Is Spacetime Truly Smooth or Discrete?

[malawi_glenn]

I think we should leave the "side track" we got into with Naty1, it is clear from the other posts by the OP (Pythagorean) that he had something different in mind :-)

 

[Fredrik]

Well, let's stick to the question of infinite energy being required then (as I've brought up twice). I think It might answer the question. I've been avoiding doing the math here, because I don't know how quantum and relativistic effects will play in, but let's do corrections for that later (where and if we can, I realize that qm mathematics won't play directly in, but I'm hoping any macroscopic consequences in reality can be considered.)

x (distance)
v = dx/dt (velocity)
a = dv/dt (acceleration)
j = da/dt (jerk)

to go from 0 to v velocity without a smooth acceleration, we would have to have infinite energy obviously, because it would mean that

a = dv/dt = inf (the slope would be vertical) and that would require infinite force:
F = ma = dp/dt = inf
so velocity must be differentiable.

now a change in acceleration:
j = da/dt = d^2v/dt^2 = inf
means a change in force:
dF/dt = m*da/dt = m*d^2p/dt^2 = inf

and at this point, my weak mathematical foundation fails me. How do I test the plausibility of an infinite change in Force?

Now you're clearly talking about curves in spacetime (or space). As I explained before, curves in spacetime are not a part of a quantum mechanical description of motion. So your question can only be interpreted as a question about the smoothness of curves that represent motion in a classical theory. In classical theories, you can choose to let your curves be smooth or you can choose to e.g. let them consist of straight line segments (constant velocity on each segment). It doesn't really matter.

It's not a problem to have curves that fail to be smooth at a finite number of points. It would however be a problem to have a curve that isn't smooth anywhere, but there's no reason to consider such curves in classical mechanics.

Also, as I've said before, and as was repeated by Civilized, the underlying manifold is smooth in all the current theories of physics, both classical and quantum. Here the word "smooth" refers to the fact that the coordinate systems that are part of the mathematical structure are such that any function that represents a change from one coordinate system to another is differentiable infinitely many times.

In my opinion, we need to get some knowledgeable moderators into this dicussion so that we can resolve this disagreement for good.

There's more than enough knowledgeable people here already. How would a moderator resolve the disagreement? By repeating what's already been said? By locking the thread?

 

[fleem]

How do I test the plausibility of an infinite change in Force?

No one has done that yet. I'm not sure if they ever will. Bring infinity into anything and you end up with infinities, and infinity is not like other numbers. Its just not fully defined. I'm not sure we can even call it a "number". In fact, physicists agree that infinity is excluded from this sort of thing, hands down. We've discovered various apparent rules of the universe, and one of those rules is that treating infinity like any other number is a no no, and we don't fully know how to treat it--maybe because there ain't no such animal in the first place. The rules of the universe are discovered empirically, and that's why they need tweaking as we learn more, but so far, infinity isn't a part of them. We've never measured infinity, let alone proved how it affects such equations as the one's you talk about.

Perhaps one of Zeno's paradoxes is more in line with what you are talking about? if so, I tend to agree that Zeno's paradoxes are more than just quaint stories. But I think the point of the other posters is that the current (classical) model ignores things like that, right or wrong. If its Zeno's paradoxes, or the indivisibility of QM intervals, then we can talk about that.

 

[Pythagorean]

Now you're clearly talking about curves in spacetime (or space). As I explained before, curves in spacetime are not a part of a quantum mechanical description of motion. So your question can only be interpreted as a question about the smoothness of curves that represent motion in a classical theory.

(edit/foreshadowing: I have an epiphany and concede to one of your former points at the end of this post)
I guess my question is more along the lines of "is it really, though?" regardless of the theory. I start answering my question by building up from my observations, and I can't frame my observations in terms of quantum mechanics, but I want to be aware of any contradictions or insights to the question provided by QM as I suspect there may be.

It's not a problem to have curves that fail to be smooth at a finite number of points. It would however be a problem to have a curve that isn't smooth anywhere, but there's no reason to consider such curves in classical mechanics.

