difference between free fall and zero gravity?

[69dodge]

Ok, gravity is acceleration.

That doesn't help anyone who doesn't know what "acceleration" means.

So, what does "acceleration" mean?

If it doesn't mean "derivative of velocity", what word does mean that?

An object's velocity is measured always with respect to some other object. So is the derivative of its velocity, therefore.

Is acceleration the sort of thing that is measured with respect to another object, or isn't it?

Sorry to keep bugging you. We both know what happens when objects are dropped, etc. That's not the problem. The problem is, what's the best way to talk about it. It's good to pick a definition for a word and then stick to it. Otherwise, people just get confused.

 

[Ziggurat]

Is acceleration the sort of thing that is measured with respect to another object, or isn't it?

It's measured with respect to a reference frame, not an object. We often use objects to identify reference frames. For example, if we want to track an inertial reference frame, we just observe an object which has no forces applied to it. But a given reference frame still exist irregardless of whether or not there's a specific object associated with it.

 

[Schneibster]

It's measured with respect to a reference frame, not an object. We often use objects to identify reference frames. For example, if we want to track an inertial reference frame, we just observe an object which has no forces applied to it. But a given reference frame still exist irregardless of whether or not there's a specific object associated with it.

Correct, but incomplete in this context; 69dodge's question rests upon the mathematical definition of acceleration in classical physics.

He asked:

Ok, gravity is acceleration.

That doesn't help anyone who doesn't know what "acceleration" means.

So, what does "acceleration" mean?

It means different things in different systems of mechanics. One is:

If it doesn't mean "derivative of velocity", what word does mean that?

You've forgotten some important things; it's the first order derivative of velocity with respect to time. But it's also the second order derivative of distance with respect to time. But that's in Newtonian, or Galilean, aka classical mechanics.

In relativity, acceleration is absolute; an object that is the origin of an accelerated frame of reference can always feel that acceleration, in other words, local experiments can be performed that will tell the vector and magnitude of that acceleration with respect to any inertial frame. This is the corollary of the fact that local experiments can be performed in an inertial frame that show it to be inertial. There is no absolute motion, no absolute velocity, but there is absolute acceleration, and it can be determined by local experiments.

Thus, in relativity, unlike classical mechanics, distance, position, and velocity are not absolute; it's acceleration that's absolute. The conceptual mistake you, 69dodge, are making, is to assume that the fact that in one system of mechanics (classical mechanics) acceleration is defined as the second order derivative of distance with respect to time, means that distance or time must be absolute. That is the underlying assumption of that system; but the underlying assumption of relativity is different. The fact that it is approximately the same for small velocities leads to the fact that use of this derivative still works; but it is no longer the definition of acceleration. The definition of acceleration is now based upon whether geodesics (i.e., the paths of inertial objects) are straight lines or not. If they are straight, then you are in an inertial frame; if they are not, then you are in an accelerated frame.

To put this another way, which is the way that Zig was speaking, the definition of acceleration in classical mechanics is dependent upon absolute space; but in relativity, it is dependent upon absolute spacetime.

Newton and Galileo missed it by one degree of the derivative, or by the failure to see that instead of being some "different kind of stuff" from space, time is actually "the same kind of stuff." It's why all the stuff about absolute motion and so forth never worked. They (or at least Newton) could feel it wasn't quite right; Newton's Bucket showed it. But it was a conundrum, because Newton never saw that the key was not motion, it was the frame in which motion occurred.

An object's velocity is measured always with respect to some other object. So is the derivative of its velocity, therefore.

Is acceleration the sort of thing that is measured with respect to another object, or isn't it?

In classical mechanics, acceleration is the sort of thing that is measured with respect to another object; but in relativity, it is not. Acceleration is measured by the curvature of spacetime in relativity. No external reference is needed; a local experiment can always show whether a frame is accelerated or inertial, but no local experiment can show whether a frame is moving in an inertial fashion or not.

Sorry to keep bugging you. We both know what happens when objects are dropped, etc. That's not the problem. The problem is, what's the best way to talk about it. It's good to pick a definition for a word and then stick to it. Otherwise, people just get confused.

That's what I've been doing, as you'll see if you go back over what I've said previously. Do not be sorry; I don't blame you at all. It took Einstein years to understand this, years after he'd already invented SR. The Equivalence Principle is, as I have said, the key to understanding the worldview of relativity.

 

[EternalSceptic]

A falling reference frame is an inertial reference frame. This means that if you're in free fall, you cannot tell based on any local measurement that you are falling and not floating in deep space.

