What's the nothingness that our universe is expanding into?

[PeterDonis]

I understand that you're saying he should have said something like "in the shaded region where the density of space had changed"

No, I don't think so. He is saying that new space is being created. In terms of the universe during inflation, he is saying that as the universe inflates, new space is created that didn't exist before.

However, thinking of this as "new space being created" is not really correct relativistically. Strictly speaking, it should just be "the geometry of spacetime is a certain way"--spacetime is shaped like an expanding funnel, so to speak. Spacetime doesn't get "created"; it just is--it's a 4-dimensional geometry that has a certain shape. The "gravitational field" is just a way of referring to the 4-dimensional shape.

In short, I think Guth here is giving a particular interpretation of the theory, which may or may not be a good heuristic to use in trying to understand gravity and energy in general. See below.

The net effect of this operation is to extract energy, and to create a new region of gravitational field. Thus, energy is released when a gravitational field is created [italics mine]...Since the region began with no gravitational field and hence no energy, the final energy must be negative.

Notice that Guth is equivocating here: first he says that a new region is "created", which implies that it didn't exist before; then he says that the region "began with no gravitational field", which implies that it did exist before, just without a gravitational field. But you can't have it both ways. This just shows that you have to be very careful when reading pop science presentations, even when they're written by scientists. Guth is not giving a rigorous scientific description of the theory; he's just giving an analogy which may help with visualization, but has serious limitations.

Notice also that viewing spacetime as a 4-dimensional geometry with a particular shape avoids this difficulty; the shape is what it is, and that's it.

 

[slatts]

I may have looked at one light cone too many, but I do have a question about the funnel analogy. I could understand the funnel with the hyperboloids nested inside it completely IF the funnel itself had curved sides, but it never does. Maybe there's a curvature so subtle that human vision could only detect it in a drawing of the funnel that extended from here to the CMB, but, if so, I've never heard it mentioned.

I'm GUESSING that this MAY have SOMETHING to do with the approach to infinity in calculus. If we could use all the trees on Earth for the paper and write limits on it with digits that could only be read with electron microscopes, would the expenditure in material and effort perhaps correspond to a retreat of the singularity downward in size and backward in time, or am I missing something?

 

[PeterDonis]

I could understand the funnel with the hyperboloids nested inside it completely IF the funnel itself had curved sides, but it never does.

I'm talking about a different "funnel" analogy. If we view the universe spatially as a hypersphere, and drop two spatial dimensions, we can think of it at any instant of time as a circle, and the spacetime of the universe is just a stack of these circles (time is vertical in this analogy). The size of the circles increases as you go upward--that's the expansion of the universe. If the expansion is accelerating, then the rate at which the size of the circles increases upward, is itself increasing, so the stack of circles looks like a funnel with sides that expand outward. It's just an analogy for visualization.

Note that in the other funnel analogy, the one you refer to, the "funnel" itself is not supposed to be part of spacetime; it's just a convenient bit of "scaffolding" to help visualize the model.

If we could use all the trees on Earth for the paper and write limits on it with digits that could only be read with electron microscopes, would the expenditure in material and effort perhaps correspond to a retreat of the singularity downward in size and backward in time

The singularity doesn't "move" in space or time; it's just a particular piece of the 4-d spacetime geometry.

 

[slatts]

I didn't mean that it would move physically; I had thought the conception of it might shift if the approach to infinity didn't have to be delineated with straight sticks laid end-to-end. (It would be something more like pi. I may be trying to say "wave function".)

You see, what I'm trying to say about the singularity is, if it happened to occur at scales whose length factor is so close to the shortest wavelength of light, the termination of the geodesics that would've otherwise continued "down" it may have been a concession to the demand for experimental verification. And, if so, i don't understand how we would be able to make judgments about the nature of whatever lay (in your analogy) "beneath" it. I'm talking about judgments like whether it might be just like "traditional" space (synonymous with traditional "nothingness"), containing non-scalar fields whose values would all be at zero, and might remain there throughout some "time" whose clocks would all have hands that would remain forever motionless to us, but might nevertheless be moving. (I understand that the clocks would have to be pretty tiny: That's more-or-less the point of my inquiry.)

