UFO propulsion, metric engineering, and horizon physics

[Realm]

Ok, so in theory, I could lift a few kilo tons of water into the air, then let it fall down a tube and turn a generator.

Part of that energy would be used to lift the water again, and the rest would be free.

It would run forever, and provide a surplus of free energy. And waste heat. An infinite amount of both.

I totally don’t buy it.

And when you build for example that as a 100m high elevator here on Earth, the expansion of space doesn't work as an explanation for where you get that energy, so you violate energy conservation also in the sense Sean Carroll mentions as linked by Thomas:

When the space through which particles move is changing, the total energy of those particles is not conserved.

It’s not that all hell has broken loose; it’s just that we’re considering a more general context than was necessary under Newtonian rules. There is still a single important equation, which is indeed often called “energy-momentum conservation.” It looks like this:

The details aren’t important, but the meaning of this equation is straightforward enough: energy and momentum evolve in a precisely specified way in response to the behavior of spacetime around them. If that spacetime is standing completely still, the total energy is constant; if it’s evolving, the energy changes in a completely unambiguous way.

 

[Thomas R Morrison]

Ok, so in theory, I could lift a few kilo tons of water into the air, then let it fall down a tube and turn a generator.

Part of that energy would be used to lift the water again, and the rest would be free.

It would run forever, and provide a surplus of free energy. And waste heat. An infinite amount of both.

I totally don’t buy it.

I've never actually seen an idea like this mathematically modeled in the academic literature - let me know if you find one. The only example I've seen was the "lasso around a receding galaxy" example, and that looks legit. I can't see where that example would be intrinsically different than the scenario that you're describing, so I'm going with that, at least until I see a more explicit treatment of it.

I'm a little hung up on the energy balance sheet though - the craft itself has equal positive and negative mass, so those cancel out just fine. But if you tie a rope to the craft and lift kilotons of water, then the net mass no longer sums to zero. So you're actually raising that positive mass, which involves work (an input of positive energy). But then, you should just be able to apply more positive energy within the craft to amplify the negative stress-energy terms, in order to compensate for that suspended/lifted mass, and restore the balance sheet to zero. You're not adding any new energy to the system, you're just changing its application within the gravitational field propulsion system, which seems like magic. But the same can be said for the acceleration of the cosmological constant effect, so I think it works out.

I'd like to see a paper on it though, just to be sure. I get where you're coming from though - abandoning the nice and tidy classical conservation of energy principle is a damned difficult, counterintuitve thing to reckon with. Perhaps even more counterintuitive than quantum teleportation, which Einstein mocked as "spooky action at a distance." But it seems that nothing is sacred here in the era of modern physics, so I tend to side with the physics over my own fallible monkey-brain intuition.

 

[marduk]

I've never actually seen an idea like this mathematically modeled in the academic literature - let me know if you find one. The only example I've seen was the "lasso around a receding galaxy" example, and that looks legit. I can't see where that example would be intrinsically different than the scenario that you're describing, so I'm going with that, at least until I see a more explicit treatment of it.

I'm a little hung up on the energy balance sheet though - the craft itself has equal positive and negative mass, so those cancel out just fine. But if you tie a rope to the craft and lift kilotons of water, then the net mass no longer sums to zero. So you're actually raising that positive mass, which involves work (an input of positive energy). But then, you should just be able to apply more positive energy within the craft to amplify the negative stress-energy terms, in order to compensate for that suspended/lifted mass, and restore the balance sheet to zero. You're not adding any new energy to the system, you're just changing its application within the gravitational field propulsion system, which seems like magic. But the same can be said for the acceleration of the cosmological constant effect, so I think it works out.

I'd like to see a paper on it though, just to be sure. I get where you're coming from though - abandoning the nice and tidy classical conservation of energy principle is a damned difficult, counterintuitve thing to reckon with. Perhaps even more counterintuitive than quantum teleportation, which Einstein mocked as "spooky action at a distance." But it seems that nothing is sacred here in the era of modern physics, so I tend to side with the physics over my own fallible monkey-brain intuition.

Ok then, screw the water.

Just lift the craft up and let it fall onto a giant piezoelectric crystal over and over again.

Electricity for free.

It really doesn’t matter, you could even build a basic heat engine.

Once you move something in a gravity well for less energy than it would take to do the work to do so, you have some kind of perpetual motion/free energy device.

 

[Thomas R Morrison]

Ok then, screw the water.

Just lift the craft up and let it fall onto a giant piezoelectric crystal over and over again.

Electricity for free.

It really doesn’t matter, you could even build a basic heat engine.

Once you move something in a gravity well for less energy than it would take to do the work to do so, you have some kind of perpetual motion/free energy device.

Yep - I can't see a way around it. Of course, as I say that I have to tell the little voice, screaming at me from the classical physics monkey part of my brain "No that can't be right you idiot!!!," to stfu and let me think about this for a minute, as I grasp at thin air to find some other explanation to restore the balance of energy somehow. But as far as I've ever seen with this subject, the conservation of energy just doesn't hold up in general relativity, or modern cosmology for that matter. Even the cosmological redshift represents a direct loss of energy. So we have direct observational evidence that energy is both gained and lost in general relativity. Mind-blowing.

I guess that answers the question of alien energy sources - once you crack metric engineering you can pull energy right out of thin air, or rather, polarized spacetime. That must keep the oil execs up at night, wondering when that one key breakthrough in metric engineering is going end the fossil fuel feeding frenzy once and for all.

It's kinda funny but my mind is incapable of fully accepting that conclusion - I always try to ignore that aspect of all of this and focus exclusively on the propulsion physics, because I can accept that part of it - probably because I've seen something that I can't explain in any other way.