The trick, though, is that in practice you aren't actually confined to local measurements. Real gravitational fields are not uniform, and this nonuniformity leads to tidal forces (the side of an object nearest the gravity source will feel a pull relative to the side farthest from the gravity source) even for free-falling objects.

Not only tidal forces AFAICT. Go to the top of a high building (no, _don't_ jump down ).
Now take two stones and hold them one about 1 ft vertical above the other. Release both at exactly the same time. Observe what happens - will their vertical distance remain constant?

 

[Ziggurat]

Thus, in relativity, unlike classical mechanics, distance, position, and velocity are not absolute; it's acceleration that's absolute.

In Galilean relativity (which is what underpins Newtonian mechanics), position and velocity are not absolute, but are completely reference-frame dependent.

The definition of acceleration is now based upon whether geodesics (i.e., the paths of inertial objects) are straight lines or not. If they are straight, then you are in an inertial frame; if they are not, then you are in an accelerated frame.

You can also treat acceleration as the deviation from a geodesic, whether or not the geodesic is curved. In that sense, free-falling is not acceleration, but standing still on the earth (which is what feels like standing in an accelerating rocket) is.

In classical mechanics, acceleration is the sort of thing that is measured with respect to another object; but in relativity, it is not. Acceleration is measured by the curvature of spacetime in relativity. No external reference is needed; a local experiment can always show whether a frame is accelerated or inertial,

Local experiments can also determine acceleration in Newtonian mechanics.

 

[Ziggurat]

Not only tidal forces AFAICT. Go to the top of a high building (no, _don't_ jump down ).
Now take two stones and hold them one about 1 ft vertical above the other. Release both at exactly the same time. Observe what happens - will their vertical distance remain constant?

That is a tidal force.

 

[Bodhi Dharma Zen]

You put it fine. You have actually touched on one of the unsolved parts of physics... ...In fact, when something happens, there are only certain parts of it we can know, or can ever have known later. This is because of the uncertainty principle.

Very interesting stuff, thanks for your answers in general.

The really interesting part is that it turns out that the 2LOT really is time-reversal symmetric, but only if the entropy is so high that it's almost constant; in a low-entropy system, like our universe, it becomes asymmetric.

So, the so called future is depending on factors that has nothing to do with "time flowing". Interesting.

Most physicists believe that the extraordinarily low entropy of the early universe is responsible for the time asymmetry that we see, but they can't prove it, and they won't really be happy until they can, or they find out something else that accounts for the asymmetry we see around us.

Assuming the asymmetry is a result of those factors, it is safe to presume that we wont be able to "travel in time" because time is not a dimension in the sense you were describing before. In any case, thats what I believe.

You must cast aside this, for want of a better word, prejudice, that the situation you see around you is the natural one, and understand that everything you see and everything you experience is influenced by this gravity field.

Cant agree more. Yes, we tend to pretend that common sense is a reliable source of information about the "true" nature of things. Can I go as far as to think that gravity is nothing but the absense of a force?

This is the true state of affairs, and thus we can see that gravity is acceleration.

Ok, let me rephrase my last question. We "countermeasure" gravity applying a force, this is, an acceleration force. But without applying any force, can we argue that what we have is a state of no force?

 

[Ziggurat]

So, the so called future is depending on factors that has nothing to do with "time flowing". Interesting.

The question is basically what happens to the laws of physics if we run everything in reverse. For Newtonian gravity, for example, that's simple: the earth just revolves around the sun in the opposite direction, but the forces are still all the same going backwards or forwards.

Now it turns out you can't actually do a straight t -> -t replacement in all the laws of physics, but according to what we know, if you created a mirror image of our universe using antimatter (reverse the charge) and reverse one coordinate axis (reverse the parity), it would evolve in time exactly as if our universe were running backwards in time. This is known as CPT symmetry (charge, parity, time). And yes, the implication is indeed that there's nothing intrinsically special about the direction we percieve time "flowing" other than that one end of the time line happens to be a low-entropy state. But that's actually a very non-trivial consideration, from a practical standpoint.

 

[boooeee]

Not only tidal forces AFAICT. Go to the top of a high building (no, _don't_ jump down ).
Now take two stones and hold them one about 1 ft vertical above the other. Release both at exactly the same time. Observe what happens - will their vertical distance remain constant?

To the naked eye, and to the tolerance of most measuring devices, yes.

If we whipped out our micrometers and atomic clocks, we would notice a difference. A very small difference. But that is due to tidal forces. The field strength is slightly less for the ball starting at a higher position.

