md65536

This is the way I begin thinking about location and energy without imagining a fixed coordinate system that defines things relative to something external to them: imagine you have two points that can't rotate. These two points can move in any way relative to each other but the one can only interpret its location relative to the other in terms of distance increasing or decreasing. It can experience changes in force and momentum as it changes directions of motion relative to other imaginary points, but its location can only be measured in relation to the only other existing point in its universe, which it only becomes more or less distant from. Does that make any sense?

You're describing relative location in terms of only distance, implying that one dimension is enough to define the relative location between 2 points exclusively.

The other spatial dimensions (representing orientation) are irrelevant -- do you mean in general, or as it pertains to this thread?

 

I don't think I agree. I don't think the most elementary particles are one-dimensional, and the relative orientation of 2 particles might be important especially when it comes to light, or velocities.

 

 

As it pertains to the conjecture, I'd say that the size and the shape of a particle's "spatial range" is what matters (the range perhaps defined by a probability wave that specifies the possible locations of the particle and the probability of it being in any particular location. A "larger wave" would mean less locational precision, which I'm suggesting corresponds to lower energy). Unless the possible range is isotropic (ie. it's shape would need to have spherical symmetry?), then the orientation would be important.

 

I am not sure what the op is saying but if you look at the Bohr model

then when you add energy to an orbiting electron it goes to a higher level and slows down

Its potential energy increases but its kinetic energy decreases.

as a result the particles wavelength is bigger and the particle is 'spread out' over a larger area.

i.e. less localized.

Yes... this seems to be in direct contradiction to my conjecture.

It would seem that the location of the particle (the electron?) is less precisely defined in a higher energy state.

Unless there's some other property that shrinks and allows greater precision, the conjecture does not account for electrons and must be wrong.

Electrons ruin all my ideas! Are you sure we have to consider their existence at all???

 

No, these are not consistent with the definitions of the terms in standard physics. Potential energy depends on position, not velocity, and a force perpendicular to the motion will change velocity but does no work, so there is no transfer of energy.

Potential energy depending on location fits the conjecture better than velocity does.

Is it a general case? Does any change in relative position involve some change in potential energy?

 

I can't actually imagine how kinetic and/or potential energy relates to the idea. I shouldn't have mentioned it.

 

 

France is a pretty big place. Can you be a bit more specific about where, exactly, in France this device is located?

 

 

This probably refers to the one built by Aldo Costa:

http://en.wikipedia.org/wiki/Aldo_Costa_(inventor)

"However, as with other devices of this kind, the energy created by the unbalanced weights falling is merely equal to what's required to lift them to become unbalanced in the first place."

 

 

Videos of it here:

http://www.blueman.name/Des_Videos_Remarquables.php?NumVideo=2274#NAVIGATION

 

 

Some explanation here:

 

http://www.besslerwheel.com/wwwboard/messages/241.html

 

"his wheel stalls"

Energy is a frame dependant quantity, which is worse than just depending on the location (points on space-time). Importantly, energy cannot be locally described by a tensor.

Meaning that energy takes different forms in different frames?

Is the total energy of a system (including for example the entire universe) invariant, and just changes form depending on frame of reference?

 

 

Perhaps I'm using the wrong word "location", if it means a precise point in space. Instead I want to describe position with a variable degree of uncertainty or precision. So size too, I guess... a quantum of energy has a range of uncertain possible locations.

 

How is 'location' in any sense absolute, or maybe I should say less than relative? To me, objects always move relative to the objects they exchange energy with.

I agree it's completely relative. So it's not location that's important, such as specified by some spatial coordinates relative to any origin. The values of those coordinates (or its distance from origin) don't affect something's energy or mass.

 

It would be precision of location that would be related to energy.

 

The conjecture might be restated: The energy of something is proportional* to the precision of its location.

 

(Now the specific location or whether it's relative to something else, doesn't matter.)

 

 

* I want to say "equivalent" but I don't know how to account for different forms of energy, or "somethings" that are made up of multiple quantities of energy and can thus have greater overall energy but may not have a proportional degree of locational uncertainty.

Here are some aspects of relationships between location and energy:

 

1. To change an object's location requires energy. If an object has velocity relative to something else (such that relative location changes), it has potential energy. To change velocity requires a transfer of energy.

