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# Is an expanding universe equivalent to a universe in which everything is shrinking?

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Why do we always think of the universe as expanding?

Surely, from our perspective an expanding universe would look exactly the same as a universe in which everything is shrinking away from everything else? "Oh, but the red shift!" I hear people exclaim. Well how about this:

The speed of light is simply slowing down.

Hear me out. If the speed of light is a measuring stick against which all things are measured, and if the speed of light is slowing down, then it means everything shrinks and high frequency waves generated in the past are observed with a lower frequency today, which causes us to make observations that the universe is expanding.

What is wrong with my alternative?

Given this, if the speed of light were experiencing, say, exponential decay, wouldn't we expect to see the universe's 'expansion' accelerating? (which I thought was a relatively new and profound discovery)

Apologies if the question is silly, I've never made a formal study of physics and the universe, but this has always baffled me and I haven't been able to find an explanation

Surely, from our perspective an expanding universe would look exactly the same as a universe in which everything is shrinking away from everything else?

This is false. If everything was shrinking away from everything else, that would imply that the recessional rate of distance we observe due to this shrinkage would be independent of distances. Afterall, all galaxies are shrinking at the same rate so the rate they "recede" is only dependent upon their shrinkage rate.

However, we observer that the more distant an object is, the faster it recedes from us. This is the premise of Hubble's law and is only explained if we assume the universe is expanding.

Furthermore, there are many objects in our visible universe which are receding from us faster than the speed of light. This is only possible because these objects are not moving through space, but rather space itself is expanding. In your scenario, these objects are shrinking in space (I presume) and there's no possible way they could shrink fast enough to appear to be receding faster than the speed of light.

"Oh, but the red shift!" I hear people exclaim. Well how about this:
The speed of light is simply slowing down.

There have been people who have tried to suggest that the universal constants (e.g., the speed of light, the mass of an electron, etc.) are not actually constant and instead time-varying (albeit slowly). No such theory has ever been successful.

Again though, your idea suffers from a few problems, even if you assume it to be true. There are multiple kinds of redshift. Redshift from receding objects occurs because space itself is expanding and causing the wavelengths to expand as a result - otherwise known as cosmological redshift. In your scenario, the redshift would be caused by the (faster-than-light) recession itself (since the galaxies are physically moving away from us), also known as doppler redshift. You then complicate the problem by making the value of the speed of light change over time. This would cause light, at the moment of emission, to be redshifted both by the doppler effect and by the slowing of $c$. As the light travelled, the time-varying of $c$ would have no effect on the wavelength. In this scenario we would have long ago realized that moving objects get a double redshift, namely the doppler effect and the time-varying $c$ effect. We just don't see that.

If the speed of light is a measuring stick against which all things are measured, and if the speed of light is slowing down, then it means everything shrinks

Those two ideas don't relate at all. There's nothing suggesting the speed of light slowing down implies everything shrinks.

high frequency waves generated in the past are observed with a lower frequency today

As explained above, your proposal would cause the redshift to occur at the time of transmission, not en route. So there wouldn't be "high frequency waves generated in the past" They would have been emitted as a lower frequency. Which itself is troubling because how then do you explain the CMB changing frequency over time?

What is wrong with my alternative?

Aside from the above mentioned points, a huge number of things:

1. All the physical constants of nature are tied together. You can't just change one and hope that the others don't notice. If the speed of light is constantly decreasing that has drastic implications throughout all of physics. For example, if the speed of light changes, suddenly the electromagnetic force strength changes, atoms aren't stable, and the universe explodes! What is your proposal for stopping that occurrence?
2. Just how exactly are things shrinking? Are the atoms getting closing together? Are the atoms themselves shrinking? At some point you're going to hit a limit and your object becomes a black hole. Are you really predicting that eventually the universe will be nothing but black holes? My guess is that if you did such a calculation, you'd find the time it took to reach that point is about a second, but the Universe has been around for a few billion years.
3. What caused this initial shrinkage? Motion requires energy input. Where did this energy come from? How did it apply itself so uniquely as to cause every individual thing to shrink into itself and only itself?
4. How did the universe get to be so distributed? Your proposal basically implies the Big Bang didn't happen since you attempt to explain things the Big Bang theory already explains. If your explanation differs and you believe yours is the correct one, then the Big Bang Theory cannot be correct. If that is the case, then how did the universe get into its current state if not the Big Bang?

I'm sure I could go on and on, but hopefully you can see there are more than a few holes in your idea. No offense, but it takes years and years of studying to contribute to the forefronts of science. Ground-breaking ideas aren't going to be had by someone who read about a few concepts from Wikipedia or A Brief History of Time and decided they could come up with a better theory. That's the academic equivalent to reading about the rules of (American) football and deciding you can play in the NFL.

This hypothesis has far too many contradictions with our current physical models. I'll list a few:

How would you actually know if the galaxies are shrinking, or if they are moving further apart and the view is just zooming out to keep them in frame?

We would see how it agrees with our modern theories. Relativity has matched our measurements with extreme accuracy, so let's just analyze why your hypotheses would go against its basic principles:

"Oh, but the red shift!" I hear people exclaim.

General relativity predicted that our universe was dynamic a decade before the first observations of redshift confirmed it. A static universe is a physical impossibility; anything, from the tiniest thermal fluctuations, would send it perpetually collapsing or expanding.

The speed of light is simply slowing down.

This would violate the second postulate of special relativity, which states the speed of light is always $c$. A massless particle cannot change its speed.

## Universe expanding or everything shrinking?

Scientist claim that space is expanding. All the evidence for this that I’ve heard, however, could also be used to say that everything in space is shrinking. That would cause the space in between everything to look like it’s growing. Doesn’t that make a little more sense than space itself expanding? Or is there even a difference?

*Title edited by mod @alexishungry. Please avoid all caps titles in the future.

Think it is a matter at looking at it…. both probably are true, depending on where you look from. But if we are shrinking, is space constant….. ?

@spiraltouch, Since time is not constant, space is probably not constant either. Scientists invented this idea of dark energy to help explain the “expansion” of the universe, but it doesn’t really make sense why it would make things go faster and faster and faster instead of slowing down. After all, things tend to lose energy rather than gain it out of nowhere.

What makes more sense to me is that matter is like energy “vibration”, kinda like in string theory. When the string of a piano is struck the amplitude of the vibration gradually shrinks. I think matter is like piano strings and the amplitude of everything is shrinking as is gets further away from the big bang. Space isn’t expanding. It just appears to be expanding as the vibrational amplitude of everything in space shrinks.

@kipgoeing, I have thought about this before. I have heard that space is like a fourth dimensional sphere, we see things as beginning at one point, an explosion (the big bang) and all this material is flying out in every direction, 3 dimensionally. But if you can imagine all this 3 dimensional stuff occuring on the surface of a 4 dimensional sphere, it all wraps around the surface until it meets the material from the same explosion on the other side of the sphere.
Like two people standing back to back and walking off in opposite directions along the equater (if that were possible) eventually they will come face to face on the other side of the world. So galaxies that shot out of the big bang in the opposite direction to our galaxy could, theoretically, be on a collision course with us.

@trek79, Yeah I think a torus explains it better than a sphere, though. Everything goes out on one side and in on the other.

@kipgoeing In the 18th century people thought that earth was expanding but now scientists have proven that it is neither expanding nor shrinking.
But who knows , right ?
Food for thought :)

@kipgoeing, The idea goes beyond that simplistic explaination. With that idea it does not matter which direction material had been shot out of the big bang, that no matter what direction it was on a collision course with all the other material. Another stretch was to say it did not even matter how fast each bit of material was moving, that it would all rendezvous at the same place at the same time, the makings for a new event not unlike another big bang.

@kipgoeing If were shrinking there must be centar of the universe :O. First you need to explain what do you mean by universe. If saying that universe is everything around us not just galaxies and stuff, but beyond that. All that dark empty space so far from every light. That space is limitless and it cant be expanding or shrinking. But if u say just galaxies and stuff and put them in that endless space i think they would all go in they seperate way as much as they can. Like when u put air in space it whould try to sort its self equaly around space. Because space is endless particals would go so far away but will be still going beacuse they cant sort them selfs when there is so much more space behind (or infornt, whatever) them.

Summed… Universe it self is not expanding or shrinking, but its when looking its part seperatly and interacting you can notice expansion/shrinkage.

But this is just my opinion, hope you understand.
And sry for bad english. :)

I would have to disagree.The “explosion” of the Big Bang is not your average conventional explosion where there is a central point from which everything is receding away from. It was an explosion of space itself not one in it. If you would like to think that space is shrinking however, the shrinking should point to a central point. This central point however does not exist.

The claim that the universe is expanding with all celestial matter exponentially moving away from each other wasn’t an arbitrary hypothesis it was a claim that is now regarded as fact due to observational data collected from studying the distance and speed of further away galaxies.

Dark energy was not “invented” but rather it is a term used to explain the already existing phenomenon of galaxies moving away from each other. It was discovered that even the vacuum of space is not a true vacuum, since every bit of “empty” space still contains trace amounts of particles (named virtual particles) that each emit their own force they fluctuate in an out of “existence” and through these violent fluctuations they emit their own unique repulsive form of gravity only seen at the quantum level.

