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

[Buckethead]

Should be, since the universe is not empty, it contains both the rocket and the reaction mass. The rocket's coordinate acceleration relative to its reaction mass should even be proportional to the proper acceleration read on an accelerometer, ie, F=ma. This leaves the question of what value m would have, since mass is the measure of the rocket's inertial opposition to acceleration, and as you've pointed out, the inertial mass may itself depend on the other mass in the universe.

But assuming we have the same laws of physics, as long as the universe contains some (reaction) mass, the rocket's inertial mass will be non zero, so acceleration should be proportional to the force applied (and felt), even if the ratio (inertial mass) is very different than in the real universe.

If reaction mass is not allowed, there would be no physical way to provide acceleration, no way to apply any force to be "felt", and no other masses to establish a reference frame to measure coordinate acceleration.

I tend to agree that even in an otherwise empty universe F=ma will hold but interestingly only because m denotes inertial mass and not the amount of matter. It might just be the case that the amount of matter an object has and it's inertial mass begin to deviate in a universe with increasingly less total matter. The end result in an otherwise empty universe is that a much much smaller force would be needed to accelerate an object to a given velocity relative to the ejected matter. If this is the case then the accelerometer would also have to be recalibrated as it's mass on the spring would be less showing a lower value than the actual increased acceleration (change in velocity relative to the ejected matter) would be.

There are some considerations that need to be taken with regard to the change in inertial mass to amount of matter in on object. For example, I mentioned earlier that it makes sense to consider the persistance of the geodesics when influenced by moving or stationary matter. In an otherwise empty universe one has to consider how long the astronaut sits in his current location before turning on the rocket as it might affect his inertial mass. This goes for rotation as well. If the astronaut turns on rotational jet packs (after sitting for awhile), he will experience a (small) degree of angular momentum and his arms will fly outward, but if he stays in this state for awhile, his arms might just fall back down to his side again as the persistent geodesics would begin to rotate with the astronaut (due to Lense-Thirring effect) rendering him essentially non rotating after awhile (when using the definition of rotation as a feeling of angular momentum).

One more point is that in on otherwise empty universe the object's active gravitational field might remain proportional to it's inertial mass, but again not to it's amount of matter. Therefore an object the size of the Earth in an otherwise empty universe would have a weaker gravitational field and objects would fall more slowly.

 

[Al68]

I tend to agree that even in an otherwise empty universe F=ma will hold but interestingly only because m denotes inertial mass and not the amount of matter.

How is the amount of matter measured other than by mass? Number of atoms, maybe? Would each atom have less mass if there were less mass in the universe? Does the mass of each subatomic particle depend on other mass in the universe?

One more point is that in on otherwise empty universe the object's active gravitational field might remain proportional to it's inertial mass, but again not to it's amount of matter. Therefore an object the size of the Earth in an otherwise empty universe would have a weaker gravitational field and objects would fall more slowly.

Wouldn't the object still fall at 9.8 m/s^2 due to it's proportionally reduced inertial mass offsetting the reduced gravitational mass of earth?

And back to the rocket, since it's being accelerated by the expulsion of reaction mass which itself would have less inertial mass, resulting in less force applied to the rocket, there would be less coordinate acceleration between rocket and reaction mass.

So, even if the mass of each atom were lower, the force used to accelerate the rocket would be proportionally lower due to the reduced reaction mass, and that would leave us with no way to detect any difference caused by "reduced" inertial mass, since inertial mass by definition is resistance to acceleration.

It seems like there would be no way to measure inertial mass in any absolute sense, only in a relative sense. We could only measure the masses of the rocket and reaction mass relative to each other, and their ratio would be the same as they are now.

For example, if a rocket accelerated by "shooting" half its mass in the other direction, in an empty universe the inertial mass of both rocket and reaction mass may be less, but the resulting coordinate acceleration (per unit mass) would be greater due to the lower inertial mass, resulting in the same measured coordinate acceleration (between rocket and reaction mass) as in a "full" universe. And the proper acceleration (felt by observers) would equal the force used to expel the reaction mass, just as it is in our "full" universe. Basically, I see no way to detect any absolute change in the inertial mass per atom, if the change is universal.