This is kind of my issue with quantum being on the back burner. Subatomic particles have a finite size (or space does, depending on who you talk to) and angular momentum is quantized. The particles are so small that we're not concerned about whether spacetime is actually smooth because there's so many of them and they're so small compared to other values that we just assume infinite and infinitesimal, spacetime might as well be smooth from that point of view. But my question is, is it really, when you get down to it?

This relates to what fleem brought up:

We've discovered various apparent rules of the universe, and one of those rules is that treating infinity like any other number is a no no, and we don't fully know how to treat it--maybe because there ain't no such animal in the first place.

I don't think we've found a genuine infinity in nature yet. I've always held the assumption that they don't exist, but I'm open to any criticism on that assumption.

Perhaps one of Zeno's paradoxes is more in line with what you are talking about? if so, I tend to agree that Zeno's paradoxes are more than just quaint stories. But I think the point of the other posters is that the current (classical) model ignores things like that, right or wrong. If its Zeno's paradoxes, or the indivisibility of QM intervals, then we can talk about that.

That's kind of where I was going with this, I guess, yeah. Didn't really make the Zeno connection though.

I guess the point of my discussion was to not ignore "things like that".

No one has done that yet

now that I start to think of simultaneity and time dilation and whatcrap in the context of actually trying to perform an experiment to answer that question, the original question is beginning to feel meaningless outside the context of classical mechanics, as Fredrik mentioned at one point.

 

[Nick666]

I don't think we've found a genuine infinity in nature yet.

Isnt the infinite energy of the vacuum a genuine infinity in nature ?

 

[fleem]

Isnt the infinite energy of the vacuum a genuine infinity in nature ?

This is new to me. Current theory is that the energy in the universe is finite.

 

[Naty1]

jambaugh:

it is a mental (mathematical) construct but an essential one...

Be cautious! Such firm "beliefs" may blind you! : such "beliefs" have tripped up physicsts for all of history and prevented them from understanding new theories and experimental findings .

also recall that light was once viewed as traveling in ether, mass was "solid", space and time were "fixed and immutable", a proton is a fundamental particle, dark matter and dark energy are "impossible" (just mathematical constructs) etc,etc,etc.

Just keep an open mind. For example, if matter is both a particle and a wave,and equivalent to energy, why can't space and time be as well?? (after all, they all came from the same place: nowhere ("empty" space))... Nobody knows.

 

[malawi_glenn]

jambaugh:


Be cautious! Such firm "beliefs" may blind you! : such "beliefs" have tripped up physicsts for all of history and prevented them from understanding new theories and experimental findings .

also recall that light was once viewed as traveling in ether, mass was "solid", space and time were "fixed and immutable", a proton is a fundamental particle, dark matter and dark energy are "impossible" (just mathematical constructs) etc,etc,etc.

Just keep an open mind. For example, if matter is both a particle and a wave,and equivalent to energy, why can't space and time be as well?? (after all, they all came from the same place: nowhere ("empty" space))... Nobody knows.

As a non-scientist, you should stay quite calm when it comes to these points...

We discuss how physics is understood contemporary here, and it is not a "belief" it is a construction, space-time is the manifold where we put our theories in, it is nothing more than a coordinate system - as understood and used today.

 

[Nick666]

This is new to me. Current theory is that the energy in the universe is finite.

http://en.wikipedia.org/wiki/Vacuum_energy
It says here that the energy of the vacuum is infinite, but they renormalize it. Whatever that means.

 

[malawi_glenn]

http://en.wikipedia.org/wiki/Vacuum_energy
It says here that the energy of the vacuum is infinite, but they renormalize it. Whatever that means.

renormalize it means that we only measure energy DIFFERENCES, we can always adjust the zero-level to whatever we like and in this case we measure the energy difference with respect to the vacuum energy

(conceptually, this might seem odd and strange the first time one hear this: we are measuring energy difference with respect to infinity LOL.. but it works and it is ok mathematically. Also, one should notice that in many supersymmetric formulations of quantum field theory and particle physics, the vacuum energy becoms finite! =D )

 

[Naty1]

As a non-scientist, you should stay quite calm when it comes to these points...

valid point; And scientists, especially calm...

