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

[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.