What Does Newton's Bucket Paradox Reveal About Motion and Inertia?

[Buckethead]

But that's why I asked if anyone really believed you could not get a dip in a bucket in an otherwise empty universe. I certainly don't believe it. So if you could, then you have to use the bucket to tell you whether or not it's rotating-- the effort to invert that logic is the source of the problem (that's where philosophy enters and muddies the science).
General relativity predicts the result of that experiment. Why do we need Mach? Don't get me wrong, I realize that asking the questions Mach did helped Einstein think "outside the box". That is generally what I view philosophy is for-- to free our thinking to see what the possibilities are. But we tend to cling to it long after it has ceased its usefulness, and mistake it for part of the theory.

From what I understand Einstein first bonded with Mach's idea, but then fell back on just accepting that there is an absolute universe. When Einstein talks about curvature of spacetime due to gravity in GR, what exactly is he referring to? (not mathamatically, but philosophically). One couldn't say it's a gravitational field because the warping of space is a result of gravitation. Is he referring to the virtual frame of reference that is created when all the mass and it's revolving/positional properties are taken into account (which would be Mach's principle)? I cannot accept that he is simply referring to a mathamatical virtual spacetime that has no physical basis in the real world. This would be nonsense.

So please, without a physical spacetime with which to say a water molocule is moving relative to, how can you still conclude that the water in the bucket will take a concave shape? The answer to this question is in my opinion very important to this discussion.

 

[Buckethead]

I don't know much about Mach's principle, but discussions about it always seem to turn into these rather silly "otherwise empty universe" discussions, which makes me question the value of Mach's principle.

Does Mach's principle have any concrete testable predictions? If not, what is its value?

I think it may. For example, if it can be shown that massive objects (or some other form of matter in the universe) and it's relative rotation/speed to an object determines the inertia (or mass) of the object, then this would indicate that counter structures could be built to alter the mass of objects. Having control over the mass/inertia of on object can open up all sorts of doors. More efficient ways to propel ships through space and countering gravity being a couple.

 

[Mentz114]

So please, without a physical spacetime with which to say a water molocule is moving relative to, how can you still conclude that the water in the bucket will take a concave shape? The answer to this question is in my opinion very important to this discussion.

Rotation can only be meaningfully defined for an extended object ( the water). Parts of the water are moving relative to other parts. There is no need to invoke physical space-time.

 

[Buckethead]

Rotation can only be meaningfully defined for an extended object ( the water). Parts of the water are moving relative to other parts. There is no need to invoke physical space-time.

I don't believe it's true when you say parts of the water are moving relative to other parts. They are all aligned and moving together. Let me restate this Newton's bucket in another way to eliminate the rotation.

Imagine a long straight stiff rod lying in empty space. Near one end of the rod and with it's nozzel parallel to it is a canon with a tennis ball inside. Just behind the tennis ball inside the canon is a laser pointing in the same direction as the nozzle of the canon.

The canon is fired, and shortly after that the laser is also fired. Two questions. Is the trajectory of the tennis ball parallel to the rod and secondly does the laser beam strike the rear of the tennis ball?

The seemingly obvious answers are yes in both cases, but I'm not so sure these are the correct answers. The reason being there is no physical relationship between the rod and the tennis ball or between the tennis ball and the laser beam.

The tennis ball can be thought of as representing water molocules in the bucket, and if it cannot be determined that the tennis ball will move parallel to the rod, then it cannot be determined that the molocules of water in the bucket will try and move tangent to the rotation of the water.

 

[newTonn]

This is the reason that water flows up the side of the bucket, but this is not the problem. The problem is determining how the water knows that it is moving in the first place and hence moving up the side of the bucket.

Can you please explain it further?water is moving because it is pressed against a moving object(bucket).since it cannot break the walls of bucket ,it is taking the next easiest path,that is tangentially with a small horizontal angle upwards.
I cannot understant why physical space time is necessary to explain this experiment.

 

[Mentz114]

Buckethead:

I appreciate that you're trying to make a subtle point, but your example fails in the first sentence.

Imagine a long straight stiff rod lying in empty space...

How do you define 'straight' ? You need some kind of reference to compare the rod with ( line of sight ?).
I don't see how this relates to the rotating water, sorry.

It is the inertial mass of the water that makes it climb the sides of the bucket, so I think it all boils down to this - will a solo object possesses inertia ?

In my opinion it will. It is simpler to believe that inertia is a local thing, either an intrinsic property of matter, or the result of a local interaction.

 

[yuiop]

What bothers me about this idea is that it seems to require that the presence of gravity alters the physics of a system in a way other than due its tidal effects, which seems to violate the principle of equivalence. In other words, if you put a box around a system, then the effect of gravity on the internal workings of that system should only come in via its tidal influences. But if you put a force on a point particle in that box, and claim that gravity from external sources are responsible for the way it accelerates, then you cannot have the equivalence principle. Note there is not a problem with kev's thought experiment about a ball bouncing back and forth in a box, because tidal stresses across that box must be responsible for the behavior observed, but inertia itself is a property of a point particle.

I would just like to point out I was talking about a ball bouncing back and forth horizontally in the box so tidal stresses do not come into that thought experiment, because tidal stresses are vertical.

Having given some more thought to the subject it seems that GR is not fully compatible with Mach's principle as pointed out by Garth. (By the way, you have to admire Garth's honesty and intellectual integrity in his handling of his own theory with respect to the GPB experiment). It would seem that inertial mass is influenced by it environment (the distribution of mass around it) but there is also a residual intrinsic inertial mass independent of its surroundings, just as there is a residual invariant rest mass/ energy. It could be thought of as Mach's principle is partly incorporated into GR but Einstein did not go the whole way. In other words, in GR a rotating bucket in a universe of "fixed stars" is not exactly the same thing as a stationary bucket in a universe of stars rotating around it, and GR can tell us if the universe is rotating or not. Mach's principle on the other hand can not tell a rotating universe from a static universe. That is my interpretation anyway, but welcome the input of the experts here ;)

 

[Buckethead]

Buckethead:

I appreciate that you're trying to make a subtle point, but your example fails in the first sentence.
How do you define 'straight' ? You need some kind of reference to compare the rod with ( line of sight ?)

The rod was manufactured just before the universe suddenly vanished. It was determined to be straight using a laser which had a straight beam when the universe existed (I'm actually not being sarcastic here even though it might sound that way)

I don't see how this relates to the rotating water, sorry.

There are three factors involved in the water rising in a bucket. 1) The water is in motion relative to something. 2) The water has mass. 3) Anything in motion with mass wants to move in a straight line. If it can be shown that inertia (mass) vanishes, or the ability to move in a "straight" line vanishes or relative motion vanishes, then the water in the bucket will have a problem. In a spinning bucket, the issue of relative motion can be answered because the water is being forced to deviate from a "straight" line, so I have removed this as being a factor and instead am just focusing on the definition of a "straight" line in my new example. The issue of inertia is also a factor, but my example is just focusing on the definition of a straight line in empty space since if a straight line becomes undefined in an empty universe this is enough of a reason for the water to be confused.

It is the inertial mass of the water that makes it climb the sides of the bucket, so I think it all boils down to this - will a solo object possesses inertia ?

In my opinion it will. It is simpler to believe that inertia is a local thing, either an intrinsic property of matter, or the result of a local interaction.

I think that inertia for objects with "mass" or more properly objects that are made of matter is a long standing assumption. I think objects are given the property of inertia because of something acting on those objects, not because inertia is an inherent property of matter.

 

[Mentz114]

JesseM:

In other words, in GR a rotating bucket in a universe of "fixed stars" is not exactly the same thing as a stationary bucket in a universe of stars rotating around it, and GR can tell us if the universe is rotating or not. Mach's principle on the other hand can not tell a rotating universe from a static universe.

Well put. That's what motivates me to call it 'Mach's conjecture'. Why is it a 'principle' if our best theory of gravity clearly disagrees ?

Buckethead:

I think objects are given the property of inertia because of something acting on those objects, not because inertia is an inherent property of matter.

Let's hope some future experiment can decide this, and lay Mach's thing to rest.

 

[Ken G]

I would just like to point out I was talking about a ball bouncing back and forth horizontally in the box so tidal stresses do not come into that thought experiment, because tidal stresses are vertical.

No, tidal stresses in a central gravitational field are not vertical on a box. This is why the Moon makes tides on the Earth-- it stretches the Earth along the Moon-Earth line, and squashes it in directions perpendicular to that line. Both effects are about equally important in making tides. In other words, I predict the effect you describe would not happen in the constant gravitational field of a huge plane of mass. If I'm right, that invalidates the argument. (And I think I am, or else your effect would occur in a reference frame in constant acceleration relative to the box, and that doesn't come out of my Lorentz transformation.)

