Need help on GR

[vano]

hi everybody

 

I'm reading a book by Green "elegant universe". i have gone through the chapter on special relativity and general relativity, both in laymen language of course. i have already thousand of questions but i will dare ask you first just one. this guy says that once upon a time a theory of special relativity was created which said, as its basic principle, that light speed is constant in all inertial frames of references. but, then turns out you cant get away with this so easily because a smart guy by name Newton would say gravity is transferred at huge distances instantaneously. so, we needed a new theory that would resolve conflict of this type. and another guy creates new theory of general relativity based on 2 things after conducting a thought experiment: 1) gravity and accelerated motion are equivalent ; 2) since accelerated motion causes warping, distortion or whatever. Accordingly the presence of matter should cause spacetime warping.

 

here comes the question:

even if special relativity is true(and which seems to be the base of spacetime warping during accelerated motion) how can we assume the equivalence of accelerated motion and gravity.

[Tormod]

here comes the question:

even if special relativity is true(and which seems to be the base of spacetime warping during accelerated motion) how can we assume the equivalence of accelerated motion and gravity.

 

I am sure someone can give you a straight answer but a good read is Wikipedia: Gravity

 

http://en.wikipedia.org/wiki/Gravity

 

Bascially, the concept of weight is the result of acceleration. When things fall towards Earth, they fall faster and faster and get heavier and heavier. In space they are weightless (or near zero-g) whereas on the surface of the Earth the weight is a measurement of the pull of the Earth there - this is known as "1g", which is why acceleration is measured in gees.

[Erasmus00]

here comes the question:

even if special relativity is true(and which seems to be the base of spacetime warping during accelerated motion) how can we assume the equivalence of accelerated motion and gravity.

 

Think about being in your car. When you slam on the gas peddle, you feel yourself pushed back into the car, the faster the car accelerates, the more you feel smashed into the seat. Imagine you were weightless in space, standing in a room (an elevator if you will, to use Einstein's famous example). The room begins to accelerate upward, pushing you into the floor. If the elevator accelerates at exactly 9.8m/s^2, you will find the situation identical to standing on the surface of the Earth. Because there is no experiment you can do to distinguish these two systems, Einstein cocluded that, as far as physical laws go, the two situations must be identical.

-Will

[vano]

Think about being in your car. When you slam on the gas peddle, you feel yourself pushed back into the car, the faster the car accelerates, the more you feel smashed into the seat. Imagine you were weightless in space, standing in a room (an elevator if you will, to use Einstein's famous example). The room begins to accelerate upward, pushing you into the floor. If the elevator accelerates at exactly 9.8m/s^2, you will find the situation identical to standing on the surface of the Earth. Because there is no experiment you can do to distinguish these two systems, Einstein cocluded that, as far as physical laws go, the two situations must be identical.

-Will

 

i do know what i feel during accelerated motion, but can i trust my perception and say both events are equivalent? how do we know, say, a piece of rock would feel the same force? or has it ever been verified by experiments that accelerated motion and gravity are identical in every regard or at least in causing space-time distortion?

[C1ay]

how can we assume the equivalence of accelerated motion and gravity.

I don't think we can. Examine two scenarios.

 

You are standing on the ground for an indefinite time. No matter how much time passes you will never feel weightless. You will always feel a constant weight on your feet.

 

You are standing in a rocket that accelerates to 9.8 m/s^2 out in space. Initially it will feel like gravity because of inertia but once you have accelerated you will no longer feel the force. With every moment that passes you will feel lighter and lighter.

 

For a brief moment you can equate the two but that's all. To equate them for any longer period of time would require the rate of acceleration to grow as well.

[GAHD]

Just a small note: Accelerating at 9.8m/second is equil force to gravity yes, as long as you are accelerating you would feel that force. The instant acceleration ceases you'd be 'weightless' because the rocket would no longer be pushing on you. Inertia would keep you moving at that same velocity.

 

I don't think you need to exponentially increase your acceleration to retain that effect. Now you will have to Keep accelerating, so that your velocity increases by 9.8m/second^2, but the acceleration would remain constant to keep the effects the same.

[Qfwfq]

You are standing in a rocket that accelerates to 9.8 m/s^2 out in space. Initially it will feel like gravity because of inertia but once you have accelerated you will no longer feel the force.

In what sense "once you have accelerated"? The acceleration can last as long as you like. However, to the purposes of GR, it is sufficient that a coordinate map can be chosen that's locally inertial.