Your analogy of piano strings is puzzling because it is not the same idea as the quantum strings of String Theory, since those strings are just fundamental building blocks of matter which will always vibrate according to their nature, or else the nature of the matter would change. You also mention matter moving “further away from the Big Bang”. But like i mentioned before, there is no central point of the Bang for anything to move away from it. Pardon me, but i think that it is a gross misconception to think that the Big Bang was like an actual explosion with one definitive point. Remember, before the Bang there was no such thing as “point” or “location”.

I may be playing my words wrong a bit here, but i am merely giving you what knowledge i have of accepted Physics from personal study of String Theory and general Physics. What you are proposing is just general speculation without the facts being accounted for. I am not attacking your knowledge in case you think that way.

@trek79, Yeah, I was saying in the other thread about black holes that around a black hole space-time decreases as gravity increases. When the increasing line of gravity meets the path of the decreasing spacetime the result is a black hole sigularity that exists in non-space-non-time. We perceive lots of black holes in different places all over the universe, but they are really “all in the same spot”, so to speak, because they all exist in non-space-non-time.

So the big bang is the opposite of a black hole where matter enters into a “universe” or realm of space-time from the realm of non-space-non-time. All back holes are in the same location, although it can’t accurately be call a location. I use the torus as a simplified example because you have and entrance and an exit which is how it would look if you where looking at it from the other side, in the realm of non-space-non-time. I think it just appears to be more complex because we are looking at it through the kaleidoscope of spacetime.

@bono95zg, No, there doesn’t need to be a “center” only an origin, perhaps multiple origins. Although I’m incline to believe that anothe origin (big bang) would create a separate bubble of spacetime.

When I say universe I mean our realm of spacetime.

@kipgoeing, if something is shrinking is has to have a point of shrinkage, otherwise its not shrinking. And universe like our realm of spacetime cant be shrinking or expanding, like i said above.

@kipgoeing, Imagine 3d coordinate system. Put some dots in it representing, i dont know, planets or something. They can go anyway they wont but it doesnt affect that system. System is infinite and not shrinking or expanding. :)

Judging by the candy bar selection at the gas station, everything is shrinking.

@bono95zg, can you clarify what you mean when you say “system” in context to your analogy?

## If the universe is expanding, what is it taking the place of?

I'm having a hard time wrapping my head around the concept of an ever-expanding universe. If the volume of the universe is increasing, then what is outside of it? Where can the edges of the universe go if there is nothing on the other side? Also isn't space just nothing? How can nothing expand? And if there's nothing on the other side of space then how do we differentiate that nothing from the nothing that is our space?

"Expanding" here means "distances within the universe get larger as time goes by".

So if we see a galaxy 1 billion light-years away, one day it will be 2 billion light-years away, not because either of us are "moving", but because "space itself is expanding".

In case this seems like arguing over semantics, not that nothing can move faster than the speed of light, but it is possible for things to be so far away from each other that as space expands, distances increase faster than the speed of light.

Imagine ants walking along an elastic band. The fastest form of communication they have is the "ant telegram", a kind of vibration in the elastic, which travels at 1 m/s.

The elastic band is very long, and you and I are stretching it very quickly - distances double every second.

If there are two ants a centimetre apart, ant A might send a message to ant B. The message takes sabout 0.01 seconds to arrive.

If the ants were half a metre apart, the message would take a bit more than half a second, since the elastic band stretches as the message travels, and the message actually needs to cover more than half a metre of distance.

If the ants were 2 metres apart, they could never send a message to each other - the distance between them is growing faster than the speed of "ant telegrams", and the message A sends gets further and further away from B, despite the fact that it's travelling towards B. A is not part of B's "observable universe".

We also are not part of their observable universe. The ants don't know we are the ones stretchign the elastic, in fact they don't know why it's stretching. In fact, their current simplest model is that the elastic band is infinitely long, and there are no ends for strange bipedal humanoids to hold onto and pull. Being infinitely long, the elastic band isn't getting "bigger" (in the sense of occupying more "space"), but it is "expanding" (in the sense that distances between things increase).

Edit: a few people said I didn't really answer the question. So I'll just repeat: "expanding" here means "distances are increasing", not "occupying more of .. something"

If the universe is infinite, it's size doesn't change as it expands. Even if it's finite, there doesn't have to be anything "off the edge" for it to expand into.

## Is the universe expanding or are its contents shrinking?

If you have an opinion one way or the other, can you explain why?

Well, if we look at the evidence for expansion (red-shift of distant galaxies), one question we could ask is whether a "shrinking matter" hypothesis would fit the evidence. As our current understanding of the speed of light is that it is related to distance not size (i.e. the speed of light isn't relative to size), the "shrinking matter" hypothesis doesn't explain the observed phenomena.

Shrinking matter might seem like a convenient alternative explanation at first glance, but it doesn't actually explain what we're seeing.

Shrinking matter could explain the perceived redshift. If the wavelength of emitted light remained constant while "in flight," that wavelength would look longer (compared to your own size) when it hit you the more time had passed since it was emitted. If we assume emission wavelength is proportional to your "scale" at the time of emission, this explains the relative redshift of distant objects just fine.

If we assume that the observed speed of light is constant over time, we would also have to assume that all light is "slowing down" as the objects in the universe shrink.

I think with those assumptions it's actually mathematically equivalent to a simple model of expansion. It's perhaps not as natural, but it's really just a matter of defining coordinates a bit differently. It's not really "wrong."

## 13 Replies to &ldquoIs Everything Actually Shrinking?&rdquo

I have written a couple of papers that have been published in peer reviewed journals describing the geometry of expansion based models.

The First Paper defines a Multidimensional Geometric Expansion of Spacetime.
file:///C:/Users/john/Downloads/10.5923.j.ijtmp.20140402.01.pdf

The Second Paper proposes a model by which inertial mass is lost over the passage of Cosmological Time which would cause matter to contract.
file:///C:/Users/john/Downloads/10.5923.j.ijtmp.20140403.08.pdf

The second paper makes a strong theoretical argument against the Big Bang Model. If someone made as scathing and valid argument against my model, I would have to admit it is wrong.

The third paper should be done in a few weeks for a publisher to review. The working title for the abstract is “Dark Matter, Quasar Distribution, and Evoluion of the Universe’s Structure”. Dark Matter is not needed and a number of heretofor unresolved issues in astonomy are resolved or “after the fact” fixes are replaced with predicted effects.

The Fourth Paper, which also is mostly done with respect to calculations, should be available to submit to a Journal by June. Dark Energy is not needed.

Ehm, we cannot download files from your harddrive.

Sorry for the wrong links to my papers This will do it.
Thank you for the interest.
No more dark matter and no more dark energy, and a simple geometry to boot.
http://article.sapub.org/10.5923.j.ijtmp.20140402.01.html
http://article.sapub.org/10.5923.j.ijtmp.20140403.08.html

I have an alternative to the statement: the “Universe is expanding” or instead is “shrinking” as commented in your article. I am thinking Instead the speed of light is really slowing down over long distances, creating the illusion of space expanding or in your theory the universe is shrinking.
I know this goes against all previous mathematical reasoning, but thought it was worth a comment let me know why this goes against all reasoning.

Before I poke holes, I’d like to specify a few things and have you clarify.
1) If you mean light from other stars is slower then normal light, then we would have noticed. The speed of light on our planet is basically constant, weather that light comes from other stars or from our own star. This has been measured time and again.
2) My thought to expand on what you have. Light slows as it gets further from the 0 point(center of the universe).

Basically, can you expand on what your saying?

Yes yes, 100 times yes.
Scroll down on the linked page to find the post I made 5 months ago concerning this. Below is a small quote from my post where I talk specifically about the universe collapsing, the entire thing is much longer.
http://www.theepochtimes.com/n3/948138-looming-crisis-in-physics-answer-could-be-in-other-dimensions/
“Waves in our universe are attempting to get back to zero, to normalize the universal equation back to 0. Think of air being sucked into a vacuum. Problem is there is a bottleneck of sorts. As 0.2*infinity*x tries to move to 0.0, 0.4*infinity*y tries to move to 0.0 at the same time. So they split the difference. 0.2 becomes 0.1 and 0.4 becomes 0.2. Keep the astrological constant of 0.2/0.4 or 0.1/02 (of course I am ignoring the 3rd coordinate). On the otherside of zero is a bunch of frequencies that add up to be the exact opposite, or the superpartner.”

Relativity is a neat thing. It means the universe can be confined in the space i, yet we can never reach the edge. It also means we can be collapsing, yet seem to be expanding. Long as everything collapses at an even rate, who would know?

All the holes science punched in this, are straight silly. If the universe is shrinking, then the vibration of sub-atomic particles is the equalizing force. Vibration at this level is what dictates time, if you change the speed of vibration then time changes and that accounts for speed of light and gravitation changes or lack there of.
As I mentioned above in my quote, it’s all relative to each other and they all move accordingly. If they keep an even movement, then you can’t detect gravity changes over time. Because from your relative stand point, it hasn’t changed.
Not magic, simple. 5 months ago, I dismissed his scientific holes – without a video to make them. The basic theory covers gravity, light, and time and why they would seem the same.
Apparently these people don’t understand the underlying theory at all. At all.

