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Tests of General Relativity

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Scrutiny of BICEP2 evidence of cosmic inflation and primordial gravitational waves suggests signals could come from dust in our own galaxy. Science News follow-up is here. Further report from the Planck survey later this year may clear the BICEP2 proposed discovery or take it down.

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.

Current status of the tests of GR is presented by Clifford Will in:

 

The Confrontation between General Relativity and Experiment

 

This review is at the site Living Reviews in Relativity. All of the papers there are by qualified physicists, and all are available for full-text download free of charge. This is a site I can endorse, along with the Einstein Online site linked in post #5.

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SL,

 

There are concretely real relations in the world, and among such relations are the physical relations of space and time. They are more than the relations of abstract geometry or topology, for not all of those have the honor of being instantiated physically in some particular physical situation that is being scientifically comprehended. To say that some geometric abstract spacetime is what is being encountered in some concrete situation is to say the relations in that structure are concretely real relations in that situation.

 

Do you agree that there are such things as concretely real relations? To say Yes to that is not to say those concrete relations are concrete entities. Is that what you mean by reification of spacetime, taking a relation for an entity?

 

I think the entity way of looking at physical spacetime might be what is called the substantival view in philosophy of physics today, in contrast to a purely relationalist view. Two good books on these different interpretations and related issues are:

 

World Enough and Space-Time

John Earman

 

What Spacetime Explains

Graham Nerlich

 

I don’t know if you have heard the GR saying for the layman: “Spacetime curvature tells mass-energy how to move; mass-energy tells spacetime how to curve.” I expect a purely relational case for spacetime might be made even in this dynamic. But I personally would not start with a presumption that a purely relational case for spacetime can be made, and that a substantival account is up-front an error, specifically a reification.

 

Stephen

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Thanks for the reply Stephen.

 

I am still trying to figure out how I conceive of relationships/relations. 

 

The relationship between entities is not inherent in either of the individual entities which has the relationship so as such it is not IN the things individually. 

 

Certainly the relationship is real in that I can identify the relationship and even in some cases quantify it.  What I identify as the "relationship" is causally linked to different outcomes.  Pushing a thing "towards" another thing leads to an interaction.  Pushing a thing "away" does not.  The relationship I perceive has consequences in reality.

 

Now, I would say relationships are objective in the sense that I identify them FROM reality, and they are not irrelevant to or independent of reality, hence they are not only in the mind.  They are not subjective.

 

The tough part comes when I am tempted to consider whether relationships "as such" are IN reality.  I think perhaps my working categorization of "as such" is causing some of my difficulty.

 

 

In my final analysis (currently... I am still working on it) I am conceiving of a relationship as

1. a property in reality attributable to the entities together (i.e. not to each indiidual entity)

2. which property is characterizable by the various causal consequences

 

So an entity A "to the left" of B is a property in reality of "A AND B", such that (i.e. this is what it means to be "to the left of" ... and this is a very rough imprecise definition for illustration only) imparting a rightward motion to A leads to A and B interacting... occupying the same line of sight... etc.  To be clear, I am conceiving of the relationship between A and B, regardless of the words I use to define it, as being exactly all the causally linked possible outcomes for A and B, and their interaction with each other or me... I wish I had far better words for this.  

 

I want to say there is nothing more to the relationship than the possible material consequences of that relationship. (Then I start mentally digressing ... what about entities?... cannot they be defined the same way?...then perhaps the only difference between attributes categorised as "relationship" versus "entity" is whether the properties are indivisible or spread across multiples...)

 

As you can see I am still working on it.

 

 

Thanks for the references to the books.

Edited by StrictlyLogical

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Stephen said:

 

 

There are concretely real relations in the world, and among such relations are the physical relations of space and time

 

In what ontology is time physical and how is this ontology justified?

 

 

SL asked:

 

 

 

 is there any alternative interpretation/visualization of GR and/or SR which avoids reification of space-time?

 

 

To which you responded:

 

 

There are concretely real relations in the world, and among such relations are the physical relations of space and time. They are more than the relations of abstract geometry or topology, for not all of those have the honor of being instantiated physically in some particular physical situation that is being scientifically comprehended. To say that some geometric abstract spacetime is what is being encountered in some concrete situation is to say the relations in that structure are concretely real relations in that situation.

