Where does new space come from as the universe gets bigger?

[CosmicVoyager]

Space is simply volume filled with matter and energy, we have tried explaining that to you numerous times.

Please read that again. I am asking whether or not you agree or disagree with what Brian Greene said. That is perfectly clear in the post you quoated, and you still did not answer the question. Yes or no?

The initial responses to my question of where new space comes from claimed that the decriptions and illustrations of space as a physical entity were only analogies, so I gave one (of countless) example(s) that seems to me to be not just an analogy, disproving those replies. So, I have been pullling teeth trying to get an answer as to whether or not those repliers think Brian Greene is using it only as an anology or not. If not, then those replies are wrong. I could give countless more examples but it would be like pulling countless more teeth due to not being able to get an answer.

Once it has been established what physicists such as Brian Greene are claiming, then we can proceed further.

 

[CosmicVoyager]

Why are you quoting a popularizer instead of a textbook? Granted, many textbooks often make such inaccurate claims about frame dragging as well so that won't necessarily help you. Space is not twisting and neither is space-time. The space-time of an isolated spinning body itself possesses angular momentum but that doesn't imply some kind of material twisting. What's twisting are the world-lines of observers fixed with respect to the distant stars due to the spin of the source and this is where frame dragging comes from because this twisting is proportional to the precession of a gyroscope relative to the distant stars.

Please read my previous reply. I am not citing it as evidence. I am asking whether or not you agree with it.

 

[craigi]

Read that again! I am asking whether or not you agree or disagree with what Brian Greene said. That is perfectly clear in the post you quoated, and you have *failed* yet again to answer the question. Yes or no?

The initial responses to my question of where new space comes from claimed that the decriptions and illustrations of space as a physical entity were only analogies, so I gave one (of countless) example(s) that seems to me to be not just an analogy, disproving those replies. So, I have been pullling teeth trying to get an answer as to whether or not those repliers think Brian Greene is using it only as an anology or not. If not, then those replies are wrong. I could give countless more examples but it would be like pulling countless more teeth due to the apparent density of the people who can't answer a yes or no question!

Once it has been established what physicists such as Brian Greene are claiming, then we can proceed further.

Part of the problem here, is that we really don't know the true nature of space-time. For that we would need a working theory of quantum gravity, but we don't. Brian Greene, is one of many, who have spent many years searching for it with little success. Some argue that there's been no signifiant progress, in that direction. He's also written a book (or books) which attempt to explain complex mathematical ideas to non-physicists and as such need to use colourful descriptions to convey them.

You started your thread in the comology sub-section of the forum, which is largely concerned with the well established theory of general relativity and you've been given answers based upon that. Brian Greene's work is concerned with the speculative attempt to unite general relativity with quantum mechanics, that is string theory. If you'd asked your question in the 'beyond the standard model' sub section, you'd have probably been given different responses, but what you're asking amounts to the same thing - do we agree that the colourful language which one physicist uses to describe an unproven speculative, mathematical theory, to non-physicists, is an accurate description of nature? The answer to that has got to be no, but it was probably not incorrect for him to offer it, in the context that he did.

There's a peculiar thing about the way we learn physics. We learn it through white lies. We need over simplifications to help us create a framework in order to learn more complex things. Then we need to cast off the simplified theories as either approximations, limiting cases, or learning aids. Physicists accept this as implicit as soon as they come to terms with undergrad physics. Analogously, mathematics carefully delinates the domain of each formalism. When physicists, speak to non-physicists, they often forget to be clear that they are talking about a specific model, while the non-physicist is usually in pursuit of an absolute truth.

 

[Mordred]

Read that again! I am asking whether or not you agree or disagree with what Brian Greene said. That is perfectly clear in the post you quoated, and you have *failed* yet again to answer the question. Yes or no?

The initial responses to my question of where new space comes from claimed that the decriptions and illustrations of space as a physical entity were only analogies, so I gave one (of countless) example(s) that seems to me to be not just an analogy, disproving those replies. So, I have been pullling teeth trying to get an answer as to whether or not those repliers think Brian Greene is using it only as an anology or not. If not, then those replies are wrong. I could give countless more examples but it would be like pulling countless more teeth due to the apparent density of the people who can't answer a yes or no question!

