At Rest with our Hubble view

[Markus Hanke]

It's a mathematical space

It's curved spacetime, Physbang, not curved space.

?!?

When you aim a light beam straight up, it doesn't curve

Huh ? Of course it does. It curves in space-time. If the null geodesics were flat, we'd have no gravitational field at all.

Because it's an unsupported myth.

Simple example - the surface of a sphere is unbounded, yet finite. That is neither hard to conceptualize, nor is it an unsupported myth. It's simple geometry.

A gravitational field is inhomogeneous space.

If that were so, then gravitational light deflection would be frequency dependend ( refraction ). Obviously that is not the case.

 

[Farsight]

?!?

Yes, it's curved spacetime not curved space. You place light-clocks around the Earth in an equatorial plane, then plot the readings. Your plot is curved. See this Baez article and note this:

"Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial. If you toss a ball, it follows a parabolic path. This is far from being a geodesic in space: space is curved by the Earth's gravitational field, but it is certainly not so curved as all that! The point is that while the ball moves a short distance in space, it moves an enormous distance in time, since one second equals about 300,000 kilometers in units where c = 1. This allows a slight amount of spacetime curvature to have a noticeable effect".

The "enormous distance in time" isn't too great, but nevermind. The point is that if we were dealing with spatial curvature instead of spacetime curvature, the tossed ball would follow the same arc regardless of how fast you threw it.

Huh ? Of course it does. It curves in space-time. If the null geodesics were flat, we'd have no gravitational field at all.

The light beam is going straight up, Markus. The "curvature in spacetime" is something abstract. Imagine you arrange your light-beam to zigzag upwards between parallel mirrors, and draw a plot of the zigzag rate. This plot is curved just like your plot of equatorial light clocks.

Simple example - the surface of a sphere is unbounded, yet finite. That is neither hard to conceptualize, nor is it an unsupported myth. It's simple geometry.

There's no issue with a sphere. The issue is with using it for an analogy of unbounded finite space when space is flat.

If that were so, then gravitational light deflection would be frequency dependent ( refraction ). Obviously that is not the case.

It wouldn't be frequency dependent. Whatever frequency of light you use in those light clocks, your plot shows the same curvature. The speed of light does not depend on frequency.

 

[PhysBang]

It's curved spacetime, Physbang, not curved space. Which demonstrates just how little you know.

You seem to be using this insult as an excuse for not actually providing any physics.


You have shown us that you know insults, but you do not know physics.

Although it is useless to say it, feel free to actually provide a reason why the physics of every cosmologist, including Einstein, is wrong about an infinite expanding universe. I am sure every textbook publisher in the world would welcome your future works and you wouldn't have to take the utterly pathetic course of publishing your own work.

 

[Markus Hanke]

It wouldn't be frequency dependent. Whatever frequency of light you use in those light clocks, your plot shows the same curvature. The speed of light does not depend on frequency.

I was talking about gravitational light deflection in the vicinity of massive bodies. I distinctly remember you putting down your "inhomogeneous space" to changes in permittivity and permeability of the vacuum ( and thus changes in light speed, as inside a refractive medium ); this leads to refraction. We have had a fairly lively debate over whether or not this is justifiable given the Maxwell equations, though I cannot at the moment find the old thread. My argument was that allowing these constants to vary would introduce an additional degree of freedom, which we quite simply don't observe.

Light would indeed by deflected by such an inhomogeneity, but in a manner depending on frequency. Gravitational light deflection due to space-time curvature is not frequency dependent. The light deflection we actually observe is also not frequency dependent ( or else the sky would be full of pretty little rainbows ).

 

[hansda]

... Gravitational light deflection due to space-time curvature is not frequency dependent. The light deflection we actually observe is also not frequency dependent ( or else the sky would be full of pretty little rainbows ).

We do observe red-shift and blue-shift. These frequency shifting of light is as per GR. This is gravitational red-shift.