 

[Buckethead]

It occurred to me that a Machian universe is a sort of democracy of mass. The mass of the "fixed stars" of mach represent the majority vote and define a sort of absolute reference frame. I think it is this implication of an absolute inertial reference frame that caused Einstein to ultimately reject the Machian viewpoint and declare it is incompatible with general relativity.

To see this on a smaller scale imagine a universe that comprises just the Earth and the Moon. Now the Earth seen from the Moon has a slightly bulged shape. Since the Earth represents the majority of mass in our reduced universe then it is declared stationary in the machian viewpoint. The bulged shape of the Earth is caused by a rotating or spiralling gravity "field". Einstein required that gravity (space curvature) is shaped by mass.Since the only objects of any significant size in this universe are the Earth and the Moon and since the Earth is considered stationary (by Mach) then the gravity "field" that is causing the stationary Earth to bulge at the equator can only be generated by the orbiting moon. The mass and motion of the Moon is insufficient to fully account for the bulge of the Earth and I imagine it this sort of reasoning that makes the Mach's principle incompatible with general relativity.

Now if we find a reference frame in which the total angular momentum of our reduced universe is zero then (I'm assuming) the gravitational curvature and the paths of the gravitational bodies can be all be accounted for by the combined gravitational effects of all the masses.


The subtle difference between the viewpoints of Mach and Einstein is that while the inertia of the water in the bucket is defined by the fixed stars in Mach's view, it is defined by the combined masses and motions of the stars and the bucket in Einstein's view.

It's hard to believe a year has passed since this thread started, but life beckoned and I had to abandon this for awhile. Still my enthusiasm for this subject seems to beckon as well. I just re-read this entire thread and I am totally blown away by all of the thoughtful posts discussing this topic. This is an amazing topic and I hope all of the previous posters and others will continue to chime in. Since posting over a year ago I have of course learned some new things (I haven't stopped reading) and some posts I wasn't completely able to comprehend fully back then came out in a new light which made re-reading that much more exciting.

I wanted to reply to so many posts, but chose this one as Kev seems to be thinking in parallel with what I am trying to pursue and represents some of the deepest parts of this thread so chose this one to start. I hope to get to others as well.

It occurred to me that a Machian universe is a sort of democracy of mass. The mass of the "fixed stars" of mach represent the majority vote and define a sort of absolute reference frame..

I believe very very strongly in this. The "concrete ring" phenonmenon shown to be true in GR is one of the reasons, but there is more to this as I will explain in my next post which will address the single atom around the bucket.

To see this on a smaller scale imagine a universe that comprises just the Earth and the Moon. Now the Earth seen from the Moon has a slightly bulged shape. Since the Earth represents the majority of mass in our reduced universe then it is declared stationary in the machian viewpoint. The bulged shape of the Earth is caused by a rotating or spiralling gravity "field". Einstein required that gravity (space curvature) is shaped by mass.Since the only objects of any significant size in this universe are the Earth and the Moon and since the Earth is considered stationary (by Mach) then the gravity "field" that is causing the stationary Earth to bulge at the equator can only be generated by the orbiting moon. The mass and motion of the Moon is insufficient to fully account for the bulge of the Earth and I imagine it this sort of reasoning that makes the Mach's principle incompatible with general relativity...

OK, now we are getting to a very philosophical crossroads that I think is very important. I think that in this reduced universe, the Earth will NOT bulge at the equator. If the universe is as it is today, then suddenly everything but the Earth and Moon were to disappear, one cannot assume that the Machian static frame of reference that was defined by the universe will remain in the state it was in. After all, this reference was by definition defined by the position of all the matter in the universe. Now that it's gone, the frame is subject to change. If indeed your "democracy" holds the answer, then it would be the Earth itself, (having the majority of the mass in this new universe) and it's rotation that would define the new Machian framework. The frame would rotate with the Earth, thereby rendering the Earth as "not rotating" and the bulge would cease except for any limited gravitational influence of the moon.

Actually, the Earth would not be completely at a state of rest as the moon would also influence the frame due to it's mass, but would be a very small "vote" and can be mostly disregarded.

The subtle difference between the viewpoints of Mach and Einstein is that while the inertia of the water in the bucket is defined by the fixed stars in Mach's view, it is defined by the combined masses and motions of the stars and the bucket in Einstein's view.

I do not understand the difference between these two viewpoints. They seem to me to be one in the same. Can you explain further?

 

[Buckethead]

Can you be sure acceleration is absolute?

Calculations using general relativity have shown that a massive rotating shell would induce a force that causes the surface of stationary water in a stationary bucket at its centre to curve exactly as if the if the water was rotating. The relativistic principle suggests there is no measurement that can destinguish a rotating bucket in a universe of of stationary stars from a stationary bucket in a universe of rotating stars. The mass of the rotating stars will drag spacetime as per the Lense Therring effect causing the water in the stationary bucket to climb up the sides of the bucket as if it was rotating. The stars will not be thrown outward by centripetal forces because the spacetime is co-moving with the stars.

Now imagine a universe with a one stationary bucket and one atom at the edge of the universe visible from the bucket. The atom is rotating around the bucket at very high speed but there is no way that the mass of a single atom at such a great distance can induce any significant gravitational field or curvature in the surface of the water in the bucket. By invoking the principle of relativity, rotating the bucket and water relative to the distant stationary atom will not induce any curvature in the surface of the water. The single atom is an approximation of an "otherwise empty universe" .

The atom it seems to me will indeed have no effect on the bucket. BUT, the lack of gravity I do not think is the reason. I again think it goes back to the "democracy of mass" (what a great phrase). The bucket in this universe defines the Machian frame by which inertia is defined because of it's relative mass compared to the atom. The atom is under this influence and if it is indeed revolving around the bucket it is experiencing acceleration due to it's change in vector.

Now, if we change the atom into the Sun, we have a different scenario on our hands. The Sun now has virtually all the mass in the universe so it defines the Machian frame and if it's relationship (and vectors) have not changed, then what we have is the entire Machian frame revolving around the bucket, which is to say the Sun is now stationary and the Bucket is revolving around the Sun. It will be the bucket that will be experiencing acceleration now, instead of the Sun. And it will be the bucket that will have to use it's side jets to stay in orbit (since gravity is too weak).

So I guess what I'm getting at is that gravity does not play a part in this at all, only (relative) mass, in other words "democracy of mass". So what I would like to know is, in the "ring of concrete" where the rotation of the ring has an influence on the water in the bucket, GR shows that this is due to gravity, but if the ring where the size of the universe and it's mass nothing more than that of a planet, AND (very important) it and the bucket were the only things in the universe, would the ring strongly influence the bucket according to GR? I think the ring would influence the bucket, because it defines the Machian frame, But what does GR have to say about this?

So my argument is that if we take a take an informal description of Mach's principle as "Inertia of a body is a property of its motion relative to the fixed stars" and restate it as "Inertia of a body is a property of its motion relative to the spacetime determined by the distribution and motion of matter in space" then Mach's principle is pretty compatible with relativity. The important notion is that inertia is not an intrinsic property of mass, independent of its surroundings.

I like this, and I think I'll use it as my standard definition of Mach's principle.

 

[Buckethead]

Buckethead:
Your logic is wrong.

Observers on the bricks could determine that the distance between the bricks remains constant over time. Therefore something must be keeping them apart. In the absence of any other candidate, centripetal force is deduced.

See above. You just keep ignoring the extended object argument. Why ?


Again - your universe is not empty - there are two bricks in it, and observers can detect the rotation without reference to any outside frame.

I agree with your determination of rotation by observation of the rope, but ONLY in a non-empty universe. In a universe filled with stars, one can observe the bricks moving relative to the stars and more importantly, so can the rope. In other words there is a reason the rope is going taught, because the bricks are rotating relative to the stars. In an empty universe however, this luxury does not exist. Since relativity says that an object can only be in relative and not absolute motion, there is no way to determine in an empty universe if two bricks are rotating around each other by simple virtue of the fact that their distance over time does not change. You state that a taught rope can determine this, but what I am suggesting is that you are putting the cart before the horse. Imagine you are the rope, and it is your job to determine if you should go taught or not (or you will be beheaded). The way you would determine this is by observing if the two bricks are trying to go past each other in the same way that two ships are trying to pass each other. If they are, then you (as a rope) are responsible for preventing this from happening and the result is a taught rope. But in an empty universe, with two bricks tied to you how are you going to determine if the two bricks are trying to pass each other? Their relative distance is not changing with time, so you cannot use this as a determining factor. In fact, if you released yourself from one of the bricks, would it suddenly take off? Why? Was it moving in the first place? You cannot say it was moving, because it was not moving relative to the other brick (it's distance did not change). In fact, it seems since it is not moving relative to the other brick, it must be stationary. Again, in a universe of stars this problem does not exist because it is easy to see the bricks are rotating relative to the stars, but in an empty universe and because SR says you can only determine motion by relative motion, if the bricks are not moving relative to each other, then you cannot (as a rope) say you must go taught, in fact you must go loose as there is no relative motion.