Once it has been established what physicists such as Brian Greene are claiming, then we can proceed further.

fair enough if your just asking if we agree with Brian Greene's descriptive use the answer is NO as its misleading

 

[Bill_K]

Part of the problem here, is that we really don't know the true nature of space-time.

Nevertheless, the premises that the OP raised are out of the question - That, as the universe expands, part of space is newly created (which part??) and must "come from somewhere."

This is only true in the sense that all of space at time t + dt is "newly created."

More generally, one could write down the Cauchy initial value problem with an arbitrary initial spacelike hypersurface. The evolution is not volume-preserving, so as we step to the next hypersurface, space may expand (or contract), giving the impression that something is being newly created. But space is a continuum, and nothing is really "new," every point in that hypersurface in fact arose from a point in the initial one. (Or from more than one point, or from a singularity.)

 

[CosmicVoyager]

Matterwave - "The picture of space-time as a "fabric" is an analogy, not to be taken seriously."Bandersnatch - "Scientists are describing space as space. It's a mathematical concept with certain well-defined properties."Matterwave - "People have to use words to describe things to other people. We can't just say to the masses "hey, look at the Einstein field equations - That's spacetime - that's gravity!" because nobody would know what we were talking about. The use of analogies is appropriate where they are appropriate."CosmicVoyager (me) - "I will begin compiling a list of examples of space described and illustrated as a thing with shape stretched, compressed, curved, twisted. Grids showing space itself as having shape."Mordred - "no need we have all seen them numerous times lol. As mentioned they are a visual aid."CosmicVoyager (me) - "In beginning to complie my list of examples I found further confirmation of physicists currently statng that space in actually a thing like a fabric and not just volume or distance...Are you aware of the physicist, Brian Green, and his books and PBS series'? One of which is titled "The Fabric of the Cosmos" in which one of the questions he addresses is "Is space a human abstraction or a physical entity?". Are you claiming his view is that space is not an actual thing just as you have stated? It is essential that this be made clear..."No one answers the question. They keep talking about what space is, but they never answer the question of whether what Brian Greene is saying is an example of a physicist using analogies.

I keep asking, they keep not answeringCosmicVoyager (me) - "It is unclear to me if you are saying 1) Brian Greene is not saying what he means or if 2) you disagree with what he means?

Quoting Brian Greene referring to the frame dragging detected by Gravity Probe B, 'Space is something real, a physical entity like a fabric. If space were nothing there would be nothing to twist.'

It seems to me he is emphasizing over and over again that space is something more than what repliers are saying.

Bandersnatch, are you also saying that by 'a physical entity' Brian Greene means the same thing you are saying? I do not see how much clearer he can say it."People keep replying but still not answering the question. I have a fit.Then finally I get an answer saying they do not agree with Brian Greene, that he is not just using analogies as multiple people stated. So what they should have said is there are multiple views as there are multiple interpretations of quantum decorehence, and stated what *their* view is.

My original question is directed at physicists whose view it is space is a physical entity. Who think Gravity Probe B's measurement of frame dragging is direct evidence that it is, because if space were nothing there would be nothing to twist.

I am *not* asking whether or not one agrees with that view of space.

 

[CosmicVoyager]

Looking for an answer I found a lecture on inflation by Dr. Paul J. Steinhardt. I do not know if it is related. I do not fully understand it.

An excerpt, "The inflation process obviously does not conserve inflationary energy because we are creating more and more space. It is an energy generating process. It is a space generating process. Where is the energy coming from? It is coming from gravity. Is there a limit to how much energy I can draw from a gravitational field and convert it into inflationary energy? The answer is no. There is something special about gravity. All the other forms of energy we know of have a bottom to them. If you draw the energy down eventually it gets to zero or some minimum. That is not true for gravity. Gravity is a unique form of energy that is bottomless. The gravitational potential energy curve gradually goes toward negative infinity as two objects are brought closer together. If you can find some way of tapping that energy continuously there is no end to how long you can do it, and inflation is a mechanism that does it automatically. So energy is conserved. You can always find more negative gravitational energy and balance it with positive inflationary energy."