I've googled "scale factor:" dozens of times, and nothing I've been able to comprehend would justify extending the funnel (or stack of discs) analogy until a funnel with curved sides would dwindle into an infinitely thin line that would finally just fade beyond any perceptibility obtainable to us through all the resources in our observable region. IS that the result of the need for experimental verification that distinguishes science from other forms of brain activity, or is there something POSITIVE in the math that would leave that extended analogy markedly less correct than the prevailing one of a straight-sided funnel ending at a singular point?

 

[PeterDonis]

I didn't mean that it would move physically; I had thought the conception of it might shift

Shifting the "conception" won't change the physics. But physically, as I said before, nobody believes the singularity is actually there.

if it happened to occur at scales whose length factor is so close to the shortest wavelength of light

There is no "shortest wavelength of light", at least not in any of our current models. If you're talking about proposed quantum gravity models in which there is no meaning to any length shorter than the Planck length, in those models, "spacetime" itself has no meaning on the Planck scale; it's an emergent phenomenon based on some other kind of physics at the Planck scale (such as strings in string theory or loops in loop quantum gravity).

the termination of the geodesics that would've otherwise continued "down" it may have been a concession to the demand for experimental verification

I'm not sure what you mean here. Nobody is claiming that any geodesics actually "terminate". The point is that the idealized model that contains terminating geodesics (i.e., classical GR in spacetimes with a singularity) can't be right at the point where the geodesics terminate in the model. So we have to find a better model. (Some of the rest of your comments might be attempts to describe a better model, but they don't seem like any of the proposals that I'm aware of.)

I've googled "scale factor:" dozens of times, and nothing I've been able to comprehend would justify extending the funnel (or stack of discs) analogy until a funnel with curved sides would dwindle into an infinitely thin line

Nobody thinks that model is valid at the point of a singularity, so no such justification is needed.

is there something POSITIVE in the math that would leave that extended analogy markedly less correct that the prevailing one of a straight-sided funnel ending at a singular point?

I don't understand. The "straight-sided funnel" is a different model: it models a spacetime whose rate of expansion never changes. We know experimentally that the rate of expansion of our universe has changed, so the "straight-sided funnel" model does not describe it.

 

[slatts]

Oh, right. I'd forgotten about the acceleration studied through the Cepheid variable stars. I guess you've answered my question. I'd hoped for a smoother curve to the funnel, but a wavy one will do the trick for this hand-waver. (Some of us are interpreters, not scientists.)

 

[Snerdguy]

We all know that the universe is expanding. What I'm curious about is what it is expanding into.

And the answer is: WE REALLY DON'T KNOW. Anytime science desribes something in an infinitive such as nothingness or O or omega or such, it just means we don't know. We have no way of observing the edge of the universe because it to far away for any means we have of detecting it. We really can't define what nothing is because, no matter how small we can measure, something is still there. We know that empty space isn't empty because something is there. They are terms that stand in for our lack of knowledge so we move on with our thought processes. So, "we really don't know" is the most accurate explanation of what is out there.

 

[phinds]

And the answer is: WE REALLY DON'T KNOW. Anytime science desribes something in an infinitive such as nothingness or O or omega or such, it just means we don't know. We have no way of observing the edge of the universe because it to far away for any means we have of detecting it. We really can't define what nothing is because, no matter how small we can measure, something is still there. We know that empty space isn't empty because something is there. They are terms that stand in for our lack of knowledge so we move on with our thought processes. So, "we really don't know" is the most accurate explanation of what is out there.

I disagree completely. Modern cosmology rejects the concept of an "edge" to the universe for a number of reasons. We don't know the size or shape of the universe (it could be finite but unbounded or it could be infinite) but no one proposes that it has an edge, and it is known empirically that it doesn't have a center (which would be implied by an edge)

 

[Hellmut1956]

I believe this exchange about linguistics and their impact when expressing physical concepts is touching an important field that the person not really expert in physics run into traps due to it.

