Could General Relativity simply be the "scale" field

[Edgard Neuman]

hi,

- What is curvature of space time ? it's a variation of relative lengths (metrics).. 
- Would a physical system be invariant if we scale it up or down ? (and why?)
- what if we consider general relativity as a field in space that define the scale of matter... the "graviton" would transmit scale variation between two spaces
- matter would always tend to accelerate where scale is smaller (picture a circle around which scale varies, just as with curvature, some part of the circle would contains "more" space is the scale is smaller). So a particle at the center of the circle would have more chance to change state  in that direction (that would be the gravitational force)
- energy/mass would define the scale around it.. at large scale it would be the gravitational field, at microscopic scale it would define particles as topological singularities (knots of spacetime, where dimension is higher than the surrounding space.. somehow like chord theory, only the space would be of higher dimension only locally as the effect of local extreme scale variation)
- if the scale is relative, that would allow laws of physics to be invariant by homothetic transformation
- the would allow the whole universe to be fully invariant by homothetic transformation (which is required for us to not have any information about what's outside of it)

Edited July 25, 2020 by Edgard Neuman

[andsm]

If the "scalar" field would include only variation of relative lengths (space), results would be different than predicted by GR.

If it would include variation of time too, how it would differ from existing theory?

 

I am not sure it is full equavalent to curved spacetime, but it looks so from first glance.

Edited July 25, 2020 by andsm

[Edgard Neuman]

1 hour ago, andsm said:

If the "scalar" field would include only variation of relative lengths (space), results would be different than predicted by GR.

If it would include variation of time too, how it would differ from existing theory?

 

I am not sure it is full equavalent to curved spacetime, but it looks so from first glance.

hi,
of course, GR is a succesfull theory, I certainly won't try to contradict its countless predictions.. and yes it would be the variation of the metrics as defined by general relativity (so space/time).. but my idea was just that it was in fact the measurement of "scale"  of physics.. it would just be a more profound way of understanding general relativity.. It has to be equivalent or my idea wouldn't fit experiment results.. 

I understand why you don't understand. Things like "distance / time" etc.. are really defined relative to one an other, in my model..
I suppose here that relationship between length time are entirely defined by relativity. (the maximum speed of information across space, relative to the scale of structures in it, and the rate of events in structures)
The speed of light is defined in « m / s ».. a second is a measure of the rate of events in a structure (that is necessarily relative.. ), and a meter is defined by the scale that a certain quantity of energy in a certain state « choose » to occupy.. (for instance : the size of a given atom at rest is a constant)..
What I mean by scale, is ultimately the variation of size the same atom would have in two part of space (but it's the equivalent of speed of time variation).
That means : if everything if defined by the speed of light (length and time relative to structures), that mean that you scale up the universe by 2, it's distinguishable with the universe you get if you slow time by 2, or if you divide the speed of light by 2.. you have to see those measurement as relative to each other to understand what I'm talking about..
Speed of light is only measured relative to structures (like a atom.. it defines the length (the size of it), and the speed of time (the speed of electrons for instance) ) 

The main reason for me to have this idea is from a metaphysical consideration : if the visible universe is really "all the information we can get"... if it's "closed" .. meaning if trully no information can be known from outside of it, it means that there must be some "equivalence principle" for each and every measurement..
We know that physics is
- invariant by translation, (we can't measure "where" the universe is)
- by variation of speed (we can't measure the speed of the universe)
- but also by variation of the speed of information (that's not obvious, but that's what i'm talking about : the speed of information ultimately defines the scale of structures) that would be special relativity.... information (and light) would always travel at the same speed in a given isolated structure (we can't measure how fast the universe is evolving)
- invariant by changing the orientation of the universe, (we can't measure the specific orientation of the universe)
- invariant by changing all the electric charges of the universe (we can't measure how charged is the universe)
- invariant by changing the angular momentum of the universe (that would imply some sort of inertia attenuation at higher scales...some sort of "MOND" theory would do the trick) ...the inertia attenuation would prevent the rotating universe from experiencing centrifugal forces (we can't measure if the universe is rotating)
- and also the "scale" of the universe (that works if the scale if defined by matter itself, and it's relative, meaning there is a field, and gravitation would be the gauge particle of the field)  (we ultimatly can't measure "how big is the universe", but only relative to structures inside of it)

 

 

 

Edited July 25, 2020 by Edgard Neuman

[swansont]

10 hours ago, Edgard Neuman said:

hi,

- What is curvature of space time ? it's a variation of relative lengths (metrics).. 

More than that. It’s not a flat geometry in the presence of mass.

 

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- Would a physical system be invariant if we scale it up or down ? (and why?)

No. Because various effects scale differently, e.g with different powers of length.

A structure of one size will usually collapse if simply scaled up. Mass and structural strength scale differently. 

 

 

[MigL]

The scale of 'objects' in space does NOT change.
But yes, the co-ordinate system we call space-time is 'scaled' (smaller ) in the vicinity of mass ( energy-momentum ).
And the grid lines of this co-ordinate system we call space-time, appear to be curved as a result. Which means geodesics, or the paths of least action followed by  masses ( paths of least time by massless light ) are curved.
IOW, curvature seems to be a much more appropriate word to use; less confusion.

[Markus Hanke]

19 hours ago, Edgard Neuman said:

What is curvature of space time ? it's a variation of relative lengths (metrics)

This is only true in spacetimes that are at least static and stationary, but not in the general case. 
The curvature of spacetime is quantified by the Riemann tensor - its formal mathematical definition aside for now, in the context of GR what this quantity measures is geodesic deviation, i.e. the failure of initially parallel geodesics to remain parallel. This is a more general concept than scale invariance.