 

[Randall]

@Usual Suspect - Here's where we left off in the Time Travel thread - I'll respond here since it's relevant to this thread as well:

This isn’t actually a logical argument – you’re saying: “ let’s take our observation that light follows a curved trajectory around a gravitating body, and then subtract that curved trajectory from the equation, so we can draw a straight line between the two points.” That doesn’t prove anything:

Okay, here's the issue then: The thought experiment I posed makes perfect sense to me and your logic seems a bit fuzzy around the edges ( and visa versa ). So that's where the disconnect is, which means we need to explore this deeper to get to the bottom of it.

... that works whether you explain the curved trajectory as curved spacetime, or if you explain the curved trajectory as a force acting between the light and the material body. But the curved spacetime model (general relativity) predicted the correct magnitude of curvature, whereas the Newtonian explanation of a force acting between the light and the gravitating body only predicts ½ of the observed curvature. So that was the first compelling evidence for Einstein’s metric curvature theory of gravitation.

I'm not saying that Newtonian formulas are more accurate, so that isn't the issue. I have no problem with the analogy of space curvature to make more accurate predictions. I have an issue with assuming that because the analogy works, that space is actually curved in reality on an intrinsic level. So let's set any debate about Einstein ian and Newtonian math aside. They're not relevant to the issue.

We can simply substitute any sort of equation, the point being that equations are abstract mathematical constructs that exist only in our mind. That makes them ideas, not realities, and the question of whether or not space is actually curved is an existential question, not an abstract one. So let's accept that as the initial premise.

When we do that, what we have is an abstract representation ( math ) that describes accurately the behavior of objects in space. The point of contention here appears to be that some people ( including yourself ) make the leap in logic of equating the abstract with the existential ( that because of the math space itself must be curved ). There is no evidence for this. There is only evidence that things in space behave according to the predictions made by the math ( abstract ). But space itself ( existential ) appears to be uniform.

The logical proof for this is in the types of thought experiments I mentioned. To reiterate. Gravitational lensing can produce two images of the same distant object. Obviously these cannot be the same object and two different objects at the same time. Therefore what has happened is not that space has warped into two separate "spaces" with two separate objects. It's simply the way light from the object has been bent around massive objects.

Similarly, as pointed out in the initial example, if the apparent position of an object and the actual position were due to the curvature of space, then the direct route to the object through space would have to be through curved space, or else to tunnel through the curvature in a straight line. But we know we don't have to tunnel through the curvature. We can simply calculate the actual position and plot a straight line through space.

Therefore, you have two logical reasons with practical applications that prove ( logically ) that space itself ( existentially ) must be uniform, even if the curved space analogy works for predicting the behavior of freely moving objects ( including photons ).

But it turns out that it’s perfectly valid to explain gravitation as a strictly quantum phenomenon acting within a flat spacetime after all – this is what quantum gravity is all about. There’s an excellent old paper about this from 1975, but incredibly, I can find no free copies of it online, which I find infuriating. Withholding essential scientific knowledge from the general public for 43 years should be illegal – science belongs to everyone. Here’s the citation anyway, in case you or a friend can get you a free copy of this paper through an online university archive:

Classical general relativity derived from quantum gravity, D. G. Boulware and S. Deser, 1975 - ScienceDirect

In a nutshell, this situation is exactly like classical electrodynamics vs. quantum electrodynamics. You can either take the classical view that entails electric and magnetic fields, and all of that math works out fine until you get down to very small spatial scales and very low energies. But in those latter situations you need quantum electrodynamics, which replaces the notion of fields with the notion of virtual particle exchanges, to get the right answers (and of course at larger scales and energies both theories predict the same, or rather indistinguishable, results).

We expect the same thing to happen with gravity. There’s only one small problem: nobody’s come up with viable theory of quantum gravity yet. And theoretical physicists have been working on it, hard, for several decades.

So you have a choice: you can either work with general relativity because it provides all of the correct answers (and will certainly continue to provide the correct answers at all non-quantum scales and energies regardless of future developments, just as classical electrodynamics does), or you can assume that sooner or later somebody will work out the correct theory of quantum gravity, comfortable in the faith that someday we’ll abandon general relativity in favor of a quantum theory of gravity that operates within the context of a flat Minkowski spacetime. Either choice is a valid one, but the first choice gives you a precise mathematical and conceptual edifice to work with today. So I favor that choice, and I’ll switch horses if and when quantum gravity works out.

Interesting, but again, none of that is relevant to the point I made. We're only dealing with the issue of the abstract versus the existential. I'll close by also reminding you about the example of the equivalency principle, another analogy that is clearly not the case in reality but forms the basis of Einstein's gravitational theory: Equivalence principle - Wikipedia

So my feeling on this is that perhaps we had our premise wrong at the outset and you've been trying to prove the case that Newtonian math isn't as accurate. I never had a problem with that in the first place. However let's not confuse the abstract with the existential. By keeping them separate we can both be right without any conflict in the bigger picture.

 

[Realm]

Once you move something in a gravity well for less energy than it would take to do the work to do so, you have some kind of perpetual motion/free energy device.

Here's one paper about somewhat similar case. Didn't have time to look it through properly.

