Effort to get us all on the same page (balloon analogy)

[thedaybefore]

the U represents a particular solution of GR. In the mother theory (GR) there is no preferred ref frame. But individual solutions to GR equation can have preferred frame specific to that solution.
So in cosmology we have a preferred frame.

Is this preferred frame based upon an analytical solution to Einsteins's equations that is solved for high field assymetric conditions? However, I guess as long as you guys don't posit some type of aether, I shouldn't be too concerned.

 

[GeorgeDishman]

I think it is also important to emphasise that the "preferred frame" isn't a frame in the usual special relativity sense, two objects, both at rest with respect to the CMB will not be at rest with respect to each other as Marcus said. Another way to look at it is that today's galaxies formed out of the gas that emitted the CMB so really we are just measuring the speed of individual items relative the average speed of all those in the neighbourhood.

 

[marcus]

Practice with a HANDS-ON approach to cosmology might help get us all on the same page. I'd like to try it with some volunteers who'd be willing to work some concrete exercises (with self-calculating formulas) and see how much it improved their comprehension.
The thought here is that purely verbal explanations tend to lead to confusion. As can too much reliance on equations with abstract symbols.

It's possible to put the equations to work in simple calculations and that can raise one's level of understanding quite a lot.

Anyway comments and reactions are very welcome. What I'm thinking of doing is carry this effort to get us on the same page, cosmology-wise, a step beyond the balloon analogy and the CMB rest frame, and see how it goes.

 

[Drakkith]

I'd be willing to give it a go.

 

[marcus]

Great! I hope two or three others will join the project. I'd like us to try using zeit (17.3 billion years) as a time unit and lightzeit (17.3 billion lightyears) for distance. It makes the formulas very simple, so they can be effectively self-calculating.
The present age is 0.8 zeit (more precisely 0.797 but 0.8 is close enough).

Fact 1 is at any time t the size of distances that are expanding at the speed of light is tanh(1.5t).

The answer comes out in lightzeits and it's especially convenient because google calculator knows the function "tanh". So you can say what size of distance is growing at speed c right now today. You just type in tanh(1.5*0.8) and press "enter", the * is for multiplication. Let me know if you have any trouble with google.

Exercise 1.1 what size distance WILL be growing at the speed of light in the future 0.1 zeit from now, i.e. when the age t = 0.9.
Exercise 1.2 what size distances WERE expanding at speed c in the past, 0.1 zeit ago, i.e at age t = 0.7.

Drakkith please let me know if this is grossly too simple or too hard. I have very little notion of what the right level is to start with. If this is OK, the focus at first will be on simple hands-on calculation of the universe, getting actual numbers so it is on more than just a verbal level.

 

[Drakkith]

Exercise 1.1 what size distance WILL be growing at the speed of light 0.1 zeit from now in the future, i.e. when the age t = 0.9.
Exercise 1.2 what size distances WERE expanding at speed c

1.1: 0.87 lightzeit, or 15.1 billion light years.

1.2: 0.78 lightzeit.
(Note that if you use another calculator than google, which I did, you have to use radians, not degrees)

 

[marcus]

Yay! BTW I got called away from computer while I was typing in Exercise 1.2, and only finished it later.

 

[Drakkith]

Yay! BTW I got called away from computer while I was typing in Exercise 1.2, and only finished it later.

I've corrected my post.

 

[Drakkith]

Drakkith please let me know if this is grossly too simple or too hard. I have very little notion of what the right level is to start with. If this is OK, the focus at first will be on simple hands-on calculation of the universe, getting actual numbers so it is on more than just a verbal level

I think it's pretty simple. You literally just plug in numbers or type it into google.

 

[marcus]

I see it's too elementary, I'll go to something a bit more complicated in a few minutes.

But what we just did was essentially equivalent to Hubble's law v(t) = H(t)D(t)
because the speed a distance is growing is proportional to its size.

So if you know what size is growing at c, and you have another distance that is HALF that then you know it is growing at half c.

In our units we can say H(t) = 1/tanh(1.5*t) and we can write Hubble law
v(t) = D(t)/tanh(1.5*t)

Exercise 1.3 So thinking back to t = 0.234, how fast was a distance growing that was size 0.337 lightzeit?

 

[marcus]

Exercise 1.4 A distance is 3/4 lightzeit in size at time 0.44, what speed is it growing?

I think you are good with these tanh(1.5t) exercises. I should move on.

How about the inverse, you very quickly got the knack of going from time t to the distance that grows at speed c. Call that R(t).
maybe we can go back from the distance R to t

Can your calculator do the natural logarithm "ln"? If so then you can calculate the inverse of the R(t) function and go back from R --> t

If at some time t, the distances growing at speed c are R of a lightzeit, then the time is
t = ln((1+R)/(1-R))/3

I think you already found that for time t=0.8 that R=0.83, so we could check by working back from R=0.83
Does ln(1.83/0.17)/3 = 0.8?

Imagine you find yourself back in a time when distances sized 0.71 lightzeit are growing at speed c.
Has the Earth formed yet? If it has, are there single-celled living organisms?

I'm hesitant about presenting the formula for the size of a generic distance growing over time, because of the 2/3 power. Does your calculator do sinh(1.5t)^(2/3)?

 

[marcus]

Great! I hope two or three others will join the project. I'd like us to try using zeit (17.3 billion years) as a time unit and lightzeit (17.3 billion lightyears) for distance. It makes the formulas very simple, so they can be effectively self-calculating.
The present age is 0.8 zeit (more precisely 0.797 but 0.8 is close enough).

Fact 1 is at any time t the size of distances that are expanding at the speed of light is tanh(1.5t).