 

Stephen, this is a reification of time. Calling time "a concrete relation" is exactly that. The real question is, by what method does one justify this reification? In the philosophy of science this is the debate over theoretical entities in the scientific realism debate. Whether or not such "instantiation" is ontologically actual is the whole debate. Particularly what epistemology justifies a theoretical entity. "Concrete relations" is simply a way of saying moving entities interact. Without the mind grasping these relations there are just entities moving. Abstract geometry and topology are linguistic-conceptual methods and can be used to represent fantasies like any other language. If I said "Spider-Man is instantiated physically in some particular physical situation that is being scientifically comprehended" any rational person would reject this claim on the basis that it is a reification of a mental construct. Time is epistemological method for Oism. Do you have direct criticisms of the Oist view of time?

Edited by Plasmatic

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SL said:

 

The tough part comes when I am tempted to consider whether relationships "as such" are IN reality.

 

 

This is central to the debate over what is ontologically objective vs epistemological tools of method.

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Scrutiny of BICEP2 evidence of cosmic inflation and primordial gravitational waves suggests signals could come from dust in our own galaxy. Science News follow-up is here. Further report from the Planck survey later this year may clear the BICEP2 proposed discovery or take it down.

 

Report from Planck indicates BICEP2 data cannot be taken as support for gravitational waves: BICEP Claim Was Wrong.

 

Planck also yields new date of first stars, resolving earlier discrepancy between Hubble and WMAP indications.

Edited by Boydstun

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Testing the Equivalence Principle

 

A fundamental postulate elaborated in general relativity is that inertial mass and gravitational mass are the same or at least directly proportional to each other. That is the equivalence principle. The sameness of the two masses is a proposition recognized in Newton’s mechanics. The mass in the second law F=ma is inertial mass. The force F on the left is identified and quantified for a variety of cases in our world. For example, the restoring force of a spring set into elastic response to a stretch or compression of the spring is quantified as in direct proportionality to the displacement. Plugging in that –kx for F  (where k is a constant and the minus sign since indicates the restoring force is opposite the direction of stretch or compression), we get a differential equation because the acceleration a is a (twice-over) derivative of displacement x with respect to time. Solving that differential equation gives equations reflecting the time course of displacements of the spring after its release from the initial stretch or compression, that is, the solution of this differential equation charts the oscillations of the spring. Where the case is one for electrostatics or electrodynamics or fluid mechanics we have a distinct expression to plug in for F in each case, and we proceed to solve the resulting differential equation of Newton’s second law to get equations of motion, that is, to get the patterns of motion distinctive of each sort of case. Better yet we use the fundamental differential equations of the Lagrangian or Hamiltonian formulations of classical, Newtonian mechanics, and these will reveal more easily the patterns of motion of somewhat more complicated cases such as an assembly of springs coupled together. Inertial mass will enter these equations also. With the illumination of special relativity, inertial mass becomes not simply a constant amount for a body, but becomes a specific function of relative velocity and the vacuum velocity of light. That function yields a negligibly different value of the inertial mass from the mass value of that body at rest (the old Newtonian inertial mass value) for the many practical cases with velocities far below light velocity.

 

I said that sameness of inertial and gravitational mass is an element in Newtonian mechanics. Gravitational mass appears in Newton’s expression for F in the case of gravitational attraction. Newton argued that the strength of the gravitational attraction between the sun and the earth is given by a constant multiplied by the mass of the sun multiplied by the mass of the earth and divided by the distance separating them squared, and he takes these masses as the same as inertial masses of those bodies. That’s what allows us to cancel the mass of the earth in ma with the mass of the earth in the gravitational expression for F on the other side of the second-law equation, which cancellation leaves us with a differential equation alleged true for gravitational force exerted by the sun on the earth, which was extensively supported as true by the empirical success of the equations of motion yielded as solutions to that differential equation.