On an even more fundamental level, you cannot capture the dynamics of gravity by a simple scalar quantity (such as a scale factor), since a scalar field would be unable to account for the necessary degrees of freedom. It can be formally shown that you need at least a rank-2 tensor field for that - represented by the metric tensor in GR.

20 hours ago, Edgard Neuman said:

the "graviton" would transmit scale variation between two spaces

If you postulate a graviton, then, as massless spin-2 particles, they can only couple to rank-2 tensors, not scalars.

20 hours ago, Edgard Neuman said:

if the scale is relative, that would allow laws of physics to be invariant by homothetic transformation

Well, they are empirically not invariant in that way, so I don’t really get the point you are trying to make?

11 hours ago, Edgard Neuman said:

invariant by changing all the electric charges of the universe (we can't measure how charged is the universe)
- invariant by changing the angular momentum of the universe

This is not true. If the universe had net electric charge and/or angular momentum, then its geometry would be very different from what we observe it to be. Here’s an example of a cosmological solution to the field equations that models a universe with non-zero angular momentum - many such solutions exist, but they don’t correspond to the universe as we observe it, which places a very stringent constraint on global angular momentum. I haven’t seen a solution for a universe with non-zero net electric charge, but I’m sure they exist too, and going by the case of the Reissner-Nordström metric, they’d be quite different from what we observe too.

[Edgard Neuman]

5 hours ago, Markus Hanke said:

This is only true in spacetimes that are at least static and stationary, but not in the general case. 
The curvature of spacetime is quantified by the Riemann tensor - its formal mathematical definition aside for now, in the context of GR what this quantity measures is geodesic deviation, i.e. the failure of initially parallel geodesics to remain parallel. This is a more general concept than scale invariance.

Ok i take your word for it

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On an even more fundamental level, you cannot capture the dynamics of gravity by a simple scalar quantity (such as a scale factor), since a scalar field would be unable to account for the necessary degrees of freedom. It can be formally shown that you need at least a rank-2 tensor field for that - represented by the metric tensor in GR.

I mean of course the gravitational force would be the gradient of the scalar.. the scalar would be something like the energy/matter density field....isn't the gravitational field entirely dependent on the energy/mass density ?

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If you postulate a graviton, then, as massless spin-2 particles, they can only couple to rank-2 tensors, not scalars.

Well, they are empirically not invariant in that way, so I don’t really get the point you are trying to make?

you don't understand because "when I mean scale" I mean relative scale.. you have to read how I define Length and time.. you put space time as a frame and matter in it. I suppose matter defines it's own length  and time, that's why the speed of light is invariant in it. If the laws of physics were invariant by scaling, you would not be able to detect it (by definition)
because everything would be the same. Except when two system have different scale : the difference would be gravitation. 
That's sad because I understand that you can't understand me, i've no way to explain myself better. I will just ask you to reconsider this : "lengths" and "time" is defined by matter. It's not "space" with "matter in it", it's "matter that create space around it".
You can't measure "space" without a ruler (made of matter) and time without a "clock" (made of matter). Imagine now a space where there is no frame at all :  only a bubble with its own clock and and its own ruler (and those measure are from inside). Now picture 2 bubble like that. How could you tell "which one is bigger" ? (in a frameless space, you can't)
I you really scale "everything", each particle at a deep level,  you scale the ruler and the clock, so there is no differences at all. Each atom defines its own size and its own frequency : so its invariant.
You can't because length and time are defined "from the inside of each system".. but what if a variation do exist between the two bubbles ? That would be what I'm talking about. The word "scale" is maybe a poorly chosen world, I speak about the very definition of "time/length" in a structure.. it is equivalent to changing the speed of light as seen from outside and not inside (if you suppose that speed of light is what define scale and not the other way around).. 
...and I know you won't understand that.. sorry I can't explain better
 

Ok I will try to explain it differently. Let's suppose "the speed of information" is "c" (it's more fundamental than the speed of light). In any matter structure, It defines what is "time" and what is "space".. because everything that happens depends on it. Let's suppose you have 2 particle A and B. A sends a message to B. A and B have no clocks, no rulers, they are blind in a dimensionless space. All A and B can do is exchanging message. When A sends a message to B, B can send it back. There is a order relationship that defines "time", as a series of events.. the messages.
but A and B can't tell how "far"  they are from each others.. they have no clock ! nothing happens at all between the message : A and B don't experience "time". the message exchange IS the clock. So with only A and B, time/length is not defined.
Now if you have a new particle C. A and B can exchange message with C. Now they can compare how easy it is for them to exchange messages relative to each others. For instance A can now tell if C is twice closer than B if he can exchange twice more message with C than with B.
In this model, space / time is entirely a relative construct.. You can scale everything, and the relationship between A B and C would be exactly the SAME, because all they can ever know is the ratio of their respective message frequency.
You can also globally change the speed of messages, there still would be now difference..  Now. Suppose that ABC are particle that self organize, and they use the messages to modify their relationship : message exchange is actively used to change the relative distances, in order to make structures (just like a atom, would resist to compression because it's shape is self-defined by EM forces).. the message could be used to add "impulsion"...for instance, A could choose to make the relative distance between B and C equal, to make a equilateral triangle. 
(by the way, that is enough to define special relativity : if the speed of messages is "anisotropic", if the message slides in one direction (from outside), the structure could still reorganize to make the distance equal... and seen by some outside observer, you would see... a deformation of the structure : the Lorentz transformation ! )
Now, what I suppose, is that somehow, the "space" in which ABC are, could have a field the define efficiency to carry message.. if the behavior of ABC is still defined by the message. variation of efficiency of messaging would be equivalent to space time curvature.. (as it directly "curve" the space/time measured by particles)

 

Edited July 26, 2020 by Edgard Neuman

[Markus Hanke]

17 hours ago, Edgard Neuman said:

isn't the gravitational field entirely dependent on the energy/mass density ?

