Gravity & Springs: Exploring the Connection

[Dale]

When we look closely at Einstein's elevator, we see that the force stretching the spring is actually not a real force, but a fictitious force.

Fictitious forces cannot stretch springs. Only real forces can do that.

Consider, in an inertial frame there are no fictitious forces so the stretching of the spring is determined by the real forces. Changing to a non-inertial frame does not remove any real forces, so the explanation of the stretching in terms of real forces is unchanged. So the fictitious forces do not contribute to the stretching.

The fictitious forces are only needed to explain the motion of the object in the non-inertial frame. They do not explain the stretching or any other physical effect.

 

[PeterDonis]

In an accelerating frame with Newtonian physics, we need to modify Newton's laws to introduce the concept of a "fictitious force".

But this fictitious force is not what stretches the spring. As @Dale says, only real forces can do that.

 

[Sagittarius A-Star]

Forces and time dilation are two different things, that are apparently unrelated. But there is a deeper connection, which can be seen by understanding the geometric version of the theory.

Can you please describe the deeper connection?

Do you have a link to a description of this deeper connection between forces and time dilation?

 

[Dr_Mike_J]

Let's have a look at those spring scenario force analyses...

1) spring is stretched horizontally attached to two walls, supported by a frictionless table to keep it straight
There is a tension in the spring acting horizontally through its whole length;
The spring is touching the table so there is electrostatic repulsion between their outer clouds of electrons acting between them along the whole length of the spring (if this were done in a free-fall lab or on ISS there would be less repulsion between them than on the Earth) the greater part of this repulsion will be due to the mass of the spring;
2) spring is unattached and unstretched as it free falls vertically
For free fall the spring will be accelerating due to the close proximity of the Earth (in GR does the existence of acceleration not necessarily imply a force? genuine question - my neurons are rusty!)
3) spring is attached to the ceiling and is stretched slightly under its own weight
Contact force at the attachment to the ceiling, small tension in the spring due to its weight usually ignored in mechanical calculations - the proverbial "massless spring"!
4) spring is stretched between my hand and a mass while accelerating horizontally across a frictionless table
contact force between the spring and the hand causing the spring and mass to accelerate
5) spring is unstretched lying on a table
see 1)
6) spring is stretched between two masses in horizontal uniform circular motion on a frictionless table
The tension in the spring supplies the centripetal force needed to keep the two masses moving in a circle plus
electrostatic repulsion between their outer clouds of electrons acting between them along the whole length of the spring and between the masses and the table
My question relates to how we describe the difference in interaction between, for example, my feet and the floor on Earth compared with my feet and the floor of the ISS were I to have the privilege of being there.
Am I not allowed to call my perception of a force a force?

 

[A.T.]

My question relates to how we describe the difference in interaction between, for example, my feet and the floor on Earth compared with my feet and the floor of the ISS were I to have the privilege of being there.
Am I not allowed to call my perception of a force a force?

The contact force between your feet and the floor is an interaction force (EM-repulsion).

 

[Dr_Mike_J]

So what causes the EM-repulsion to be greater when I'm standing on the floor on Earth compared with standing on the floor of the International Space Station?

 

[A.T.]

So what causes the EM-repulsion to be greater when I'm standing on the floor on Earth compared with standing on the floor of the International Space Station?

The EM-forces are distance dependent: If your atoms get too close to the floor atoms, they repel each other.

 

[Dr_Mike_J]

So, what causes the atoms of my feet to be closer to the floor atoms on Earth than to the floor atoms on the ISS?

 

[A.T.]

So, what causes the atoms of my feet to be closer to the floor atoms on Earth than to the floor atoms on the ISS?

The "cause" of the proximity is irrelevant for the EM-force. In general, questions about "the cause" are vague, because it's not clear what qualifies as a "cause". They are usually irrelevant to the actual physics (quantitative predictions).

In GR a "cause" that could be named here, is that everything tends to move along a geodesic in space-time (free fall). Your atoms are trying to free fall, while the floor atoms are not in free fall, and thus they get closer together, resulting in repulsion.

