andrew s

Ok at @Olly, we will have to agree to differ. I don't  find relativity or quantum mechanics strange, amazing and powerful yes strange no. I suspect  it is a matter of familiarity.

I accept that with the success of the science of the Industrial Revolution scientists thought science was complete. Maybe I am similarly mistaken but we have now probed the extent of the observable universe and the subatomic at Tev. There will undoubtedly be better new theories but just a Newtons laws work well at our normal every day encounters so will our current theories at the energies we can reasonably muster. 

Broadly what do you think is unknown? I suspect you will say dark energy and dark matter but we can characterise them quite well and measure their effects as well as say an electron.

Regards Andrew 

1 hour ago, ollypenrice said:

 When we climb the mountain of scientific discovery it gives us the best possible vantage point from which to marvel at the mysterious unknown. Indeed I think that Relativity and, even more so, Quantum Theory, have increased what is known to a far lesser degree than they have increased our awareness of what is not known. I think this is absolutely excellent!

Olly

Not sure I subscribe to that. Science certainly has built a vantage point from which to marvel at the the Universe from the very large to the very small. However, it has also provided a language, mathematics, in which to encode its mysteries.  Like poetry  it can be read at many levels. Unfortunately,  at the surface pop level, it is all to often presented as magical almost occult with spooky interactions. Leading, I feel, to the view a lot is not known.

We know a vast amount about what happens (in this sense not much is left to know, at least in the energy range accessible to us) but science is mute on the why it happens. For that we need poetry and the other creative arts.

Regards Andrew 

PS Consider reading "Paradise Lost" without knowing the Bible well. It would be a good story but much would be missed. So it is with science if you don't have the mathematical tools to behold its creations.

Lots of good science but also a lot of extrapolation presented as fact.

Cox has finally learnt to let the science speak rather than showing himself off.

Regards Andrew 

7 minutes ago, vlaiv said:

Do we account for position of the star in the sky when doing spectroscopy? Is this effect noticeable? I'm talking about difference between stars that are towards galaxy center and ones that are on the opposite side in relation to our Sun. In first case light will be "escaping" gravity potential of much of the galaxy - so it will be red shifted, while second case should be blue shifted as light is "falling" towards the galaxy?

Radial velocity dominates any GR effect. RV causes small shits seen in line positions. You have to account for the motion of the earth but once that is done you can follow pulsations and other shift e.g. material ejection of a stars photosphere. With SN you get both RV shifts and delays due to the metric expansion.

Regards Andrew

@vlaivif you want to get very subtle then there is always atmospheric transmission to take into account 🤔  

Not sure how important this us to your calibration but in spectroscopy we have to find catalogues with spectra that have not had interstellar reddening removed or if it has apply the reverse transform. 

If it is important have a look here http://www.spectro-aras.com/forum/viewtopic.php?f=6&t=207&p=2159&hilit=Berardi#p2159

Regards Andrew 

You have to go to the AAVSO site the navigate to the database and then the access form. You can put in an RA &Dec plus search radius and download a file. 

Not tried it myself!

Regards Andrew 

Ps you can down load the whole file.

Hi @vlaiv, you could try the AAVSO Photometric All-Sky Survey . It has BV and sloan data. At a minimum you could test your transform.

Regards Andrew 

You could try ground to air missiles but they can leave a vapour trail.

Other than that as above.

Regards Andrew 

Hi Stuart, have you checked other people's images to see if it's there?  Worth doing and getting a confirmation image if not as you may have discovered something new.

Regards Andrew 

25 minutes ago, Tiki said:

 

I suppose it could be argued that it is not surprising since we are here talking about it at all. A slightly less flat Universe would have collapsed long ago or would have disallowed the formation of galaxies and stars.

What is truly surprising though is that there are a whole bunch of constants at critical values (Omega being just one of them) that conspire to make a habitable Universe. (cf. 'Just Six Numbers' by Martin Rees or 'The Road to Reality' by Roger Penrose)

The whole range of anthropic principles from hard to weak is indeed thought provoking. 