This would be the case in Newtonian gravity, but in GR it's much more complex than that. Here, the source of gravity is the stress-energy-momentum tensor, which is a tensorial quantity with 16 (not necessarily independent) components. Energy density is in there as well, but so are other things such momentum fluxes, stresses, strains, momentum density etc.

Also, it has to be remembered that the GR field equations are a local constraint - so even in the vacuum of free space where there are no local sources of energy-momentum, you still get gravity. Lastly, unlike in Newtonian gravity, the field equations are non-linear, which physically means that in some sense gravity is also its own source, i.e. gravity is self-interacting. You can in fact get gravitational constructs in the complete absence of any sources of energy-momentum.

17 hours ago, Edgard Neuman said:

I mean of course the gravitational force would be the gradient of the scalar.. the scalar would be something like the energy/matter density field

See above - the source term is a rank-2 tensor, not a scalar. Also, in GR gravity is described purely geometrically, it doesn't use the notion of 'force' as such.

17 hours ago, Edgard Neuman said:

If the laws of physics were invariant by scaling, you would not be able to detect it (by definition)
because everything would be the same. Except when two system have different scale : the difference would be gravitation. 

Some laws of physics may be scale invariant, but most are not. Specifically, the Standard Model is not scale invariant, and there isn't any self-consistent way to make it so.

17 hours ago, Edgard Neuman said:

I will just ask you to reconsider this : "lengths" and "time" is defined by matter. It's not "space" with "matter in it", it's "matter that create space around it".

You don't need matter to have gravity. Also, space isn't 'around' matter - spacetime is everywhere, both in the exterior and the interior of energy-momentum distributions.

17 hours ago, Edgard Neuman said:

I you really scale "everything", each particle at a deep level,  you scale the ruler and the clock, so there is no differences at all.

The coupling constants for the three fundamental interactions are dimensionless; they wouldn't scale along with your clocks and ruler. And if they did scale, you would break the weak and strong interactions in the process, because their Lagrangians are not invariant under such changes.

17 hours ago, Edgard Neuman said:

You can't because length and time are defined "from the inside of each system".. but what if a variation do exist between the two bubbles ?

You'd have two regions of spacetime where the fundamental interactions work in two different ways. This is obviously not what we observe in the real world.

17 hours ago, Edgard Neuman said:

...and I know you won't understand that..

I understand perfectly well, thank you. I'm simply trying to point out that this can't work.

I also understand that the complete Lagrangian of the Standard Model isn't invariant under scalings, regardless of how you try to twist the fundamental constants - in fact, because many of the constants have mutual dependencies, and some are dimensionless, it isn't possible to scale them all simultaneously in a consistent manner.

When I first participated on online forums, many years ago, the idea of "shrinking matter" was in vogue for a time - the idea was that the universe is actually static, and just appears to be expanding because all matter in it is shrinking in such a way as to be locally undetectable. The mechanism was supposed to be the same - a scaling of local frames. So not only I am familiar with the essential idea of scaling fundamental laws, I've even been through some of the maths to show why it doesn't work (and can't work).

17 hours ago, Edgard Neuman said:

variation of efficiency of messaging would be equivalent to space time curvature..

As I said already, spacetime curvature is a tensorial quantity (it is in fact a rank-4 tensor) - so how would that work, do you think?

Edited July 27, 2020 by Markus Hanke

[Edgard Neuman]

5 hours ago, Markus Hanke said:

This would be the case in Newtonian gravity, but in GR it's much more complex than that. Here, the source of gravity is the stress-energy-momentum tensor, which is a tensorial quantity with 16 (not necessarily independent) components. Energy density is in there as well, but so are other things such momentum fluxes, stresses, strains, momentum density etc.

Also, it has to be remembered that the GR field equations are a local constraint - so even in the vacuum of free space where there are no local sources of energy-momentum, you still get gravity. Lastly, unlike in Newtonian gravity, the field equations are non-linear, which physically means that in some sense gravity is also its own source, i.e. gravity is self-interacting. You can in fact get gravitational constructs in the complete absence of any sources of energy-momentum.

See above - the source term is a rank-2 tensor, not a scalar. Also, in GR gravity is described purely geometrically, it doesn't use the notion of 'force' as such.

Some laws of physics may be scale invariant, but most are not. Specifically, the Standard Model is not scale invariant, and there isn't any self-consistent way to make it so.

You don't need matter to have gravity. Also, space isn't 'around' matter - spacetime is everywhere, both in the exterior and the interior of energy-momentum distributions.

The coupling constants for the three fundamental interactions are dimensionless; they wouldn't scale along with your clocks and ruler. And if they did scale, you would break the weak and strong interactions in the process, because their Lagrangians are not invariant under such changes.

You'd have two regions of spacetime where the fundamental interactions work in two different ways. This is obviously not what we observe in the real world.

