Edit by Pete - this thread is a sidetrack from zanket's (Alpha) General relativity is self-inconsistent thread. I think that it's collected enough discussion that it's worth a thread of its own. Let me know if you think this is bad moderation. - end edit

Sorry to butt in, but: You can't have a proper gravitational field without those "tidal forces" Pete. If you did, then in that frame, things wouldn't fall down, and that includes your frame. Yes c is always measured at 300,000km/s, but it has to be a larger 300,000km/s at the top of the frame than at the bottom. That inertial frame is a contradiction in terms here. You can see this intuitively just looking at your picture. There's just no way you can get to that line and keep the diamonds the same shape. Yes, you can say your frame is very small, but you are still accelerating, so there is a gradient across your frame. Approximating it away to zero is the cause of all the problems. Einstein knew this. The principle that got him started isn't quite right. But it's been muzzed over the years. And Zanket makes too big a deal of it, IMHO it doesn't invalidate General Relativity, it just pushes us towards a new interpretation. Which actually is more like Einstein's.

http://casa.colorado.edu/~ajsh/st0.gif

Yes, you can say your frame is very small, but you are still accelerating, so there is a gradient across your frame. Approximating it away to zero is the cause of all the problems. Einstein knew this.
I put it a little differently: A tidal force indicates differences in acceleration in different parts of a frame. If all parts of a frame accelerate exactly identically, the frame is perfectly inertial and the spacetime in the frame is perfectly flat. But there is a gravitational acceleration gradient (a tidal force, or a curvature of spacetime) in any nonzero-sized frame in our gravity-endowed universe. And Einstein, Taylor, Thorne and Wheeler are all in agreement that an inertial frame need not be zero-sized. That is, what we call an inertial frame need not be perfectly inertial and the spacetime in the frame need not be perfectly flat. If an inertial frame had to be zero-sized, we could not experimentally test special relativity to any precision.

I put it a little differently: A tidal force indicates differences in acceleration in different parts of a frame. If all parts of a frame accelerate exactly identically, the frame is perfectly inertial and the spacetime in the frame is perfectly flat. But there is a gravitational acceleration gradient (a tidal force, or a curvature of spacetime) in any nonzero-sized frame in our gravity-endowed universe. And Einstein, Taylor, Thorne and Wheeler are all in agreement that an inertial frame need not be zero-sized. That is, what we call an inertial frame need not be perfectly inertial and the spacetime in the frame need not be perfectly flat. If an inertial frame had to be zero-sized, we could not experimentally test special relativity to any precision.

Not when it came to a "proper" gravitational field they didn't. You're approximating away the very cause of the acceleration. It's like taking the gradient in the rubber-sheet analogy and pronouncing that this small part of it has no gradient, then arguing about the mysteries of gravity.

Hi Farsight,
zanket is approximating away the curvature of the rubber sheet, not its slope. He's rightly saying that a small section of a rubber sheet deformed by a bowling ball is essentially the same as a small section of a large rubber sheet that is tilted at an angle but not deformed.

Pete: We know that the rubber sheet analogy is wrong because it uses gravity to give us a picture of gravity. So we use it with caution. But it is still useful. When we talk about gravity as "curved spacetime", we can look back at the rubber sheet to see that it isn't the curvature of the rubber sheet at that location that causes the marble to accelerate towards the bowling ball. It's the gradient at that location. At any location in our "gravitational field", no matter how small, there is a gradient. This gradient extends across the reference frame. Something at the top of the frame is different to something at the bottom of the frame, and that's why the frame accelerates. If you try to say everything in the frame is uniform, you're removing this crucial factor. You are effectively talking about a "flat" gravitational field where things don't fall down. IMHO the gradient is the "curved spacetime", not the change in the gradient, and not the curve in the rubber sheet.

Not when it came to a "proper" gravitational field they didn't. You're approximating away the very cause of the acceleration. It's like taking the gradient in the rubber-sheet analogy and pronouncing that this small part of it has no gradient, then arguing about the mysteries of gravity.
I agreed with you that there is a gradient in any nonzero-sized frame.

At any location in our "gravitational field", no matter how small, there is a gradient. This gradient extends across the reference frame. Something at the top of the frame is different to something at the bottom of the frame, and that's why the frame accelerates.
Yes, in any nonzero-sized frame, there is a gradient in the local gravitational acceleration. The local gravitational acceleration g varies in the frame. It changes from the top to the bottom of the frame, relative to a source of gravitational attraction.

IMHO the gradient is the "curved spacetime", ...
I agree. The supporting info in the OP notes that spacetime curvature is synonymous with the tidal force. A tidal force indicates a gradient of g. A tidal force is the indicator of gravity, of spacetime curvature. A gradient is a measure of change in something; in this case it's the change in g.

