Time, Time Travel, and Closed Timelike Curves

[Thomas R Morrison]

These time-related topics came up in The Extraterrestrial Hypothesis : Fact and Fallacy thread because I think it’s likely that most ufos are genuine spacetime vehicles. If they’re exploiting a gravitational field propulsion system, which very much appears to be the case, then that’s spacetime technology by definition. So in this thread we can focus on the time component of that equation, and perhaps a kind mod would be willing to transfer our time discussions from the ETH thread to this one =)

Everyone finds time to be a fascinating subject, and nearly everyone has their own ways of thinking about time, so here’s a thread where we can talk about all of our time-related notions.

I’ll start by responding to Usual Suspect’s recent post about time in the ETH thread, so we can seamlessly transition the topic into this spin-off thread:

Time travel does seem counterintuitive to us, but we really do have to reckon with it in real-world terms – here’s a mundane example that we absolutely know is real: the twin paradox (it’s not really a paradox, btw – it’s just kinda strange).

I think most people already know the scenario: an astronaut departs from the Earth and travels in space near the speed of light for awhile, leaving his identical twin brother behind on the Earth. The traveling astronaut twin is traveling through space at relativistic speed, which slows his rate of motion through time relative to his initial rest frame at the Earth (this conjoined space and time geometry is the key feature of special relativity). So when he gets back to the Earth, his brother is an old man, but only some smaller interval, perhaps mere days, have passed for the travelling astronaut twin. It seems unrealistic to our human intuition that a pair of identical twins could end up at different physical ages, standing side by side, simply by moving one of them through space at a high rate of speed, but it’s an absolutely proven scientific fact that this actually happens in physical reality. And gravity has the same effect of aging you more slowly, just like high-speed travel does.

Right. I get all that. But relative changes in localized systems involve different frames of reference. It's not really time travel in the sense we're talking about. It's more a time dilation situation. Let me try to illuminate the perspective I'm coming at this from this way: It may take a few steps, and then we can come back to the rest of the points. This is all very interesting, so maybe we'll both have some sort of epiphany ( or end up equally confused ). To make sure we're on the same page, let's start with what we mean by time in the first place. I'll go first:

Time is change, and all measurements of time depend on being able to detect change. So if change can be detected, time necessarily exists. Are we okay with that or do we need to refine that to some extent?

Given the high-precision successes of special relativity and general relativity with regard to time, I consider time to be a dimension that’s different from, but in many ways equivalent to, space. And I find this model to be very intuitive: just as space is measured by the physical interval between two points, time is measured by the temporal interval between two events, and in fact the two can be defined interchangeably using the speed of light C as the conversion constant.

In relativity, 1 second is equivalent to 3x10^8 meters, just as 1 gram is equivalent to 9x10^20 ergs.

But I think that what clinched it for me – this equivalence between space and time, is the incredibly elegant relationship between space and time in special relativity that I stumbled across while studying the science books by Daniel Fry, the controversial alleged contactee. Here's his diagram illustrating a similar relationship between mass and energy:



The relationship between the rate of time (second/second) and speed (meter/second) defines a perfect circle. This is the Lorentz transform, which is the central geometrical concept at the heart of the special theory of relativity:


Note that we can substitute the rate of time (second/second) on the x-axis, with the scale of space (meter/meter), to get the length contraction associated with the same speed:


To me, this is unassailable mathematical and geometrical proof that time and space are equivalent physical dimensions. So we can describe them interchangeably: we can talk about a length of time, and measure that length in either seconds or meters. Similarly, we can talk about space in units of meters or seconds, or even years aka “light-years” in common parlance.

So in my mind, the issue is settled: time is a physical dimension that’s equivalent to the spatial dimension - just as objects are arranged in space, events are arranged in time, and the two can be described interchangeably. Therefore objects can be moved around in time and space in any manner permitted by physical law.

 

[marduk]

These time-related topics came up in The Extraterrestrial Hypothesis : Fact and Fallacy thread because I think it’s likely that most ufos are genuine spacetime vehicles. If they’re exploiting a gravitational field propulsion system, which very much appears to be the case, then that’s spacetime technology by definition. So in this thread we can focus on the time component of that equation, and perhaps a kind mod would be willing to transfer our time discussions from the ETH thread to this one =)

Everyone finds time to be a fascinating subject, and nearly everyone has their own ways of thinking about time, so here’s a thread where we can talk about all of our time-related notions.