 

[Bodhi Dharma Zen]

... And yes, the implication is indeed that there's nothing intrinsically special about the direction we percieve time "flowing" other than that one end of the time line happens to be a low-entropy state. But that's actually a very non-trivial consideration, from a practical standpoint.

Mind bending. If I have to give an answer I would say that those theoretical accounts are wrong. I can get it that time is not a flow, I can understand that entropy kind of explains the apparent flux, even that our consciousness give us an inapropriate understanding... but time traveling? or fixated and tangible future? Guess I dont understand a thing.

 

[Ziggurat]

but time traveling? or fixated and tangible future? Guess I dont understand a thing.

Time travel, as it's commonly understood, is not an option. When I talk about reversing time, I'm talking about how you model the universe, not any actual mechanism where we can physically do that. The fixated future thing comes about because all the laws we know of are completely deterministic (and yes, that actually covers quantum mechanics as well). Our understanding of physics is incomplete, and perhaps lurking somewhere in what we don't know is something non-deterministic, but we've done pretty well assuming otherwise.

 

[Schneibster]

So, the so called future is depending on factors that has nothing to do with "time flowing". Interesting.

I'll leave this until I've seen what Zig has to say.

Assuming the asymmetry is a result of those factors, it is safe to presume that we wont be able to "travel in time" because time is not a dimension in the sense you were describing before. In any case, thats what I believe.

I'm not clear on why that would make time any less a dimension. I can see why it would make the way we perceive "the passage of time" an illusion, but I simply don't see why it rules out time as a dimension, made of the same "kind of stuff" as space. After all, SR tells us that velocity is a rotation such that one observer's time "direction" is, for another observer, a mixture of time and space; and if time can so easily turn into space and vice versa, how can they be "different stuff?"

Cant agree more. Yes, we tend to pretend that common sense is a reliable source of information about the "true" nature of things. Can I go as far as to think that gravity is nothing but the absense of a force?

No. Gravity is a force, from the point of view of an inertial observer in relatively flat spacetime. Such an observer sees inertial objects, in the curved spacetime of the gravity field, accelerating; and the only explanation for acceleration is a force. What many people find confusing is that the inertial observer in flat spacetime agrees with the accelerated observer in the gravity field; this makes them think that the accelerated observer's point of view is somehow "natural."

Ok, let me rephrase my last question. We "countermeasure" gravity applying a force, this is, an acceleration force. But without applying any force, can we argue that what we have is a state of no force?

This is precisely the type of confusion I spoke of in my previous paragraph.

 

[Schneibster]

To the naked eye, and to the tolerance of most measuring devices, yes.

If we whipped out our micrometers and atomic clocks, we would notice a difference. A very small difference. But that is due to tidal forces. The field strength is slightly less for the ball starting at a higher position.

First, I'll point out that this is a result of the fact that real gravity fields are spherical, and the force of gravity falls off as the square of the distance. Second, I'll concur with Zig that this is an example of true tidal forces, specifically the difference in pull at different distances that results in two high tides every day on Earth. Finally I'll point out that it's the other effect, the one lateral to the vector of the gravity force, that pinches together, that causes the two low tides that come between the high tides. Tidal forces, you see, work both along and across the vector of the gravity field that creates them.

 

[Schneibster]

Time travel, as it's commonly understood, is not an option.

I have spoken about modeling spacetime using hyperbolic geometry. One of the advantages of this is the fact that in hyperbolic geometry, the angle that corresponds to a right angle in circular geometry is infinite. In other words, no matter how fast you rotate (i.e., how fast you accelerate, since in this model acceleration is modeled as rotation), you can't ever reach a right angle (i.e., the speed of light). But to reverse your direction in time by a continuous rotation (the only kind possible for a macroscopic object, whatever individual quanta might be able to do), you would not merely have to rotate to the infinite angle, but rotate past it. This is not merely unimaginable. And it's obvious why this must be if you stop trying to impose circular geometry on hyperbolic spacetime.

When I talk about reversing time, I'm talking about how you model the universe, not any actual mechanism where we can physically do that.

Feynman showed that an electron moving backward in time would have to display reversed charge and parity from the point of view of an observer moving forward in time, which means an electron moving backward in time is perceived by such an observer as a positron. Feynman believed this was an actual description of reality, and went so far as to propose that there is only one electron, alternately moving backward and forward, comprising all the electrons and positrons in the universe. I think that he's right about the first part; I'm pretty skeptical of the one-electron model, Feynman was a well-known prankster and this sounds like a prank to me; particularly amusing, of course, is that it could be true.