The answer comes out in lightzeits and it's especially convenient because google calculator knows the function "tanh". So you can say what size of distance is growing at speed c right now today. You just type in tanh(1.5*0.8) and press "enter", the * is for multiplication. ..

So far we have one self-computing formula (and its inverse). t→R (and R → t)
It is simply tanh(1.5*t), and it relates the size and growth speed of distances at any given time t.
It gives the size of distances that are growing at speed c at time t. From that you can figure out the speeds that OTHER distances are growing, because speed is proportional to size.

I'm thinking we might be able to make do which just three basic formulas. The next one is more complicated and it calculates the ratio of distance size (or wavelength size) at any two times, call them "then" and "now".
Substitute numbers for the words then and now.
sinh(1.5*then)^(2/3)/sinh(1.5*now)^(2/3)

\frac {size\ then}{size\ now} = \frac{sinh(1.5*then)^{2/3}}{sinh(1.5*now)^{2/3}}

Fact 2: This compares wavelengths and distances then to what they are now. or actually between any two times you choose, including times in the future.

An example would be to take 0.44 zeit as the age when acceleration began and to take 0.797 as the present.
sinh(1.5*0.44)^(2/3)/sinh(1.5*0.797)^(2/3)
That calculates the size of distances back then compared to what they are today. And if some light arrives here today that some galaxy emitted back at that time its wavelengths will arrive stretched out by the the reciprocal of that number, the factor by which distances have expanded between then and now. You can use it to predict future size of distances compared with their size now---or the wave stretch of some signal we send today that is received some time in the future.

 

[marcus]

This post is a review.
We're looking for a way to present the standard model of expanding universe that can get the maximum number of people on board, the broadest possible hands-on understanding.

the google calculator knows the "tanh" function and it happens that the cosmic expansion rate is well-described by it. that was Fact 1.

So let's get to know this function better. As I see it, at least, it's the simplest function you can build with e^x which starts out at zero at x = 0 and increases steadily leveling off at 1.$$\tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$$ Readers may find that picturing the graph of the basic exponential function e^x---how it tends to zero at -∞, equals 1 at x=0 and rises steeply for x---helps understand how the "tanh" function defined this way equals zero at x = 0 and rises steadily leveling off at 1.

The simplicity of this function, I would say, is shown by its having a simple inverse---you can UNDO it easily. If you plug x into tanh, and get tanh x, you can always get x back again.

If$$R = \tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$$ then $$2x = \ln\frac{1+R}{1-R}$$ Checking this just involves simplifying a fraction by multiplying numerator and denominator by the same thing, namely e^x+e^-x
$$\frac{1+\frac{e^x - e^{-x}}{e^x + e^{-x}}}{1 - \frac{e^x - e^{-x}}{e^x + e^{-x}}} = \frac{e^x}{e^{-x}}= e^{2x}$$
and the natural logarithm of e^2x is 2x.

In the case of our universe, the R = tanh 1.5t, instead of x we have 1.5t, and 2x = 3t, so $$3t = \ln\frac{1+R}{1-R}$$ and $$t = \frac{1}{3}\ln\frac{1+R}{1-R}$$

 

[marcus]

So if you want to know the SPEED any given distance D is expanding, at some point t in history, you just find R(t)=tanh(1.5t) which is the size of distances expanding at c, and compare D to that. At any given moment, expansion speed is proportional to size.

If D is twice R, then the distance is growing at twice the speed of light.
If D is half R, then the distance is growing at half the speed of light.

Its expansion speed is the distance's size divided by R. Also notice that at any time t, R(t) is the critical size that distinguishes distances growing faster than c from those growing slower than c. That's one of several ways R(t) can give us a handle on the expansion rate history: It is also reciprocal to the "percentage" or fractional growth rate. The larger R is, the slower any given-sized distance is growing (think: larger denominator---the farther out you have to go to get to where distances are expanding at the speed c.)

So R(t) is the critical distance size at time t and it changes over time like this (the blue curve in this picture)

In professional circles this critical distance size R(t) is called the "Hubble radius". One way to picture its role is to think of a bit of light coming from far away aimed in our direction. As long as the light is farther than R(t) (outside the "Hubble radius") it will lose ground. It can't make headway because the distance to us is expanding too fast. So it is swept back. You can see that by looking at the red curve in the picture in the interval from t=0 to t=0.2 where the distance to the light (red) is greater than critical (blue) and the light is swept back--gets farther from us even though traveling towards us thru its surrounding space.

But the critical distance increases until it finally takes the light in (actually around time t = 0.234 is when this happens). At that moment the speed of the light is exactly canceled and you can see the slope of the red curve is flat, zero progress. Then after the moment t = 0.234 has passed the light begins to make progress and narrow the distance to us. It arrives here at t = 0.8 which is the present time in history.

You could say (figuratively of course) that our universe has "chosen", for this critical size, the simplest function you can build from basic exponential e^x that starts at zero, levels off at one, and has a simple inverse. I didn't mention earlier that it has a nice flip symmetry too: tanh(-x) = -tanh(x). Flip it left-to-right and then flip it head-to-toe and you get back what you started with. Maybe that doesn't matter. : ^) To me it suggests a prior contracting phase. The negative branch of the tanh(x) function could describe contraction, mirroring the expansion. Here the red curve is the size history of a sample distance, which is contracting and expanding in accordance with the blue (tanh) curve.