That is at 33 minutes. http://youtu.be/IcxptIJS7kQ

 

[craigi]

Nevertheless, the premises that the OP raised are out of the question...

Agreed. My comment was specifically directed at the latter section of the thread pertaining to the Brian Greene reference from post #13.

To be clear, neither Greene nor any other proponent of any theory, that I'm aware of, at least, suggest that the volume of space is a property that should be conserved either in itself or as converted from another quantity.

 

[Ken G]

There's a peculiar thing about the way we learn physics. We learn it through white lies.

That is wonderfully said, I often try to make that same point.

When physicists, speak to non-physicists, they often forget to be clear that they are talking about a specific model, while the non-physicist is usually in pursuit of an absolute truth.

Again I completely agree. Indeed on another thread I critiqued a famous physicist who said words to the effect that the search to understand space was a search to find out if Aristotle "was right" that space is absolute, or if Einstein "was right" that space is relative. I said they were both right if we understand what they (and what all scientists) were actually saying, which is no more than "here is the insight that will propel the advance of science forward to the next step." Science is not a quest for absolute truth, it is a process of discovery. To set it up as something that it is not only sets us up for ultimate disappointment in it, and also sells short its exquisite mixture of doubting, testing, and grabbing at the insights that propel it along.

To be clear, neither Greene nor any other proponent of any theory, that I'm aware of, at least, suggest that the volume of space is a property that should be conserved either in itself or as converted from another quantity.

CosmicVoyager, if that does not answer your question, then I don't know what would. I would just add one point. The only empirically demonstrable fact we can point to to say that space is expanding is that the number of rigid meter sticks that would fit between the galaxy clusters now is more than in the past (we can't really lay rigid rulers between them, but we think we have tests that are the equivalent). Thus we cannot even say that space actually is expanding, it is just as possible that rulers are shrinking (and all gravitationally bound systems as well). No law of physics is violated by that picture, and no observational test comes out any different. Hence, we cannot say that space is a physical thing, as we have no theory that says it is. Frame dragging doesn't say it is either, as we equally have no specific mechanism that would make space twist, than we have a specific mechanism that can make a gyroscope precess relative to that space. In the absence of theories that give demonstrable meanings to our words, all our words should be regarded as interpretational pictures.

 

[chill_factor]

I do not think that shrinking matter is equivalent to expanding distances, as shrinking matter should be detectable through changes in the moment of inertia of a gyroscope which scales as the radius squared.

 

[Ken G]

I do not think that shrinking matter is equivalent to expanding distances, as shrinking matter should be detectable through changes in the moment of inertia of a gyroscope which scales as the radius squared.

The radius of a shrinking object does not change, if the rulers you'd use measure it shrink too. That is not to say the object may unambiguously be said to be shrinking if the rulers shrink too, indeed the whole point is, one cannot actually tell if an object is shrinking or not, any more than you can tell if space is expanding. General relativity is a theory of the dynamics of a metric, and a metric always involves ratios of lengths or ratios of times, where the numerator is the quantity you are measuring and the denominator is your standard of measurement. The theory only tells you the ratio is changing, it doesn't tell you why the ratio changed, or whether it was a change in the numerator or the denominator. A metric theory does not even distinguish such changes as different things. You would need a deeper theory for that, just like you would need a deeper theory to give space any physical attributes or mechanisms by which it can be expanded. GR doesn't do either of those things, it is purely a metric theory. But framing it as shrinking matter, rather than expanding space, sure makes the question "where does the new space come from" go away!

 

[Chronos]

Ken G, you know full well we have observational evidence that refutes your 'proposition'. Stirring the pot only serves crank views.

 

[Ken G]

No, there is no such evidence, and no stirring. Crank views are not assisted by the truth, they will find their own path, ignoring the truth, the truth never matters to them. But it should matter to the scientist, so the scientist must know the difference between what is an observed fact, and what is simple convention of language. We have evidence that GR works. GR is a metric theory. Metric theories tell you how ratios between measurements and standards evolve. That's what a metric does.