TO: Dalibor Frívaldský : The correct Web address for the paper.

Seems like a careless error to me.

The problem with the speed of light objection is that the speed of light is constant in any reference frame, but if the reference frame changes?
That is how anybody can slow light down (in a lab) to an “apparent” walking speed without a violation of the theory of relativity.
It has to be noted that speed changes seen by astronomers can have many causes besides the Doppler effect, such as gravity lenses, polarization changes due to electric fields, etc.
This is a very complicated area of physics, which, unfortunately, still needs a lot more research.

I disagree with the reasoning why the universe is not shrinking. According to the universal law of gravity the shrinking would imply creating larger distances and thus weaker gravity forces. Double the distance will the Force of gravity is fourthed.

You hear a lot about if the universe is shrinking or expanding or the speed of light is speeding up or slowing down. Imagine the universe in a wave form. ( A ripple of formation). It slows as it gets to the top and speeds up as it lowers to the bottom. The speed of light remains constant only to bend, being dependent on the gravitational pull of the massive suns. Depending on how close the massive suns are to each other and their gravitational strength, light can create an arc or a small S pattern. Something to think about in one’s spare time.

How about the universe is expanding/shrinking (changing) because there is a force outside its realm and time acting upon it, and that force is not subject to the realm, time and laws of nature/physics of the universe?

Condensing is a better analogy. A theory I have held for many years. If you are going to rethink it, you can’t just change one aspect and use the theories you did not change to prove it can’t be true. The notion that the gravitation constant would not change is of no more use in this model than our current model because everything is absolutely relative to the observer’s frame of reference, besides which, as we already know, gravity is not a force in non-Newtonian mechanics, which is where the constant comes from and it has been out the door for what, a hundred years? Why? Because Everything is absolutely relative and the gravitation constant can only tell you that basically, you, the observer, exists in the same way Newton, as an observer existed.

Gravity is not a force, it is travel through space-time – we are spiraling into our own gravity well. Deeper = More Dense is one way to think about it, but how in the heck can or should an assumption about mass remaining constant be made, justified or defended. In our grand rethink, what do we suppose radiation to be – well, it can certainly be energy given off as particles condense.

The notion of a vacuum or of a universally rigid ether – that space is a certain volume within which reality happens continues to hold back our understanding. Matter and energy define space and are wholly responsible for it’s existence. Get enough energy condensed in a given volume and it collapses into matter – under the right conditions, all the energy in a long weightless wave is trapped, it spirals in and forms a stable little chunk of ball lightning. The electrical forces in/out balanced with the magnetic forces out/in. There is actually no more mass than there was when the energy was stretched out as a wave (i.e. – no mass) – mass is a secondary construct created by the electro-magnetic interactions of this little ball lightning with others nearby.

Being absolutely relative within the same density framework, which we can envision as directly related to our radial distance from a ‘gravitational’ center, determines the size/strength of force/total energy – call it what you will, but every bit of everything is stuck in the same relative soup surrounding the observer. Relatively, everything is in the same proportions with the same relative energy levels as everything else in that framework, thus the constants will not change.

A rock falling to earth must give up energy to get there and we must pump energy into a system to lift it up, off and push it away from the gravitational center. This may very well be the key to how propulsion with no reaction mass works – the microwaves pump everything up and it drifts to the density level associated with where it belongs in terms of the radial distance from the gravitational center.

In a similar fashion, the speed of light will do you no good. Here we may envision the wave as containing a certain amount of energy and we may even imagine both the frequency and amplitude as being scaled up in regions of low gravity, condensing back down in perfect unison relative to the density of space-time where said energy is harvested (aka – measured, aka, condensed into a photon)

No problems with wave particle duality – it is all energy and one condenses it to a particle by the very act of detecting its existence. If an observer harvests the light energy in the dead of near gravity free space – they themselves, their spaceship and all of their equipment are within the same density state as will be the light that they measure at that particular point of observation.

Regardless of any of it, it brings up a great example of how we cherry pick the axioms that suit the conclusion we hope to draw – just like invoking the gravitational constant in a universe where gravity is not a force.

One that has always bugged me is, again, holding on to a classical notion that is clearly at odds with our obviously non-classical actual existence. And that is the doppler shift. Throughout the long, arduous process of accepting space-time curvature and dispensing with Euclidean geometry, we still presume and calculate our physics based on the notion that light travels in a straight line from point A to Point B across the vastness of space and time. The presumption that red shift is and can only be doppler shift as rendered by Euclidean geometry in a Newtonian universe while simultaneously dispelling such notions is absolutely maddening. We base everything on the red shift – the size and age of the universe, the ‘fact’ that it is expanding, the Big Bang theory – Everything! Yet, magically, light is exempt from the curvature of space-time – it makes a direct bee-line from point A to point B, traveling on a straight chord undercutting every curve of space-time. Is that what sub-space is? All the more maddening because the answer, I’m sorry, is, duhh. kind of obvious – isn’t it?

Take a sinusoidal shaped length of rubber band in a straight line and uniformly stretch it into a curve while keeping the endpoints fixed – well of course it is overall longer than it was before and the result is the frequency of the sinusoid decreases – it shifts toward the red! Red shift must be a measure of curvature more so, or in addition to, increasing distance. One might be inclined to think exclusively curvature because, say at the time some light escaped from a star 10 billion years ago, the star was 10 billion light years from earth. If the light is travelling free from the source, there is nothing to pull it no matter how fast the star is moving away from us. If we are similarly moving away from the star, perhaps the light reaches us 10.5 billion years later – but how in the heck can that red shift we observe have anything to do with how fast the 2 bodies are moving apart? Light is emitted and travels at the speed of light and nothing can travels faster, but the notion of a red shift tied to the source forces us to have an emission source traveling faster than the speed of light before any red shift occurs at all – it doesn’t make any sense and the stretching of the wave as a whole by being forced to follow a curved path makes complete sense.

So why do we cling to the former notion and beat the latter with a stick? On the other hand, the notion of light not travelling at all, but simply being the instantaneous excitation of an existing string by the 2 smallest distance apart end points to interact with it is also compelling and worthy of consideration to explain entanglement. Is anyone investigating how entangled photons from a distant start might be used for instantaneous communication across the galaxy, or between galaxies? Seems to me, if you are going to go there and say it is an instantaneous bridge immune to our feeble notions of distance, well then that is how advanced civilizations will be communicating, by manipulating naturally entangled photons. I get a little laugh every time I see an article saying something along the lines of “demonstrated quantum entanglement over the greatest distance yet, when distance, is in fact meaningless to the theory itself ” – Shouldn’t SETI be looking at twinklings from stars rather than searching the entire sky for radio waves?

So, back to everything condensing into its own gravity well. An astronaut flies into deep space at a very fast speed and comes back and everyone he/she knew has died of old age a long time ago. Did the astronaut really travel such a great distance at great speed? Or was it a smallish distance at a modest speed and it is simply that the further and further he/she moved away from the gravitational center of his/her home planet, the slower and slower became the rate of the passage of time within his/her relative framework? I put it to you that the universe doesn’t care and math will always serve it up just the way you like it. Such is the inescapably pervasive nature of relativity – The universe is going to do what the universe does and math is a superbly amenable descriptive labeling system whose one and only promise is “if you build it, they will come”. Rebuild your view of the universe with different assumptions or axioms that play together nicely and math will always reward consistently built input with valid predictions and punish you with ridiculous notions from inconsistent or flawed input. The universe doesn’t care how we describe it and math doesn’t care how we go about using it.

What possible experiments might be helpful to test the inward spiraling, condensing universe?
1) Instantaneous quantum entangled measurement comparisons between a LaGrange point and the surface of the earth, somehow, perhaps.
2) Ancient dead flesh and/or plant matter – the dinosaurs were huge, but were they really, at the time, relatively? Based on what we know about biomechanics in Earth’s family tree, we must be able to get a sense of how many cells, how many moving parts there are in a living animal-machine. With access to preserved ancient flesh, can we determine if the number of cells in a brontosaurus is more similar to those in a sperm whale or perhaps closer to the number of cells in Blue-Jay. If the latter, it favors an argument that everything was on a relative ‘puffed up’ scale millions of years ago.
3) This bit might actually demonstrate the yang of the yin and go toward an argument of a natural sustaining or hedging of size and or mass of Earth or any planet with photosynthetic life. Regardless, a great thought experiment with possible physical experiments to back it up. Here goes – we understand by conservation of mass and energy that when a photon strikes the right molecule in the right way, the energy is absorbed and excites the molecule into a higher energy state. Later, perhaps, the molecule collapses to the previous lower energy state accompanied by an emission of energy equivalent to the energy of the photon – all is preserved. Energy is absorbed and things heat up and then they cool as the excess energy is released. We also know energy and mass can be converted between these two forms. But it takes a tremendous amount of energy to produce a small mass and likewise a small mass can yield a tremendous amount of energy. Let’s set our sites on something a little less dramatic than nuclear bombs or turning lead into gold – Photosynthesis – magical life – producing food from sunlight. One photon and one molecule of a plant or microbe. What really happens is a mystery and the mysteries of life and the universe are vast and intricate. Just because we have lots of trouble converting energy into mass, should we then assume that photosynthesis is merely a trick of heating and cooling, or are we looking at a microscopic process that does just that, one photon at a time. A tiny, tiny amount of mass to be sure, but over nearly half the surface of the earth exposed at all times, and accounting for periodic cloud cover, snow and rocky outcroppings, but also multiple ‘addressable’ depths within bodies of water, how many photons participate in photosynthesis over the course of an eon? And if photosynthesis actually converts the energy of every participating photon into mass, how much more massive is the planet with life on it compared to a lifeless rock of similar initial mass? That’s the thought experiment. A physical experiment, assuming the thought experiment actually results in any kind of appreciable mass, may be out of reach in terms of the sensitivities required, but the idea would be a living plant within a closed system encased in glass, sitting on a scale in the sun. I would be afraid the glass could actually ‘breathe’ enough mass to render the experiment futile, unless the plant could be kept alive for a very long time. Perhaps the plant in a closed glass container with air pressure, the system itself then enclosed in a larger glass container in which a near vacuum is pulled and then direct sunlight onto it all and see if it gains weight.