I’ll start by responding to Usual Suspect’s recent post about time in the ETH thread, so we can seamlessly transition the topic into this spin-off thread:





Given the high-precision successes of special relativity and general relativity with regard to time, I consider time to be a dimension that’s different from, but in many ways equivalent to, space. And I find this model to be very intuitive: just as space is measured by the physical interval between two points, time is measured by the temporal interval between two events, and in fact the two can be defined interchangeably using the speed of light C as the conversion constant.

In relativity, 1 second is equivalent to 3x10^8 meters, just as 1 gram is equivalent to 9x10^20 ergs.

But I think that what clinched it for me – this equivalence between space and time, is the incredibly elegant relationship between space and time in special relativity that I stumbled across while studying the science books by Daniel Fry, the controversial alleged contactee. Here's his diagram illustrating a similar relationship between mass and energy:



The relationship between the rate of time (second/second) and speed (meter/second) defines a perfect circle. This is the Lorentz transform, which is the central geometrical concept at the heart of the special theory of relativity:


Note that we can substitute the rate of time (second/second) on the x-axis, with the scale of space (meter/meter), to get the length contraction associated with the same speed:


To me, this is unassailable mathematical and geometrical proof that time and space are equivalent physical dimensions. So we can describe them interchangeably: we can talk about a length of time, and measure that length in either seconds or meters. Similarly, we can talk about space in units of meters or seconds, or even years aka “light-years” in common parlance.

So in my mind, the issue is settled: time is a physical dimension that’s equivalent to the spatial dimension - just as objects are arranged in space, events are arranged in time, and the two can be described interchangeably. Therefore objects can be moved around in time and space in any manner permitted by physical law.

You had me up until that last sentence. You can move things forward in time at varying rates, as described by Einstein. But once you try to go backward - or even stop, you encounter a nasty divide by zero error.

In your graph, it would be an asymptote with a discontinuity as you approach zero from either direction - positive time or negative time.

Interestingly, if you were in negative time, you'd encounter the same discontinuity.

It's also the reason time slows down as you go faster, but never quite stops, and your energy requirement to accelerate goes all hyperbolic on you.

 

[Thomas R Morrison]

You had me up until that last sentence. You can move things forward in time at varying rates, as described by Einstein. But once you try to go backward - or even stop, you encounter a nasty divide by zero error.

In your graph, it would be an asymptote with a discontinuity as you approach zero from either direction - positive time or negative time.

Interestingly, if you were in negative time, you'd encounter the same discontinuity.

It's also the reason time slows down as you go faster, but never quite stops, and your energy requirement to accelerate goes all hyperbolic on you.

That's true within the context of the special theory of relativity, which only permits time dilation, not closed timelike curves as general relativity permits - and as we've seen with Gödel's rotating universe, can actually mandate.

It's easy to work within special relativity on this stuff, because you're limited to dilating time faster and slower; causality is always preserved in that context. You can never move through Minkowski spacetime faster than the speed of light, so you run into that asymptotic relationship.

General relativity is a whole other ballgame, and features like closed timelike curves, metric propulsion, and wormholes, outright defy the limitations of the special theory of relativity. Gravitational field propulsion is perhaps the simplest example: no matter how fast you move using that metric, you don't experience any time dilation: your clocks run at the same rate as those at your departure point even at superluminal velocities. Dr. Everett (author of the MWI) wrote an interesting paper that illustrates how this simple capability results in closed causal loops:

"Warp drive and causality," Everett, 1996

 

[marduk]

That's true within the context of the special theory or relativity, which only permits time dilation, not closed timelike curves as general relativity permits - and as we've seen with Gödel's rotating universe, can actually mandate.

It's easy to work within special relativity on this stuff, because you're limited to dilating time faster and slower; causality is always preserved in that context. You can never move through Minkowski spacetime faster than the speed of light, so you run into that asymptotic relationship.