If the mass of every atom in the universe is half today of what it was yesterday, how could we tell? Does the concept even make sense?

 

[Buckethead]

How is the amount of matter measured other than by mass? Number of atoms, maybe? Would each atom have less mass if there were less mass in the universe? Does the mass of each subatomic particle depend on other mass in the universe?

The number of subatomic particles can be used to determine mass (see Wiki "mass") as can F=ma (inertial mass), as can gravity and a few other things. Wiki mentions that if any of these prove to be unable to determine mass (because they are the odd one out), then they would be thrown out. In our universe, they all agree, but in an otherwise empty universe, one or more of these may deviate.

Wouldn't the object still fall at 9.8 m/s^2 due to it's proportionally reduced inertial mass offsetting the reduced gravitational mass of earth?

I would say no for the same reason that a golf ball and cannon ball fall at the same rate on Earth and both fall at a slower rate on the Moon. A small objects rate of decent toward a planet is not determined by it's mass, only the mass of the planet. But in this peculiar universe in which this happens there may be other factors involved such as the deviation between inertial mass and the amount of matter.

And back to the rocket, since it's being accelerated by the expulsion of reaction mass which itself would have less inertial mass, resulting in less force applied to the rocket, there would be less coordinate acceleration between rocket and reaction mass.

The force would remain constant as this is a given. Therefore the 2 objects of lower mass will accelerate away from each other to a greater degree than than the two objects of greater mass. The expelled propellant would simple shoot out faster offering a greater reaction.

However, you do bring up a good point in that we can't really forsee the effect of this empty universe on all matters of force. For example, if we use a spring to push a cannon ball away from the astronaut, we would expect the accelerations to be greater but only if a given spring produces the same amount of force in this empty universe. Springs work by depending on the electromagnetic force between atoms in the spring. If electromagnetism, and for that matter the weak and strong force are all related to each other and to gravity, then it's possible that if anyone of them is proportionally changed (such as gravity) relative to the amount of matter in an object in an otherwise empty universe that the others could change as well in linear proportion. If this is the case, then this might mean that we could never detect the difference. On the other hand, if the changes between forces is non linear, then we would be able to tell.

Finding the changing relationship of these forces to each other and to the overall mass in the universe might be a pathway to unifying the forces.

If for some reason all forces but one, say gravity, did not change it's strength in this new universe, then I think it could safely be said gravity and the other 3 forces were not related in anyway and unification would be impossible. I doubt that's the case however.

If the mass of every atom in the universe is half today of what it was yesterday, how could we tell? Does the concept even make sense?

Even if all 4 forces were proportionally changed in a linear way relative to the overall mass of the cosmos, it would make a difference on a grand scale because overall mass has to be considered as local. If for example our galactic cluster has a different amount of matter than another galactic cluster in the universe (which no doubt it does), then the inertial mass of particles in our galactic cluster could be different than that of other clusters. This would make interactions between clusters predictable only if these fudge factors were taken into account. Also a particle traveling at a given speed in our galactic cluster, would have a change in velocity when entering another galactic cluster due to the change in it's inertial mass. Measuring the expansion of the universe would be affected as well.

 

[Al68]

The number of subatomic particles can be used to determine mass (see Wiki "mass") as can F=ma (inertial mass), as can gravity and a few other things. Wiki mentions that if any of these prove to be unable to determine mass (because they are the odd one out), then they would be thrown out. In our universe, they all agree, but in an otherwise empty universe, one or more of these may deviate.

Well, I was shooting in the dark predicting the way things might work in an empty universe, but we certainly agree on one thing: We just don't know enough about gravity or mass.

The one thing that seems apparent is that inertial mass and gravitational mass aren't just equal or equivalent, but are in fact the same thing. It would be hard to believe that they are separate things that just coincidentally seem identical in every way (in GR, not in Newtonian physics).

As I'm sure you know, there have been many attempts to detect the hypothesized Higgs boson, theorized to be responsible for the mass of subatomic particles, and there are more planned that might eventually shed some light on the subject. The Large Hadron Collider in Geneva is expected to either confirm or deny its existence once and for all, within a few months, or so they say.

