Omega(matter) = 1/3

[john hunter]

Here is a website which gives omega(matter) = 1/3

It uses just two simple principles - rescaling symmetry and conservation of energy.

www.rescalingsymmetry.com

It consists of 3 short web pages.

John Hunter.

[Nereid]

Here is a website which gives omega(matter) = 1/3

It uses just two simple principles - rescaling symmetry and conservation of energy.

www.rescalingsymmetry.com

It consists of 3 short web pages.

John Hunter.Are you prepared to defend this ATM idea, john hunter?

[john hunter]

Are you prepared to defend this ATM idea, john hunter?


I'll try my best!

Also, here is a challenge. Can anyone come up with a simpler way, with fewer assumptions, to derive omega = 1/3, (or 0.3, or any value close to WMAP)?

John Hunter.

[Nereid]

I'll try my best!Thanks.

To what extent does this idea include General Relativity (GR), either explicitly or implicitly?

To what extent does it conflict with (is inconsistent with) GR?

[john hunter]

The value of omega was derived using Newtonian P.E, which may not match GR exactly, however the value of omega derived using GR, would probably be similar.

One value using a volume of space of 2*pi^2*r^3 (found in a text book on GR) gives omega of 8/(9*pi), which is about 0.28. So any corrections may not be large.

John Hunter

[Nereid]

The value of omega was derived using Newtonian P.E, which may not match GR exactly, however the value of omega derived using GR, would probably be similar.(my bold)

Please clarify what you mean.

Have you derived omega using GR? If so, how?

What is the 'match' to "Newtonian P.E." in GR?One value using a volume of space of 2*pi^2*r^3 (found in a text book on GR) gives omega of 8/(9*pi), which is about 0.28. So any corrections may not be large.

John Hunter(my bold)

Which textbook?

[john hunter]

Dear Nereid,



Please clarify what you mean.

Have you derived omega using GR? If so, how?

Which textbook?

As you've probably noticed, I'm not (and don't claim to be) an expert in GR.

However I've had a go deriving omega using the volume of a hypershpere, which in D.F. Lawden 2nd edition "General Relativity, Gravitation and cosmology", gives the volume of the universe as 2*pi^2*r^3

Also in this link in answers to question b), about half way down
http://hypertextbook.com/physics/modern/general-relativity/
---------------------------------

So instead of putting mc^2 = integral of [Gm (4*pi*r^2*rho)/r] dr from 0 to R, as in www.rescalingsymmetry.com/value_of_G.html (bottom half)

I used mc^2 = integral of [Gm (6*pi^2*r^2*rho)/r] dr from 0 to R

The 6*pi^2*r^2 came from differentiating 2*pi^2*r^3, just as 4*pi*r^2 comes from differentiating 4/3*pi*r^3
---------------------------------

The value of 8/(9*pi) is obtained if we use R=c/H (not R= c/0.5 H), and is close to 0.3 as in WMAP.
There is still a possibility, that rescaling symmetry, determines G, even if the recaling is not occuring at present.

That is,the universe should have rescaling symmetry, so that if ever the universe where to rescale, in this symmetric (unnoticeable) way, conservation of energy would be preserved. This uses R=c/H.
It seemed neater to assume an ongoing rescaling, which also accounted for the redshift of light.This uses R=c/0.5H
These approaches of deriving G from the rescaling symmetry principle all give omega of order unity, which has always been was a long standing problem for cosmology.

A question will be posted in BAUT, to see if someone can do a more 'professional job' of reconciling this symmetry principle with GR.

John Hunter.

[grav]

Can anyone help do a 'professional job' on reconciling GR, with the rescaling symmetry principle described in www.rescalingsymmetry.com

This approach gives omega = 1/3, but uses Newtonian arguments.

It has been discussed in http://www.bautforum.com/showthread.php?t=48301, especially posts 5, 6 and 7.
Another value for omega from this symmetry principle is 8/(9*pi). But the maths may not be 100% right.