 

[malawi_glenn]

valid point; And scientists, especially calm...

why should they? we actually know what we are dealing with...

 

[jambaugh]

jambaugh:
Be cautious! Such firm "beliefs" may blind you! : such "beliefs" have tripped up physicsts for all of history and prevented them from understanding new theories and experimental findings .

This caution runs both ways... but if you look at history the mistakes made in "too dogmatic beliefs" have been in reification of models and failure to pay attention to operational meaning. Einstein was able to revise his view of time and thence unify space-time by acknowledging that "time is what a clock indicates" and "distance is what a measuring rod measures". Hence the reality is in the dynamics of the clock and the measuring rod. His open-mindedness on this point allowed him to then generalize the previously fixed relationships between these. However the success of his theory led to the opposite position, with followers taking the geometric model as an ontological fact. This tends to be the nature of scientific progress.

also recall that light was once viewed as traveling in ether, mass was "solid", space and time were "fixed and immutable", a proton is a fundamental particle, dark matter and dark energy are "impossible" (just mathematical constructs) etc,etc,etc.

Again the aetheric interpretation of light was a mistake of reifying a model. It was in acknowledging that the reality of the aether was not necessary to describe the dynamics of light which led to relativity. Relativity doesn't assert the ether is real and doesn't assert the ether is unreal. It shows that the question is irrelevant because the physics is in the empirical observations of how light behaves.

Dark matter was and still is simply matter which is not visible due to its not being radiant stars. Speculations about exotic dark matter grab headlines but are still fringe speculation. Personally I suspect the majority of it will end up being stellar sized black holes.

Let me add that the dark matter requirement is extrapolated from weak approximations to the full GR description of the dynamics of galaxies. I've seen at least one paper which suggests a fully general relativistic treatment may greatly reduce or eliminate the necessary amount of dark matter to get predictions to agree with observations. Again the "open mindedness" goes both ways. We shouldn't take dark matter as dogma.

Dark energy is nothing more than Einstein's cosomological constant relabeled. I believe it is just the (non-flat) boundary conditions in cosmological applications of Einstein's equations. There is also the possibility of a systematic misinterpretation of the doppler shift of distant objects as purely due to recessional velocity. In the curved space-time cosmologies there is also an effect of time dilation depending non-linearly on distance. I'm not sure the computer models use by cosmologists take this into account. I know some papers I've read in the past make the mistake of taking the hyperbolic shape of the embedding of a deSitter space-time within an euclidean coordinate system as the literal Big Bang-esque expansion of space over time when the proper spatial cross-sections of the deSitter manifold for a given observer does not change size over time. This mistake again occurs from viewing this manifold as a physical object rather than a geometric realization of the relationships between physical objects. (also due to not correctly visualizing the proper embedding within a 4 space + 1 time Minkowski space).

Note "fundamental" has a contextual meaning. Protons are still "fundamental" in nuclear chemistry as electrons + elemental nuclei are "fundamental" in chemistry. Note also that it was not dogma about the fundamentalness of the proton which inhibited the development of the standard model. Rather it was the absence of data. As soon as accelerators reached higher energies and began giving us data and we began seeing the huge particle spectrum and theorists immediately began speculation about parton models of the nucleons.

Just keep an open mind. For example, if matter is both a particle and a wave,and equivalent to energy, why can't space and time be as well?? (after all, they all came from the same place: nowhere ("empty" space))... Nobody knows.

My mind is quite open, but I am skeptical of many of the "kludges" (such as dark energy/matter and inflation) to get them to fit empirical data.

BTW Matter is not "both particle and wave" it is neither. It is rather quanta which behavior we translate into the old classical "wave" or old classical "particle" paradigms when we wish to describe specific aspects of their behavior in classical terms.

