I understand Einstein’s quote to mean the interdependence of gravity and 4 dimensional spacetime geometry. Neither may be prominent over the other, but one cannot function without the other. Spacetime (a universal) is a metaphysical (latent) geometry, i.e. it is founded on the abstract concepts of speed and location in spacetime. Gravity is also a universal (a latent constant). Gravitational action between two massive bodies reveals this geometry which mathematically determines the paths they must follow in relation to each other.

I may well be wrong, but intuitively I feel comfortable with these concepts of potential inherent in the geometric structure of spacetime, which becomes disturbed in the presence of massive objects.

Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with.

From the introduction:

A contradiction in terms:

A uniform gravitational field has, by definition, no tidal forces and thus no space-time curvature. Thus according to the interpretation of gravity as a curvature in spacetime a uniform gravitational field becomes a contradiction in terms (i.e. no tidal forces where there are tidal forces).

From the conclusion:

Einstein did not interpret gravity as a curvature of space-time, rather that space-time curvature is a manifestation of gravity.

The nature of Nature:

Nature has Her own way of doing things regardless of what physicists believe.

Not much. It is funny to see how in this thread mere scientific speculation is confused with philosophy. Speculation is a necessary part of science. It is the creative part of it. But then it must get back to the ground. It must make empirical predictions that do not fit in existing theories. It must still explain known facts. Or, it must explain known facts only, but with less presuppositions. (Special relativity is a nice example: it explains the Lorenz transformations, and the Fitzgerald contractions. Poincaré explained them as solution for the incompatibility of Newtonian physics and Maxwellian electro magnetic equations. Einstein brought them back to only 2 principles: that there is no preferred inertial frame of reference, and the constancy of light in all inertial frames).

Now how does Verlinde’s theory do in this respect? As far as I can understand it (here is the original), it belongs to exactly such a proposal: to derive known theories from more fundamental principles. But I am not sure he really has a point. E.g. take ‘my derivation’ from Newton’s law of gravity from geometry:

We know that an the force with which an object is attracted to the earth is proportional to its mass. From this it follows that:

F = 4.π.g.Mm
(g is a constant, M mass of the earth, m mass of the object)
The reason for putting in the factor of 4π, will become apparent soon.
We can safely assume that the gravitational field of the earth is spherical symmetric. It is natural to assume that gravitational force will be reversely proportional to the area of any sphere around the earth. Now the surface of a sphere is:

A = 4.π.r^2

So F = g.Mm/r^2.

QED.

I leave it to kkwan to see if I really made an interesting point here… Compare this to Verlinde’s article (pages 7 and 8). I actually took a few sentences from his article.

We must leave it to the scientific community to find out if Verlinde really has found something.

It is funny to see how kkwan and write4u discuss gravity, geometry etc, without really understanding it. Try Susskind on general relativity, it is a very good introduction (but you need a lot of time, about 12 videos of 2 hours each…)

The article by Peter M. Brown might not be taken seriously. Having just a hotmail email address is a little suspicious, I think. I found no reference that he is a real scientist. But I am not sure.

Forgot: thanks kkwan for the link to Verlinde. Let see what his idea means in the coming years.

Is gravity contingent? Is it a brute fact? Is gravity a force? Does It govern what stuff does? Is it a man made scientific law? Is it something that exists independently of us and our science? What is space/ time? (Remember space/ time is not physical)

This is ridiculous. These kind of questions can be asked about every fundamental natural law. Gravity is not special in this respect. This is science.

StephenLawrence - 20 October 2011 01:40 PM

And lots more, these are all philosophical questions.

Yes, some of your questions are philosophical questions, but very naive philosophical questions.

Now how does Verlinde’s theory do in this respect? As far as I can understand it (here is the original), it belongs to exactly such a proposal: to derive known theories from more fundamental principles. But I am not sure he really has a point.