In the case of Omega I think it would be interesting to no what magnitude range (+ve or-ve) is allowable but I have not researched it.

Regards Andrew 

55 minutes ago, vlaiv said:

Could you expand a bit and clarify both reasoning and calculations on density in decoupling era, no need to go beyond that (just to avoid issues with inflation) - how does it impact curvature? From what I can gather, and this is at a glance - due to change in scale factor curvature will behave differently?

Very roughly, The current age of the Universe is about  4 x10^17s and if the current density were about 0.5 then at time t = 10^13 and assuming  |Ω(t) – 1|) α t (I.e. a^2*H^2  α t^-1)

gives  Ω(10^13) ~ 0.5 * 10^13/ 4 *10^17 ~10^-5.

The model excludes inflation. If I recall correctly the topology can't change under GR i.e. the k is constant)

On the constraints on topology the Plank 2015 results put constraints on the nature of the topology see https://arxiv.org/abs/1502.01593 .  There are lots of papers on trying to constrain the topology but they can only provide limits given the size of the observable Universe.

In a similar discussion on PhysicsForms

"That said, I don't think that it's accurate at all to state that "cosmologist tend to believe that the universe is infinite". A more precise statement would be that cosmologists rarely think about whether the universe is finite or infinite because it's not really something that is answerable. Most cosmologists tend to try to stay within the bounds of answerable questions that have an impact on observations we can potentially make."

Reference https://www.physicsforums.com/threads/what-is-the-probability-that-the-universe-is-absolutely-flat.971984/

I was not trying to reopen the the discussion on what the curvature was but rather point out how close to "flat" it must have been in the past (with or without inflation) to be as close as it is to flat today.

Regards Andrew 

No not imaging flats but the spatial flatness of the Universe.

In a thread started by @vlaiv he asked why cosmologists took the Universe to be infinite, with all the problems that poses, rather than finite and closed. While the thread discussed many issues especially about infinity it did not touch on why the Universe being close to spatially flat is surprising.

Well why is it surprising?

The main reason is the Big Bang Model based on GR normal cosmological assumption (homogeneous and isotropic) and the current LCDM model derived from the latest measurement which put it close to being flat.

So what? Well the Friedmann equation (derived from the above) tells us that:

|Ω(t) – 1| = |k|/(a^2 H^2)

Where Ω(t) is the total mass energy density, a = the scale factor and H is Hubble’s constant.

k is a constant that defines of the curvature of spacetime:

k = 0 gives a flat Universe, k < 0 Hyperbolic and k > 0 Hyperspherical

Now if k = 0 the Ω(t) = 1 a constant i.e. the Universe is and always has been spatially flat.

This is just amazing why should it be so? It could be that physics says it has to be like that.

No one has shown this to be the case or even got close.  It was/is a major problem for the original Big Bang theory.

If |k| > 0 then why is it so close to 1 now?

The Universe was initially radiation dominated where |(a^2 H^2) α t^1

Then matter dominated where |(a^2 H^2) α t^2/3

So |Ω(t) – 1|) α t or t^2/3 in the past. (It is now thought to be Dark Energy Dominated)

Again, so what? Well if it has grown like t or t^2/3 what was it like in the past?

At the very worst now 0.5 < Ω < 1.5 so at:

decoupling t ~ 10^13 s we need |Ω(t) – 1| <10^-5

and at nucleosynthesis t ~ 1 s we need |Ω(t) – 1| < 10^-18 !

The same issue as before.

This was why cosmic inflation was introduced to help solve this problem, as well as the horizon problem, with all the fun issues it brings!

Regards Andrew

PS Please forgive the indulgence of this post but it helped me get it straight in my mind.

All Data and equations from “An Introduction to Modern Cosmology” by Andrew Liddle.

1 hour ago, DaveS said:

I think M90 is falling into the Virgo cluster and happens to be heading in our direction. I'm not sure the local group is sufficiently bound to the Virgo cluster to overcome the local expansion.

Do you have a reference for your last point as I would like to follow it up.