 

2. In a Bose-Einstein condensate, which has very little thermal energy, the location of particles becomes undefined. Particles act as if they are simultaneously everywhere in the matter.

 

3. If an object falls into a black hole, light from it is redshifted indefinitely. Is it reasonable to say that one wavelength of the light is simultaneously traveling to our eyes at c, and stuck at the event horizon, so the infinite redshifting is equivalent to stretching that one wavelength of light across an ever-expanding distance? As the light energy is lost to the black hole, its location becomes undefined... instead of being in a specific point, it gets stretched indefinitely.

 

4. According to the conjectured holographic principle, a location in our 3d universe maps to all locations on a 2d topological manifold and vice versa. In some vague sense, any quantum of energy can exist everywhere, but some property gives it locational definition in our 3d universe.

 

 

Can these ideas be combined into one relationship between location and energy?

The energy of something would be related to the degree to which that something is "focused" or well-defined locationally. Greater energy means sharper focus into a specific location. If you want to determine the precise location of something either you would need to use a lot of energy to do so, or that something would need to have a lot of energy. The more precision you need, the more energy is needed.

 

Mass, which is a form of energy, would be related to the specificness of location. More energy means more specific location. Inertia could be expressed in terms of specific location (including moving locations); the difficulty in overcoming inertia is related to the difficulty of modifying locational specification. This would probably imply that the location of a moving object is better defined (ie can more precisely be determined) than a similar stationary object??? -- is there any accepted theory that speaks to this?

 

 

 

One last conjecture in case there's nothing zany enough in the above: If location is emergent (which I believe it is, along with all of geometry), would this imply that energy is also emergent? I'd previously thought that energy was invariant and a fundamental aspect of the universe... I still think it must be, but I'm not sure.

 

(Energy is conserved -- except for vacuum energy??? -- which means it is invariant, but it can be converted to different forms which are different for different observers, so the form that energy takes is not invariant. In conclusion I don't quite know what this means.)

 

Or does this conjecture make sense?: The form of a quantity of energy is equivalent to its location. (I don't think I said that right... anyone have ideas?)

because if it's right then i dont understand how an object can be moving .866 c and still move at half lightspeed through time.

If for example it's a rocket moving at .866 c relative to "our inertial reference frame", its velocity is .866 c according to us.

 

No velocity is halved in this example. The Lorentz factor is 2.0, which means that according to us, a clock on the rocket ticks at a half rate.

 

However, lengths in the rocket's frame are also contracted by the same factor of 2.0, so both distance and time in the rocket's frame are scaled by the same amount, and the rocket's velocity = d/t remains unchanged at 0.866c despite time dilation and length contraction.

 

Lengths in the rocket's frame (including distance to it) are halved, and its time passes half as quickly, according to us.

 

what is the trejectory like then?

 

if a spaceship in an inertial frame were to shoot out a beam/pulse of light in front and backward and was moving at a steady speed, would the two beams be moving at the same speed away from the ship?

If we're in an inertial frame, its trajectory follows the curvature of space, which is a straight line in the absence of a gravitational field (essentially straight in this example. Einstein believed we'd never be able to detect spacetime curvature in our local weak gravity fields so let's say it's negligible).

 

Yes, the speed of light of the beams would be c in both directions, relative to us.

(They'd also both be c according to the rocket, or any other inertial frame.)

It would not diminish GR to just refer to the curved path of objects, however, without the superfluous insistence on " curved spacetime" with ruts or grooves, or whatever which "guide" objects' trajectories.

And with that, I formally abandon this hopeless conversation. Thank you for your time.

GR assumes that space is an entity

Citation? I don't think that's true.

You've stated in this thread that you don't consider space to be an entity. Would you then conclude that GR is based on false assumptions? Would you also say that because of this, GR can be safely ignored, and that an understanding of GR is irrelevant to this discussion?

 

 

 

Also, before you declare victory for the established fact of spacetime, please do the required* research into what the International Society for the Advanced Study of Spacetime (ISASS) has been debating for most of the last decade.

 

*(If you care about what spacetime is)

 

Any search will get you there... if your mind were not already 'made up.'

On the website that you are referencing, they have the question "Is Space Infinite?" on their Open Questions page: http://www.spacetime...nquestions.html

Your source does not seem to agree that the question has been answered.