General relativity is a whole other ballgame, and features like closed timelike curves, metric propulsion, and wormholes, outright defy the limitations of the special theory of relativity. Gravitational field propulsion is perhaps the simplest example: no matter how fast you move using that metric, you don't experience any time dilation: your clocks run at the same rate as those at your departure point even at superluminal velocities. Dr. Everett (author of the MWI) wrote an interesting paper that illustrates how this simple capability results in closed causal loops:

"Warp drive and causality," Everett, 1996

Totally agree. If you're moving by creating a bubble of spacetime and moving that bubble through 'normal' spacetime, there wouldn't be a relativistic effect - probably.

The big question with CTCs is:

Existence of CTCs places restrictions on physically allowable states of matter-energy fields in the universe. Propagating a field configuration along the family of closed timelike worldlines must eventually result in the state that is identical to the original one. This has been explored by some scientists as a possible approach towards disproving the existence of CTCs.

Closed timelike curve - Wikipedia

In other words, if you can go back in time, you can only do it in a way that results in the same state you started with. Which feels like a very artificial constraint and impossible to actually achieve.

 

[marduk]

PS cool article here: Time Travel Simulation Resolves “Grandfather Paradox”

Instead of a human being traversing a CTC to kill her ancestor, imagine that a fundamental particle goes back in time to flip a switch on the particle-generating machine that created it. If the particle flips the switch, the machine emits a particle—the particle—back into the CTC; if the switch isn't flipped, the machine emits nothing. In this scenario there is no a priori deterministic certainty to the particle's emission, only a distribution of probabilities. Deutsch's insight was to postulate self-consistency in the quantum realm, to insist that any particle entering one end of a CTC must emerge at the other end with identical properties. Therefore, a particle emitted by the machine with a probability of one half would enter the CTC and come out the other end to flip the switch with a probability of one half, imbuing itself at birth with a probability of one half of going back to flip the switch. If the particle were a person, she would be born with a one-half probability of killing her grandfather, giving her grandfather a one-half probability of escaping death at her hands—good enough in probabilistic terms to close the causative loop and escape the paradox. Strange though it may be, this solution is in keeping with the known laws of quantum mechanics.

 

[mike]

Well now you've opened a can of wormholes lol.
I have a whole folder of links about this stuff. I think our concept of time is limited because we are stuck in linear time. I dont think UFO's are though.

The universe has two axis, distance and duration and i think its entirely possible to travel both axis to a spacetime co-ordinate of your choice.

We know the speed of time is a variable, it can be dialed up or down, and as you mention it has something to do with mass and or gravity.

Researchers in the United States have for the first time shown that time passes faster the higher up you are.

In a curious aspect of Albert Einsten's theory of relativity, they show that someone living or working long hours in a top floor apartment or office will age more quickly than someone on the ground floor.

To understand this research, you first need to grasp an idea thrown up by Einstein more than 100 years ago.

In his theory of general relativity, Einstein predicted that a clock at a higher elevation would run faster than a clock on the planet's surface because it experiences a weaker gravitational force.

The theory has been proven before, using jumbo jets flown at high altitudes, but this is the first time scientists have shown the theory holds if you elevate one of the clocks by just 33 centimetres.

Time passes faster the higher you are

 

[mike]

Let’s get this out of the way first: Obviously time travel exists, because it’s already the third week of 2014. We’re all time travelers (chrononauts), technically, moving 1 second per second through time. Certain weird side effects of relativity theory also mean time can travel more quickly under certain conditions, so it’s even possible for you to travel into the future (someone else’s future, at least) faster than the usual rate.

The “useful” kind of time travel, though, for sci-fi authors and dreamers alike, is into the past, Back to the Future style. And, happily, relativity theoretically can make that possible, too, by warping the fabric of reality, space-time, so much that it loops back on itself. A so-called wormhole (again, officially deemed possible by science) could be the bridge that connects two different times.


Okay, so a wormhole-based time machine might actually be possible, if not necessarily very likely. That’s enough for theoretical physicists and mathematicians (often proud to work on things divorced from our reality) to study wormholes and learn what characteristics they’d have, if they existed. A paper in Physical Review Letters does just that, and concludes that a certain kind of wormhole breaks quantum physics a little.
Time Travel Via Wormhole Breaks the Rules of Quantum Mechanics - The Crux

 

[mike]

http://www.gravitywarpdrive.com/

GENERAL RELATIVITY

 

[mike]

Lots of good reading here:

UFO Connections to Time Travel

 

[mike]

As Time Goes By: UFOs and Time Distortions

 

