What is the physics of motion through space?

[Netspirit]

The metric expansion of the Universe does not seem to cause some of the mechanical effects typically associated with motion (commute) of massive objects through space. For example, distant galaxies can be "flying away" from each other at speeds exceeding the speed of light. It seems that space expansion and commute through space may be different processes, regardless of the fact that GR nicely quantifies both: expansion may be a "mathematical" property of spacetime ("over time, it will take longer for light to move from A to B") while commute seems to be a physical, "heavy", "energetic" process, with side effects like gravitational waves, and subject to the speed limit.

What do we know about the micro-physics of commuting through spacetime - apart from being able to measure it geometrically? How exactly does a particle leave a local region of spacetime and land in a neighboring region? Drawing analogies with how a dot moves on TV (pixel is switched off, a neighboring one is switched on, creating an illusion of motion) - does the particle disappear into vacuum, for a clone to appear in the "neighboring cell", with some properties like momentum, energy, etc. preserved? Described as such, commute would indeed be quite an energetic process, with clear limits on the maximum achievable speed that would depend on how fast the cause-effect relationship propagates locally (how quickly adjacent regions of spacetime can influence each other, how fast the "cloning" cycle is processed).

Perhaps a more important question: regardless of how motion through space actually happens and whether my computer-inspired analogy is actually valid, is there any scientific value that can be obtained from viewing motion is an energetic, as opposed to geometric, phenomenon? In other words, would such depictions of motion as an energetic process in the vacuum explain anything, simplify anything, or just serve to increase the number of entities unnecessarily, violating Occam's razor?

 

[lekh2003]

I feel that you are unnecessarily complicating the idea of motion. When an object must move, it moves. All experimental theories have confirmed that when an object moves, it moves. Sure you could say that the particles is disappearing and reappearing constantly, but then we can take that to a whole new level. I can say that the sun is a dragon's eye and that we can't see the dragon because it keeps hiding. You created a theory for the sake of creating one.

As for all of the other question, do you mind simplifying what you are trying to say, I really can't understand what message you are trying to convey.

 

[Netspirit]

I am not questioning motion, I am trying to understand how it works. How exactly can anything leave one region of space to occupy another? What makes that process continue indefinitely in the same direction? One does not need to ask these questions if one views motion geometrically - i.e. just says "object X has velocity V" and ends there. I feel, however, that it is a very macroscopic, statistical view of how a large number of particles simultaneously change their locations.

Is there one type of motion, or more? Are these 2 types of motion the same, or different: 1) galaxies flying away from each other due to space (but no time?) expansion, and 2) my finger commuting (i.e. pressing a key)? If the two are the same, why is the former not subject to any speed limits, while the latter is? Do objects commute through spacetime by interacting with the vacuum that occupies it (until it does not)? Is commute through space related to local causality, and is the "c" speed limit, in programming jargon, simply the "latency of local cause-effect propagation"?

 

[lekh2003]

Is there one type of motion, or more? Are these 2 types of motion the same, or different: 1) galaxies flying away from each other due to space (but no time?) expansion, and 2) my finger commuting (i.e. pressing a key)? If the two are the same, why is the former not subject to any speed limits, while the latter is?

I think I see what you are getting at... However, you are mistaken in saying that galaxies are not subject to the speed limit. They most definitely are, they just happen to be going at such high speeds due to colossal amount of energy generated from the big bang. The types of motion of galaxies moving and your hand moving are the same. The only difference is that one of them was subject to massive energy from the big bang.

Do objects move via interacting with the vacuum they move through?

Again, you are trying to ask a question which does not need to be asked. The matter is moving. There is no need for any theory as to how the matter is interacting with the "vacuum". If you really want to look at theories of how matter moves, maybe you would like to look at matter moving through the spacetime.

This theory you are coming up with is not needed and was never observed. Matter just moves and there is no theory that is needed to answer this.

 

[Ibix]

The problem is that it is not, in general, possible to define the relative velocity of two things unless they are actually in the same place, or at least close enough together that any definition gives the same answer to acceptable precision.

We never say that nothing can travel faster than the speed of light (alright - we do, but we're being sloppy). We say that the relative velocity between two co-located objects never exceeds the speed of light. We don't say anything at all about allowed relative velocities of galaxies, because they're not in the same place so we can't define a relative velocity.

