Exploring Newton's Bucket Paradox

[yossell]

Nevertheless it is, and (correct me if I'm wrong) the alternative to Mach's principle is acceleration relative to background spacetime (Minkowski spacetime?)?

Not quite acceleration relative to a *space-time*; rather idea is that if the notion of acceleration cannot be grounded in distribution of matter, then properties of space-time must take up the slack. In SR and Minkowski case, primitive notion of inertial lines in space time, which is independent of distribution and behaviour of matter in space time.

Issue more murky in GR as, inspired by Mach, Einstein designed GR so that inertial properties of space-time are not independent of distribution of matter. However, whether inertia can be reduced to properties of matter and distribution of matter in GR, as Mach would have liked, or whether there is rather just a weaker causal or lawlike relation between space-time structures and matter distributions, is still tricky. Empty solutions of GR and rotating universe solutions suggest Mach's principle not fully realized by GR, but there is some debate.

 

[Buckethead]

Not quite acceleration relative to a *space-time*; rather idea is that if the notion of acceleration cannot be grounded in distribution of matter, then properties of space-time must take up the slack. In SR and Minkowski case, primitive notion of inertial lines in space time, which is independent of distribution and behaviour of matter in space time.

Issue more murky in GR as, inspired by Mach, Einstein designed GR so that inertial properties of space-time are not independent of distribution of matter. However, whether inertia can be reduced to properties of matter and distribution of matter in GR, as Mach would have liked, or whether there is rather just a weaker causal or lawlike relation between space-time structures and matter distributions, is still tricky. Empty solutions of GR and rotating universe solutions suggest Mach's principle not fully realized by GR, but there is some debate.

Thank you for the concise clarification. There is something however that troubles me. Without matter (or gravity) spacetime has very few properties. The only one I can think of (and I'm not even sure about this) is it's ability to define a straight line for light, and again I'm not even sure this is true as Mach's principle may include in it that property as well. So without any properties, how can GR depend on space-time at all even to take up the slack that you refer to? And to support this question there are many who feel (not me) that Mach's principle depends on gravity as the vehicle that is referred to when explaining the Mach effect in the first place. So without matter, and hence gravity, Mach's principle disappears and what is left is space-time (with seemingly no real properties) to take up 100% of the slack in determining the outcome of Newton's bucket.

 

[yossell]

Not sure I quite follow the question.

So without any properties, how can GR depend on space-time at all even to take up the slack that you refer to?

GR? First paragraph is about SR and Minkowski spacetime. As I say, it's more complex in the case of GR.

No properties? Space-time? Why do you say this? Quite a rich mathematical structure to Minkowski spacetime. Dimensionality, metrical properties, affine properties, topological properties - the question is the degree to which these properties can be understood as just coding the properties and relations of matter or fields.

 

[Buckethead]

Not sure I quite follow the question.

GR? First paragraph is about SR and Minkowski spacetime. As I say, it's more complex in the case of GR.

No properties? Space-time? Why do you say this? Quite a rich mathematical structure to Minkowski spacetime. Dimensionality, metrical properties, affine properties, topological properties - the question is the degree to which these properties can be understood as just coding the properties and relations of matter or fields.

This is the question, "the degree to which these properties can be understood as just coding the properties and relations of matter or fields". Can I assume you are basically saying that without matter in the universe, all of these properties of space-time are either useless or undefined? The one exception that I can see is as I mentioned above, the relationship of light to space-time regardless of the presence of matter. Can spacetime define a straight line for light in an otherwise empty universe or is the concept of a straight line in this case truly meaningless? And if it is meaningless then again, there are no properties for space-time in an empty universe that I can see.

My question, to be more clear, rests on my general concern that if the properties of spacetime are simply used to describe properties and relations of matter or fields (which makes total sense to me) and if a matterless universe results in space-time with no sensible properties, then space-time is intimately related to matter to such a degree that they can be said to be inseparable. If this is the case, then in your first paragraph, where you say space-time can take up the slack where acceleration cannot be grounded in matter, if matter and spacetime are inseparable the slack cannot simply be pawned off to space-time.

With regard to GR, since GR is based on adding gravity (and/or inertia?) to the problem, and since gravity and inertia are dependent on matter, doesn't this again just reduce to space-time having no real properties once matter is out of the picture. Doesn't all of this just boil down to saying that inertia and the path that an object would take are 100% reliant on the matter in the universe?