Abstract:

Overcoming the force of gravity is an important part of space travel and a signicant obstacle preventing many seemingly reasonable space travel schemes to become practical. Science fiction writers like to imagine materials that may help to make space travel easier. Negative mass supposedly causing anti-gravity is one of the popular ideas in this regard. But can mass be negative? In this paper, we show that negative masses are not possible their existence would enable us to create energy out of nothing, which contradicts to the energy conservation law.

http://www.cs.utep.edu/vladik/2017/tr17-89b.pdf

 

[Randall]

Ok then, screw the water. Just lift the craft up and let it fall onto a giant piezoelectric crystal over and over again. Electricity for free. It really doesn’t matter, you could even build a basic heat engine. Once you move something in a gravity well for less energy than it would take to do the work to do so, you have some kind of perpetual motion/free energy device.

I'm not entirely sure I'm following what's going on in your line of thinking, but I'll throw this in as potential food for thought. There is no free energy from moving things within a gravity well. The motion of the Earth and Moon are a pretty good example of this. The motion results in tidal forces that suck up kinetic energy changing the rotation and orbit. Energy is either transformed from one form to another, but doesn't appear to be free.

 

[marduk]

I'm not entirely sure I'm following what's going on in your line of thinking, but I'll throw this in as potential food for thought. There is no free energy from moving things within a gravity well. The motion of the Earth and Moon are a pretty good example of this. The motion results in tidal forces that suck up kinetic energy changing the rotation and orbit. Energy is either transformed from one form to another, but doesn't appear to be free.

The earths rotation is slowing down because of the tides.

And the moon is moving further away because of energy loss.

Nothing comes for free. Conservation of energy is a bitch to get around.

If the energy to move something using some kind of antigravity device were equivalent to doing it by Newtonian means, it would balance.

Even ‘zero point’ energy is neither zero nor a point. It still likely obeys the laws of thermodynamics, although in weird ways.

Basically what I’m saying is I can’t see that working out for this line of propulsion concept, and if it does work out they get free energy as a side benefit.

But the universe appears to not like either antigravity or free energy, so that makes me doubt the deal.

 

[marduk]

Yep - I can't see a way around it. Of course, as I say that I have to tell the little voice, screaming at me from the classical physics monkey part of my brain "No that can't be right you idiot!!!," to stfu and let me think about this for a minute, as I grasp at thin air to find some other explanation to restore the balance of energy somehow. But as far as I've ever seen with this subject, the conservation of energy just doesn't hold up in general relativity, or modern cosmology for that matter. Even the cosmological redshift represents a direct loss of energy. So we have direct observational evidence that energy is both gained and lost in general relativity. Mind-blowing.

I guess that answers the question of alien energy sources - once you crack metric engineering you can pull energy right out of thin air, or rather, polarized spacetime. That must keep the oil execs up at night, wondering when that one key breakthrough in metric engineering is going end the fossil fuel feeding frenzy once and for all.

It's kinda funny but my mind is incapable of fully accepting that conclusion - I always try to ignore that aspect of all of this and focus exclusively on the propulsion physics, because I can accept that part of it - probably because I've seen something that I can't explain in any other way.

I wonder if you could make it balance somehow by slowing down the expansion of the universe or something.

Maybe that’s why inflation only appears to happen in empty space, matter passively extracts energy from it somehow.

Now I’m just BSing and should put down my glass of wine.

 

[Thomas R Morrison]

But space itself ( existential ) appears to be uniform.

No it doesn't. It actually appears to be curved, according to all of our direct physical observations. You can say "don't believe your lying eyes," but then you'd need to demonstrate how exactly our eyes are being fooled. A quantum theory of gravity might do that someday, if we ever achieve one. But until that happens, it makes 100% sense to proceed working with what we actually observe, which is curved spacetime.

Gravitational lensing can produce two images of the same distant object. Obviously these cannot be the same object and two different objects at the same time. Therefore what has happened is not that space has warped into two separate "spaces" with two separate objects. It's simply the way light from the object has been bent around massive objects.

You seem to be arguing in favor of gravitational lensing here, which is modeled accurately as spacetime curvature. GR doesn't say that space has warped into two separate spaces with two different objects when gravitational lenses produce dual images of the same object - it describes it exactly as a lens of curved spacetime producing the illusion of two objects. Which is exactly what you're saying. So what exactly is your point?

Interesting, but again, none of that is relevant to the point I made. We're only dealing with the issue of the abstract versus the existential.

What? How can a theory of quantum gravity that would argue for the exact same flat spacetime interpretation that you seem to be advocating here, not be relevant?

I'll close by also reminding you about the example of the equivalency principle, another analogy that is clearly not the case in reality but forms the basis of Eisteins gravitational theory: Equivalence principle - Wikipedia

What? How in the world is the equivalence principle, in any sense, "not the case in reality?" I mean, I'd love to see a violation of it, but the equivalence of inertial mass and gravitational mass is one of the most precisely experimentally proven concepts in all of physics. And Dennis Sciama's 1953 model of inertial mass ties it in with gravitational mass beautifully - explaining the equivalence of the two using a single elementary postulate.

However let's not confuse the abstract with the existential

I have no idea what you're talking about (and honestly I suspect that you don't either - sorry). How on earth can you assert that you know what the existential reality is? All we have to go on, are our observations of nature. Those observations describe a very clear and consistent picture, which we've described mathematically to high precision, and which has made a series of totally unexpected predictions that were subsequently verified by additional observations. That's the only method for describing existential reality that we have - the scientific method.

That's the best we can do. And the metric curvature model fits everything that we've observed as perfectly as we can observe it. So if you want to draw a distinction between the abstract and the existential, then you're in the position of advancing an abstract idea, not an existential one, because the real, measured, observational and experimental data all points to an existential reality replete with metric curvature.

It has been mathematically (abstractly) calculated that a quantum theory of gravity could in principle explain our observations of a universe with metric curvature, by using quantum phenomena acting in a background of flat Minkowski spacetime. I thought you'd be delighted to hear about that. But you dismissed it instead.