Thanks,

John Hunter.
[I was going to post this in Q&A, but figured I had better not, for obvious reasons]

Well, I cannot yet. That is what I've been attempting to do ever since I joined this forum. My posts appear to scatter this way and that with every attempt. But I have followed a few of your posts and I am impressed. I haven't fully explored all of the concepts you are putting forward yet, but I intend to. Your thoughts and methods appear to be very similar to my own. That is undoubtedly one reason I have taken an interest. We seem to have come to very similar conclusions as well. I have also found omega to be exactly 1/3, at least in the context in which you appear to be defining it. But I have taken that to mean that the universe is infinite and static, instead of expanding. And that has taken me away from the notion that the universe began with a Big Bang, as it would not be with such a value, as far as I can tell. Also, your formula fo=fe*e-Ht (or e-2Ht with H at half the observed value, as you apparently use) would indicate tired light, as far as I know. And that would also indicate a static universe. So it would appear that you are trying to incorporate the "illusion" of a stationary universe into an expanding one. First of all, why do you think that should be the case? What would that accomplish? Second, why would the second set of formulas shown here relate to anything other than tired light (light losing energy as it travels through space)?

[john hunter]

Dear Grav,

The rescaling principle can be confusing at first sight.

i) It appears to give an 'expanding universe' in the sense that all length scales are increasing.

But ii) This means that the universe would appear static, to an observer who lived in this universe

...However iii), The rescaling principle also leads to a reduction of G for dense objects, which would allow 'Bangs' for dense objects...

So the final result is: A rescaling universe, which appears static (mainly), but with regions where explosions have occured due to a reduction of G, giving the foam like large scale structure.

Good luck in persuing the approach which we both seem interested in (also Snowflake proposed something similar). As for the value of Omega the original 1/3 seems better, the 8/(9*pi) value uses a radius R, which is the scale factor radius, not the radius of the observable universe, so the 1/3 is probably OK.

The redshift of light, due to a changing Plancks constant, is different from tired light, as there would be no 'scatter' of the light as it goes through space, with this model.
The main reason for proposing the theory is: The phenomenon of gravity, and the value of G are 'explained' - i.e. gravity exists in order to conserve energy as the universe rescales. GR 'describes' gravity, very accurately, but does not explain it any more than Newtons theory does.

John Hunter.

[grav]

First, a dumb question. You don't think that gravity is created by an accelerated expansion of the universe, do you, where the acceleration of gravity inward is really caused by an acceleration of bodies outward? Probably not, I'm sure, especially since you say that all length scales expand in such a way to make the universe appear static, so they must expand at the same rate, and this form of gravity would require different rates depending on the mass of a body. So surely not, but I had to ask. A simple no will suffice.

But secondly, and not so dumb, I think, if all length scales expand equally, then regardless of a changing value for the constants, wouldn't the values of the redshifts appear to remain static as well? That is, if everything expanded to twice the original scale, and so does the wavelength of light, then how are the redshifts observed in the first place? Wouldn't they have to expand faster than the rest of the universe does? And if this is the case, wouldn't that still imply that the universe is expanding, if not by tired light, since the redshift is what originally caused us to believe it is expanding to begin with?

[john hunter]

Dear grav,

On the first point,

Gravity exists, so that the universe can have rescaling symmetry, without violating conservation of energy.

It's a bit different to saying that the acceleration causes gravity, and with the rescaling symmetry model, the value of G is the same for all masses (with the exception that masses with m/r near c^2/G, have a reduced value for G).

Secondly, the redshift of, say, the virgo cluster, will always remain the same, in this model, if we neglect peculiar velocities. The redshift is caused by a changing of Plancks constant with time, www.rescalingsymmetry.com even in a rescaling universe, the apparent distance to the Virgo cluster will be constant, and hence the redshift too.

John Hunter.

[grav]

It would appear that you are saying that the universe expands, but in such a way as to make it appear static. But that it is static in such a way that we can still tell it expands. But if this were the case, then we would know it is not static, but expands. And if the equations are the same for if it were static, they why wouldn't we just assume it to be static anyway? But the observations we make are what make us think it is expanding to begin with. I could go round and round with this all day (but I won't, don't worry :)). It appears to be circular reasoning to me.

And here's one reason why. Let me know if I am off the mark with any of this, though. It seems that you are saying that energy is really conserved in all frames, so E=hf=hc/w is constant. c is also constant, so if the wavelength expands, h must expand along with it. Is that right? So if all length scales doubled, w and h both double as well. We would not be able to tell w expands, since everything else, including our rulers, expands equally. But we could tell h doubled. So if the energy stays the same, and all lengths double, and so does h, then light pressure, or energy density, will fall by eight times. This is because the energy stays the same but the volume that contains it increases eight fold. The equation for this pressure is P=(8pi5/15)(kT)4/(hc)3, so with everything else remaining constant, and the value of h doubling, it would indeed appear that the pressure would drop by eight-fold.