 

[yossell]

Can I assume you are basically saying that without matter in the universe, all of these properties of space-time are either useless or undefined?

I didn't mean to be saying this. Indeed, The notion of an inertial line is NOT defined in terms of distribution of matter. However, I believe that something like what you say is the intent of Mach's principle - that is, Mach wants to eliminate primitive properties of spacetime in terms of distribution of matter.

In standard formulations of Minkowski spacetime, inertial lines are not defined in terms of the distribution of matter, and acceleration is absolute. There is no obvious guarantee that inertial lines can be defined in relational terms to matter distribution.

Can spacetime define a straight line for light in an otherwise empty universe or is the concept of a straight line in this case truly meaningless?

Yes, spacetime can support inertial lines independently of existence of matter.

My question, to be more clear, rests on my general concern that if the properties of spacetime are simply used to describe properties and relations of matter or fields (which makes total sense to me) and if a matterless universe results in space-time with no sensible properties, then space-time is intimately related to matter to such a degree that they can be said to be inseparable.

Yes, this seems to be the Machian and, more generally, relationist viewpoint.

If this is the case, then in your first paragraph, where you say space-time can take up the slack where acceleration cannot be grounded in matter, if matter and spacetime are inseparable the slack cannot simply be pawned off to space-time.

Yes, *if* it is the case. Newton argued for the contrapositive: since absolute acceleration couldn't be explained in terms of relational matters, there needed to be such a thing as space, something which grounded absolute acceleration and absolute rotation.

I think 'the slack cannot simply be pawned off to space-time' needs to be justified. I don't believe one has a priori insight into whether or not there is space or spacetime. I would prefer an explanation that postulated only matter, but if it turns out that there are effects which cannot be explained in such a way, but which can be explained by taking space-time seriously, then I think it is rational to accept spacetime, much as we accept other theoretical entities. But this is an old and rich and interesting debate, and there are strong views on either side, so you are by no means alone here.

With regard to GR, since GR is based on adding gravity (and/or inertia?) to the problem, and since gravity and inertia are dependent on matter, doesn't this again just reduce to space-time having no real properties once matter is out of the picture. Doesn't all of this just boil down to saying that inertia and the path that an object would take are 100% reliant on the matter in the universe?

The issue is the sense of `dependent'. In GR, there is a lawlike relation between the distribution of matter, and the `geometry' of space. But it is not clear that this dependence is strong enough to show that geometry has been reduced to distribution of matter, or just codes it up. I think this question is very difficult to answer, but it is a very interesting one. There seems to be strong feeling on both side, but I am not sure which view is correct. And many dismiss the whole question as merely philowsophicawl (sic).

 

[Austin0]

Mach's Principle speculates that inertia, or a body's resistance to acceleration is directly caused by all of the matter in the universe. No matter, no resistance..

Hi Buckethead
Just a thought . If all the matter in the universe is limited to the bucket and water
wouldn't both acceleration and inertia simply apply as usual??

Indeed! Which makes me wonder why the debate about Mach's principle is still going on. Nevertheless it is, and (correct me if I'm wrong) the alternative to Mach's principle is acceleration relative to background spacetime (Minkowski spacetime?)? Sorry, but I can't say I really understand what is meant by acceleration relative to spacetime. This doesn't make much sense to me.

This thread you started is a demonstration of the longevity of the debate.
Certainly the concept of spacetime in the absence of matter is problematic in all cases.

 

[Austin0]

Not sure I quite follow the question.



GR? First paragraph is about SR and Minkowski spacetime. As I say, it's more complex in the case of GR.

No properties? Space-time? Why do you say this? Quite a rich mathematical structure to Minkowski spacetime. Dimensionality, metrical properties, affine properties, topological properties - the question is the degree to which these properties can be understood as just coding the properties and relations of matter or fields.

Aren't these properties basically considered as purely kinematic. Not as having a causal relationship like that which is assumed regarding the geometric properties of GR spacetime?
If they are coding the properties of matter or fields than they would also seem to not apply in the absence of matter ,no?

 

[Austin0]

Mach's principle - that is, Mach wants to eliminate primitive properties of spacetime in terms of distribution of matter.

I had always interpreted it that he wanted to eliminate the primitive property of matter i.e. inertia.
And explain it as an emergant quality from the more fundamental property of gravity. Live and learn.

In standard formulations of Minkowski spacetime, inertial lines are not defined in terms of the distribution of matter, and acceleration is absolute. There is no obvious guarantee that inertial lines can be defined in relational terms to matter distribution.