 

[Dr_Mike_J]

A.T. you seem to have an aversion to the notion of cause and effect.
The universe is replete with one thing causing another thing ("The fundamental interconnectedness of all things" [Dirk Gently], the Butterfly Effect etc).
Also what about the floor itself, why are the atoms of my feet trying to free fall whilst the floor atoms are not?

 

[PeterDonis]

Am I not allowed to call my perception of a force a force?

You never perceive gravity as a force; any force you actually feel will not be gravity, but something else. When you're standing on the floor on Earth, the force you feel is the floor pushing up on you, not gravity.

Your atoms are trying to free fall, while the floor atoms are not in free fall

The floor atoms are "trying" to fall just as your atoms are. See below.

what about the floor itself, why are the atoms of my feet trying to free fall whilst the floor atoms are not?

The floor atoms are trying to fall, but they are being pushed on by the atoms below them, and so on all the way down to the center of the Earth.

 

[Sagittarius A-Star]

geodesics are by definition straight.

Is this a coordinate-dependent definition? Does it depend on describing the geodesic in the coordinates of an inertial reference frame?

I think, a coordinate-independent definition would be to say, geodesics are world lines of objects not influenced by real forces.

 

[A.T.]

Also what about the floor itself, why are the atoms of my feet trying to free fall whilst the floor atoms are not?

As I said, everything tends to move along a geodesic in space-time (free fall). The floor is prevented from free fall by some other upwards forces, just like you are prevented from free fall by the upwards force from the floor.

 

[Dr_Mike_J]

OK someone is standing on my shoulders. I feel the downward radial force of their feet. I know from experience that this radial force depends on the mass of the person above me. Thus I am experiencing the result of being in proximity to the earth. I also know by people's accounts that this experiment performed on the ISS results in very little force experienced. So I connect the two experiences and deduce that there is a downward radial pressure which seems compatible with the notion of a force. Why can we not use the word "force"? Does a force have to be communicated by billions of virtual particles? I think we are in danger of losing sight of the fact that science is about making observations of the way the universe behaves and seeking to find patterns in these observations. If we detach our theories from our own minds it is like Michelangelo burning the scaffolding he's lying on.

 

[A.T.]

...seems compatible with the notion of a force.

That's why it is modeled as an interaction force in Newtonian gravity. But being proportional to mass it can also be modeled as an inertial force, as is the case locally in GR.

 

[PeterDonis]

Is this a coordinate-dependent definition?

No. A more technical way to state it is that a geodesic is a curve that parallel transports its own tangent vector along itself.

I think, a coordinate-independent definition would be to say, geodesics are world lines of objects not influenced by real forces.

If by "real forces" you mean "forces that cause proper acceleration", i.e., that are actually felt, then your definition is indeed coordinate-independent and equivalent to the definition I gave above (though showing the equivalence takes some work).

 

[PeterDonis]

I feel the downward radial force of their feet.

And they feel the upward force of your shoulders. So there is a force in both directions (Newton's Third Law).

Also, you feel an upward force from the ground, and the ground feels a downward force from you (again Newton's Third Law).

So focusing on downward forces is simply ignoring half of the forces present.

Thus I am experiencing the result of being in proximity to the earth.

No, that's not the cause. The ISS is almost as close to the center of the Earth as you are, and if you were standing on a tower whose height was the same as the orbital altitude of the ISS, and someone else stood on your shoulders, the force you felt (and the force they felt) would be virtually the same. So "proximity to Earth" can't be the cause.

I connect the two experiences and deduce that there is a downward radial pressure

No, that's not what you should deduce. As noted above, there are forces in both directions, downward and upward. So just looking at the downward forces can't be right.

Why can we not use the word "force"?

You can use the word "force" in GR for things that are felt as forces. Gravity is not felt as a force. Astronauts in the ISS are just as much subject to Earth's gravity as you are, yet they feel no force. So "gravity" cannot be the force you are feeling when you stand on Earth and someone else stands on your shoulders.

think we are in danger of losing sight of the fact that science is about making observations of the way the universe behaves and seeking to find patterns in these observations.

It is you who are losing sight of that, by ignoring the obvious pattern I just described in my previous paragraph above.

 

[Dale]

Excellent, thanks for taking the exercise seriously.

1) spring is stretched horizontally attached to two walls, supported by a frictionless table to keep it straight
There is a tension in the spring acting horizontally through its whole length;

OK, so in the lengthwise direction we have contact force from the wall, no gravity, and tension.