 

[Grumpy]

Farsight

Light beams don't cross spacetime, Grumpy

So photons don't travel? Non-sense. And a light beam is a common term for a continuous train of photons. So light beams do travel through spacetime, or cross it in common vernacular. Time is a distance as well as an interval. Spacetime is a 4D manifold, gravity is a distortion in spacetime cause by the presence of mass/energy(which are the same thing)that distortion by even the littlest hint of mass/energy means there are no straight lines. Of course, concentrations of mass make this distortion more evident, and mass above a certain level bends spacetime completely into a circle/sphere.

I know about it. It's called gravitational lensing because space acts like a lens.

It acts as a lens ONLY if mass has distorted(bent)it. Space that is empty does not act as a lens.

The light beam is going straight up, Markus. The "curvature in spacetime" is something abstract.

When you aim a light beam straight up, it doesn't curve. It doesn't matter how much you increase the gravitational field, it never starts curving.

Ever heard of frame dragging? The Earth is rotating, it's mass distorts that spacetime as does it's rotation, there are no straight lines in spacetime near any rotating mass. In addition, emitting photons "straight up" from a rotating surface gives you a curved light beam, like a water hose does when you rotate. The faster the rotation, the more curved it is, intrinsically. And the rotating mass drags spacetime around with it, the more mass/ higher rates of rotation the more frame dragging. Around Earth the effect is minuscule, around a rapidly spinning supermassive Black Hole the effect is huge. We will soon be able to directly image the area around the BH at the center of Andromeda, but like the observations that confirmed curved spacetime, it will just be the final, visual confirmation of this theory. I hope Hawking lives long enough to see his life's work vindicated.

And time is a dimension of spacetime, frequency shift caused by gravity is "curvature in time" and like time, there is only frequency shift caused by gravity towards the red end of the spectrum, a "slowing" of the frequency(not the speed). The higher the gravity, the more curved in time, the lower the frequency.

Grumpy, it's a concentration of energy that causes gravity, not just mass.

Matter and energy are only two aspects of the same thing, both have mass. Somewhat analogous to water and steam.

but the fact is EVERY point in space was in the middle of whatever the Big Bang was, and sees itself at the center of the Universe today.

It's not a fact Grumpy. It's an assertion.

So our being in the exact center of everything we see is unique? We are special? Is it not a FACT that every point in the Universe once occupied the same place, a place of zero dimensions? Does that not mean that every point in the Universe was the point at which the BB occurred? Would every point not see every other point expanding away from them?

The surface of sphere is unbounded in two dimensions. A hypersphere is unbounded in three. The Universe is unbounded in four dimensions. A consequence of this is that all points in space throughout time see themselves as being in the exact center of the Universe(because they are)and they always will(because they always will be). There are no edges of this Universe, there is only the center as EVERY point is in the center(in it's own frame of reference). Not only is Relativity relative, the whole Universe is relative as well.

Grumpy

 

[Layman]

Simple example - the surface of a sphere is unbounded, yet finite. That is neither hard to conceptualize, nor is it an unsupported myth. It's simple geometry.

The surface of sphere is unbounded in two dimensions.

I don't think you guys even know what unbound even means, maybe you should learn that before you start putting out your own ideas about the state of the universe as scientifically accepted proof.

A sphere shaped universe would be bound. A hyperbolic universe would be unbound. Bound or unbound only means if you can travel in a circle around the universe and then come back to the same point. But, we know that the universe is large enough that there wouldn't be enough time to allow something to travel such a great distance to do this if it was limited by the speed of light even though it was bound. Therefore, there is really no way to tell.

I don't think the universe would be a bound sphere. Take this image for example from the wiki page Shape of the Universe.

"Universe in an expanding sphere. The galaxies furthest away are moving fastest and hence experience length contraction and so become smaller to an observer in the centre."