Yes, spacetime can support inertial lines independently of existence of matter.

If you assign the absoluteness of acceleration to Minkowski spacetime isn't this implying that Minkowski spacetime is an active agent or geometry??

Buckethead...My question, to be more clear, rests on my general concern that if the properties of spacetime are simply used to describe properties and relations of matter or fields (which makes total sense to me) and if a matterless universe results in space-time with no sensible properties, then space-time is intimately related to matter to such a degree that they can be said to be inseparable.

Yes, this seems to be the Machian and, more generally, relationist viewpoint.

Also Einstein seemed to be saying the same thing with"space has no existence independant of matter"

Yes, *if* it is the case. Newton argued for the contrapositive: since absolute acceleration couldn't be explained in terms of relational matters, there needed to be such a thing as space, something which grounded absolute acceleration and absolute rotation.

But this is an old and rich and interesting debate, and there are strong views on either side, so you are by no means alone here.



The issue is the sense of `dependent'. In GR, there is a lawlike relation between the distribution of matter, and the `geometry' of space. But it is not clear that this dependence is strong enough to show that geometry has been reduced to distribution of matter, or just codes it up. I think this question is very difficult to answer, but it is a very interesting one. There seems to be strong feeling on both side, but I am not sure which view is correct. And many dismiss the whole question as merely philowsophicawl (sic).

yes difficult and interesting
I think to dismiss the whole question indicates a metaphysical or philo sophical view.

 

[Buckethead]

Hi Buckethead
Just a thought . If all the matter in the universe is limited to the bucket and water
wouldn't both acceleration and inertia simply apply as usual??

I believe (although it's been so long I'm not sure now) that something along this line was the reason I started this thread. Check some of the posts earlier in the thread and you will find a speculative discussion with regard to inertial lines and related matters in a universe that has only one or two bodies in it. I like to ponder this type of scenario because it helps to "see the forest for the trees" when thinking about things such as inertia, or the shape of an inertial line or the meaning of acceleration.

 

[Buckethead]

In standard formulations of Minkowski spacetime, inertial lines are not defined in terms of the distribution of matter, and acceleration is absolute. There is no obvious guarantee that inertial lines can be defined in relational terms to matter distribution.

Yes, spacetime can support inertial lines independently of existence of matter.

If this is correct, it would seem then that space-time has at least one inherent property that is independent of matter and that is that inertial lines can be defined in the framework of space-time alone and Newton's bucket in an otherwise empty space would simply act as it would on Earth and curve if the water were spinning relative to the grid defined by the inertial lines in space-time. I'm skeptical of this and was wondering if you could hint at a possible mechanism that might allow for this to be true. The reason I am skeptical is that the entire idea behind Mach's principle is that it is the matter in the universe that determines the outcome of Newton's bucket which includes inertial lines. So if inertial lines are an inherent property of space-time alone, then this throws Mach's principle out the window. Also, it seems that the popular view among's Machinists is that gravity is the mechanism behind the inertial lines. I don't think it is, but if it is, then matter of course would be required.

In addition, if space-time can support inertial lines alone, then what is the mechanism? Obviously not gravity, but something. Is space-time a literal "grid" of inertial lines? What are these lines made of? A large self sustaining field of somekind? Some kind of new darker- dark matter?

Now the thing is, I think I can go either way with this. I can be convinced that Mach's principle is wrong if it can be shown that space-time alone can describe inertial lines, or I can go with Mach's principle if it can be shown that space-time can describe inertial lines, but only as a result of the effect of matter on space-time. In either case, I don't think gravity is the mechanism. Also it should be noted, that I'm also saying that if Mach's principle holds, then this indicates that inertial lines might be undefined in an empty (or otherwise empty) universe.

The issue is the sense of `dependent'. In GR, there is a lawlike relation between the distribution of matter, and the `geometry' of space. But it is not clear that this dependence is strong enough to show that geometry has been reduced to distribution of matter, or just codes it up. I think this question is very difficult to answer, but it is a very interesting one. There seems to be strong feeling on both side, but I am not sure which view is correct. And many dismiss the whole question as merely philowsophicawl (sic).

I might be missing something here but I see these as two very distinctly different theories with measurable distinctions. For example if space-time can support inertial lines, then it can support inertia and this can mean that a single body in an empty universe can have traditional inertial values and predictable trajectories. If Mach's view is correct, then this can lead to the possibility that a single body in an empty universe can have no mass at all, no inertial, and an undefined trajectory (if there were some way to propel it). This is a very important distinction.