The spring is touching the table so there is electrostatic repulsion between their outer clouds of electrons acting between them along the whole length of the spring (if this were done in a free-fall lab or on ISS there would be less repulsion between them than on the Earth)

Yes. And we are ignoring the transverse forces. I did it that way so that we wouldn’t have to go to deep space to get rid of gravity, but all of those horizontal scenarios could be replaced by going to deep space to get rid of gravity.

2) spring is unattached and unstretched as it free falls vertically

So gravity is present, contact forces are absent, and it is unstretched

3) spring is attached to the ceiling and is stretched slightly under its own weight
Contact force at the attachment to the ceiling, small tension in the spring due to its weight

Excellent, so there is a small contact force, there is the usual gravity force, and there is a small tension.

4) spring is stretched between my hand and a mass while accelerating horizontally across a frictionless table
contact force between the spring and the hand causing the spring and mass to accelerate

Excellent, so there is a contact force, there is no gravity, and there is tension.

5) spring is unstretched lying on a table
see 1)

So no contact force, no gravity, and no tension.

6) spring is stretched between two masses in horizontal uniform circular motion on a frictionless table
The tension in the spring supplies the centripetal force needed to keep the two masses moving in a circle

Finally, we have contact forces, no gravity, and tension.

So in summary we can put the results in the following table:
$$\begin{array}{cccc}
\text{Scenario} & \text{Contact} & \text{Gravity} & \text{Stretching} \\
1 & \text{Yes} & \text{No} & \text{Yes} \\
2 & \text{No} & \text{Yes} & \text{No} \\
3 & \text{Yes} & \text{Yes} & \text{Yes} \\
4 & \text{Yes} & \text{No} & \text{Yes} \\
5 & \text{No} & \text{No} & \text{No} \\
6 & \text{Yes} & \text{No} & \text{Yes} \\
\end{array}$$
Looking at the summary it is pretty clear. Whenever there is a contact force there is stretching, regardless of whether or not there is gravity. Whenever there is no contact force there is no stretching, regardless of whether or not there is gravity. And in 4 we found a small contact force and a small amount of stretching, so the amount of stretching is even related to the amount of the contact force.

So clearly, gravity does not cause the stretching. Scenarios 1, 2, 4, and 6 all contradict the idea. Also, this is all done using Newtonian physics and treating gravity as a force. Even in that case it is clearly not gravity that causes a spring to stretch, it is the contact forces.

My question relates to how we describe the difference in interaction between, for example, my feet and the floor on Earth compared with my feet and the floor of the ISS were I to have the privilege of being there.
Am I not allowed to call my perception of a force a force?

Sure. Such forces are are also called inertial forces or fictitious forces (I prefer the first). But what you cannot do is claim that they cause a spring to stretch.

 

[Dale]

The ISS is almost as close to the center of the Earth as you are, and if you were standing on a tower whose height was the same as the orbital altitude of the ISS, and someone else stood on your shoulders, the force you felt (and the force they felt) would be virtually the same. So "proximity to Earth" can't be the cause.

This is a really good point. @Dr_Mike_J I would recommend thinking about this quite a bit. Gravity is still present in the ISS and is in fact almost the same as on the surface of the earth. So the absence of a force in the ISS is not attributable to a lack of the gravitational force.

 

[MikeeMiracle]

Feel the need to thank all the contributers to this thread. I learned about contact forces, special thanks to Dale and his questions method, made it very clear.

 

[Dr_Mike_J]

Thank you @Dale for your patience.
Your table does not constitute evidence that gravity has no part in the stretching.
Just because stretching of the spring happens in situations where there is no gravity does not mean that gravity does not cause stretching.
Consider taking the spring and the same mass to the moon where the strength of gravity is about 1/6 of that at the surface of Earth. You would find that the extension of the spring would be about 1/6 that found on Earth.
It's hard not to make the conclusion that gravity has something to do with the stretching of the spring.
The contact forces don't arise out of nowhere they come from the system altering its position variables so as to reach equilibrium. So what is the mechanism by which this adjustment to attain balance comes about?
Do not forces have to be balanced for equilibrium or is that a purely Newtonian concept?

