Gravity/acceleration equivalent?

[LightStorm]

No, but you can certainly figure out what the results would be in a series of small regions (which I assume is what you mean by 'reference frame', although this is incorrect terminology), each one of which is smaller than the last.

LS:The principle was designed for "reference frames". Not to individual points in a reference frame. My thought experiment deals with a reference frame too. Read the definition of the principle...

http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/grel.html

"Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field. "

See the principle talks about "experiments". Measuring the weight of an object at different locations in a given reference frame is an "experiment", correct? You agree that, measuring the weight of an object at different locations in any given reference frame is an experiment?

Are you familiar with what a "limit" means in calculus? Would you understand what it means to say "the limit as x approaches zero", for example?

LS: I am not a mathematician. But as the limit approaches zero, you are getting into the realms of QM. We already know QM invalidates GR in quantum scales.

 

[JesseM]

LS:The principle was designed for "reference frames". Not to individual points in a reference frame. My thought experiment deals with a reference frame too. Read the definition of the principle...

You're wrong. The definition of the principle states that general relativity reduces to special relativity locally, ie in an arbitrarily small region of spacetime. Most statements of the principle will say something to this effect. From this page:

The equivalence principle can be stated as "At every spacetime point in an arbitrary gravitational field, it is possible to chose a locally inertial coordinate system such that, within a sufficiently small region of the point in question, the laws of nature take the same form as in unaccelerated Cartesian coordinate systems

And from http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/Principle%20of%20Equivalence%20in%20Mathematical%20Form.htm :

General relativity yields the special theory of relativity as an approximation consistent with the Principle of Equivalence. If we focus our attention on a small enough region of spacetime, that region of spacetime can be considered to have no curvature and hence no gravity. Although we cannot transform away the gravitational field globally, we can get closer and closer to an ideal inertial reference frame if we make the laboratory become smaller and smaller in spacetime volume. In a freely falling (non-rotating) laboratory occupying a small region of spacetime, the laws of physics are the laws of special relativity. Hence all special relativity equations can be expected to work in this small segment of spacetime.

http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/grel.html

"Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field. "

In this case, they specify that the frame is in a uniform gravitational field where the intensity of the gravity field is the same at every point. This is physically unrealistic, but in this case I suppose you can dispense with the requirement that you only look at a small region.

Are you familiar with what a "limit" means in calculus? Would you understand what it means to say "the limit as x approaches zero", for example?

LS: I am not a mathematician. But as the limit approaches zero, you are getting into the realms of QM. We already know QM invalidates GR in quantum scales.

Yes, but the equivalence principle is solely about the fact that the mathematical theory of GR reduces to SR locally--the question of whether it does is independent of whether you believe this mathematical theory is a completely accurate description of the real world or not (as you say, it almost certainly isn't, although it's quite possible the equivalence principle would hold for a theory of quantum gravity as well).

 

[Mike2]

What may be of interest is how the Unruh affect applied to accelerating frames of reference might be applied to small regions of space at a fixed distance from a gravitating body.

Good point; however, the effect is generally considered equivalent; and can be considered equivalent to Hawking radiation at the extreme, although there are some differences.
See:
http://www.emis.ams.org/journals/LRG/Articles/lrr-2001-6/node3.html

Creator

Has the Unruh effect been confirmed? I think this is the same as confirming the existence of the zero point energy, right?

OK... If the gravitational acceleration has an Unruh temperature, then... what reference frame is the gravitational field being compared to? If there is a temperature associated by the mere fact that some point is in a deeper well then other points, then aren't there an infinite number of frames that are accelerating differently from the point in question so that it depend what you are comparing that point to when calculating the Unruh temperature? Thanks.

 

[rbj]

rbj sez: you see, it's a thought experiment so, being so i will restate it as one comparing the accelerating room to a stationary one in a gravitational field created by an infinite plane of mass with sufficient mass per unit area to result in an acceleration of gravity of 9.8 m/s². how does your proof of invalidation deal with that?

LS: I don't underestand your scenario. Mayeb you could restate it in a different manner?

do you know what would be the nature of the gravitational field created by a hypothetical infinite plane of mass?