First I learned many years ago something that has a huge impact when trying to "understand" concepts" in physics! Physics does not claim to say what is real! Physic theories just represent a model of a possible reality. If this model is good in explaining and forecasting aspects that are reflected in experiments and observation, fine! This has helped me to be cautious when trying to grasp theories in physics!

A second aspect of what was written here about linguistics is the reason why there is a mathematical "language" and this is really reflecting the strength of mathematics. If we look into any science in this days we will find that nearly everywhere the scientist use the "mathematical language". If you write a mathematical formula using mathematical annotation, what this is saying can be understood from a mathematically trained person anywhere on the planet, independently what "human language" he speaks natively!

Now back to what the thread dealt with at the beginning. The BigBang created this "universe". This means it did not just create the space, it also created time. So the question what was there before is meaningless. It comes from our day to day understanding of time as an infinite flow of something that separates before, from now, from next! When there was no time, how an there be something before it! This is the result of our thinking along causal paths!

Same is true about where the universe is expanding too! The best model, analogy is the surface of a balloon being inflated. Our spatial universe in this analogy is the surface of the balloon! Nobody would have a problem understanding that at the surface of a spherical balloon there is no edge, there is not something behind it. The surface is just this, the surface of a spherical object which is growing in "diameter" in a dimension that does not exist but which has the effect that the surface expands!

Remember is just an analogy, is just a model, has no other reason to be than just in being an analogy that helps us to grasp, what using mathematics is trivial! I have sometimes the impression myself, that I am a mathematical analphabet or legasthenic person! being interested in science I also try to grasp the concepts expressed in the different fields of science. But it is like being limited to watch the picture in an illustrated book and not being able to read. As soon as you try to get deeper into concepts presented, as soon as you try to grasp it to a level were you are able to understand the differences between string theories and such around quantum gravity, I already have trouble to remember if I using the right names! But to understand why one or the other theory have their supporters and their opponents, mathematical skills are required that I confess are beyond my abilities!

 

[andrewkirk]

Unknown. The Big Bang Theory has nothing to say about what came before one Plank time.

Why one Planck time specifically? I understand that the Big Bang theory says nothing about why the expansion commenced - ie nothing about 'time zero', or whether there even was a time zero - but I was not aware of the theory identifying a cut off at a positive cosmic time coordinate.

I read on Wikipedia that the concepts of Planck time and Planck length have specific significance only within hypotheses like loop quantum gravity that are designed to try to unite QM and GR, but which do not have theory status.

Is the reference to the Planck time as a lower bound for the reach of the Big Bang theory, a reference to what is suggested by some of those hypotheses? If not, what aspect of accepted QM (or GR, although that seems unlikely) is it that identifies the Planck time as a specific lower limit for what the Big Bang theory says about the history of the universe?

Thank you

 

[phinds]

Why one Planck time specifically?

I have always taken that to be an approximation, not an exact specification. It's more specific and useful than saying "a REALLY, REALLY small amount of time after the singularity" and as I understand it, it is at least approximately correct.

 

[magneticnorth]

I think the best answer to what is the Universe expanding into , is " We don't know " .We may know at some future time but at the moment we know just about the same as what we know about the inflation a.k.a. Big Bang . Physics can extrapolate back to 2 or 3 Planck time segments after the expansion , but we know absolutely nothing of what was or what came before . We can only assume a singularity ,as there is not any mathematics to describe such a thing or physical laws to allow it .

 

[andrewkirk]

I have always taken that to be an approximation, not an exact specification. It's more specific and useful than saying "a REALLY, REALLY small amount of time after the singularity" and as I understand it, it is at least approximately correct.

Sorry but I'm afraid I still don't follow you. If it's approximately correct, however rough, it must be an approximation to some quantity. Presumably that quantity is specified by some theory. If so, I'm wondering what the theory is, because I can't see anything in the current accepted theories of QM or GR per se that implies there will be a particular very small but nonzero unit of time or length that has a special significance.