[mike]

Doctor Who's time-traveling TARDIS could theoretically exist, says new study - ExtremeTech

 

[Thomas R Morrison]

These all have some interesting material, but they're sort of a mixed bag:

http://www.gravitywarpdrive.com/

GENERAL RELATIVITY

This does a nice job with some concepts in special and general relativity, but I cringe when people talk about "nuclear gravitation" theories - we've got a pretty good handle on the nuclear strong force and its mediating particles: one would have to explain away all of that data and simultaneously present a formal differential geometry model of nuclear gravitation to make such a claim reasonable, and that all seems very unlikely. I'd love to see somebody pull it off though, if that's even possible, because it would be so much fun to play with and it would open up so many prospective new technological frontiers.

Lots of good reading here:

UFO Connections to Time Travel

Dr. David Anderson talks some good smack, but I don't think he's a doctor of physics, and I don't think he's built a time compression machine. He seems to be a smart guy who simply loves the subject of time travel, and decided to capitalize on Art Bell's fascination with the subject.

I'm also not as bewildered by the idea that other humanoid species would take an interest in us. I see no reason to conclude that humanoid life forms are all that rare - there are solid empirical reasons why we're upright, and right-left symmetrical, and have two eyes facing more or less forward. So I expect sentient humanoids to be fairly common throughout the universe. And I think that they'd take a special interest in beings like us, just as we will once we're an interstellar species. Other forms of intelligent life, like perhaps sentient octupi from other worlds that require high-density fluid environments to survive, would probably be more interested in studying other aquatic worlds where octopi-like civilizations are arising - I think it's natural to be drawn to your own kin.

As Time Goes By: UFOs and Time Distortions

To me the most interesting aspect of reports like this - which are oddly common, is the apparent manipulation of time devoid of the corresponding influence on space that's associated with the gravitational field. We have no idea how to do that. But if any of these reports are true, it seems to be an inescapable conclusion - because if this magnitude of time dilation were produced by a gravitational field, then the witnesses would be either shredded by the gravitational tidal forces, or everything in the vicinity of these craft would be drawn to it like iron to a magnet. The only places in nature where such extreme time dilation takes place is near neutron stars and the event horizons of black holes.

I'd love to see some theoretical proposal on how we could manipulate time without generating a phenomenally powerful gravitational field in the process, but I've never encountered such an idea. I don't see why it would impossible; it's simply beyond our current theoretical understanding. And, perhaps, it could be the key to generating a field propulsion system without the incredible energy densities that we associate with them. If only we had a viable theory of quantum gravity, we might be able to figure out how to decouple time and space in the wavefunction of material bodies.

Doctor Who's time-traveling TARDIS could theoretically exist, says new study - ExtremeTech

It does seem clear that genuine spacetime technology is possible in theory, so this finding doesn't surprise me. I wish they would've mentioned this wonderful feature of the Tardis though: it's also been shown that its theoretically possible to engineer a larger spacetime inside of a smaller outer volume. That came out in detailed theoretical arguments about warp bubble physics, as a way to reduce the energy requirements. It's so bizarre to think about, but general relativity does allow you to fit a 100ft room inside of a 30ft vehicle, if you have mastery of spacetime engineering.

 

[Randall]

I've presented a crash course on the logical basis for time as a dimension equivalent to space in the Time, Time Travel, and Closed Timelike Curves thread. Please have a look at that opening post. In my experience, the more thoroughly a person understands relativity, the more they appreciate its conceptual and mathematical elegance and economy, as well as the incredibly accurate predictions that it makes which in some cases have been verified to more than 20 decimal places.

Regardless of the accuracy of the predictions, analogies that work for calculations don't translate to them actually being that way in the real world. The closest example I can think of to illustrate this point is that from a relative point of view, gravity is indistinguishable from acceleration. The math can be worked out identically. To quote Eistein:

"Einstein’s ground-breaking realization (which he called “the happiest thought of my life”) was that gravity is in reality not a force at all, but is indistinguishable from, and in fact the same thing as, acceleration."​

However it is obvious that while the math can be worked out to make acceleration and gravity appear to be identical, we can all plainly see that the reason we all stick to the Earth isn't because we're standing on an ever accelerating flat plane hurtling straight ahead through space. The same thing applies to the idea that space is curved. What's happening there is that the math uses the curvature analogy to predict how things behave, but that doesn't necessarily translate to space actually being curved like a flexible rubber sheet. Basically, it's a logical fallacy to assume that because something behaves as if it's a certain thing, that it is that thing.