 

The preceding is only from off the top of my head from studies forty years ago, so please forgive me if I’ve gotten anything somewhat off the mark. As I recall its contours, also: In Einstein’s mind, extending his relativity principle of frame-independence of the form of physical laws from the (special-relativity) case of frames in uniform relative motion (constant relative velocity) to the case of frames having a constant non-zero relative acceleration brings consideration of his gedanken that a person confined to a chamber with no information about what is going on outside it, but only able to determine that he and the chamber are undergoing a constant acceleration, would not be able to tell (using accelerometers and strain gauges, let us suppose) whether he was pressed against the floor by gravity of the earth or whether he and the chamber were in field-free space undergoing a constant value of acceleration by a rocket propulsion. The gravitational case is equivalent to the inertial case provided gravitational mass is equivalent to inertial mass. Einstein was able to cast gravitational force as effect of curved spacetime geometry because of that equivalence.

 

Sorry for all the gaps and opacity of the preceding paragraph, but I cannot afford to pause to open some books for improvement at this time. With that sketchy background, we come to this note’s headline, experimental tests of the equivalence of inertial and gravitational mass. The issue of Science for 6 March 2015 has a nice article on these tests. It reminds us of Galileo’s proposition that objects of different materials, but having the same mass (as measured by a balance or other scale, I suppose), would fall to the earth at the same rate. They would have the same value of constant acceleration. (That proposition is rather less famous than his proposition that bodies of different masses fall at the same rate.) The article includes survey of tests of the equivalence going back to Newton and right up to three kinds of tests given the postulate by physicists today. The ways in which these current tests do indeed test the equivalence principle are somewhat complex ways to be sure. One is along Galileo’s line for testing material-independence of gravitational attraction, dropping objects from heights.


About a year from now, a satellite will blast into orbit to perform the legendary test more precisely than Galileo could have imagined.

 

Rather than dropping things to the ground, the Drag-Compensated Micro-Satellite for Observation of the Equivalence Principle (MicroSCOPE) will contain two free-floating weights of different materials and will monitor whether one feels a stronger tug from the Earth’s gravity than the other. If so, the result would sink general relativity, Albert Einstein’s theory of gravity.

 

 

I underscore, as ever we must, that in science we continue to test fundamental postulates of even highly successful theories, not only ramifications of the theory when its fundamental postulates are joined with additional conjectures. 

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100 Years of Relativity: Space-Time Structure – Einstein and Beyond - Abhay Ashtekar, editor

General Relativity and Gravitation: A Centennial Perspective - Abhay Ashtekar et al., editors

2 October 1915 is the 100th anniversary of Einstein’s paper presenting his theory of General Relativity. Here is a good commemorative presentation about him and his work and our continuing development and experimental tests of General Relativity: Gary Horowitz

~~~~~~~~~~~~~~~~

Advanced LIGO began listening yesterday.*

 

Edited by Boydstun

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On December 23, 2013 at 4:46 PM, Boydstun said:

Einstein was the first to realize, in 1916, that his GR equations predicted the existence of gravitational waves under certain conditions. Russell Hulse and Joseph Taylor obtained strong indirect evidence in 1981 for the existence of gravitational waves by observing a reduction in orbital energy from an orbiting pulsar system in the amount predicted by GR for dissipation of that energy in such a system were the energy carried away in gravitational waves.

 

LIGO aims to detect gravitational waves directly using laser interferometers sited far apart in the US mainland. The sensitivity of the LIGO detectors so far has been only enough to detect gravitational waves resulting from pulsar collapses (a big though rare event) at distances from us wherein hundreds of centuries could go by without a collapse. No waves have been detected at this sensitivity. LIGO is now being enhanced to achieve a sensitivity to binary-pulsar collapses in space much farther from us wherein the total volume would have hundreds of collapses each year. The advanced LIGO* is scheduled to get to work in 2016.

 

For a look at future interferometer detectors operating from outer space capable of detecting gravitational waves so pervasive that they could be used to infer activities inside the event horizon of a black hole or to infer conditions in the part of the cosmic expansion before the universe lighted up with what is now known as the cosmic background radiation, see the cover article of the October 2013 issue of Scientific American, authored by Ross Andersen.

Direct detection of gravitational waves by LIGO announced today.

 

 

 

Edited by Boydstun

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“Had J. Robert Oppenheimer not led the US effort to build the atomic bomb, he might still have been remembered for figuring out [1939] how a black hole could form. . . .

Landmark papers in classical general relativity, after Einstein’s 1915, are presently available here.

~~~~~~~~~~~~~~~~

The following book is marvelous.