In this paper, we argue that these screens are Rindler horizons and gravity (both Newtonian and General Relativity) behaves as an entropic force in Rindler space. Our results also apply to space-times that reduce to Rindler space such as the near horizon geometries of Schwarzschild and de Sitter space-times and those of black branes.

If you took away the gravitational field, this meant that “g-mu-nu” would be everywhere and for all time equal to zero, but so too would the metric for spacetime. Spacetime would lose its metric, the distance between points in the manifold would vanish, and the manifold itself would disappear into nothingness. In Relativity: The Special and General Theory page 155, Einstein expressed this quality of spacetime as follows,

“Spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field”

And:

.....Einstein’s view point sounds a lot like the old philosophical discussion of the Void which emphasized that without bodies, ‘place’ and therefore vacuum could not exist. If we consider that all bodies produce gravitational fields, we see that Einstein’s general relativity arrives at nearly the same Aristotelian conclusion.

In other words, without bodies (which all produce gravitational fields), space-time does not exist.

In Einsteinian physics, bodies and their gravitational fields are primal and space-time is only a manifestation of their presence. This concept of reality is radical and not intuitive at all.

OTOH, for most practical purposes, Newtonian physics (which is more intuitive and simpler as well) is quite adequate.

Although Newton’s theory has been superseded, most modern non-relativistic gravitational calculations are still made using Newton’s theory because it is a much simpler theory to work with than general relativity, and gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

Consequently, for falling apples it is ridiculous to invoke Einsteinian physics.

GdB, stipulating my limited knowledge of hard physics, precisely where do my musing show a lack of philosophical understanding of the relationship between gravity and spacetime curvature?

#17 Write4U - 22 October 2011 12:28 AM

Thus gravity and spacetime curvature are interdependent, no? No matter which is a priori, one is an expression of the other, either way.

From link in #16

GRAVITATION AND SPACE-TIME CURVATURE
“Gravity is not a foreign and physical force transmitted through space and time. It is a manifestation of the curvature of space-time.”
That, in a nutshell, is Einstein’s theory 25.

My conclusion in #17 seems right on the mark in a general philosophical sense.

If you took away the gravitational field, this meant that “g-mu-nu” would be everywhere and for all time equal to zero, but so too would the metric for spacetime. Spacetime would lose its metric, the distance between points in the manifold would vanish, and the manifold itself would disappear into nothingness. In Relativity: The Special and General Theory page 155, Einstein expressed this quality of spacetime as follows,

“Spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field”

And:

.....Einstein’s view point sounds a lot like the old philosophical discussion of the Void which emphasized that without bodies, ‘place’ and therefore vacuum could not exist. If we consider that all bodies produce gravitational fields, we see that Einstein’s general relativity arrives at nearly the same Aristotelian conclusion.

In other words, without bodies (which all produce gravitational fields), space-time does not exist.

IMO, that is not quite correct. Without bodies, spacetime is reduced to a single point, as was the case before the BB (the beginning). This single point of spacetime expanded with the appearance and movement of physical/energetic phenomena, created during the BB.

Thus,

In Einsteinian physics, bodies and their gravitational fields are primal and space-time is only a manifestation of their presence. This concept of reality is radical and not intuitive at all.

OTOH, for most practical purposes, Newtonian physics (which is more intuitive and simpler as well) is quite adequate.

Perhaps for practical purposes that may be true, but that is like asking which came first. The point is that we have both a chicken and an egg, who came first is philosophically pertinent.

As explained below,

From the wiki on gravitation
Although Newton’s theory has been superseded, most modern non-relativistic gravitational calculations are still made using Newton’s theory because it is a much simpler theory to work with than general relativity, and gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

Consequently, for falling apples it is ridiculous to invoke Einsteinian physics.

Why is it ridiculous? It is the universal explanation of a locally determined and observed phenomenon. If Newton’s theory was sufficient, why the need for a more in-depth explanation of the inherent (potential) causalities and manifestations of gravity within the geometry of spacetime?