If all the reference is trying to communicate is that neither GR nor QM tells us anything about time zero, or whether there was one (ie is the set of spacetime points with cosmic (FLRW?) time coordinate zero non-empty?), then that's quite clear. It's only if it's trying to say something more than that that I can't see what that something more would be.

 

[julcab12]

, I'm wondering what the theory is, because I can't see anything in the current accepted theories of QM or GR per se that implies there will be a particular very small but nonzero unit of time or length that has a special significance.

... Planck time is just the implication or perhaps computational threshold by combining such constants. It's the lowest(not absolute) they can possibly make as scale of time when combining such values using power series and dimensional analysis. They can speculate that during that era http://hyperphysics.phy-astr.gsu.edu/hbase/astro/grav.html#grav force begins to differentiate from the other three forces. It is not actually understood what really happened during that moment but it is used/integrated (at least they are trying^^) as a part of the model for High energy physics mainly fundamental forces.

 

[magneticnorth]

It's like saying I trillionth ,of a trillionth , of a trillionth of a second AFTER the expansion began .Physics can look back , extrapolating of course, using known physical laws and mathematics to such a point in time . Whatever happened looking back beyond that time is at present totally unknown . I'm a layman , so from my purview , I liken it to being catapulted with my back facing the direction of the acceleration , and all my observations are made looking back towards the point of acceleration , however I can only see up to a certain point after, or slightly after which I was catapulted - not being able to see that mechanism [catapult ] nor the source of it's energy. We look out into the Universe and can measure that acceleration , based on our estimates of gravity , observed [or unobserved ] mass ,combined with known Physics according to Relativistic, Mathematic , and Quantum calculations.

 

[Murdstone]

I agree with the statement advanced by Snerdquy and reinerated by magnetinorth - "We Really Do Not Know."

Not only is it unknown as to what matter is expanding into - we have no definition of space. Space is just assumed.

It is a carnard to suggest if one is not sufficiently versed in the mathematics then they just can not understand what is going on.

Use any mathematics you like, it would be most welcomed if using your tools you could construct a definition of space.

 

[PeterDonis]

we have no definition of space

This is not correct. In our models in relativity, "space", and more generally "spacetime", is defined as a manifold (3-dimensional for space, 4-dimensional for spacetime), with particular properties. All of this is perfectly well-defined mathematically. Physically, "points" in the manifold (for spacetime) correspond to events--physical happenings, such as "lightning strikes location X at time T by observer O's clock". The mathematical properties of the manifold correspond to the physical fact that, as far as we can tell, the set of physical happenings is continuous--there is no "minimum separation" in space or time between physical happenings. (There are speculations in quantum gravity that this may not hold at the Planck scale, but that scale is twenty orders of magnitude smaller than the smallest scale we can access experimentally, so the model of spacetime as a continuous manifold works at all the scales we can actually experiment with.)

Once you have spacetime as a manifold, "space" can be defined as some particular submanifold of spacetime, picked out according to some criterion (such as being a surface of constant coordinate time in some coordinate chart).

 

[andrewkirk]

... Planck time is just the implication or perhaps computational threshold by combining such constants.

Implication from what equations?
Computational threshold estimated by what equations?
Deduced from what postulates?

I'm just trying to get clear in my head whether the physical significance of Planck Time and Planck Length that one sees so often referred to in physics discussions as if it were accepted science, is deduced from the GR postulates, from the QM postulates, from the combination of the two, or whether some additional postulates, such as are used for Loop Quantum Gravity, are used.

Until recently, I had been under the impression that the significance was part of currently accepted science, and could be derived from the QM postulates, but I have never seen such a derivation. The derivation of the Heisenberg uncertainty inequality does not mention Planck time or length. Recently I read the Wikipedia article, which suggests that the Planck time and length are only significant in speculative hypotheses like LQG. I don't take Wiki as gospel, so I'm asking here to see if someone knowledgeable about the issue can confirm or deny it.