But it appears like you do understand my scenario and it clearly shows gravity and acceleration are distinguiable in all reference frames that have dimensions greater than zero.

it's only because of the geometry, a specific geometry that creates an inverse-square field (coming from a nice spherically symmetrical mass) and you are citing the different strengths of the gravitational field in such a geometry as your "proof" that the EP is wrong. so i changed the geometry to one where the strength of the graviational field does not change with distance. then, no matter how sensitive your instruments, you would not be able to tell the difference, because there would be no difference. EP lives.

 

[Creator]

Hello, Mike.

Has the Unruh effect been confirmed? I think this is the same as confirming the existence of the zero point energy, right?

Not really.
First, what do you mean by confirmed? Unruh-Davies radiation is a prediction of QED and is generally accepted as valid. Experimental confirmation hasn't yet arrived (to my knowledge) due to the extremely high accelerations required; however, several interesting exp. tests have been proposed.

On the other hand, zero point energy was first predicted by Max Planck around 1911. Einstein and Otto Stern (not related to a screwball named Howard ) also recognized zero point energy and took account of it in their calculations.
Unbeknownst to many is the fact that it was first experimentally detected in the vibrational spectra of diatomic molecules by a physical chemist named Robert Mullikan; (I think it was in mid or late 1920's). [This is not the same as the Robert Millikan who measured the electron charge to mass ratio - notice the difference in spelling).

Later (1947) Willis Lamb (and Rutherford) discovered the 'Lamb shift' in the Hydrogen spectrum, which can also be considered direct exp. confirmation of zero point vacuum fluctuations.
There are other exper. validations also, Casimir, etc.

OK... If the gravitational acceleration has an Unruh temperature, then... what reference frame is the gravitational field being compared to?

I guess the usual,... the Minkowski (flat space time) frame.
Maybe I missed the point of the question.

Let me be a bit more explicit about my previous answer which apparently escaped your attention.
The differences between Unruh radiation and Hawking radiation near a BH in effect may be considered an EP violation; i.e., the Unruh radiation from acceleration will appear different from that of Hawking rad. due to a gravitational field. So you were on the right track if you were trying to look for an apparent EP violation here.

This link gives the type of conundrum that can arise by trying to apply Equivalence Principle here.
http://www.lns.cornell.edu/spr/2000-05/msg0024778.html


Creator

 

[pervect]

do you know what would be the nature of the gravitational field created by a hypothetical infinite plane of mass?

You'd better tell him, I doubt he realizes that the gravitational field at the axis of a large disk does not vary with height until the height is >> radius.

This makes the gravitational field of such a disk essentially constant. It also means that "real" gravitational fields from such a disk do mimic the gravitational fields of an accelerating rocket, including the fact that losely speaking, gravity doesn't change with height. (I'm cutting a few corners here, deliberately, considering my best guess of Lighstorm's level of physics understanding, but I'm not cutting any corners when I say that the gravitational field / metric of a large plane is identical to that of an accelerating spaceship).

It is simply physically difficult (though not impossible in principle) to build a large enough disk to mimic the field configuration (including invariance with height) of a rocket - not impossible as Lighstorm seems to think.

But the whole objection was really poorly motivated in the first place, it was basically missing the point.

In Newtonian physics, we have two sorts of mass - inertial and gravitational. There is no explanation for why they are the same.

The whole point of the equivalence principle is to assume that inertial mass and gravitational mass are fundamentally related, and that the equivalence between gravitational mass and inertial mass is not an accident.

That's the broad picture, the quibbling about the details is missing the point, rather like being unable to see the forest for the trees.

I've personally become somewhat jaundiced about arguing with people with an axe to grind against relativity. I've found it much more useful to talk to people who are actually interested in learning the theory.

 

[LightStorm]

You're wrong. The definition of the principle states that general relativity reduces to special relativity locally, ie in an arbitrarily small region of spacetime.

LS: What is wrong with the definition that I posted?

In this case, they specify that the frame is in a uniform gravitational field where the intensity of the gravity field is the same at every point. This is physically unrealistic,

LS: My point exactly. There are no uniform gravitational fields in this universe. To claim gravity and acceleration are equivalent is unrealistic. Any observer in any given reference frame can distinguish between the effects of real gravity and uniform acceleration.

I don't deny that gravitational and inertial mass are equivalent. All I'm sayng is an observer can observe/tell/measure/distinguish between the effects of gravity and uniform acceleration. If you ask me how, all it takes is a sensitive weight measuring device. The more precise the device the more easy it is to tell the difference between an accelerating frame and a frame in a real gravity field.