The fixated future thing comes about because all the laws we know of are completely deterministic (and yes, that actually covers quantum mechanics as well).

Heh, we'll see if that dog hunts. A lot of people (not me, though) have trouble with the idea that something that only predicts probabilities can be deterministic.

Our understanding of physics is incomplete, and perhaps lurking somewhere in what we don't know is something non-deterministic, but we've done pretty well assuming otherwise.

Interestingly, at the individual interaction level, there is something non-deterministic; but when you lump many interactions together, they become deterministic. More interestingly, this is precisely the way the fluctuation theorem builds up to the 2LOT, and most interestingly, this is also the way decoherence builds up to the laws of classical mechanics. I believe there is a deep principle here that we are in the process of coming to understand at this time. The definitive test of the FT, after all, was only a few years ago.

 

[Ziggurat]

I'm pretty skeptical of the one-electron model, Feynman was a well-known prankster and this sounds like a prank to me; particularly amusing, of course, is that it could be true.

I like the idea conceptually but it doesn't address what happens if you create an electron-positron pair and then have that same pair anihilate each other. So I don't think it can be true (though looking at positrons as backwards-moving electrons still works).

 

[Cuddles]

I'm pretty skeptical of the one-electron model, Feynman was a well-known prankster and this sounds like a prank to me; particularly amusing, of course, is that it could be true.

I wouldn't go so far as to say it was a prank. It is a useful way of looking at things. It may not be completely accurate, but Feynman diagrams do not represent how particles actually behave, but they still give sensible results. The one-electron model is just a different way of looking at things, this doesn't mean it was a joke.

 

[Schneibster]

this doesn't mean it was a joke.

That's why I called it a prank.

FitzGer'd is a joke. Spraypainting "Free all radicals!" on the wall of a chemistry building is a prank.

 

[Thabiguy]

No. Gravity is a force, from the point of view of an inertial observer in relatively flat spacetime. Such an observer sees inertial objects, in the curved spacetime of the gravity field, accelerating; and the only explanation for acceleration is a force. What many people find confusing is that the inertial observer in flat spacetime agrees with the accelerated observer in the gravity field; this makes them think that the accelerated observer's point of view is somehow "natural."

Hmm. I'm afraid I would have to disagree with you there, just slightly.

What you said would be correct in special relativity. There, a distant intertial observer and an observer on the planet's surface agree about their observations (they, in fact, share the same reference frame) and gravity is indeed a force in this reference frame. A probe that swings by the planet will be observed equally by both.

In general relativity, a distant inertial observer and an observer on the surface of the planet, even though at rest in each other's reference frame, will disagree about their observations. They experience time dilation, they will disagree about the velocity of the probe etc.

It seems to me that for the distant inertial observer, gravity is not exactly a force. The results will be different if the probe swings by the planet, and if a (charged) probe swings around a large massless charged sphere, or if the probe uses its engines to fly around the same path. When the distant observer re-catches the probe and checks its internal clock, in all three cases she will see the effects of time dilation due to acceleration (as per special relativity), but in the first case, the value will still be different (as per general relativity). Effects of gravity will be distinguishable from effects of common force.

I think that while curvature of spacetime due to presence of mass (=gravity) can be approximated as a spherical, inverse-square-falloff force, it holds only for relatively mild curvatures, and differs from this approximation more and more as the curvature grows larger.

From this, it would follow that gravity is not really a force. The equivalence principle is of course still true - free fall is locally equivalent to being inertial, and resisting free fall is locally equivalent to acceleration. But the importance of the word local is paramount. When one says, "acceleration due to gravity", one necessarily speaks about an object that is in a different reference frame than the observer - and at that moment the experiment is no longer local and the equivalence principle no longer applies.

I apologize if this seems to be nitpicking, as your posts are generally excellent and amazingly informative, while at the same time remaining very accessible. And of course, please correct me if I'm wrong in my assumptions or inference.

 

[Schneibster]

Hmm. I'm afraid I would have to disagree with you there, just slightly.
{moved from the bottom}
I apologize if this seems to be nitpicking, as your posts are generally excellent and amazingly informative, while at the same time remaining very accessible. And of course, please correct me if I'm wrong in my assumptions or inference.

On a personal level, your delicacy is admirable. On the material, it's well worth nitpicking; really, all of relativity is a nitpick on classical mechanics!