I understand perfectly well, thank you. I'm simply trying to point out that this can't work.

Thanks for your answer.. Ok I know general relativity is complicated. 
I understand your way of understanding space time ("space time" with objects in it). I understand it (I understand at least special relativity). There is no point in trying to "tell me how it is". I'm not trying to understand relativity, but to make you understand it differently. that's the object of this thread.. I'm telling you, that you can understand it differently : the matter structuring itself in the information medium.. it should gives you back special relativity and general relativity, I don't see what you risk in trying to see things the way I do.
For instance you say "quantum mechanic is not invariant by scaling". If you scale everything, including the metrics and the time, the definition of length, it's invariant (because you made it so). You scale the speed of light, you scale the planck length. You scale "every length of the theory". If you just project "the reality" and everything that happens in it, into a "bigger space" . The same things happen in both case (because you scale everything).. In that case it's obviously invariant (but of course you have to really think about what i'm saying instead of repeating old arguments). Now suppose that the definition of length vary for place to place (that's general relativity really).. and that graviton is the vector of this information. 

In a broader sense the fact that quantum mechanics is not invariant by scale is easy to understand : a atom at rest "defines" a length and a time. BUT. If you define length and time as the size and frequency a atom organize itself in space, you can define a specific data that is in that space, and that give you the scale. (In quantum mechanic, it's coded into the constant lengths of the theory)..
I know I'm right of a simple reason : IF quantum mechanic is not invariant, it means something in space has to define length. You put a atom in space : it take "a certain length". Why ? Where does this length come from, and could vary from place to place ? (you would say "because of quantum mechanics that use constants.." but why those constants have those values ??) I simply suppose the value depends on a scale field. 
That's the field I'm talking about. I suppose that ultimately it is the speed of light, the speed of information, because it also conveniently define special relativity and general relativity. 

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I also understand that the complete Lagrangian of the Standard Model isn't invariant under scalings, regardless of how you try to twist the fundamental constants - in fact, because many of the constants have mutual dependencies, and some are dimensionless, it isn't possible to scale them all simultaneously in a consistent manner.

What is a "meter".. 
What you say, is equivalent to "matter define length"  that I understand, that's what I 'm saying.. but, that doesn't mean that this metrics can't vary relatively from place to place ! (and in fact, that's what General Relativity says). Imagine two atoms, in two space : if you stand close to them and measure them, you always get the same length (that's obvious, because your ruler is made of atoms).. but that doesn't mean that you can't imagine two different scale frame exists.

 

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When I first participated on online forums, many years ago, the idea of "shrinking matter" was in vogue for a time - the idea was that the universe is actually static, and just appears to be expanding because all matter in it is shrinking in such a way as to be locally undetectable. The mechanism was supposed to be the same - a scaling of local frames. So not only I am familiar with the essential idea of scaling fundamental laws, I've even been through some of the maths to show why it doesn't work (and can't work).

The thing you don't understand is that it's only a "point of view" problem.. Whether matter shrink or universe expand isn't a real question, it's irrelevant, unless you suppose you has a observer defines a "reference scale".. (that doesn't make sense, because a observer can't be out of the universe). That's the same reasoning behind every equivalence principles.. (does the universe have a scale ? do the universe have a position ? do the universe have a speed ?)..
The only thing that can be observed (by definition) is a variation of something. That's why I said the universe as a whole should be "invariant by scale". If it's invariant in scale (it means a global scale doesn't make any difference). but each part of it can defines a scale relative to the other parts of it. 

My solution is simple : matter, with forces, organize itself, therefor creating "spacetime metrics" of space : a atom takes it own size.
What's fascinating, that if you modify the way information travels in space (for instance, you add a speed to all traveling information), you get special relativity.. (that's just the train explanation)... and if you suppose the speed of information varies from place to place, you get general relativity (that's just the "curvature").

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As I said already, spacetime curvature is a tensorial quantity (it is in fact a rank-4 tensor) - so how would that work, do you think?

No, I don't know how it would work . But the problem is somehow Einstein tries to defined relativity as "out of frames".. but that also mean that describing reality in a single frame is enough to describe it in all the other frames.. so I don't see the point of understanding everything in a out of frame.

Sorry i've not finished my comment.. (i publish too fast)

 

 

Edited July 27, 2020 by Edgard Neuman

[Markus Hanke]

8 minutes ago, Edgard Neuman said:

For instance you say "quantum mechanic is not invariant by scaling"

I didn't say this. I said that the Standard Model (taken as a whole, or specific parts in it) are not scale invariant.

10 minutes ago, Edgard Neuman said:

In that case it's obviously invariant

Can you show this mathematically?

13 minutes ago, Edgard Neuman said:

IF quantum mechanic is not invariant, it means something in space has to define length.

Again, this isn't about QM, it's about the Standard Model specifically. Different terms (and there are many!) scale differently within the Lagrangian, and most of the coupling constants are dimensionless and don't scale at all. So no matter what you change in terms of the constants, you can't get a consistent scaling for the overall Lagrangian.

17 minutes ago, Edgard Neuman said:

but of course you have to really think about what i'm saying instead of repeating old arguments

I'm simply pointing out to you how the maths work - it's up to yourself what you do with that information. Ideally, you shouldn't take my word for it at all, and instead learn to do the maths yourself. 

19 minutes ago, Edgard Neuman said:

I know I'm right

Well then, I don't suppose you have any need for my - or anyone else's - input.