But now, here's the thing. We actually do see a drop in the energy of light coming from a distance. So if it becomes redshifted to the degree that the wavelength is twice as great, and the observed energy is half of the emitted energy, then what you are saying would mean that all we can really measure is the energy, not the difference in wavelength, because the wavelength expands along with the rest of the universe. So it must really be a change in h over time that we measure. Correct? Okay, but if we are really measuring a change in h, and the energy halves, then h must halve as well. And this would be just the opposite of what we just went through, where h doubled. Obviously, it can't be both ways. But it would seem both ways are required for it to work this way (to be observed one way but actually work the other). As I said, please let me know if I am overlooking anything. Can you resolve this?

[john hunter]

Dear grav,

The photon was emitted when h was lower than it is today. For this, h depends on 'cosmological time' i.e. the photon has travelled in space, and time, to a region where h has increased.

So it is assumed that the energy. of the photon, rescales according to the time which has passed for the photon, which is zero. But h rescales according to the time which passes for the rest of the universe. The rescaling theory gives the result that G depends on the proximity of the surrounding matter, so maybe h does too, that's the justification for assuming that h depends on cosmological time.

John Hunter.

[grav]

So you are saying that zero time passes for the photon? I disagree, but I think that is probably the mainstream view, so let's go with it. If zero time passes for the photon, then wouldn't that mean that it hasn't had time to expand either? It would remain at the same wavelength as when it was emitted. So when all other length scales double, the photon will not, and it will actually have twice the energy it would if it were emitted today, but only if h remained the same. So that would mean that the value of h at the time it was emitted must then be reduced by four-fold. Either that or, if h rescales during the time that passes for the rest of the universe, and it has no affect on the photon until it is absorbed, then h must decrease by four-fold with time as the length scales double. Just to be sure, are you saying that the value of h does not figure into the energy of the photon until it is actually absorbed, or from the time it was emitted?

[john hunter]

Dear grav,

According to the model:

The energy of the photon remains constant. So from E=hf, if h increases with cosmological time, then an observer receiving the photon must see a decreased f.

The confusing thing might be the concept 'wavelength of a photon'. This could be defined as c/f , according to this model if h increases, f must reduce and wavelength increases.

There are different ways of looking at this, but the quantity that is conserved is the energy, and wavelength and frequency should come next (IMO).

John Hunter.

[grav]

Okay, let me piece this all together. So from what you are saying, h increases directly in proportion to the rest of the universe. If the length scales double, so does h. The wavelengths of light also scale in proportion, but to me, that would mean that light does experience time, since it must then still be affected by the rest of the universe during this time. In any case, though, the increase of h with the length scales does seem to be the only logical way to piece this all together the way you are attempting to, where the energy would remain the same but the pressure drops according to the volume or h equally.

Sounds good so far. BUT, we still have a problem. If all length scales double, including our own, and yet we actually observe light expanding to twice the original wavelength, then it would have actually had to quadruple. Do you see what I'm saying? If it merely doubled, it would match those emitted today, since the length scales today would have doubled since then as well, and we would observe no redshift. So for us to actually observe it as doubling, it would have had to double twice over. It's as if light would have to experience, far from no time, more like the square of the time we do.

[john hunter]

Dear grav,

You mentioned that if length scales double, then h would double, but the rescaling depends on the number of length dimensions in the physical quantity.
h has m^2, so h would quadruple, if length scales double.

Your point about the wavelength, is a fair one...does wavelength actually exist for a photon in motion, or just energy? Does plancks constant exist for a photon in motion, or just for the region where the experiment is done to measure h.

Which constants are dependent on the proximity of the surrounding universe, and which 'belong' to a particle intrinsically?

These are difficult questions, and to add to the trouble, light shows two properties...wave and particle, depending on the experiment that is done to observe it.

My own view is this, for light:

energy - intrinsic
Plancks constant - depends on surrounding universe.

For a mass:

m - intrinsic (a type of energy)
G - depends on rest of universe

For a mass, time passes, and total energy is conserved (during rescaling), by gravitation
For light, no time passes (and there is no rest mass), so it conserves energy by changing frequency - i.e. the energy is always constant, but the measured frequency is less, due to plancks constant increasing.

These are difficult philosophical questions, but if a rescaling is occuring, this is the best answer I can give at the moment.

John Hunter.