So... is it time to kill off this [P and M] sub-forum yet?

Even if the universe is not infinite, it can not have an edge - this would violate not only the homogeneity of space, but also the idea that spacetime in general relativity is a smooth manifold. If the universe is finite, then it would be analogous to a 3-sphere, such that travelling in one direction will eventually bring you back to your original location. As CptBork pointed out, the expansion in cosmology is a property of space itself, not the objects in it. If we let the distance between two galaxies right now be \(d_{0}\) and the distance at any other time be \(d(t)\), then the two distances are related by \(d(t) = a(t)d_{0}\), where \(a(t) \) is called the scale factor. To say the universe is expanding means that the scale factor has a positive time derivative - its increasing. So, in an expanding universe, the galaxies don't actually move (well, they have unrelated motion relative to the CMB), and space doesn't physically "expand" like some rubber sheet in an analogy. Instead, the distance between galaxies simply increases with time. This may seem counter-inuitive, but its how general relativity works. The scale factor will have a positive time derivative for certain homogeneous distributions of matter (see the Friedman Equations).

 

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Translation : I have no idea about topology or geometry, the underlying principles of general relativity or just 'spatial structures' so I'm going to go with my gut instinct, which has no experience of any detailed mathematics or physics beyond high school level. After all, I'm John Duffield.

Just another example of how your lack of experience with concepts beyond everyday experience hinders you, yet you don't realise it. You've previously waxed lyrical about inflation, curvature and cosmology and now, as then, you show how little you understand. MarkM125 has given a quick pointer at the relevant bit of cosmology, namely the length scale factor in the FRW metric. Funny how the counter example to your claim was the central thing in cosmology, something which you've pretended to understand in previous discussions but once again illustrate you do not.

Seriously John, you could open your mind to so much more if you just accepted you aren't the font of all understanding when it comes to physics. Electromagnetism, cosmology, string theory, quantum mechanics, these are things you've claimed to have insight into which no one else has had, yet you demonstrably have no quantitative understanding and you show time and again you don't even have qualitative understanding of even basic principles.

Given you cannot do any calculus or linear algebra you obviously cannot do any of the tensor calculus which is used to define said tensor. Would you care to explain how you have insight into a mathematical construct when you cannot do said mathematics?

No doubt you'll ignore me, seeing as the answer would require you to admit you're just BS'ing.

Slow down there, I couldn't keep up with all the quantitative detail. No, sorry, I meant vapid arm waving.

Preaching about things you only pretend to understand? You're an example for everyone John. Shame it is the wrong kind of example, one of dishonesty.

Yes, which is why I think your actions are somewhat detestable, pretending to understand the quantitative details, ie tensors, of a physics domain you have no actual experience of beyond pop science books/magazines/websites. The above example of the FRW length scale, the main mathematical object in inflationary cosmology, is just the latest example. Clearly Mark and I thought of the same thing immediately, thanks to the fact we've actually learnt something about the specifics cosmology rather than just ignored it all.

Please explain to me how you're in any position to discuss tensors, mathematical constructs, when you cannot do any of the mathematics? You have had a go at me (and others) more than once when we talk about the space-time metric, reminding us the metric isn't a real thing, it is a mathematical non-physical thing, yet here you are talking about the stress-energy tensor, a mathematical construct just as physically real (or not) as the metric, both are conceptual formalisations of physical phenomena/structures. At least in my case I understand the mathematics underlying the tensor about which I spoke. If you really understood the current state of cosmology, enough to blow holes in it etc and understood the tensor construction of the FRW metric etc then you'd have known how a(t) counters your claim. But you didn't because you don't. You never do.

Now you can (and likely will) ignore my criticisms but they are all completely valid. It isn't an ad hom to point out you don't know tensor calculus, it is a statement of fact. A fact you might not like to acknowledge but a fact nonetheless. Thus questioning how you're in a position to be throwing around such concepts as if you understand them is a valid question. Likewise for how you 'know the trick' of string theory when you lack all of the necessary mathematical knowledge required to do anything but read pop science books or watch TV documentaries on it. Likewise it is a valid criticism of your actions when I point out your hypocrisy for railing against the supposed unfalsifiability of string theory when your work has less falsifiable quantitative modelling connections to reality. By which I mean it has none. Is it an ad hom for me to point that out? No, since I'm criticism your work for having absolutely no structured connection to reality, rather than saying "It is wrong because you wrote it". Likewise when I point out the ridiculousness of you claiming to be a world leading expert in (amongst other things) electromagnetism. Why can you not do any of the mathematical stuff then? Hard to be a world leading expert in a physics domain when you cannot model any physical system, despite accurate, well tested quantitative models existing. Is that an ad hom? No, the claim is ridiculous because it is demonstrably false, rather than because you said it.