... just as space is measured by the physical interval between two points,

Maybe we could say "space is measured by the physical interval between two points" in a really generic sense, like the amount of space left across the width of a bookshelf to add books. But more accurately, the interval between two points is distance. Distance is used to calculate d2 ( area ) and d3 ( volume ). In Spacetime, d3 is the space in the spacetime component.

... time is measured by the temporal interval between two events ...

Okay.

... and in fact the two can be defined interchangeably.

Not okay ( that is of you mean you can use time and volume interchangeably ). There is no logically coherent way to make v ( volume ) = t ( time ) in the real world. That would be like saying you can have a cubic meter of nanoseconds. It's nonsense. But it would be nice to go to the supermarket and purchase a few cans of time, especially when they go on sale. You never know when a few extra hours could come in handy .

 

[ALPHA ROMEO UNIFORM]

Now need plenty of time to read all this stuff and time travel using nuclear energy? Also can the brain time travel?https://www.researchgate.net/profil..._tunneling/links/55912bf308ae1e1f9bae550c.pdf

 

[Randall]

... I’ll start by responding to Usual Suspect’s recent post about time in the ETH thread, so we can seamlessly transition the topic into this spin-off thread ...

Just an aside here: In the above post's signature line there are some links to your artwork. Very nice! There's that creativity thing again with respect to experiencers, but the link to your sighting doesn't work. Can you post that again? After that maybe we can carry on. I need to go back and find where your answer was to my post about time being synonymous with change. I'm not seeing how progress toward a common understanding can take place yet because it seems we're looking at the question from two different perspectives. One depends on viewing time as a variable in mathematical equations while the other depends on identifying the fundamental nature of the concepts. It's like we're talking two different languages.

 

[Thomas R Morrison]

Regardless of the accuracy of the predictions, analogies that work for calculations don't translate to them actually being that way in the real world. The closest example I can think of to illustrate this point is that from a relative point of view, gravity is indistinguishable from acceleration. The math can be worked out identically. To quote Eistein:

"Einstein’s ground-breaking realization (which he called “the happiest thought of my life”) was that gravity is in reality not a force at all, but is indistinguishable from, and in fact the same thing as, acceleration."

However it is obvious that while the math can be worked out to make acceleration and gravity appear to be identical, we can all plainly see that the reason we all stick to the Earth isn't because we're standing on an ever accelerating flat plane hurtling straight ahead through space. The same thing applies to the idea that space is curved. What's happening there is that the math uses the curvature analogy to predict how things behave, but that doesn't necessarily translate to space actually being curved like a flexible rubber sheet. Basically, it's a logical fallacy to assume that because something behaves as if it's a certain thing, that it is that thing.

No, no, no. I’m sorry Usual Suspect, but you simply haven’t understood the general theory of relativity (don’t feel badly about it, it’s quite difficult to get one’s head around). I suggest studying special relativity first - it's far easier to work with, and it demonstrates the equivalency of space and time very beautifully using simple geometry.

Spacetime really is curved, and most dramatically curved near massive bodies. Rulers actually get shorter in gravitational fields when seen from an observer outside of the field. Time gets compressed by the exact same degree – clocks on the Earth actually run slower than the clocks in space: this is proven by the GPS satellite system every day because they have to account for it. The curvature of spacetime has been proven in many ways, but the most famous test was the deflection of starlight around the Sun conducted by Sir Arthur Eddington in 1919 (and confirmed to far greater precision subsequently). If the universe were “flat” and gravity were simply a force, then the deflection of starlight around the Sun would only be ½ of the observed angle. But if gravity is actually a deformation of spacetime, as Einstein described, then the correct value is observed:

How a Total Solar Eclipse Helped Prove Einstein Right About Relativity

Einstein wasn’t making an analogy when he said that gravity is acceleration, he was stating an equivalency. E=mc^2 is also an equivalency, not an analogy. And his statement is correct: the curvature of spacetime that we call “gravity” is physically indistinguishable from acceleration. When space and time are orthogonal/perpendicular, say, in a region very far from all gravitating bodies, the relationship between space and time produces no acceleration. But when the spacetime metric is curved, space (meters) and time (seconds) are no longer orthogonal, so they don’t perfectly “cancel out,” so to speak. The disparity in the perpendicular angle between the two dimensions manifests in space and time units: meters/second^2. That’s acceleration, by definition. And that’s why gravity is often called “an acceleration field.”