[Edgard Neuman]

13 minutes ago, Markus Hanke said:

I didn't say this. I said that the Standard Model (taken as a whole, or specific parts in it) are not scale invariant.

Can you show this mathematically?

Multiplicating "every" length in a theory, you get the same theory with bigger length. Instead of meter, for instance, you use "centimeters". So every 1 length units , become 100 length units. You can't "prove" a change in axiomatic you made arbitrarily. Also, the fact something is "arbitrary" should indicate that it could vary from place to place, and that a "field" exists. It's somehow a metaphysical  requirement of every constants, because the opposite would imply there is a "reference" somewhere outside of the theory (so out of the universe). 
 

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Again, this isn't about QM, it's about the Standard Model specifically. Different terms (and there are many!) scale differently within the Lagrangian, and most of the coupling constants are dimensionless and don't scale at all. So no matter what you change in terms of the constants, you can't get a consistent scaling for the overall Lagrangian.

I'm simply pointing out to you how the maths work - it's up to yourself what you do with that information. Ideally, you shouldn't take my word for it at all, and instead learn to do the maths yourself. 

Well then, I don't suppose you have any need for my - or anyone else's - input.

I've published my answer too fast, your answer was useful


What I think you physicist should do is frontly define the "equivalence principle" for all "constants" of physics, and always suppose that if you see a constant (just like the size of a atom) it must imply that a "field" defines it, and that a particle carries the information. 

Edited July 27, 2020 by Edgard Neuman

[Markus Hanke]

5 minutes ago, Edgard Neuman said:

Multiplicating "every" length in a theory, you get the same theory with bigger length. Instead of meter, for instance, you use "centimeters". So every 1 length units , become 100 length units.

The Lagrangian contains very many terms - some of them contain units of space and time, others do not; some contain mixes of different parameters, others contain higher powers of some dimensions, but not others. If you simply scale units, then some parts of the Lagrangian change, whereas other parts do not, so the overall Lagrangian is never the same. That's the point - because the Lagrangian is so complicated, it is simply not possible to adjust everything in such a way that it remains overall invariant. Especially the weak and strong interaction parts will cause problems here.

And then of course, even if it did somehow remain invariant, you still can't recover the dynamics of gravity from a simple scalar field. You need at least a rank-2 tensor.

[Edgard Neuman]

33 minutes ago, Markus Hanke said:

Well then, I don't suppose you have any need for my - or anyone else's - input.

I'm talking about information and metaphysical consideration. 
"if quantum mechanic (or standard model or any theory) is not invariant, it means something in space has to define length"
How would you contradict that ? 

18 minutes ago, Markus Hanke said:

The Lagrangian contains very many terms - some of them contain units of space and time, others do not; some contain mixes of different parameters, others contain higher powers of some dimensions, but not others. If you simply scale units, then some parts of the Lagrangian change, whereas other parts do not, so the overall Lagrangian is never the same. That's the point - because the Lagrangian is so complicated, it is simply not possible to adjust everything in such a way that it remains overall invariant. Especially the weak and strong interaction parts will cause problems here.

And then of course, even if it did somehow remain invariant, you still can't recover the dynamics of gravity from a simple scalar field. You need at least a rank-2 tensor.

If you change scale, it's just equivalent of changing the length units. For instance using "inches" instead of "meters". Are you saying that the standard model can't be expressed in inches ? ?? I don't understand everything you say, but I don't have to, because I just can prove this can't work. How complicated is your theory, there is no way you can't replace a arbitrary unit by another unit. 🤷‍♂️
In the other hand if you trying to say that a given atom always has the same size : I agree !! The ruler you can use to measure "length" is made of atoms. There's nothing surprising here. That doesn't mean that the length can't vary from places to places (the fact that a atoms is squeezed from a inertial frame is in special relativity).. .. On the contrary : the fact that "something" is absolute locally implies it can vary globally..(it's the same thing as the elevator thought experiment).. because the whole universe can't have "absolute" measurement, without an external frame of reference (that would be outside of it, contradicting the "whole universe" hypothesis). That's a metaphysical consideration.
 

Edited July 27, 2020 by Edgard Neuman

[swansont]

1 hour ago, Edgard Neuman said:

If you change scale, it's just equivalent of changing the length units. For instance using "inches" instead of "meters". Are you saying that the standard model can't be expressed in inches ? ?? I don't understand everything you say, but I don't have to, because I just can prove this can't work. How complicated is your theory, there is no way you can't replace a arbitrary unit by another unit. 🤷‍♂️

You don't seem to be using this consistently. Scaling something up or down is not the same as using a different set of units.

[Markus Hanke]

1 hour ago, Edgard Neuman said:

How would you contradict that ?

The model contains coupling constants that define the relative strengths of the various interactions. They are dimensionless themselves, but are related in specific ways to other fundamental constants that do have dimensions. This (along with boundary conditions in the Euler-Lagrange equations) defines a unique scale for the model as a whole, that cannot be changed without affecting physically detectable changes.

1 hour ago, Edgard Neuman said:

If you change scale, it's just equivalent of changing the length units. For instance using "inches" instead of "meters". Are you saying that the standard model can't be expressed in inches ? ??

Of course you can express the SM in inches, if you are so inclined - but that is not the same as resling the Lagrangian. When you scale something, you are scaling the actual dynamics of the system, which is a physical change; using different units just means expressing the same physics in a different way. Today's temperature can be 20 celsius or 68 fahrenheit - this isn't a scaling, because it refers to the same physical temperature. You can say 'this house's temp is 20C' and 'that house's temp is 68F', and there is no difference whatsoever between them.