So what exactly are you trying to say, if not exactly that? o.0

I'm not entirely sure I'm following what's going on in your line of thinking, but I'll throw this in as potential food for thought. There is no free energy from moving things within a gravity well. The motion of the Earth and Moon are a pretty good example of this. The motion results in tidal forces that suck up kinetic energy changing the rotation and orbit. Energy is either transformed from one form to another, but doesn't appear to be free.

Energy is conserved in celestial mechanics, that's well-established. It's only when you're dealing with the negative pole of gravitation that you run into trouble. The universe is expanding under the influence of the cosmological constant, for example, which represents a negative gravitational field. So the total kinetic energy of the universe appears to be increasing at every instant. Unless somebody can show where an equal amount of negative energy is being created to balance out that increase in kinetic energy, then we're forced to accept that energy is not always conserved in general relativity. And it gets even hairier when we consider a warp field propulsion device - if there's a way to preserve the conversation of energy in a system driven by that effect, I haven't seen it yet. The physicist in me wants somebody to solve that problem and restore the conservation of energy, but the dreamer in me hopes that nobody can.

But the universe appears to not like either antigravity or free energy, so that makes me doubt the deal.

Actually – I’ve pointed this out before, the inflationary epoch appears to be driven by antigravity (a logarithmic expansion of the spacetime metric, yadda yadda), and the current cosmic acceleration (which fits the cosmological constant beautifully) also appears to be a form of antigravity. A lot of physicists are still very uncomfortable with that term, after spending several decades crapping all over people like us who invoke that notion to explain ufo behavior, but general relativity has always been cozy with the idea of antigravity (or in more modern sanitized language, “negative gravitation”). Which has always been totally hypocritical of course, because Einstein was fine with the cosmological constant when he introduced it into GR for the wrong reason, and that was an antigravitational term from word “go.”

Here's a really nice post by one of the best physicists at physics.stackexchange that delves into the violations of energy conservation in GR, without all of the differential geometry mathematics that usually makes these things miserable to traipse through:
https://physics.stackexchange.com/a/35438

I wonder if you could make it balance somehow by slowing down the expansion of the universe or something.

Maybe that’s why inflation only appears to happen in empty space, matter passively extracts energy from it somehow.

Now I’m just BSing and should put down my glass of wine.

Haha. I've been mulling this over ever since I listened to our episode about The Origin of Inertia, and I have a wisp of an idea that might work (since we're just BSing at this point, lol). According to Dennis Sciama's model of inertial mass, it's the gravitomagnetic forces acting between a body and every other body in the universe that produces inertial mass (and I have a hard time arguing against this idea, because gravitomagnetism is very well-established at this point - mundane, even). So as the universe expands, the most distant galaxies cross over the horizon of the observable universe, and as they do so, their interaction with our local matter (gravitational and everything else) drops to zero. So with less matter in the sphere of the observable universe, the inertial mass of all matter should drop. So maybe the cosmological acceleration (increasing kinetic energy) is balanced by the gradual drop in inertial mass (potential energy). It's probably a BS idea but I thought I'd throw it out there. It's probably good for one's sense of humility to drink some wine while posting online and risk being totally wrong about stuff sometimes.

 

[Randall]

No it doesn't. It actually appears to be curved, according to all of our direct physical observations.

Okay, it's quite clear now that you're missing the fundamental difference between the abstract and the existential. Space doesn't appear curved according to all of our direct physical observations because it's not space that those physical observations are observing, it's the behavior of stuff in space and how well an abstract analogy ( math ) predicts the behavior of that stuff.

What? How can a theory of quantum gravity that would argue for the exact same flat spacetime interpretation that you seem to be advocating here, not be relevant?

Again the difference between the abstract and the existential. The leap in logic is like if someone discovered that ants accurately predicted earthquake behavior it wouldn't mean that earthquakes are caused by the behavior of ants. However people are prone to jumping to those sorts of conclusions. Interestingly, I just pulled that out of thin air and figured I'd look it up and guess what ... Ants Lead the Way on Earthquake Prediction ... lol.

What? How in the world is the equivalence principle, in any sense, "not the case in reality?"

Equivalency isn't the case in reality because Earth's gravity isn't caused by acceleration. We don't stick to the surface because we're on an ever accelerating surface hurtling through space. It purely an analogy, just like curved space.

I have no idea what you're talking about

I can see that.

(and honestly I suspect that you don't either - sorry).

Since you have no idea what I'm talking about, logically, you cannot know that.

How on earth can you assert that you know what the existential reality is?

One doesn't need to know the existential reality of a particular situation in order to know the difference between the two concepts and from there make logical deductions about what must be the case, which is what the thought experiments I've proposed do.

All we have to go on, are our observations of nature. Those observations describe a very clear and consistent picture, which we've described mathematically to high precision, and which has made a series of totally unexpected predictions that were subsequently verified by additional observations. That's the only method for describing existential reality that we have - the scientific method.

While that is superficially true, it does not address the context of the point made.

That's the best we can do.

Not always. Philosophy, logic, and critical thinking don't always require observation and measurement in order to provide a proof.

And the metric curvature model fits everything that we've observed as perfectly as we can observe it. So if you want to draw a distinction between the abstract and the existential, then you're in the position of advancing an abstract idea, not an existential one, because the real, measured, observational and experimental data all points to an existential reality replete with metric curvature.