That’s all the manifesto I can muster for now. Happy Physicing!

The accelerating expansion of the universe is due to the repulsive gravity of diffuse antimatter. Just as matter’s interaction with spacetime is attractive, antimatter’s opposing interaction with spacetime must be repulsive. This accounts for all observations and solves some of cosmology’s biggest mysteries, not the least of which is baryogenesis. As the early universe cooled, matter and antimatter coalesced from the primordial energy. They would usually self annihilate, but antimatter with repulsive gravity would tend to diffuse while matter with attractive gravity would tend to concentrate. Eventually enough concentrated matter gathered to form galaxies, stars, and planets while antimatter continued to diffuse and spread. Antimatter with repulsive gravity would be unable to form stars and therefore would never be fused into higher atomic number nuclei. So antimatter exists primarily as antiprotons or anti-hydrogen as positrons permit. There could be versions of anti-helium too, but only as created during the earliest moments after the Big Bang. This is why no antimatter structures have been observed in the empty regions of intergalactic space. It also explains why gamma rays from annihilations are not observed since they can only occur at the particle or atomic level. So the makeup of the universe is such that matter is concentrated in galaxies which are surrounded by diffuse antimatter in the spaces between. As the spaces between galaxies grows, the repulsive gravity of diffuse antimatter will first neutralize and then dominate over the attractive gravity of concentrated matter causing the accelerating expansion of the universe observed today.

## Question What are we expanding into?

In such an environment, I always remember that <5% is "ours" and the other >95% is dark energy and dark matter. Perhaps you could fill your "nothing" with some of these?

#### Spacedweller

I'm afraid I could not because that's something according to video in my post #4

Maybe someday we'll know more about dark energy and dark matter.

#### Catastrophe

##### Approaching asteroid? Is this THE one?

Or if you like linear expansion:

Is Minkowski spacetime a solution of the Friedmann Equations? (1 Viewer)

timmdeeg
Gold Member
1,13182
The empty FRW-universe with curvature parameter k=−1 and expanding linearly is well known. Also that it is mathematically equivalent (after a coordinate transformation) with the Milne universe which also expands linearly.

I wonder if the Friedmann Equations have another solution (I remember something like that, but perhaps wrongly): The static Minkowski spacetime. If true this seems to require H=0 and k=0 and thus ρ/ρc=1. However this doesn't seem to make sense because in the empty universe the densities are zero and thus k has no defined value.

The mind doesn't create the truth - but rather stumbles across it
- Aurelius Augustinus -

From: Cosmology Forum My emphasis.

#### Helio

I'm not someone who has even tried to study GR, but from what I have gathered over time.

Originally, Friedmann demonstrated that gravity in GR would either expand or contract the universe based on his math. His work given to Einstein was on a mathematical level not a physics approach (suggesting a real expansion or contraction). Einstein later recognized Friedmann's, and Lemaitre's, work. [Lemaitre, however, took his work beyond math and into physics he calculated the first attempt at an expansion rate using Slipher's redshifts.]

Einstein recognized, but inadequately, that his model had no expansion but that some pushing force within spacetime itself must exist to keep it from collapsing, hence his light-duty cosmological term, that proved way too short for modern observations with acceleration.

Yes, and deSitter discovered that redshifts would exist in his Static universe but. with no matter!. I'm sure he was just simplifying GR to get on a path to a better model. But he was able to show that a static universe could have increasing redshifts with distance in a static universe. Einstein's own model was fine with matter but he could not figure out how redshifts would work in what all knew was the actual universe - a static one. Lemaitre solved both their problems with expansion.

I do know that Hubble had worked with deSitter at IAU events in Europe and Hubble, no doubt, respected de Sitter. So, IMO, since redshifts could be shown within GR, by the great deSitter, then perhaps redshifts were not a result of expansion. He chose to letter theorists duke it out and he not once argued that the universe is expanding. He did produce, with Humason, the best known data giving the correlation of redshift and distance, hence people just connected the two big dots and assumed he was demonstrating an expansion rate, which, again, he never did.

#### Catastrophe

##### Approaching asteroid? Is this THE one?

My thought here:
"In such an environment, I always remember that <5% is "ours" and the other >95% is dark energy and dark matter. Perhaps you could fill your "nothing" with some of these?
was that, since we are aware of "absence of matter" only within the <5% have we any justification to assert that that same "nothing" is applicable to the other >95%? Do we know that our "nothing" is not simply brought about by dark whatever, taking up the space vacated by mass?

#### Spacedweller

This opens a whole host of interesting questions one may ask, but if your point is that dark matter and/or energy could explain "nothing" then this is theoretically impossible.

Isn't the effect of dark energy supposed to be visible in observable space?, that is the expansion of the universe.

#### Catastrophe

##### Approaching asteroid? Is this THE one?

This opens a whole host of interesting questions one may ask, but if your point is that dark matter and/or energy could explain "nothing" then this is theoretically impossible.

Isn't the effect of dark energy supposed to be visible in observable space?, that is the expansion of the universe.

#### Spacedweller

No actually this is really interesting because I never considered dark energy, vacuum or pressure for these kinds of questions.

A vacuum, dark energy, dark matter, nothing etc. may have something in common or related, I think I'll read more about this stuff only for the purpose to understand more.

#### Catastrophe

##### Approaching asteroid? Is this THE one?

No actually this is really interesting because I never considered dark energy, vacuum or pressure for these kinds of questions.

A vacuum, dark energy, dark matter, nothing etc. may have something in common or related, I think I'll read more about this stuff only for the purpose to understand more.

Sorry I can't refer to anything. It just came out of my philosophically flighty senile left hemisphere. If you find anything, I'd be grateful if you would inform me

P.S If it helps, it was shortly after I wrote post #8 in "What intrigues you about space".

#### IG2007

##### "Don't criticize what you can't understand. "

That is more of a Philosopher's approach than a Physicist's approach. But, I respect that.

According to the Big Bang Theory, the Universe is everything that exists. The word "Universe" comes from the Latin word "Universus" or "Universum," which literally means everything combined into one single whole. Now, if we consider the Universe to be something that is everything-that-exists and infinite, we get that there is no question of the Universe having an edge or having a centre, because something like that cannot exist. So, there is no question of an expansion or reduction, because infinity plus anything is infinity. But, if we consider the universe to be everything-that-exists and finite, we get that there is indeed a so-called "edge" of the universe and also a centre, but due to the way of expansion that happens in our Universe, it is impossible to find it. I can literally call myself the centre of the Universe and I won't even be lying! ( ) Now, if you strictly adhere to the Big Bang Theory, there is no question of the Universe or time or space or matter or energy, being infinite, because. well, I guess I have again misplaced the sentences.

But now, you might say, Science believes nothing but proof, what proof do I have that the Universe has nothing outside it? Well, nothing. And so do you, if you say that the Universe has infinity outside it. Now, as we are without proof, and Science ends here. I guess, I also have to take the help of Philosophy here. I have never beheld or heard or felt or tasted or smelled infinity. And nor has any human ever. I am about to make a parody of an old quote, "Nature abhors infinity."

## Cosmon Field

Since the 1990's Wetterich has been playing with 'cosmon' models containing a Higgs-type scalar field that interacts with gravity. The energy-momentum of such a scalar field acts as dark energy that causes the Hubble expansion of the universe to accelerate.

In the present paper Wetterich again toys with a cosmon model. He considers a model in which the cosmon field strength couples to gravity thereby defining the Planck mass scale, and in which a simple harmonic oscillator potential for the cosmon field is included. The model results in the field strength increasing exponentially with time. The present value of this field strength can be associated with the Planck mass, while the present value of the harmonic potential term accounts for the dark energy density. Interestingly, at very early stages of the universe's evolution this same term causes an inflationary expansion.

When describing the evolution of the universe from a cosmon field perspective, depending on the stage of evolution, cosmological distances remain constant or even shrink. The Planck mass, however, keeps growing and the Planck length and Planck time both keep shrinking. As a result, the Planck density sharply increases.

The other way around, the further one goes back, the more the Planck density shrinks. The consequence is that there is no limit to how far one can go back, no big bang singularity is ever encountered. The further one goes back in time, the slower clocks tick and in a way the universe becomes static.