Others in this thread accept that it remains an open question. So how is it that their minds are made up while yours is not?

 

 

 

 

 

It is amusing to watch you attempt to address the ontology of spacetime when you have no idea what spacetime is and harbor so many gross misconceptions regarding general relativity.

I also find it amusing, but at the same time it is really bothersome to see the same misinformation repeatedly posted. As someone who doesn't have a firm grasp of relativity, I find it harmful to my attempts to understand relativity, and I think it does not belong in a relativity forum.

 

I also think it's sad that what is claimed to be an expertise in the ontology of spacetime, seems to me to be based not only on a lack of understanding of relativity, but also some confusion about the very meaning of ontology (due to the apparent assumptions that for spacetime to have properties implies that it is an entity). I am not an expert on the philosophy of science, but to me this seems naive.

 

Btw, presentism is another study which inquires beyond local frames of reference and "time environments" and the usual "who sees what and when" of relativity. It can be ignored, but it will not go away. The most simple and obvious illustration of presentism is that now is now for both earth and sun even though it obviously takes over eight minutes for sunlight to travel to earth.

Then, this "now" can be extended to "now everywhere," that the universal present is not limited by lightspeed.

Now this is an interesting topic relevant to my interests. But I think discussion of it is off topic and probably belongs in the Speculations forum anyway.

c is a constant in an inertial frame. If you are accelerating you are not in an inertial frame, and you will not measure the speed of light to be c. Acceleration due to rotation gives rise to the Sagnac effect.

In the context of the original post, is the Sagnac effect equivalent to saying that...

1. Rotation of the reference frame will cause the paths of light (aimed in different directions) to curve in different ways.

2. There is no possible common path (geodesic) that the light can travel in opposite directions, from the rotating reference point.

3. Light in opposite directions travels a different distance in each direction in a given time, due to the differently curved paths.

?

 

 

 

For the purpose of the thought experiment, it might suffice to imagine an inertial frame that approximates the Earth's motion through a portion of its orbit.

if not then what speed would it take for time to be halved?

About .866 c

 

No, since we are not in an inertial frame. We orbit the sun, so we are in an accelerating frame. It's not a big effect, though.

??? The speed of light is invariably c, for all observers, regardless of relative motion.

There's nothing you can do to change that.

Acceleration won't change the speed of light. What effect are you speaking of?

 

 

DrRocket is very fluent in math and the "higher dimensional" non-Euclidean geometries, for instance, while my forte' is in the philosophy of science, specifically the ontology of such "dimensions." The two realms of expertise are obviously not in communication in this thread, and DrR seems to believe that ontology is irrelevant to this discussion. (Correct me if I'm wrong.)

But you are giving a philosophical answer to a question that pertains to General Relativity, in a Sciences > Physics > Relativity forum, not a philosophy forum.

 

You could very well be right, but you can't prove it in terms of relativity, science, or math. The reasoning in what you considered the best answer is this: "I don't see how the universe couldn't be infinite." That's simply not acceptable. I think it does a disservice to anyone who comes here trying to understand relativity (and not the philosophy of science), to find answers that are based on not being able to see how some potential implications of GR can be real.

 

The question remains an open problem (whether considered from a scientific perspective, or a philosophical one).

If you had reasoning that addressed why closed (curved) space should be considered impossible, in terms of GR, that would be interesting.

 

 

Since "anti-time" doesn't seem to be defined, you might define it as negative time, so that an equal duration of time and anti-time "annihilate" each other when added together.

 

But time and distance are abstractions, as swanstont has pointed out, whether positive or negative. If you push 2 things together, you're not actually physically destroying anything as you reduce the distance to 0.

 

 

Negative values of time and distance are useful for describing differences in the measurements.

If you move something closer to me, my distance to it changes by a negative value.

The difference between today and yesterday is -1 day.

 

Meanwhile, the length or magnitude of any distance or time will be non-negative. It is probably easy to think of physical objects with lengths and events with durations, yet negative values may only come up when speaking of something relative to something else. So it might be easy to confuse distance as "something that is real", but it is only a measurement or a property of something real (or abstract).

Unless you're speculating otherwise, spacetime usually consists of 3 spatial dimensions and 1 time dimension, so time and space are hard to compare. If you want to compare time to a 1D aspect of space, comparing time and spatial distance would be easier.