Not exactly. A curved space analogy just says that the behavior of certain things in space can be calculated by thinking of space as curved and developing math around that model. However for the reasons I pointed out in the thought experiments, space cannot actually be curved. Therefore to invalidate what I'm saying you'd have to address the points made in that context. Equations don't do that. No equations can. You need to get your mind out of the equations and abstract representations. It is just as real an observation to point out that the apparent and actual positions of an object are different and logically deduce from that situation that it's not space that's curved, but the path of the light.

It has been mathematically (abstractly) calculated that a quantum theory of gravity could in principle explain our observations of a universe with metric curvature, by using quantum phenomena acting in a background of flat Minkowski spacetime. I thought you'd be delighted to hear about that. But you dismissed it instead.

I haven't dismissed the value of using the concept if it is useful in making predictions about the behavior of things in the real world. Let me try this approach. I'm talking about the fundamental nature of space as some purely volumetric quantity, lets say a cubic parsec. Now the behavior of stuff inside that volume can be predicted using formulas that are based on math that uses the concept of curved space, which is just fine, but from a God's eye view, a perfectly straight line can still be drawn between any given object, which means space itself cannot be curved.

I'll put together some sort of diagram to help illustrate over the next few days. This is where I wish I knew someone with 3D animation skills. You could use the equations to create accurate ray tracing algorithms for the path of light past massive objects, and yet the entire scene can still be mapped out in perfectly uniform volumetric space. There's no reason to assume real space is any different.

 

[Randall]

Intersting Aside - Ants Predict Earthquakes
and Speed Up Internet

 

[Thomas R Morrison]

Okay, it's quite clear now that you're missing the fundamental difference between the abstract and the existential. Space doesn't appear curved according to all of our direct physical observations because it's not space that those physical observations are observing, it's the behavior of stuff in space and how well an abstract analogy ( math ) predicts the behavior of that stuff.

Okay then explain to me how we can observe the geometry of space without observing the way that a perceptible form of matter or energy interacts with it. I'll wait.

Again the difference between the abstract and the existential. The leap in logic is like if someone discovered that ants accurately predicted earthquake behavior it wouldn't mean that earthquakes are caused by ant behavior. However people are prone to jumping to those sorts of conclusions. Interestingly, I just pulled that out of thin air and figured I'd look it up and guess what ... lol. Ants Lead the Way on Earthquake Prediction

Haha, that was awesome. The universe loves to f*ck with us =)

But back to the point. You seem to take exception to the process of observation and mathematical modeling at the heart of the scientific method, and yet you haven't offered an alternative.

Equivalency isn't the case in reality because Earth's gravity isn't caused by acceleration. We don't stick to the surface because we're on an ever accelerating surface hurtling through space. It purely an analogy, and equivalency in this case is synonymous with analogy.

Uhm, you understand that nobody's saying that the Earth is expanding at an accelerating rate, but that an acute geometric angle between space and time generates an acceleration field, right? Because general relativity states that, and it's been 100% accurate to the limits of our experimental precision. No other model has been presented which can predict the experimental observations. That should count for something, yes?

Since you have no idea what I'm talking about, logically, you cannot know that.

My point is that I should be able to discern what point you're making after reading your words. But I can't. And I'm a pretty bright guy. So I'm reasonably confident that the problem isn't here on the receiving end, capiche?

One doesn't need to know the existential reality of a particular situation in order to know the difference between the two concepts and from there make logical deductions about what must be the case, which is what the thought experiments I've proposed do.

No, they don't. You've convinced yourself, but your thought experiments are unconvincing on the logical grounds that I've pointed out: to wit, they can be explained in either of two ways (the manner that you favor and the manner that you don't) equally and indistinguishably. So I'm waiting for you to resolve that problem, by explaining a method to discern between them - empirically, if possible.

While that is superficially true, it does not address the context of the point made.

The point you made could be equally interpreted in either of two ways, which are in direct conflict. So you've failed to provide a discerning mechanism between them. That's not my problem - it's yours. I'd be psyched if you could resolve it, but frankly I don't think t's possible, and I think it's weird that you're so confident that one interpretation is correct over the other, when the observable evidence could be interpreted both ways with equal validity.

Philosophy, logic, and critical thinking don't always require observation and measurement in order to provide a proof.

Holy tamole - if you actually mean this seriously, then we'll never achieve any kind of consensus, because meausrement and observation are the *only rational foundation* for defining a consensual reality. And it would be madness to rely upon philosophy in lieu of empirical science - the Greeks tried that and they stalled out at the concept of the gear.

A curved space analogy just says that the behavior of certain things in space can be calculated by thinking of space as curved and developing math around that model. However for the reasons I pointed out in the thought experiments, space cannot actually be curved.

Your thought experiments don't prove that space cannot be curved. And all of the emprical evidence available confirms that it *is* curved. You only proved that if you subtract the curvature from the observations, then space doesn't appear to be curved. Do you see the problem there? God I hope so.

It is just as real an observation to point out that the apparent and actual positions of an object are different and logically deduce from that situation that it's not space that's curved, but the path of the light.

I simply pointed out that both interpretations explain the data perfectly, which is true. There's no logical basis for choosing one interpretation over the other. And it kinda freaks me out that you can't see that. Believing that your interpretation is correct when both interpretations explain the data perfectly, is not a valid basis for choosing one interpretation over the other.

Also, you seem to be allergic to the time dilation data, which apparently you can't explain with your "flat spacetime" idea. Tell me right now why time passes more slowly upon the Earth than in space - which is an observed fact - if spacetime geometry is not curved around the Earth. Take your time.

the behavior of stuff inside that volume can be predicted using formulas that are based on math that uses the concept of curved space, which is just fine, but from a God's eye view, a perfectly straight line can still be drawn between any given object, which means space itself cannot be curved.