 

[PeterDonis]

Your table does not constitute evidence that gravity has no part in the stretching.

Gravity as a force has no part in the stretching. That's what we've been talking about.

Gravity as spacetime curvature does have a part in the stretching, since it determines what worldlines the individual pieces of the spring would follow if there were no internal forces in the spring and no contact forces between the spring and masses or suspension points. Which in turn determines what those forces have to be to make the individual pieces of the spring follow the worldlines they actually follow.

Consider taking the spring and the same mass to the moon where the strength of gravity is about 1/6 of that at the surface of Earth. You would find that the extension of the spring would be about 1/6 that found on Earth.

Yes, but this is because of gravity as spacetime curvature, not gravity as a force. The spacetime curvature in the vicinity of the Moon is different than in the vicinity of the Earth.

 

[Dale]

Just because stretching of the spring happens in situations where there is no gravity does not mean that gravity does not cause stretching.

Actually it does. Scenarios 1, 4, and 6 show that gravity is not necessary for stretching. Scenario 2 shows that gravity is not sufficient for stretching. In contrast the contact forces are both necessary and sufficient. So it does very clearly identify the causality.

Consider taking the spring and the same mass to the moon where the strength of gravity is about 1/6 of that at the surface of Earth. You would find that the extension of the spring would be about 1/6 that found on Earth.

Sure, but you would also find that the contact force is about 1/6 of that found on earth. So this scenario also supports the claim that the contact force is the cause of the stretching. That was the point of scenarios 3 and 5. Even when it seems like gravity is the explanation, that is just because it is going along with the contact force.

To distinguish which is the cause you must vary them separately, not together. This is a common mistake in experimental design.

Do not forces have to be balanced for equilibrium or is that a purely Newtonian concept?

They do, but equilibrium is a frame dependent concept. In an inertial frame the spring attached to the ceiling is not in equilibrium. It is accelerating.

But in any case equilibrium is different from stretching. So something could be necessary for equilibrium but not for stretching and vice versa.

 

[A.T.]

Do not forces have to be balanced for equilibrium or is that a purely Newtonian concept?

Do you actually understand Newtonian mechanics? In particular, the difference between inertial and non-inertial frames of reference? Or the difference between interaction and inertial forces? Or the difference between Newtons 2nd and 3rd Law?

I would strongly suggest getting a good grasp on these concepts before starting with GR.

 

[pervect]

Can you please describe the deeper connection?

Do you have a link to a description of this deeper connection between forces and time dilation?

I don't think, that you need a concept with a fictitious force at Einstein's elevator in space. In the accelerated elevator, you have a pseudo-gravitational time-dilation. If a lamp at the ceiling of the elevator sends a light-pulse, it will be received blue-shifted by a sensor at the floor of the elevator. From the viewpoint of an external inertial observer, the reason is the Doppler effect. This pseudo-gravitational time-dilation curves gedesics. The concept does not differ locally from the "real" gravitation of the earth.

Actually, I rather think we do. Consider any other sort of force. Say for instance, an electric field. Do electric fields, no matter how strong cause time dilation, for an observer at rest? The answer is basically no, with the exception that a strong enough electric field could cause gravitational effects, which would then cause time dilation. But we already know that gravitational effects case time dilation, the point of the argument is to consider what happens in the non-gravitational case. And in the non-gravitational case, forces do not cause time dilation.

So, if forces do not cause time dilation, but gravity does, something different is going on with gravity - it's not "just a force". What is it then? Basically, we can regard "gravitational force" as the pseudo-force associated with describing things in a non-inertial frame. And the other effects, such as the effects on time, are related to our choice of using an accelerated frame.

In Newtonian mechanics, the only effect of going to an accelerated frame of reference is to introduce a "fictitious force", equal and opposite to the acceleration of the observer. A special relativistic analysis of the accelerated observer shows that things are much more complicated.