One thing I see differently than you: Things can start falling even in a zero-sized frame in which there's no tidal force (no gradient of g). Things fall by default in our universe, due to the fact that g is positive everywhere (our universe is gravity-endowed everywhere). Things fall unless they are prevented from falling. When you hold an apple, you are preventing it from falling, by nongravitationally (noninertially) accelerating it against the tide of gravity. When you release it, no gradient of g is required to start it falling. Rather, the apple no longer accelerates upward like you continue to do. Einstein thought likewise. Let a rocket run its engine to accelerate at a constant 1 Earth g (as the crew feels) in an idealized, gravity-free universe. An apple dropped in the rocket will fall almost like it does on Earth, even though there's no gradient of g in the rocket. The only difference will be that the apple's rate of acceleration won't change as it falls, like it slightly does on Earth.

Pete: We know that the rubber sheet analogy is wrong because it uses gravity to give us a picture of gravity. So we use it with caution. But it is still useful. When we talk about gravity as "curved spacetime", we can look back at the rubber sheet to see that it isn't the curvature of the rubber sheet at that location that causes the marble to accelerate towards the bowling ball. It's the gradient at that location. At any location in our "gravitational field", no matter how small, there is a gradient. This gradient extends across the reference frame. Something at the top of the frame is different to something at the bottom of the frame, and that's why the frame accelerates. If you try to say everything in the frame is uniform, you're removing this crucial factor. You are effectively talking about a "flat" gravitational field where things don't fall down. IMHO the gradient is the "curved spacetime", not the change in the gradient, and not the curve in the rubber sheet.

Hi Farsight,
It is easy to describe a flat spacetime with uniform and non-zero gravity throughout - think about a reference frame undergoing constant acceleration through flat space. In that frame, there is a constant and uniform gravity field pervading the entire Universe.

This is the whole point of the equivalence principle - there is no physical difference a gravity field produced by mass and the apparent gravity produced by accelerating reference frame.

Curved spacetime is only a factor when the gravity field is not constant. The curvature of spacetime describes changes in gravity - ie tidal forces.

In the rubber sheet analogy, it doesn't directly describe the "slope" of spacetime (which is arbitrary, and can be altered by changing your frame of reference), it describes changes in that slope.


Be careful with terminology... we need to be clear what we mean when we say "gradient" - the rate of change in the gravitational field strength, or the strength of the gravitation field.

Hi Farsight,

It is easy to describe a flat spacetime with uniform and non-zero gravity throughout - think about a reference frame undergoing constant acceleration through flat space. In that frame, there is a constant and uniform gravity field pervading the entire Universe.

This is the whole point of the equivalence principle - there is no physical difference a gravity field produced by mass and the apparent gravity produced by accelerating reference frame.

Curved spacetime is only a factor when the gravity field is not constant. The curvature of spacetime describes changes in gravity - ie tidal forces.

In the rubber sheet analogy, it doesn't directly describe the "slope" of spacetime (which is arbitrary, and can be altered by changing your frame of reference), it describes changes in that slope.

Be careful with terminology... we need to be clear what we mean when we say "gradient" - the rate of change in the gravitational field strength, or the strength of the gravitation field.

I have to say that IMHO the equivalence principle that started Einstein thinking about GR actually doesn't hold when it comes to "proper" gravity. I'm rather an Einstein fan and don't like to be seen to be critical, but there's an important subtlety here. If you haven't already, do read this essay by Pete Brown. That said, I've probably said enough for the time being, so I'll leave it there for now.

http://xxx.lanl.gov/abs/physics/0204044

I agreed with you that there is a gradient in any nonzero-sized frame... Yes, in any nonzero-sized frame, there is a gradient in the local gravitational acceleration... I agree. The supporting info in the OP notes that spacetime curvature is synonymous with the tidal force...

All points of agreement noted Zanket.

One thing I see differently than you: Things can start falling even in a zero-sized frame in which there's no tidal force (no gradient of g). Things fall by default in our universe, due to the fact that g is positive everywhere (our universe is gravity-endowed everywhere). Things fall unless they are prevented from falling. When you hold an apple, you are preventing it from falling, by nongravitationally (noninertially) accelerating it against the tide of gravity. When you release it, no gradient of g is required to start it falling. Rather, the apple no longer accelerates upward like you continue to do. Einstein thought likewise. Let a rocket run its engine to accelerate at a constant 1 Earth g (as the crew feels) in an idealized, gravity-free universe. An apple dropped in the rocket will fall almost like it does on Earth, even though there's no gradient of g in the rocket. The only difference will be that the apple's rate of acceleration won't change as it falls, like it slightly does on Earth.

Sorry Zanket, IMHO the above is wrong. A zero-sized frame is not a useful concept for grasping what's going on. Things do not have zero size, and unless you believe in magical mysterious undetectable action-at-a-distance, there has to be something there to cause that acceleration, even across the jittering width of an electron. Yes, our Universe is gravity-endowed everywhere, but "the g" is the gradient. If there was no gradient, there's nothing to make things "fall", they would continue in dead straight lines. My mental model here is described in GRAVITY EXPLAINED, see thread. In essence it's a slight variation in the impedance, or permittivity, of space which can be likened to an extended tension gradient that counters localised mass/energy stress. It means Gravity is not technically a force, and the kinetic energy of a falling body actually comes from a reduced c. Please do study it, I'd be grateful for any feedback you can offer.