"from a God's eye view?" Please tell me that you're joking. Because I don't have the benefit of "a God's eye view" of anything, and I'm frankly mortified that you seem to think that you do. We humans only have our sense perceptions - our observations and our measurements, to determine the nature of our reality. That's it. If you're relying upon some special divine power to discern a more fundamental ontological truth about perceived reality, then the only people you'll ever be able to convince of your elevated perspective, are the chosen few who are also endowed with this special gift of "a God's eye view."

Because us mere mortals who are doomed to perceive reality through the mere human's eye view, have noticed that the shortest distance between two points in not in fact a straight line, but rather a geodesic, which is perfectly defined by the general theory of relativity that describes spacetime as curved around massive bodies. And we depend upon this empirical truth to send probes to other worlds.
Geodesic - Wikipedia

The fact that you can draw a straight line between two points, on a flat star map for example, doesn't prove that space isn't curved - it only proves that you can't see a 4D curvature on a 2D map. The only valid test to find out if space if flat, is if the shortest distance between two points is a straight line. But we know that it isn't, because it takes more energy to follow a straight line from point A to point B, than it takes to follow the geodesic defined by the spacetime curvature of the gravitational field.

Granted, this isn't definitive proof that spacetime is actually curved, because it's possible in principle to model the geodesic as a product of quantum phenomena acting upon matter and energy, and there's no empirical or logical method to determine which model is correct. But we know that the curved spacetime model works perfectly to within the precision of all empirical observations, and yet nobody has devised a working quantum gravity model that can boast the same level of predictive accuracy (or even work within the content of quantum mechanics), so the prevailing victor is clearly the curved spacetime model, at least until somebody can offer an equivalent or superior alternative theory.

That's all I'm saying. Whew.

Honestly it's a bummer to debate the validity of GR - there's so much experimental and theoretical evidence available online already to support it, that it's a really tedious and profitless exercise to debate it again here. Nobody else wants to trudge through this kind of debate. So if you want to bang your head against the wall some more, then let's move it back where this all started, so we can focus on more forward-moving concepts here in this thread.

Mucho gracias, amigo.

 

[Randall]

Uhm, you understand that nobody's saying that the Earth is expanding at an accelerating rate, but that an acute geometric angle between space and time generates an acceleration field, right?

That's the whole point. It's an analogy, meaning analogous to acceleration, just like curved space is an analogy.

My point is that I should be able to discern what point you're making after reading your words. But I can't. And I'm a pretty bright guy. So I'm reasonably confident that the problem isn't here on the receiving end, capiche?

Absolutely. You come across as exceedingly bright, that's why this is such a curiosity. I see where the disconnect is with you, but I can't seem to figure out how to bridge it.

Holy tamole - if you actually mean this seriously, then we'll never achieve any kind of consensus, because meausrement and observation are the *only rational foundation* for defining a consensual reality. And it would be madness to rely upon philosophy in lieu of empirical science - the Greeks tried that and they stalled out at the concept of the gear.

Ironic that you should mention the Greeks because they are the ones that came up the theorems for Euclidean geometry which can be worked out entirely conceptually.

Your thought experiments don't prove that space cannot be curved.

That is a proclamation, not an explanation that addresses the logic used in the thought experiments.

"from a God's eye view?" Please tell me that you're joking.

It's a figure of speech, like writing from an omniscient point of view. It doesn't literally make the author God. It is a point of view.

Honestly it's a bummer to debate the validity of GR - there's so much experimental and theoretical evidence available online already to support it, that it's a really tedious and profitless exercise to debate it again here. Nobody else wants to trudge through this kind of debate. So if you want to bang your head against the wall some more, then let's move it back where this all started, so we can focus on more forward-moving concepts here in this thread.

We're not debating the value of the math. I'm not sure why I can't get that across to you. That's the most interesting part to me. Maybe someone else will come along who also sees both sides of this and do a better job of explaining.

In the meantime, you have a mind for visualization ( I assume because of your sculpture work ), so how it is that you can't imagine a simple cubic volume of space inside of which objects are placed and see that formulas can be mapped onto those objects in a way that causes them to behave exactly like they are predicted to behave in the real world, without having to distort any of the space, and in addition to that, you could draw a straight line between any two objects in that space. You should be able to plainly see that no curved space is necessary to create a system that does everything the math you're referring to predicts. Therefore there is no reason to think real life space is curved either. Stuff just behaves as if it is curved due to the forces that are imparted on them by nature.

If you don't have the capacity to visualize such a system, that would explain a lot. Not everyone does. It's not a measure of intelligence either: Why some people can't see pictures in their imagination

 

[marduk]

Inflation isn’t antigravity, I think.

Gravity bends space time. Inflation expands it.

You could have inflation in a curved region of space time, and it would just expand the curve.

Antigravity should flatten space time.