 

[LightStorm]

do you know what would be the nature of the gravitational field created by a hypothetical infinite plane of mass?

LS: Infinite plane of mass? Hehehe I don't know. I am not sure how to deal with an infinite quantity. Everything is infinity is guess. I don't know what the nature of the field would be.

But it is an observed fact that at least in this universe gravity is a gradient and is never uniform in any given reference frame.

you are citing the different strengths of the gravitational field in such a geometry as your "proof" that the EP is wrong.

LS: I am citing something that is true. The field is not uniform in this universe.

so i changed the geometry to one where the strength of the graviational field does not change with distance.

LS: In this universe it has been observed that gravitational field does change with distance.

then, no matter how sensitive your instruments, you would not be able to tell the difference, because there would be no difference. EP lives.

LS: In this universe gravity is a gradient. Maybe your argument would hold in a different universe where infinite quantities rule. Not in this universe.

 

[jtbell]

It seems to me that you are merely arguing against the imprecise statements of the equivalence principle that appear in pop-sci books and even some introductory physics textbooks. Nobody here disputes that gravitation has effects (e.g. tidal effects) that cannot be mimicked by accelerated reference frames. A precise statement of the equivalence principle such as the ones JesseM quoted, allows for those effects.

 

[rbj]

do you know what would be the nature of the gravitational field created by a hypothetical infinite plane of mass?

You'd better tell him, I doubt he realizes that the gravitational field at the axis of a large disk does not vary with height until the height is >> radius.

i'm not going to bother. the guy certainly has not had 2 semesters of physics (or, if he has, he hasn't brought away from it what he should have been exposed to).

This makes the gravitational field of such a disk essentially constant. It also means that "real" gravitational fields from such a disk do mimic the gravitational fields of an accelerating rocket, including the fact that losely speaking, gravity doesn't change with height. (I'm cutting a few corners here, deliberately, considering my best guess of Lighstorm's level of physics understanding, but I'm not cutting any corners when I say that the gravitational field / metric of a large plane is identical to that of an accelerating spaceship).

but LS doesn't care. he has his instruments of infinite precision and can detect the difference in graviational field from a finite disk (or planet), no matter what the finite size. he has already convinced himself that he's smarter than Einstein and, say, the thousands of physicists that understand and affirm SR and GR.

It is simply physically difficult (though not impossible in principle) to build a large enough disk to mimic the field configuration (including invariance with height) of a rocket - not impossible as Lighstorm seems to think.

But the whole objection was really poorly motivated in the first place, it was basically missing the point.

that's what i was saying. he misses the point. he blames this discrepency of geometry on physical principle (thus giving him an excuse to reject the physical principle) and when i take that discrepency away (by introducing a hypothetical gravitational field one would get from an infinite plane of mass) he doesn't get it. we've seen kooks like that around other times and places.

In Newtonian physics, we have two sorts of mass - inertial and gravitational. There is no explanation for why they are the same.

The whole point of the equivalence principle is to assume that inertial mass and gravitational mass are fundamentally related, and that the equivalence between gravitational mass and inertial mass is not an accident.

That's the broad picture, the quibbling about the details is missing the point, rather like being unable to see the forest for the trees.

I've personally become somewhat jaundiced about arguing with people with an axe to grind against relativity. I've found it much more useful to talk to people who are actually interested in learning the theory.

i think i am there, too.

 

[Mike2]

The differences between Unruh radiation and Hawking radiation near a BH in effect may be considered an EP violation; i.e., the Unruh radiation from acceleration will appear different from that of Hawking rad. due to a gravitational field. So you were on the right track if you were trying to look for an apparent EP violation here.
Creator

As I recall, you also confirmed my suspicion that the expansion of the universe was also an acceleration that had an Unruh particle creation effect to it. I wonder if this is the mechanism of particle creation during inflation, nevermind Higgs particles.

Anyway, if there is this Unruh radiation/ particle creation due to the expansion of the universe, then I have to wonder at that point how does one calculate the Unruh temperature? For every point of space is accelerating differently with respect to different distances. So do all the different accelerations/temperatures calculated from all the different reference points all add up? And would this temperature from expansion then result in a energy density equivalent to the cosmological constant? Thanks.

 

[JesseM]

LS: What is wrong with the definition that I posted?

