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Mister T

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These visualizations can never really be the correct way to think about gravity or the expanding universe. The only correct way to think about them is to think about the math. So in some sense when you leave out the math you can't be thinking about them in a way that's entirely correct. It will always be at best only partially correct.

I like what Dirac said when asked to explain his work in non-mathematical terms. He said that it would be like a blind man trying to appreciate the beauty of a snowflake. As soon as he touches it, it disappears.

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If we imagine the loaf to be spacetime, an individual object is not a single raisin; it's a whole sequence of raisins in a line extending through the loaf. And if the loaf represents the entire universe, the lines representing two different objects move apart as you move "up" the loaf (i.e., in the future time direction); that's the expansion of the universe.I visualize a raisin enmeshed in a bread loaf in which the loaf represents the full continuum of space-time

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Suppose you have a big single mass, floating more or less isolated through space. Then one could assume that the space around it follows the global expansion of the universe. Next, put a tiny mass in a large orbit around this mass. Now, by some magic, the space between the tiny mass and the large mass suddenly stops expanding.

My feeling (not scientific, I agree), is that the space within a galaxy or a cluster of galaxies, is different in a way from the space around it as if some kind of "bubble" exists in space with different properties. Maybe one could see this as some sort of dimple in space time.

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The explanation is that space does not expand, period. The universe expands, but that is not the same as "space expanding". The spatial scale factor increases with time in a particular set of coordinates used in cosmology, but that is not the same as "space expanding" either. In short, "space expanding" does not refer to any actual physical process, so there is no need to "explain" why this nonexistent process takes place in some places but not others. In gravitationally bound systems, individual parts of the system are not flying apart; in the universe as a whole, galaxiesIt is often mentioned that the space within gravitationally bound systems, such as galaxies, does not expand. However, I have never heard a good explanation for this.

Please review the PF rules on personal theories. This kind of speculation is out of bounds here at PF.My feeling (not scientific, I agree), is that the space within a galaxy or a cluster of galaxies, is different in a way from the space around it as if some kind of "bubble" exists in space with different properties

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Ibix

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Be very,Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion in the realm of pedagogy and communication of scientific concepts.

Our current observations suggest that the universe is spatially flat (given a certain definition of "space" that I won't get in to). Our models say that such a universe is infinite in extent. How can something infinite be getting bigger? Certainly distances between distant galaxies are increasing (the return leg of any round trip will always be longer), but that is not the same thing.

The reason why galaxies don't expand is similar to the reason that two coins sitting on a rubber sheet will move apart if the sheet is stretched but won't disintegrate. They're too tightly bound by their own internal forces.

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Regarding the cosmological red-shift, contradicting statements seem to exist. Also from wikipedia https://en.wikipedia.org/wiki/Redshift , one can read "As a result, the wavelength of photons propagating through the expanding space is stretched, creating the cosmological redshift.". It keeps me wondering who is right.

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Ibix

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PAllen

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"...how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better"

from:

New Scientist, Martin Rees & Steven Weinberg(1993)

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Of course, this statement does not take into account quantum physics: In quantum field theory space is not empty at all but filled with a vibrant sea of virtual particles. Maybe that in this context, space can expand after all.

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On the scale of galaxies and clusters, gravity is strong enough to overcome the general expansion.

The stars and other constituent parts of galaxies are said to be gravitationaly bound.

At the scale of atoms gravity becomes irrelevant, here the two nuclear forces bind particles together even more powefully.

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This is also an ordinary language description that does not really capture the actual physics. And no, the actual physics does not make "space expanding" anything physically real.In quantum field theory space is not empty at all but filled with a vibrant sea of virtual particles.

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No, read this:In quantum field theory space is not empty at all but filled with a vibrant sea of virtual particles.

https://www.physicsforums.com/insights/misconceptions-virtual-particles/

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/

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PAllen

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http://philsci-archive.pitt.edu/10033/1/Granada2011_paper.pdf

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Raisins (representing events) embedded in a loaf (representing space) is a common popularization of how to visualize space. But it's really oriented to expaining "curved space" and not "curved space-time". Which is common to most popularizations, due to the abstractness of curved space-time.

As far as "expanding space" goes, one interesting paper that I think makes some good points is "Expanding space, the root of all evil?" <<Link>>

My summary of the paper would be that the concept of expanding space has its detractors, and can be and frequently is mis-used and leads to notable misconceptions (many of which we try to straighten out here on PF, with varying degrees of success). But it has supporters, as well, amongst them I would include the authors of this paper, who attempt to present the idea of "expanding space" in a way that they claim is less likely to cause confusion.