In terms of "how things move", I'm not sure there's an answer in the way you are posing the question. There is no sense of absolute motion in relativity, so whether or not something is moving is a matter of opinion. So "how it's moving from one bit of space to another" doesn’t make sense: I am always free to transform to a frame where it isn't moving.

It makes more sense to think of worldlines in the block universe. In that model, nothing is moving and what we call motion is an effect of our minds' model of the universe being an updating model of a slice of the 4d whole.

 

[Ibix]

However, you are mistaken in saying that galaxies are not subject to the speed limit. They most definitely are,

Locally, this is true. But the speed of a galaxy with respect to one cosmological distances away is not well-defined.

 

[Netspirit]

We don't say anything at all about allowed relative velocities of galaxies, because they're not in the same place so we can't define a relative velocity.

If this was true, wouldn't there be a continuum between the two extremes (the farther away 2 objects are, the less you would say about their allowed relative velocities). I believe I have read that the "separation" due to the metric space expansion has no speed limit at all, which has been verified by measuring red shifts of galaxies receding from us at speeds greater than "c", while any local commute has the hard limit of "c". If there is no middle ground between the two, aren't they fundamentally-different?

There is no sense of absolute motion in relativity, so whether or not something is moving is a matter of opinion

Yes, but moving objects will collide trying to occupy the same region of spacetime, producing very objective outcomes.

It makes more sense to think of worldlines in the block universe. In that model, nothing is moving and what we call motion is an effect of our minds' model of the universe being an updating model of a slice of the 4d whole.

I can observe it, yes. However, it is a purely geometric view, and sooner or later I'd want to understand if there is an underlying mechanism that makes the wordlines smooth, continuous, and bounded.

 

[Ibix]

If this was true, wouldn't there be a continuum between the two extremes (the farther away 2 objects are, the less you would say about their allowed relative velocities).

Not really. In curved spacetime you have to be at the same place to define relative velocity. However, if you are happy to approximate spacetime as flat over some volume then you can define relative velocities between separated objects in that volume. This is analogous to using Cartesian coordinates for a street map on the surface of the Earth. You can use Euclidean geometry, but if you make the map big enough errors will become apparent. Equally, if you make the map detailed enough you will find errors (an ant will not regard a patch of grass as flat even if you do). Similarly, you can regard a patch of spacetime covering nearby galaxies as flat for the purposes of defining relative velocities of galaxies. But not one covering super clusters, nor if you need detail within a galaxy.

The scale over which you can consider relative velocities to be well-defined is basically the scale over which you can ignore the curvature of spacetime.

I believe I have read that the "separation" due to the metric space expansion has no speed limit at all

Where did you read this? Cosmologists typically don't talk about the speed of galaxies, at least not in a professional context, since that isn't well defined. They talk about their redshift without taking a position about what this means about speed or not.

Yes, but moving objects will collide trying to occupy the same region of spacetime, producing very objective outcomes.

So?

However, it is a purely geometric view, and sooner or later I'd want to understand if there is an underlying mechanism that makes the wordlines smooth, continuous, and bounded.

Not in relativity, so far as I am aware. That's just the way it's modeled, which is justified post hoc because it's the simplest theory explaining known experimental results.

 

[Netspirit]

Where did you read this? Cosmologists typically don't talk about the speed of galaxies, at least not in a professional context, since that isn't well defined. They talk about their redshift without taking a position about what this means about speed or not.

https://en.wikipedia.org/wiki/List_of_cosmological_horizons#Hubble_horizon
"It is true that particles on the Hubble radius recede from us with the speed of light"

I do agree that the definitions of "speed" and "distance" are somewhat different in presence of the increasing scale factor. However, that is the very point I am trying to make - the observable effects of the increasing scale factor (measured redshift values, expected communication delays, etc.) seem different enough to consider space expansion fundamentally different from what, in flat spacetime, we call "commute". I do understand that relativity makes no difference between the two, that it does not "explain" how motion in flat space "works", it just observes and measures it - which is simple, but not very satisfying.

So?

