Matter tells matter how to move

[jonmtkisco]

Hi Randall,

Referance frame differances are not what you were proposeing to compare.

I don't know where you got that idea. The velocity-based component of my scenario (blueshift and time contraction) was definitely supposed to measure reference frame differences, nothing more nothing less. That's what the Doppler effect is, reference frame differences, nothing more, nothing less.

I really don't get the point you're trying to make.

Jon

 

[RandallB]

Hi Randall,

I don't know where you got that idea. The velocity-based component of my scenario (blueshift and time contraction) was definitely supposed to measure reference frame differences, nothing more nothing less. That's what the Doppler effect is, reference frame differences, nothing more, nothing less.

I really don't get the point you're trying to make.

IMO the point is only way your original objective only makes sense at all is if you only consider the transverse effects of the SR motions portion of your problem.

Apparently you are evidently unwilling to even consider that approach.
Or it might be I have completely misunderstood your original objective.
Either way this discussion as passed any productive purpose,
I’ll unsubscribe from the thread so you may continue with your own line of reasoning.

 

[jonmtkisco]

Hi Randall,
I'm willing to consider transverse Doppler, but it made sense to me that we get straight on the meaning of radial Doppler first. Sorry the discussion didn't work out.

Jon

 

[atyy]

Thorne, Black Holes and Time Warps, 1994
-Chapter 11, What is Reality: Is spacetime really curved? Isn’t it conceivable that spacetime is actually flat, but clocks and rulers with which we measure it, and which we regard as perfect in the sense of Box 11.1, are actually rubbery? Might not even the most perfect of clocks slow down or speed up, and the most perfect of rulers shrink or expand, as we move them from point to point and change their orientations? Wouldn’t such distortions of our clocks and rulers make a truly flat spacetime appear curved? - Yes.
-Notes to Chapter 11: The flat spacetime paradigm was devised more or less independently by a number of different people; it is known technically as a “field theory in flat spacetime formulation of general relativity.” For an overview of its history an dconcepts, see the following passages in MTW: Sections 7.1 and 18.1; Boxes 7.1, 17.2, and 18.1; Exercise 7.3. For an elegant generalization of it, which elucidates its relationship to the curved spacetime paradigm, see Grishchuk, Petrov, and Popova (1984).

Rindler, Relativity: Special, General and Cosmological, 2006
-Chapter 11: One way to visualize any curved 3-space like that of the Schwarzschild lattice, whose metric is given by ... is to pretend that it is really flat, but that rulers in it behave strangely.

Hestenes, Gauge Theory Gravity with Geometric Calculus, Foundations of Physics, 35: 903-970, 2005
-A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein's principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance.

Also, there's a comment in Thurston, Three Dimensional Geometry and Topology, 1997 to the effect that "ds²=g_ijdxⁱdx^j" gives the Riemannian metric in terms of the Euclidean metric.

 

[kahoomann]

Thorne, Black Holes and Time Warps, 1994
-Chapter 11, What is Reality: Is spacetime really curved? Isn’t it conceivable that spacetime is actually flat, but clocks and rulers with which we measure it, and which we regard as perfect in the sense of Box 11.1, are actually rubbery? Might not even the most perfect of clocks slow down or speed up, and the most perfect of rulers shrink or expand, as we move them from point to point and change their orientations? Wouldn’t such distortions of our clocks and rulers make a truly flat spacetime appear curved? - Yes.
-Notes to Chapter 11: The flat spacetime paradigm was devised more or less independently by a number of different people; it is known technically as a “field theory in flat spacetime formulation of general relativity.” For an overview of its history an dconcepts, see the following passages in MTW: Sections 7.1 and 18.1; Boxes 7.1, 17.2, and 18.1; Exercise 7.3. For an elegant generalization of it, which elucidates its relationship to the curved spacetime paradigm, see Grishchuk, Petrov, and Popova (1984).

Rindler, Relativity: Special, General and Cosmological, 2006
-Chapter 11: One way to visualize any curved 3-space like that of the Schwarzschild lattice, whose metric is given by ... is to pretend that it is really flat, but that rulers in it behave strangely.

Hestenes, Gauge Theory Gravity with Geometric Calculus, Foundations of Physics, 35: 903-970, 2005
-A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein's principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance.

Also, there's a comment in Thurston, Three Dimensional Geometry and Topology, 1997 to the effect that "ds²=g_ijdxⁱdx^j" gives the Riemannian metric in terms of the Euclidean metric.

What does this, flat or curved, has anything to do with "Matter tells matter how to move"?
The tenet of special relativity is that any interaction must be local. So the "Matter tells matter how to move" is some kind of "spooky action at a distance" due to Einstein

 

[jonmtkisco]

Hi atyy,
Excellent post. Let me look at some of these references and I'll share my thoughts.

Jon

 

[jonmtkisco]

Hi atyy,
I've looked through the references you cited. I have to say that my comprehension of the Grishchuck et al paper is very limited.

I think most of these references are trying to convince the reader that it makes more sense to assume that the background geometry has been warped by gravity than to assume that multiple rulers applied in various different locations and directions have changed size. There is no doubt that the simple mathematical elegance of the spacetime concept is compelling. This explains why it is widely adopted by mainstream GR.

But, in my opinion a MORE IMPORTANT question to ask is: Is it possible to apply SR, on a principled basis, to a collection of individual local reference frames immersed in a cosmic gravitational background, so as to calculate that indeed the rulers which tell us that space is curved are themselves actually lengthend or shortened by Lorentz contraction and dilation? I submit that the integration of Lorentz transformations over an infinitude of adjacent local SR reference frames can explain that the supposed curvature of space is in fact merely a manifestation of lengthened and shortened rulers.