The problem here is that galaxies that are traveling with the expansion of the universe have not been shown to be affected by spacetime dilation or mass increase, otherwise every galaxy on the edge of the visible universe would have the mass of a black hole.

 

[Layman]

And at no time in the past has spacetime expanded at infinite velocity, so no matter it's shape it is finite in size. The unbounded part is really hard to conceptualize, but the fact is EVERY point in space was in the middle of whatever the Big Bang was, and sees itself at the center of the Universe today. No point in the Universe is on an edge of any dimension but time(now is the edge of time, the past does not exist and the future has yet to occur). Now is the only edge in our Universe, whatever shape you think it is. Topology is a 2D representation of a 3D+time(4D)reality, the Universe is not saddle shaped, it is a representation of the flatness of flatland that tells us something about whether the Universe will expand forever(open) or collapse into a big crunch(closed). Currently it appears to be perfectly flat.

Spacetime expansion isn't limited by the speed of light, therefore it could have infinite velocity at an infinite distance away from any observer. Unfortunately Einsteins theory of the possibility of a finite but yet unbound universe means that there would be some edge to the universe, and hence why it is hard to accept as the correct model. It is unbound so it does not curve back around on it's self, and then it is finite so the distance space can go out is limited. A finite yet unbound universe would have an edge that Einstein most likely thought would be unachievable to reach because of the limit of the speed of light, but I don't think he was aware that spacetime expansion wasn't limited by the speed of light as well.

 

[Farsight]

Although it is useless to say it, feel free to actually provide a reason why the physics of every cosmologist, including Einstein, is wrong about an infinite expanding universe.

I've already given the reason, PhysBang. Stress is directional pressure. The stress-energy-momentum tensor has an energy-pressure diagonal. The FLRW metric assumes the homogeneity of space on the large scale. This space has an innate pressure. In an infinite universe it's counterbalanced at all locations, so space can't expand.

 

[Layman]

I've already given the reason, PhysBang. Stress is directional pressure. The stress-energy-momentum tensor has an energy-pressure diagonal. The FLRW metric assumes the homogeneity of space on the large scale. This space has an innate pressure. In an infinite universe it's counterbalanced at all locations, so space can't expand.

That seems like it could be something if we actually knew what causes space to expand to begin with, and the last time I checked empty space was close to being a perfect vacuum with a small amount of energy steadily soothing from it. It seems like you could be incorrectly assuming that gravitational pull was responsible for the expansion of space itself.

 

[Farsight]

I was talking about gravitational light deflection in the vicinity of massive bodies. I distinctly remember you putting down your "inhomogeneous space" to changes in permittivity and permeability of the vacuum ( and thus changes in light speed, as inside a refractive medium ); this leads to refraction. We have had a fairly lively debate over whether or not this is justifiable given the Maxwell equations, though I cannot at the moment find the old thread. My argument was that allowing these constants to vary would introduce an additional degree of freedom, which we quite simply don't observe.

Our conversations on that mirror conversations you see elsewhere, such as on arXiv. I would encourage you to look into this. Search arXiv on VSL and variable speed of light and varying speed of light. Also see this Baez article and note the contradiction within the GR section.

Light would indeed by deflected by such an inhomogeneity, but in a manner depending on frequency. Gravitational light deflection due to space-time curvature is not frequency dependent. The light deflection we actually observe is also not frequency dependent ( or else the sky would be full of pretty little rainbows ).

Yes, the deflection we see is not frequency-dependent. Gravitational lenses are not rainbow-makers. But then neither are ordinary lenses. I'd say though that the important point here is the causative reason. Light doesn't bend because spacetime is curved. Your parallel-mirror light clock near the ground does not "tick slower" than a higher clock because your plot of all such clocks is curved.

 

[Farsight]

We do observe red-shift and blue-shift. These frequency shifting of light is as per GR. This is gravitational red-shift.

Rather surprisingly hansda, gravity does not change the frequency of light. You can work this out very simply: convert a 1kg mass into light, and throw this light into a black hole. A blue-shift is said to occur. But the black hole mass increases by only 1kg. Conservation of energy applies. The light doesn't gain any energy.