I am open minded but I don't buy every new speculation just because it generates juicy headlines in the popular media. (E.g. FTL tunnelling). Neither do I take orthodox views (such as the Big Bang Theory) and (Renormalized Field Theory) as "T"ruth. I rather take these as tentative theories with a large body of empirical confirmation which future alternatives must also account for.

Now my position (space-time is parametric rather than physical) is not an ontological dogma it is an acknowledgment of space-time's operational meaning. Recall Einstein's caution to look at what physicists do in the lab and ignore what they say.

We use coordinates as parameters, specifically as parameters of transformation between classes of similar modes of measurement. E.g. when comparing two spin measurements of a given quantum system we express the relationship between these measurements in terms of space-time translations and of rotations and velocity frame boosts (of the measuring apparatus). In short we select an element of the Poincare group parameterized by a duration, spatial displacement, rotation angle and boost pseudo-angle.

Quantum theory then tells us how to represent this group element in the dynamics of the quantum system so that we can identify equivalent measurements in the sense of being exactly correlated. It at the same time gives us the transition probabilities between not-quite correlated measurements.

This is all we need to describe outcomes of quantum experiments and this thus is all the meaning we need for space-time position--orientation--velocity. Adding additional meaning i.e. overlaying an ontological interpretation imposes additional assumptions and thus is as you phrase it being less than "open minded".

I assert that it is exactly the over reification of parametric quantities like space-time which leads to the over-counting of physical degrees of freedom resulting in the divergences we find in QFT. Renormalization is a "quick fix" which gives good answers but doesn't address the fundamental problem...and as we have learned cannot always be applied as with canonical quantum gravity. I think that string/brane models perpetuate this problem by adding additional non-physical structure...so much so that the researchers are lost in the beauty of the mathematics and have little to say about physical nature.

Maybe I'm wrong. The proof will be in the next (empirically) successful class of theories. I'm working on my own pet theories based on my assertions. Give me 0.01% of the grant funding which has been poured into string theory and I might be able to make substantial progress.

P.S. Pardon the length of the reply but you struck a nerve.

 

[Fredrik]

http://en.wikipedia.org/wiki/Vacuum_energy
It says here that the energy of the vacuum is infinite, but they renormalize it. Whatever that means.

Astronomical observations have shown that the (energy) density of vacuum is rather small. It's certainly not infinite.

The process of canonical quantization of a classical field theory leads to an infinite density of vacuum. The problem doesn't quite go away just by thinking "Why the frak would anyone want to start with a classical theory?", because there's something called "effective field theory" that suggests that all the terms that are consistent with the symmetries of the problem should appear in the Lagrangian. This includes non-renormalizable terms, which can be ignored because they don't contribute much to interactions at low energies, and it also includes a vacuum energy.

So quantum theory at least strongly suggests that a non-zero energy of vacuum is possible, and it's natural to try to estimate its value. A simple order-of-magnitude estimate (similar to guessing that the volume of a sphere with radius r is r³ because it's the simplest quantity with the right units) gives a result that's wrong (too large) by at least 120 orders of magnitude. No one really knows why the true value is so much smaller than the estimate.

 

[DrFaustus]

Pythagorean -> You keep asking questions about "Reality" (whatever that is) and are trying to come up with answers starting from physics. And this is the main problem you're having, that is not realizing that we can only infer properties about "Reality" by working out the consequences of the assumptions we make. And our assumptions so far have always been that "spacetime is a smooth manifold". And it is from this viewpoint that you can say that "spacetime is smooth". But questions like "Is spacetime a manifold?" are on the one hand not for physicists to answer (as you have noted it easy to cross the borderline with philosophy) and on the other completely irrelevant. As long as your assumptions allow you to describe and predict the result of experiments, that's all you need. Bottom line, do not mistake a "model" for "Reality".