It's the same with time, by the way-- the proper time between two events can be predicted and tested. What are you predicting, what are you testing? Clearly, just look, you are predicting and testing the number of times some standard clock will tick between the two events. Let the two events be the arrival of successive wave fronts of the observed CMB. GR tells us that as the universe ages, that number increases. It certainly does not tell us, and this is quite important, if some absolute time between the wave fronts is increasing, or if the clocks are ticking faster. To claim otherwise is both to ignore the central lessons of relativity, and to mistake simple pedagogical conventions for statements of physical fact.

Now, of course the convention is fine. We choose to say space is expanding, we say light is redshifting, it's a standard language and we all know what we mean. But it becomes dogma if we really believe that we think we know that is true, and if we think we know objects are not shrinking and clocks are not ticking faster. It's not even what we do in SR, for crying out loud-- there we tend to make the opposite choice and say that objects are shrinking and clocks are ticking differently as we change our frame of reference! But all physics tells us, in either case, is what we will measure, that's it-- and all measurements are ratios between some physical quantity and some standard, so we have no idea which one is responsible for the change, or if it even makes sense to ask which one is responsible.

The point is clearly true, but why bother making it? Because people ask questions like, where does the space come from? And the truth is, we have no idea if there is any more space in there in the first place, that's just not something that GR tells us, it's a convention of language.

 

[Frank Weyl]

Riemann Sphere

Think of the universe as created from a Planck-like object some 1.6160X10^-33cm diameter.
Imagine now, as an example, a mobius curve or strip which has only one side. Now imagine this object as an inner tube to a bicycle and cut it opposite the valve and give it a twist and glue the two ends together. Again, imagine that the inner tube is made of a special material which will not flex or distort as it is filled with air/energy. As the inner tube expands, the internal diameter decreases until it its size becomes Planck length, the shortest distance that has any meaning in quantum mechanics, and we then have a sphere which has only one side. As there is absolutely nothing external to the expanding sphere, the expanding edge, or 'event horizon', creates space and time continuously as it increases in size. The actual name for this theoretical topological object is a Riemann sphere.
There is no doubt that the creation of the universe from its expansion has spawned many theories and this is only a small attempt to explain in words, in analogous form, the imagined shape which would explain the nothingness in which the universe is expanding into.

 

[phinds]

... which would explain the nothingness in which the universe is expanding into.

You're just making this up, right? There is zero evidence that the universe is expanding INTO anything and if it were, there would be a boundary which would cause serious problems in physics. The consensus among cosmologists is solidly that there is no such thing.

 

[Ken G]

I believe here we have an example where the "shrinking matter" picture actually defeats crankism, rather than promoting it, as there is no analog to the scenario we just heard in the shrinking picture!

 

[Frank Weyl]

Thank you phinds,
I used it as an abstract pleonasm.
Of course I could have used as reference; Penrose, Feynman, Greene, Susskind, Stewart, Kumar, et al. but I looked at the question and the questioner and decided upon a analogous form and not to get bogged down in twistor theory or compactified Minkowski space.

 

[Matterwave]

What would one even mean by "shrinking matter"? Elementary particles are, by fiat, point particles. So unless we know the internal structure of elementary particles (which at this point we definitely do not), the only way to define "shrinking matter" is by defining distances between elementary particles to be shrinking. But surely we cannot define "shrinking matter" to be "distances between all elementary particles are growing smaller", as that would directly be falsified by any two particles moving away from each other. So how should we go about making a good, precise definition of "shrinking matter"? I think if one is thinking relativistically (get rid of notions of rigid bodies!), one must conclude that the idea of "shrinking matter" is ill defined at best.

 

[Mordred]

Thank you phinds,
I used it as an abstract pleonasm.
Of course I could have used as reference; Penrose, Feynman, Greene, Susskind, Stewart, Kumar, et al. but I looked at the question and the questioner and decided upon a analogous form and not to get bogged down in twistor theory or compactified Minkowski space.