The frequency of light doesn't increase as the photon descends. Instead the clocks you use to measure that frequency go slower when they're lower. For some reason that I can't explain, nobody seems to know this.

 

[Farsight]

So photons don't travel? Non-sense. And a light beam is a common term for a continuous train of photons. So light beams do travel through spacetime, or cross it in common vernacular.

Photons travel through space. There's no motion in spacetime. It a static all-times mathematical model. It isn't what space is.

Time is a distance as well as an interval. Spacetime is a 4D manifold, gravity is a distortion in spacetime cause by the presence of mass/energy(which are the same thing)that distortion by even the littlest hint of mass/energy means there are no straight lines. Of course, concentrations of mass make this distortion more evident, and mass above a certain level bends spacetime completely into a circle/sphere.

That's what people say, Grumpy. But they mix up cause and effect.

It acts as a lens ONLY if mass has distorted(bent)it. Space that is empty does not act as a lens.

Space acts as a lens all right. But when it does, the space isn't curved. See what I said to PhysBang and Markus about curved spacetime and curved space.

Ever heard of frame dragging? The Earth is rotating, it's mass distorts that spacetime as does it's rotation, there are no straight lines in spacetime near any rotating mass. In addition, emitting photons "straight up" from a rotating surface gives you a curved light beam, like a water hose does when you rotate. The faster the rotation, the more curved it is, intrinsically. And the rotating mass drags spacetime around with it, the more mass/ higher rates of rotation the more frame dragging. Around Earth the effect is minuscule, around a rapidly spinning supermassive Black Hole the effect is huge. We will soon be able to directly image the area around the BH at the center of Andromeda, but like the observations that confirmed curved spacetime, it will just be the final, visual confirmation of this theory. I hope Hawking lives long enough to see his life's work vindicated.

I know about frame-dragging. It's called gravitomagnetism. And yes, then space is curved. You will be aware that gravitomagnetism is related to electromagnetism.

And time is a dimension of spacetime, frequency shift caused by gravity is "curvature in time" and like time, there is only frequency shift caused by gravity towards the red end of the spectrum, a "slowing" of the frequency(not the speed). The higher the gravity, the more curved in time, the lower the frequency.

Sorry Grumpy, but gravity does not change the frequency of a photon. It changes the tick rate of the clock you use to measure that frequency.

So our being in the exact center of everything we see is unique? We are special? Is it not a FACT that every point in the Universe once occupied the same place, a place of zero dimensions? Does that not mean that every point in the Universe was the point at which the BB occurred? Would every point not see every other point expanding away from them?

We don't know that the universe started as a point singularity.

The surface of sphere is unbounded in two dimensions. A hypersphere is unbounded in three. The Universe is unbounded in four dimensions. A consequence of this is that all points in space throughout time see themselves as being in the exact center of the Universe(because they are)and they always will(because they always will be). There are no edges of this Universe, there is only the center as EVERY point is in the center(in it's own frame of reference). Not only is Relativity relative, the whole Universe is relative as well.

We'll have to disagree about that, Grumpy.

 

[Farsight]

Spacetime expansion isn't limited by the speed of light, therefore it could have infinite velocity at an infinite distance away from any observer. Unfortunately Einsteins theory of the possibility of a finite but yet unbound universe means that there would be some edge to the universe, and hence why it is hard to accept as the correct model.

I don't think Einstein proposed that, but nevermind. The question is this: what's harder to accept, a universe with an edge, or a universe that's infinite, and always has been infinite? And has been expanding? I know which one I'm going for. Whether we can reach it or not isn't the point. If it does have an edge, then somebody born near to that edge would know about it. They could reach it.

That seems like it could be something if we actually knew what causes space to expand to begin with, and the last time I checked empty space was close to being a perfect vacuum with a small amount of energy steadily soothing from it. It seems like you could be incorrectly assuming that gravitational pull was responsible for the expansion of space itself.