For the sample distance to plot, I chose one which is just slightly over 1.3 lightzeits at the present. That is at t = 0.8. That has the simplest growth history to plot: D(t) = sinh(1.5t)^2/3

 

[marcus]

The third formula (those three may be all we need to do basic cosmology) is going to be the wavestretch-distance relation. The wavestretch is the factor by which wavelengths and distances are enlarged while the light is on its way to us. It equals the conventional "redshift" number plus one.
It's more convenient to work with than the conventional redshift, which when you use in equations you usually have to add one to, so that you are actually working with the wavestretch. I'll denote it with the letter S.

We want to know, if some light comes in stretched by a factor S, how far the source is NOW. Let's call that distance D(S). It turns out that this is an integral that is easy and quick to get evaluated online. There is a website that does this and it remembers what you keyed in the last time you visited, so once you have gone once and done the distance integral D(S) you have very little to do the next time except change one of the limits of integration.

$$D(S) = \int_1^S R(s)ds = \int_1^S ((s/1.3)^3 + 1)^{-1/2}ds$$

Here's a good website for online integration
http://www.numberempire.com/definiteintegralcalculator.php

 

[marcus]

Wavestretch and current distance to the source are the two most important things we more or less directly observe. The first is measured from the incoming light itself, the second (the current distance to the source) is told from the dimness of standard brightness sources (called "standard candles").

Fortunately the critical distance size R(t), for which we already have the formula relating it to time R(t) = tanh(1.5t) is also simply related to the wavestretch of incoming light that was emitted at the time in question. R(S) = ((S/1.3)³ +1)^-1/2

For example suppose some light comes in stretched by a factor of 3, so its wavelengths are 3 times as long as they were in the original light. You want to find the distance to the source galaxy. You go here
http://www.numberempire.com/definiteintegralcalculator.php
put 1 and 3 in for lower and upper limits, change the variable from x to s, put
((s/1.3)^3 + 1)^(-1/2) in the main box and press "calculate"

If greater precision were needed one could use 1.3115 instead of 1.3. I'll have more to say in the morning and hopefully will be able to explain this third formula somewhat. Using this wavestretch-distance formula is basically how the positive cosmological curvature constant was discovered, in 1998, and it's how the longterm value of 17.3 billion lightyears has been determined (by fitting wavestretch-distance data).

 

[Drakkith]

Exercise 1.3 So thinking back to t = 0.234, how fast was a distance growing that was size 0.337 lightzeit?

Just now saw this and your next few posts. I'll have to get back to you, tomorrow hopefully.

 

[marcus]

No rush! Your reactions are a good guide. Help me see which explanations work, which don't. I could review where we are at this point.
The aim is a widely accessible basic introduction to cosmology which goes beyond merely verbal description. The reader should be enabled to calculate a few things (if he or she wishes to) like expansion speeds, expansion ratios, distance to source, or how long ago light with a given stretch factor was emitted...

I'm thinking now that we might narrow it down essentially to three self-calculating formulas. "google-ready" formulas (ones that you can paste into google)

A. tanh(1.5t) gives the "Hubble radius" at time t---the critical size that separates distances growing faster than c from those growing slower. This is the size of those distances which are growing at speed c and by proportionality you can use it to find the expansion speeds of other distances. Reminder: use an asterisk for multiplication as in tanh(1.5*0.8)

B. sinh(1.5"now")^(2/3)/sinh(1.5"then")^(2/3) where you replace "now" and "then" by two different times. It gives the ratio of distance size between those two times, and the ratio of wavelength size. So it gives the expansion factor between those two times.
I would like to call this ratio "stretch" and denote it S, in the special case where "now" is 0.8 or more exactly 0.797.
The stretch factor S compares present day size to that of the same distance or wavelength at another time which can be either in past or future.
That's a special case though. The formula can be used with any two times---it doesn't need for one of the two to be the present.

C. ((s/1.3)^3 + 1)^(-1/2) computes R(S) the "Hubble radius" at a time in the past (or future) corresponding to a given stretch factor S. Pasting that in for the integrand at numberempire gets us
D(S) = ∫₁^S((s/1.3)^3 + 1)^(-1/2)ds, the distance from its source of light arriving today with stretch S.

Example: People are often interested in knowing the radius (today's distance) of the currently observable region. We are currently getting CMB light stretched by roughly a factor of 1000, so we can use that D(S) formula to find out the distance to that matter---roughly the same as the radius of the currently observable region. The latter is only a bit larger to allow for other possible signals from even earlier and more distant matter.
So numberempire integrator can be used to find D(1000), a reasonably good estimate of the radius of the observable.
To improve the accuracy some, we use 1.3115 instead of 1.3.

 

[Drakkith]

Exercise 1.3 So thinking back to t = 0.234, how fast was a distance growing that was size 0.337 lightzeit?

I get 0.215 c.

Exercise 1.4 A distance is 3/4 lightzeit in size at time 0.44, what speed is it growing?

I get 0.416 c.

 

[Drakkith]

I'm hesitant about presenting the formula for the size of a generic distance growing over time, because of the 2/3 power. Does your calculator do sinh(1.5t)^(2/3)?

Plugging in 0.5 for t, I get 0.8778 using this calculator online. Is that right?

 

[marcus]

Plugging in 0.5 for t, I get 0.8778 using this calculator online. Is that right?

Yes! Google calculator agrees with your answer.
When I put this into the google search window
sinh(1.5*0.5)^(2/3)
and press enter, I get 0.8777... hardly any difference at all!
======
tanh(1.5*0.234) ≈ 0.337

.75/tanh(1.5*0.44) ≈ 1.3

 

[marcus]

Since we just turned a page, I'll bring forward this summary of the essentials.

...
The aim is a widely accessible basic introduction to cosmology which goes beyond merely verbal description. The reader should be enabled to calculate a few things (if he or she wishes to) like expansion speeds, expansion ratios, distance to source, or how long ago light with a given stretch factor was emitted...