I love cosmology, I love science and I wish more people knew more of it but that is also why I see your actions as somewhat reprehensible. By misrepresenting yourself as understanding something you are demonstrably ignorant of and telling others 'how things are' without making it clear when you're injecting your own 2 cents into things then you take a proverbial **** on science. If you cared more about science and less for making a name for "John Duffield" you'd not be as you are. Ignoring these valid criticisms of your behaviour and mindset is your prerogative but it's those behaviours which hold you back from do actual science, in whatever capacity, large or small, you are capable of.

 

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Hi MarkM125, can you please tell me naively what the "scale factor" term actually represents?

I can understand naively that a "Cosmological Constant Factor is a symbolic term "stand in" for an UNknown "something" which is used in the Relativity model equations to prevent the results being inconsistent with current interpretations about the Universal Observations.

Is that "Scale Factor" also a "stand in" symbolic term for similarly UNknown "something" (akin to the Cosmological Constant as I naively understand it above?).

Thanks.

 

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Hi przyk,.

Can you please explain briefly and naively for me how you understand the conventional hypothetical universal expansion is defined, laying out exactly the physical nature and effect of what those terms are that you say expansion should be defined in? Thanks.

 

Hi CptBork.

Thanks for your interest and suggestion. Unfortunately I am still very busy and cannot start new threads because I will not have time to fully engage with all respondents (which may leave me open to whatever the usual troll accusations some troublemaking 'personal baggage' troll wants to make).

So may I trouble you to start a thread of your own with my quoted post as part of your OP setup for that thread?

I would be very interested, and very grateful too, to have the question/issues therein discussed more fully between you and other knowledgeable and polite members who may be interested in discussing it until a common learned consensus understanding which could be comprehended by everyone (lay and professionals alike) sufficiently 'backgrounded' in the matter is agreed based on both the facts and the hypotheses extant applying to the context?

Even if I don't have time to fully engage myself, I will have brief opportunities to read-only and/or comment/observations to the flow of discussion as it develops between you and other participants in it! I'm sure it would make (at least for myself) some very interesting and informative reading!

I hope you will have the time to do it, as I don't at this time. Cheers and thanks again, CptBork. Gotta go. Bye for now!

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Let me address the cosmological constant first. The CC is not a stand-in for something unknown. The "unknown something" that causes the acceleration of the expansion of space (i.e. the scale factor also has a positive second derivative) is called dark energy (which has absolutely nothing to do with dark matter, just a naming coincidence). The CC, along with other models such as quintessence, attempt to explain the phenomenon quantitatively. These different models differ by their equation of state, namely, the CC has an equation of state of -1. This result is consistent with experimental data, leaving it as the prime candidate for dark energy. It also is not put into relativity by hand, it emerges from simple considerations - for example, in GR, a negative pressure can drive accelerated expansion. The CC can be considered a geometric property of spacetime, or a negative pressure fluid (this is how it is modeled in cosmology) with pressure \( p = -\rho m c^{2} \), where \(\rho\) is the (positive) energy density of the CC.

The universe we live in is, over large distances, homogeneous and isotropic. That means that it is roughly the same everywhere, expands the same everywhere, has no center or boundary, and looks the same in all directions. Using these assumptions we can derive a cosmological solution to the Einstein Field Equations called the FRW metric. This metric has the property that distances are time-dependent, thus, space expands. The solutions to the FRW metric are called the Friedmann Equations, of which there are two. Here's one:

\(\left ( \frac{\dot{a}}{a} \right )^{2}+\frac{kc^{2}}{a^{2}} =\frac{8 \pi G}{3}\rho \)

Where I've suppressed the cosmological constant term. So, the scale factor tells us how large distances are in comparison with some reference time. Let me walk through some of the basics of this equation. You can see that if the density of the universe (that's \(\rho\)) is very high, the time derivative of the scale factor must be very large (as all of the other terms would be constant, or purely time dependent). Therefore, when the universe was very young, and very dense, it expanded much faster than it did today. As distances between objects got larger, the universe got less dense, and so the rate of expansion slowed. So - positive time derivative, negative second time derivative. This is exactly what we observe in experimental data - up until a point. Eventually, the expansion becomes constant, and then begins to "speed up". This is where the cosmological constant enters the story. That's the very basic picture of modern cosmology.