about the size of a proton, 10E-9 cm, but we are aware of a continuous scale down to the Planck length of 10E-32 cm. Forgive me if I have missed the mark on the numbers a bit, but this is about the size of it.

I propose that on the Planck scale, background becomes meaningless as the ideas of space and time begin to break down. However, even on these scales, there is still geometry. Can we go on from here to consider the geometry of quarks, electrons, and the other most fundamental particles?

I am aware that quantum theorists will find this a risky business. It has been held as a common belief for almost a century now that there is no use trying to visualize qualities like spin on the quantum scale. But I think I see a way, using the ideas of Mach as modified above, to explain the measurable behaviors of quantum particles in a visual model, one which may be better than that currently in place. Would this not be a benefit to students of quantum physics? Perhaps such a model would even allow us to find answers to questions about grand unified theories, problems in cosmology, and even in other unforseen places. Or at least, better questions.

Thanks for your help. Please help me sharpen the language. The above is only a draft of an idea, and I am not really nailed to any of the terms. Have I achieved communication? Can we go on and explore this new model of quantum processes? I assure you in advance that as far as I can see, it does not contradict the findings of special or general relativity, or of the standard model of particle physics. It may, however, provide some new insight into cosmology.

Thanks,

nc

 

[nightcleaner]

nc - It is good to respond your posts.
Mach's Principle: There is no absolute frame that defines inertial frames of reference, inertial mass is determined by the distribution of mass and energy in the rest of the universe.

Although I am not competent to extend MP to quantum physics, it would seem to me that if you had a sole electron in an otherwise empty universe you would not be able to determine its spin. Not only would you need an observer to "collapse the probability wave function", but also the direction of spin would be dependent on the orientation of that observer - but which way is 'up' in that empty universe?

Apart from that I am concerned that quantum spin does not infer motion or rotation and acceleration as classical spin does, therefore it may be completely independent of any Machian-type considerations.

Garth

Thank you for the complement.

I have just finished a long post to jcsd, which you may find interesting. I solicit your comments.

You defined "Mach's Principle: There is no absolute frame that defines inertial frames of reference, inertial mass is determined by the distribution of mass and energy in the rest of the universe."

This definition is harder to deconstruct than that of jcsd. Still, I guess the absolute frame in this model would have to be the frame of the observer. Then to say that there is no absolute frame would be to say that there is no observer, in which case the definition would seem to have no physical meaning.

And then, if inertial mass is determined by the distribution of mass and energy in the rest of the universe, I have to wonder how and why this rest mass is separated from the mass of the object under consideration? Again, why is the internal structure of the object not sufficient to provide a frame of reference which would be inertial?

Finally, I suggest that Mach's idea may yet have useful application in the lower bounds of the Planck scale, where our notions of space and time begin to break down. Without space and time, what is mass and energy?

Geometry, however, does not have to have time as an axis. X, Y, and Z are sufficient to have many liesurely and productive arguments in a space that seems timeless, altho I suppose if the universe we inhabit crunches, then all our pretty geometry will have to crunch also.

Nevertheless, as long as we are here, what is to stop us from considering a 4 dimensional spacetime matrix, where time and space are unified and matter and energy take on geometric forms? I know it is difficult, but is it really impossible? The early quantum theorists had no way to imagine or visualize a universe in which their measurements made sensible pictures, but does that mean that no such universe exists? They could find no way to rationalize an object whose spin was always and only plus or minus, and never any value in between. So they said there was no use trying to visualize quantum structures. They (the quantum structures, not the physicists) behaved in a way that was, visually, irrational. Instead, they (the quantum physicists this time) just followed the math, and accepted ideas like collapseing waveforms. Is it a kind of taboo, a "don't go there?"

I am proposing a model which I think may be useful, but it requires exploration with physical tools that I do not have at my disposal. That is why I have come to the Physics Forum to seek help. To give you an idea, I have extended the model out to ten Planck lengths, but need to bring it out to 10E22 lengths to compare it to current observation based theory. I don't have the computational power to do this. Any ideas?

nc

 

[Garth]

nc - from the above posts, (which took some reading!) it is acceleration that MP is concerned with, 'motion' or 'movement' is entirely relative as with Galilean or SR relativity.
There is no shell around the observer in an empty universe, it is empty, the reason why acceleration and rotation have no meaning in an empty Machian universe is because there is nothing to accelerate or rotate with respect to.