==quote==
I'm thinking now that we might narrow it down essentially to three self-calculating formulas. "google-ready" formulas (ones that you can paste into google)

A. tanh(1.5t) gives the "Hubble radius" at time t---the critical size that separates distances growing faster than c from those growing slower. This is the size of those distances which are growing at speed c, and by proportionality you can use it to find the expansion speeds of other distances. Reminder: use an asterisk for multiplication as in tanh(1.5*0.8)

B. sinh(1.5"now")^(2/3)/sinh(1.5"then")^(2/3) where you replace "now" and "then" by two different times. It gives the ratio of distance size between those two times, and the ratio of wavelength size. So it gives the expansion factor between those two times.
In the special case where "now" is 0.8 or more exactly 0.797.I would like to call this ratio "stretch" and denote it S. This agrees with the notation in Lightcone calculator. The stretch factor S compares present day size to that of the same distance or wavelength at another time which can be either in past or future.
That's a special case though. The formula here can be used with any two times---it doesn't need for one of the two to be the present.

C. ((s/1.3)^3 + 1)^(-1/2) computes R(S) the "Hubble radius" at a time in the past (or future) corresponding to a given stretch factor S. Pasting that in for the integrand at numberempire gets us
D(S) = ∫₁^S((s/1.3)^3 + 1)^(-1/2)ds, the distance from its source of light arriving today with stretch S.

Example: People are often interested in knowing the radius (today's distance) of the currently observable region. We are currently getting CMB light stretched by roughly a factor of 1000, so we can use that D(S) formula to find out the distance to that matter---roughly the same as the radius of the currently observable region. The latter is only a bit larger to allow for other possible signals from even earlier and more distant matter.
So numberempire integrator can be used to find D(1000), a reasonably good estimate of the radius of the observable.
To improve the accuracy some, we use 1.3115 instead of 1.3.
==endquote==

 

[marcus]

I'll add just one more formula, to close the circle, and see how that looks. Is it an adequate set of tools for basic cosmology?

D. Given a figure for the Hubble radius R > 1, you can find the time in history t when that was the R(t). Namely t = ln((1+R)/(1-R))/3

As a check try putting in 0.83 for R because at present the R is about 0.83 lightzeit. You should get t = 0.8

The reason I say to close the circle is because formulas B, C, and D, enable one to compute t→S→R→t

B. t→S
C. S→R
D. R→t
We already saw formula D, it being the inverse of A. Back in posts#511 and #513.$$t = \frac{1}{3}\ln\frac{1+R}{1-R}$$======================
How can we visualize the fractional growth rate that goes along with a given Hubble radius R? This has to involve taking the RECIPROCAL of R because the larger R is the slower the growth of any given size distance. Remember that you DIVIDE the size by R to get the speed. Let's take the largest R that's in the cards for our universe (according to standard cosmic model), namely R = 1 lightzeit = 17.3 billion lightyears.
Suppose we've reached that point and that is the distance that is growing at the rate of one lightyear per year.
Imagine a microzeit, a millionth of a zeit---that is 17,300 years (longer than human civilization has existed so far, but there were hunt&gather folks that looked like us that long ago.)
What fraction of itself does a distance sized 1 lightzeit grow in a millionth of a zeit? It expands by a millionth of itself.
It expands by 1 ppm---by one part per million---per microzeit.

That works for all. Right now the Hubble radius R(now) = R(0.8) is about 0.833 and the reciprocal of that is about 1.2. To picture the corresponding fractional rate of distance growth, we can think 1.2 ppm per microzeit. 1.2 parts per million in 17,300 years.
Maybe you or somebody else can think of a better way to visualize it. Cosmic expansion is really really slow, in human terms.
Does this way of imagining the expansion rate work?

 

[Drakkith]

Does this way of imagining the expansion rate work?

It's a little abstract, being all numbers, but I think so.

 

[marcus]

======================
How can we visualize the fractional growth rate that goes along with a given Hubble radius R? This has to involve taking the RECIPROCAL of R because the larger R is the slower the growth of any given size distance. Remember that you DIVIDE the size by R to get the speed.
Let's take the largest R that's in the cards for our universe (according to standard cosmic model), namely R = 1 lightzeit = 17.3 billion lightyears.
Suppose we've reached that point and that is the [size of distance that is growing at the rate c.]
Imagine a microzeit, a millionth of a zeit---that is 17,300 years (longer than human civilization has existed so far, but there were hunt&gather folks that looked like us that long ago.)
What fraction of itself does a distance sized 1 lightzeit grow in a millionth of a zeit? It expands by a millionth of itself.
It expands by 1 ppm---by one part per million---per microzeit.

...Right now the Hubble radius R(now) = R(0.8) is about 0.833 and the reciprocal of that is about 1.2. To picture the corresponding fractional rate of distance growth, we can think 1.2 ppm per microzeit. 1.2 parts per million in 17,300 years.
Maybe you or somebody else can think of a better way to visualize it. Cosmic expansion is really really slow, in human terms.
Does this way of imagining the expansion rate work?

It's a little abstract, being all numbers, but I think so.

I'm glad it seems OK, also you put your finger on what I think is the weakness. The fractional growth rate is abstract and harder to picture, because it is too numerical. By contrast, the Hubble radius is more concrete and easier to visualize---the size of a distance that is growing at speed c.

 

[Gaz]

Well i have learned a lot today about the cosmos today. I can actually read a lot of what you guys are saying and understand it thanks for all the help =) the balloon seems like a pretty good explanation.

 

[Lucky123]

I have a question regarding space-time (space).

I have read a large part of this thread and numerous others; both here and elsewhere. (Thank you everyone!).