 

[Buckethead]

The one thing that seems apparent is that inertial mass and gravitational mass aren't just equal or equivalent, but are in fact the same thing. It would be hard to believe that they are separate things that just coincidentally seem identical in every way (in GR, not in Newtonian physics).

I think they are the same thing, but of course you will find many that think they are only equivelent.

As I'm sure you know, there have been many attempts to detect the hypothesized Higgs boson, theorized to be responsible for the mass of subatomic particles, and there are more planned that might eventually shed some light on the subject. The Large Hadron Collider in Geneva is expected to either confirm or deny its existence once and for all, within a few months, or so they say.

The Higgs field, which is responsible for giving mass to all particles including the Higgs boson itself might be a candidate for the Machian effect, but I don't know the properties of the Higgs field enough to have an opinion on this. Perhaps someone with more knowledge of this field can chime in.

The field or effect that I am searching for would have these properties, and these are based on gravity and mass being the same thing and not just eqivalent. Some of these properties seem contradictory, but they are not contradictory, they are simply peculiar.

1. It uniformly saturates galaxtic clusters and it's density is dependent on the total galactic mass.
2. It's density decreases near massive objects which may imply mass absorbs it.

3. It's density changes when a massive object is accelerated through it with the leading edge having a higher density. This change in density looks like gravity from behind
4. If it's density is non uniform across an object, then the object will accelerate (gravity) toward the less dense region.

5. It's density does not change if an object moves through it at a constant velocity.
6. It offers no resistance to an object, as long as it's density is uniform across the object

7. It interacts with each and every particle in an accelerating object. (A 1 kg disc for example offers no more resistance than a 1 kg spear, both of which are traveling at the same speed)

8. It is defined as a geodesic and the geodesics are shaped by both mass and by the acceleration of a given mass. The greater the gravity or the greater the acceleration, the greater the distortion in the geodesic.

9. The shapes of the geodesics are persistent and the degree of persistance is proportional to the amount of mass, and duration of the mass in a specific location or the degree of acceleration of a mass.

10. If the geodesic rotates as a whole, this causes a change in density across the objects within it, causing the objects to accelerate rotationally until they match the rotation of the geodesic as a whole.

11. Light curves if passing through an area of density change (such as near a planet, or near an accelerating object.

Number 11 has some predictive properties. For example, light will bend near an accelerating object in the same way it would near a gravitational mass.

Number 3 makes a prediction as well. If a massive cylinder is rotated at a high speed, the density would increase inside the cylinder due to angular acceleration. The inside of the cylinder would be the leading edge of the accelerating cylinder and therefore the gravity inside the cylinder would be higher than Earth gravity. A particle passing through the cylinder would have an increase in mass for the duration of it's time in the cylinder. It would also slow down entering the cylinder due to the change in density, but speed up again on exiting so these effects would cancel. The increase in mass however and it's associated decrease in speed due to it's mass change would be measurable.

Number 7 is particularly interesting because in a traditional gravitational field all the particles in an object are affected by all the particles in the large body. This is why two objects of different mass fall at the same rate, the amount of force on each particle in the two objects are the same which follows f=ma.

These properties are bizaar to say the least, and I have racked my brain trying to come up with something that could possibly have such properties, but fall short. Whatever it is, it's different than what we can commonly imagine. If something can be found to match these properties, then we have found what gravity is and what inertia is and also solve Newton's bucket.

 

[inflector]

Even if you take the absolute value (in other words, ignore cancellation) of all the gravity in the cosmos and sum it together the strength of the gravitational force would be much weaker than the gravitational field near Earth. I say this because you can use all the light from all the stars as a weak but usable analogy. Even though there are magnitudes more light being emitted by all the stars than say the sun, the sun easily washes out the starlight and light is a good example as it doesn't suffer from cancellations in the same way gravity does.

I know this thread is six months old, but I see a problem with the above logic.

In particular, unless I'm missing something important, the reach of gravity could be infinitely larger than that of photons/electromagnetic energy.

Consider this. The oldest light we can see is from the CMB which is about 15 billion years old. This is some 400 thousand years after the Big Bang. The reason we have this limit is because before this time, the universe was opaque to photons.

It was not, however, opaque to gravity.