Yes, our Universe is gravity-endowed everywhere, but "the g" is the gradient.
A gradient is by definition a measure of change. What changes with g? It's a constant. Or are you thinking of the alternative definition, like a grade (a slope)?

No problem re the sidetrack Pete.

Zanket: see above. IMHO it's a slight variation in the impedance, or permittivity, of space. What changes is c.

Let's say you're sitting at your desk. You pick up a pencil. You let go, and it falls clattering on to the wooden surface. That's because there's gravity there. You walk to the window and look at the Moon in its orbit, because of gravity. Or the next morning the sun rises, and you are reminded that the earth orbits the sun. Because of gravity. Or you gaze through a powerful telescope at a spiral galaxy, rotating as a whole because of gravity. Or you see galaxies colliding, because of gravity. The world is full of gravity, it is everywhere. And wherever there is gravity, there is some form of gradient, or curvature, or whatever you decide to call it, and it's local, within the frame, across the frame. And if it wasn't there there wouldn't be any acceleration.

There are no inertial reference frames. They are mathematical idealism, like point particles. In the real world they have zero size. And zero consequence. Einstein worked this out a hundred years ago.

But here we still are.

Hi Farsight,
The curvature of spacetime is the change in the gravity field, not the gravity field itself. Your argument is based on a misunderstanding of the terminology.

Pete,
It is easy to describe a flat spacetime with uniform and non-zero gravity throughout - think about a reference frame undergoing constant acceleration through flat space. In that frame, there is a constant and uniform gravity field pervading the entire Universe.
That is incorrect, Pete. You have described a force due to acceleration, not a uniform gravitational field. That force is completely local to the accelerating body only and unidirectional, it does not prevade the universe. No particle not directly contained within the accelerating body will be affected by your 'uniform gravity field'.
This is the whole point of the equivalence principle - there is no physical difference a gravity field produced by mass and the apparent gravity produced by accelerating reference frame.
Of course there are differences. (1) There is no gradient in the strength of the acceleration force between the lowest point and the highest point even if the accelerating ship is one mile long. Gravitational fields follow the inverse square rule of decreasing potential. (2) Proven by experiment, acceleration does not slow atomic clocks, regardless of the g-forces involved. Gravitational fields slow atomic clocks according to the gravitational potential at specific locations. Atomic clocks in freefalling frames that feel no acceleration will still slow as the move lower in the gravitational field. (3) A rocket accelerating at a constant one g above the event horizon of a stellar-sized black hole will eventually be torn apart by tidal forces as it is drawn closer to the event horizon. The rocket will be 'stretched' in all frames of reference, including the rockets own frame of reference. A rocket accelerating at one g in a void will experience no tidal forces, but will be 'seen' to contract, not stretch, by an inertial observer relatively stationary wrt the accelerating rocket as the relative velocity nears 'c'.
Hi Farsight,
The curvature of spacetime is the change in the gravity field, not the gravity field itself. Your argument is based on a misunderstanding of the terminology.

You will have to explain your logic here, Pete. General Relativity is a geometric theory, consisting of geodisics (straight lines in curved spacetime). Curved spacetime models the gravity field itself, not just the tidal forces. Tidal forces cannot curve the path of a photon moving through a gravitational field. Tidal forces are directional. Please answer this question Pete, or BenTheMan. Does the orientation of an atomic clock near the event horizon of a stellar size black hole affect the rate at which the clock beats?

And why do u all believe that space can be bend ?

Here is the explanation that Janus58 gave
http://sciforums.com/showpost.php?p=1334458&postcount=179

But he didnt care to answer the next question

Curved spacetime is a model, Singularity. Remember Newton's law that states that a body stationary in the vacuum will remain stationary unless acted upon by a force? It also says that a body moving through the vacuum will continue to move in a straight line, and at the same velocity, unless acted upon by a force. Now, what happens when a body is orbiting another body? It 'feels' no force, it is in gravitational freefall (some laymen refer to this as weightlessness), but it does not move in a straight line according to a distant observer. From the point of view of an observer onboard the orbiting body, she can assume she is moving in a straight line because she can feel no force to change her trajectory. She is moving in a straight line through curved spacetime, following the 'curvature' of spacetime.

Pete,

That is incorrect, Pete. You have described a force due to acceleration, not a uniform gravitational field.
The eqiuvalence principle says it's precisely the same thing.
That force is completely local to the accelerating body only and unidirectional, it does not prevade the universe. No particle not directly contained within the accelerating body will be affected by your 'uniform gravity field'.
It's a reference frame that I specified as accelerating, 2inq, not a particle.
In that frame of reference, every particle in freefall will be accelerating. In that frame, there is a frame force that pervades the universe. This force is precisely as real as gravitational force.