 

Anti-time might be like anti-distance. I don't know how that'd be defined, but I'd expect it to only be abstract, not anything "real".

The bounded infinite spaces I proposed are metric spaces that are only bounded according to a different metric. I don't think they can be called bounded metric spaces. Pure imbecility!, sorry about that.

 

I think we should stop talking about boundaries, because that only answers the question about whether or not space is infinite, if there IS a boundary. Since no one is arguing for the existence of a boundary, we may as well assume there is no boundary.

 

 

 

For a metric space to be finite and have no boundary, does this mean that no spatial dimension has a bound, yet the distance metric has an upper bound?

Is it a confusion of spatial dimensions and the distance metric that is causing all the trouble?

In the context of a space-like slice of spacetime, aka "space", a manifold is "finite" if it is compact as a topological space -- or equivalently has finite volume. It is "infinite, or "open" otherwise. In either case there is no boundary (aka edge).

Posit any form with boundaries/edges any size and shape you want. Beyond that, there is no limit, no "brick wall", and if there were (duh!), ... beyond that, either more stuff scattered about in space or infinite empty space.

 

No, I have not concluded "that there has to be something beyond." Nothing beyond is still empty space, whether or not there is more "stuff" out there or just endless (what end!?) no-thing-ness, empty space.

If there's no boundary either way (whether or not space is finite) I don't see what it would prove to imagine such a space. I won't posit it (as in, "assume the existence of") because that goes against the assumptions that DrRocket laid out early in this thread: "Under the assumptions of homogeneity and isotropy it can be decomposed as a one-parameter foliation of space-like 3-dimensional hypersurfaces (aka "slices"), without boundary." I have no special understanding that supersedes all of known science, that would even suggest that space (whether finite or not) has a boundary.

 

But for the sake of imagination, I'll try anyway.

 

Here's how to imagine it. Imagine first a flat and infinite homogeneous space, which is what I think you are claiming is the only possibility.

Now curve or stretch that space so that you map any point at a distance of d from some arbitrary point, to a distance of 1/(d+1). This effectively turns space inside out, which I know is weird. All of space is now contained in a sphere with a radius of 1 unit. This is an infinite bounded space; if we remove the singularity at the center, it becomes a finite bounded space.

 

Imagine existing within this sphere. There is NO SPACETIME beyond the sphere. There is no emptiness, there is no volume to the emptiness, there is no measurement of the emptiness. All of space, all emptiness and all "stuff" (energy and matter) within that space, are contained within the sphere.

 

Now, I will admit this: I don't know if this even counts as a bounded space, because from within the universe, you can still measure space with your original mapping in which the space was flat and infinite and unbounded. It requires defining distance from some external perspective, which has its own measure of distance, which we might again be compelled to imagine as another space in which the first is embedded. We must resist that compulsion, but in doing so I may be forced to concede that this is an abstract concept only, which may not have any possible real existence in any way.

 

But that doesn't even matter, because this space requires severe curvature. It is not homogeneous and isotropic in terms of curvature or distance.

 

This whole discussion of bounded space may be a complete waste of time discussing, because even if it does make sense (I'm not sure it does) and even if it made sense and you understood it (doubtful), it's still not the finite space that we should be talking about, which is closed, unbounded space of a constant curvature.

 

 

 

 

I know that you and michel123456 don't get it that space can have properties such as curvature without making it an entity (which by the way I'm taking to mean "The existence of something considered apart from its properties"), and I don't know if anyone gets anything out of what I'm saying, so it probably indicates "pure imbecility" on my part to bother writing at all. Yes, it does seem to indicate moderate or severe mental retardation.

 

Thank you.

 

Everybody here, except Owls, feels O.K. to discuss about "nothing" as it was 'something' with properties. But IF "nothing" has properties, then "nothing" is not nothing anymore, it becomes "something" mysterious. The ontologic problem that Owls tries to discuss is very well existing.

I don't understand what you are saying here.

Ontology is a branch of philosophy dealing with existence.

An entity is something that has a physical existence.

What is the ontology of a non-entity? I think there is none. There's only a problem if spacetime is an entity.

 

I also don't get how defining something's properties makes it mysterious.