Therefore, if gravity propagated at the speed of light beginning with the Big Bang, it seems possible that we are currently feeling the gravitation of a much greater proportion of the matter in the universe, perhaps even all of it. This is in contrast with the light we can see which is limited due to the fact that we can only see back to about 400,000 years after the big bang.

So, it may be that the gravitational effects of the entire universe dominate even when on the surface of the Earth from the perspective of Newton's Bucket.

- Curtis

 

[utesfan100]

Let's take two bricks tied together by a rope and define that the bricks are not spinning (one face of each brick always faces the other). If there is tension on the rope, then one can say the bricks are revolving about each other. But in an empty universe, this would mean the system would be revolving relative to absolute space. If there is no absolute space, then there could be no tension on the rope since the objects are not rotating relative to anything (not even to each other if their faces are stationary)

I like this version. In an empty universe a spinning bucket of water would send out water uniformly in a big mess that I don't want to clean up.

It is my understandings that GR allows great flexibility in selecting reference frames. Mach's principle can be viewed as stating that we can use a rotating reference frame in classical mechanics.

This produces complicated curvature to the space-time that reduces to the pseudo-forces in classical rotating frames.

For a localized system I would think that a reference frame that minimized the curvature at infinity would offer a preferred reference frame. I suspect this convention would eliminate rotating reference frames and frames where the net momentum of the system of interest is not 0.

As for a non-mathematical explanation of scalars and tensors ... I'll provide that once you provide me with a non-mathematical explanation of integrals.

Tensors are generalizations of scalars, vectors and matrices to an arbitrary dimension of indexes. GR is written in the language of Riemannian Geometry, and this would be a good place to start.

 

[Buckethead]

I know this thread is six months old, but I see a problem with the above logic.

In particular, unless I'm missing something important, the reach of gravity could be infinitely larger than that of photons/electromagnetic energy.

Consider this. The oldest light we can see is from the CMB which is about 15 billion years old. This is some 400 thousand years after the Big Bang. The reason we have this limit is because before this time, the universe was opaque to photons.

It was not, however, opaque to gravity.

Therefore, if gravity propagated at the speed of light beginning with the Big Bang, it seems possible that we are currently feeling the gravitation of a much greater proportion of the matter in the universe, perhaps even all of it. This is in contrast with the light we can see which is limited due to the fact that we can only see back to about 400,000 years after the big bang.

So, it may be that the gravitational effects of the entire universe dominate even when on the surface of the Earth from the perspective of Newton's Bucket.

- Curtis

I thought light was opaque from the earliest universe because it is traveling away from us faster than light, and 2) because it's frequency is too low (actually negative) because of this. Gravity would fall into the same category.

 

[Buckethead]

It is my understandings that GR allows great flexibility in selecting reference frames. Mach's principle can be viewed as stating that we can use a rotating reference frame in classical mechanics.

This produces complicated curvature to the space-time that reduces to the pseudo-forces in classical rotating frames.

For a localized system I would think that a reference frame that minimized the curvature at infinity would offer a preferred reference frame. I suspect this convention would eliminate rotating reference frames and frames where the net momentum of the system of interest is not 0..

I agree with all you are saying here and it would be fine to just stop at that if it weren't for what I see as a possibility that there might be a case where a complicated curvature to space time does not reduce to the pseudo-forces in a classical rotating frame. What if there are curvatures caused by the movements of concentrated masses in the universe that lagged or were otherwise out of phase with the pseudo-forces we observe? A lag for example between a spacetime curvature and the pseudo-forces in a rotating galaxy would give the appearence of a the galaxy having a flattened rotational curve which we are currently attrributing to being caused by dark matter.

 

[matheinste]

I thought light was opaque from the earliest universe because it is traveling away from us faster than light, and 2) because it's frequency is too low (actually negative) because of this. Gravity would fall into the same category.

Can you elaborate on what you mean by light being opaque and of negative frequency.

Matheinste.

 

[Buckethead]

Can you elaborate on what you mean by light being opaque and of negative frequency.

Matheinste.