It's not wrong, it's just too specific to qualify as a general definition of the equivalence principle--it only deals with the case of a uniform gravitational field. The two definitions I posted work for arbitrary gravitational fields--do you think anything is wrong with those definitions?

In this case, they specify that the frame is in a uniform gravitational field where the intensity of the gravity field is the same at every point. This is physically unrealistic,

LS: My point exactly. There are no uniform gravitational fields in this universe. To claim gravity and acceleration are equivalent is unrealistic.

Not if you use the more general definitions I provided, which don't require the gravitational field to be uniform.

 

[LightStorm]

the guy certainly has not had 2 semesters of physics (or, if he has, he hasn't brought away from it what he should have been exposed to).

LS: You are right. I am a student. Starting to learn a few things these days.

he has his instruments of infinite precision

LS: I have read sites that claim the principle has been verified to very high levels of accuracy and precision. Like this one here:

http://www.absoluteastronomy.com/reference/equivalence_principle

difference is less than 1 part in a trillion (trillion: The number that is represented as a one followed by 12 zeros) (most accurate to date)​

If I use a weight measuring device that can be accurate enough to identify a difference of 1 part in a trillion, surely every observer can tell/observe/distinguish between the effects of a real field and uniform acceleration.

he has already convinced himself that he's smarter than Einstein and, say, the thousands of physicists that understand and affirm SR and GR.

LS: You are making stuff up.

he misses the point. he blames this discrepency of geometry on physical principle (thus giving him an excuse to reject the physical principle)

LS: I have a valid thought experiment as an excuse which can be verified experimentally. You are blaming the universe for having only non-uniform gravitational fields. You can't have everything your way. This universe has NO uniform gravitational fields. Period.

and when i take that discrepency away (by introducing a hypothetical gravitational field one would get from an infinite plane of mass) he doesn't get it.

LS: This universe has no uniform gravitational fields and you don't get it.

 

[LightStorm]

It's not wrong, it's just too specific to qualify as a general definition of the equivalence principle--it only deals with the case of a uniform gravitational field.

LS: That is the correct definition because it doesn't use ciruclar logic.

The two definitions I posted work for arbitrary gravitational fields--do you think anything is wrong with those definitions?

LS: Yes they use circular logic.

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

In logic, begging the question is the term for a type of fallacy occurring in deductive reasoning in which the proposition to be proved is assumed implicitly or explicitly in one of the premises. For an example of this, consider the following argument: "Politicians cannot be trusted. Only an untrustworthy person would run for office; the fact that politicians are untrustworthy is proof of this. Therefore politicians cannot be trusted." Such an argument is fallacious, because it relies upon its own proposition, in this case, "politicians are untrustworthy", in order to support its central premise. Essentially, the argument assumes that its central point is already proven, and uses this in support of itself; the question remains, "begging" to be answered.

Begging the question is also known as petitio principii, and is related to the fallacy known as circular argument, circulus in probando, vicious circle or circular reasoning.​

Not if you use the more general definitions I provided, which don't require the gravitational field to be uniform.

LS: See above.

I don't deny that gravitational mass and inertial mass are equivalent. This equivalence is the reason why all objects on this planet free fall at the same rate. (Newtonian Equivalence.)

All objects of differing masses fall at the same rate droppped from a given height and touch down simultaneously regardless of the size of the reference frame on this earth. And this has been verified. This is Newtonian Equivalence.

Newtonain equivalence works for all sized reference frames, from the really small to the reall really big. It works for a small tower or a really really big tower. The objects always touch down simultaneously. There are no reference frames on this Earth where Newtonain equivalence becomes invalid.

But Einstein's equivalence is unrealistic. It not only claims the entire reference frames are equivalent but also includes the various experiments performed in it. And this is not true as seen in my thought experiment.

 

[HallsofIvy]

We're still waiting!

 

[rbj]

the guy certainly has not had 2 semesters of physics (or, if he has, he hasn't brought away from it what he should have been exposed to).

LS: You are right. I am a student. Starting to learn a few things these days.

well 35 years ago when i was taking my first Drivers Ed. class, about the first thing the teacher said to the class was that "the first mistake of a bad driver is thinking he's a good driver."

if you're a student, you need to position yourself to learn or it's all for naught.

LS: I have a valid thought experiment as an excuse which can be verified experimentally. You are blaming the universe for having only non-uniform gravitational fields. You can't have everything your way. This universe has NO uniform gravitational fields. Period.