I will state my understanding/assumptions in layman’s terms first. I would appreciate if someone could check I have correctly understood to this point. I will post further understanding and direct questions after that. Thank you.

Understanding

Space is expanding everywhere from all points in all directions.

The universe is bigger than we can see or detect.(think flashlight in endless black room; room goes on after visability stops)

It can expand at faster than the speed of light (C); space is expanding not moving.

The rate of expansion can and has changed since the big bang (BB). (Is the rate of expansion currently increasing?)

Space was created at the BB.

The universe may or may not be infinite: it depends on curvature and the size of curvature.

The universe may be too big for us to detect the curvature (point on a sphere would appear flat)

If curvature is positive enough the universe can meet back up and is finite (describes a sphere with universe on the line, Space is not inside the sphere but on the line)

If the curvature is zero or too small the universe is flat and infinite

There appears to be two main groups of answers as to what the fabric of space is:

Description A – Nothing its Mathematics

· Space is really just a Geometrical construct.

· Space (3d) only exists as a function or description of the location of matter; Time is a function of describing a point of matter moving with respect to another point of matter.

· Curvature of space by gravity; nothing else

· It’s a mathematical model or a function; nothing real

Description B - Something

· The Higgs field

· Gravitons (is this the same as Higgs boson; a piece of Higgs field?)

· Probability/Potential energy field

· Aether/ether

· Other alternatives.

It would appear that both answers can be correct depending on your philosophical disposition.

My observations on fabric of space:

I appreciate the answer (Description A) intellectually and although it is undoubtedly correct (by definition of the model) it is also unsatisfying on a deeper level as an explanation. The universe is clearly more than just a mathamatical model.

Mathamatics is just patterns; our models replicate patterns from the real world in the maths world. Our maths world in this context is imaginary; even if it predicts what will happen in the real world.

This thought and my growing realisation of the depth of models/mathematics in our understanding of the universe may lead me to consider the possibility of the universe simulation scenario a little more seriously than previous.

Mathamatics models a pattern independent of the medium (in this context) and can be considered a description. The universe models patterns in the medium of the universe it is physical in that sense and exists. I don’t find semantics much help i.e. “what’s an idea or thought made of”.

Philosophically (to me anyway) space should be made of something whether that is a medium or a field, it should be something; nothing existed before something so it's not nothing.

 

[marcus]

Gravitons do not exist in curved geometry especially if the geometry is dynamic. The definition of a "particle" is problematic in a realistic geometry. It is a mathematical idealization that depends on geometric simplification (e.g. FLAT SPACETIME).
The Higgs field is of course a mathematical idealization.
You might ask what is the Higgs field "made of".

I suppose events, interactions, are real, relationships are real---one can measure them. One can measure the angles of a triangle. Compare areas, compare volumes etc.

Geometry is one of the realest things in our experience. We experience whether the angles of a triangle add to 180 degrees, or more, or less.

Much of the rest of physics---of what we observe, control, measure in physics---involves geometry in large part. A large part of physics is made of geometry. Think of electromagnetism, the relations of moving charge and changing magnetic field---in large part geometric.

Much of the rest of physics (besides the bedrock reality of geometry) consists of imagined creations of the mind, useful idealizations.

 

[marcus]

the moment anyone says "fabric of space" they have been distracted by a metaphor and have lost contact with reality.
what is "fabric"? what is "space"? why should "space" be created.

There are distances and angles that are very real, there are measurable relationships.
the idea of space as a substance comes out of popular mass-market books like Brian Greene stuff. Seductive metaphors mess up our minds so somebody can be on television and collect royalties.

It's not necessarily true that BB was beginning of time evolution, there are alternatives. Google "LambdaCDM bounce" or look up papers by Edward Wilson-Ewing on arXiv.org---he is one of dozens of cosmologists working on testable bounce cosmology (no singularity, no need for a mythical "inflaton" field, simple Occam explanations)
==quote==
Space was created at the BB.

...groups of answers as to what the fabric of space is:...
...
My observations on fabric of space:
...
...
Philosophically (to me anyway) space should be made of something whether that is a medium or a field, it should be something; nothing existed before something so it's not nothing.

==endquote==

What is a "photon" made of? I think photons occur at emission, absorption, scattering events.
I don't think anyone has ever seen a photon absent some interaction.
It is a mathematical codification of our expectations, one that works well in flat Minkowski space time

If a photon does not need to be "made of" anything, why should geometry be "made of" something?

One can be led astray by language, by WORDS----like the noun "space". By the mental habits of language--oh for sure! if it is a NOUN then it must be "made of" something. Look at all these other nouns like "dog" "cat" "apple pie"---they are all made of something! BTW Lucky I liked your post, it sounds intelligent and articulate. I see things in a different light, from a different perspective, however, so wanted to respond.

 

[Lucky123]

Marcus,

Thank you very much for your reply.

My actual style of thinking is more akin to "out loud" and can appear a bit jumbled to others (particularly online); so I try to organise my thoughts coherently before posting to enable others to follow.

I have a million questions I would like to blurt out right now however in the spirit of the above statement I will contemplate your points and read/scan BB alternatives suggested before reposting. Possible BB alternatives are something I have considered also but wanted to state my understanding of the mainstream perspective first.

cheers

 

[marcus]

My thinking too. You mentioned "mainstream" So just now thinking out loud, I went to the central listing of conferences to see what topics are of interest to mainstream cosmologists these days. Here are a few I noticed. It's a special year (centennial of Einstein GR) so that affects the makeup of the conferences.

