Newton's Bucket

Pythagorean

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

Buckethead

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

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

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.



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.

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

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 realised by GR, but there is some debate.

Buckethead

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.

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

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

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.

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

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

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.

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

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??




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

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

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.

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

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


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

Buckethead

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

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.

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

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'.

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.

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

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

That sounds right.

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

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

Right - and, in Mach's favour, a lot of people do find the idea of acceleration in a one object universe absurd.
No. Well - it doesn't follow from Mach's principle - maybe there are variations that include it.