"Period." is indicative of an unwillingness to learn anything. you have all of the answers and no need to open your mind.

i am not blaming the universe for anything. the premise of the Einsteinian ER thought experiment is that of comparing a stationary room in a uniform graviational field to an identical room, in free space, constantly accelerated by the same amount as the (uniform) acceleration of gravity. it also compares the room free falling with gravity to one that is unaccelerated in free space unaffected by any gravity. (gasp! LS says that no such place exists!)

you think that some instruments with 12 significant digits (as an engineer, i have my doubts that any such instrument exists - there is no A/D converter with 40 meaningful bits of data) can measure the difference in pull between the floor of a room and the ceiling 3 meters above it here on this planet Earth? have you done the math to check it out? can you do the math? (show us that you can do the math.) is the gravitational field ostensibly non-uniform or ostensibly uniform in this room on the Earth with 3 meters between the floor and the ceiling?

LS: This universe has no uniform gravitational fields ...

how do you know? the universe is a pretty big place, have you been to or looked everywhere in the universe to confirm your blanket assertion? can there be no place in the universe with such a geometry of mass so that in a finite volume the gravitational field is uniform? the onus is on you to prove that.

... and you don't get it.

so said Pharoah to Moses (or was it the other way around)?

 

[LightStorm]

"the first mistake of a bad driver is thinking he's a good driver."

LS: I am not a bad driver. Therefore the first mistake I make cannot be the one that you stated. Hence my first statement: "I am not a bad driver" stands. You see circular logic there? That is exactly how you're defending EP. Your first assumption is: EP is right. Therefore one should not perform any experiments that invalidate EP. If someone tried to perform such an expeirment, limit the size of the reference frame to 3 meters and then question the accuracy of the instruments involved in the reference frame as if the inaccuracy of the instruments is proof that EP is right. LOL!

You don't find that funny? I do!

Keep in mind, Newtonian equivalence works for all towers. From 3 meters to 100 meters. The problem is Einstein's equivalence doesn't work for all towers. Whose fault is it, mine?

if you're a student, you need to position yourself to learn or it's all for naught.

LS: Every student has the right to question dubious principles, particularly the ones that involve circular logic.

"Period." is indicative of an unwillingness to learn anything.

LS: Gee you jump to conclusions or what. I meant to indicate that gravitational fields in this universe are NOT uniform.

you have all of the answers and no need to open your mind.

LS: You're good at making stuff up.

i am not blaming the universe for anything.

Your first assumption is "EP cannot be wrong". Therefore if an experiment finds it wrong, you can either modify EP or modify the universe. Because your first assumption cannot be wrong, the only option you're left with is to modify the universe by introducing infinite quantities. You think the universe is at fault and not the principle for having uniform graivity fields.

there is no A/D converter with 40 meaningful bits of data) can measure the difference in pull between the floor of a room and the ceiling 3 meters above it here on this planet Earth?

A 3 meter tower is all I get to work with huh? Why can't I get the tallest building in the world? Why, relativity is afraid of tall buildings or something? Afraid of heights, maybe?

Or maybe you think that EP works only for a reference frame that has a height of 3 meters? Is that the standard operating reference frame? A 3 meter tower and boast the accuracy to 1 part in a trillion?

When I ask for a 20 meter tower (or taller, like the one that Galileo used) I won't get it because I may invalidate the principle, right? Dont you think a principle that works for a 3 meter tower must also work for all kinds of towers. You know this one clearly doesnt. Why doesn't this work? Maybe there is a chance it could be wrong?

how do you know? the universe is a pretty big place, have you been to or looked everywhere in the universe to confirm your blanket assertion?

LS: How do you know that the speed of light is only 300000 km/sec? Did Einstein look everywhere in the universe to confirm this blanket assertion?

can there be no place in the universe with such a geometry of mass so that in a finite volume the gravitational field is uniform?

LS: Can there be no place in the universe where the speed of light is only 10000 km/sec?

the onus is on you to prove that.

LS: Yea right. Whose onus is to prove that the speed of light is c in every corner of the universe? Did Einstein travel at 0.8c when he wrote relativity? How did you believe him when he never traveled at 0.8c? Oh wait, space-time curves right? Why does it curve and what is it made of? If you know it curves, you must know what it is made of too right? Onus? LOL! Forget Onus.