The Road to Relativity - 

The History and Meaning of Einstein’s “The Foundations of General Relativity”

Gutfreund and Renn (Princeton 2015)

There is an Introduction telling the story of Einstein’s journey to the theory, and there is a Postscript summarizing developments to the present. The fantastic thing is what lies between those two. That is a reproduction page by page of Einstein’s manuscript for the classic 1915 paper. Each page of the manuscript is shown on the left page in this book, and on the facing, right page is annotation, an explanation in English of what is going on. Look at the Table of Contents. The manuscript pages are to the left in the table. The title questions shown for each MS page (questions formulated by Gutfreund and Renn) and their answers pertain to that part of the MS; these are explained and put into historical background context by Gutfreund and Renn on those right pages. This is a great way to get hold, serious hold, of the theory. There is an English translation of the manuscript at the end of this book.

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.

Ayn Rand's 1936 novel We the Living opens in Petrograd 1922. She lived there at that time (age 17, at university), and so did Alexander Friedmann (age 34, died 3 years later). 

Alexander A. Friedmann: The Man who Made the Universe Expand

Friedmann Equations

 

Edited by Boydstun

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.

Pulsar and Companions Will Put GENERAL RELATIVITY to the Test - Clifford Will (1/6/14)

Science News - 2/3/18 -  “The complex orbital dance of the three former stars conforms to a rule known as the strong equivalence principle, researchers reported January 10. That agreement limits theories predicting Einstein’s general theory of relativity should fail at some level.” That is, this measurement puts a tighter constraint on theories unifying quantum field theory with general relativity by supposing the strong equivalence principle does not hold at sufficiently small scales.

~~~~~~~~~~~~~~~~

The Confrontation between GENERAL RELATIVITY and Experiment - Clifford Will (3/28/14)

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On 2/9/2018 at 11:07 PM, Grames said:

Keep posting these please, I always read these updates.

Interesting thread.

One thing that hasn't been emphasized here is that modern presentations of SR based of symmetry are rather difficult to refute:

http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Of course physics is an experimental science and its ultimate validation is experiment not theory.   But it does show if its wrong some of our basic notions about the world would be wrong - which would be a very very interesting and surprising thing.

That''s SR - what about GR.  That's actually quite interesting.   In SR where t is the proper time the principle of inertia implies a particle moves that maximizes the proper time when you integrate it along the path it follows.  If dt is a infinitesimal amount of proper time in turns out dt = Nuv dXu dXv and the path is the one that maximizes the integral dt = Nuv dXu dXv - this is called the principle of maximal time.  That's in the usual Cartesian coordinates and time as usually measured.   But you can mathematically transform to general coordinates so  Nuv dXu dXv becomes Guv dXu dXv when dXu are the new generalized coordinates and Guv is called the metric.

This means Guv acts like a field - determining the motion of a particle.   One of the principles of physics is you can derive field changes by whats called the principle of least action.  OK lets apply that to Guv.   Here we make use of a very interesting theorem called Lovelock's Theroem:

https://en.wikipedia.org/wiki/Lovelock's_theorem

That shows that GR ie the Einstein Field Equations are the only solutions.

If you are not a math type just in a general way accept what I said above.

If you want the gory detail see the following by Lovelock and Rund:

https://www.amazon.com/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406

Now the question is where does the Equivalence principle enter into it.  Its not that easy to answer.  Also it raises the same issue as SR.  If GR is wrong some of out basic notions would be wrong.

Thanks

Bill

Edited by William Hobba

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Thanks, Grames. Thanks, Bill Hobba.

~~~~~~~~~~~~~~~~~~~~~~~~

 

Famaey, Khoury, and Penco 2018

“The observed tightness of the mass discrepancy-acceleration relation (MDAR) poses a finetuning challenge to current models of galaxy formation. We propose that this relation could arise from collisional interactions between baryons and dark matter (DM) particles, without the need for modification of gravity or ad hoc feedback processes.”

 

Berezhiani, Khoury, and Wang 2016

“Cosmic acceleration is widely believed to require either a source of negative pressure (i.e., dark energy), or a modification of gravity, which necessarily implies new degrees of freedom beyond those of Einstein gravity. In this paper we present a third possibility, using only dark matter and ordinary matter.”

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