Of course there are differences. (1) There is no gradient in the strength of the acceleration force between the lowest point and the highest point even if the accelerating ship is one mile long. Gravitational fields follow the inverse square rule of decreasing potential.
You are correct. I should have said that there is no local difference, or that there is no difference between a uniform gravity field produced by a distant body and the apparent gravity in an accelerating frame.

(2) Proven by experiment, acceleration does not slow atomic clocks, regardless of the g-forces involved. Gravitational fields slow atomic clocks according to the gravitational potential at specific locations. Atomic clocks in freefalling frames that feel no acceleration will still slow as the move lower in the gravitational field.
I think you've read a summary of that result without bothering about the details, resulting in a common misunderstanding (http://van.physics.uiuc.edu/qa/listing.php?id=1360).

(3) A rocket accelerating at a constant one g above the event horizon of a stellar-sized black hole will eventually be torn apart by tidal forces as it is drawn closer to the event horizon. The rocket will be 'stretched' in all frames of reference, including the rockets own frame of reference.
Correct - tidal forces are real. They are not frame forces like gravity is.

You will have to explain your logic here, Pete. General Relativity is a geometric theory, consisting of geodisics (straight lines in curved spacetime). Curved spacetime models the gravity field itself, not just the tidal forces.
The gravity field is completely arbitrary - a simple choice of reference frame. In a free-fall reference frame, there is no gravity field.

Tidal forces cannot curve the path of a photon moving through a gravitational field.
I'm not sure about that... but I do know choosing an accelerating reference frame can curve the path of a photon just as gravity can.

Please answer this question Pete, or BenTheMan. Does the orientation of an atomic clock near the event horizon of a stellar size black hole affect the rate at which the clock beats?
I don't know.

“ (2) Proven by experiment, acceleration does not slow atomic clocks, regardless of the g-forces involved. Gravitational fields slow atomic clocks according to the gravitational potential at specific locations. Atomic clocks in freefalling frames that feel no acceleration will still slow as the move lower in the gravitational field. ”

I think you've read a summary of that result without bothering about the details, resulting in a common misunderstanding.
And what do you believe is my 'common misunderstanding', Pete?? Your link was in complete agreement with what I stated.
Correct - tidal forces are real. They are not frame forces like gravity is.
You've lost me here, Pete. Gravity is not modelled as a force in General Relativity, in any frame, but as an acceleration. The 'force' is provided by the surface of the Earth, for example, resisting the acceleration. Are you stating this resistance to acceleration is frame dependent?

Now will anyone explain how length contraction was discovered.

2inquisitive: I find your posts immensely refreshing. Curved spacetime is a model. Yes! Gravity is not a force? Hurrah!

Pete: the terminology is the problem. If there were no problems with the words we use, we'd all have a crystal clear understand and wouldn't need to talk about it. Let me illustrate:

You're sitting there at your desk, and I snap my fingers. Snap, now you're wearing a spacesuit. Snap, now you're in deep space looking at the galaxies. Snap, now you're a million miles long. No wider, just longer. Snap, now there's a planet a mile under your feet. Feel that tidal force? Snap, no that wasn't your legs, instead you're back at your desk and everything's back how it was.

When you felt that "tidal force" stretching you, what you felt was the gravity of the planet. But there was no tidal force in your frame. Your head was in one frame, and your feet were in another. You were being stretched across the two different frames. If you'd have been falling into a black hole, it would have been getting worse and worse and worse.

That's why the "inertial reference frame" in a gravity situation has to have a zero size, and zero consequence. When you talk about the tidal force within a frame, it's a contradiction in terms. The gravity is the continuous frame-change.

I dislike "reference frames". They have no actual existence, and I rather think they blinker us when we try to look at the world and understand how it works. That's why I don't talk about them much, and why I think of gravity as continuous change in permittivity.

Singularity: look up George Fitzgerald. http://en.wikipedia.org/wiki/George_FitzGerald

All: Sorry to be a nag, I'd be really grateful if anybody could study these essays and give me some sincere feedback. I've deliberately set out to make them accessible to the layman, so there's pretty pictures but no real mathematics. I find it difficult to include mathematics anyway, because I'm examining axioms - the assumptions we rather take for granted. It's merely a toy model, but it all seems to "fit", and it seems to "fly". Please can you try to shoot it down, but with careful reasoning and logic around the details rather than axiomatic rebuttal. The last essay is GRAVITY EXPLAINED, but you need to read them in sequence. I will be writing more, but would feel more comfortable with some validation.

RELATIVITY+ (http://www.sciforums.com/showthread.php?t=64240)

And what do you believe is my 'common misunderstanding', Pete?? Your link was in complete agreement with what I stated.
Your mistake is in confusing accelerating objects with accelerating reference frames.