If there is a derivation from the postulates of a currently accepted theory, I would really appreciate a link to such a derivation so that I can work through it and understand it. On the other hand, if there is no such derivation, because the quantities are only significant in speculative hypotheses, I'll leave it for now because I want to learn more about the currently accepted theories of GR and QM before I start learning about speculative hypotheses.

Thank you

 

[PeterDonis]

I'm just trying to get clear in my head whether the physical significance of Planck Time and Planck Length that one sees so often referred to in physics discussions as if it were accepted science, is deduced from the GR postulates, from the QM postulates, from the combination of the two, or whether some additional postulates, such as are used for Loop Quantum Gravity, are used.

It certainly isn't deduced from GR postulates, since those postulates assume that spacetime is continuous.

You can't really deduce anything useful just from "QM postulates", because those postulates in themselves don't tell you what actual quantum particles or fields exist. Any quantum theory has to make additional assumptions about that.

The usual justification for giving Planck scale quantities physical significance is that, if we try to describe gravity by a quantum field theory, similar to the way we describe the other three fundamental interactions, we find that the strength of gravity becomes the same as the strength of the other three interactions at the Planck scale. (The other three interactions actually become unified into one, with a single strength, before the Planck scale is reached.) One way of expressing this is that, in the units natural to particle physics, Newton's gravitational constant is equal to the inverse Planck mass squared.

 

[julcab12]

Hi Andrewkirk,

According to what I've read. We get the value by combining powers constant -- ℏ (Reduced Planck), G (Newton's gravitational), and c0 (speed of light or a massless particle in a vacuum), such that the result has units of distance (metres).

Implication from what equations?
Computational threshold estimated by what equations?
Deduced from what postulates?

I'm just trying to get clear in my head whether the physical significance of Planck Time and Planck Length that one sees so often referred to in physics discussions as if it were accepted science, is deduced from the GR postulates, from the QM postulates, from the combination of the two, or whether some additional postulates, such as are used for Loop Quantum Gravity, are used.
Thank you

They really don't if has any physical meaning. The 'Planck thing' is constructed based on the assumption that all fundamental constant are equal to one. So they set a scale where C, ℏ G are relevant in their description and we get that value, this would imply we would presumably need a quantum theory of gravity to explain phenomena in that setup. Since we no have such theory, many physicist think they mark a boundary to our current understanding of nature. Of course, these ideas are speculative, but are the things we expect to find, we don't know what exactly happen at that scales.

"

Implication from what equations?If there is a derivation from the postulates of a currently accepted theory, I would really appreciate a link to such a derivation so that I can work through it and understand it. On the other hand, if there is no such derivation, because the quantities are only significant in speculative hypotheses, I'll leave it for now because I want to learn more about the currently accepted theories of GR and QM before I start learning about speculative hypotheses.

Thank you

As Peterdonis mentioned; It certainly isn't deduced from GR postulates, since those postulates assume that spacetime is continuous as a classical rule. However QM has some quantities such as angular momentum or energy of bound states, can only take "quantized" or discrete values (eigenvalues) but it doesn't mean that all observables in quantum mechanics have to possesses a discrete spectrum as already mentioned. LQG ODOH is viewed as discrete - spatial distances and temporal intervals are multiples of Planck L and time respectively. The proposition that distances or durations become discrete near the Planck scale is a scientific hypothesis and it is one that may be - and, in fact, has been - experimentally falsified. For example, these discrete theories inevitably predict that the time needed for photons to get from very distant places of the Universe to the Earth will measurably depend on the photons' energy.

 

[PeterDonis]

these discrete theories inevitably predict that the time needed for photons to get from very distant places of the Universe to the Earth will measurably depend on the photons' energy.

Do you have a reference for this? I wasn't aware that all such "discrete theories" had been ruled out by this method.

 

[cptstubing]

We all know that the universe is expanding. What I'm curious about is what it is expanding into.