1 hour ago, Edgard Neuman said:

In the other hand if you trying to say that a given atom always has the same size : I agree !!

No, what I am trying to say is that all atoms of the same kind have the same structure regardless of where and when they are, because their fundamental constituents are subject to the same laws and dynamics. And you can't keep those laws and dynamics the same if you rescale them. It's about the dynamics of the system. As for relativity, the Standard Model is CPT invariant, which implies Lorentz invariance, so compliance with the laws of relativity is both guaranteed and required.
Essentially, the dynamics of a system isn't the same as its spatiotemporal embedding.

Actually, all this if off-topic, because the original question was whether GR can be rewritten in terms of just a scalar field. The answer to this is "no", because a scalar field (irrespective of what it physically refers to) cannot capture all the dynamics of gravity. Even a vector field can't. You need at least a rank-2 tensor field. You can see this most clearly if you consider that gravity can propagate as gravitational radiation fields - such fields have two polarisation modes (+ and x) that are distinct, so you will need at least a rank-2 tensor to fully capture all its degrees of freedom. A scalar field simply can't do the job, which can even be formally proven.

Edited July 27, 2020 by Markus Hanke

[SergUpstart]

1 hour ago, Markus Hanke said:

Actually, all this if off-topic, because the original question was whether GR can be rewritten in terms of just a scalar field. The answer to this is "no", because a scalar field (irrespective of what it physically refers to) cannot capture all the dynamics of gravity. Even a vector field can't. You need at least a rank-2 tensor field. You can see this most clearly if you consider that gravity can propagate as gravitational radiation fields - such fields have two polarisation modes (+ and x) that are distinct, so you will need at least a rank-2 tensor to fully capture all its degrees of freedom. A scalar field simply can't do the job, which can even be formally proven.

But decompose into scalar and vector fields according to the Helmholtz theorem?

[Edgard Neuman]

1 hour ago, Markus Hanke said:

The model contains coupling constants that define the relative strengths of the various interactions. They are dimensionless themselves, but are related in specific ways to other fundamental constants that do have dimensions. This (along with boundary conditions in the Euler-Lagrange equations) defines a unique scale for the model as a whole, that cannot be changed without affecting physically detectable changes.

Of course you can express the SM in inches, if you are so inclined - but that is not the same as resling the Lagrangian. When you scale something, you are scaling the actual dynamics of the system, which is a physical change; using different units just means expressing the same physics in a different way. Today's temperature can be 20 celsius or 68 fahrenheit - this isn't a scaling, because it refers to the same physical temperature. You can say 'this house's temp is 20C' and 'that house's temp is 68F', and there is no difference whatsoever between them.

so the explanation is "i'm not resling the Lagrangian".. I'm not scaling the actual "dynamics of the system". I'm scaling "the system". I'm scaling "every" constant.. You saying that somehow, dimensionless constant define the size of atoms : I agree with that. The atoms is measured relative to atoms, anyway. But you can still suppose that 2 unrelated systems have a different scale relative to each other.. 

Quote

No, what I am trying to say is that all atoms of the same kind have the same structure regardless of where and when they are, because their fundamental constituents are subject to the same laws and dynamics. And you can't keep those laws and dynamics the same if you rescale them. It's about the dynamics of the system. As for relativity, the Standard Model is CPT invariant, which implies Lorentz invariance, so compliance with the laws of relativity is both guaranteed and required.
Essentially, the dynamics of a system isn't the same as its spatiotemporal embedding.

that makes no sense.. you can' tell the size of the universe "from outside" the universe.. It's not a "physics" fact, it's a deep logical fact.

Quote

Actually, all this if off-topic, because the original question was whether GR can be rewritten in terms of just a scalar field. The answer to this is "no", because a scalar field (irrespective of what it physically refers to) cannot capture all the dynamics of gravity. Even a vector field can't. You need at least a rank-2 tensor field. You can see this most clearly if you consider that gravity can propagate as gravitational radiation fields - such fields have two polarisation modes (+ and x) that are distinct, so you will need at least a rank-2 tensor to fully capture all its degrees of freedom. A scalar field simply can't do the job, which can even be formally proven.

ok but if I follow my logic, what make the difference between two system, is basically the "scaling", the matrix describing two set of dimensionless space.. I realize why I was wrong, but the thought experiments still works. I will say it again. Picture 2 closed universes. In each of them, the same matter organize the same way : in each, the size of atoms is equal, relative to rulers inside of each other respectively.
But since there are no topological connection between the 2, can you tell if one is bigger than the other ? A property of space must tell this one is this size, the other one is the other size. Something must represent the way each other are related.. it's a field. And so ok, a scalar isn't enough : maybe one universe is "squeezed", maybe one is "compressed in one direction".. so what would describe the transformation of one into the other, from a local point of view  ? Maybe it's a rank-2 tensor field ! (that would be funny if a rank-2 tensor simply describe the transformation of a infinitesimal local spacetime frame into an other... )
That would still be interesting to understand that there is a field and a particle that carry it.. 
You have to understand, that I think from a metaphysical point of view.. What is absolute, what is not.. 

2 hours ago, swansont said:

You don't seem to be using this consistently. Scaling something up or down is not the same as using a different set of units.