 

[yossell]

I'm skeptical of this and was wondering if you could hint at a possible mechanism that might allow for this to be true.

No mechanism in Minkowski or Newtonian theories. But no mechanism in Mach's view either. Mach just thought bucket spun relative to fixed stars, Newton: relative to space; neither gives `mechanism'.

The reason I am skeptical is that the entire idea behind Mach's principle is that it is the matter in the universe that determines the outcome of Newton's bucket which includes inertial lines.

Well, yes - I'm not taking sides on the absolute truth of Mach's Principle. Newtonian theory is false; SR has to be modified in the light of gravity; who knows what tomorrow will bring? Just telling you how and why Newtonian theory, and SR seem not to embody Machian principles, while in GR it's unclear. Yes, if you're a Machian, you'll probably look for something else; historically, this seems to have been something that motivated Einstein in his creation of GR.

Also, it seems that the popular view among's Machinists is that gravity is the mechanism behind the inertial lines. I don't think it is, but if it is, then matter of course would be required.

Yes, but now we're talking about GR, as opposed to the other theories.

Now the thing is, I think I can go either way with this.

That's the spirit - rational, disinterested, unprejudiced inquiry.

Also it should be noted, that I'm also saying that if Mach's principle holds, then this indicates that inertial lines might be undefined in an empty (or otherwise empty) universe.

That sounds right.

I might be missing something here but I see these as two very distinctly different theories with measurable distinctions. For example if space-time can support inertial lines, then it can support inertia and this can mean that a single body in an empty universe can have traditional inertial values and predictable trajectories. If Mach's view is correct, then this can lead to the possibility that a single body in an empty universe can have no mass at all, no inertial, and an undefined trajectory (if there were some way to propel it). This is a very important distinction.

Agree with your description of these differences. The trouble is, in a very strong sense, it's not measurable. We can't make a universe with just a single body and see if it spins. We can't rotate the stars around the bucket and see if the water in the bucket rises just as it were the bucket alone that is rotating. Still, it's exactly that pure Newtonian and Minkowski theories predict that lone spinning buckets would behave differently from lone non-spinning ones that have made people think that these, *these*, theories do not embody Mach's Principle.

 

[A-wal]

So basically Machs principle is that acceleration is just as relative as velocity? I'm not sure how acceleration would be possible in a one object universe. Space-time is a measurement of the distances between objects.

So an extension of this is that if there were more matter in the universe then everything would require more energy to accelerate, and obviously the reverse if there's less?

 

[yossell]

So basically Machs principle is that acceleration is just as relative as velocity?

I can't speak for all of them, but many Machians would welcome this.

I'm not sure how acceleration would be possible in a one object universe.

Right - and, in Mach's favour, a lot of people do find the idea of acceleration in a one object universe absurd.

So an extension of this is that if there were more matter in the universe then everything would require more energy to accelerate, and obviously the reverse if there's less?

No. Well - it doesn't follow from Mach's principle - maybe there are variations that include it.

 

[yuiop]

So an extension of this is that if there were more matter in the universe then everything would require more energy to accelerate, and obviously the reverse if there's less?

No. Well - it doesn't follow from Mach's principle - maybe there are variations that include it.

A-Wal's extension seems reasonable. If in an one object universe, the object has no mass mass or inertia (in the Machian view), the introduction of a single additional atom anywhere in the universe would endow the initial object with its full quota of mass and inertia. This implies the mass and inertia endowing properties of the second object are independent of the mass and distance of the second object from the first. If the mass and inertia endowing properties of the second object are independent of the mass and distance of the second object from the first, then a second particle with zero mass located infinitely far from the first object would endow the first object with mass and inertia. A single object and a second particle with zero mass located infinitely far away from the first object, is as good an aproximation to a single object universe as you could hope for.

Thought for the day. (Something to chew on)

Linear momentum and angular momentum are always conserved, so the total momentum of the universe never changes. If we start with a non rotating neutron star (Schwarzschild metric) and cause the neutron star to rotate, we should obtain the Kerr metric which is a spinning object in an otherwise empty universe, in the GR view. However it is impossible to obtain the second situation from the first, because in order to spin the neutron star, a sufficient amount of mass and energy has to be ejected, so that the amount of mass and energy external to the spinning neutron star, has exactly the opposite angular momentum to the spinning neutron star.