See for instance the Wiki article on "Rindler Coordinates", https://en.wikipedia.org/w/index.php?title=Rindler_coordinates&oldid=962334733

Rindler coordinates are basically the special relativistic equivalent of the Newtonian "accelerated frame". A few highlights. We can see the height-dependent time dilation in the form of the associated metric, namely

$$ds^2 = -\alpha^2 x^2 dt^2 + dx^2 + dy^2 + dz^2$$

The space-time geometry in these coordinates can be regarded as a normal spatial geometry, but the description of time in this geometry is different - the relationship between proper time, $\tau$, that a clock measures, and the coordinate time, t, imposed by our coordinate system, depends on the coordinate height, x.

The "deeper connection" that I mention is simply the fact that time and space are unified into a 4-dimensional space-time. The origin of this unification are not in GR, but in SR. The best exposition of this unification is "The Parable of the Surveyor", in Taylor & Wheeler's "Space-time physics.

To recap my argument. Trying to shoe-horn gravity into the mold of a force fails in many ways, one of the most obvious and basic is that forces cannot cause time dilation, while gravity can. Regarding gravity as a pseudo-force , associated with an accelerated frame of reference, rather than as a force, is a step forwards in understanding gravity, though it is far from complete. While it is far from complete, regarding it as a pseudo-force allows one to retain some of the intuition from Newtonian mechanics. While it is not complete, it's a step forwards. People used to Newtonian mechanics know that in Newtonian mechanics, the only effect of going to an accelerated frame is to introduce a pseudo-force. They tend to assume things are the same in special realtivity - they are not the same. The effects of an accelerated frame are more complicated, as the analysis in Wiki shows, and these effects involve time as well as space. This may seem mysterious to someone with a strictly Newtonian viewpoint, but when one understands why time and space are unified (a topic for another thread, I think), it becomes less mysterious.

There is a reason that we talk about the geometry of space-time as best describing General relativity, rather than talking about gravity being a "force". It's not just word salad.

 

[Sagittarius A-Star]

The "deeper connection" that I mention is simply the fact that time and space are unified into a 4-dimensional space-time. The origin of this unification are not in GR, but in SR. The best exposition of this unification is "The Parable of the Surveyor", in Taylor & Wheeler's "Space-time physics.

The "The Parable of the Surveyor" seems to explain the invariant spacetime-interval:
http://spiff.rit.edu/classes/phys200/lectures/intro/parable.html

To recap my argument. Trying to shoe-horn gravity into the mold of a force fails in many ways, one of the most obvious and basic is that forces cannot cause time dilation, while gravity can.

Agreed. Gravity is not a real force.

While it is far from complete, regarding it as a pseudo-force allows one to retain some of the intuition from Newtonian mechanics.

My question is, if we really need pseudo-force and an intuition from Newtonian mechanics.

Reason of my question is, that I found a really good video "General Relativity: Principle of maximum proper time" from Professor Josef Gaßner. Unfortunately, it is in German. I think you can understand the mathematical formulas he is writing and I can write a short English summary:

First he derives the principal of maximum proper time from the classical principal, that the integral about the Lagrange function is a minimum. His derived formula for proper time contains the sum of a velocity-dependent part and a gravity potential dependent part.

Then he throws an orange, that follows a parabolic trajectory. He explains this trajectory step by step with the appoach of the orange, to accumulate maximum proper time. The orange tries for example to stay longer in high altitude, where it can acquire more proper time, but not too high, because that would need a too high velocity for a too long time, which would reduce the gain of proper time.

The parabolic trajectory can be calculated from the principal of maximum proper time, I think by "variational calculus". A "Gravity force" is not needed to calculate the parabolic trajectory. Professor Josef Gaßner did not mention "pseudo-force". Do we really need it?

It seems, according to Peter Donis, that I used formally the wrong formulation "curved geodesic", when I meant a parabolic trajectory.

Here is the video (unfortunately in German), sorry:

 

[PeterDonis]

It seems, according to Peter Donis, that I used formally the wrong formulation "curved geodesic", when I meant a parabolic trajectory.

Yes, the parabolic trajectory is a geodesic (actually, it's a uniform field approximation to the true geodesic, which will be a segment of an elliptical orbit about the Earth's center). The geodesic looks curved when plotted in space, but it is straight in spacetime (or as straight as a curve can get in the curved spacetime around the Earth).

 

[DrStupid]

OK someone is standing on my shoulders. I feel the downward radial force of their feet. I know from experience that this radial force depends on the mass of the person above me. Thus I am experiencing the result of being in proximity to the earth.