Not gravitational pull, stress-energy. Look at the stress-energy tensor. See that pressure? And it's got shear stress in it. It's bloody elastic. Compressed elastic. Like a stress-ball squeezed in your fist. imagine it's dotted with galaxies. Open your fist.

 

[PhysBang]

I don't think Einstein proposed that, but nevermind. The question is this: what's harder to accept, a universe with an edge, or a universe that's infinite, and always has been infinite? And has been expanding? I know which one I'm going for. Whether we can reach it or not isn't the point. If it does have an edge, then somebody born near to that edge would know about it. They could reach it.

Ok, but you have claimed, without scientific evidence, that an infinite expanding universe is impossible. Can you please provide us with a description of such a spacetime along with a real and detailed critique of these spacetimes with the relevant mathematical details included?

Not gravitational pull, stress-energy. Look at the stress-energy tensor. See that pressure? And it's got shear stress in it. It's bloody elastic. Compressed elastic. Like a stress-ball squeezed in your fist. imagine it's dotted with galaxies. Open your fist.

Please show us mathematical details of this strange spacetime you describe? Can you then show how this strange spacetime you describe and advocate shows up in any of the mathematical details of current cosmology?

So far you are making a lot of claims that directly contradict what is in every textbook and you have not provided any mathematical details about what you mean by "pressure" and "stress". You say that, "Stress is directional pressure," but Maxwell, for example, says that it can be, "Attraction, Repulsion, Tension, Pressure, Shearing stress, Torsion, etc. " So do you mean that all stress is pressure or just this stress? And if so, how do we come to this conclusion?

 

[Grumpy]

Farsight

Photons travel through space. There's no motion in spacetime. It a static all-times mathematical model. It isn't what space is.

NON-SENSE! Spacetime is one single thing, you cannot speak of time and space as two separate things. It is real, not a model, nor is it static.

That's what people say, Grumpy. But they mix up cause and effect.

The mixup is with you, it seems.

Space acts as a lens all right. But when it does, the space isn't curved. See what I said to PhysBang and Markus about curved spacetime and curved space.

Again, non-sense. Spacetime without mass in it is not curved(a situation that is extremely rare if it exists at all)and spacetime is curved in direct proportion to the amount of mass it contains and it's configuration. What you said is simply wrong.

Sorry Grumpy, but gravity does not change the frequency of a photon. It changes the tick rate of the clock you use to measure that frequency.

Yes, gravity does affect the frequency of photons emitted in the field(gravitational red shift), it also affects time(gravitational time dilation). As I said before, mass/matter/energy/gravity, motion/lightspeed and time are connected, changes in one affects the other two.

We don't know that the universe started as a point singularity.

It certainly had a start in time and was incredibly hot and dense at the beginning. It started very, very small(microscopically small)so this is a distinction without a difference. I don't think singularities can exist due to quantum effects, even in the largest BHs(not that it makes a difference to the Universe). But the homogeneity of the CMB REQUIRES a singularity like situation(if not an actual singularity)to account for the smoothness. When the CMB was released by the surface of last scattering it was billions of light years in size yet so uniform it had to be in contact at the beginning.

Layman

Spacetime expansion isn't limited by the speed of light, therefore it could have infinite velocity at an infinite distance away from any observer.

It could conceivably have a speed faster than light, but that is not speed through local space at either end. There are no infinities, of any sort, outside of math or our concept. The Universe had a beginning(therefore it cannot be infinite in duration). At no time in the past did it expand at infinite speeds for infinite time, so it is finite in size. You could say it will expand to infinity but it will never actually be infinite. Anywhere in science that you get infinity for an answer something is wrong with your understanding, it's a sign that we have entered the twilight zone.