I think it is inaccurate to describe the universe as expanding. It is better to think about space and time (space time) as expanding. Instead, it's possible that the space between celestial bodies is expanding. The rubber band idea, think of a thick rubber band with points on it that is stretched out.
Really though, this topic is full of unknowns.

 

[tressure]

We all know that the universe is expanding. What I'm curious about is what it is expanding into.

what a coincidence, your question doesn't differ from mine check mine out at: https://www.physicsforums.com/threads/is-the-universe-truly-expanding.804886/ ... you might find information that might come helpful to you!

 

[Murdstone]

This is not correct. In our models in relativity, "space", and more generally "spacetime", is defined as a manifold (3-dimensional for space, 4-dimensional for spacetime), with particular properties. All of this is perfectly well-defined mathematically. Physically, "points" in the manifold (for spacetime) correspond to events--physical happenings, such as "lightning strikes location X at time T by observer O's clock". The mathematical properties of the manifold correspond to the physical fact that, as far as we can tell, the set of physical happenings is continuous--there is no "minimum separation" in space or time between physical happenings. (There are speculations in quantum gravity that this may not hold at the Planck scale, but that scale is twenty orders of magnitude smaller than the smallest scale we can access experimentally, so the model of spacetime as a continuous manifold works at all the scales we can actually experiment with.)

Once you have spacetime as a manifold, "space" can be defined as some particular submanifold of spacetime, picked out according to some criterion (such as being a surface of constant coordinate time in some coordinate chart).

This is not an independent definition of space. All of the above is being assumed. LET'S ASSUME...Space enters the model by necessity.

An alternative perspective is to ponder whether space has a physical aspect or is just a theoretical construction. Most approaches to "space" are theoretical. At best the above is saying that space is continuous but its composition is undefined.

There is a need for a definition of space framed in terms of its composition.

 

[PeterDonis]

This is not an independent definition of space.

If you mean it's not "independent" of the definition of spacetime, I agree, but I don't see why that's a problem.

All of the above is being assumed.

That's true of any scientific model. You assume a model with certain properties; then you compute the consequences of the model and compare them with experiment. Again, I don't see why this is a problem.

There is a need for a definition of space framed in terms of its composition.

Some quantum gravity theories are attempting something like this: spacetime is no longer a fundamental entity, but emerges from something else (such as strings or loops). But then you just have a need for a definition of the strings or loops in terms of their composition. Such a demand never ends; so I don't see why it's any particular issue for space or spacetime as opposed to just a general property of scientific models, that there is always more to be explained.

 

[Drakkith]

I think it is inaccurate to describe the universe as expanding.

I disagree. In fact, expansion is by far the most accurate way of explaining our observations. The way that distances increase both over time and distance is exactly how an expansion process works.

 

[julcab12]

Do you have a reference for this? I wasn't aware that all such "discrete theories" had been ruled out by this method.

http://motls.blogspot.ae/2009/08/fermi-kills-all-lorentz-violating.html
http://arxiv.org/abs/1102.2784
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3270.html

 

[Chronos]

This thread has gone over the 'edge'. Philosophical 'nothingness' is not a confirmed property of the universe. It lacks observational, and even mathematical support.

 

[PeterDonis]

http://motls.blogspot.ae/2009/08/fermi-kills-all-lorentz-violating.html
http://arxiv.org/abs/1102.2784
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3270.html

The Fermi observations set fairly stringent constraints on a particular class of discrete models, yes. But that is not at all the same as ruling out all discrete models. (Yes, I know Lubos Motl makes the stronger claim--well, actually he makes a different claim, that all models that violate Lorentz invariance are ruled out, which is not the same as saying all discrete models are ruled out. But in any case, that's a blog post, not a peer-reviewed paper.)

 

[rootone]

. We can only assume a singularity.

Which actually means that in terms of our present understanding,we don't have a clue what is going on.
Need to be careful not to perpetuate the myth that a singularity is a physical object of some kind.