 

"Nothing" was a bad word for me to use, because it is too ambiguous. It can be used as a name for empty space, or it has even been used to describe vacuum energy (which I'd agree could be an entity with an "ontological problem"), or something that has no properties, but I meant only that it has no physical existence apart from its properties. It is nothing besides its properties.

 

 

It is an evidence, better say an axiom: if something (some-thing) has properties, it is an entity. It is Not a false assumption.

I don't think that's an axiom at all.

The Earth is not an analogy. The earth is curved, we are living on its curved surface, but we are 3D objects. We are not 2D individuals living in a 2D world.

The Earth is an analogy, which means it is similar in some aspects but not all.

The Earth is not equivalent.

Moving upward through a 3rd dimension (whether you could do so infinitely or not) does not change the the fact that the 2D surface is closed.

The possible existence of higher dimensions does not need to change the properties of the lower spatial dimensions.

 

 

 

 

 

 

In general relativity spacetime is a 4-dimensional Lorentzian manifold. Under the assumptions of homogeneity and isotropy it can be decomposed as a one-parameter foliation of space-like 3-dimensional hypersurfaces (aka "slices"), without boundary. Those slices are spaces of constant curvature and are what is called "space" in cosmology.

 

Homogeneous and globally isotropic spaces of constant curvature are of one of three types: the zero curvature case -- Euclidean 3-space, the positive curvature case -- the 3-sphere, and the negative curvature case -- hyperbolic space.

 

Only the 3-sphere is compact, aka "finite".

 

It is not known which, if any, case represents the physical universe.

I think DrRocket's post back on page 1 is the best answer to the question of this thread. We don't know the answer, and we're not going to find it in an argument. The best we can do is to discuss what the alternatives really mean, so we can have a better understanding of what exactly we're discussing. For me, the most beneficial thing would be to stop discussing, and go read up on all of the topics that DrRocket has mentioned, which I don't understand.

 

This is pure imbecility IMHO.

It's hardly pure.

So you assign "properties" to "nothing."

Exactly. Now you are starting to understand.

 

Spacetime is nothing besides its properties (otherwise it would be an entity). Just like the basement of a house that hasn't been built can have a size and shape, it is still nothing.

 

Finite space is easy to imagine. The space within any geometric form will do, or any form at all of finite size and the boundaries which de-fine it.

This is such a bad example for this discussion, because it is hard not to imagine the geometric form existing in a larger volume.

If you imagine only the simplest example of finite space, and then try to draw general conclusions from that example, you'll tend to draw false conclusions. Then you'll ask questions like "Even with a supposed 'finite universe,' what lies beyond an 'enclosed, finite universe?'" because you've falsely concluded, from your example, that there has to be something beyond.

 

Infinite means without boundary, edge, or end.

That's not what it means. The rational numbers between 0 and 1 are bounded by [0, 1] but they are infinite. They include "edges" at 0 and 1.

 

If we allow infinite spatial curvature (such as with a black hole singularity), we might have infinite but bounded space. The singularity would also be an example of a space without volume, that contains other things. However, I think scientists expect black hole singularities to not physically exist.

An electromagnetic wave travels in a straight line at the velocity of c but it is a WAVE and the tiny packets called photons have both the properties of waves and particles. Something is going through the chocolate bar and causing the melting spots, if it is not photons then what is it?

I've never been able to reason about the wave-like nature of light, but I accept the wave-particle duality without understanding it.

My conjecture is based only on reasoning involving a particle-like nature.

I think that's valid... you can discuss particle-like properties of light that are valid despite the duality.

 

Either way, I still think it's valid to say "light never jumps backward in any direction while propagating".

 

If this conjecture can't stand on its own without addressing the wave-like nature of light, I am unable to provide that.

 

 

I have always argued that space (and time and spacetime) are not entities. Things are entities. Some argue that relationships between things are entities too... as in the substantive vs relational spacetime debate, which I am not going into here.

If you posit that something is being curved or stretched (space in this case), it is up to you to explain what that something is in a coherent ontological argument. That is why the spacetime ontology argument is still ongoing with no consensus in sight.

No, we can speak about the properties of something (spacetime) without explaining anything more about what it is.

That is EXACTLY what makes it not an entity. It doesn't have an existence independent of its properties. We don't need to discuss anything besides its relevant properties.

Perhaps you falsely assume that if something has properties, then it is an entity.