 

[Ken G]

Another important point to make is that for any discussion on Mach's principle, we must first stipulate that we simply do not know what would happen in an "otherwise empty universe", expressly because we have no such universe to do experiments in. If we instead start with the presumption that we do know what would happen to water in a bucket in an "otherwise empty universe", then we cannot discuss Mach's principle, as we have to have already incorporated it or outlawed it by fiat when we specify what happens to that bucket.

 

[Buckethead]

Another important point to make is that for any discussion on Mach's principle, we must first stipulate that we simply do not know what would happen in an "otherwise empty universe", expressly because we have no such universe to do experiments in. If we instead start with the presumption that we do know what would happen to water in a bucket in an "otherwise empty universe", then we cannot discuss Mach's principle, as we have to have already incorporated it or outlawed it by fiat when we specify what happens to that bucket.

Wouldn't what you are saying only hold true in a completely empty universe? By virtue of the fact that the bucket and atom (or Sun) exist and have mass, we have a starting point for incorporating Mach's principle. If we invision Mach's principle to be a effect generated by the mass in the universe, and their relative motions, then this would apply to any amount of mass.

 

[Ken G]

I don't think so, to apply Mach's principle to the bucket of water, you need more than just the bucket and the water. You basically need a boundary condition for your spacetime, at infinity or at least embedded in something substantial that you can consider to be stationary. The mass invoked by Mach's principle must be effectively infinite, in other words. If you just use the bucket itself, then you are asking a different question, about water sloshing inside a bucket, rather than water and bucket moving together. If the water is moving relative to the bucket, you'll have frictional forces that will be much more important than anything that looks like a gravity, and if the water is not moving relative to the bucket, then there's no gravity from the bucket that can make the water bulge. Mach's principle comes from a huge distant mass distribution that can have a significant enough gravity to anchor the concept of being absolutely stationary.

Put differently, I would say that Mach's principle basically asks the question, do we characterize motion by the presence of various effects we attribute to motion (say, ficticious forces), or does the motion and those various other effects both originate as results of some deeper phenomenon. The latter is Mach's claim-- that there is some deeper influence that an effectively infinite mass distribution has, which simply would not be there if that mass were not there. The former is the situation without Mach's principle. So, in an otherwise empty universe, if you spin a bucket and you need Mach's principle to get the ficticious forces, then the water would simply not bulge in that bucket-- there would never be any way to tell whether it was the bucket or the water that was originally spinning, and also no way to tell which one ultimately adopts the other's speed (i.e., which one has the greater inertia). The equilibrium would always be a stationary bucket and stationary water in it, in effect whichever object was taken to be the stationary one is the one that would have all the inertia.

Alternatively, in a universe where motion is as motion does and no more, then we could still have a bucket and water that were all stationary in their own frame, yet still showed ficticious forces creating a bulge, even in an otherwise empty universe. That's the universe with no Mach's principle. Which universe are we in? How could we ever tell? And what do we do with seemingly physically based questions that actually come with no way to answer? I would simply restate Mach's principle as the general observation that any elements of our universe that are unavoidable and inescapable could play an implicit role in all our physical theories in ways that we can never test or understand.

 

[Buckethead]

I don't think so, to apply Mach's principle to the bucket of water, you need more than just the bucket and the water. You basically need a boundary condition for your spacetime, at infinity or at least embedded in something substantial that you can consider to be stationary. The mass invoked by Mach's principle must be effectively infinite, in other words. If you just use the bucket itself, then you are asking a different question, about water sloshing inside a bucket, rather than water and bucket moving together. If the water is moving relative to the bucket, you'll have frictional forces that will be much more important than anything that looks like a gravity, and if the water is not moving relative to the bucket, then there's no gravity from the bucket that can make the water bulge. Mach's principle comes from a huge distant mass distribution that can have a significant enough gravity to anchor the concept of being absolutely stationary.

Put differently, I would say that Mach's principle basically asks the question, do we characterize motion by the presence of various effects we attribute to motion (say, ficticious forces), or does the motion and those various other effects both originate as results of some deeper phenomenon. The latter is Mach's claim-- that there is some deeper influence that an effectively infinite mass distribution has, which simply would not be there if that mass were not there. The former is the situation without Mach's principle. So, in an otherwise empty universe, if you spin a bucket and you need Mach's principle to get the ficticious forces, then the water would simply not bulge in that bucket-- there would never be any way to tell whether it was the bucket or the water that was originally spinning, and also no way to tell which one ultimately adopts the other's speed (i.e., which one has the greater inertia). The equilibrium would always be a stationary bucket and stationary water in it, in effect whichever object was taken to be the stationary one is the one that would have all the inertia.

Alternatively, in a universe where motion is as motion does and no more, then we could still have a bucket and water that were all stationary in their own frame, yet still showed ficticious forces creating a bulge, even in an otherwise empty universe. That's the universe with no Mach's principle. Which universe are we in? How could we ever tell? And what do we do with seemingly physically based questions that actually come with no way to answer? I would simply restate Mach's principle as the general observation that any elements of our universe that are unavoidable and inescapable could play an implicit role in all our physical theories in ways that we can never test or understand.

I think we have to accept that even a minimal universe (a universe with any amount of mass) will have to allow us to measure relative linear and relative rotational motion. If we cannot allow even that then all logic goes out the window. With this in mind I think we have to allow either of the 2 scenarios you suggest, either a universe "where motion is as motion does" or a universe where Mach's principle holds, again, regardless of how much mass is in the universe. If we accept the first, then if I read you correctly you are accepting an absolute frame of reference. Otherwise "motion is as motion does" does not mean anything. If a single bucket spins and it is showing concaveness, then (by definition) the bucket is spinning. And if it is spinning then it must be spinning relative to something even if that something is nothing we can define. I do not favor this as it implies that the absolute frame of reference is moving relative to the bucket and there is no logic behind this. This implies that the frame somehow as an independant nature relative to the bucket. As if it could be somehow "fixed" allowing the bucket to spin relative to it. But again, as you have explained, unless you can tell if it's the frame spinning and not the bucket or the bucket spinning and not the frame, then we go in circles. It then becomes your POV (the spinning frame or the spinning bucket) that determines if the water should be concave or flat.

On the other hand if we allow Mach's principle to be described as something real formed by the motion and rotation of an object and if this "frame" is influenced by a democracy of mass then clear concise predictions about the water in the bucket can be made. For example, if there is only a bucket of water and nothing else in the universe, then the bucket can never become concave. You can try and spin it, and it will remain flat, in other words it can never spin. The Machian frame will spin with it. If you try and move it in a linear direction, then it will show no movement of the water to one side of the bucket, again it will remain flat because the Machian frame gets pushed right along with it.

If we now introduce a smaller and distant object (a pebble, millions of light years away) into our universe, according to democracy of mass if we try and spin the bucket, the water in the bucket will still not rise, but what we will observe is that suddenly and seemingly inexplicably, the distant pebble will appear to begin revolving around the bucket! In addition if we try and move the bucket from it's current location, the water still does not slosh up one side, because it is not moving relative to the frame, but instead the distant pebble now moves closer or further from the bucket since it is moving relative to the frame.

If we now introduce more and more massive and relatively stationary objects to the universe, the democracy of mass continues to define the relative position and relative rotation of the Machian frame. If (most) all of the mass in this new universe are stationary with respect to each other then the Machian frame will encompass their position and their "so called" rotation (which would not actually exist since rotation would be defined by relative rotation with respect to the Machian frame and there would be none). In such a universe (such as our own) smaller objects such as galaxies can then be defined as rotating, or moving relative to this machian frame and their inertial forces would be measured directly relative to this frame as well.

 

[Ken G]

I think we have to accept that even a minimal universe (a universe with any amount of mass) will have to allow us to measure relative linear and relative rotational motion. If we cannot allow even that then all logic goes out the window. With this in mind I think we have to allow either of the 2 scenarios you suggest, either a universe "where motion is as motion does" or a universe where Mach's principle holds, again, regardless of how much mass is in the universe.

There's still another possibility-- if we have a universe with a kind of "minimal" mass in it, we could simply have weaker ficticious forces than in our universe, for the same acceleration. So yes, we could have relative rotation, but just a weaker centrifugal force. This of course would have to mean that inertia works differently than in Newton's laws, but that's exactly what we don't know about such "minimal" universes. It might be fun to imagine the various possible forms of Newton's laws that reduce to the familiar one in a "maximal" Machian universe, but they would be impossible to test.