Atomic clocks in freefalling frames that feel no acceleration will still slow as the move lower in the gravitational field.
In an accelerating frame far from all masses, clocks in freefall that feel no acceleration will slow as they move lower in the apparent gravity field.
Any instance that you can describe regarding clocks in uniform gravity fields, I can give you a corresponding instance describing clocks in an accelerating frame of reference.

You've lost me here, Pete. Gravity is not modelled as a force in General Relativity, in any frame, but as an acceleration. The 'force' is provided by the surface of the Earth, for example, resisting the acceleration. Are you stating this resistance to acceleration is frame dependent?
In GR, a uniform gravity field is a pseudo-force, just like centrifugal force and the apparent gravity in an accelerating frame.

The force that Earth applies to a rock is not frame dependent, but the rock's motion is:
In a free-fall frame, the rock is accelerating upward. The force making it accelerate is the Earth pushing on it.
In the rock's rest frame, it has two forces applied: gravity (a frame force), and the force applied by the Earth, with a net force of zero.

When you felt that "tidal force" stretching you, what you felt was the gravity of the planet. But there was no tidal force in your frame. Your head was in one frame, and your feet were in another. You were being stretched across the two different frames.
"My frame" is the frame in which I'm at rest... and in that frame, there are certainly tidal forces.
If you want to limit yourself to inertial frames, then yes, my different parts are in different inertial frames. The whole point of GR is that no inertial frame in a gravitational field can have more than zero size... and it gives us other tools to describe what happens.

That's why the "inertial reference frame" in a gravity situation has to have a zero size, and zero consequence.
Nice sound bite, but of zero consequence.

When you talk about the tidal force within a frame, it's a contradiction in terms. The gravity is the continuous frame-change.
So you say.... but your example suggests that the tidal force is the frame change, not the gravity.

I dislike "reference frames". They have no actual existence, and I rather think they blinker us when we try to look at the world and understand how it works.
They're a tool. A necessary tool that you use all the time whether you realise it or not. Whenever you describe where something is, when something happens, or how fast and in what direction something is going, you have to use some reference frame, either explicitly or implicitly. It's impossible to communicate those things otherwise.

They're a tool worth learning to use. If you feel blinkered by them, perhaps it means you haven't learned to use them well enough.

Thanks FarSight.

Amazing guys here, they dont even know what they all are talking about. They have no idea how space bending was proved and yet shamelessly chat about it as if its real.

Its time for the women to take control it seems from these testosterone driven ego boasting male maniacs.

Science is still struck in 1889 it seems.

Pete: Maybe. I won't know until I get detailed feedback. Can you give me some on this post?

Imagine yourself back in space. You're a million miles long and there's a planet a mile under your feet. No, let's make it a small black hole. You feel a "tidal force" pulling along your length. This "tidal force" is there because your head is in a reference frame that's almost inertial. For simplicity let's say it's completely inertial and your head is "at rest". Your feet however are in a reference frame that's emphatically non-inertial. You span different "frames". If your feet were in the same sort of "at rest" frame as your head, you wouldn't feel any tidal force, you wouldn't experience any gravity, and you wouldn't fall down.

In a gravity situation, inertial reference frames have zero size. Are we agreed on that? It's the same with non-inertial reference frames. They have zero size too because there are no uniform gravitational fields. You are not in a "frame" with a "tidal force" across it. You aren't at rest. You're falling, faster and faster. You're accelerating, and the acceleration is getting bigger and bigger. The "tidal force" is getting bigger and bigger. And all these things are there because something isn't uniform across this block of zero-sized frames that you're calling "your frame". You can tell you're not in some accelerating capsule, because the tidal force is growing so strong you're turning into spaghetti. You can feel why "proper" gravity really isn't equivalent to constant acceleration.

Snap! Back to normal, back at your desk. Yes, the Principle of Equivalence is the idea that gave Einstein his idea for GR, but it actually doesn't hold for proper gravity. Einstein knew this. It doesn't mean General Relativity is wrong, just the current interpretation, or the way its taught, or presented to laymen, I'm not quite sure. But every time I see uniform gravitational field, whap, up comes a flag.

Ow, Singularity, that's shouting. It's bad manners. And I'm afraid I'm something of a testosterone-driven ego boasting male maniac myself! :) Seriously though, it's just a matter of interpretation, and digging down past the postulates and working out why they hold and what they really mean.

Ow, Singularity, that's shouting. It's bad manners. And I'm afraid I'm something of a testosterone-driven ego boasting male maniac myself! :) Seriously though, it's just a matter of interpretation, and digging down past the postulates and working out why they hold and what they really mean.

If this is shouting then why dont SCIFORUMS remove the SIZE 7 option ?

Well I Know it, they are humans.

Mr. PETE if u cant respect freedom of expression then get off this forum.

Just shoo away, ok. Specially since u dont know why u should believe in length contraction:puke:

Is all this weirdness, PETE ?

If this is shouting then why dont SCIFORUMS remove the SIZE 7 option ?
Size 7 is potentially useful. But it's stupid and obnoxious to use it for a complete post.