My thought experiment is "just scaling everything".. you supposed scaling some part of the laws and not others, or the metrics and not the energy etc.... I've never said that.
but my scaling is from the start precisely scaling the length units.. My idea of scaling is the simplest scaling possible : the same universe, the same story, the same laws,
but I discuss the absolute meaning of "length", not relative to "the content" of course : I know that wouldn't work. As I said repeatedly : the matter defines its own length (and time).. 

It's really a abstract consideration (a simple one, I'll admit I don't understand what a rank-2 tensor exactly is).. but because it's a metaphysical consideration, that doesn't mean I'm wrong.. What is the "length"  of the universe, not relative to what's inside, but in a no dimension space, and could it be something else.. 

Edited July 27, 2020 by Edgard Neuman

[swansont]

5 minutes ago, Edgard Neuman said:

so the explanation is "i'm not resling the Lagrangian".. I'm not scaling the actual "dynamics of the system". I'm scaling "the system". I'm scaling "every" constant.. You saying that somehow, dimensionless constant define the size of atoms : I agree with that. The atoms is measured relative to atoms, anyway. But you can still suppose that 2 unrelated systems have a different scale relative to each other.. 

 

...

 

My thought experiment is "just scaling everything".. you supposed scaling some part of the laws and not others.. I've never said that.
but my scaling is from the start precisely scaling the length units.. My idea of scaling is the simplest scaling possible : the same universe, the same story, the same laws,
but I discuss the absolute meaning of "length", not relative to "the content" of course : I know that wouldn't work. As I said repeatedly : the matter defines its own length (and time).. 

You keep using that word, but it makes no sense. If you scale length by a factor of 2, there are other parameters that do not scale by a factor of 2. If you are simply changing the value of all terms as you might if you went from MKS to cgs (or other) units, that's not scaling.

 

 

[Edgard Neuman]

25 minutes ago, swansont said:

You keep using that word, but it makes no sense. If you scale length by a factor of 2, there are other parameters that do not scale by a factor of 2. If you are simply changing the value of all terms as you might if you went from MKS to cgs (or other) units, that's not scaling.

 

 

I'm scaling "the universe" relative to another universe. That's very important. I discussed why a closed universe would have a certain size, and relative to what .
I understand what you say, so please consider what I say : I'm placing myself out of the universe. You seem to have some preconceived idea about what scaling is..
So that's not "that scaling" I'm talking about. When I say "matter defines length and time".. that tells the same thing that "you can't change only the length". .i agree with that from the start !! (the lenght of the atom is defined by the strength of the EM force, by some relativity etc.. of course !)
I'm talking about the property of space and a medium transmitting information.. I don't see why I can't scale (absolutely) everything.. You take the whole movie, and you project it onto a bigger screen. Length are defined relative to matter, ok, but if you were outside of the universe, what would length mean ? From the beginning, I said : if you scale the universe by 2, that's equivalent to double the speed of light etc.. that's because one of my axiom is that speed of information through space (or light) defines everything and everyother law (you can see it in special relativity.. that what I explained with ABC blind particles)
Take a spaceship with a certain speed, seen from outside : apply the lorentz transformation.. is the life in the spaceship changed  ?? NO.  Are the length you measure from outside different  ? Yes : it's the lorentz transformation.. the ship is compressed. And yet, the picture you have from outside totally respect law of physics. So that already contradict the idea that "you can"t scale the universe".. you can obviously squeeze it : we call it the lorentz transformation.

 

Edited July 27, 2020 by Edgard Neuman

[MigL]

I understood the OP to be asking whether GR can be expressed in terms of changing scales of the 4 constituent dimensions, NOT whether GR can be expressed as a scalar field.
I think we all agree it cannot be expressed as a scalar field, but neither can changing scales in 4 dimensions.

I believe I've read some of K thorne's work where he claims aspects of GR can be expressed as either 'changing lengths/intervals' at constant scales, or 'changing scales' at constant lengths/intervals.
I'll have to look into the standard model Lagrangian problem with changing scales.

[Edgard Neuman]

10 minutes ago, MigL said:

I understood the OP to be asking whether GR can be expressed in terms of changing scales of the 4 constituent dimensions, NOT whether GR can be expressed as a scalar field.
I think we all agree it cannot be expressed as a scalar field, but neither can changing scales in 4 dimensions.

I believe I've read some of K thorne's work where he claims aspects of GR can be expressed as either 'changing lengths/intervals' at constant scales, or 'changing scales' at constant lengths/intervals.
I'll have to look into the standard model Lagrangian problem with changing scales.

Let's just say this : my definition of "scaling" is from the start precisely the same as changing the length units.. (not relative to something else in the same set of laws)
It's a very naive and simple scaling, not a change of length relative to matter. There's no point in talking about "just scaling the length".. I've never said "that" would work, and that's not the object of this thread. It's really the idea that "a dimensionless space" can't define the size of what's in it.. so that can vary (and ok it's not a simple scalar). 

Edited July 27, 2020 by Edgard Neuman

[swansont]

2 minutes ago, Edgard Neuman said:

Let's just say this : my definition of "scaling" is from the start precisely scaling the length units. 
It's a very naive and simple scaling, not a change of length relative to matter. There's no point in talking about "just scaling the length".. I've never said "that" would work, and that's not the object of this thread. It's really the idea that "a dimensionless space" can't define the size of what's in it.. so that can vary (and ok it's not a simple scalar). 

This seems contradictory. You say you are scaling the length, but then you are saying you aren't scaling the length.

 

[Edgard Neuman]

38 minutes ago, swansont said:

This seems contradictory. You say you are scaling the length, but then you are saying you aren't scaling the length.