jambaugh -> A quick remark on renormalization. It is true that in most of the books on QFT it does indeed appear as a "quick fix", but it not need be so. The mathematical reason for divergences to appear (at least some of them) is because a rigorous mathematical treatment of quantum fields requires quantum fields to be "operator valued distributions" and not operators. The reason is simply that you cannot satisfy the canonical commutation relations with operators and because if you consider the CCR at the same spacetime point, e.g. for the simple scalar field you have $$[\varphi(t,\vec{x}), \partial_t \varphi(t,\vec{x})] = \delta(0)$$, which is infinite, or better, meaningless. The reason for this is that you're multiplying distributions, and multiplication between distributions is in general ill defined. (Think about Dirac's delta, which is a distribution, and the fact that $$\delta^2(x) = \infty$$, or, again, ill defined. So you could talk about "renormalizing products of Dirac deltas at the same spacetime point".) And if you take into account all the mathematical subtleties that stem from here, you can construct, and compute various quantities with no infinities.

Is renormalization gone? Not really. But it does not involve "subtractions of infinite quantities" as it usually does. Renormalization is now carried over as the "extension of products of distributions to points where such a product is ill defined". But this can be, and is done in a finite way. And also perturbation theory is based on causality so the formalism is perfectly well defined at all steps (this is the method of Epstein and Glaser). The reason why this is not thought is that it involves a lot of mathematical work and is generally not needed in current physical research. In any case, this really suggests that renormalization is in some sense an intrinsic feature of QFT.
(For the latter point, you can have a look at Bogoliubov's book "Introduction to the theory of quantized fields". As for renormalization being carried over in a mathematically rigorous way by handling products of distributions, have a look at "Finite QED" by Scharf.)

 

[jambaugh]

Pythagorean -> You keep asking questions about "Reality" (whatever that is) and are trying to come up with answers starting from physics. And this is the main problem you're having, that is not realizing that we can only infer properties about "Reality" by working out the consequences of the assumptions we make. [...] Bottom line, do not mistake a "model" for "Reality".

Here Here!

jambaugh -> A quick remark on renormalization. It is true that in most of the books on QFT it does indeed appear as a "quick fix", but it not need be so. The mathematical reason for divergences to appear (at least some of them) is because a rigorous mathematical treatment of quantum fields requires quantum fields to be "operator valued distributions" and not operators. The reason is simply that you cannot satisfy the canonical commutation relations with operators and because if you consider the CCR at the same spacetime point, e.g. for the simple scalar field you have $$[\varphi(t,\vec{x}), \partial_t \varphi(t,\vec{x})] = \delta(0)$$, which is infinite, or better, meaningless.

Yes. I agree that renormalization methods are valid and meaningful in the successful QFT of the standard model. Your point about the necessity of renormalization and how it relates to the canonical commutation relations is an important one. My past research has been in deformation expansion of the canonical commutation relations. The "necessity" of the canonical relations themselves stems from the very use of a field theory namely the fibration of space-time-gauge parameters into gauge fields over a space or space-time. The foundational assumption is that each point in space (or even each cell of space) has a physical quantum system associated with it. One is forced to count their ground contributions leading to the divergent vacuum energies. (One interesting result I've yet to publish is a relativity to the bosonic vacuum which I think could "hook" into GR.)

The analogue this follows is the pre-relativistic fibration of space-time into space/time with the corresponding contracted Gallilean group's Lie algebra. Its expansion to Poincare unified space-time but breaks Born reciprocity in that with the unification of space-time in classical relativity spatial coordinates must now be treated in the same fashion as time namely as parametric coordinates rather than as physical observables. The duality involution no longer maps observables to observables but rather observables to group parameters indicated by Noether's theorem.

The momenta and energy (along with angular momenta) are the fundamental physical observables and the canonical algebra ceases to be an appropriate context even for the classical treatment since canonical transformations mix what I view as parameters with observables. One is forced to identify and isolate gauge constraints in an extended phase space to recover meaningful observables. The methodology brings to mind the old theory of epicycles. Ultimately one no longer is using the canonical format except as an embedding algebra to express the underlying Lie algebra. It seems more sensible that one should start there.