Mr. PETE if u cant respect freedom of expression then get off this forum.

Just shoo away, ok. Specially since u dont know why u should believe in length contraction
Thanks for the suggestion.

Singularity, I know that you're frustrated by what you see as the illogic of relativity, and the blindness of those who don't see it the same way, but it's not appropriate to spam other threads with your difficulties. Your posts in this thread are off-topic, and seem to be an attempt to hijack this thread into a discussion that you're already having or have already had in another thread. Please try not to do that again.

Imagine yourself back in space. You're a million miles long and there's a planet a mile under your feet. No, let's make it a small black hole. You feel a "tidal force" pulling along your length. This "tidal force" is there because your head is in a reference frame that's almost inertial. For simplicity let's say it's completely inertial and your head is "at rest". Your feet however are in a reference frame that's emphatically non-inertial. You span different "frames". If your feet were in the same sort of "at rest" frame as your head, you wouldn't feel any tidal force, you wouldn't experience any gravity, and you wouldn't fall down.
Hi Farsight,
It doesn't follow that no tidal force means no gravity. If the gravity strength was the same at my head as my feet, I'd still fall down, right? And yet I'd feel no tidal force. The tidal force is the difference between how fast my head and my feet are falling, not the rate of fall.

In a gravity situation, inertial reference frames have zero size. Are we agreed on that?
Strictly, yes.In practice, no.

It's the same with non-inertial reference frames. They have zero size too because there are no uniform gravitational fields.
Can you explain what you mean when you say "reference frame"? You seem to mean something different to the norm.

Snap! Back to normal, back at your desk. Yes, the Principle of Equivalence is the idea that gave Einstein his idea for GR, but it actually doesn't hold for proper gravity. Einstein knew this. It doesn't mean General Relativity is wrong, just the current interpretation, or the way its taught, or presented to laymen, I'm not quite sure. But every time I see uniform gravitational field, whap, up comes a flag.

You clearly don't know the "current interpretation" of General Relativity. If GR was just the equivalence principle, there would be no need for GR.
The difference between an accelerating reference frame in flat space and a rest frame in a gravitational field is precisely what GR is for.

I'm focusing on uniform gravitational fields, because I think you need to understand the equivalence principal before you can begin to think about GR. Don't try to run before you can walk.

I don't pretend to understand GR well - but I do understand the equivalence principal, its limitations, and its applicability.

Size 7 is potentially useful. But it's stupid and obnoxious to use it for a complete post.


Thanks for the suggestion.

Singularity, I know that you're frustrated by what you see as the illogic of relativity, and the blindness of those who don't see it the same way, but it's not appropriate to spam other threads with your difficulties. Your posts in this thread are off-topic, and seem to be an attempt to hijack this thread into a discussion that you're already having or have already had in another thread. Please try not to do that again.

So in short u have no shame for your blind faith that u push as being science.

Yeah, that's it. You figured me out.

Hi Farsight, It doesn't follow that no tidal force means no gravity. If the gravity strength was the same at my head as my feet, I'd still fall down, right? And yet I'd feel no tidal force. The tidal force is the difference between how fast my head and my feet are falling, not the rate of fall.

Yes, you're right. I was trying to give a dramatic example. The tidal force would be really noticeable if you were a million miles long falling into a small black hole. But you wouldn't notice it much if you fell into a really big black hole. It comes back to the rubber sheet analogy we were talking about, where you've got the gravity down as the curvature. I said the gravity is the gradient. In my (toy) mental model the tidal force is the change in the gradient - the curvature. It all comes back to the same point that there has to be some kind of local gradient across the "frame", and this is at odds with a "uniform gravitational field", a non-zero-sized inertial reference frame in a gravity situation, and arguably a non-zero-sized non-inertial reference frame.

Can you explain what you mean when you say "reference frame"? You seem to mean something different to the norm. I think I do see things differently here. My reference frame is my viewpoint, my point of observation, I measure things from it, and in it I consider myself to be at rest. If I'm motionless with respect to say the Universe, we would agree that I'm in an inertial reference frame. If I'm accelerating, I'm in a non-inertial reference frame. Maybe the $64,000 dollar question here is: if I go from an inertial reference frame to a non-inertial reference frame, have I changed frames? The answer appears to be both yes and no.

You clearly don't know the "current interpretation" of General Relativity. If GR was just the equivalence principle, there would be no need for GR. The difference between an accelerating reference frame in flat space and a rest frame in a gravitational field is precisely what GR is for. I'm focusing on uniform gravitational fields, because I think you need to understand the equivalence principal before you can begin to think about GR. Don't try to run before you can walk. I don't pretend to understand GR well - but I do understand the equivalence principal, its limitations, and its applicability. Maybe. It's good to talk, and I need that feedback. Interestingly, I seem to recall that this started with Zanket shouting that the Principle of Equivalence was wrong so GR had to come tumbling down. I said he was both right and wrong. I seem to see quite a lot of this "shades of grey" sort of thing. Like the speed of light is constant, and yet it's not!