 

[Realm]

Here's one paper about somewhat similar case. Didn't have time to look it through properly.
http://www.cs.utep.edu/vladik/2017/tr17-89b.pdf

Getting back to this paper, here's the scenario they are considering:

Suppose that negative masses are possible. Then, by attaching an object with a negative mass m < 0 to a regular object with a similar positive mass |m| = −m, we get a combined object whose overall mass M is 0 (or at least is close to 0). Since the mass M is close to 0, even a very small force F will lead to a huge acceleration a = F M . Thus, without spending practically any energy, we can accelerate the combined object to as high a velocity as we want. Once the object reaches this velocity, we dis-attach the negative-mass object let it y away. As a result, we now have an object of positive mass |m| with a very large kinetic energy and we can use this energy to perform useful work. This scheme is not as clear-cut as the previous schemes, since here, we do not exactly go back to the original state we lose a negative-mass body. However, we can do this for negative-mass body of arbitrarily small size and still gain a lot of energy. Thus, while we cannot gain energy and get back to exactly the same original state, we can get back to a state which is as close to the original state as we want and still gain as much energy as we want. This clearly contradicts to the idea of energy conservation. Thus, negative masses are not possible

It's somewhat similar to what I thought with that elevator idea, but I think with that you can get back to the original state. Here's a reminder of how negative masses are expected to behave:

For an ordinary apple, the Earth’s positive mass exerts an attractive force downward, and so, according to Newton’s second law, the apple will accelerate in that direction, toward the Earth. For a negative mass apple, the force would be negative, and therefore upward. But the acceleration would also be negative — that is, in the opposite direction of the force. So the negative mass apple would still fall downward.
...
Bondi worked out the general relativistic math for the case of two bodies, one with ordinary (positive) mass and one negative. Positive mass attracts all masses, so Body P (positive mass) attracts Body N (negative mass). But negative mass repels all masses, so Body P would fly away from Body N. So N tries to get closer to P, because P attracts it, while P tries to get farther away from N, because N repels it. Consequently N chases P across the universe at an ever accelerating speed.
...
All this is very interesting, but also probably moot, as there doesn’t seem to be any reason to believe that negative mass actually exists. But that doesn’t stop physicists from speculating (or even theorizing) about it.

Fact and fiction about negative mass

So, my idea could be illustrated as follows (while ignoring all sorts of practical difficulties). Imagine we could create a slab of negative mass matter weighting -1 tons, and place it on the ground, next to a 100 meter high tower for example. As described above, it falls down so it stays on the ground(*). Now attach 1 ton of ordinary matter on top of it. That combination now supposedly becomes "weightless" and lifts easily up with runaway motion without energy input. When it gets at the top of that tower, you take away that ordinary matter, and let the slab fall back to ground. Then you can utilize all that potential energy you gained in various ways. Unlimited free energy that comes from nowhere?

Handwaving about the strangeness of relativity doesn't really help, since this setup basically has as little to do with relativity and expansion of space as some regular elevator out there. And as explained by Sean Carroll, even in GR, energy conservation is still supposed to work in a well defined manner relative to how the spacetime changes.

(*) Actually rather drill through it, but let's assume we can somehow stop that from happening or are fast enough to load it before it does...

 

[Realm]

Another relevant paper:

The inclusion of negative mass into Newton's laws of motion and gravitation is considered, and, as in previous investigations, no contradictions are discovered. A necessary modification to the principle of least action is proposed, which takes into account negative mass. The statistical thermodynamics of an ideal classical gas, composed of negative-mass particles, is then examined. The proposal that such systems can only be described by a negative temperature provides an extra constraint, and lends support to the already conjectured hypothesis that positive and negative mass cannot coexist. This rules out runaway motion commented upon in previous papers. The conclusion is, then, that negative mass can only exist at negative temperature, and must be adiabatically separate from positive mass.
...
The work of this paper, in line with other research, does not produce any
conclusive reason as to why negative mass ought to be absent in the Universe. It
does, however, propose a plausible conjecture, that negative mass necessarily exists
at negative temperature, which may explain the lack of experimental observation of
negative mass, negative temperatures being a rare occurrence. Furthermore, the
negative-mass/temperature system should be adiabatically separate from its
surroundings so as to prevent unwanted runaway phenomena. Although not
dismissing negative mass altogether, these constraints leave little room for manoeuvre.

A consideration of the possibility of negative mass

"positive and negative mass cannot coexist" sounds pretty difficult to combine with the need to produce them in pairs:

But negative mass exists only in an expanding universe, and because of energy conservation it can only be produced in positive–negative mass pairs.

http://physicstoday.scitation.org/do/10.1063/PT.6.3.20170524a/full/

 

[marduk]

Here's a really nice post by one of the best physicists at physics.stackexchange that delves into the violations of energy conservation in GR, without all of the differential geometry mathematics that usually makes these things miserable to traipse through:
https://physics.stackexchange.com/a/35438

Wow, I don't buy this guy's argument at all.

The energy conservation becomes vacuous or invalid in the general theory of relativity and especially in cosmology. See

The Reference Frame: Why and how energy is not conserved in cosmology

Why and what does it imply? First of all, Noether's theorem makes the energy conservation law equivalent to the time-translational symmetry. In general backgrounds in GR, the time-translational symmetry is broken (especially in cosmology), so the corresponding energy conservation law is broken, too, despite the fact that the energy conservation law (and the corresponding time-translational symmetry) is an unassailable principle in all of pre-general-relativistic physics.

One example of a possible subtlety we have to be careful about: &#x2207;&#x03BC;T&#x03BC;&#x03BD;=0" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">∇μTμν=0∇μTμν=0 holds in GR but because it contains the covariant derivative &#x2207;" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">∇∇, this law can't be brought to the equivalent integral form. The extra Christoffel symbol terms explicitly measure how much the energy conservation law is violated at the given point. There's no way to redefine T&#x03BC;&#x03BD;" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">TμνTμν so that the conservation law would hold with partial derivatives &#x2202;&#x03BC;" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">∂μ∂μ but the energy would still retain a coordinate-independent value that actually constrains the final state in any way.

If one views the background as variable and appreciates that the underlying laws as being time-translational-invariant, it doesn't help because the time-translational symmetry is a subgroup of the diffeomorphism group which is a local (gauge) symmetry in GR, and all physical states must therefore be invariant under it. The invariance is the same thing as saying that the generator – the energy itself – identically vanishes. So we may declare that there's a conserved energy in GR but it's zero.