Sounds like your referring to string theory and its added dimension descriptives correct?

here is an article covering expansion and redshift,
https://www.physicsforums.com/showpost.php?p=4687696&postcount=10

the second article I already posted on geometry in terms of the FLRW metric
https://www.physicsforums.com/showpost.php?p=4697773&postcount=30

and here is a professionally written textbook style coverage of Cosmology including the Einstein field equations and FLRW metric that is free

http://arxiv.org/pdf/hep-ph/0004188v1.pdf

just to get this thread back on track lol

edit just for added measure Phind's balloon analogy is also worth reading
http://www.phinds.com/balloonanalogy/

 

[Frank Weyl]

Thank you Mordred,
Yes. at this juncture, it is a good idea to make a direct comparison between twistors and superstrings. As you are aware superstrings are massless, one-dimensional objects having an extreme short length. Twistors, as null lines or light-rays, have no length, no sense of scale, and no mass. Superstrings are defined in a ten-dimensional space, which, will compactify down to our own four-dimensional space-time. Twistors, by contrast, are defined in a space of complex dimensions. This complex twistor space is then used to generate our four-dimensional space-time, along with its rich structure of null lines. Superstrings carry a series of internal symmetries, which are broken as the ten-dimensional space compactifies.
Some people do not accept twistor theory or superstring theory but as it is these days, it is always the squeaky wheel that gets the oil!
An added encumbrance is that although I live in England and teach at the O.U. my mother tongue is Norwegian.

 

[Mordred]

Gotcha thought I recognized your earlier descriptive so I'm glad I asked for clarification. By the way welcome to PF. I haven't gotten around to studying much on string theory, have too many ongoing projects with improving my understanding of perturbations, field theory, (QFT) thermodynamics (which includes improving my knowledge of particle physics, QCD, QED etc. I found that in order to better understand those I had to also improve my differential geometry lol. However that being said I plan on getting to string theory one of these days lol. Thanks for the break down on the various types of strings.

 

[craigi]

What would one even mean by "shrinking matter"? Elementary particles are, by fiat, point particles. So unless we know the internal structure of elementary particles (which at this point we definitely do not), the only way to define "shrinking matter" is by defining distances between elementary particles to be shrinking. But surely we cannot define "shrinking matter" to be "distances between all elementary particles are growing smaller", as that would directly be falsified by any two particles moving away from each other. So how should we go about making a good, precise definition of "shrinking matter"? I think if one is thinking relativistically (get rid of notions of rigid bodies!), one must conclude that the idea of "shrinking matter" is ill defined at best.

Notice that Ken G used the word 'matter', rather than 'elementary particles'. Basically any system of particles would get smaller.

You'd need to continously scale the range of the forces. You could achieve this by changing some of our constants of nature, to variables, with laws to describe how they evolve over time. We don't have a reason for why these constants exist anyway. They just happen to appear constant whenever we measure them.

Is it worth it? Of course not, as already explained, but it would be another way to formulate the models that we already have.

 

[Frank Weyl]

Superstrings and twistors.

However that being said I plan on getting to string theory one of these days lol. Thanks for the break down on the various types of strings.

Superstrings and twistors do not represent the only approach that are attempting to go beyond the Cartesian order or that seek to transform quantum theory and the general theory of relativity and I fully understand the entries by the guys earlier on...! On the one hand, there are a number of mathematical excursions into new forms of descriptions. But often, while being speculative, they do not have a firm philosophical underpinning or a compelling physical motivation. At times they almost seem like shots in the dark...but where does inspiration and breakthrough come from? Of course, it is possible that one of these shots will hit the target, and then physicists will be faced with the major question of just why..
Then there are the more philosophical approaches, and here I have in mind David Bohm's notion of the implicate order. Bohm's ideas are well argued, and it is convincing that a new order is required by quantum theory, an order that is essentially nonlocal and of an enfolded, rather than an explicate, nature. The problem is that such an order does not yet have a mathematical form, and needs to be translated into formal relationships that could replace the more conventional treatment of space and time.
On the one hand, there are mathematical excursions with no deep foundation; on the other, there are ideas for new approaches that have not evolved an explicit mathematics. There is the promise of twistor theory, which has yet to be fully worked out and there is the juggernaut of superstring theory, which can no longer continue unless some challenging issues are faced and resolved. And so the deepest questions remain. But at least more and more physicists are realizing that a crisis does indeed exist in physics, that hard work is required and profound new ideas are called for.
We need to do a lot less scribbling and a lot more thinking.
After all, what does the Ph in Ph.D. stand for...