... or the result of being in an accelerating rocket or in a centrifuge.

I also know by people's accounts that this experiment performed on the ISS results in very little force experienced.

That seems you accept that there is very little gravitational force in a space station. What do you think keeps this guy on the ground:

So I connect the two experiences and deduce that there is a downward radial pressure which seems compatible with the notion of a force.

... or of a fictitious force.

Why can we not use the word "force"?

Because this thread is in "Special and General Relativity" and not in "Classical Physics".

 

[pervect]

The "The Parable of the Surveyor" seems to explain the invariant spacetime-interval:
http://spiff.rit.edu/classes/phys200/lectures/intro/parable.html

Yes.

Agreed. Gravity is not a real force.My question is, if we really need pseudo-force and an intuition from Newtonian mechanics.

We don't necessarily need it, IMO - but it's handy. Especialy if we're talking to someone who thinks gravity is or should be a force. We can then say "Well, in part it's a pseudo-force", but that's not the whole story, so they can build on their outlook. But certainly there are other approaches.

Reason of my question is, that I found a really good video "General Relativity: Principle of maximum proper time" from Professor Josef Gaßner. Unfortunately, it is in German. I think you can understand the mathematical formulas he is writing and I can write a short English summary:

First he derives the principal of maximum proper time from the classical principal, that the integral about the Lagrange function is a minimum. His derived formula for proper time contains the sum of a velocity-dependent part and a gravity potential dependent part.

Then he throws an orange, that follows a parabolic trajectory. He explains this trajectory step by step with the appoach of the orange, to accumulate maximum proper time. The orange tries for example to stay longer in high altitude, where it can acquire more proper time, but not too high, because that would need a too high velocity for a too long time, which would reduce the gain of proper time.

The parabolic trajectory can be calculated from the principal of maximum proper time, I think by "variational calculus". A "Gravity force" is not needed to calculate the parabolic trajectory. Professor Josef Gaßner did not mention "pseudo-force". Do we really need it?

Nope, I don't think we really need the notion of a pseudo-force. But see my other comments.

I believe I've seen that general approach used in "Exploring black holes". ((I could be mistaken, unfortunately, my memory isn't what it used to be)). The principle of maximum proper time has various other names, one of which is "the principle of maximal aging". It's good for calculating trajectories of objects if you know the metric.

It looks like there have a second edition of "Exploring Black Holes" that's only published online . It can be found at Taylor's website, http://www.eftaylor.com/exploringblackholes/. But I haven't read it.

The principle of maximal aging is not quite sufficient for understanding Einstein's equations fully, IMO, though, as it doesn't give you much insight into how the metric is determined from the matter content. If we use Wheeler's adage, "Spacetime tells matter how to move, matter tells spacetime how to curve", the principle of maximal aging answers the first question, it explains how spacetime tells matter how to move, but it doesn't really demonstrate how "matter tells space-time how to curve"

The second part is explained by Einstein's field equations, $G_{uv} = 8 \pi T_{uv}$ in geometric units, there's some additional factors in non-geometric units.

One of my favorite explanations of the second part is Baez & Bunn's "The Meaning of Einstein's Equation". You can find it on arxiv, also at Baez's webstie . http://math.ucr.edu/home/baez/einstein/einstein.pdf

We promised to state Einstein's equation in plain English, but have not done so yet. Here it is

Given a small ball of freely falling test particles initially at rest with respect to each other,the rate at which it begins to shrink is proportional to its volume times the energy density at the center of the ball, plus the pressure in the x direction at that point, plus the pressure in the y direction, plus the pressure in the z direction.

However, in the footnotes they mention

To see why equation (2) is equivalent to the usual formulation of Einstein's equation, we need a bit of tensor calculus.

It turns out there is actually quite a bit of tensor calculus, and it involves knowing how some entities transform to go from their statement about a ball of test particles to the usual and full formulatio of Einstein's equations. To my mind there are actually extra unstated assumptions hidden in the footnotes. But I still like the paper, it gave me a lot of insight.

I am also fond of regarding gravity not as a force, but as the curvature of space-time as given by the Riemann curvature tensor. I also like to decompose this tensor via the Bell decomposition into various parts, but that's another story, though I will mention that one of these parts is just tidal gravity in Newtonian physics.