If we accept the first, then if I read you correctly you are accepting an absolute frame of reference. Otherwise "motion is as motion does" does not mean anything.

It requires absolute frames only in the same way that special relativity treats inertial frames in a special way-- the frames that have no ficticious forces. I should have said "acceleration is as acceleration does", and by that I mean, the appearance of ficticious forces. In this picture, we don't say we have ficticious forces because we have an absolute acceleration, but rather we say that the presence of ficticious forces provide the definition of absolute acceleration (that's essentially how an accelerometer works).

If a single bucket spins and it is showing concaveness, then (by definition) the bucket is spinning. And if it is spinning then it must be spinning relative to something even if that something is nothing we can define.

Right, that's the "acceleration is as acceleration does" non-Machian approach.

I do not favor this as it implies that the absolute frame of reference is moving relative to the bucket and there is no logic behind this.

Mach didn't like it much either, but it's probably the picture that has best survived general relativity, though I believe that issue is still debated among real GR experts (of which I am not one).

On the other hand if we allow Mach's principle to be described as something real formed by the motion and rotation of an object and if this "frame" is influenced by a democracy of mass then clear concise predictions about the water in the bucket can be made.

Yes, the whole approach to the "center of mass" of a system is very much a kind of "vote", as you say. It still has strange properties though-- as you say, if we have a spinning bucket with 99% of the mass of the universe, and an outside observer with 1% of the mass, the spinning bucket could "vote" that the observer is actually in orbit and the bucket is not spinning at all, and we conclude the bucket is 1% spinning and the observer is 99% orbiting. Hence we only expect a 1% bulge in the water in the bucket. Now in a universe where the observer had a million times more mass, the bulge is back to its usual scale. But the problem is, this would hold no matter how small those masses actually are, so the gravitational constant G would have to be "renormalized" based on the mass in the universe, otherwise the influences would be too small with our current G to do anything. I prefer to think of G as a fundamental constant, and only the nature of spacetime is influenced by the mass. That's why I think you need the rest of the universe to have essentially infinite mass for Mach's principle to seem reasonable, because then the gravitational influence is not negligible, it "anchors" the spacetime. Nevertheless, I could not argue that your way of renormalizing G to whatever is the total mass is impossible or wrong.

For example, if there is only a bucket of water and nothing else in the universe, then the bucket can never become concave. You can try and spin it, and it will remain flat, in other words it can never spin.

Yes, that's the fundamental question-- can a bucket spin if it is the whole universe? Mach says no, "motion is as motion does" says yes. It would be an issue of what is possible in the "initial conditions" of such a universe. Now, how would we ever know which holds true in our universe? It seems a matter of personal philosophy, as we can never do experiments in such a universe, and the testable distinctions in GR are debated even among the experts.

 

[yuiop]

Hi,

It is has been a while since I have given this subject any serious thought so the following comments are just some casual thoughts to resume the conversation and see where we are at.

First of all Mach's principle is hard to prove or refute because it it is not clear what exactly is meant by that principle and there are no "Mach's principle equations" to calculate exactly what it predicts or exactly how it differs from General Relativity.

Reading between the lines I get the impression the principle that Mach was trying to establish was a fully relativistic notion of acceleration that only has meaning relative to other objects. Einstein of course was drawn to Mach's idea because of its relativistic nature but ultimately he rejected that notion in formulating his final version of GR. So here is the surprise. General Relativity is not fully relativistic. Here is an example. Say you are a universe like ours but it contains only you and a glowing particle many light years away. The particle appears to circumnavigate a large circle once every minute. Now is it you rotating at 1 rpm or are you stationary and the particle is orbiting you? Mach's principle would seem to indicate that either view point of view is equally valid (the fully relativistic idea). However if we assume for a moment that it is you that is stationary (after all by the democracy of mass your mass is orders of magnitude larger) then the particle would be orbiting at velocity much greater than the speed of light. This is why I think Einstien rejected the fully Machian universe. Much as Einstein liked the idea of everything being fully relativistic, he really hated the idea of anything exceeding the speed of light, so he settled for a not fully relativistic description of the universe which gives an absolute nature to accelerating motion which includes rotation.

Here are some other points to consider. The Schwarzschild metric describes the spacetime around a non-rotating body in an "otherwise empty universe" and the Kerr metric describes the spacetime around a rotating body in an "otherwise empty universe". (Both metrics assume an uncharged body). Whether or not the body is rotating or not, is relative to the spacetime it is embedded in and is not relative to any other bodies. The Schwarzschild or Kerr body curves and shapes the spacetime around it. The vacuum outside of the body is not entirely nothing. After all you cannot curve and shape nothing.

In modern cosmology it is known that distant galaxies are receding at velocities that greatly exceed the speed of light. However, this is not considered a violation of General Relativity because the distant receding galaxies are stationary with respect to the expanding spacetime that they are embedded in. Again, what looks like a vacuum is not entirely nothing because a pure vacuum that is entirely nothing can not expand or do anything else for that matter. This sort of relates to the ZPE field that Mentz referred to. It is also generally accepted that if a body accelerates sufficiently quickly that it will see virtual particles popping out of the vacuum. This is the "Unruh effect" and again it only requires that a body is accelerating relative to the vacuum or spacetime and is not relative to any other bodies. Again the vacuum should not be thought of as entirely nothing.

Finally a little thought experiment. Imagine an Earth sized body in an "otherwise empty universe" that is rotating so fast that it oceans would be flung into space by centripetal forces but from the Machian viewpoint it is "unaware" that it rotating and retains its oceans and perfectly spherical shape. Now imagine a single particle popping up anywhere in this otherwise empty universe due to some quantum fluctuation. Would the Earth like body suddenly lose its oceans as a result of the appearance of this single tiny particle? That seems unlikely.

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

 

[Buckethead]

There's still another possibility-- if we have a universe with a kind of "minimal" mass in it, we could simply have weaker ficticious forces than in our universe, for the same acceleration. So yes, we could have relative rotation, but just a weaker centrifugal force. This of course would have to mean that inertia works differently than in Newton's laws, but that's exactly what we don't know about such "minimal" universes. It might be fun to imagine the various possible forms of Newton's laws that reduce to the familiar one in a "maximal" Machian universe, but they would be impossible to test..

I don't feel easy about this theory. One has to wonder about the nature of these fictitious forces and why they would suddenly appear when a bucket starts to spin in the presence of other matter.

Yes, the whole approach to the "center of mass" of a system is very much a kind of "vote", as you say. It still has strange properties though-- as you say, if we have a spinning bucket with 99% of the mass of the universe, and an outside observer with 1% of the mass, the spinning bucket could "vote" that the observer is actually in orbit and the bucket is not spinning at all, and we conclude the bucket is 1% spinning and the observer is 99% orbiting. Hence we only expect a 1% bulge in the water in the bucket. Now in a universe where the observer had a million times more mass, the bulge is back to its usual scale. But the problem is, this would hold no matter how small those masses actually are, so the gravitational constant G would have to be "renormalized" based on the mass in the universe, otherwise the influences would be too small with our current G to do anything. I prefer to think of G as a fundamental constant, and only the nature of spacetime is influenced by the mass. That's why I think you need the rest of the universe to have essentially infinite mass for Mach's principle to seem reasonable, because then the gravitational influence is not negligible, it "anchors" the spacetime. Nevertheless, I could not argue that your way of renormalizing G to whatever is the total mass is impossible or wrong.

You bring up some really interesting questions here. I too would prefer to see G remain constant and if we chose to use this as a given, then it can help define the nature of the Machian frame. For example, we can now say that the sum total influence of the Machian frame generated by individual masses are a ratio of the masses and (very important) the relative motions between the masses (both linear and rotational). It is not necessary to assign an absolute value to the strength of the frame (and indeed we cannot) if G is to remain constant. In other words we can say the inertia of an object in any size universe remains constant if the mass and velocity of the object in question remains small compared to the overall mass and overall relative velocity of the rest of the universe. Even a bucket with a ratio of 1:100 will approach the inertia of a bucket with a ratio vastly larger than that.

All of this of course implies that the Machian frame is not related directly to gravity. This begs the question of what exactly is it. It may be that it's influence extends in all directions indefinitely and does not decrease in relative influence with distance. This would make sense in a minimal universe. Also it is strickingly different from gravity in that it's influence is directly related to it's relative velocity and rotation.