The 8th International Conference on Gravitation and Cosmology (ICGC)
December 14 - 18, 2015.
http://icgc2015.in/index.php/invited-speakers (Parampreet Singh)

THE 2ND CONFERENCE OF THE POLISH SOCIETY ON RELATIVITY: 100 YEARS OF GENERAL RELATIVITY
23-28 November 2015
Warsaw, Poland
http://potor.fuw.edu.pl
Invited plenary speakers include:

• Jan Ambjorn (University of Copenhagen)
• Giovanni Amelino-Camelia (La Sapienza, Rome)
• George Ellis (University of Cape Town)
• Jerzy Kowalski-Glikman (University of Wrocław)
• Yongge Ma (Beijing Normal University)
• Ezra T. Newman (University of Pittsburgh)
• Tomasz Pawłowski (Universidad Andres Bello, Santiago)
• Roger Penrose (Oxford University)
• Martin Reuter (Universitaet Mainz)
• John Stachel (Boston University)
• Thomas Thiemann* (University of Erlangen-Nürnberg)
• Kip Thorne (California Institute of Technology, Pasadena)

* TBC

The Planck Scale II
XXXV Max Born Symposium
Wroclaw, Poland, 7 - 12 September 2015
http://ift.uni.wroc.pl/~mborn35/index.html
A few of the invited plenary speakers are:

• Giovanni Amelino-Camelia (Rome)
• Aurelien Barrau (Grenoble)
• Martin Bojowald (Penn State)
• Laurent Friedel (Perimeter Institute)
• Kirill Krasnov (Nottingham)
  
• Jerzy Lewandowski (Warsaw)
• Krzysztof Meissner (Warsaw)
  
• Daniele Oriti (Golm)
• Thanu Padmanabhan (Pune)
• Alejandro Perez (to be confirmed) (Marseille)
• Roberto Percacci (Trieste)

Gravity @ all scales
Nottingham - 24 to 28 August 2015
http://thomassotiriou.wix.com/gravityallscales2015#!speakers/c10mn (Eugenio Bianchi, also Saueressig, Sakellariadou, Mercati and others)

Hot Topics in General Relativity and Gravitation
August 9th – 15th, 2015, Quy Nhon, Vietnam
http://www.cpt.univ-mrs.fr/~cosmo/HTGRG-2/DOCUMENTS/Booklet-HTGR-2.pdf
http://www.cpt.univ-mrs.fr/~cosmo/HTGRG-2/index.php?page=speakers (Wilson-Ewing, Yongge Ma and others)

Here is the full list at the University of Frankfurt site that keeps track of current and upcoming conferences
http://hyperspace.uni-frankfurt.de/category/Conferences/

 

[marcus]

Earlier this summer there was the fourteenth Marcel Grossmann meeting at Rome. One of the really big ones. Pope Francis gave the opening talk. Abhay Ashtekar was one of the plenary speakers. He also gave a half hour talk in one of the parallel sessions listed here (namely QG3). Typically over 1000 cosmology and relativity researchers attend the Marcel Grossmann. They hear the plenary speakers in the big hall together and they divide up into different parallel sessions according to their specialties.
MG14
Rome 12 - 18 July, 2015
Here are several of the parallel sessions:

QG1 - Loop Quantum Gravity, Quantum Geometry, Spin Foams
Thursday session. Chairperson: Jerzy Lewandowski
http://mg14reg.icra.it/mg14/FMPro?-...tField=order2&-SortOrder=ascend&-Max=50&-Find

QG1 - Loop Quantum Gravity, Quantum Geometry, Spin Foams
Friday session. Chairperson: Jerzy Lewandowski
http://mg14reg.icra.it/mg14/FMPro?-...tField=order2&-SortOrder=ascend&-Max=50&-Find

QG3 - Loop quantum gravity: cosmology and black holes
Chairperson: Jorge Pullin, Parampreet Singh
http://mg14reg.icra.it/mg14/FMPro?-...tField=order2&-SortOrder=ascend&-Max=50&-Find

 

[Lucky123]

I gained an insight into my own thinking from Marcus’s replies (#528,529) that I will share in the spirit of this thread; as others may also be making the same mistake.

It is easy for the educated layperson (that’s people like me) to confuse what is confirmed in physics and what is still a theory and to conjoin or combine elements of various theories together (incorrectly) to form a view of the universe and assume this is the accepted view of science.

This becomes more likely if the layperson pays attention (without significant discrimination) to the daily media, Internet and YouTube; has undertaken reading or research on the subject without making a considered differentiation in their own mind as to what is confirmed and what is still theory and between theories.

 

[Lucky123]

Marcus,

I see and accept what you are saying regarding geometry and mathematics. I always have I just find it unsatisfying (to me) on a deeper intuitive level. It’s a paradox I’ll just have to live with.

Although I do note the maths definition (in our discussion) is independent of the medium; as pointed out geometry does not need any medium for space to exist:

“If a photon does not need to be "made of" anything, why should geometry be "made of" something?”

That does not exclude the possibility of space being made of something; the deduction being the medium is irrelevant.

As mentioned in #527 “It would appear that both answers can be correct depending on your philosophical disposition”.

It could be we see two answers to one question when in fact it’s actually two questions.

--------------------------------------------------------------------------------------------------------------

I haven’t followed up on the suggested reading yet but would like to contribute a thought about the BB at this point.

Just to be clear so some don’t make the wrong conclusion and think I’m mad. The following are thought exercises as to other possible explanations for the BB and Universe. I don’t believe them just entertaining alternative thoughts.

Description A

The currently accepted view of the BB (continuation of my understanding)Nothing existed before the BB

All energy & matter, (including dark matter and dark energy) and space-time were created at the BB: this is the universe.