While this is very useful, and how I look at gravity, and also has reasonable support in the literature (MTW does this, I think), it can be confusing. I just got through talking at length about "gravity" on Einstein's elevator. With the Riemann tensor approach, I would probably be arguing instead that there is no gravity on Einstein's elevator, because the space-time there is flat.

And it's true that the space-time on the elevator is flat, and it's true that we often talk about gravity as curved space-time. However, it's also true that in popularizations, and in history, we also do talk about "gravity" on Einstein's elevator.

So, there are different way of looking at things, and while the math in the end is perfectly self-consistent, English language descriptions in general may not be.

 

[Nugatory]

So, there are different way of looking at things, and while the math in the end is perfectly self-consistent, English language descriptions in general may not be.

The truth is indeed in the math... but I have often thought that the English language explanations would be better if we all were in the habit of using “gravitational acceleration” to refer to what we observe in Einstein’s elevator, and “tidal gravity” to refer to the effects of spacetime curvature.

 

[Dr_Mike_J]

Indulge an ageing juvenile and let's consider a gedanken experiment.
I am sitting on a chair which rests on the Earth's surface and enjoying the security that sensing the contact forces give me. Suddenly the Earth disappears into nothingness in the same way that Douglas Adams's whale appeared. It would appear that the contact forces between myself and the chair would become vanishingly small. It appears that the contact forces were only there in the former situation because the Earth was there and that it may justifiably be said that the Earth caused the contact forces, that is, the phenomenon of gravity causes the forces. The exact cause can be enquired into and at present the best theory we have is Einsein's theory of General Relativity. However that does not remove the implication that gravity causes forces to come into being. I suppose the problems we have are to do with the inherent inadequacy of language. What is the most recent received definition of "force"?

 

[Dale]

It appears that the contact forces were only there in the former situation because the Earth was there and that it may justifiably be said that the Earth caused the contact forces, that is, the phenomenon of gravity causes the forces

A few points.

First: even if gravity causes forces that does not imply that gravity is a force itself. Causes of forces need not be forces themselves.

Second: spring stretching is not a force, so even if gravity causes forces that does not imply that gravity causes spring stretching.

Third: an analysis of other scenarios will show that gravity is neither a necessary nor a sufficient condition for the contact forces between the chair and your butt. As such, it is not the cause of those forces.

Fourth: you came here with a question which has been clearly answered. You no longer seem to be trying to learn about general relativity. You now seem to be pushing a private viewpoint. Please focus on learning rather than arguing.

 

[A.T.]

I suppose the problems we have are to do with the inherent inadequacy of language.

Your problem seems twofold:

- You complain about aspects of GR that equally apply to Newtonian mechanics, because you apparently don't understand Newtonian mechanics in the first place.

- You are focusing on issues that are irrelevant to physics and mainly philosophical or semantic.

 

[Dr_Mike_J]

@A.T. I am sorry you feel that way. I do object to assumptions regarding what I do or do not understand.
I am sure there are many who would say that philosophy and logic are not irrelevant to physics.
@Dale I thank you again for your patience. I do not agree that my initial question has been answered but I am happy to agree to disagree. Thank you for what I found was, for the most part, a really stimulating discussion.

 

[Dale]

I do not agree that my initial question has been answered

How can you disagree?

Q:

According to Einsteins general theory of relativity gravity is not a force.
How then does it cause a spring to stretch?

A: gravity does not cause a spring to stretch, even in Newtonian mechanics.

I am sorry, but to disagree that your question has been answered is factually false. The fact that it has been answered is clearly observable.

What I see is that you came with a question, and received some answers that challenged your preconceived notions (about Newtonian gravity among other things), but you do not want to adjust your thinking. But how can you hope to learn if you are not willing to change your preconceptions?

I am happy to agree to disagree

I am willing to agree to disagree regarding the correctness of the answers, but not their existence. It is an observable fact that your question has been answered, even if you reject those answers. Saying that your question has not been answered is dismissive of the effort that respondents put into the answers. Dismissing other’s efforts is not a good way to participate in a community, particularly not a community of experts where respondents have put in decades of effort merely to be in a position to answer questions like yours.