We recently recorded a Physics Frontiers episode about the constraints on alternative gravitation theories, and the long and short of it is that all non-metric models of gravitation have been ruled out. Some slightly different types of metric theories are still possible, but the constraints on them are very, very tight. It appears from every scientific experiment and observation in the canon of physics and astrophysics that Einstein’s model is the correct one (which is a little disappointing for people like myself who are hungry for new physics, but it’s a testament to Einstein’s model that even after a century, we can still find no way to “improve” his theory, or even alternative that actually works).

Maybe we could say "space is measured by the physical interval between two points" in a really generic sense, like the amount of space left across the width of a bookshelf to add books. But more accurately, the interval between two points is distance. Distance is used to calculate d2 ( area ) and d3 ( volume ). In Spacetime, d3 is the space in the spacetime component.

That’s a distinction without a difference: “space” and “distance” are synonyms. We colloquially sometimes mean “space” in the sense of “a volume of nothing,” but that’s just all three axes of space/distance considered at once, meters^3 rather than simply meters^1.

Not okay ( that is of you mean you can use time and volume interchangeably ). There is no logically coherent way to make v ( volume ) = t ( time ) in the real world. That would be like saying you can have a cubic meter of nanoseconds. It's nonsense

A “cubic light-year” is a perfectly sensible concept that measures a volume of space in units of time, because time and space are equivalent. Just as E=mc^2, d=tc (meters = seconds x the speed of light). Time is a dimension equivalent to space, just as energy is equivalent to mass, and kinetic energy is equivalent to velocity.

Just an aside here: In the above post's signature line there are some links to your artwork. Very nice!

Thank you – I can’t wait to show you the new life-scale sculpture of Venus; she’s downright dreamy =P

but the link to your sighting doesn't work. Can you post that again?

The forum software doesn’t offer a specific link address to the “Information” page on our profiles, so you have to click the link to get to my profile, and then click on the Information tab to read about my sighting experience. I amended the footnote in my signature to clarify that – thanks for pointing it out. We’ve discussed it previously though – a pair of zig-zagging lights in the clear daytime sky, moving in perfect formation at a fast and constant speed even while undergoing sharp ~30-angle changes in direction. I’ve still never seen any human technology maneuver even remotely like that. But compared to the experiences that other board members here have had, it’s pretty mundane. To me though, it’s direct evidence of a gravitational field propulsion system, because that’s the only explanation that conforms to the observation.

I need to go back and find where your answer was to my post about time being synonymous with change. I'm not seeing how progress toward a common understanding can take place yet because it seems we're looking at the question from two different perspectives. One depends on viewing time as a variable in mathematical equations while the other depends on identifying the fundamental nature of the concepts.

My opening post in this thread was my response to that. I see change as something that’s measured in time and space units, not as time or space themselves.

The fundamental nature of time is a dimension equivalent to space (or if you prefer, distance). I’ve looked for any alternative definition because I’m a rebel and a contrarian by nature so I love to find new ways of looking at things, but I’ve never found one that actually makes any sense. Frankly I don’t understand why people get hung up on the idea of time as a dimension, but blithely accept the idea of space as a dimension: why should things be separated in the first place, what the hell is “space” after all? That question is just as valid, imo, but nobody ever asks it.

 

[marduk]

The fundamental nature of time is a dimension

I think this is it.

equivalent to space (or if you prefer, distance).

If you mean, equivalent to the dimensions we use to describe space, then I don't think so.

Space allows freedom of movement in all 3 dimensions. Time is how long it takes to do that motion, among other things. They're related at a fundamental level, so the more you move in space, the slower you move in time relative to other observers.

Gravity is the warping of space/time caused by mass/energy. Gravity in itself may not exist as a thing at all; it may just be the warpage of space/time - like a fold in a piece of paper isn't a thing in itself, it's a configuration of the piece of paper.