Fortunately some predictions can be made if this Machian frame is described this way. For example the Machian frame would not be static throughout the universe as Mach originally invisioned. Take 2 galactic clusters spaced 100 million ly apart. If one were to rotate clockwise and the other counterclockwise, the mid point between them would have a Machian space that moved in a linear direction perpendicular to the line drawn between the two clusters. Light traveling though this space against the flow of the movement would slow down (relative to an outside observer) whereas light traveling the other way would speed up. Light traveling near one of the rotating clusters would be deflected and so on. By closely examining galactic lensing effects we could predict rotations and relative movements of clusters.

 

[Buckethead]

First of all Mach's principle is hard to prove or refute because it it is not clear what exactly is meant by that principle and there are no "Mach's principle equations" to calculate exactly what it predicts or exactly how it differs from General Relativity..

Yes, which I think is very exciting as it makes this subject undiscovered territory. :)

Reading between the lines I get the impression the principle that Mach was trying to establish was a fully relativistic notion of acceleration that only has meaning relative to other objects. Einstein of course was drawn to Mach's idea because of its relativistic nature but ultimately he rejected that notion in formulating his final version of GR. So here is the surprise. General Relativity is not fully relativistic. Here is an example. Say you are a universe like ours but it contains only you and a glowing particle many light years away. The particle appears to circumnavigate a large circle once every minute. Now is it you rotating at 1 rpm or are you stationary and the particle is orbiting you? Mach's principle would seem to indicate that either view point of view is equally valid (the fully relativistic idea). However if we assume for a moment that it is you that is stationary (after all by the democracy of mass your mass is orders of magnitude larger) then the particle would be orbiting at velocity much greater than the speed of light. This is why I think Einstien rejected the fully Machian universe. Much as Einstein liked the idea of everything being fully relativistic, he really hated the idea of anything exceeding the speed of light, so he settled for a not fully relativistic description of the universe which gives an absolute nature to accelerating motion which includes rotation.

If this is what Mach intended, then I would have to disagree with him as well. I do believe that there is a framework as you and Einstein are suggesting, but I think i differ with Einstein in that the framework is not static but instead is a product of the motion of, and the mass of the bodies in the framework. Therefore it is to a degree fluid.

In your example, the particle would never go faster than light. If both you and the particle start out stationary and you decide to rotate at 1 rpm, your efforts would be fruitless. Since you hold most of the mass, you would not feel any inertial forces on you as the spacetime around you (the Machian frame) would rotate with you. This would force the particle to follow your rotation and both of you would end up stationary (relative to each other) regardless of your efforts to circumvent it.

Here are some other points to consider. The Schwarzschild metric describes the spacetime around a non-rotating body in an "otherwise empty universe" and the Kerr metric describes the spacetime around a rotating body in an "otherwise empty universe". (Both metrics assume an uncharged body). Whether or not the body is rotating or not, is relative to the spacetime it is embedded in and is not relative to any other bodies. The Schwarzschild or Kerr body curves and shapes the spacetime around it. The vacuum outside of the body is not entirely nothing. After all you cannot curve and shape nothing

Since the spacetime is being curved by the body, this supports my definition of Machian space nicely. In other words, it is the body and not just "absolute space" that defines the space around the body. This is good news.

In modern cosmology it is known that distant galaxies are receding at velocities that greatly exceed the speed of light. However, this is not considered a violation of General Relativity because the distant receding galaxies are stationary with respect to the expanding spacetime that they are embedded in. Again, what looks like a vacuum is not entirely nothing because a pure vacuum that is entirely nothing can not expand or do anything else for that matter. This sort of relates to the ZPE field that Mentz referred to. It is also generally accepted that if a body accelerates sufficiently quickly that it will see virtual particles popping out of the vacuum. This is the "Unruh effect" and again it only requires that a body is accelerating relative to the vacuum or spacetime and is not relative to any other bodies. Again the vacuum should not be thought of as entirely nothing.

In my definition of Machian space allows for dynamic changes in the space at large distances and sizes. It is possible to have a Machian space surrounding a galactic cluster and this space is moving away relative to another Machian space millions of ly away. In fact, it is almost necessary to have multiple Machian spaces ( or at least a fluid continuum of spaces) otherwise if you had a cluster embedded (and not moving relative to) a static space then a neighboring cluster expanding would mean that it would be moving relative to it's own space since that space were part of a "static, non expanding continuum" of the neighboring cluster.

With regard to the Unruh effect, a Machian space would be sufficient to allow for this as such a space would allow for a small moving object to move relative to it as long as there were a larger mass that was defining the space position and rotation.

Finally a little thought experiment. Imagine an Earth sized body in an "otherwise empty universe" that is rotating so fast that it oceans would be flung into space by centripetal forces but from the Machian viewpoint it is "unaware" that it rotating and retains its oceans and perfectly spherical shape. Now imagine a single particle popping up anywhere in this otherwise empty universe due to some quantum fluctuation. Would the Earth like body suddenly lose its oceans as a result of the appearance of this single tiny particle? That seems unlikely.

Agreed. The particle, as soon as it appeared, would find itself rotating around the Earth such that it would appear that the Earth was not rotating relative to the particle. In other words, in such a universe, it would be impossible for the Earth to ever spin since it holds most of the mass and therefore would force the Machian frame to rotate along with it.

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

I am mostly in agreement with this to the limitation that it is still the masses in the universe that define this spacetime. I don't believe you could ever have a scenario for example where all the mass in the universe was moving (in the same direction) relative to the underlying space time.

Thanks for joining in.

 

[Ken G]

I agree that vacuum isn't nothing, but I don't think it could be quite said that GR isn't fully relativistic. Instead, I would say that GR requires some boundary condition at infinity to get a solution, but that's common in physics-- we always need to impose some manual constraint on anything we do. So it is that manual constraint that breaks the relativity, not GR itself-- we must tell GR what the boundaries are doing. If we say the boundaries are rotating with the Earth, then the spacetime is rotating with the Earth, which is a lot like saying the Earth isn't rotating. Spacetime is only as "real" as the boundary conditions we impose on it, but what is "real" about them? At some point it seems you would have to trace back to an initial condition, and it is in that initial condition where Mach's principle would enforce some constraint, or not.

 

[phyti]

Newton's bucket

Tidal forces - clarification:
An object in a gravitational field experiences greater acceleration at the near end than at the far end, thus elongation in the vertical. The convergence to the center of the field causes the horizontal dimension to contract. A sphere would become an ellipsoid as it falls. Research tides to see if it's the water that is distorted, not the earth. In general the less
massive objects are accelerated before the more massive.

Absolute rotation:
If the rotation of the water in the bucket can be equivalently attributed to the rotating
universal mass, then two counter rotating buckets would require the universe to rotate
simultaneously in opposite directions, i.e. a net rotation of zero. What if two buckets
rotated on perpendicular axes?

The shell theorem demonstrates zero gravity inside a hollow mass. If the universal mass is
approximately uniformly distributed, the net gravitational effect would average zero. With
the current (miniscule) angular motion of distant masses, would any effect be detectable?

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction.
If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the
equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

The case of linear motion with an acceleration is shown in the drawing. The same argument
applies, the remote objects would have had to start moving in the past at a time proportional to their distance. On the left, person-a accelerates, on the right, the rest of the universe accelerates. If considering multiple objects, this idea becomes nonsense.

If acceleration has no relative counterpart, it can be considered absolute.

https://www.physicsforums.com/attachments/17923

 

[Al68]

A better example of Mach's Principle may be Einstein's spinning globes: Imagine two fluid masses, each rotating wrt the other, with a common axis. Now imagine that one and only one of the globes has a bulging equator. If the situation is analyzed as a "closed" system, without regard to any distant masses, how can the bulging equator be explained? What causes the bulging equator on one globe but not the other?

Einstein's conclusion was that the cause must lie outside the system. (only one of the globes is rotating relative to the "fixed" stars).

As a closed system, there is no way to explain a cause for the empirically measured bulge of only one equator. And an observer on each globe would agree which one bulged, but no cause of the preferential bulge would exist within the system.

 

[Buckethead]

Tidal forces - clarification:
An object in a gravitational field experiences greater acceleration at the near end than at the far end, thus elongation in the vertical. The convergence to the center of the field causes the horizontal dimension to contract. A sphere would become an ellipsoid as it falls. Research tides to see if it's the water that is distorted, not the earth. In general the less
massive objects are accelerated before the more massive.

This holds because of gravity. It is not affected by my version of Mach's principle as the principle only affects objects in relative linear and/or rotational motion.

Absolute rotation:
If the rotation of the water in the bucket can be equivalently attributed to the rotating
universal mass, then two counter rotating buckets would require the universe to rotate
simultaneously in opposite directions, i.e. a net rotation of zero. What if two buckets
rotated on perpendicular axes?