Basically what I am saying, is it impossible to start with a non rotating bucket in an otherwise empty universe and end up with a spinning bucket in an otherwise empty universe.

Now what would be interesting, would be if someone tried to measure and sum all the linear and angular momentum of the major visible galaxies in the universe and see in the total linear and angular momentum of the universe relative to the CMB frame is zero in both cases. I am pretty sure it would be, but I am not sure that actually proves anything.

 

[A-wal]

The speed of light would also change. So would the energy requirement to make an atom. Relatively everything should stay the same, meaning it's the only way it can be. There wouldn't be a big bang either. I've thought that for ages. It would mean the values of everything are determined by some magic number, presumably Pi.

Thought for the day. (Something to chew on)

Linear momentum and angular momentum are always conserved, so the total momentum of the universe never changes. If we start with a non rotating neutron star (Schwarzschild metric) and cause the neutron star to rotate, we should obtain the Kerr metric which is a spinning object in an otherwise empty universe, in the GR view. However it is impossible to obtain the second situation from the first, because in order to spin the neutron star, a sufficient amount of mass and energy has to be ejected, so that the amount of mass and energy external to the spinning neutron star, has exactly the opposite angular momentum to the spinning neutron star.

How could a lone object spin anyway? Spin relative to what?

Now what would be interesting, would be if someone tried to measure and sum all the linear and angular momentum of the major visible galaxies in the universe and see in the total linear and angular momentum of the universe relative to the CMB frame is zero in both cases. I am pretty sure it would be, but I am not sure that actually proves anything.

Makes sense. Total momentum always has to be 0. It wouldn't make sense if it wasn't.

 

[Austin0]

The speed of light would also change. So would the energy requirement to make an atom. Relatively everything should stay the same, meaning it's the only way it can be. There wouldn't be a big bang either. I've thought that for ages. It would mean the values of everything are determined by some magic number, presumably Pi.




How could a lone object spin anyway? Spin relative to what?


Makes sense. Total momentum always has to be 0. It wouldn't make sense if it wasn't.[/QUOTE]

Could you elaborate on this a little.

It seems to make some sense regarding conservation of momentum but isn't the vast majority of energy in the universe, outside of that which resides in matter, simply momentum?? In this sense photons are simply transmitted momentum.
DO you consider the total enrgy of the universe to be 0 ??
Or am I just misunderstanding you?
Thanks

 

[A-wal]

I was just thinking out loud and extending the principle. The total momentum would be 0. Energy causes acceleration but that could be relative, so maybe. A four-dimensional view would be static, so definitely yes literally speaking.

 

[A-wal]

Just to elaborate

The universe is curved like the surface of the Earth. The total distance separating two objects is the same regardless of your movement relative to it. It's the length of the universe in that direction because you move an equal distance towards an object in one direction as you move away from it in the opposite direction. The same should apply to time.

The differences with time are in our heads. The illusion of a moving timeline comes from the fact that we remember the past but not the future. We're not even aware of a single thought in our heads until we remember having it. And there's nothing special about the present. We have a sense of being in the moment in every second of our lives. It's always now.

A four dimensional sphere would have certain properties. You wouldn't be able to see around its curvature because we see in straight lines. But objects over a certain distance away wouldn't just vanish from view. It would be gradual. Objects would be more red shifted the further away they are.

If we try to see around the curvature of the universe into the past then we get a singularity. But that would be true if we lived six billion years ago, or at any other time. It would look the same size and there would still be a singularity if you looked back to about six billion years before that. This doesn't mean that time would be repeating itself. There is no moving timeline. It would just mean that events get closer in the future as they get further in the past. It's a circle.

It doesn't cause any paradoxes either because there's no way to get a message through a singularity.

 

[A-wal]

Does this work then? It wouldn't really change anything from our perspective. Relative to us the big bang would still have happened six billion years ago. It doesn't mean anything changes when you look back. It's just that it would look like that whenever you did it. Looking through curved space over long distances should noticeably red-shift whatever you're looking at, and it would be more red-shifted the more space you were looking though, yes?

I've never liked having a beginning. I used to think of it as bouncing but this is much simpler. It would mean no beginning or end. It just exists and that's it. That's way more elegant than a big explosion.

 

[AWA]

Sure, it works.
Just a little problem, it also sends current cosmology to the trash can, in case you hadn't noticed.

 

[A-wal]

Had noticed. Not my problem. Mine's better.