This all seems in stark contrast with our mental picture of the big bang. However, Wetterich shows that when describing the cosmological evolution in terms of a scalar field obtained by rescaling the cosmon field via a logarithmic transform, the common picture of the evolution of the universe emerges: the Planck scale and all particle masses remain fixed, the universe expands, and a Big Bang singularity pops up.

Wetterich stresses that his model provides an alternative perspective on the standard cosmological model, rather than an alternative model:

"Our model should be interpreted as a new complementary picture of cosmology, not as opposing the more standard picture of an expanding universe. The different pictures are equivalent, describing the same physics. This can be seen by a redefinition of the metric, which leads to the “Einstein frame” with constant Planck mass and particle masses and an expanding universe. In the Einstein frame the big bang has a singularity, however. The possibility of different choices of fields describing the same reality may be called “field relativity”, in analogy to general relativity for the choice of different coordinate systems. Field relativity underlies the finding that strikingly different pictures, as an expanding or a shrinking universe, can describe the same reality."

So is the universe expanding or are we shrinking?

The correct answer is "whatever you prefer". Physicists like such freedom of choice as it gives them the opportunity to simplify their models by changing perspective whenever convenient. The key question then is: "will Wetterich's perspective allow us to simplify our cosmological models?" So far, cosmologists have worked with models in which gravity remains constant, simply because allowing for a dynamic gravitational constant was assumed to represent a burden without any clear advantage. Wetterich now has challenged this assumption. Time will tell how useful varying gravity models will be.

I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune

## The Incredible Expanding/Shrinking Universe

T he Observable Universe is roughly 90-Billion Light Years in diameter, and estimated to be 13.5-Billion years old, because it cannot be younger than the objects that exist within it, and by calculating the age of the objects within the Observable Universe we are able to put a limit on its age. Now if your wits are quick about you, and you understand that a ‘light-year’ is simply a measure of ‘how far light can travel in a single Earth-year’, you may be asking yourself: “If the Observable Universe is only 13.5-Billionyears old then how can it be 90-Billion Light Years in diameter?”

the answer: Expansion! …for the past 13-Billion-plus years, the Universe has been expanding at a momentously terrifying rate.

We all are probably aware of the cosmic force known as Gravity, which is the force of attraction that which masses exert upon one another, it’s what keeps your feet planted on the ground, and is not only the force stabilizing the inertia of our Solar System, but the force stabilizing the revolutions (or orbits) of these massive celestial bodies such as Galaxies a force that which will one day cause the Andromeda Galaxy and the Milky Way Galaxy to meet in a collision or merger of epic proportions. Creating an all new type of Galaxy in the process.

The Observable Universe may seem to be extremely packed with matter: Planets, Stars, Solar Systems, Galaxies, Superclusters etc., all enforcing their gravitational will on one another, but it is also exponentially massive, and these objects are all substantially spread out, with great swaths of empty space existing between them.

And this is where the Expansion of the Universe comes into play.Think of Expansion as the opposite of the force of Gravity, instead of attracting masses together, it is actively repelling masses away from one another. And instead of this force being generated by a large mass, it is emanating from one of these huge swaths of empty space.

The Hubble Constant is the rate at which astrophysicists have measured the current Expansion occurring within the Observable Universe, and it is close to 46-miles per second per a distance of 3-million light years. That’s a bit of a mouthful, but basically just means, the expansion of the universe is happening really, really fast- and the further away you are from something, than the faster and faster the rate at which that something and you are moving (or expanding) away from one another. This is where the language of the “acceleration” of the universe comes from.

So as Gravity pulls certain areas of space closer together, such as condensing all the Galaxies of the Local Group to one day collide/merge, an area of space that contains a sufficient amount of matter (or mass) to stem the tide of Expansion and stabilize its proximity there is another force pushing everything outside of the Local Group further away from it. And in this particular instance the repelling force of Expansion is winning the tug of war against the attracting force of Gravity.

As this expansion continues to occur it will create smaller and more concentrated gravitational pockets of objects and matter, among vaster-widening voids of deep darkness and as the expansion of the universe keeps “accelerating” in these ever widening swaths of empty space, and exceeds the speed of light, all the billions and billions of Stars outside the Local Group (the rest of the Laniakea Supercluster and beyond) will completely vanish from our sight they’ll just be too far away, and thus, moving away at such a fast rate, that not even the speed of their light will ever be able to reach us. Eventually, all we will be able to see from Earth is the Local Group, and that will ‘in effect’ become the (new) Observable Universe, our very scope of the Cosmos will be further diminished by the continuous Expansion of the Universe.

The expansion of the universe is happening at large-scales. This means that, if you choose two galaxies, they are moving away from each other at a speed proportional to their distance. The space between the Sun and the Earth, for instance, is not expanding. In fact, some galaxies close to us appear blue-shifted due to their peculiar velocities. The physical constants must be very complicated functions of space and time to mimic such a phenomenon. The almost-FRW universe yields the expansion quite naturally. So, in a sense, you are right that it is because of Occam's razor, but, isn't all of "established" physics due to Occam's razor? :)

Whether a quantity such as length is "shrinking" depends on the choice of units of length. If we used a time-dependent unit of length, we could make the numerical value of each length shrink or expand or do anything we like.

But we are using sensible units of length that are "naturally constant". For example, one meter is defined as 1/299,792,458 of a light second (the distance traveled by light in the vacuum in 1 second) and one second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

So we know that the wavelength of some atomic radiation is a constant multiple of one meter. The same is true for other types of atomic radiation because the ratios of wavelength are constant in time. And the same is true for various other lengths such as radii of planets or stars composed of a fixed material at normal pressure: their size is also de facto fixed as a multiple of the wavelength of some atomic radiation.

So as long as we use sensible units of length, and we do, the constancy of the lengths of various things enumerated above is automatically guaranteed. What you describe may be easily achieved by using unnatural time-dependent units of length, however.

## Alvy Singer’s Terrible Fear

One of my favorite moments in Woody Allen’s film Annie Hall is when Alvy Singer (Allen’s alter ego) is shown having an existential crisis as a little boy. His mother summons a psychiatrist, one Dr. Flicker, to find out what’s wrong.

“Why are you depressed, Alvy?” Dr. Flicker asks.

“The universe is expanding,” Alvy says. “The universe is everything, and if it’s expanding, some day it will break apart and that will be the end of everything.”

“Why is that your business?” interrupts his mother. Turning to the psychiatrist, she announces, “He’s stopped doing his homework!”

“What’s the point?” Alvy says.

“What has the universe got to do with it!” his mother shouts. “You’re here in Brooklyn! Brooklyn is not expanding!”

Dr. Flicker jumps in: “It won’t be expanding for billions of years, Alvy, and we’ve got to enjoy ourselves while we’re here, eh? Ha ha ha.” (Cut to a view of the Singer house, which happens to be under the Coney Island roller coaster.)

I used to take Dr. Flicker’s side in this matter. How silly to despond about the end of everything! After all, the cosmos was born only around 13 billion years ago, when the Big Bang happened, and parts of it will remain hospitable to our descendants for a good hundred billion years, even as the whole thing continues to spread out.

A half-dozen years ago, however, astronomers peering through their telescopes began to notice something rather alarming. The expansion of the universe, their observations indicated, was not proceeding at the stately, ever-slowing pace that Einstein’s equations had predicted. Instead, it was speeding up. Some “dark energy” was evidently pushing against gravity, sending galaxies hurtling away from one another at a runaway rate. New measurements earlier this year confirmed this strange finding. Last July 22, the New York Times ran an ominous headline: “ASTRONOMERS REPORT EVIDENCE OF ‘DARK ENERGY’ SPLITTING THE UNIVERSE.” David Letterman found this so disturbing that he mentioned it several consecutive nights in his Late Show monologue, wondering why the Times buried the story on Page A-13.

Until recently, the ultimate destiny of the universe looked a little more hopeful—or remote. Back around the middle of the last century, cosmologists figured out that there were two possible fates for the universe. Either it would continue to expand forever, getting very cold and very dark as the stars winked out one by one, the black holes evaporated, and all material structures disintegrated into an increasingly dilute sea of elementary particles: the Big Chill. Or it would eventually stop expanding and collapse back upon itself in a fiery, all-annihilating implosion: the Big Crunch.

Which of these two scenarios would come to pass depended on one crucial thing: how much stuff there was in the universe. So, at least, said Einstein’s theory of general relativity. Stuff—matter and energy—creates gravity. And, as every undergraduate physics major will tell you, gravity sucks. It tends to draw things together. With enough stuff, and hence enough gravity, the expansion of the universe would eventually be arrested and reversed. With too little stuff, the gravity would merely slow the expansion, which would go on forever. So, to determine how the universe would ultimately expire, cosmologists thought that all they had to do was to weigh it. And preliminary estimates—taking account of the visible galaxies, the so-called “dark matter,” and even the possible mass of the little neutrinos that swarm though it all—suggested that the universe had only enough weight to slow the expansion, not to turn it around.