I mean that a specific location in spacetime is absolute, as all observers will agree on what object occupies it. If one defines motion as a process of occupying specific neighboring locations in spacetime, it becomes hard to see how motion becomes nothing but a matter of opinion, and everything "factual" and "absolute" about coordinates vanishes completely when we talk about changing them.

If someone throws a stone at me, I will find it hard to call its motion a matter of opinion, in any reference frame. One can say that motion is a matter of opinion until a cause-effect event occurs (and I don't understand how relativity explains causality, apart from saying that all effects lie in the future cone of their causes, which is just an observation, not an explanation), but then it becomes hard to visualize how or why a transition from "opinion" to "fact" occurs, and is much easier to assume that no such transition took place and the motion through some relativistic physical vacuum was real in the first place (https://en.wikipedia.org/wiki/Luminiferous_aether#Einstein's_views_on_the_aether).

 

[PeterDonis]

"commute"

Before commenting on anything else, I need to comment on this: this word, "commute", in English, has a very specific meaning in the context of math physics, which is not "motion". (The meaning of "commute" in English is, basically, "the result of doing two operations does not depend on the order in which the operations are performed".) Please use the word "motion" in English for what we are discussing here.

the observable effects of the increasing scale factor (measured redshift values, expected communication delays, etc.)

These aren't observable effects of increasing scale factor; scale factor is a coordinate quantity. These are observable effects of objects following particular worldlines in spacetime--to a first approximation, they are the "comoving" worldlines in the FRW model of the universe. The set of all such worldlines has a positive expansion scalar, which is an invariant quantity that does not depend on coordinates; that is the technically precise way of saying what we mean when we say the universe is "expanding".

a specific location in spacetime is absolute, as all observers will agree on what object occupies it

Yes, this is correct.

If one defines motion as a process of occupying specific neighboring locations in spacetime

That is the definition of the "worldline" of an object: the set of neighboring locations in spacetime that it occupies. But that does not mean the object has to be "moving"; "motion" is a different concept (more precisely, one of at least two different concepts--see below).

If someone throws a stone at me, I will find it hard to call its motion a matter of opinion, in any reference frame.

That's because the stone's motion relative to you is not a matter of opinion: it's the same in any reference frame. The technically precise way of stating this is that the angle in spacetime between your worldline and the stone's worldline, at the point in spacetime where they intersect, is the same in any reference frame; it's an invariant.

The problem you are having is that you are confusing this invariant concept of "motion"--which, since it refers to the event where two worldlines intersect, is a local definition, not a global one--with another concept of "motion", which is not invariant and depends on your choice of coordinates. The usual term for this in GR is "coordinate velocity", and it is unfortunate that cosmologists so often refer to it, since it confuses lay people into thinking it has some physical meaning. It doesn't; it's just a convenient number to quote if one is being lazy and doesn't want to explain the details of what's actually going on.

 

[Mister T]

I am not questioning motion, I am trying to understand how it works. How exactly can anything leave one region of space to occupy another?

I don't understand this question. Can you move, taking with you this region of space that surrounds you?

What makes that process continue indefinitely in the same direction?

Nothing. What makes something remain motionless, continuing indefinitely to stay in the same place?

Yes, but moving objects will collide trying to occupy the same region of spacetime, producing very objective outcomes.

When two objects try to occupy the same place at the same time we call it a collision?

 

[Ibix]

That's because the stone's motion relative to you is not a matter of opinion: it's the same in any reference frame. The technically precise way of stating this is that the angle in spacetime between your worldline and the stone's worldline, at the point in spacetime where they intersect, is the same in any reference frame; it's an invariant.

OP - I don't have a lot to add to what Peter said, but wanted to expand on this. As Peter says, it's not a matter of opinion that you and the stone are not in the same state of motion. But what those states of motion are is a matter of opinion. You can be at rest and the stone moving; or the stone can be at rest and you moving; or both of you can be moving towards each other, or one overtaking the other.

 

[Netspirit]

The set of all such worldlines has a positive expansion scalar, which is an invariant quantity

Let's call it "quantity A".

That's because the stone's motion relative to you is not a matter of opinion: it's the same in any reference frame. The technically precise way of stating this is that the angle in spacetime between your worldline and the stone's worldline, at the point in spacetime where they intersect, is the same in any reference frame; it's an invariant.

And let this be "quantity B".