 

 

 

I think the ontology of spacetime is only relevant to this discussion if it IS an entity. Let us assume it is not, since the alternative would be a needless sidetrack to the discussion. Accept that spacetime can have properties (like length) without getting bogged down in the question of "what IS spacetime?" The most useful answer for this discussion is "nothing". Only its properties matter. Either that's a consensus, or a consensus on that point is not needed for the discussion to progress.

 

My "point" was that a geometric point is just a locus without dimension. Specifically a point has no volume, which is required to "contain" anything... like all the matter in the cosmos squeezed into such a point of zero volume, as per Hawking's absurd statement quoted above (re: the ultimate singularity.)

I don't see why something that has no volume can't contain other things that have no volume.

To me this is key to understanding a 2-dimensional manifold without needing to envision it existing in a 3-dimensional volume (ie. "embedded in 3-space" if I understand DrRocket).

 

 

There is an simple experiment that most peoples can do to measure the speed of light, which relies on the fact that light actually does move back and fourth physically at its frequency like this:

Obviously there is a difference between the distance a photon travels, in a straight line, at a velocity of c, versus the oscillation of the photon at a given frequency.

 

Do you agree that the red line in your diagram does not show the distance d that a photon travels, when we speak of the velocity of light being v = d/t?

 

Do you agree that light travels in a straight line and is not constantly changing directions?

d is a straight-line distance when we speak of the speed of light. Photons travel in a straight line.

THIS is the movement that applies to my conjectures.

 

If some part of light physically moves back and forth, it is something else. Clearly, there can be different types of oscillation that behave differently in spacetime, and would need to be described differently.

 

My conjecture would apply to photons themselves, and probably massive particles as a whole, and possibly any components of a particle that make up its mass. It would not apply to whatever part of a photon could be said to be oscillating. It would not apply to oscillations that do not contribute to a particle's mass.

 

---

 

Granted, my conjecture does really on oscillation to explain gravity.

If all oscillations are physically equivalent, and there is no way to explain how it applies to some but not all oscillations, then the conjecture is probably wrong.

As is, I have no way to explain a difference, or why the oscillation that you're talking about does not apply.

 

(I could always guess, and say that the oscillation of light is continuous, and does not involve any random or quantum "leaping back and forth" of the wave-like aspects of light.)

Perhaps nothing lies beyond the closure. Not the nothing like empty space, but the nothing of it being a meaningless question. Similar to the question of "What is in the basement of a house that has not yet been built?".

Nothing must lie beyond the closure. Nothing that can be considered part of this universe. Otherwise, the closure doesn't enclose the universe, which means it's not a closure.

 

Owl, you're the only one talking about space being an entity, as far as I can see. You're arguing against imaginary foes who, apparent only to you, are arguing that it is. Think of it only as a measure. If it is curving or being stretched etc, it is the measure that we're talking about. If matter and energy is in that space, the measure affects their shape and size, but that doesn't mean that the space itself is an entity. You can measure the distance (and the curvature) of the space between earth and moon but that doesn't imply there's an "entity" attaching one to the other.

 

Disclaimer: I'm not a physicist. If the following doesn't make sense, it's not you, it's me.

 

Imagine taking some infinitesimal distance, and stretching it to infinity. I think this is what you'd have beyond the "closure" of the universe. This would mean that there is no distance at all beyond the edge of the universe. The distance beyond it is ZERO.

 

Also there should be no abrupt change between an "inside" and "outside", as in a membrane on one side of which there is distance and on the other side there is no distance. It would probably have to be a "soft" or continuous, gradual closure, which you could not possibly travel to. I think that this "no distance" or "infinitesimal distance stretching to infinity" describes infinitely open curved space, and if you approached a potential "edge of the universe" beyond which there is infinite open curvature, local space would still (as always) be flat, meaning that it would have to appear that space continues on for additional distance (smoothly going between your flat space and the infinitely open space beyond). By approaching the edge of space, you would necessarily move the edge of space.

 

It only makes sense (to me at least!) because we're not talking about an "entity" here.

If we again consider the two dimensional, positive curvature surface of a sphere, I think we can both agree that even though two dimensional, it must curve in a higher dimension ( the third ) to reconnect to itself.