Thanks Andrew

PS I found a paper with a simulation that supports your comment. The local cluster remains bound

4 hours ago, barkis said:

Astronomers have determined that Messier 90,  a  lovely Spiral in Virgo, which contains many galaxies,is heading for a collision with our Milky Way galaxy, and there is no doubting it. 

As M90 is about 60 million light years away,  it sure ain't gonna happen next week, but happen it will they say. The movement contradicts the expansion theory of Red Shift, but M90 is definitely Blue Shifted.  

 

The Virgo cluster is gravitationally bound. The force of gravity on the scale of the local cluster is 10^7 stronger than the tension caused by the metrical expansion of space. (Sorry I don't have the figure for the virgo cluster.)

So this observation is consistent with the expansion theory as @vlaiv explained. Indeed many local galaxies are blue shifted as can be seen in Hubble's original data.

Regards Andrew

See later post we will not stay bound to the virgo cluster but the local group will remain bound.

11 minutes ago, saac said:

Ssssh , I think it's listening Olly.  

 

Jim 

There is an infinity of infinities and some have very big ears.

Regards Andrew 

Oh course @saac you have at this very moment an infinity of masses depending on the velocity of the reference frame you measure it in with relative velocity v where |v| < c 😱

Regards Andrew 

43 minutes ago, vlaiv said:

'd like to point out, with risk of it sounding that I'm again trying to put discussion back in certain direction, which I'm not - is that my conclusions stem from exactly what you pointed out - infinite spatial extent. This and basic assumption of cosmology - homogeneity, and the fact that we observe finite density in our observable patch indeed leads to those things that I mentioned.

I realise that and fully acknowledge it. However, you also apply an argument that in essence says that if you have an infinite state space then repetition is inevitable, there will be boltzmann brains etc. This is a common view and you will find many serious deployments of this argument by many much more capable than I.

I however, think it is wrong. I think the way probability is employed  in these arguments is in error similar to the error that leads to Olblers' paradox.  It is this area I am not motivated to discuss further. Not because I fear being proved wrong but it is just too complex for me to articulate clearly enough. 

Please forgive my reticence. 

Regards Andrew 

39 minutes ago, Alien 13 said:

I cant remember specifics but my door number was not pleasant, a sort of burnt plastic/cucumber combination.

I dont however recall this odd effect in reverse i.e. smells producing numbers. I did look around on the net and this type of cross sensor anomalies is not uncommon in stroke victims and did make me wonder if our concept of Maths and numbers is actually hard wired into our brains. This might explain why the concepts of zero and infinity cause problems and why we struggle with using alternative reasoning to view the world.

Alan

How we perceive the world is indeed very complex and in some cases quite anomalous to the norm as your experience confirms. This is why I teased @saac about what is real. Our perception may all differ to a more or less significant degree and what we naturally take as real might be quite different if evolution had equipped us differently. 

All the worlds a concept and we are just avatars of a boltzmann brain .🤔

Regards Andrew 

13 minutes ago, Alien 13 said:

Its funny you mention this but for quite a few weeks after my stroke (I am fine now) I could smell numbers and it was very distinctive, looking at a digital clock at 7.30 am was an especially nice smell.

Alan

And at what time was the worst pong?

Regards Andrew 

1 hour ago, Kev M said:

True, but I think it shows a point.

The above example shows that if you treat infinity as a number it becomes nonsense.

Infinity is not a number... so you cant think of it as such, you cant perform mathematical operations with it ( its not a number ).

Hence the universe cant be infinite because there would be an "infinite number" of something ( maybe Apples... I like Apples ).

Can't have an "infinite number" as this is meaningless... might as well have a " red number" or a "fluffy number" again meaningless.

 

 

 

You are right infinity is not a number. You can, however, do mathematical manipulation on it. Not that they are particularly relevant to this discussion. 

I think as @vlaiv has pointed out you need to be careful what infinity means in this context. 