The problem you are having is that you are confusing this invariant concept of "motion"--which, since it refers to the event where two worldlines intersect, is a local definition, not a global one--with another concept of "motion", which is not invariant and depends on your choice of coordinates. The usual term for this in GR is "coordinate velocity"

And let this "coordinate velocity" be "quantity C".

A involves all reference frames and B involves two, making both invariant. C is a relative "coordinate velocity".
I am tempted to call invariant side effects (that all observers agree on) "real", calling the rest (C) mathematical tools / matters of opinion.

I am interested in the inner workings of B, and whether A works any differently from B.

Does invariant motion of two objects through spacetime require each object interacting with physical vacuum at every point/moment, or is the intersection of the wordlines the only special point where GR and quantum physics must connect? Using the TV screen analogy and trying to visualize that on-the-fly interaction I can picture particles being "pushed into vacuum" in their current locations and their clones "popping out of vacuum" in the neighboring locations, which would take effort & time and therefore explain the speed limit. It would also generalize all invariant processes (motion, information transfer, causality) into some fundamental "local action".

 

[Netspirit]

Nothing. What makes something remain motionless, continuing indefinitely to stay in the same place?

I don't know. I have heard an explanation that all objects move through spacetime with the same speed of "c".

It went like this. Picture 1 space dimension as X, and the time dimension as Y. Imagine that every velocity is a vector of the length 1 (normalized "c"). Something that remains motionless in space has their entire velocity aligned with the time axis Y, so they are only moving through time ("vertically"). Light, which only moves through space ("horizontally") has zero time velocity component Y. Everything else moves through both space and time, having non-zero projections on X and Y.

If that explanation has anything to do with the reality, then my answer to your question would be: it is the same fundamental clock (or a simulation cycle, if that's your view) that causes everything in spacetime to change coordinates. The problem is: if motion (through time and/or space) is what happens to everything, the term kind of loses its meaning.

 

[PeroK]

Using the TV screen analogy and trying to visualize that on-the-fly interaction I can picture particles being "pushed into vacuum" in their current locations and their clones "popping out of vacuum" in the neighboring locations, which would take effort & time and therefore explain the speed limit. It would also generalize all invariant processes (motion, information transfer, causality) into some fundamental "local action".

Ironically, of course, the apparent motion of an object created by images on a screen is an example of where you can exceed the speed of light.

 

[Netspirit]

Ironically, of course, the apparent motion of an object created by images on a screen is an example of where you can exceed the speed of light.

Yes, but "jumping over a few pixels" requires non-local context - the logic that turns pixel 3 on must skip pixel 2 and be aware of pixel 1. In physics, the metric expansion of space is apparently global ("quantity A" earlier in this thread) which allows "faster-than-light" redshift measurements. I don't know if it is possible to alter what I called "the fundamental local action" so that particles "pop up" in "non-adjacent" regions of space, making faster-than-light motion, causality, and information transfer possible. It is certainly not what we see happening naturally. That fundamental mechanism may not exist to begin with, which I feel is the consensus in this thread.

...By the way, another analogy is Conway's "Game of Life" and it's "speed of light" limit (https://en.wikipedia.org/wiki/Speed_of_light_(cellular_automaton) defined by the processing rules.

 

[PeroK]

@Netspirit I wonder whether it's the time you have spent in the digital world that makes you distrustful of a continuous/analogue reality?

All this excessive theorising of yours seems designed simply to avoid having a non-digital spacetime without spacetime pixels. I suspect you have no experimental justification for your theories?

 

[Dale]

I am interested in the inner workings of B,

It is just geometry. As @PeterDonis mentioned above, it is an “angle” in spacetime.

You mentioned in the OP that you wish to reject the geometrical explanation. But that is not justified. The geometrical explanation is exceptionally simple and covers all of the observed phenomena to date. Furthermore, it is accepted by the scientific community and is the standard. You are not justified in discarding the geometric explanation a priori.

 

[Netspirit]

@Netspirit I wonder whether it's the time you have spent in the digital world that makes you distrustful of a continuous/analogue reality?

It certainly influences the examples I understand and use. However, just to clarify, I am not starting with the assumptions about discrete vs. continuous nature of motion - I am mainly concerned with the local (intrinsic, quantum) vs. geometric (relativistic) interpretation of motion through flat space.