Now, as cosmic fates go, the Big Chill might not seem a whole lot better than the Big Crunch. In the first, the temperature goes to absolute zero in the second, it goes to infinity. Extinction by fire or by ice—what’s to choose? Yet a few imaginative scientists, haunted, like Woody Allen, by visions of the end of the universe, came up with formulations of how our distant descendants might manage to go on enjoying life forever, despite these unpleasant conditions. In the Big Chill scenario, they could have an infinity of slower and slower experiences, with lots of sleep in between. In the Big Crunch scenario, they could have an infinity of faster and faster experiences in the run-up to the final implosion. Either way, the progress of civilization would be unlimited. No cause for existential gloom.

So, Letterman had reason to be upset by the dark energy news. It spells inescapable doom for intelligent life in the far, far future. No matter where you are located, the rest of the universe would eventually be receding from you at the speed of light, slipping forever beyond the horizon of knowability. Meanwhile, the shrinking region of space still accessible to you will fill up with a kind of insidious radiation that would eventually choke off information processing—and with it, the very possibility of thought. We seem to be headed not for a Big Crunch or a Big Chill but something far nastier: a Big Crackup. “All our knowledge, civilization and culture are destined to be forgotten,” one prominent cosmologist has declared to the press. It looks as if little Alvy Singer was right after all. The universe is going to “break apart,” and that will indeed mean the end of everything—even Brooklyn.

Hearing this news made me think of the inscription that someone once said should be on all churches: important if true. Applied to cosmology—the study of the universe as a whole—that is a big “if.” Cosmic speculations that make it into the newspapers should often be taken with a pinch of salt. A few years ago, some astronomers from Johns Hopkins made headlines by announcing that the cosmos was turquoise two months later they made headlines again by announcing that, no, it was actually beige. This may be a frivolous example, but even in graver matters—like the fate of the universe—cosmologists tend to reverse themselves every decade or so. As one of them once told me, cosmology is not really a science at all since you can’t do experiments with the universe. It’s more like a detective story. Even the term that is sometimes applied to theorizing about the end of the universe, “eschatology” (from the Greek word for “furthest”) is borrowed from theology.

Before I was going to start worrying about the extinction of absolutely everything in some inconceivably distant epoch, I thought it would be a good idea to talk to a few leading cosmologists. Just how certain were they that the cosmos was undergoing a disastrous runaway expansion? Was intelligent life really doomed to perish as a result? How could they, as scientists, talk about the ultimate future of “civilization” and “consciousness” with a straight face?

It seemed natural to start with Freeman Dyson, an English-born physicist who has been at the Institute for Advanced Study in Princeton since the 1940s. Dyson is one of the founding fathers of cosmic eschatology, which he concedes is a “faintly disreputable” subject. He is also a fierce optimist about the far future, one who envisions “a universe growing without limit in richness and complexity, a universe of life surviving forever and making itself known to its neighbors across unimaginable gulfs of space and time.” In 1979, he wrote a paper called “Time Without End,” in which he used the laws of physics to show how humanity could flourish eternally in a slowly expanding universe, even as the stars died and the chill became absolute. The trick is to match your metabolism to the falling temperature, thinking your thoughts ever more slowly and hibernating for longer and longer periods while extraneous information is dumped into the void as waste heat. In this way, Dyson calculated, a complex society could go on perpetually with a finite energy reserve, one equivalent to a mere eight hours of sunlight.

The day I went to see Dyson, it was raining in Princeton. It took me a half-hour to walk from the train station to the Institute for Advanced Study, which sits by a pond in 500 acres of woods. The institute is a serene, otherworldly place. There are no students to distract the eminent scientists and scholars in residence from pursuing their intellectual fancies. Dyson’s office is in the same building where Einstein spent the last decades of his career fruitlessly searching for a unified theory of physics. An elfin, courtly man with deep-set eyes and a hawklike nose, Dyson frequently lapsed into silence or emitted snuffles of amusement. I started by asking him whether the evidence that the universe was caught up in an accelerated expansion had blighted his hopes for the future of civilization.

“Not necessarily,” he said. “It’s a completely open question whether this acceleration will continue forever or whether it will peter out after a while. There are several theories of what kind of cosmic field might be causing it and no observations to determine which of them is right. If it’s caused by the so-called ‘dark energy’ of empty space, then the expansion will keep speeding up forever, which is bad news as far as life is concerned. But if it’s caused by some other kind of force field—which, out of ignorance, we label ‘quintessence’—then the expansion might well slow down as we go into the future. Some quintessence theories even say that the universe will eventually stop expanding altogether and collapse. Of course, that, too, would be unfortunate for civilization since nothing would survive the Big Crunch.”

Well, then, I said, let’s stick with the optimistic scenario. Suppose the acceleration does turn out to be temporary and the future universe settles into a nice cruise-control expansion. What could our descendants possibly look like a trillion trillion trillion years from now, when the stars have disappeared and the universe is dark and freezing and so diffuse that it’s practically empty? What will they be made of?

“The most plausible answer,” Dyson said, “is that conscious life will take the form of interstellar dust clouds.” He was alluding to the kind of inorganic life forms imagined by the late astronomer Sir Fred Hoyle in his 1957 science fiction novel, The Black Cloud. “An ever-expanding network of charged dust particles, communicating by electromagnetic forces, has all the complexity necessary for thinking an infinite number of novel thoughts.”

How, I objected, can we really imagine such a wispy thing, spread out over billions of light-years of space, being conscious?

“Well,” he said, “how do you imagine a couple of kilograms of protoplasm in someone’s skull being conscious? We have no idea how that works either.”

Practically next door to Dyson at the institute is the office of Ed Witten, a gangly, 50-ish fellow who is widely regarded as the smartest physicist of his generation, if not the living incarnation of Einstein. Witten is one of the prime movers behind superstring theory, which, if its hairy math is ever sorted out, may well furnish the Theory of Everything that physicists have long been after. He has an unnerving ability to shuffle complicated equations in his head without ever writing anything down, and he speaks in a hushed, soft voice. Earlier this year, Witten was quoted in the press calling the discovery of the runaway expansion of the universe “an extremely uncomfortable result.” Why, I wondered, did he see it that way? Was it simply inconvenient for theoretical reasons? Or did he worry about its implications for the destiny of the cosmos? When I asked him, he agonized for a moment before responding, “Both.”

Yet Witten, too, thought there was a good chance that the runaway expansion would be only temporary, as some of the quintessence theories predicted, rather than permanent, as the dark-energy hypothesis implied. “The quintessence theories are nicer, and I hope they’re right,” he told me. If the acceleration does indeed relax to zero, and the Big Crackup is averted, could civilization go on forever? Witten was unsure. One cause for concern was the possibility that protons will eventually decay, resulting in the dissolution of all matter within another, oh, 10^33 years or so. Freeman Dyson had scoffed at this when I talked with him, pointing out that no one had ever observed a proton decaying, but he insisted that intelligent beings could persist even if atoms fell to pieces, by re-embodying themselves in “plasma clouds”—swarms of electrons and positrons. I mentioned this to Witten. “Did Dyson really say that?” he exclaimed. “Good. Because I think protons probably do decay.”


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## Find the electric field

Inside a sphere of radius a and dielectric constant ε1, there is a uniform charge density ρv1. Butted up against this sphere is another sphere extending from r=a to r=b having a dielectric constant ε2 and a uniform charge density ρv2. Outside the sphere is free space and the conductivity is zero everywhere. Find the electric field everywhere.

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# Need Help with Abstract Algebra Please

1. Oct 15, 2004

My question is regarding abstract algebra.

Suppost that B is a 10-cycle.
For which integers i between 2 and 10 is
B^(i) also a 10-cycle?

I know that the answer is 3, 7, and 9 I just don't know
how you arrive at these numbers. If someone could explain the
process clearly to me I would greatly appreciate that.
Thank you sooo much. :-)

2. Oct 15, 2004

### NateTG

The $$i$$ are values that are coprime (have no common factors other than 1) with 10.

Here's a general proof:

Let's say we have some element $$g$$ with order $$n$$. Then $$g^i$$ has order $$\frac{n}{<n,i>}$$ where $$<n,i>$$ is the greatest common factor of $$n$$ and $$i$$.

Proof:
$$({g^{i}})^{\frac{n}{<n,i>}}=g^{i \times \frac{n}{<n,i>}}$$
but
$$i = k \times <n,i>$$
for some $$k$$ so
$$g^{i \times \frac{n}{<n,i>}}=g^{k \times <n,i> \times \frac{n}{<n,i>}}=g^{k \times n}=g^{n\times k}=(g^{n})^{k}=e^k=e$$
so the order ok $$g{i}$$ is at most $$\frac{n}{<n,i>}$$

Now, let's say we have some $$j$$ so that
$$e=({g^{i}})^j=g^{ij}$$
then, since the order of $$g$$ is $$n$$
so $$n | ij$$ ($$n$$ divides $$ij$$)
so $$\frac{n}{<n,j>} | j \Rightarrow j \geq \frac{n}{<n,i>}$$

So the order of $$g^i$$ is $$\frac{n}{<n,i>}$$.

In this particular case, you have $$\frac{n}{<n,i>} = n$$ so $$<n,i>=1$$.