 

how can we assume the equivalence of accelerated motion and gravity

It isn't a difficult thing to understand. It was stated even by Newton, back in the late 16 hundreds, as one consequence of his famous three laws of motion. Essentially, it's a consequence of the assumption that gravity is a force exactly proportional to mass and therefore all bodies have the same acceleration, in the same gravitational field. This assumption was first demonstrated by Galileo in the early 16 hundreds at the tower of Pisa and has since been verified with increasing precision.

[UncleAl]

You timeline is way off.

 

Galilei, Galileo. Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze (Appresso gli Elsevirii, Leida: 1638). Science is empirical.

 

Newton, Isaac. 1687, Philosophiae Naturalis Principia Mathematica. Science can be mathematically modeled subject to empirical falsification. Tacit assumption of c=infinity, h=0, G=G.

 

James Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vols. 1-2 (1891). Unites electricity and magnetism. Tacit assumption of c=c, h=0, G=0. Incompatible with Newton.

 

Einstein, Albert. Annalen der Physik 4 XVII 891-921 (1905). Special Relativity unites Newton and Maxwell except for gravitation. Tacit assumption of c=c, h=0, G=0.

 

Einstein, Albert. Annalen der Physik 4 XLIX 769-822 (1916). General Relativity encompasses all of classical physics. Tacit assumption of c=c, h=0, G=G.

 

1920s: Quantum mechanics tactly assumes c=infinity, h=h, G=0; then quantum field theory with c=c, h=h, G=0. Nobody has any idea how to build predictive physical theory with c=c, h=h, G=G simultaneously. Planck's constant (h) enforces uncertainty in measurement; h-bar is the fundamental unit of action. Newton's constant (Big G) scales gravitation). Lightspeed © enforces information transfer delay.

 

even if special relativity is true (and which seems to be the base of spacetime warping during accelerated motion) how can we assume the equivalence of accelerated motion and gravity.

The Equivalence Principle is a postulate. It is no stronger than its first reproducible empirical counterdemonstration. Special Relativity is a self-consistent geometry. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic.

 

The Equivalence Principle states that inertial (push a car in neutral on flat ground) and gravitational (lift a car) mass are fundamentally indistinguishable. All local bodies in vacuum fall identically - same rate of acceleration and parallel paths.

 

Special Relativity does not include gravitation. To include gravitation one can take two routes: Make no additional assumptions (Weitzenböck/Weizenboek) and sweat through huge volumes of truly awful math to a arrive at affine gravitation. Assume the Equivalence Principle (Einstein) and immediately derive metric gravitation (e.g., General Relativity as a special case of affine gravitation).

 

The maths of Newton and Einstein are parity-even or gerade. Inverting the signs of all coordinates (turn a glove inside-out) has no effect upon the answer. Weitzenboeck's math is parity-odd or ungerade. Inverting the signs of all coordinates can change the answer.

 

There are no known exceptions to GR in any venue at any scale,

 

http://math.ucr.edu/home/baez/RelWWW/tests.html

Mathematics of gravitation

 

http://relativity.livingreviews.org/Articles/lrr-2001-4/index.html

http://arXiv.org/abs/gr-qc/0311039

http://www.weburbia.demon.co.uk/physics/experiments.html

Experimental constraints on General Relativity

 

http://www.eftaylor.com/pub/projecta.pdf

http://www.public.asu.edu/~rjjacob/Lecture16.pdf

http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html

Relativity in the GPS system

 

There are no known exceptions to the EP to one part in ten trillion difference/average. All chemical compositions of matter, gyroscopes, magnets, superconductors, binding energies... and hyper-bound, hyper-spinning, hyper-magnetized, superconducting spheres of neutronium (binary pulsars) all fall identically.

 

http://www.mazepath.com/uncleal/eotvos.htm#b22

 

http://wugrav.wustl.edu/people/CMW/update98.pdf

http://www.astro.northwestern.edu/AspenW04/Papers/lorimer1.pdf

Equivalence Principle testing

 

http://arXiv.org/abs/gr-qc/0411113

http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf

http://arXiv.org/abs/gr-qc/0301024

Phys. Rev. Lett. 93 261101 (2004)

Nordtvedt Effect

 

http://arXiv.org/abs/astro-ph/0401086

http://arxiv.org/abs/astro-ph/0312071

http://relativity.livingreviews.org/Articles/lrr-2003-5/index.html

http://skyandtelescope.com/news/article_1473_1.asp

Deeply relativistic neutron star binaries

 

If you find two lumps that reproducibly fall differently in vacuum and the EP is thus falsified, GR is falsified without ever having made an invalid prediction. FR dies for having a founding postulate empirically falsfiied. An axiomatic system is no stronger than its weakest axiom.