I suspect you have no experimental justification for your theories?

I am not a physicist and I do not have the qualification to develop a theory that would unify quantum physics with GR. I am just baffled by how easy and effortless it seems for distant galaxies to recede from us with redshifts corresponding to speeds faster than light vs. how objects moving through space appear "burdened" by all sorts of fields and limits (as if they were "powering through" some field that gave them mass, as if they would either sink through time or skip through space at every Plank moment, etc.) making me suspect that local motion / action had some underlying physics to it that produced the complex macroscopic behaviors that GR described geometrically.

 

[Netspirit]

It is just geometry.

OK, thanks. That's all I wanted to ask.

 

[Dale]

I am mainly concerned with the local (intrinsic, quantum) vs. geometric (relativistic) interpretation of motion through flat space

I don’t think that this dichotomy you are making exists. Modern quantum field theory is built on Minkowski’s relativistic geometry. The geometry of special relativity is part of QFT, down to its basic mathematical foundations.

 

[PeterDonis]

A involves all reference frames and B involves two, making both invariant.

No. Neither A nor B "involve" any frames. You can define them without choosing a reference frame at all. That is why they are invariant. Being the same when calculated in any frame is really a side effect of that.

A better way of stating what you might be groping towards here is that the invariant A is defined with respect to a whole infinite family of worldlines, whereas the invariant B is defined with respect to just two worldlines.

I am interested in the inner workings of B, and whether A works any differently from B.

Of course they both work differently, since they are different invariants defined in different ways.

invariant motion of two objects through spacetime

Where did I use the word "motion" in defining either A or B? The whole point is to discard that word since all it's doing is confusing you.

The rest of what you are saying in this post looks like something one might read in a pop science discussion of quantum field theory, not classical relativity. In classical relativity, spacetime is a 4-dimensional geometry, and worldlines are just continuous curves within that geometry. That's all there is to it.

 

[PeterDonis]

I have heard an explanation that all objects move through spacetime with the same speed of "c".

That is a pop science misrepresentation that you would do best to simply ignore.

If that explanation has anything to do with the reality

At best it's focusing in on a particular re-framing of the math that causes much more confusion than it solves.

 

[PeterDonis]

That fundamental mechanism may not exist to begin with, which I feel is the consensus in this thread.

As I commented in a previous post, any "fundamental mechanism" like this would be part of quantum field theory, not classical relativity. Discussion of this kind of thing belongs in the quantum physics forum. But I would strongly recommend taking some time to learn what QFT actually says first.

 

[PeterDonis]

I am just baffled by how easy and effortless it seems for distant galaxies to recede from us with redshifts corresponding to speeds faster than light

This "correspondence" is a coordinate artifact and does not have any physical meaning. In your letter system of an earlier post, it is C, not A or B. And you agreed that C was "mathematical tools/matters of opinion".

What the redshift of a distant galaxy is actually telling you is by what factor the universe expanded while the light was traveling from the galaxy to us. In terms of the expansion scalar invariant that I defined earlier, it is the integral of that scalar (whose numerical value changes with time, which is why you have to do an integral instead of just multiplying) over the time the light traveled. (Making this precise requires some technical points that are beyond the scope of a "B" level thread.)

objects moving through space appear "burdened" by all sorts of fields and limits

"Moving through space" here is vague; you seem to want to treat it as like your letter B, but the way you are defining makes it a case of letter C. The "speed of light limit" is a limit on B--the angle in spacetime between two worldlines. But that limit is also geometry; it's not a "burdening" on "motion", it's just a geometric fact about the kinds of curves that worldlines can be--that they can only be timelike or null, not spacelike. Those are geometric properties.

local motion / action had some underlying physics to it that produced the complex macroscopic behaviors that GR described geometrically

Once more, this kind of thing sounds like QFT, not classical SR/GR. But you really need to spend some time learning QFT before trying to form an understanding along these lines.

 

[Mister T]

I don't know. I have heard an explanation that all objects move through spacetime with the same speed of "c".

If you're interested in understanding this I suggest you go back and read again the post you were responding to (my Post #11). It was a response to your Post #3 in which you were talking about motion of objects. What I see in your posts is a lingering notion that space is something physical that objects move through, and that it's possible to make a distinction between objects moving through space and objects not moving through space.