Two rotating buckets opens up some very wild phenomenon. For example, from above, a bucket on the right spins counterclockwise and a bucket on the left spins clockwise. Between the two buckets any atoms in between the two buckets will pass from top to bottom at a constant velocity. Interestingly atoms to the right of the right bucket or to the left of the left bucket will also flow in the same direction, from top to bottom (against the directions of the buckets on these sides) and to a lesser degree than the atoms in the middle of the buckets. Far to the left or right of the buckets the movement of atoms falls off so that a distant observer at rest will not see either bucket moving relative to himself but will see atoms near the buckets moving past them. In other words there will be a curve in the spacetime in the area of the two spinning buckets.

In addition the water in the buckets will be flat. If the rotation of the buckets however is increased, the water will move toward the bottom (-y) direction of the two buckets for as long as the acceleration in applied.

If the bucket on the right changes direction so that both buckets are now spinning clockwise, then from the overall frame of the universe both buckets will precess around each other at 1/2 the rotational speed of the buckets in a counterclockwise direction. In otherwords an observer at rest far away from the two buckets will see them precessing around each other.

In addition I believe the water in the two buckets will ride up a wall of the bucket on the side opposite it's direction of motion as if it were accelerating in a straight line.

For two buckets where one is on a z axis, similar anomolies will occur although I have not yet worked out exactly what those anomolies would be.

The shell theorem demonstrates zero gravity inside a hollow mass. If the universal mass is
approximately uniformly distributed, the net gravitational effect would average zero. With
the current (miniscule) angular motion of distant masses, would any effect be detectable

The net gravitational effect is zero, but the Machian frame is not determined by gravity alone, it is determined by the relative velocites and rotations of all the bodies in question. If all the masses in the universe seem at rest relative to the center of all these masses, then this center is also at rest and an object placed here will resist movement relative to the stars.

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction.
If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the
equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

In my version of the Machian frame, If an observer rotates relative to a distant star, he may percieve a star moving around him, but this would only be an illusion. The observer would be rotating relative to the Machian frame and the star would remain stationary.

PLEASE NOTE: I'm obviously expressing my opinion here and not stating a fact. I am suggesting that if a Machian frame behaves according to the individual velocites and rotations of masses then the above observations would be the likely result. It's all just a mind experiment. I don't want to come off as some kind of pompous head, just a buckethead.

 

[Al68]

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction.
If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the
equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

This is incorrect. The speed of light is not limited to c wrt an accelerating (or rotating) reference frame. It can have any value up to infinity.

 

[Ken G]

What causes the bulging equator on one globe but not the other?

Einstein's conclusion was that the cause must lie outside the system. (only one of the globes is rotating relative to the "fixed" stars).

I guess Einstein tended to see causes and effects as a fundamental requirement of any description of reality, though of course one might also view them as effective constucts, shadows of some deeper principle, with no such fundamental status.

As a closed system, there is no way to explain a cause for the empirically measured bulge of only one equator. And an observer on each globe would agree which one bulged, but no cause of the preferential bulge would exist within the system.

This raises a possibility to imagine alternate approaches whereby, if that universe truly were a closed system, either observer might claim the other globe bulged. In our universe, the issue would need to be resolved by the action of the distant masses. That would seem to be the fully Machian/relativistic approach to these hypothetical possibilities. Alternately, of course, one might simply state that the bulging does not require a cause, it just is, but the fact that it is there decides which globe is "really" rotating. In short, we interpret rotation because of the presence of the bulge (and other things that come with it), rather than the other way around.

 

[Al68]

I guess Einstein tended to see causes and effects as a fundamental requirement of any description of reality, though of course one might also view them as effective constucts, shadows of some deeper principle, with no such fundamental status.
This raises a possibility to imagine alternate approaches whereby, if that universe truly were a closed system, either observer might claim the other globe bulged. In our universe, the issue would need to be resolved by the action of the distant masses. That would seem to be the fully Machian/relativistic approach to these hypothetical possibilities. Alternately, of course, one might simply state that the bulging does not require a cause, it just is, but the fact that it is there decides which globe is "really" rotating. In short, we interpret rotation because of the presence of the bulge (and other things that come with it), rather than the other way around.

Einstein definitely viewed physics very differently than most do today, that is obvious from his writings.

Stating that we don't need to know the cause of the bulge is fine, maybe we don't need to know. Maybe some would be satisfied with just a mathematical description..

Einstein obviously was not, fortunately.

 

[phyti]

Buckethead;

The net gravitational effect is zero, but the Machian frame is not determined by gravity alone, it is determined by the relative velocites and rotations of all the bodies in question. If all the masses in the universe seem at rest relative to the center of all these masses, then this center is also at rest and an object placed here will resist movement relative to the stars.

Don't quite understand this part.
Currently a mass anywhere in the universe offers inertial resistance.

 

[Ken G]

Stating that we don't need to know the cause of the bulge is fine, maybe we don't need to know.

Indeed, I think it could be said that Einstein was ultimately unsuccessful in identifying a "cause" of the bulge. Though of course, the effort to do so certainly resulted in many other useful things!

 

[Al68]

Indeed, I think it could be said that Einstein was ultimately unsuccessful in identifying a "cause" of the bulge.

You're right, at least not to his satisfaction. But just the conclusion that the cause must lie outside the system (containing just the globes) is significant to the issue of Newton's bucket, and it's a simpler example, since it's not complicated by the downward force of gravity holding water in the bucket.

 

[Ken G]

Yes, it's an excellent example, and it's certainly a conclusion that is relevant here, but I think we are still left to wonder if Einstein and Mach were actually right about that external cause. I can agree the cause isn't internal to the globes, but my feeling is that the whole concept of cause and effect is simply not a useful one in that context. I suppose that would put me in the "motion is as motion does" school of thought, whereby what we identify as motion is a kind of shadow of some much deeper phenomenon that we are mostly oblivious to and therefore cannot successfully apply our simplified concepts like cause and effect. We have only demonstrated a use in applying them to the concept of a change in motion, starting from an initial condition of some kind, but we are always left to wonder what was the cause of the initial condition. Such is the basic structure, and limitation, of physics thinking.

 

[Buckethead]

Yes, the whole approach to the "center of mass" of a system is very much a kind of "vote", as you say. It still has strange properties though-- as you say, if we have a spinning bucket with 99% of the mass of the universe, and an outside observer with 1% of the mass, the spinning bucket could "vote" that the observer is actually in orbit and the bucket is not spinning at all, and we conclude the bucket is 1% spinning and the observer is 99% orbiting. Hence we only expect a 1% bulge in the water in the bucket. Now in a universe where the observer had a million times more mass, the bulge is back to its usual scale. But the problem is, this would hold no matter how small those masses actually are, so the gravitational constant G would have to be "renormalized" based on the mass in the universe, otherwise the influences would be too small with our current G to do anything. I prefer to think of G as a fundamental constant, and only the nature of spacetime is influenced by the mass. That's why I think you need the rest of the universe to have essentially infinite mass for Mach's principle to seem reasonable, because then the gravitational influence is not negligible, it "anchors" the spacetime. Nevertheless, I could not argue that your way of renormalizing G to whatever is the total mass is impossible or wrong.

I wonder if G really is a fundamental constant. A few years ago I was researching the various experiments being performed around the world to measure this constant and at the time none of the numbers matched. Experimental error of course is the first thing to look at, yet I got the sense that these experimenters were more baffled than accepting of errors they may have made. But even with this aside and more to the point, SR says the mass of an object increases with it's velocity, hence it's gravitational attraction increases. If this speeding object were suddenly to find itself in an almost empty universe, would it's graviational attraction (and it's increased mass) remain, or would it's gravity return to an expected value, or more interestingly, would it's gravity suddenly become zero? The possibility of it becoming zero is related to your observation that ("a third possibility might be") the spinning bucket in a universe with a distant particle, might show a reduced curve for a given relative rotational rate. Because of the equivelency principle, this reduced curve(mass?) might also come with it a reduced gravitational pull. Hence G may not be constant but instead may relay heavily on the total number of particles (I was going to say total mass, but that would be a non-sequiter) in the universe.