What you said would be correct in special relativity. There, a distant intertial observer and an observer on the planet's surface agree about their observations (they, in fact, share the same reference frame) and gravity is indeed a force in this reference frame. A probe that swings by the planet will be observed equally by both.

I disagree here. I intentionally did not say that they share a frame; what I said was, unless very minor (unless the gravity field is extreme, unmeasurable) differences are considered, what the inertial, far away observer sees appears the same as what the motionless observer accelerating in the gravity field sees. My point was not that they are the same; it was that they're not, but they look the same, and that confuses people.

The highlight in your quote shows precisely what I did not intend to say, and do not believe is the case.

In general relativity, a distant inertial observer and an observer on the surface of the planet, even though at rest in each other's reference frame, will disagree about their observations. They experience time dilation, they will disagree about the velocity of the probe etc.

They may; but unless it is a very strong gravity field, if they agree they are motionless relative to one another, the differences will be unmeasurable save by the most sensitive instruments we can conceive of. Gravity Probe B used such instruments to gather data for over a year (IIRC), and it's looking like it'll take most of a year, or even more than that, to analyze that data and extract the measurements out of it.

It seems to me that for the distant inertial observer, gravity is not exactly a force. The results will be different if the probe swings by the planet, and if a (charged) probe swings around a large massless charged sphere, or if the probe uses its engines to fly around the same path. When the distant observer re-catches the probe and checks its internal clock, in all three cases she will see the effects of time dilation due to acceleration (as per special relativity), but in the first case, the value will still be different (as per general relativity). Effects of gravity will be distinguishable from effects of common force.

What an excellent and illustrative nit to pick! Very well done. I had thought a couple times about characterizing the difference between gravity and EM, but never thought of time!

Now, while I don't agree that this makes gravity not exactly a force, I do agree that its action is different in this manner from the EM force; your notes about the time difference are, to the best of my knowledge, correct. What it means is that gravity is not a classical force. In the case of matter pushing against matter, which many people think of as a "force," note that this is an EM interaction at the atomic level; Van der Waals forces are residual EM forces. That means EM is the only force other than gravity. In fact, gravity and EM are the only forces that are long-range; the color and weak forces operate at atomic scales, not in macroscopic reality.

This brings up the essential reason why we still have not reconciled QM with GR. That reason is that gravity warps time, as well as space. Trying to include full spacetime warping in a QM description of reality causes the QM description to exhibit unrenormalizable infinite terms, rendering it meaningless in a physical context. I believe that the key to this is quantization of spacetime; but the exact manner in which this is to be done is not clear to the brightest physicists out there, much less to me. String physics may have shown a way this can be done, but evidence to support it is lacking, primarily because we cannot attain high enough energies to test its predictions.

I think that while curvature of spacetime due to presence of mass (=gravity) can be approximated as a spherical, inverse-square-falloff force, it holds only for relatively mild curvatures, and differs from this approximation more and more as the curvature grows larger.

I'd have to defer to those with more knowledge deeper in the subject than I can bring. I have to think about the fact that the inverse-square falloff is a matter of the geometry of spacetime in order to even guess at an answer. Off the top of my head, I suspect you are correct, and that the precession of the major axis of Mercury's orbit proves it, but let me think and let's see if someone who really knows their way around the math can confirm this conjecture.

From this, it would follow that gravity is not really a force. The equivalence principle is of course still true - free fall is locally equivalent to being inertial, and resisting free fall is locally equivalent to acceleration. But the importance of the word local is paramount. When one says, "acceleration due to gravity", one necessarily speaks about an object that is in a different reference frame than the observer - and at that moment the experiment is no longer local and the equivalence principle no longer applies.

I'm going to have to think about this a little while, and we may need an answer to the question of whether the inverse-square falloff is not precisely correct to get to this. I think that the definition of acceleration is a matter not of measurement, but of spacetime geometry- and the fact that inertial frames are possible in both says that your conjecture here may not be correct. Think of how two different inertial frames would see each other in a gravity field, and how that might vary from how they would see each other outside it, or from how one inside and one outside might see each other. I think that might be the key to this. I sense that it is, based on Einstein's use of this to get to the Equivalence Principle.

 

[Ziggurat]

I'm going to have to think about this a little while, and we may need an answer to the question of whether the inverse-square falloff is not precisely correct to get to this.

I mentioned this in a previous debate we had: gravity is indeed not a 1/r² force. The force diverges at the event horizon, not at r=0 (in fact, force diverges at event horizons created by using an accelerated reference frame as well).