 

[Ken G]

Is it worth it? Of course not, as already explained, but it would be another way to formulate the models that we already have.

It might be worth it-- if only to see that it is not necessary to "do anything to space or time" to get GR. It's really all just a question of prejudice-- do we think it's harder to monkey with matter, or with space? As for the constants, if expressed in non-dimensional form, which is the sensible form for constants anyway, nothing would need to happen to them.

 

[Mordred]

Yeah I've been encountering some of the metric misnomers and misinterpretations which this particular article is covering, I'm still going through it as I just received it yesterday lol. Needless to say its changing my understanding on a number of aspects of space-time I thought I had understood. Its particularly handy as he does an excellent job of covering some of the pitfalls of chosen metrics systems by comparing them to other metric forms.

the article was posted to me by a forum moderator and I can't thank him enough for that

"Lecture Notes on General Relativity" by Matthias Blau

http://www.blau.itp.unibe.ch/newlecturesGR.pdf

the article has already changed my understanding of redshift both gravitational and cosmological. lol.

Another lengthy article I'm still fighting my way through is
"Fields" http://arxiv.org/pdf/hep-th/9912205v3.pdf strings are in the later sections so its on my hit list lol

 

[Ken G]

But at least more and more physicists are realizing that a crisis does indeed exist in physics, that hard work is required and profound new ideas are called for.
We need to do a lot less scribbling and a lot more thinking.

I hope you didn't think my "crank" comment applied to you. It only applied to my uneducated reaction to you! But the point I was making still holds-- if all GR does is tell us ratios of scales, we can never know what is "causing" the ratios to change, be it changes in spacetime, changes in matter, or even if there is any meaning in that distinction. Would you say the situation is different in twistor theory?

 

[Frank Weyl]

You could achieve this by changing some of our constants of nature, to variables, with laws to describe how they evolve over time. We don't have a reason for why these constants exist anyway. They just happen to appear constant whenever we measure them.
Is it worth it? Of course not, as already explained, but it would be another way to formulate the models that we already have.

All four of the Planck constants mass, length, time and temperature are themselves defined by constants.
For example:
planck mass = √ hc/G = 5.56 X 10^5 gram...and so forth.

Allowing the constants to become variables would alter the complete structure of the universe.
Even altering just one would affect all the others and the universe would become chaotic for the first Planck-second and then all the atoms would simply disjunct.

 

[Ken G]

But we can agree that all the constants can be expressed in dimensionless form, for nature cannot care what a "gram" is. Hence having matter shrink (and clocks speed up) to match the usual changes in spacetime, the latter being our common arbitrary interpretation of the change in the metric, would not alter the constants in dimensionless form, any more than expanding space and redshifting light does.

Indeed, the current state of affairs is that we interpret cosmological redshifts differently from gravitational redshifts (the former is said to be due to "expanding space", the latter is said to be due to "clocks slowing down in a gravitational potential"). I think it's pretty clear that any physical description that claims such fundamentally different sources for cosmological vs. gravitational redshifts must be arbitrary convention, and perhaps not so well unified of a convention at that.

 

[Frank Weyl]

I hope you didn't think my "crank" comment applied to you. It only applied to my uneducated reaction to you! But the point I was making still holds-- if all GR does is tell us ratios of scales, we can never know what is "causing" the ratios to change, be it changes in spacetime, changes in matter, or even if there is any meaning in that distinction. Would you say the situation is different in twistor theory?