 

[Buckethead]

Hi,


Reading between the lines I get the impression the principle that Mach was trying to establish was a fully relativistic notion of acceleration that only has meaning relative to other objects. Einstein of course was drawn to Mach's idea because of its relativistic nature but ultimately he rejected that notion in formulating his final version of GR. So here is the surprise. General Relativity is not fully relativistic. Here is an example. Say you are a universe like ours but it contains only you and a glowing particle many light years away. The particle appears to circumnavigate a large circle once every minute. Now is it you rotating at 1 rpm or are you stationary and the particle is orbiting you? Mach's principle would seem to indicate that either view point of view is equally valid (the fully relativistic idea). However if we assume for a moment that it is you that is stationary (after all by the democracy of mass your mass is orders of magnitude larger) then the particle would be orbiting at velocity much greater than the speed of light. This is why I think Einstien rejected the fully Machian universe. Much as Einstein liked the idea of everything being fully relativistic, he really hated the idea of anything exceeding the speed of light, so he settled for a not fully relativistic description of the universe which gives an absolute nature to accelerating motion which includes rotation. .

(regarding bold text:) My take on this is that in this scenario, it would not be possible for the bucket to rotate at any speed (very very slowly perhaps due to the particle having some small mass). Due to democracy of mass, if the bucket attempted to rotate (strap on those jets) the entire frame would rotate along with it including the particle, rendering the bucket essentially non-rotating. The particle could revolve around the bucket however, and it's speed would be limited to c. Another thing to observe here (if my take on this is correct) is that it would also be impossible for the bucket to "go concave" (over and above that small amount allowed by a revolving particle) .

If we now start adding stars to this universe, giving democracy of mass to the stars, and if the bucket started spinning (which it now could) relative to the stars, it would go concave, it would actually be "spinning" and it would not make sense to say it was the particle that was actually moving and the bucket being at rest. So in either scenario, nothing would ever travel faster than light.

Here are some other points to consider. The Schwarzschild metric describes the spacetime around a non-rotating body in an "otherwise empty universe" and the Kerr metric describes the spacetime around a rotating body in an "otherwise empty universe". (Both metrics assume an uncharged body). Whether or not the body is rotating or not, is relative to the spacetime it is embedded in and is not relative to any other bodies. The Schwarzschild or Kerr body curves and shapes the spacetime around it. The vacuum outside of the body is not entirely nothing. After all you cannot curve and shape nothing.

I'm not sure what your point was here. I personally think though that the Kerr metric would not make sense in an otherwise empty universe, as rotation (rotation being defined as a non zero centrifugal force) would not be possible for an object in such a universe.

In modern cosmology it is known that distant galaxies are receding at velocities that greatly exceed the speed of light. However, this is not considered a violation of General Relativity because the distant receding galaxies are stationary with respect to the expanding spacetime that they are embedded in. Again, what looks like a vacuum is not entirely nothing because a pure vacuum that is entirely nothing can not expand or do anything else for that matter. This sort of relates to the ZPE field that Mentz referred to. It is also generally accepted that if a body accelerates sufficiently quickly that it will see virtual particles popping out of the vacuum. This is the "Unruh effect" and again it only requires that a body is accelerating relative to the vacuum or spacetime and is not relative to any other bodies. Again the vacuum should not be thought of as entirely nothing.

(Interesting about the virtual particles) I don't consider the vacuum as being entirely nothing as certainly in the Machian view, the large masses are communicating with all other objects through some means, filling the universe. This would be through the motions of gravitons or some yet undiscovered (dark matter/energy) particle, or possibly something even more mysterious such as the non-local particle interaction phenomenon.

Finally a little thought experiment. Imagine an Earth sized body in an "otherwise empty universe" that is rotating so fast that it oceans would be flung into space by centripetal forces but from the Machian viewpoint it is "unaware" that it rotating and retains its oceans and perfectly spherical shape. Now imagine a single particle popping up anywhere in this otherwise empty universe due to some quantum fluctuation. Would the Earth like body suddenly lose its oceans as a result of the appearance of this single tiny particle? That seems unlikely.

I agree it would be unlikely. The reason being that since it is showing no bulging or flinging, the Earth could not be said to be spinning. In other words, spinning in this universe is impossible. If a particle were suddenly to appear, it would not be spinning relative to the Earth or the Earth to it, so flinging would still not happen. As I mentioned above, I think that once the particle appeared, due to democracy of mass, the Earth could still not spin as the whole frame (particle included) would spin right along with it if it tried, rendering the whole thing as non-spinning. The particle could BTW revolve around the Earth, limited by lightspeed relative to the inertial frame (defined by the Earth), but the Earth could not spin.

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

I absolutely agree.

 

[A-wal]

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

I absolutely agree.

I completely but respectfully disagree. All movement is relative. These are just my thoughts:

Absolute rotation:
If the rotation of the water in the bucket can be equivalently attributed to the rotating
universal mass, then two counter rotating buckets would require the universe to rotate
simultaneously in opposite directions, i.e. a net rotation of zero. What if two buckets
rotated on perpendicular axes?

From one frame it would rotate in one direction, while it would be rotating in a different direction from the other frame. If the were on different axes then the universe would rotate on different axes from the different frames. You could argue that the fact that they can't both be right at the same time proves that the buckets must be spinning, or at least one of them must be, but you can always say things look different from other frames.

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction. If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

Yes they would have to of started moving before you were born. That doesn't mean they didn't. Maybe they were thrown back in time due to the fact that they're moving faster than c. The further away they are, the faster their relative movement, so the further back in time they go, which is handy. That was either really cool or I need to lay off the smoke. What if two people rotated at different rates? See above.

The case of linear motion with an acceleration is shown in the drawing. The same argument applies, the remote objects would have had to start moving in the past at a time proportional to their distance. On the left, person-a accelerates, on the right, the rest of the universe accelerates. If considering multiple objects, this idea becomes nonsense.

No, it just becomes relative to the observer.

If acceleration has no relative counterpart, it can be considered absolute.

The counterpart of acceleration is the acceleration of everything else in the universe at the perfect individual timing to coincide exactly with your position in space-time when you can be said to be accelerating. It's not an alternative, it's exactly the same.

In a universe with just the bucket, there would be no other matter to move round the bucket with increased mass brought about by increased the relative velocity, and therefore nothing to pull the water up the sides of the bucket. That's basic Galilean relativity surely?

 

[Al68]

Yes they would have to of started moving before you were born. That doesn't mean they didn't. Maybe they were thrown back in time due to the fact that they're moving faster than c. The further away they are, the faster their relative movement, so the further back in time they go, which is handy. That was either really cool or I need to lay off the smoke.

It's not hard to claim that all the mass in the universe changed velocity billions of years ago because a small force was applied to a bucket today, if we keep in mind that we are talking about a change in relative velocity.

But we do have to acknowledge that accelerated reference frames are fundamentally different from inertial frames: not only can distant objects exceed c, change velocity with no force applied, etc., but causality itself can be violated, ie effect can precede cause.

Acknowledging that accelerated frames are fundamentally different from inertial frames is equivalent to acknowledging that (proper) acceleration wrt an inertial frame due to applied force is different from coordinate (relative) acceleration due to using a non-inertial frame.

Proper acceleration may not be "absolute", but a change in velocity relative to every other mass in the universe is as close to absolute as it gets.

 

[Max™]

The bucket itself has mass, curves spacetime within it's local frame, and should be possible to be identified as rotating/under a rotating gravitational field.Two bricks could pull a rope taught without rotating if one brick was being accelerated in a straight line more than the other, tie two bricks together, hold one brick, let the other hang free. Naturally this would be distinguishable due to the forces exerted on one brick differing from the other.Yes a single massive particle would curve spacetime in an empty universe, mass does not arise from groups of particles alone.

Rest Mass represents the amount of energy a body has when in a hypothetically perfect rest frame, it would be like sitting at the bottom of a hill.

Moving it would require pushing it up the hill some, imparting relativistic mass, increasing the total energy of the system.Note that GR doesn't exclude the concept of an absolute frame, it merely excludes the identification of an absolute frame, as does SR. SR does allow a definition of an inertial frame to be given and used.

GR only allows this in limited cases, not as a global rule due to cases where the curvature of spacetime is large enough to transform the general inertial frame concepts into one of geodesic motions.

I find it easier to just consider the geodesic cases (i.e. free of external forces) than the inertial ones.

If something is rotating, it was acted upon in some way (be it a kinetic impact, or simply it's collapse under gravitation, both impart angular momentum which can be defined), and is no longer considered a valid inertial frame.

 

[MeJennifer]

GR can tell us if the universe is rotating or not.

If a universe is rotating or not is simply dependent on what chart you use and is ultimately only a coordinate effect.

And spacetime obviously never rotates.

 

[A-wal]

Yea I knew that. I got carried away because I was thinking that if a spinning bucket has force applied to it because the bucket is stationary and the universe is moving around it and therefore has increased mass, then acceleration could be seen as all other objects accelerating relative to you. Even if that could cause the sensation of acceleration it would be different because time dilation would work if reverse. Everything else would be traveling along a longer world line, so you would be ageing faster with respect to everything else rather than slower. I was right about the bucket though.