We see also in separating parametric coordinate from physical observable an equivalence between say the angle parameters and their dual observable angular momenta with the linear (duration-distance) parameters and their dual observable linear 4-momenta. The duality of which I speak is not Born's but rather the co vs contra variances of differential Lie group coordinates and Lie generators under the adjoint representation of the relevant group.

I suggest a similar unification of gauge-field parameters (namely phase and other gauge group parameters) and their dual charges with Poincare (or deSitter) group parameters and a resulting non-field theoretic (likely pre-local) quantum theory.

Born reciprocity demands the Heisenberg relations hold which correlates to preserving a pre-relativistic view of physical space in the quantum theories. As you point out this in turn leads to the necessity to renormalize which indicates one is indirectly obtaining predictions from the given formulation where we would prefer a formulation giving direct predictions. The canonical Heisenberg relations should either be maintained as manifestations of coordinate calculus (wherein coordinates are simply parameters) or replaced with more stable (within the group deformation context) and more generic (with respect to historically supplanted theory) relations when we consider their use in e.g. the algebra of bosonic particle actions.

My point in all of this is that I see potential alternatives to QFT which may eliminate the need to renormalize and I see the necessity of renormalization as an indication of where we need to consider relaxing some built in assumptions. Those assumptions IMNSHO relate to inappropriate reification of space and space-time.

(The "Elephant in the Room" of all this however is locality. Such a unification as I describe is pre-local and the causal structure we see needs to somehow be explained...possibly via condensation process or some higher order analogue to the Higgs mechanism.)

Is renormalization gone? Not really. But it does not involve "subtractions of infinite quantities" as it usually does. Renormalization is now carried over as the "extension of products of distributions to points where such a product is ill defined". But this can be, and is done in a finite way. And also perturbation theory is based on causality so the formalism is perfectly well defined at all steps (this is the method of Epstein and Glaser). The reason why this is not thought is that it involves a lot of mathematical work and is generally not needed in current physical research. In any case, this really suggests that renormalization is in some sense an intrinsic feature of QFT.

I agree (w.r.t. QFT) and of course the non-renormalizability of Grav in QFT suggests an alternative to QFT is necessary for the next theory. (Hence string-brane mathematics but as I said I see these as promulgating some of the same problems).

(For the latter point, you can have a look at Bogoliubov's book "Introduction to the theory of quantized fields". As for renormalization being carried over in a mathematically rigorous way by handling products of distributions, have a look at "Finite QED" by Scharf.)

Thanks for the references I'll compare them to my own library. However as I'm not looking to improve theory within QFT but rather to supplant it I'm not as concerned (yet) with improved expositions of renormalization or field theory. I may take a look at the Scharf book.

 

[Fredrik]

Very good post, DrFaustus. I hope you'll stick around to get a post count in the thousands.

 

[Pythagorean]

But questions like "Is spacetime a manifold?" are on the one hand not for physicists to answer (as you have noted it easy to cross the borderline with philosophy) and on the other completely irrelevant. As long as your assumptions allow you to describe and predict the result of experiments, that's all you need.

when I'm working the office, I generally agree with you, but I work in the office for money, so I conform to the scientific standard of being cold and rational in that setting. As far as I'm concerned though, that's a hoop I have to jump through.

I got into physics in the first place because I'm also interested in these questions on a philosophical level (I realize that now, after trying to shoe the philosophy away, my apologies).

Bottom line, do not mistake a "model" for "Reality".

I do try. This is a hang-up of mine. I've heard that line once or twice before (in my pre-physic curriculum), and I have to remind myself. But, as scientists, we do talk about our little discoveries and "ah-ha!" moments as if they were reality. "Oh! this system works like this!" It's easy to do when you're not spending much time in the regions where the model fails.

 

[DrFaustus]

Phytagorean -> We're here to help each other and try to solve our doubts... glad I could help :)

Fredrik -> Thanks. Am still trying to figure out QFT for good myself, but if I'll be able to help, I sure will.

 

[Naty1]

jambaugh posted :

I am open minded but I don't buy every new speculation just because it generates juicy headlines in the popular media. (E.g. FTL tunnelling). Neither do I take orthodox views...

oustanding!