Some years ago there was a paper examining the apparent polarisation of quasar radio radiation, it tended to be one way in one part of the sky and the other way in the opposite part of the sky. It was thought that this might be caused by the whole universe rotating coherently.

My question was, "If so what is it rotating with respect to?" Talk of rotation with respect to the space-time fabric did not satisfy me as there was no way of pinning that 'fabric' down.

The effect was subsequently declared to be caused by the galactic electric field.

The inertial mass is compared to the gravitational mass. If both are declared invariant as the norm of the object's four-momentum, then an effect might reveal itself as a variation in G the Newtonian Gravitational 'constant'; this is the approach of the Brans-Dicke theory. Self Creation Cosmology allows the (inertial) rest mass to vary and it is the observed Newtonian parameter that remains constant.

Garth

 

[nightcleaner]

Ok Garth, and thanks.

My post was lengthy in part because I always try to tie my ideas directly to first principles, rather than use the physicists shorthand of referring to things like MP and then just assuming that the reader knows the reference. Thank you for your time spent reading through it.

Your shorter post contains some terms I am not familiar with and will have to go elsewhere to study before I can get the sense of the post. But it seems that we have pared down the argument to one of motion and acceleration, anyway.

I tried to show in the long post that motion in a universe that is otherwise empty except for an object is unthinkable, so Mach is right to say that in such a universe, there could be no accelertion. However, if we add the point of view of a disembodied observer, we can distinguish between rotation of the object about an axis and orbit of the point of view about the object by means of the complexity of the calculation necessary to construct a simulation. Essentially, the presense of an observer, even though disembodied, provides a mark on the otherwise unmarked universe, so that we can make sense out of the notion that the object is moving, in this case rotationally. Since rotation makes sense to the observer, the concept of acceleration is restored.

The conundrum in Mach's Principle is then reduced to one of invoking motion in a universe where motion is meaningless, and the solution, imho, is to appeal to the position of an observer, which then restores meaning to the notion of motion.

THen I wish to go one step further and restate Mach's conditions, such that the object under observation has in itself no parts that can be compared for motion by the observer, which is to say that the object is thought of as a perfect indivisible unmarked sphere, which can be rotated in any sense without providing any difference to be measured, even with the presense of the disembodied observer. This restores Mach's assertion that such an object will experience no motion and so no acceleration.

If my reasoning holds, then this is the condition in which we find quantum point-like objects. We can then reintroduce motion again by examining systems containing two and three point-like objects and an observer, and by doing so can find a model that explains the quantum behavior of fundamental particles. We would look to explain quantum spin, tunneling, and probability waves, with a physical model, so making the paradigm shift between quantum processes and statistical probabalistic processes easier to negotiate.

I invite criticism of this approach. Following the approach will involve a lot of thought work and several more long papers, so if someone can provide good reason for not going there, it could save me and others a lot of work.

Thanks,

nc

 

[turbo]

The inertial mass is compared to the gravitational mass. If both are declared invariant as the norm of the object's four-momentum, then an effect might reveal itself as a variation in G the Newtonian Gravitational 'constant'; this is the approach of the Brans-Dicke theory. Self Creation Cosmology allows the (inertial) rest mass to vary and it is the observed Newtonian parameter that remains constant.

Garth

Garth, here is a paper on Machian General Relativity that I bumped into today. The model seems to share a lot of features with SCC. Are there any points of strong divergence that pop up?

http://arxiv.org/abs/gr-qc/0106007

 

[Garth]

Thank you for that link, I will follow it up with Booth.
Booth's approach has many points of contact with SCC. However he keeps particle masses (energy-momentum) conserved and varies G. Although G varies 'in the background' in SCC, all Cavendish type measurements of G would not be aware of this as GM remains constant in the theory.
Garth