It comes back to the rubber sheet analogy we were talking about, where you've got the gravity down as the curvature. I said the gravity is the gradient. In my (toy) mental model the tidal force is the change in the gradient - the curvature.
Right. The pull of gravity is the gradient of the rubber sheet. The difference in pull is the curvature of the sheet.
Now, in GR, the angle of the sheet is arbitrary, a simple choice of point of view. An inertial frame of reference is one in which the sheet is locally horizontal, but any point of view is allowed.

It all comes back to the same point that there has to be some kind of local gradient across the "frame",
Well, there doesn't have to be. A flat rubber sheet is conceivable.
Most ordinary situations are for all intents and purposes, flat... for most experiments, there is no significant difference in g between the ceiling and the floor, right?

I think I do see things differently here. My reference frame is my viewpoint, my point of observation, I measure things from it, and in it I consider myself to be at rest.
You're certainly free to see things differently, but if we're using the same words to mean different things we'll run into trouble.

In the usual parlance, a reference frame is a set of potential rulers and clocks. So your reference frame is a way of defining where things are and when things happen relative to you.

If I'm motionless with respect to say the Universe, we would agree that I'm in an inertial reference frame
I'm not sure whether that's actually measurable, but that's beside the point...

We would agree that your rest frame is inertial. But it would be trivial to define a non-inertial reference frame in the same region... your rest frame isn't the only frame that you're "in".

If I'm accelerating, I'm in a non-inertial reference frame. Maybe the $64,000 dollar question here is: if I go from an inertial reference frame to a non-inertial reference frame, have I changed frames? The answer appears to be both yes and no.
We can happily define a reference frame in which you are always at rest. In this case, the frame would be inertial at times, and non-inertial at other times. We'd say that such frame is not inertial, but it has inertial regions.

We can also choose not to change our point of view when you begin accelerating. In this case, your motion changes while the frame doesn't. You were at rest, now you're accelerating.

Or, we could choose to use you're accelerating rest frame all along... In that case, we'd say that first you were accelerating, then you became motionless.

It's all a case of choosing what rulers and clocks to measure your motion against. What GR does is gives us a lot more flexibility in choosing those rulers and clocks, which is necessary precisely because the flat frames of SR don't work when the curvature of spacetime is significant.

Maybe. It's good to talk, and I need that feedback. Interestingly, I seem to recall that this started with Zanket shouting that the Principle of Equivalence was wrong so GR had to come tumbling down. I said he was both right and wrong. I seem to see quite a lot of this "shades of grey" sort of thing. Like the speed of light is constant, and yet it's not!
That's a good attitude.

Yeah, that's it. You figured me out.

Thats right, i had good respect for u but now your true nature has been revealed.

I hope your daughter teaches u a lesson or two in the near future about relativism.

I'm sorry you feel that way, Singularity.

Pete,
Your mistake is in confusing accelerating objects with accelerating reference frames.

me:
(2) Proven by experiment, acceleration does not slow atomic clocks, regardless of the g-forces involved. Gravitational fields slow atomic clocks according to the gravitational potential at specific locations. Atomic clocks in freefalling frames that feel no acceleration will still slow as the move lower in the gravitational field.
Pete,
In an accelerating frame far from all masses, clocks in freefall that feel no acceleration will slow as they move lower in the apparent gravity field.
The atomic clocks I described are not accelerating, they are in inertial motion. They 'slow' as they move lower in the gravitational potential. In your 'accelerating frame', there is no gradient in your 'apparent' gravity field and clocks do not slow as they move lower in your uniform 'pseudo'-gravity. There are also no tidal forces in your 'pseudo' field because there is no gradient in potential.
Pete,
Any instance that you can describe regarding clocks in uniform gravity fields, I can give you a corresponding instance describing clocks in an accelerating frame of reference.
I cannot describe ANY instance regarding clocks in uniform gravity fields because uniform gravity fields do not exist except at specific gravitational potentials. I CAN describe an accelerating clock in a fixed gravitational potential. It does not slow due to the acceleration. I can also describe two atomic clocks on the Earth's surface that are synchronized to beat at the same rate while in the same gravitational potential. Accelerate one clock into high Earth orbit. The clock that was accelerated will then beat faster than the one left undisturbed on Earth's surface.

Pete: I'll get back to you properly later, maybe tomorrow. It's my Wedding Anniversary today.

Right. The pull of gravity is the gradient of the rubber sheet. The difference in pull is the curvature of the sheet. Now, in GR, the angle of the sheet is arbitrary, a simple choice of point of view. An inertial frame of reference is one in which the sheet is locally horizontal, but any point of view is allowed.