 

Can the EP be falsifed? There is one screamingly obvious physical difference between two compositionally identical lumps that has never been tested, as described above. It bears directly upon the geometry of space. That test is currently in progress in China. Results are due in mid-September; qz.pdf, below.

[C1ay]

The acceleration can last as long as you like.

Well yes you are correct until you reach the speed of light. Constant acceleration can't last forever. Gahd did point out this error on the side but it took me a while to get back to it.

[Erasmus00]

i do know what i feel during accelerated motion, but can i trust my perception and say both events are equivalent? how do we know, say, a piece of rock would feel the same force? or has it ever been verified by experiments that accelerated motion and gravity are identical in every regard or at least in causing space-time distortion?

 

Put a rock on your dashboard, and slam on the gas. What happens? The rock flies accelerates back at you. So, obviously, a piece of rock feels the same force.

 

As to experiments, the equivalence principle can be restated to say that gravitational mass and inertial mass are equivalent. (It means the same thing, more or less, as acceleration and gravity are equivalent). This has been tested to 1 part in 10^13 I believe. Google lunar laser ranging or Eotvos experiments.

-Will

[Erasmus00]

You are standing in a rocket that accelerates to 9.8 m/s^2 out in space. Initially it will feel like gravity because of inertia but once you have accelerated you will no longer feel the force. With every moment that passes you will feel lighter and lighter.

 

As long as you keep accelerating, you will feel like that extra force. As soon as you stop accelerating, no more force. There isn't this gradual feeling lighter and lighter.

-Will

[Little Bang]

Can the EP be falsifed? There is one screamingly obvious physical difference between two compositionally identical lumps that has never been tested, as described above. It bears directly upon the geometry of space. That test is currently in progress in China. Results are due in mid-September; qz.pdf, below.

 

Is there a link that talks about this test?

[C1ay]

As long as you keep accelerating, you will feel like that extra force. As soon as you stop accelerating, no more force. There isn't this gradual feeling lighter and lighter.

-Will

Wouldn't that depend on how abruptly you stop accelerating? For instance, many solid propellant rocket motors do not just go from full impulse to zero impulse as they burn down.

[UncleAl]

Constant acceleration can't last forever.

Aside from the engineering difficulty, it certainly can. It simply asymptotes to an external observer's zero as KE=mv^2/2 goes into apparent unlimited relativistic mass increase. Inside the accelerated reference frame you can maintain 1 gee acceleration for an unlimited length of time, again subject to engieeering diifficulties like fuel. It all comes out in the wash consistent with Special Relativity in the internal as well as external reference frames. Either way, you never get to lightspeed no matter how long you accelerate or how hard.

[Boerseun]

You can accelerate indefinitely, due to time dilation.

 

As Uncle Al said, ignoring engineering difficulties, your velocity would approach c, but never get to it - the closer you get to c, the longer it takes to accelerate. For instance, if you accelerate at 9.8m per second, your seconds in the "real" universe would stretch out. It'll take you (for the sake of the argument) a thousand years to increase your speed with 9.8mps whilst you'll only experience one second going by. And the closer you get to c, the longer it'll take. Time's supposed to stand still at c, so - if you've been travelling at 99.99999999%c it'll appear to you as if the Big Bang took place only a couple of minutes ago.

 

As you increase your speed, it's only the digits that keeps adding up. For instance, 99.99%c increases to 99.999%c which increases to 99.9999%c ad infinitum.

[Qfwfq]

For instance, if you accelerate at 9.8m per second, your seconds in the "real" universe would stretch out.

Which one is the "real" universe? :xx:

Well yes you are correct until you reach the speed of light.

I's a matter of which observer. In your own frame of reference you're always still and there is a gravitational field. This can go on forever. In Boerseun's "real" universe your speed will approach c asymptotically but this is irrelevant, it's only a change of coordinates; your "universe" is just as real as Boerseun's.

[C1ay]

I's a matter of which observer. In your own frame of reference you're always still and there is a gravitational field. This can go on forever. In Boerseun's "real" universe your speed will approach c asymptotically but this is irrelevant, it's only a change of coordinates; your "universe" is just as real as Boerseun's.

You're right. I should have thought it through a bit more.