As far as curvature goes, most discussions of curvature really only visualize the curvature of space, and not space-time. The "rubber sheet" would need to be not a spatial rubber sheet, but a space-time diagram, for the analogy to represent space-time curvature. Unfortunately, the concept of a space-time diagram seems to be hard to get people to utilize, for reasons that I don't really understand.

There's another analogy to curved space (and not space-time) due to Einstien that I think has some merit, the "heated slab" approach. See for instance , A Einstein, "Relativity, the special and general theory" <<link>>.

I believe that the expanding slab idea has some limitations as to what it can model, but it serves as a conceptual model that may help people who are extremely used to envisioning only Euclidean geometries. A generalization of the approach may be general enough to handle small sections of actual space-time, for instance in Straumann, "Reflections on Gravity" <<link>>. In the generalization, one includes the idea that gravity affects clocks as well as rulers.

While the idea is helpful and probably less prone to misconceptions than the rubber sheet analogy, it does have some limits, though I haven't seen these limts discussed in the literature. For instance, the relativity of simultaneity is a basic feature of special relativity that is frequently not understood is not well-represented by this kind of model, which tries to "tweak" familiar notions of geometry into a more general form. Another concern is handling global topology.

I was going to comment more on curved space-time geometry as opposed to just spatial geometry, but, I think the post has already gone on long enough , and possibly too long.

One final note. Popularizations are not a replacement for learning the full theory - which, ultimately, involves a lot of math. They do the best they can to present some features of the theory in a way that's understandable without the math, but they are not the full theory. Frequently people criticize the full theory by criticizing the popularizations (because the populariations are all they understand). Well, the popularizations ARE flawed, in many cases. The flaws can be minimized by applying them only to the situations for which they are intended and suitable for, but one should not expect a full understanding based only on popularizations :(.

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And I have seen the word "space"used many times, when I'm pretty sure it should be spacetime.

Albert Einstein's at one time teacher said it like this

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality".

The main point with the spacetime expansion, is that we do see over large scales a recessional velocity of galaxies, that is evidenced in a cosmological redshift.

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Ibix

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The problem with "expanding space" is the "expanding", not the "space". The scale factor applies to a particular set of spacelike slices, each one of which has a larger scale than its predecessor. We are definitely not talking about spacetime as a whole expanding.The main point with the spacetime expansion

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Nugatory

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There are perfectly satisfactory ways of calculating the Casimir force between two plates without using the concept of virtual particles - so observations of the Casimir effect do not demonstrate the existence of virtual particles.The Casimir force, which has been experimentally demonstrated seems to disprove this statement.

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That is interesting. Could you give a reference to this (from a refereed journal)?

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No, that is how QFT is done. Did you take any course on that? Here is a very illuminating discussion about the article:Well, that is the opinion of one author.

https://www.physicsforums.com/threads/misconceptions-about-virtual-particles-comments.865706/

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Hi, yes I took courses on QFT and have some books at home. So, all other effects such as vacuum polarization, lamb shift, ... can be explained without virtual particles?No, that is how QFT is done. Did you take any course on that? Here is a very illuminating discussion about the article:

https://www.physicsforums.com/threads/misconceptions-about-virtual-particles-comments.865706/

Even when the concept of a virtual particles just comes from a representation of some terms in an integral, I prefer to think of space as a soup of virtual particles instead of a collection of mathematical objects (invented by mathematicians or physicists) floating (or doing their "job") somehow in space. To me reality is not identical to mathematics. Somehow, these mathematical terms must correspond to something physical.

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Yes.all other effects such as vacuum polarization, lamb shift, ... can be explained without virtual particles?

As a heuristic this can work (although it is limited). But you always have to be careful with heuristics, and you always have to be aware that they're just heuristics--they aren't telling you "this is how it is", they are only telling you "this is an analogy that might work in some cases".I prefer to think of space as a soup of virtual particles

As you state it this is obviously way too strong. Consider a simpler example from Newtonian mechanics: a center of gravity. We can calculate the center of gravity of any system in Newtonian mechanics; but that does not mean there must be something physical corresponding to it. It's just a useful abstraction in our analysis.Somehow, these mathematical terms must correspond to something physical.