Thank you Ken,
The great triumph of Penrose's twistor approach has been the elegant new way in which it describes the various fields used in physics. As you know, fields have become one of the most important tools in modern physics. In the nineteenth century the electromagnetic field was created in order to explain the phenomena of light, electricity, and magnetism. Then at the subatomic level, the idea of the field was to reappear as quantum field theory.
Take as an example Schrödinger's equation that describes the motion of the electron. This equation does not in fact explain the electron's origins or properties. Something more is needed. Quantum field theory, an extension of the quantum theory of Schrödinger and Heisenberg, attempts to go deeper. It begins with "classical" fields for matter and force and then goes on to quantize them. The quantum excitation of the electromagnetic field, for instance, become photons of light, while the quantum excitation of the electron field are electrons and positrons. The unified field theories begin with a single grand field whose basic symmetry is then broken. The quantum excitations of these symmetry-broken fields are approximations of the various hadron and lepton elemental particles.
The field description is fundamental in both classical and quantum physics, and it is here that twistors are able to provide a powerful new formulation----fields appear in a particularly natural way in the twistor space picture. But since Penrose's approach is based on the proposition that mass is a secondary quality that arises in the interaction of more fundamental massless objects, the twistor formulation begins with massless fields such as those for the photon and graviton (at the time, the formulation included the neutrino, but the twister's mathematical resultant gave the neutrino mass..!) With luck, and some new insights, physicists may one day be able to discuss fields for massive particles within the same general formalism.
It turns out that these massless fields fall so naturally into the twistor scheme of things that it becomes possible to throw away the field equations themselves and discuss fields using a pictorial, geometrical approach!
Until Penrose and the twistor program came along, it was necessary to use what are called field equations in order to determine a field's behaviour. But today, with the help of the rich cohomology of twistor space. It becomes possible to get rid of the differential equations that determine the field. The twistor picture relies purely on the geometrical (or cohomological) properties of the field as it it expressed in terms of twistors and twistor space. This is a truly amazing result, for it means that the twistor approach can deal with the various fields of nature without ever needing to bother about field equations!
Your question, therefore, is mute in reference to twistor space, because the picture is radically different in Penrose's twistor approach, for the massless fields are now defined in (projective) twistor space. But since this space has only three complex dimensions, it turns out that the information about the field's structure will totally fill twistor space!
There is no room left in the twistor picture, nothing else for the field to do, no additional slice of space to fill...and, because twistor space is totally filled with the field's structure, there is no need for a field equation...the field along with all its dynamics is already totally defined, fully represented within the twistor picture.

 

[Ken G]

Thank you for the effort you put into that insightful summary. My next question is, how does the twistor picture account for the redshifting of the CMB?

 

[Mordred]

Also can you explain in more detail the amplituhedron? I understand that it simplifies the calculations to the eight fold way. But haven't understood how.

 

[Matterwave]

Notice that Ken G used the word 'matter', rather than 'elementary particles'. Basically any system of particles would get smaller.

You'd need to continously scale the range of the forces. You could achieve this by changing some of our constants of nature, to variables, with laws to describe how they evolve over time. We don't have a reason for why these constants exist anyway. They just happen to appear constant whenever we measure them.

Is it worth it? Of course not, as already explained, but it would be another way to formulate the models that we already have.

"Any system of particles would get smaller". Does that include the universe itself as a whole? Is the whole universe getting smaller? If so, doesn't that completely defeat the purpose of this model trying to describe an expanding universe? How about a galaxy cluster? A galaxy? Where do we draw the line of "any system of particles"?

 

[Chronos]

You can model our universe using shrinking matter and variable constants of nature, if you wish. Is that a 'simpler' model? I think not. Some, like Wetterich's model, can resolve certain issues - like a primordial singularity - but, at the price of introducing more issues than they resolve. I've always felt the goal of science is to model reality using the fewest possible variables.

 

[Ken G]

I've always felt the goal of science is to model reality using the fewest possible variables.

I don't see why there are any more variables. You write all the constants in dimensionless form, and you write the EFE. That's it, there's your physics, that's everything you can test. The metric is dynamical, the CMB is redder than when it was emitted.

Next you want to say in words what you are seeing there. So you say "something happened to space, relative to the matter", or you say "something happened to the matter, relative to the space." No more variables, no testable difference. Until we have a theory that says otherwise, I don't even see that any distinction exists at all between the two pictures. But only one answers the OP without another word.

 

[Ken G]

"Any system of particles would get smaller". Does that include the universe itself as a whole? Is the whole universe getting smaller?

In GR, bound systems don't "expand with space." That answers your question-- what would need to shrink, in the other picture, is bound systems. The universe is not one of those, so no, it does not shrink, it stays put. Nothing happens to it at all, that's kind of the point.

Where do we draw the line of "any system of particles"?

The same way you draw the line when you say "space expands"-- I could just as well ask you, "how about the space inside atoms?"