Count me out of all this agreement. I don't think you need to add dimensions to figure any of this out.

 

If we have a spherical shell in 3 dimensions, and we remove all distance, we get a degenerate sphere which is a single point in 3 dimensions. Isn't it also a 2D surface? Doesn't this still describe topologically a 2D manifold that reconnects to itself in 2 dimensions? You don't need a 3rd dimension to describe this.

 

I might be wrong.

 

...

 

Similarly, we can describe a closed infinite space without the need for a 4th dimension. How? Using spacetime curvature.

Imagine we were able to arbitrarily curve spacetime, so that we could arbitrarily map distances in one view of the universe, to different distances in another view.

 

Then suppose you have an infinite ruler in your view of space that counts distance from you in intervals of 1 meter (starting with 0, 1, 2... say).

Suppose I map interval number n on that ruler, with a length of 1m in your view, to a length of 1/2^n in my view.

The infinite ruler in your view will map to a length of 2 m in my view. I could fit your infinite universe into a bounded sphere and keep it in my garage.

 

Then, you could travel indefinitely along this ruler, while I see you slowing and approaching 0 velocity as you approach the boundary of the sphere in my garage.

 

If you think this "arbitrary mapping" has no connection to reality, let's toss something into a black hole and see what happens. (Empty space should curve in the opposite way so it may be a bad example.)

 

...

 

But the thing is, you're not going to have a model of the universe that's completely flat, while I have one that is closed. We're all going to have equivalent models of the universe, but we're also all going to have different views of the universe, that appear differently curved depending on our location, velocity, gravity field, and whatever else. So as you travel along an imaginary ruler, distant space will not appear to stay flat while allowing an actual infinite ruler to remain infinitely long.

 

I have a to get a bit vague cuz I've passed the limits of my knowledge, but I imagine that a part of space that appears to stretch to infinity (ie to the horizon) from one location, might appear arbitrarily small from another location. This means that instead of you having an infinite universe that can be curved to fit in my garage, rather you have an infinite universe that can fit in your own finite universe.

 

As you move through this seemingly infinite space, it keeps changing its appearance, so that it can always appear infinite, and yet always fit within a finite 3 dimensional space.

 

Another way to think about it is this: Take an infinite cosmological horizon, and imagine squeezing that into an arbitrarily small length. You have just imagined connecting space that is infinitely far away in one direction with space infinitely far away in an opposite direction, into a closed manifold, without resorting to adding extra dimensions. Instead of "curling" it into extra dimensions, just stretch across 3 dimensions.

 

If this is too vague, it's because I don't really know what I'm talking about! But I hope that I sound like I do , enough that you can imagine and contemplate.

 

...

 

I don't mean to derail this thread with black holes or unnecessary complications, but my opinion is this: You don't need extra dimensions to curve an unbounded space and connect it to itself. You can do that by curving space in whatever dimensions you're already working with. ???

 

 

 

 

Edit: And now that I've said all that, I'm wondering... doesn't spacetime curvature not mean just stretching, but actually curving into the 4th dimension so that the reason a 3D distance looks stretched or compressed is that the distance includes an unseen time component? Which makes me kinda a little bit totally wrong?

For example, if the above is true, then wouldn't "The Big Freeze" be the only possible end result of the big bang?

I don't think so.

 

If we assumed all the above was true, I don't see how a big freeze follows and allows no other alternatives.

I don't see anything that concludes that energy, once slowed, can never speed up. Speeding up, by the way, appears to be happening with cosmic expansion. "Heat death" seems the most plausible end of the universe (Big Crunch would require at the very least a slowing of the rate of expansion of the universe and the evidence is against that and I don't expect that to change). Heat death might be called a "Big Freeze", but I don't think your assumptions or logic apply to it.

 

Nuclear fusion would be an example of your "slowed energy" being made fast again.

 

 

Problems with assuming your "all the above" is true:

Information at hand 2: The states of matter are not only dependent on the speed of molecules, but also pressure, and maybe other things. I think you're suggesting that the Big Bang implies a one-way strict slowing of energy (seems false), and that all very slow energy/matter is a solid, and that a Big Freeze would be a solidification of the universe. Heat death on the other hand would have (much or all?) matter spread so thin that I don't think it could be called a solid. Are individual particles in deep space considered a gas? Or is that not even considered a state of matter?