It expanded from a singularity; that is it came into existence everywhere (reference frame inside singularity) and expanded from there.

Description B

Space-time existed before the BB.

The BB by this definition then is: when all energy and matter (including dark matter and dark energy) are added to (inserted into) space-time.

Any expansion is a result of the interaction with energy and matter and the rest or pre-existing state of space-time (thinking bounce rebound stretch or splash ripple).

The universe may or may not be infinite in this description.

Description C

Space-time did not exist before the BB but something else did.

Something in this description can be thought of as a very big container or field.

All energy & matter, (including dark matter and dark energy) and space-time were added at the BB: this is the universe.

Space-time is made of some medium {separate from energy and matter or at least in a different state}.

In this example space-time expansion could be explained in two ways:

1. Space-time is being “warmed up” so is expanding or;

2. More space-time is being added to the system; (think adding more liquid to a virtually limitless container).

The universe is finite in this example.I will go off and have a look at the suggested reading material to see what real scientists are thinking. Cheers.

 

[marcus]

I like your perspective, it is in some ways akin to my own. I suspect you could find "real scientists" (in the general sense of professionals who attend conferences, publish, give talks :^) all over the map described by your A, B, and C. And the "real scientists" can be partly or maybe even entirely wrong, we can't know the future of research, fundamentally new ideas can show up, new directions can be taken. But I still like to check out what is being talked about at the major conferences.

The two biggest international conferences about General Relativity/Gravity/Spacetime etc are TRIENNIAL. They are the GR series and the MG series.
The last GR was GR20 in 2013, attended by 844 participants
http://gr20-amaldi10.edu.pl/index.php?id=1
http://gr20-amaldi10.edu.pl/index.php?id=29
So the next GR conference will be GR21 in 2016. It will be interesting to see who the invited plenary speakers will be, what the topics will be, who will chair the various parallel sessions. There should be announcements and a website soon, if not already.

The last MG was MG14, just this year, attended by 1220 participants, so the next will not be until 2018. But we can glance at the speaker lists, parallel session topics etc. and maybe learn something.
http://www.icra.it/mg/mg14/
The MG organizers do tend to pick attractive locations: MG11, 12, and 13 were held in Berlin, Paris, and Stockholm. The MG14 website has links to the websites of past conferences if you want to check those out.

The rationale for at least not completely ignoring these bigtime international conferences is, I think, that the organizers are smart people and they want their conference to be a success, so they invite speakers who reflect the current interests of the community---they arrange for talks about research that the community of people who attend conferences want to hear about and they pick chairpersons for the parallel sessions who want their parallel sessions to be successful and attract a lot of participants so these in turn reflect the live interests and hot research topics in the particular specialized areas, to some extent.

One can be skeptical too. I'm a bit suspicious of the MG series because it is so glamorous. The plenary speakers tend to be famous---perhaps deservedly so, but...maybe too much focus on reputation/celebrity---and the venues have glitz.

I wonder where GR21 will be held. It's next year. Do they have a website yet? New York!
So says http://www.isgrg.org/activities.php
And there is a preliminary web page:
http://www.gr21.org
http://www.markalab.org/GR21/
It will be held on the Columbia University campus, July 10-15 2016.

 

[marcus]

...
I will go off and have a look at the suggested reading material to see what real scientists are thinking. Cheers.

I didn't mean to burden you with a lot of "suggested reading material", Lucky. All this conference material is just a window on "mainstream". One opportunity to get an impression of it.

I only meant to suggest ONE ARTICLE as something you might read. I had a particular reason for suggesting it. Let me try to recall. It was what you get when you google "LambdaCDM bounce".
It was by two postdocs: Yi-Fu Cai and Edward Wilson-Ewing.
I suggested it back in post #529

They provide a scenario that is as plausible as any, I think, for the start of expansion. Nothing as exotic as inflation. No "something from nothing" no original "quantum fluctuation" no "singularity". No "breakdown of the laws of physics". No "beginning of time".

And they check that it is consistent with observations so far, at least in a preliminary way. they just came out with it around end of 2014, more work is needed. The takeaway message is that some of the more drastic and exotic stuff is not necessary to accept.

Their scenario does not have to be TRUE. IT MERELY MEANS YOU DON'T HAVE TO ACCEPT ALL THE hype and propaganda about inflation and "the singularity" and breakdown of the laws of physics. There are other ways to explain the flatness and sameness-in-all-directions that inflation was invented to explain back around 1980. And to fit CMB data.

Cai and W-E paper is not unique. There are plenty of people working on bounce cosmologies, and on alternatives to inflation. There are also bounce cosmologies that involve inflation., the two aren't mutually exclusive. And there are non-bounce cosmologies that also don't need inflation, but still have time going back before start of expansion without hitting a singularity. All kinds of variations. I just think Cai and Wilson-Ewing's paper is a particularly clear, short, unexotic, example. It is based on the standard cosmic model (cosmological constant Lambda, cold dark matter) and they are very interested in connecting with various kinds of observations

Reading the non-technical understandable parts of one 14 page paper is, I think, an easy way to gain a measure of immunity to a lot of unconsidered (and probably unnecessary) assumptions people make about the start of expansion.
BTW here is Ed W-E list of papers on arXiv.org
http://arxiv.org/find/gr-qc/1/au:+Wilson_Ewing_E/0/1/0/all/0/1
You can see he has written some follow-up to the December 2014 one with Yi-Fu Cai.
I'll get his author's profile
http://inspirehep.net/author/profile/E.Wilson.Ewing.1
It needs updating. He is now at the Albert Einstein Institute at Gölm, outside of Berlin.
PhD 2011 advisor Abhay Ashtekar.