 

[Randall]

No, no, no. I’m sorry Usual Suspect, but you simply haven’t understood the general theory of relativity ...

I don't think that's the case, and I don't feel bad. I feel frustrated because what seems to be happening is that like I was saying in my previous post. We're talking two different languages with respect to the subject. I will leave it at this until we find a way to reconcile that situation. Put specifically this way:

1. An analogy that explains the behavior of real things does not make the analogy the real thing ( no matter how accurate the resulting predictions are ). I've used the relationship between gravity and acceleration to illustrate this point. There is no getting around the truth of this example by mere proclamation that it isn't that way or that either of us don't understand the concepts. Mathematically, gravity and acceleration can both be used to described the same behavior of stuff in space, but that doesn't mean gravity is acceleration. Similarly, saying that stuff in space moves as if space is curved doesn't necessarily mean space is curved, but I get the analogy just fine.

 

[Thomas R Morrison]

If you mean, equivalent to the dimensions we use to describe space, then I don't think so.

Look up the concept of "four-velocity." We're always moving at C. When we're at rest (which is a relative concept, but useful nevertheless) we're moving at C in units of time: 1 second per second. As we approach a relative of velocity of C through space, the time component approaches zero. But in all reference frames, our four-velocity is constant, C.

Gravity is the warping of space/time caused by mass/energy. Gravity in itself may not exist as a thing at all; it may just be the warpage of space/time - like a fold in a piece of paper isn't a thing in itself, it's a configuration of the piece of paper.

Yep - that's it exactly. The really neat part though, is that the curvature of spacetime induces stress in the "paper," so there's actually energy in the curvature of spacetime. And that's why the equations of general relativity are nonlinear - the mass-energy of an object curves its spacetime environment, and that curvature itself contains energy which further contributes to the gravitational curvature of spacetime a little bit, and on and on ad infinitum. That's why it takes tensor calculus to model the curvature to high precision. But we can get by quite well with the "linearized weak-field-limit equations" in most scenarios - the nonlinear contributions are minuscule until you get close to neutron stars and black holes, where the nonlinear contributions become substantial.

I don't think that's the case, and I don't feel bad. I feel frustrated because what seems to be happening is that like I was saying in my previous post. We're talking two different languages with respect to the subject. I will leave it at this until we find a way to reconcile that situation. Put specifically this way:

1. An analogy that explains the behavior of real things does not make the analogy the real thing ( no matter how accurate the resulting predictions are ). I've used the relationship between gravity and acceleration to illustrate this point. There is no getting around the truth of this example by mere proclamation that it isn't that way or that either of us don't understand the concepts. Mathematically, gravity and acceleration can both be used to described the same behavior of stuff in space, but that doesn't mean gravity is acceleration. Similarly, saying that stuff in space moves as if space is curved doesn't necessarily mean space is curved, but I get the analogy just fine.

It's not an analogy, it's an equivalency. There's a huge difference.

 

[marduk]

I don't think that's the case, and I don't feel bad. I feel frustrated because what seems to be happening is that like I was saying in my previous post. We're talking two different languages with respect to the subject. I will leave it at this until we find a way to reconcile that situation. Put specifically this way:

1. An analogy that explains the behavior of real things does not make the analogy the real thing ( no matter how accurate the resulting predictions are ). I've used the relationship between gravity and acceleration to illustrate this point. There is no getting around the truth of this example by mere proclamation that it isn't that way or that either of us don't understand the concepts. Mathematically, gravity and acceleration can both be used to described the same behavior of stuff in space, but that doesn't mean gravity is acceleration. Similarly, saying that stuff in space moves as if space is curved doesn't necessarily mean space is curved, but I get the analogy just fine.

Does this work?

The force of gravity is equivalent to the force of acceleration. The causation of the force are not equivalent, though - me accelerating when I jump off a cliff is because the earth warps space/time (until 'sudden deceleration trauma' when I hit the ground). But me taking the leap off the cliff is because I've converted potential energy in the form of sugar in my muscles into kinetic energy when I jump off of it, accelerating from zero when standing to do so.

Gravity is the bending of space/time (that's not an analogy, that's it's definition within relativity):

Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass.

Gravity - Wikipedia

We can 'spoof' gravity by accelerating something, or spinning it. It will feel the same to the observer. But it's cause isn't the same.

Is that a better answer?