Unfortunately Einsteins theory of the possibility of a finite but yet unbound universe means that there would be some edge to the universe

Einstein thought the Universe was infinite, eternal and static, he was wrong. Unbounded, by definition, means it has no edge. The surface of a sphere has no edge in two dimensions. A hypersphere 3D. The Universe is unbounded in 4D. The only possible edge in the whole Universe exists in the time dimension, now is that edge.

It is unbound so it does not curve back around on it's self, and then it is finite so the distance space can go out is limited.

The Universe is it's own container, it is unique in this(everything else in within that Universe). Your mind is not built to understand this(just as it struggles with Relativity). Unbounded also means unconstrained, there is no limit to the size, it's just not infinite and is continuing to expand.

The problem here is that galaxies that are traveling with the expansion of the universe have not been shown to be affected by spacetime dilation or mass increase, otherwise every galaxy on the edge of the visible universe would have the mass of a black hole.

That's because their velocity is APPARENT speed relative to us, not ACTUAL speed through local spacetime, apparent speeds have no relativistic effects. You are aware that we see the Universe inside out, aren't you. The furthest things we see are seen when the Universe was it's smallest, the closest things we see are seen when the Universe is it's largest. The CMB was not the largest visible structure, it was much smaller when it's light was emitted.

Grumpy

 

[Layman]

I don't think Einstein proposed that, but nevermind. The question is this: what's harder to accept, a universe with an edge, or a universe that's infinite, and always has been infinite? And has been expanding? I know which one I'm going for. Whether we can reach it or not isn't the point. If it does have an edge, then somebody born near to that edge would know about it. They could reach it.

It had become a popular idea in the media because of some of Einsteins theories. Any type of universe is considered to be a possibility in theoretical physics. We just haven't discovered one that is accurate enough to make predictions that would then tell us that it is the only possibility. I find the hardest one to accept is the idea that the big bang was infinite in size, but in a bound universe that curves in on itself would appear to be infinite in size from the inside. Personally, I would think that it is bound with negative curvature and it is finite but than could grow infinitely for the rest of time and the entire multiverse would rest inside of this one single megaverse that repeats different versions of itself in cycles at different periods of time.

Not gravitational pull, stress-energy. Look at the stress-energy tensor. See that pressure? And it's got shear stress in it. It's bloody elastic. Compressed elastic. Like a stress-ball squeezed in your fist. imagine it's dotted with galaxies. Open your fist.

I would think that you would just be suffering from the same problem Einstein had with Newton's infinite lines of force. Every value no matter how strong the force of gravity was would give you an infinity in that type of problem. I don't see how you could scientifically justify that method as providing real solutions that are not infinite.

 

[Layman]

Einstein thought the Universe was infinite, eternal and static, he was wrong. Unbounded, by definition, means it has no edge. The surface of a sphere has no edge in two dimensions. A hypersphere 3D. The Universe is unbounded in 4D. The only possible edge in the whole Universe exists in the time dimension, now is that edge.

This is where you are wrong.

XXXI. The Possibility of a “Finite” and Yet “Unbounded” Universe

Clearly Einstein thought the universe was "Finite" and Yet "Unbounded". This means that it isn't infinite in size and that it doesn't curve back around on itself as a type of sphere.

The Universe is it's own container, it is unique in this(everything else in within that Universe). Your mind is not built to understand this(just as it struggles with Relativity). Unbounded also means unconstrained, there is no limit to the size, it's just not infinite and is continuing to expand.

No, it just means that it doesn't curve back on itself like a circle or sphere. If a unbound universe was finite in size then it would have to have an edge. But, scientist have not shown that Einsteins possibility of this type of universe was wrong. An unbound universe that was infinite in size would then have no edges. Like I said, Einstein may have thought this edge would prevent people from being able to venture to it because of the speed of light limit, this is in contrary to what has been stated more recently about universal expansion in the media.