We are discussing the LCDM cosmological model in which spacetime is geometry. The geometry of Einstein's Gerneral Relativity. In this context a spatially flat universe has and always has had infinite spatial extent. All this  means is that you can continue in any spatial direction without bound. This is a totally respectable geometrical notion.

You and others may read more into this beyond the geometrical meaning. For example as@vlaiv does that this leads to multiple repetitions etc. These require logic and physical reasoning beyond LCMD. Perfectly legitimate but I tend to the view that they are often misguided.

Regards Andrew 

Hi @vlaiv yes I know about analytical continuation etc. As I said a bit of fun !

Hi @saac playing only slightly. I am not trying to say infinity is real in the sense of you or I are  but for me it is as real as a googleplex or 0. Although it is not a number!

However,  I do find it difficult to know if the entities of our physical models are real or not. If you take an electron as an example do they exist in a solid where they have no well defined location or only when free or not at all in the sense a pebble does. I don't  know.

@vlaiv on renormalistaion that is an interesting quote but I do get tired of physicist saying all problems will dissolve when we "quantise" spacetime and gravity. I have a sneaking feeling we will not find a theory of everything and gravity and QM will remain unreconciled.(No evidence just a hunch. )

Regards Andrew 

25 minutes ago, saac said:

Yes but those are more than the predictions of mathematics Andrew. While mathematics can use the concept of infinity as a useful operator it does not define what in reality exits. Consider that our laws of mathematics and physics no longer hold in the realm of infinity - the singularity whether it exists or not cannot be described by our mathematical laws of physics.  In a sense I accept infinity exists in one respect - as I 've said if our universe has a size then that is by definition infinity but in practice I do not believe it has the meaning that mathematics ascribes to or tat which it holds in popular culture.  When it appears in our equations we generally take a sharp intake of breadth and say we have an incomplete understanding here as with the singularity. 

Jim 

 

Ok Jim no problem with that.

However, I want you to give me example of what does exist in nature.

This is so I can understand how you decide what does and doesn't exist in nature or is real however you prefer to put it.

Regards Andrew 

On 21/05/2019 at 23:13, vlaiv said:

However, there might be mathematical identity that is only true for infinite sums and diverges considerably when finite version is used, and such identity used to derive physical law.

Not quite this but fun for a Thursday morning.

Consider the sum 1+2 +3 +4 +5...     (where ... means keep going for as long as there are new integers to add - forever) 

If you try this on your calculator you will find it diverges (continues to get bigger) and does not converge to a specific number.

(Note the avoidance of the term infinity)

All well and good no objections so far I trust!

Now Riemann came up with a function now called the Riemann zeta function

zeta(s) = 1/1^s  + 1/2^s + 1/3^s ... which is defined for all values of s but for s = 1

Now if you put s = -1 you get zeta(-1) = -1/12  (try it here https://keisan.casio.com/exec/system/1180573439  as I doubt it is on you calculator )

All well and dandy. Now put s = -1 into the equation above for zeta(s) and you get

zeta(-1) = 1 + 2 + 3 + 4 + 5....

So the same sum both diverges and converges!

Does this matter is it just proving the unreality of Mathematics.

Well the first divergent sum is just counting (albeit forever). The second crops up in QED and the calculation of the correct strength of the Casimir force.

Zee in "Quantum Field Theory in a Nutshell" derives the answer without using the zeta function but there is no reason not to use it any more than not using sin, cos or tan.

Happy days.

Regards Andrew

PS in QED it is often the opposite of @vlaiv request in that you get excellent agreement with the first few term but it diverges when you add significantly more.

8 hours ago, saac said:

The language we use to define the circle (mathematics) produces what we define as infinity. Infinity is a consequence of that language it does not follow it exits in nature. 

Jim 

I am not sure what this means. What do you feel does exist in nature. 

Elections, em fields, quantum fields, energy and entropy are all components of our mathematical models of reality.

Chairs, tables and pebbles are objects of our naming and of our perceptual model of the world. 

The integers, reals and irrational are part of our  mathematics   

Which if any of these are part of reality? If not what is?

Regards Andrew