 

[George Jones]

As for renormalization being carried over in a mathematically rigorous way by handling products of distributions, have a look at "Finite QED" by Scharf.)

I'm not sure, but I don't think that all experts who think about these things are comfortable with Scharf's work. Also, even after regularization and renormalization, QED is still (almost certainly) divergent, that is, individual terms in a particular series are all finite, but the series itself diverges. Physicists think this is okay because:

1) divergent series often converge faster than convergent series ;

2) this just indicates the presence of other physics not taken into account by QED.

 

[DrFaustus]

George -> Don't really want to go into this... just a quick reply. It's no need for physicists to be comfortable with the rigorous approach to QFT as essentially all the physics that was and is currently extracted from QFT is done so within the standard Lagrangian QFT framework. Scharf's book is a book mathematical physicists are more comfortable with simply because it's rigorous. And I can reassure you that ALL the mathematical physicists are familiar with that book. But as I said, it's not worth the effort for the vast majority of physics research.

Physicists may be happy about the non-convergence of the perturbative series, but mathematical physicists most definitely are not. And in fact, the rigorous construction of an interacting QFT model in 4D does not exist as of now. A lot of effort has been put into this an in 2D and 3D rigorous models have been constructed. But not in 4D. And Witten knows this all too well and it's the reason why he, amongst others, insisted in putting the Yang-Mills problem amongst the Millenium prizes. In other words, construct a QFT model in 4D and win a million (more or less).

As for the "other physics beyond QED" claim, that's really just a heuristic interpretation of the entire situation. The reason is that supersymmetric non-commutative Yang-Mills models offer some hope in such a rigorous construction, and yet there is physics beyond such models. Stated differently, the problem of the rigorous construction of an interacting QFT model is (almost) a purely mathematical problem. And it's resolution will tell us very little, if anything, about physics beyond any particular model.

 

[john 8]

Pythagorean asked; Is Spacetime Smooth? Smooth: infinitely differentiable.

You said;

as far as we/I know, yes, it is smooth

How do you know it is smooth? If this spacetime thing is smooth that means it is a physical object with a surface. Most smooth objects reflect light. And all objects have a location in space.

So please give more data on this statement that you made.

 

[john 8]

Just wanting to add another witness to the fact that every mainstream book on quantum mechanics and quantum field theory treats space / spacetime as a smooth manifold.

Well said, all the currently established mainstream theories (the standard model) and the mainstream extensions to these (GUTs, string theory) always treat spacetime as a smooth manifold.

Naty1, Malawi and I have both gone through a mainstream graduate education in physics, and we are telling you that spacetime is smooth in the standard model and in string theory. You are disagreeing with us on the basis of vague statements in wikipedia and popularized books, when we each have shelves full of textbooks that leave no doubt that spacetime is smooth in all of our current physical theories. In my opinion, we need to get some knowledgeable moderators into this dicussion so that we can resolve this disagreement for good.

If you don't mind, could you please clarify something for me and the others on this form.

When you say spacetime is smooth, are you referring to a mathematical model or a physical structure?

 

[Naty1]

For those who may be interested a related thread is "Are we digital or analog?"
at https://www.physicsforums.com/showthread.php?p=2269227#post2269227

 

[ibcnunabit]

Is Spacetime Smooth?

Smooth: infinitely differentiable

I don't think anyone really knows, at this point. It hasn't been proved either way, but we do know that if it's quantized it must be a pretty fine-grained quantization. Reiner Hedrich, for one, has written a number of papers on the idea of quantum spacetime.

If quantum mechanics is universally true, then it's quantized. If quantum gravity turns out true, then spacetime must be quantized, so gravitons would mean quantum spacetime. As would chronons, if you believe in quantum time, but that's pretty speculative at this point.

Right now most (non-QM) models start with an assumption of smoothness, but hey--a HD TV looks pretty smooth from a distance, but we all know there are pixels when you look closely enough. I'd like to see it proved one way or the other; I'm very curious to find out which way it comes out.