3. Oct 15, 2004


text:
## Atheist to lead "Prayer" in Florida council meetin

Hot topics in delusion and rationalization.
Andonyx
Posts: 660
Joined: Wed Jun 09, 2004 3:47 pm

### Atheist to lead "Prayer" in Florida council meetin

It was Councilman John Dingfelder's turn to pick prayer givers for July. After talking with Ed Golly, chairman of Atheists of Florida, Dingfelder chose an atheist for one meeting.

Everybody deserves their opportunity, as long as it's respectful,'' he said.

What's interesting is that pretty much everybody interviewed in the article had an attitude of, "Yeah, okay whatever."
Last edited by Andonyx on Fri Jul 16, 2004 7:16 pm, edited 1 time in total.
Sundog
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That was probably the actual text of the prayer, too!
Scot C. Trypal
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I was asked by my rep. to do this in my state legislature, but decided it wasn’t appropriate (also worried it would hurt me politically much more than help). The Unitarian minister took my place and did a much better job than I could have.

Should an agnostic or atheist involve themselves in these sort of religious/governmental ceremonies? It just seemed right to decline but I’m not sure. I still don’t even know what to do when my in-laws pray at dinner. Say amen or no? Both options seem disrespectful.
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Andonyx
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### UPDATE!

Here's a little follow-up:
TAMPA -- Three Tampa city council members walked out of chambers rather than listen to an atheist give the opening invocation.

Council members Kevin White, Mary Alvarez and Rose Ferlita left their seats Thursday rather than listen to Michael R. Harvey, a member of Atheists of Florida who had been invited by council member John Dingfelder to offer the invocation.

Even before Harvey spoke, White was pushing to cancel the invocation. These are sacred moments that refer to a supreme being, White said, and this speaker doesn't believe in God.

We have never had people of an atheist group represent Americans,'' White said. And I don't think it is appropriate in this setting.''
Quester_X
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We have never had people of an atheist group represent Americans,'' White said. And I don't think it is appropriate in this setting.''
Jackasses.
You'll all be mine, in the end.
Nyarlathotep
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Quester_X wrote:
We have never had people of an atheist group represent Americans,'' White said. And I don't think it is appropriate in this setting.''
Jackasses.
Hey, at least it's not as bad as when Bush Sr. said that atheists shouldn't even be considered citizens.

It's just more evidence that atheists are a convenient group for politicians to bash. Replace the word 'atheist' in that sentence with just about any religion except maybe Satanists, and people would flip out. But since they bashed atheists, it's okay with most people and a certain (large) segment of the population is likely scrambling for their wallets even now to assure these guys' re-election.
MLynn
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Nyarlathotep wrote:
Quester_X wrote:
We have never had people of an atheist group represent Americans,'' White said. And I don't think it is appropriate in this setting.''
Jackasses.
Hey, at least it's not as bad as when Bush Sr. said that atheists shouldn't even be considered citizens.
O, tentacled one, did Bush really say this about atheists?
Obey the zombie whippet or she will eat your brain
I for one welcome our zombie Christian overlord - Philip
Quester_X
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O, tentacled one, did Bush really say this about atheists?
Yes, he did. And more. To the face of the head of American Atheists. Jerkwad.
You'll all be mine, in the end.
MLynn
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Quester_X wrote:
O, tentacled one, did Bush really say this about atheists?
Yes, he did. And more. To the face of the head of American Atheists. Jerkwad.
So much for the First Amendment...
Obey the zombie whippet or she will eat your brain
I for one welcome our zombie Christian overlord - Philip
Nigel
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Quester_X wrote:
O, tentacled one, did Bush really say this about atheists?
Yes, he did. And more. To the face of the head of American Atheists. Jerkwad.
[derail]I love this phrase Quester: To the face of the head

I'm not making serious fun of you....I do like that phrasing.....

[/derail]
If you can't laugh, what good are you?

I thought I won't submit this...but who cares...let it roll. -Pillory
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MLynn wrote: ...[D]id Bush really say this about atheists?
"I don't know that Atheists should be considered as citizens, nor should they be considered patriots. This is one nation under God." -- George H.W. Bush, August 27, 1987
[size=75]"I was misinformed." - Rick Blaine, from [i]Casablanca[/i][/size]
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Nyarlathotep
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MLynn wrote:
Nyarlathotep wrote:
Quester_X wrote:
We have never had people of an atheist group represent Americans,'' White said. And I don't think it is appropriate in this setting.''
Jackasses.
Hey, at least it's not as bad as when Bush Sr. said that atheists shouldn't even be considered citizens.
O, tentacled one, did Bush really say this about atheists?
AS other have pointed out, yes he did. It wasn't just some little slip of the tongue either. When pressed on the issue, his spokespeople neither apologized nor explained his comments. His spokespeople told one guy who was hounding him on the issue "Belive in God and get off our backs"

Here is a little history on the incident


text:
View Poll Results: Indefinite integration of log(cos(x))? Does not Exist 0 0% No Idea 0 0% Can be Solved 4 100.00% Multiple Choice Poll. Voters: 4. You may not vote on this poll

## Indefinite Integration of function's like log(cos(x))???

Can anyone please help me to calculate Indefinite Integration of function's like log(cos(x))???.
 PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor
 Recognitions: Homework Help To integrate something like f(g(x)) you need to use a trick - and it is not always easy. Usually you hope that you can make a substitution like u=g(x) so that dx=du/g'(x) and g'(x) can be expressed in terms of u. If h(u)=g'(x) then f(g(x))dx becomes f(u)du/h(u) which may or may not be an improvement. For a function like log(g(x)) you could be tempted try for g(x)=eh(x) and realise that log(x)=ln(x)/ln(10). then log(g(x))dx becomes h(x)dx/ln(10) ... but just try doing that non-trivially ... since you are just saying that h(x)=ln(g(x)) which is proportional to what you started with. For a sin or a cos inside the log, express the function as a sum of exponentials. Then substitute (in the case of cosine x) u=eix+e-ix ref: AIEEE forum [edit: why is this a poll? It's not a matter of opinion...]
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus The integral $\int \log(\cos(x))dx$ can not be solved by elementary functions. To solve the integral, we need the polylogarithmic function. So the integral does exist, but we just can't find it.

## Indefinite Integration of function's like log(cos(x))???

 Quote by micromass The integral $\int \log(\cos(x))dx$ can not be solved by elementary functions. To solve the integral, we need the polylogarithmic function. So the integral does exist, but we just can't find it.
Sorry if this question sounds stupid, but what is polylogarithmic function?

And more importantly, when do we use it?

 Quote by Najmoddin Can anyone plz help me to calculate Indefinite Integration of function's like log(cos(x))???.
I haven't thought of the method yet, but the answer looks complicated:
http://www.wolframalpha.com/input/?i...8cos%28x%29%29

Courtesy Wolfram Alpha.

Even the graph of the integral is not simple and continuous and there is an imaginary component.

Blog Entries: 8
Recognitions:
Gold Member
Science Advisor
Staff Emeritus
 Quote by Byron Chen Sorry if this question sounds stupid, but what is polylogarithmic function?
It is not stupid at all. It's an advanced function. It is defined as

$$Li_s(z)=\sum_{n=1}^{+\infty}{\frac{z^k}{k^s}}$$

for |z|<1. It is defined for $|z|\geq 1$ by "analytic continuation".

An example: if s=1, we get $Li_1(z)=\log(z)$ the ordinary logarithm.
For s=2, we get
$$Li_2(z)=\int_0^z \frac{\log(z)}{z}dz$$
For s=3, we have
$$Li_3(z)=\int_0^z \frac{Li_2(z)}{z}dz$$

In general, we always have
$$Li_s(z)=\int_0^z \frac{Li_{s-1}(z)}{z}dz$$

This might look confusing. The only thing I want to make clear is that the polylogarithm is usually not always a elementary function (except for special values such as s=1)

 Quote by micromass It is not stupid at all. It's an advanced function. It is defined as $$Li_s(z)=\sum_{n=1}^{+\infty}{\frac{z^k}{k^s}}$$ for |z|<1. It is defined for $|z|\geq 1$ by "analytic continuation". An example: if s=1, we get $Li_1(z)=\log(z)$ the ordinary logarithm. For s=2, we get $$Li_2(z)=\int_0^z \frac{\log(z)}{z}dz$$ For s=3, we have $$Li_3(z)=\int_0^z \frac{Li_2(z)}{z}dz$$ In general, we always have $$Li_s(z)=\int_0^z \frac{Li_{s-1}(z)}{z}dz$$ This might look confusing. The only thing I want to make clear is that the polylogarithm is usually not always a elementary function (except for special values such as s=1)
Thanks a lot.

Can you also explain when we usually use this function?

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 Quote by Byron Chen Thanks a lot. Can you also explain when we usually use this function?
You can use it for a lot of things. One example is of course to calculate integrals. Many integrals can be calculated using polylogarithmic functions.

Another example is the connection between the Riemann-zeta function. We have that

$$Li_s(1)=\zeta (s)$$

and the zeta function has of course many applications in number theory. As such, the polylogarithmic functions become important in number theory.

But to be honest, you'll never see these functions unless reading quite advanced books in complex analysis or (analytic) number theory.