 

[Lucky123]

what real scientists are thinking.

I didn't mean to burden you with a lot of "suggested reading material", Lucky. All this conference material is just a window on "mainstream". One opportunity to get an impression of it.

It was meant a bit tongue in cheek and a bit as protection. Some sites whilst claiming to share knowledge are non-inclusive to those not deemed worthy. I can see that does not apply here now.

As mentioned above I do need to get clear in my mind what QM, String (various) and GR theories etc. state and not to confuse.

A philosophical thought as I think philosophy and physics have a lot in common.

The universe follows patterns; both on a grand scale and a quantum scale and all scales between.

I am surprised by the similarities between the universe and the brain; particularly in some images of the universe showing dark matter (or was it dark energy?) between galaxies and images of galaxies in different EMR wavelengths. Other images look like what might be seen through microscope. (Edit. I know the images are not photos but a representation of data collected)

No I don’t think the universe is part of some gigantic brain just an example of similar patterns. Perhaps contemplation of patterns elsewhere in nature may lead to insight at another level.

However we are part of the universe.

As part of the system can you ever know the whole: by definition I would suggest no. {Open to debate but in absolutes its no. If we think we understand the universe then perhaps it’s part of a bigger multiverse}.

The very fact we can imagine the universe from an external reference frame (as Max Tegmark attempts with maths and others as thought) may be a clue our universe is part of something bigger. Man after all has proven time and time again: if we can imagine it we can make it happen; or in science we prove it.

 

[Lucky123]

An amusing thought on the universe brain analogy: are we part of the brain or a parasite?

 

[ebos]

Whenever I have trouble understanding a concept, the balloon analogy always clears things up for me (so far). I am a visually oriented person. I just have to remember that the real universe has one more dimension than the balloon. However, perhaps some people may have a more difficult time with visual examples like the balloon. One poster above complained about galaxies being stuck to the surface of a balloon. When I imagine the balloon I don't have that issue so I need to remember that some people are stronger in areas other than visualizing. They use methods which I find difficult to imagine. Therefore it would be great for us 'visuals' to use it but not so great for others. Perhaps instead of fighting about how we understand things we can learn to share. So I would prefer not to subscribe to a gospel because it alienates people whose ideas might otherwise complement mine. As long as I can keep an open mind, that is.

 

[ebos]

Whoops, again forgot to check the date... oh well, it's still a good post.

 

[Bill McKeeman]

Perhaps this point is obvious to all, but at the time the CMB was released, I suppose every point in space sent photons in every direction. What we observe now are just the photons that happened to be headed in our direction from every point (on a sphere) that has a (current) radius of 41 B LY. That is obviously much less than all of the CMB photons. Are there any numbers to go with either our local rate of arriving photons or the total number of photons that were released?

 

[Bill McKeeman]

Please ignore what I said about counting photons. Not well thought out.

 

[RelativeRelativity]

Does space expand and should one think of it as a 'real' substance?
Do static structures experience disruptive stresses because the balloon or dough substrate is expanding?

Cosmology is a mathematical science. There is no mathematical necessity for a surrounding space for our space to expand into. All expansion means is a pattern of increasing distances between object stationary with respect to CmB. It is a bunch of distances that are increasing according to Hubble law, not a material that is swelling up.

If we can't say space is expanding because it doesn't constitute a real expansion of any "stuff", then couldn't we conversely point at the "stuff" for what is occurring and say that relatively, matter is compressing?

 

[Jorrie]

The way in which the redshifts of different objects at great distances vary, makes it impossible to explain with "shrinking" or "compressing" matter. In other words, irrespective of how you "shrink the ants" on the balloon, it cannot explain observations.

 

[RelativeRelativity]

The way in which the redshifts of different objects at great distances vary, makes it impossible to explain with "shrinking" or "compressing" matter. In other words, irrespective of how you "shrink the ants" on the balloon, it cannot explain observations.

Thank you, but its now confusing for me that the terms aren't interchangeable whether you think of the model running and see the balloon expand or imagine the model while preserving a certain balloon size?

 

[Jorrie]

I referred to a fixed balloon size and a shrinking ant size - it cannot fit Hubble's law.

There is however still a possibility that dark energy density is not completely homogeneous. Cosmologist David Wiltshire is a proponent of this idea. Check
Wager between DL Wiltshire and T Padmanabhan.

 

[RelativeRelativity]

There is however still a possibility that dark energy density is not completely homogeneous. Cosmologist David Wiltshire is a proponent of this idea. Check
Wager between DL Wiltshire and T Padmanabhan.

from the material there:
"The mystery of dark energy is explained purely in Einstein's theory, through a deeper understanding of those parts of general relativity, which Einstein himself recognised as being difficult: the understanding of gravitational energy, given that space itself is dynamical and may contain energy and momentum."
- David Wiltshire

(which makes me wonder about dark energy and how much energy space contains in terms we already know about like photons, and what about sound even, but this is by the way)

So mechanically compression is outside the accepted model and Hubble observations, I see, thankyou.

I suppose I was asking in terms of both the actual mechanics and also in terms of becoming familiar with the analogy.

I see the problem of gravity leaves a gap for much speculative investigation that I wouldn't lately want to get into.

 

[Nugatory]

I see the problem of gravity leaves a gap for much speculative investigation that I wouldn't lately want to get into.

The first step in closing that gap is to acquire an understanding of general relativity, so that you will at least know what is already known.

 

[Nugatory]

This thread has been open for many hundreds of posts, and it's becoming increasingly difficult to keep it organized and useful so we are closing it.

Followup questions should go in new threads, and as always if you want to add something specifically to this thread, ask a mentor and we can reopen as needed.