Sorry, my response was a little obscure. At the furthest reaches of the universe (the earliest times) there is a horizon where, due to expansion, the universe is theorized as moving away from us faster than light. Because of this the light past this point cannot ever be seen by us. I took this to be what you meant by "opaque". The frequency of the light just on this side of the horizon would be below the microwave frequency, at the horizon it would be zero, so beyond that it would be a negative frequency if we could see it which we can't so it's really a nonsense term that I threw out there for illustrative purposes. Since gravity from the earliest universe is also beyond this horizon and also traveling at the speed of light, it cannot reach us either.

 

[Al68]

I thought light was opaque from the earliest universe because it is traveling away from us faster than light, and 2) because it's frequency is too low (actually negative) because of this. Gravity would fall into the same category.

The universe was opaque to light because of its density. Gravity is much different, because unlike light, there is no opaqueness, and we can't rule out the possibility that we could be under the gravitational influence of masses that are not even part of our universe at all, or that predate our universe.

Of course that's pretty speculative, but I'm only saying we can't rule it out based on the opaqueness of the universe prior to 400,000 years after the big bang, like we can with light. And we can't rule out the existence of masses beyond the "horizon" that aren't moving away from us faster than light.

We can only rule out light from such masses because of the previous opaqueness (density) of the universe, but that wouldn't apply to gravity.

 

[Buckethead]

The universe was opaque to light because of its density. Gravity is much different, because unlike light, there is no opaqueness, and we can't rule out the possibility that we could be under the gravitational influence of masses that are not even part of our universe at all, or that predate our universe.

Of course that's pretty speculative, but I'm only saying we can't rule it out based on the opaqueness of the universe prior to 400,000 years after the big bang, like we can with light.
.

I might be wrong here but it seems to me that if the density of the early universe (that is not going faster than light) was so high that it would block light, then the energies must have been so high that everything emited light and the sky would be a wash with light. If the time of this opaque universe was beyond the horizon, then there wouldn't be a wash, but there would also be no effect of gravity at this distance since gravity also travels at c.

And we can't rule out the existence of masses beyond the "horizon" that aren't moving away from us faster than light.

What would be traveling slower than light beyond the horizon, since everything in this area of the universe started from the big bang?

 

[Al68]

I might be wrong here but it seems to me that if the density of the early universe (that is not going faster than light) was so high that it would block light, then the energies must have been so high that everything emited light and the sky would be a wash with light. If the time of this opaque universe was beyond the horizon, then there wouldn't be a wash, but there would also be no effect of gravity at this distance since gravity also travels at c.

What would be traveling slower than light beyond the horizon, since everything in this area of the universe started from the big bang?

I was referring to the speculative, but very real possibility that our universe, the result of the big bang, isn't all that exists or ever existed. Our universe could be subject to the gravitational influence of masses that aren't part of our universe, and predate the big bang.

The previous opacity of our universe restricts any light we can detect to sources within our universe's horizon, but gravitational influence cannot be ruled out the same way.

Of course, this probable belongs in the cosmology or string theory forums instead of SR/GR.

 

[Buckethead]

I was referring to the speculative, but very real possibility that our universe, the result of the big bang, isn't all that exists or ever existed. Our universe could be subject to the gravitational influence of masses that aren't part of our universe, and predate the big bang.

The previous opacity of our universe restricts any light we can detect to sources within our universe's horizon, but gravitational influence cannot be ruled out the same way.

Any gravity that would be present previous to the big bang from other universes would be accompanied by light from those universes as well since again, they both travel at light speed. However, we are getting into a very speculative area here, not so much the extra universes, but the physics of what is allowed before the big bang. Does light or gravity even propagate in a pre-big bang univserse?

Not to loose the point of this discussion, I was speculating whether or not gravity is the carrier of the Newton's bucket effect. Is the web of fields generated by the gravity of distant stars the reason behind Newton's bucket, and if so, what particular property of gravity is it? It can't be the sheer strength because Newton's bucket is unaffected by the gravity of the Earth, but rather the gravity (or something else) of the stars. This is very peculiar. It more likely is caused by an effect of gravity, a shadow or echo of gravity, a residual that is more persistent than the gravity of the Earth that moves with it's orbit around the sun. Or it could be something other than gravity, a new force maybe that has different characteristics than gravity such as persistance. I've no idea, but it's clearly not just the gravitational pull itself.