--Mike from Shreveport

 

[ibcnunabit]

Is Spacetime Smooth?

Smooth: infinitely differentiable

I don't think anyone really knows, at this point. It hasn't been proved either way, but we do know that if it's quantized it must be a pretty fine-grained quantization. Reiner Hedrich, for one, has written a number of papers on the idea of quantum spacetime.

If quantum mechanics is universally true, then it's quantized. If quantum gravity turns out true, then spacetime must be quantized, so gravitons would mean quantum spacetime. As would chronons, if you believe in quantum time, but that's pretty speculative at this point.

Right now most (non-QM) models start with an assumption of smoothness, but hey--a HD TV looks pretty smooth from a distance, but we all know there are pixels when you look closely enough. I'd like to see it proved one way or the other; I'm very curious to find out which way it comes out.

--Mike from Shreveport

 

[john 8]

I don't think anyone really knows, at this point. It hasn't been proved either way, but we do know that if it's quantized it must be a pretty fine-grained quantization. Reiner Hedrich, for one, has written a number of papers on the idea of quantum spacetime.

If quantum mechanics is universally true, then it's quantized. If quantum gravity turns out true, then spacetime must be quantized, so gravitons would mean quantum spacetime. As would chronons, if you believe in quantum time, but that's pretty speculative at this point.

Right now most (non-QM) models start with an assumption of smoothness, but hey--a HD TV looks pretty smooth from a distance, but we all know there are pixels when you look closely enough. I'd like to see it proved one way or the other; I'm very curious to find out which way it comes out.

--Mike from Shreveport

Look, this space-time thing is not a real physical entity. If it was then think about where does it exists? What exists around it? What is it made of? If you say it is made of particles then what do you call that area between these space-time particles? And particles of what?

If you say that space-time is a E/M wave then where is this wave eminating from?

Please stop believing in fantasy and use science to solve your questions regarding science, physics, astronomy, etc.

There is no scientific reference or definition that states that space-time is a thing that exists as an entity. Please stop this science fiction fantasy. The field of science does not define space-time as a physical thing.

 

[WaveJumper]

There is no scientific reference or definition that states that space-time is a thing that exists as an entity. Please stop this science fiction fantasy. The field of science does not define space-time as a physical thing.

As far as physics and science are concerned, there is no such thing as physical matter or as you say "Physical thing"(the daily usage of the word "physical stuff"). There is only quantum fields that exchange force carrier bosons to create the illusion of solid physical stuff.

"Physical things" cannot be touched. You have never really touched anything at all, as the electrons in the outer shells repel the electrons of matter at 10^-8m.

Having said that, I think spacetime appears as much a thing as solid matter. And they are both relative to the frame of reference of the observer.

 

[john 8]

As far as physics and science are concerned, there is no such thing as physical matter or as you say "Physical thing"(the daily usage of the word "physical stuff"). There is only quantum fields that exchange force carrier bosons to create the illusion of solid physical stuff.

"Physical things" cannot be touched. You have never really touched anything at all, as the electrons in the outer shells repel the electrons of matter at 10^-8m.

Having said that, I think spacetime appears as much a thing as solid matter. And they are both relative to the frame of reference of the observer.

You have put this space-time thing in the same category as solid matter. You say that as far physics and science are concerned, there is no such thing as physical matter.

Sounds like you are confused.

Please refer to science reference books and look up matter.

There are many things around us that we agree exist because we can percieve their presence. We notice things around us because they are made of something that our bodies can percieve.

However you want to look at the world around you, you have to agree that there are things that are detectable by us.

This universe is filled with things that are either made of atoms, electrons and such, and those things that are E/M waves. Either way, if we consider something to be a thing then that thing is a form of energy. There is no doubt about the many things that we call real or physical in that they are a form of energy that occupy a location in space.


So, please be clear in what you are saying about this space-time thing. Is it a particle, a wave such as quantum fields that exchange force carrier bosons to create the illusion of solid physical stuff.

You contradicted yourself in your explanation of physical stuff, and what space-time is.

Please clear up your explanation.