 

Conclusions 1 to 3: Energy doesn't really slow. It is always moving and it is always moving at a fixed relative speed of c. Lower levels of thermal energy means less vibration or something, but the energy doesn't slow down. Disclaimer: I'm fairly clueless about this.

 

 

 

 

For example, if the above is true, then wouldn't "The Big Freeze" be the only possible end result of the big bang?

 

It's not, so it's not...

Logically, if "the above" is not true, then the statement "if the above is true, then The Big Freeze is the only possible end result of the big bang" is true.

 

 

But I'm being a bit pedantic. Klaynos is right that your conclusion is false, but your false assumptions don't logically prove that it's false.

We might drop the requirement that oscillation is evenly distributed in all directions, and instead only require that for any given direction, forward and backward motion occurs on average with equal probability or rate.

Nope, I change my mind again. If energy is oscillating in one dimension I assume it will be along a geodesic?, in which case it will never leave that geodesic. Then if you could "polarize" energy so that it's oscillating in only one direction, it wouldn't be accelerated due to gravity in a direction perpendicular to its oscillation, yet it could still be accelerated back or forth along the geodesic. That means 2 equal masses might accelerate you differently depending on your orientation relative to them. This does not match reality.

 

1D oscillation might produce specific acceleration. Universality of gravity would require that the oscillation happens in all directions (including all spatial dimensions) with a uniform probability distribution, at least on average.

 

 

I've made a mistake and want to correct it.

 

If space is continuous, the travel distance from A to B should be the same as from B to A. You should be able to keep splitting up that distance into smaller steps until you're only moving a distance of epsilon each step, where epsilon is small enough such that it is completely within local "flat" space, such that the forward distance from X to X+epsilon is the same as the backward distance. Therefore continuous movement from A to B, through continuously changing space, would be the same distance as traveling through continuously changing space in the opposite direction.

 

One way to fix it is to assume continuous movement is impossible, ie. that there is a quantum distance across which energy "leaps" rather than travels through. This quantum distance would place a minimum bound on epsilon, and if it's large enough so that the spacial curvature across that distance is not absolutely negligible, then the theory might still have hope.

 

Version 3 of the conjecture:

- Assume energy leaps across some distance of epsilon. Let point B be separated from A by a distance of epsilon, in a direction toward a gravitational mass. Again, the distance from A to B (viewed from A) will be smaller than the distance from B to A (viewed from B), and so it is slightly easier to leap toward a gravitational mass than away from it.

- Assume energy continuously oscillates at some fixed rate, and in doing so physically moves toward and away from a gravitational mass, then it will move toward it more easily. This slight bias will build momentum and produce a noticeable acceleration after millions or trillions of oscillations.

- Therefore: Spacetime curvature, plus constant motion evenly distributed in all directions, plus energy leaping across a quantum distance, implies gravitation.

 

 

 

 

When a distant observer sees a particle traveling along a curved geodesic, they will see the particle rotate to follow the curve, while the particle itself does not experience any rotation (it is following a straight geodesic). Therefore, if the particle is moving in all directions with equal probability from the particle's perspective, it will not be moving in all directions with equal probability according to a distant observer. It will appear to favor moving toward the gravitational mass, as the distribution of directions seems "pinched" into higher density in that direction. This requires moving along a curving geodesic, which means not just moving toward and away from the mass, but also perpendicular to that, which seems to restore the requirement that the oscillations must be in 2 or more dimensions.

 

But then again... you wouldn't need to see the particle rotate at all. If the particle is leaping back and forth across a fixed distance (from the particle's perspective), then from the distant perspective the particle is leaping a different distance toward gravitational masses than away from it, on each oscillation. So again only 1 dimensional oscillation may suffice.

 

I don't know how the changing mass of the particle would come into the picture, and whether or not it would only affect the distant observer's take on it. Perhaps the mass times leap distance remains invariant, so each leap seems to take a fixed amount of energy, regardless of observer location.

 

I think that the 2 different explanations for a distant observer (1 for traveling toward and away from the mass, and one for traveling perpendicular to that) might mean that there will be a gravitational effect regardless of the direction of oscillation. We might drop the requirement that oscillation is evenly distributed in all directions, and instead only require that for any given direction, forward and backward motion occurs on average with equal probability or rate.