 

The length relative to the matter that obey the physical laws versus the length relative to some other universe with a scaled set of laws.. 

- A given atom is "always"  X meter, because a meter is defined by the local laws of physics (the speed of light, the fine structure constant,etc).
- two universe, with different set of laws, scaled differently, could have the same atoms, and there would be no way to define why one is bigger or the other. Special relativity tends to show that matter organize itself depending of the flaw of information.
If the laws of physics defines a constant length (like the size of a atom or planck length).. that already mean that "space and the law in it" defines "length". There is no reason that it is a absolute constant.. no more than there is a absolute 0 position or an absolute 0 speed in that space.
My idea is that : a field define the scale of local laws and the atom (yes ok a rank 2 tensor field define the matrix transformation between the set of laws).. There is no reason why "space" has exactly the same scale of laws everywhere : that's why I suppose that's what general relativity is : the effect of the variation of the scale of laws. 

 

Edited July 27, 2020 by Edgard Neuman

[swansont]

1 hour ago, Edgard Neuman said:

The length relative to the matter that obey the physical laws versus the length relative to some other universe with a scaled set of laws.. 

You keep using "scale" so this doesn't solve the confusion about how you are using the term.

 

Quote

- A given atom is "always"  X meter, because a meter is defined by the local laws of physics (the speed of light, the fine structure constant,etc).
- two universe, with different set of laws, scaled differently, could have the same atoms, and there would be no way to define why one is bigger or the other. Special relativity tends to show that matter organize itself depending of the flaw of information.
If the laws of physics defines a constant length (like the size of a atom or planck length).. that already mean that "space and the law in it" defines "length". There is no reason that it is a absolute constant.. no more than there is a absolute 0 position or an absolute 0 speed in that space.

If length were scaled, interactions would change.

The Coulomb interaction, which varies as 1/r^2, would change relative to the magnetic interaction, which scales as 1/r^3 (for a dipole). Which means that the Hyperfine splitting (magnetic) would change at a different rate than the energy-level spacing (electrostatic).   

Certain molecular bonds vary differently with distance, so you wouldn't necessarily get the same chemistry.

Quote

My idea is that : a field define the scale of local laws and the atom (yes ok a rank 2 tensor field define the matrix transformation between the set of laws).. There is no reason why "space" has exactly the same scale of laws everywhere : that's why I suppose that's what general relativity is : the effect of the variation of the scale of laws. 

Given that we have not unified the gravitational interaction with the others, I don't see what the basis is for this confidence that GR tells you anything about other interactions. Changing gravity would have no known effect on the other interactions. The dynamics of stellar and planetary evolution would change, of course, because multiple interactions are present.

Further, space has the same laws everywhere because momentum is conserved (and vice-versa) — the laws are symmetric under translational symmetry.  If this were not true, we would be able to see the effect, and we don't see it. The above-mentioned hyperfine transition in hydrogen would be an obvious thing to check, but no, we see 1420 MHz coming from everywhere (adjusted for known effects, of course)

 

 

[Edgard Neuman]

1 hour ago, swansont said:

You keep using "scale" so this doesn't solve the confusion about how you are using the term.

 

If length were scaled, interactions would change.

The Coulomb interaction, which varies as 1/r^2, would change relative to the magnetic interaction, which scales as 1/r^3 (for a dipole). Which means that the Hyperfine splitting (magnetic) would change at a different rate than the energy-level spacing (electrostatic).   

Certain molecular bonds vary differently with distance, so you wouldn't necessarily get the same chemistry.

Given that we have not unified the gravitational interaction with the others, I don't see what the basis is for this confidence that GR tells you anything about other interactions. Changing gravity would have no known effect on the other interactions. The dynamics of stellar and planetary evolution would change, of course, because multiple interactions are present.

Further, space has the same laws everywhere because momentum is conserved (and vice-versa) — the laws are symmetric under translational symmetry.  If this were not true, we would be able to see the effect, and we don't see it. The above-mentioned hyperfine transition in hydrogen would be an obvious thing to check, but no, we see 1420 MHz coming from everywhere (adjusted for known effects, of course)

 

 

you still don't understand, that I scale "everything". every law. I change all the dimensionless constants accordingly..  Interaction would be transformed accordingly. 
(In reality, you should really understand that I'm really talking about changing the speed of light, assuming of course "light" drive time or length at the deepest level.. which I suppose true because of special relativity... that would be equivalent..  )...It a very simple  transformation of coordinates.. I'm scaling every particle, every wavelength, every speed (so the speed of light).. Relative to itself, It's the same universe.. relative to the observer, it's a different universe with a different set of constants.. 
I scale the universe, without changing the story inside of it.. It's a different set of law. Mathematically what I do is exactly equivalent to changing meters to inches or other simple unit change.. in reality all measures are nothing but numbers.. Now I compare "2 universes" .. one being the homothetic version of the other.. They change only by the very most numerical definition of length, and one relative to the other.
Imaging a atom in a void space. How can you measure the size of the atom ? The only answer is "the atom is 1 atom length"... There is nothing in this universe except the atom to compare to.. there is no "scale frame" except the content of the universe itself.. you can say "it's x time the speed of light when the atom vibrate n times..".. but you would use the light from the atom and the time from the atom... (because there is no other photons in this universe). The things you could use to measure distance.. are made of particles.. particles make the length.. 
You can't say how big is a atom without..atoms (or particles).. 

 

Edited July 27, 2020 by Edgard Neuman