 Quote by micromass You can use it for a lot of things. One example is of course to calculate integrals. Many integrals can be calculated using polylogarithmic functions. Another example is the connection between the Riemann-zeta function. We have that $$Li_s(1)=\zeta (s)$$ and the zeta function has of course many applications in number theory. As such, the polylogarithmic functions become important in number theory. But to be honest, you'll never see these functions unless reading quite advanced books in complex analysis or (analytic) number theory.
Just a little curious about the integration part. In which cases do you usually use the polylogarithmic functions when you do integration? Like is there certain types of functions where taking the integral in such a manner is useful?

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Homework Help
 Quote by Byron Chen I haven't thought of the method yet, but the answer looks complicated
<mutter> I tells people the method, I gives them a link to a walkthrough, does anybody follow the link? Hah! When I was young we followed advice oh yes ... we didn't have links: we had to go to these big buildings with papery things in them and thumb through drawers and drawers of small typed cards to find our information and we were better for it <grumble> time for bed...

Blog Entries: 8
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 Quote by Byron Chen Just a little curious about the integration part. In which cases do you usually use the polylogarithmic functions when you do integration? Like is there certain types of functions where taking the integral in such a manner is useful?
Well, for example, if you encounter an integral like

$$\int \frac{\log(x)}{x}dx$$

then you can solve it using $Li_2(x)$. Likewise, if you can reduce an integral to that, then you can also solve it.

I'm sure there's more to it, but I'm not an expert on this (by far).

Recognitions:
Homework Help
 Quote by Simon Bridge ... For a function like log(g(x)) you could be tempted try for g(x)=eh(x) and realise that log(x)=ln(x)/ln(10). ...
I would assume the OP was using the mathematician's convention of $\log x = \ln x$ rather than the engineering convention that $\log(x) = \log_{10}(x)$.

 Quote by micromass It is not stupid at all. It's an advanced function. It is defined as $$Li_s(z)=\sum_{n=1}^{+\infty}{\frac{z^k}{k^s}}$$ for |z|<1. It is defined for $|z|\geq 1$ by "analytic continuation". An example: if s=1, we get $Li_1(z)=\log(z)$ the ordinary logarithm. For s=2, we get $$Li_2(z)=\int_0^z \frac{\log(z)}{z}dz$$ For s=3, we have $$Li_3(z)=\int_0^z \frac{Li_2(z)}{z}dz$$ In general, we always have $$Li_s(z)=\int_0^z \frac{Li_{s-1}(z)}{z}dz$$ This might look confusing. The only thing I want to make clear is that the polylogarithm is usually not always a elementary function (except for special values such as s=1)
Actually, just to correct a slight mistake, the sum for s =1 gives $\mbox{Li}_1(z) = -\log(1-z)$, and so

$$\mbox{Li}_2(x) = - \int_0^x dt~\frac{\ln(1-t)}{t},$$
(reverting to ln notation because I'm using real variables for the integral representation).
 On a related note, the definite integral can sometimes be calculated for such functions. For example $$\int_{0}^{\frac{\pi}{2}} {\ln(\cos(x))dx} =$$ *something involving pi and the natural log of 2 (but I don't remember right now). It can be proven using a substitution trick, and trig identities.

 Quote by Boorglar On a related note, the definite integral can sometimes be calculated for such functions. For example $$\int_{0}^{\frac{\pi}{2}} {\ln(\cos(x))dx} =$$ *something involving pi and the natural log of 2 (but I don't remember right now). It can be proven using a substitution trick, and trig identities.
I think this guy gets the u= x-pi/2 treatment. symmetry :)

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 Similar Threads for: Indefinite Integration of function's like log(cos(x))??? Thread Forum Replies Calculus 1 Calculus & Beyond Homework 1 Precalculus Mathematics Homework 21 General Math 6


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Discussion in 'Physics & Math' started by timewarp, Oct 22, 2011.

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1. ### TachBannedBanned

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5,265
It isn't clear in what frame they are defined in your inaccurate description, it is quite clear that they are defined in S in my web solution. It says quite clearly in the text: "in the initial rest frame S, one clock moves at $+\Delta u$, the other clock moves at $- \Delta v$, therefore, the separation L is reached at $t=\frac{L}{\Delta u +\Delta v}$". The clocks move in opposite directions with infinitesimal speeds $+\Delta u$ and $- \Delta v$ , respectively, so there is a separation distance L at time $t=\frac{L}{\Delta u +\Delta v}$. Quite clear.

Last edited: Oct 25, 2011

3. ### PeteIt's not rocket surgeryRegistered Senior Member

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Tach's frame S is different. It's described in a document he linked a while ago:

5. ### TachBannedBanned

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Ahem, no. Frame S is the initial rest frame of the clocks. Try reading the web file before you jump in. Ah, Pete already corrected you, beat me to it.

Last edited: Oct 25, 2011

7. ### TachBannedBanned

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....but JamesR doesn't read, he just trolls my posts so there is no way for him to know the facts. He just waits in the wings and pounces.

8. ### PeteIt's not rocket surgeryRegistered Senior Member

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Feel free to ask for clarification on anything I say that isn't clear enough for you.
Given the statement "A moves at v + du", I don't see how you could possibly think that du is defined wrt A's rest frame, but we have it sorted now, so let's move on.

So what?
We are discussing your objection to my solution, remember?
Are you now clear that I'm working in a single reference frame?
Feel free to update your document to accurately reflect the scenarios it's supposed to be describing.

9. ### TachBannedBanned

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How about you tried to formulate your scenario in a precise manner? Define the frames, define the speeds. Start from the top.

10. ### PeteIt's not rocket surgeryRegistered Senior Member

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Which bit is still not clear to you?

11. ### TachBannedBanned

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Since you never did a complete, clear , writeup , why don't you take the time to do it?

12. ### PeteIt's not rocket surgeryRegistered Senior Member

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The writeup's there to read, Tach.
What do you find unclear?

13. ### TachBannedBanned

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You mean $\frac{\gamma Lv}{c^2}$, right? What you wrote does not have dimensions of time.

Not necessarily. The clocks are synchronized from the perspective of a frame F that move with speed $+v$ wrt your frame of reference.

No, it is $\Delta \tau = \frac{Lv/c^2}{\sqrt{1 - (v/c)^2)}$. It should also have a sign that is dependent on the relative motion between the clocks and the frame of reference. The correct equation falls out straight from the Lorentz transforms. There is a lot of cleanup that you can do if you took the time to re-write your stuff from scratch. The way it is, it is a collection of posts with various mistakes.

14. ### PeteIt's not rocket surgeryRegistered Senior Member

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That's right. Thanks.

What you say is correct, but I don't understand why you say "not necessarily".
If v=0, then $\Delta \tau=0$, meaning the clocks are synchronized in the scenario reference frame, right?

That's right. Thanks.
That's right.
That can be built in by ensuring that v and L have a consistent sign convention.

I think the essential idea was clear enough way back at post 42:
This is an internet discussion forum.
If you expect publication quality rigor, you're in the wrong place.

15. ### TachBannedBanned

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Read the writeup I did, it is explained there.

No, it isn't. Think about the way you formulated the post, the clocks are "initially at rest" with respect to WHAT? It is this type of sloppy stuff that detracts from your posts.

16. ### OnlyMeValued Senior Member

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That's cheap Tach. Pete's post back on page 3 of this thread was directed toward an explanation that did not require the kind of "rigor" you are demanding or would have been noticed by the original poster.

The questions and examples were clear within that context to those involved at the time.

And have you noticed that largely this obsession seems to have driven most others into the shadows if not completely away.

This thread began as a question about slow clock transport and a description of what that was and what effects it would have on the clocks.

Most of the original discussion was completely obscured by the next three pages, after you joined the discussion.

17. ### PeteIt's not rocket surgeryRegistered Senior Member

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The statement works for any (x,t) inertial reference frame.
Choose any inertial (x,t) reference frame.
If the clocks were initially at rest in that frame, then they will stay synchronized in that frame on slow separation.
If the clocks were not at rest in that frame, then they will not stay synchronized in that frame on slow separation.

You can call it sloppy. I call it concise.
Remember, this is an internet discussion forum, not a journal.
Here, conciseness trumps rigor.

18. ### TachBannedBanned

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There is a fallacy in this type of reasoning. The desynchronization is predicated on $L$ being non null. But $L$ is a linear function of $\Delta u$ and $\Delta v$: $L=(\Delta u +\Delta v )t$.

When $\Delta u->0$ and $\Delta v->0$ so does $L->0$. So, the second sentence is not correct, you can't have it both ways.

19. ### PeteIt's not rocket surgeryRegistered Senior Member

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What? The clocks are separated.

20. ### TachBannedBanned

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Not when $\Delta u->0$ and $\Delta v->0$. You can't have it both ways, your argument for the second sentence holds no water.

21. ### OnlyMeValued Senior Member

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Lol and I was worried if I asked a question it could be dangerous.

The saga goes on.

22. ### PeteIt's not rocket surgeryRegistered Senior Member

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To spell out the bleeding obvious for Tach (again):

The clocks are slowly separated by some given distance L.
The slower the separation, the longer it takes.
As the separation velocity approaches zero, the time taken approaches infinity.

This is ridiculous. 80-odd posts to explain a very simple sentence. Tach seems bent on deliberate misunderstanding. I don't know why, but I'm done explaining for him.