IMO, that is not quite correct. Without bodies, spacetime is reduced to a single point, as was the case before the BB (the beginning). This single point of spacetime expanded with the appearance and movement of physical/energetic phenomena, created during the BB.

Without bodies, (according to Einstein) space-time does not exist. This is not the same as what you say i.e. “a single point of space-time” which is meaningless.

According to a naive interpretation of general relativity that ignores quantum mechanics, the initial state of the universe, at the beginning of the Big Bang, was a singularity. Both General Relativity and Quantum Mechanics break down in describing the Big Bang, but in general QM does not permit particles to inhabit a space smaller than their wavelengths.

Curvature:

The classical version of the Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all time-like geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe of size 0 in all spatial dimensions, infinite density, infinite temperature, and infinite space-time curvature.

But, a causal singularity with size 0, infinite density, infinite temperature, and infinite space-time curvature is clearly absurd.

Perhaps for practical purposes that may be true, but that is like asking which came first. The point is that we have both a chicken and an egg, who came first is philosophically pertinent.

No, there is no chicken and egg problem wrt the use of Newtonian physics for all practical purposes.

Why is it ridiculous? It is the universal explanation of a locally determined and observed phenomenon. If Newton’s theory was sufficient, why the need for a more in-depth explanation of the inherent (potential) causalities and manifestations of gravity within the geometry of spacetime?

An apple is a small body and the earth is only moving at a miniscule fraction of light speed. Hence, to describe it’s falling to the earth, Newtonian physics is simpler and sufficient and it is quite ridiculous to resort to Einsteinian physics.

IMO, that is not quite correct. Without bodies, spacetime is reduced to a single point, as was the case before the BB (the beginning). This single point of spacetime expanded with the appearance and movement of physical/energetic phenomena, created during the BB.

Without bodies, (according to Einstein) space-time does not exist. This is not the same as what you say i.e. “a single point of space-time” which is meaningless.

Is it? A single point/instant which was the initial spacetime coordinate itself, the point of origin, perfectly flat in 4 dimension.

According to a naive interpretation of general relativity that ignores quantum mechanics, the initial state of the universe, at the beginning of the Big Bang, was a singularity. Both General Relativity and Quantum Mechanics break down in describing the Big Bang, but in general QM does not permit particles to inhabit a space smaller than their wavelengths.

That is the whole point! For a single instant such a condition existed and inevitably was causal to a single mega quantum event (BB) and the subsequent inflation of space/time.
But before the beginning there were no physical attributes to the cosmos, only potentials. Latencies (compressed into a singularity).

Curvature:
The classical version of the Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all time-like geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe of size 0 in all spatial dimensions, infinite density, infinite temperature, and infinite space-time curvature.

But, a causal singularity with size 0, infinite density, infinite temperature, and infinite space-time curvature is clearly absurd.

Again, is it? Actually, a causal singularity as described is the only state in which all potential energy would be in a frozen state of stasis with infinite potential.
Without physical properties potentials individually have no impact on each other. But compressing them inside a singularity of (near) infinite potential we force those potentials interact. When all potentials are forced to interact with each other in a single instant, chaos results, i.e. BB.
Note: IMO. the BB was the first (mega) quantum event in the history of the universe.

Perhaps for practical purposes that may be true, but that is like asking which came first. The point is that we have both a chicken and an egg, who came first is philosophically pertinent.

No, there is no chicken and egg problem wrt the use of Newtonian physics for all practical purposes.

In limited applications yes, I agree completely. But the question of what came first is moot, like Spacetime, Gravity (field or influence) becomes observable only for its impact on spacetime curvature. Spacetime, Gravity, Quantum are Universals. They always were and always will be inevitably causally interconnected (from obesrvation).

Why is it ridiculous? It is the universal explanation of a locally determined and observed phenomenon. If Newton’s theory was sufficient, why the need for a more in-depth explanation of the inherent (potential) causalities and manifestations of gravity within the geometry of spacetime?