I think that's the "shades of grey" Pete. I'm reminded of my recent holiday. We were coming home on the plane and I was looking out of the window at the sea, the mountains and the sky. Then I was distracted by the wife and the drinks trolley, and when I looked again I saw only sky. We were banking, accelerating in a long slow curve. I lifted a pack of cigarettes to head height and dropped them, noticing that they fell straight down into my lap rather than towards my wife's lap. My horizontal was still my horizontal, but unnoticed to me, it had changed.

Well, there doesn't have to be. A flat rubber sheet is conceivable. Most ordinary situations are for all intents and purposes, flat... for most experiments, there is no significant difference in g between the ceiling and the floor, right? Well yes, there's not much difference. But the point of what I've been saying is that it is significant. Without it there would be no gravity. Take a look at this image. It isn't ideal, but it's the best one I could find:

http://www.bized.ac.uk/images/gradient.gif

The overall curve is an analogy of your curved spacetime. If you mentally extend it over to the right it would be fairly flat. But if it really was totally flat it just wouldn't curve. When you say it's totally flat across some arbitrarily small frame you've "thrown the baby out with the bathwater" and done away with what's causing the acceleration. I don't think of gravity as some magical mysterious "action-at-a-distance" force zimming and zumming like some cartoon magnet. I don't think there's some sleeting hail of "gravitons" flying between that black hole and your body. I think that whatever it is, it's local. It's somehow in the space you're in.

You see the dots and the gradient lines at various points of the curve? Each line is akin to your "frame" at a given point in time. When you look at the gradients, from your perspective they're always flat. But your whole frame is following the curve. They look flat and horizontal to you like my horizontal in the plane looked like the same old horizontal to me.

But if I look at it all from the outside I can see that the gradient is changing. It's getting steeper. It keeps getting steeper. And there's no point on that curve where it was ever horizontal and flat. There's always some kind of gradient across your frame.

You're certainly free to see things differently, but if we're using the same words to mean different things we'll run into trouble... I know. I hope we're not, or at least not deliberately. The thing is, I'm starting to have some issues with reference frames. I've said to myself look at what's actually there, be ontological. But the frames don't actually exist, I can't see them. Yes I see the world from my frame, but it's skewing something, and I can't see the skew.

I know this is rather trivial: but think about inertial reference frames. If I'm "at rest" and you zoom by at a constant velocity, we say we're in different inertial reference frames. If I accelerate to catch you up, I've changed frames and I'm now in "your" inertial reference frame. I changed frames. If however I keep on accelerating steadily, we talk about me being in a non-inertial frame rather than constantly changing inertial frames. My view of the world is skewing skewing skewing, my rulers are contracting and my ticks are dilating, but I can't see any of it and we somehow wipe this all away and say it's my view of the world.

I want to see the world how it really is, not just how I see it.

But if I look at it all from the outside I can see that the gradient is changing. It's getting steeper. It keeps getting steeper. And there's no point on that curve where it was ever horizontal and flat. There's always some kind of gradient across your frame.
Agreed, except that "flat" to me doesn't mean "horizontal", but rather just "straight". Google for this quote by Taylor and Wheeler: “The constant, ever-present "force of gravity" that we experience on Earth is gone, eliminated as we step into a free-float frame. What remains of "gravity"? Only curvature of spacetime remains. What is this curvature? Nothing but tidal acceleration. Curvature is tidal acceleration and tidal acceleration is curvature.” The gradient you talk about is the tidal force, which is the same as spacetime curvature.

Yes, the Principle of Equivalence is the idea that gave Einstein his idea for GR, but it actually doesn't hold for proper gravity. Einstein knew this. It doesn't mean General Relativity is wrong, just the current interpretation, or the way its taught, or presented to laymen, I'm not quite sure. But every time I see uniform gravitational field, whap, up comes a flag.
After reading your posts in this thread, I see what you mean by “proper gravity”. You just mean gravity in our real, gravity-endowed universe. But look at Einstein’s statement of the equivalence principle here (http://www.sciforums.com/showpost.php?p=1304481): “In any small, freely falling reference frame anywhere in our real, gravity-endowed Universe, the laws of physics must be the same as they are in an inertial reference frame in an idealized, gravity-free universe.” You can see there that the principle explicitly applies to our real, gravity-endowed universe.

Although the equivalence principle is strictly true in our universe only for points (zero-sized regions), and the term “uniform gravitational field” strictly applies only to points in our universe, that does not mean that we should not apply the principle or the term to larger regions; Einstein was clear about that by using the word “small” rather than “point-sized”. Einstein felt that it isn’t necessary to be strictly correct, and I agree. The tidal force (= spacetime curvature) can in principle be as small as you want in a frame of any frame. Would it makes sense to deny the use of the principle to a frame in which the tidal force is 107000 times smaller than the tidal force in your room now? No. SR should predict motion in such a frame to a precision far beyond our capability of detecting a deviation between its predictions and observations. And the prime focus of physics is improving predictions of observations. By using the word “same” even for a nonzero-sized frame, Einstein implies that a negligible imprecision can be neglected. Where what constitutes “negligible” depends on the experiment.