We may see the same point if we try to associate energy to gravitational waves. In general spacetimes, we will fail to find a good formula. It's not hard to see why. The total stress-energy tensor comes from the variation of the action with respect to the metric tensor. The variation of the "matter-field" part of the action gives us the matter part of the energy/momentum density. However, the variation of the gravitational part, the Einstein-Hilbert action, gives us an additional term, the Einstein curvature tensor. Of course, the sum of both vanishes – this condition is nothing else than Einstein's equations – because the metric tensor is a dynamical variable in GR and the action has to be stationary under variations of all dynamical fields.

We may also try to invent other definitions of the total energy in general spacetimes. They will either explicitly refuse to be conserved; or they will be identically zero; or they will depend on the chosen spacetime coordinates (in the latter case, it will actually be the case that the whole "beef" of the energy will be just an artifact of the choice of coordinates and there will be no "meaningful piece" that would actually depend on the matter distribution). There's no way to define "energy" in general (cosmological) situations that would be nonzero, coordinate-choice-independent, and conserved at the same moment.

For asymptotically flat or other asymptotically time-translationally-invariant spacetimes, we may again define the total energy, the ADM mass, but it is not possible to exactly say "where it is located" and the cleanest way to determine the ADM mass is from the asymptotic conditions of the spacetime.

Cosmology

In cosmology, the most explicit example of the text above is the FRW uniform and isotropic cosmology. In that case, the total energy stored in dust which has p=0" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">p=0p=0, vanishing pressure, is conserved. However, the total energy stored in radiation is decreasing as 1/a" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">1/a1/a where a" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">aa are the linear dimensions of the Universe simply because each photon (or particle of radiation) sees its wavelength grow as a" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">aa and energy goes like 1/&#x03BB;" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">1/λ1/λ i.e. 1/a" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">1/a1/a.

There are other states of matter I could discuss such as cosmic strings and cosmic domain walls which obey different power laws. But the most interesting example I will mention is the cosmological constant. It's an energy density of the vacuum. Because the cosmological constant is "constant", this energy density is always and everywhere the same. So because the density is constant and the volume of spacetime grows as, too.

Cosmic inflation is driven by a "temporary cosmological constant" so the total energy of the Universe grows with the volume of the Universe, too. In Alan Guth's words, inflation (or the Universe) is the ultimate free lunch. Inflation explains why the mass/energy of the visible Universe is so much hugely larger than the mass scales of particle physics.

For different mixtures of matter obeying different equations of state (roughly speaking, with different ratios of pressure and energy density), one will see the total energy increase or decrease or be constant. Generally, the total energy of the Universe will tend to increase as the Universe expands if the Universe is filled with matter of increasingly negative pressure; the total energy will decrease if it is filled with matter of increasingly positive pressure.

He's pushing the problem around here instead of getting at it, in my opinion.

And "Cosmic inflation is driven by a "temporary cosmological constant" so the total energy of the Universe grows with the volume of the Universe, too." is just flat out wrong.

Guth described the inflationary universe as the "ultimate free lunch":[109][110] new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the first law of thermodynamics (energy conservation) and the second law of thermodynamics(entropy and the arrow of time problem).

Inflation (cosmology) - Wikipedia

 

[DROBNJAK]

Yeah, you are all confused, because you haven't been paying attention to what Germans had been doing?

Negative mass had been experimentally created in a lab and physically equivalent systems had been researched.

Anybody who is into AG knows Martin Tajmar, professor at University of Dresden. Here he gives a great presentation about negative mass.

Its well worth watching the lecture in its entirety, but here are the highlights if you are in hurry:


@14:00 president of Austrian Academy of Sci. prof. Zeilinger in 1990s experimentally created negative mass by passing neutrons through crystal lattice. Positive mass neutrons fell down in gravitational field and, shock and horror, negative mass neutrons rose in gravitational field. This didn't violate conservation of momentum because negative mass creates negative momentum so sum is zero. Same with energy, negative mass creates negative energy, Earth's gravity is positive energy, sum is zero. Or, something like that ;-) You can see on the above diagram that positive and negative mass neutrons diverged up & down in gravitational field.


@18:08 Max Plank Institute researchers introduced photons into a special meta-material that made photons split into two groups. One group of photons behaved as if they had positive "effective mass", another group behaved as it had negative "effective mass". Than they directed these two groups towards each other, et voila, spontaneous acceleration was created where positive effective mass photon was chasing up negative effective mass photon. Max Plank team called it post-accelerating photons and paper was published in Nature Physics after a thorough peer review. Here is a brief review of the experiment in New Scientist:

Running Circles Around Newton

 

[Randall]

Interesting counterpoint to "Negative Mass: https://gizmodo.com/no-scientists-didnt-just-create-negative-mass-or-defy-1794525465

Personally, while I do think antimatter is possible, I don't think there can be "negative mass", at least not in the truest sense of the word because I don't believe that gravitation is something quantum, e.g. caused by a "graviton". Yes we know about the claims of discovering the Higgs Boson, but that discovery remains contentious. If you really dig into it, it appears to be about a "new class of particles", but even if they had discovered it, they still wouldn't have an answer as to what gives it gravity any more than they'd have the answer to how anything else gets it. They're just playing with numbers to see if they can find clues. It's like giving someone a truckload of apples and assuming that there's so many ways they can be arranged, that sooner or later they'll figure out a way to arrange them so that all turn into oranges. It will never happen. Gravity is imparted somehow. We don't know how. I think it has something to do with an external construct that imparts other rules as well.