Anyway, a bucket on it's own couldn't spin because it would have nothing to spin relative to.

And spacetime obviously never rotates.

What about frame dragging?

 

[Ken G]

I would say that "what is rotating" is a purely observer-dependent issue, albeit not a purely coordinate-dependent issue. The distinction I have in mind is that if we are inertial observers, and we attach rotating coordinates to a rotating body, it will be static in those coordinates. However, those coordinates will identify themselves as being rotating, by virtue of fictitous coordinate forces that will appear. But, if the observer is also rotating, then we have a different matter-- the object is no longer rotating with respect to the observer, the rest of the universe is, and now we can attribute the fictitious forces with something real-- the gravity of the rotating universe. The coordinates no longer identify themselves as rotating, as those forces are no longer fictitious. I suppose one might describe that as a Machian view, but I believe it is fully consistent with general relativity.

 

[Buckethead]

I would say that "what is rotating" is a purely observer-dependent issue, albeit not a purely coordinate-dependent issue. The distinction I have in mind is that if we are inertial observers, and we attach rotating coordinates to a rotating body, it will be static in those coordinates. However, those coordinates will identify themselves as being rotating, by virtue of fictitous coordinate forces that will appear. But, if the observer is also rotating, then we have a different matter-- the object is no longer rotating with respect to the observer, the rest of the universe is, and now we can attribute the fictitious forces with something real-- the gravity of the rotating universe. The coordinates no longer identify themselves as rotating, as those forces are no longer fictitious. I suppose one might describe that as a Machian view, but I believe it is fully consistent with general relativity.

I have a hard time with this. Doesn't this fly right in the face of Einsteins main reason for rejecting frames of reference when dealing with rotational acceleration, namely , that galaxy way in the distance can suddenly be moving faster than the speed of light if the observer were to be rotating, but be considered non-rotating from its frame of reference and instead the galaxy was considered to be revolving around the observer.

 

[Buckethead]

This thread has revealed a lot of really great thought generating ideas and I want to thank everyone for contributing so much. I am going to fully admit right now I am completely obsessed with Netwon's Bucket and I can't get enough of it and all the thoughtful posts have really got my brain working overtime.

There are some things about the Machian view (i.e. the "democracy of mass" in the universe defining a spatial reference to determine whether or not a bucket is actually "spinning" or not) that I would like to get some opinions on.

One thing that I'm having a hard time with is the force or field that might contribute to the metric. I think a lot of us here are assuming that gravity plays the dominant role here, but my problem with this is that if the bucket is rotating because it is rotating against the "stationary" metric, then this is strong evidence that the metric (due to gravity?) has drag. Drag may not be the right word, perhaps "influence" might be more accurate, but I'll say drag to make my point. If the metric is stationary any object flying through the metric at a constant velocity will be subject to the same drag that causes the bucket to show itself as "spinning". The result would be something, such as the object slowing down (which it doesn't) or some other effect.

No it seems to me that what we are looking at here is some makeup of the metric that can influence a rotating body without interfering with a body that is not accelerating but instead moving at any given velocity. Can gravity fit this effect?

One thought I have on this is that an object moving at a constant velocity is similar to a DC magnetic field. For example a wire can pass through a magnetic field and as long as the field strength or polarity don't change, no work is done and no electric current is induced in the wire. A rotating body first pushes against a stationary gravitational field then pulls on it, an AC movement through the gravitational field, which might induce resistance.

Another thought is that it's not gravity we are dealing with here, but some other field that can create a metric that is sensitive to acceleration but has no other effect on matter, and also a field that is created by matter.

I'd love to hear speculative opinions about this.

 

[Ken G]

Doesn't this fly right in the face of Einsteins main reason for rejecting frames of reference when dealing with rotational acceleration, namely , that galaxy way in the distance can suddenly be moving faster than the speed of light if the observer were to be rotating, but be considered non-rotating from its frame of reference and instead the galaxy was considered to be revolving around the observer.

I don't know to what extent Einstein "rejected frames of reference", I think he tried pretty hard to keep general relativity a completely relative description of motion. I believe the prevailing view is that he did not succeed in keeping motion entirely relative to other masses, but he did keep it entirely relative to other masses and/or to the fields that are proxies for those masses, thinking of inertia as a kind of interaction with a gravitational field. But what I'm saying is, if we place the observer at the top of the food chain, such that even the fields are subordinate to the perspective of the observer, then we can have the whole universe rotating for any given observer, and galaxies and even planets in our own solar system can move faster than c. There are already galaxies receding from our vantage point at speeds greater than c, cosmologically, so why should we object?

 

[Buckethead]

And spacetime obviously never rotates.

This may not necessarily be true. If the universe is expanding, it indicates a separation of local spacetimes that surround galaxy clusters. Certainly if spacetime in clusters can move relative to spacetime in other clusters, it also has the freedom to rotate relative to the spacetime of other clusters.

 

[Buckethead]

The net gravitational effect is zero, but the Machian frame is not determined by gravity alone, it is determined by the relative velocites and rotations of all the bodies in question. If all the masses in the universe seem at rest relative to the center of all these masses, then this center is also at rest and an object placed here will resist movement relative to the stars. .

Don't quite understand this part.
Currently a mass anywhere in the universe offers inertial resistance.

I didn't mean to be vector specific. I was just taking the sum total of the relative placement of the stars in general and any particle that was stationary (or moving at a constant velocity) relative to the sum of these stars would resist change, so yes that's right that this body in question could be anywhere in the local spacetime.

 

[Hal King]

Did the observer die?

 

[MeJennifer]

This may not necessarily be true. If the universe is expanding, it indicates a separation of local spacetimes that surround galaxy clusters. Certainly if spacetime in clusters can move relative to spacetime in other clusters, it also has the freedom to rotate relative to the spacetime of other clusters.

Space can, given the appropriate chart and/or solution, rotate, however spacetime cannot. Spacetime includes time and rotation is something that obviously happens in time.

 

[Buckethead]

Space can, given the appropriate chart and/or solution, rotate, however spacetime cannot. Spacetime includes time and rotation is something that obviously (cannot) happen in time.

I don't think this is correct. Spacetime is a construct that can describe the motions of bodies or energies through space taking time into account. For example: Light passes by the sun and deflects. Pure space would not allow for this, but spacetime describes this bending. Spacetime is a geometric shape that uses time to define the geometric form. It is still spatial in nature and as such can rotate.

 

[A-wal]

I would say that "what is rotating" is a purely observer-dependent issue, albeit not a purely coordinate-dependent issue. The distinction I have in mind is that if we are inertial observers, and we attach rotating coordinates to a rotating body, it will be static in those coordinates. However, those coordinates will identify themselves as being rotating, by virtue of fictitous coordinate forces that will appear. But, if the observer is also rotating, then we have a different matter-- the object is no longer rotating with respect to the observer, the rest of the universe is, and now we can attribute the fictitious forces with something real-- the gravity of the rotating universe. The coordinates no longer identify themselves as rotating, as those forces are no longer fictitious. I suppose one might describe that as a Machian view, but I believe it is fully consistent with general relativity.

If the observer is rotating and the universe is rotating around the observer at the equivalent rate then there is no rotation.

There are already galaxies receding from our vantage point at speeds greater than c, cosmologically, so why should we object?

In a straight line? Does that imply false red shifting or is special relativity only local? I didn't think it had a range.

 

[Buckethead]

So something has been bothering me about using gravitational attraction of stars as the "web" that defines the "absolute space" that is used as a reference point for determining whether or not Newton's bucket is spinning.

I was reading a section of "Matter and Motion" by James Clerk Maxwell and he talks about Newton's bucket on the north pole of the Earth. If the bucket is made to spin with the Earth, once every 24 hours relative to the stars, and then against the Earth again once every 24 hours, the bucket would show the same amount of concaveness in either direction indicating that the velocity of the overwhelming gravitational field of the Earth has zero effect on the bucket. Since rotation of the bucket relative to the stars (or the stars relative to the bucket) is the reason for the water's concaveness, and since the rotating gravitaional field of the Earth is not influencing the bucket and since the rotating gravitational field of the Earth is several magnitudes stronger than the rotating gravitational fields of the stars, it seems to me this indicates that it is not a gravitational field that determines the outcome of Newton's water.

Even if we just consider the buckets position relative to the Earth we have a problem. If for example the bucket were orbiting the Earth with it's surface parallel to it's plane of rotation and not spinning relative to the stars (in other words the face of the bucket walls change from the viewpoint of the earth), it would not be concave even though the gravitational pull of the Earth is much stronger than any residual gravity in space from the stars.

It is clear that whatever it is that defines what is stationary and what is rotating in the universe is NOT defined by gravitational influence.