 

[bahamagreen]

The metric expansion of the Universe does not seem to cause some of the mechanical effects typically associated with motion (commute) of massive objects through space.

The missing effect that used to puzzle me was that the expansion seemed to be operating without regard to inertia of the objects accelerating. It helped to consider objects in gravitational free fall (the changing distance between two objects dropped from the same height).

In the hierarchy of position, velocity, acceleration, change in acceleration, change of change in acceleration, etc..., it seems curious that all have proper values except the first two; inertial frame of reference allows setting to either.

Verbal mistake is to take a relative motion between two objects and deduce that therefore at least one of the pair is in absolute motion.

 

[Grinkle]

it seems curious that all have proper values except the first two

I think the curious thing is that the speed of light is invariant across inertial frames. The other curious consequences follow.

 

[bahamagreen]

I think the curious thing is that the speed of light is invariant across inertial frames. The other curious consequences follow.

I don't know where the postulate of a minimal observable interval of space and time stands with respect to the standard model, so I won't post the link. Shan Gao makes an argument that this postulate leads directly to a maximum signal speed and its invariance, because c is the ratio of the minimum observable length to the minimum observable time interval... same in all inertial reference frames.

 

[PeterDonis]

I don't know where the postulate of a minimal observable interval of space and time stands

It's a common speculation, but so far no evidence has been found to support it. The usual view of that fact, by proponents of the speculation, is that the minimum scale is something like the Planck scale, which is about 20 orders of magnitude smaller than the smallest scales we can currently probe, so we have no way of actually seeing any evidence of the minimum scale with our current technology. We won't know whether this is valid unless and until we get some evidence one way or the other.

 

[Grinkle]

Shan Gao makes an argument that this postulate leads directly to a maximum signal speed and its invariance

Is Shan Gao making an argument that the experimental observation of an invariant maximum signal speed implies spacetime is discrete?

 

[bahamagreen]

Is Shan Gao making an argument that the experimental observation of an invariant maximum signal speed implies spacetime is discrete?

I don't think so, better to judge for yourself; paper is titled On the invariance of the speed of light

 

[Grinkle]

@bahamagreen Thanks. I also don't read him to be arguing in that direction.

 

[Netspirit]

I'd like to thank everyone who contributed to the thread. I have read all your replies, but I cannot respond to every one without turning my post into an unreadable mess.

@bahamagreen is right about some of the things that puzzle me.

One is the mentioned disconnect between the coordinates plus their first derivative (which seem relative and therefore suspicious - like those projections of the same fish on the different walls of the aquarium - an effect sometimes used to speculate about the nature of quantum entanglement) and higher-order derivatives like acceleration, change in acceleration, etc. (which seem objective and linked to physical forces). For example, it feels non-intuitive how photons, traveling at the speed of light, allegedly "experience zero time" and, from their perspective, "instantly" connect the emitter (cause) with the absorber (effect) - as if both were directly adjacent on some deeper dimension (unlike their observer-specific spacetime "projections").

The other puzzle is whether the Universe is an emergent phenomenon so the properties of spacetime, such as the speed of light limit, have local, quantum origins (such as the abovementioned relationship between the Planck units). I admit I find geometric explanations of motion to be utterly boring, since they only seem to describe how objects move, not explain why they do - which is very practical, but seems like a problem already solved 100 years ago, with not much potential for surprising discoveries.

(Peter is right - let me read up on QFT).
Thanks again everyone!

 

[Nugatory]

For example, it feels non-intuitive how photons, traveling at the speed of light, allegedly "experience zero time" and, from their perspective, "instantly" connect the emitter (cause) with the absorber (effect) - as if both were directly adjacent on some deeper dimension (unlike their observer-specific spacetime "projections").

That's easy - just look at the word "allegedly". The allegation is false and a pretty good rule of thumb is that if whatever you're learning from says things like that, you're wasting your time with that source.

I admit I find geometric explanations of motion to be utterly boring, since they only seem to describe how objects move, not explain why they do

However, that's all that empirical science ever does. On close scrutiny, all scientific explanations of why something works the way it does turn out to be statements of how the universe behaves, not why.