The physical interpretation of specific components of the Einstein Field Equations is well understood to be at best ambiguous and at worst downright murky. The question I'm raising here is what physical interpretation should be given to the precise mathematical results calculated by GR. I do not disagree with the latter at all.

Jon

 

[fakrudeen]

Yes - "matter tells spacetime how to curve, which in turn tells the matter how to move" looks like a round about way saying "matter tells matter how to move" - I can understand where you are coming from.

But I think spacetime curvature is as real as spacetime itself. How physical is spacetime?
Space and time separately are certainly not physical, because they are "in the eye of beholder".
time as something standing separately from space broke down with loss of "concept of simultaneouty".
in fact we can measure [and do measure] both in same units [through speed of light].
there is no meaning in saying space is curved - there is no consistent way to separate space from time [that is assign an one and same coordinate-frame] across the whole of spacetime [that is the whole point of GR]!
Only spacetime is real and to the extent it is real, for me curvature is real - which just means extremal "distance" [which is actually proper time in case of spacetime] from A to B is not necessarily euclidean straight line. For example, on Earth's [which is not space but matter] surface I do believe shortest distance is through great circle.
In a sense from the point of probability it would more surprising for spacetime to be flat than curved, because there are more ways to be curved that flat.
Just like we would be surprised if the Earth orbit were to be an exact circle, compared to so many ways for an ellipse to deviate from a circle.

Also how real is quantum states? Al we can get from them as something physical is their "length" as probability of something occurring. Is it just a mathematical tool?

 

[Fra]

Philosophical reflection

I hope this philosophical reflection is not inappropriate here. It seems this thread is firing philosophical question at GR in a way so I might as well throw in my info-perspective here.

John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move."

Not to speak for the Wheeler or the correct historical reasoning but my association to this kind of expression is that it's a beautiful statement of an induction principle.

Ie. Matter tells matter how to move, is basically to suggest that matter mysteriously contains the information for it's own differential changes. This has the exact form of an induction, except for it's deterministic tone (which I don't like).

If I may boldly suggest an even better philosophical phrasing that might be more compatible with the quantum indeterminism then one might say that

The matter/energy distribution suggests, by some logic(EinsteinsEquations), how the same is likely to change, give no other a priori reason.

So, what's the meaning of the matter/energy distribution having it's own opinon on it's own change?

The most plausible association I make here is that of uncertainty. If we consider the matter/energy distribution as the information at hand, and that information is generally uncertain, then this contains a self-judgement, where one may expect that the less confident parts are more likely to change than the more confident parts. Here is a seed to the concept of relative inertia. IE. the changes expected to take place, are relational to the current state.

So perhaps we can

- associate the stress energy tensor to information.

- associate the geometry of spacetime as the expectation on the differetial change thereof, induced from the information. This can also be thought of as a self-relating measure, of changes. The state of information, contains a "natural measure" of self-rating, if it's own state.

- the test-particle scenario can be interpreted as a small perturbative change, which is small enough to not distort the measure. The geodesics are the expectations, induced from the current state of information. The evolution of the geodesics are the expected changes of the measures itself.

I think the major lesson from GR is that it contains an element of self-reference, that is the key to the inductive evolution implicit in Einsteins equations. This is philosophically extremely appealing. This is lacking in QM.

So the last thing... what of all this is physical? To me, physical, means more like "physical evidence". Actual data, read by a real observer who is facing real decision problems. To ponder what is real, and not imagine how it's ever going to be established is not sensible to me - it does not answer to real problems. That's more sign of realism ideals.

Real problem for me, are making decisions on incomplete information among other things. It's from this perspective I choose to see GR like the above. It's purpose is to take a grip on GR, that is consistent with a scientific ideal. That IMO originates from limited observations. And this is why the inductive essence of GR is so extremely fascinating. Yet it seems no one has yet unravelled it to it's full beauty (beyond calculational tool).

I hope that one day we will learn to formalize this deeper.

/Fredrik

 

[jonmtkisco]

Hi Fredrik & Fakrudeen,

I want to reiterate that I have no problem with GR's mathematical predictions, I think they give a very accurate mathematical model for whatever the underlying physical process is.

My inquiry in this thread is about trying to not believe in any particular physical theory for gravity, on the grounds that the available data and logic fall far short of what is needed to draw defensible conclusions. I'm not saying that "gravity as a force" should be the preferred theory, just that it should be taken seriously. I'm fairly indifferent to philosophical approaches to the issue.

The mathematical underpinnings of GR seem overwhelmingly complex to experts and amateurs alike in this field. I'd like to break the problem down one step at a time. For example, can we nail down exactly what the sources of this mathematical complexity are, so that we can focus on the fact that gravity mostly has a very simple action?

I'm fairly well convinced that almost all of the mathematical complexity arises from the simple fact that gravitating mass particles (such as protons, neutrons and electrons) are spherically symmetrical point particles. The spherical symmetry of the resulting microscopic gravitational fields seems to be the sole cause of (1) the inverse-square law, (2) tidal effects, and (3) the complexity of the tensors in the Einstein Field Equations used to calculate geodesics through the field. If gravitating particles would exist naturally in the form of infintesimal self-tiling 2-dimensional planes rather than as point spheres which self-pack into larger spheres, the math to describe gravitational action would be really easy: gravity would be a simple, uniform acceleration field. Instead, we are forced to cram a round peg into a square hole, which motivates us to attribute exotic metaphysical properties to many aspects of our universe, including to emptiness itself.

I submit that the idea of warped spacetime as a physically real phenomenon has gained such widespread traction primarily because most people fundamentally overestimate the complexity of the gravitational action. As they say, when the going gets tough, a picture is worth 1000 words.

Jon