An apple is a small body and the earth is only moving at a miniscule fraction of light speed. Hence, to describe it’s falling to the earth, Newtonian physics is simpler and sufficient and it is quite ridiculous to resort to Einsteinian physics.

True, why use the Cadillac in the garage to go to the grocery store, when you have a VW parked on the street…...

GdB, stipulating my limited knowledge of hard physics, precisely where do my musing show a lack of philosophical understanding of the relationship between gravity and spacetime curvature?

The confusion is not in every sentence you write, especially not if you are citing from reliable sources. The problem is that you see it as philosophical problems. You may base your personal philosophy on physical truths (you would contradict science if you would not), but that does not make physical truths to philosophical statements. But as there are a lot of physicists who are bad philosophers (not all!) one should always try to evaluate if a statement of a physicist is really a scientifical statement. That is not always easy.

It makes no sense to ask what is prior: gravity, mass or spacetime. They go together. Mass does not cause gravity, or gravity does not cause spacetime. When there is spacetime, then there is gravity. When there is gravity there is spacetime. Same with mass and gravity.

Newtonian mechanics is definitely replaced by relativity. In Newtonian physics, there is no maximum velocity, in relativity the speed of light is the maximum.. In Newtonian physics mass is a pure intrinsic property of an object, in relativity it depends on how objects move relatively to each other. However, in the limit of slow velocities and small masses, we can neglect certain terms in our calculations ((v^2/c^2) becomes immeasurable small). What is left over are the Newtonian laws.

2 Examples:
- in the calculation of any space vehicle trajectory, Newtonian physics is used
- In GPS the atomic clocks must be corrected for relativity (the satellites move relatively to us, but they are in a less strong gravitational field).

It makes no sense to ask what is prior: gravity, mass or spacetime. They go together. Mass does not cause gravity, or gravity does not cause spacetime. When there is spacetime, then there is gravity. When there is gravity there is spacetime. Same with mass and gravity.

Quite so. However, this is circular.

What is gravity is not resolved at all.

Entropic gravity aims to resolve this issue starting from a larger interpretation of the holographic principle.

In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies.

High level summary

The physical universe is widely seen to be composed of “matter” and “energy”. In his 2003 article published in Scientific American magazine, Jacob Bekenstein summarized a current trend started by John Archibald Wheeler, which suggests scientists may “regard the physical world as made of information, with energy and matter as incidentals.” Bekenstein quotes William Blake and asks whether the holographic principle implies that seeing “the world in a grain of sand,” could be more than “poetic license”.

Unexpected connection:

Bekenstein’s topical overview “A Tale of Two Entropies” describes potentially profound implications of Wheeler’s trend in part by noting a previously unexpected connection between the world of information theory and classical physics.

Energy, matter, and information equivalence:

Bekenstein summarizes that “Thermodynamic entropy and Shannon entropy are conceptually equivalent: the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information one would need to implement any particular arrangement…” of matter and energy.

Now, back to the holographic principle:

The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a hologram which is isomorphic to the information “inscribed” on the surface of its boundary.

Hence, the proposal that gravity is not fundamental, but it is an emergent “entropic force” resolves the issue of circularity completely as information (expressed as energy/mass/gravity/space-time) is fundamental in the universe.

This way of looking at gravity is also deeply connected to the Erik Verlinde’s idea of gravity as an entropic force, being the holographic principle the result of the “conservation” of quantum information—a founding axiom of Quantum Theory

Can quantum theory be derived from more fundamental principles?

In a paper appearing in Physical Review A, Giulio Chiribella at the Perimeter Institute in Waterloo, Canada, and Giacomo Mauro D’Ariano and Paolo Perinotti at the University of Pavia, Italy, offer a framework in which to answer these penetrating questions. They show that by making six fundamental assumptions about how information is processed, they can derive quantum theory.