 

[A-wal]

Can't this simply be explained be inertia? If you swing an object round then it wants to go in a straight line away from you but you've got hold of it so it can't, but it flies off as soon as you let go. The forward energy of the water in a spinning bucket has to go somewhere so it pushes the sides up because the water wants to go in a straight line outwards.

 

[Pythagorean]

Can't this simply be explained be inertia? If you swing an object round then it wants to go in a straight line away from you but you've got hold of it so it can't, but it flies off as soon as you let go. The forward energy of the water in a spinning bucket has to go somewhere so it pushes the sides up because the water wants to go in a straight line outwards.

The point is about where inertia comes from. Mach's principle is that it comes from all the other mass in the universe.

 

[Buckethead]

Can't this simply be explained be inertia? If you swing an object round then it wants to go in a straight line away from you but you've got hold of it so it can't, but it flies off as soon as you let go. The forward energy of the water in a spinning bucket has to go somewhere so it pushes the sides up because the water wants to go in a straight line outwards.

In addition to what Pathagorean said it is also a matter of what defines a "straight" line. If you swing an object on a string around your head and you let it go, where exactly will it go? If Mach's principle holds, then it will head out toward whatever star it was pointing to when it was released and continue on to that star even if that star and all other matter in the universe moves out of position relative to "empty" space. If Mach's principle does not hold, then it will head out toward a star, but miss the star if the star (and all other matter) moves. In other words, the "straight" line will be straight in only one of those scenarios, but it is not clear which one. I'm a Machian person, so I think the object will follow the stars. Keep in mind that light will follow only one of these trajectories as well, so in either case the path of the object will be parallel to beam of light that is projected parallel to the initial path of the object when it is released, which is why it will look "straight" regarless of which path it is following.

 

[A-wal]

The point is about where inertia comes from. Mach's principle is that it comes from all the other mass in the universe.

I thought inertia was simply due to the fact that an object doesn't have a true rest state, or do you mean why an object with a relatively different velocity carries a force with it that's transferred to anything it hits? Machs principle says that it's because of the rest of the mass in the universe?



@Buckethead:
"Does light or gravity even propagate in a pre-big bang univserse?"

There's no space in a pre-big bang universe, so no.


"If Mach's principle holds, then it will head out toward whatever star it was pointing to when it was released and continue on to that star even if that star and all other matter in the universe moves out of position relative to "empty" space. If Mach's principle does not hold, then it will head out toward a star, but miss the star if the star (and all other matter) moves."

There's no such thing as movement relative to empty space. If everything moves by the same amount then nothing moves.


"In other words, the "straight" line will be straight in only one of those scenarios, but it is not clear which one. I'm a Machian person, so I think the object will follow the stars. Keep in mind that light will follow only one of these trajectories as well, so in either case the path of the object will be parallel to beam of light that is projected parallel to the initial path of the object when it is released, which is why it will look "straight" regarless of which path it is following."


Why would it always look straight? Light doesn't, it always follows at least a slightly curved path, just not locally.

 

[Buckethead]

I thought inertia was simply due to the fact that an object doesn't have a true rest state, or do you mean why an object with a relatively different velocity carries a force with it that's transferred to anything it hits? Machs principle says that it's because of the rest of the mass in the universe?.

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.

"If Mach's principle holds, then it will head out toward whatever star it was pointing to when it was released and continue on to that star even if that star and all other matter in the universe moves out of position relative to "empty" space. If Mach's principle does not hold, then it will head out toward a star, but miss the star if the star (and all other matter) moves."

There's no such thing as movement relative to empty space. If everything moves by the same amount then nothing moves..

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.

"In other words, the "straight" line will be straight in only one of those scenarios, but it is not clear which one. I'm a Machian person, so I think the object will follow the stars. Keep in mind that light will follow only one of these trajectories as well, so in either case the path of the object will be parallel to beam of light that is projected parallel to the initial path of the object when it is released, which is why it will look "straight" regardless of which path it is following."

Why would it always look straight? Light doesn't, it always follows at least a slightly curved path, just not locally.

Are you talking about light bending due to gravity? If so then I'll clarify by saying that a straight path (used in this context of a released object) can be defined as the path light takes when unaffected by gravity. And this can be considered the path that the object in question would take if it were also unaffected by gravity.

 

[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.