That's because their velocity is APPARENT speed relative to us, not ACTUAL speed through local spacetime, apparent speeds have no relativistic effects. You are aware that we see the Universe inside out, aren't you. The furthest things we see are seen when the Universe was it's smallest, the closest things we see are seen when the Universe is it's largest. The CMB was not the largest visible structure, it was much smaller when it's light was emitted.

The furthest things we see in the visible universe are traveling at speeds close to the speed of light, one of Einsteins theories was that the reason why we can only see that far is because light just wouldn't have had enough time to travel from a distance greater than that yet(I think this same type of concept has been applied to black hole physics for light not escaping), so then it could be infinite it is just that the speed of light barrier has prevented us from knowing of its entirety. We would just think that it is actually growing because we are just able to continually view it at a greater distance that is the same distance it would take light to get to us from there, that is the size of the visible universe. For example, you wouldn't be able to view an infinite amount of spheres if you shined a light around a sphere, you would only be able to see as many spheres as light has been able to travel since you created the light source.

 

[Layman]

WMAP - Shape of the Universe

"Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

All we know is that it looks flat, but if it was so large that the visible universe was very small to the entire universe we wouldn't be able to detect the curvature. So all they know for certain is that it just looks flat, but then it could be so big that it just appears to be flat. Then if it was flat and really didn't have any curvature then it would either have to be infinite or finite with an edge.

IDK, from Einsteins biography it seems like his description of not bound is the same of what I would think of as being bound, it curves back on itself. It seems like saying finite and unbound would be bit redundant, but then even a spherical universe that curves back on itself would have the same potential to have an infinite influence be felt across it from an object being able to go around the universe indefinitely, so maybe that is why he says it is unbound, IDK. Then it would seem like a universe that does curve on itself or doesn't would be left without names. I don't think Einstein wrote it himself or maybe it would have said it was an autobiography, maybe there was a misinterpretation in the biography.

 

[Grumpy]

Layman

If we can still see the CMB(and we can)we are seeing the entire Universe as it was then. It is actually much bigger than it appears, but time is a dimension, a distance just like the other three dimensions, and we can see the entire history of the Universe(in principle if not yet in fact)all the way back to the beginning.

All we know is that it looks flat, but if it was so large that the visible universe was very small to the entire universe we wouldn't be able to detect the curvature. So all they know for certain is that it just looks flat, but then it could be so big that it just appears to be flat. Then if it was flat and really didn't have any curvature then it would either have to be infinite or finite with an edge.

You are mistaking the map for the territory, the Universe is only flat in the calculations of topology, it is a two dimensional chart that has edges only because it leaves out two whole dimensions, it is not the 4D reality. And open or closed is simply about whether the Universe will collapse back into a Big Crunch(closed), eventually reach stasis(flat) or expand forever more(open), it says nothing about what shape or size the Universe is. The shapes of topology do not represent reality, just certain aspects of it. The Universe has no edge, there is nothing "beyond" the Universe, nothing outside of the Universe for there to be an edge between it and something else, the Universe is not expanding into anything, it IS everything. And curvature can never lead back to the same point, that is simply wrong. Even if you got back to the point of origin it would be far in the future in the dimension of time, everything you left behind would no longer exist. But you cannot make the trip, you can never reach most of what you see in the Universe, as most of what you see no longer exists and is way too far away in time and space. See, it's hard to think in 4D, we're really not cut out to understand a hypersphere, much less when you add the dimension of time. The Universe is finite in size, but that does not mean what we think of as a finite size or shape within the Universe, it adds another whole dimension(time), but it is finite, nonetheless. And there are no edges to spacetime except the leading edge of travel through time(the now), every point exists on the leading edge of time and the only geometrical point we can identify is dead center to the entire thing, every point still dwells at that center and always will. The Universe must be finite in size(no infinite time or speed at any time in the past, it had a beginning, therefore not infinite in either space or time), and it also must be unbounded(there's nothing the Universe can have an edge with, an edge is a boundary between two things, the Universe is the only thing there is, so there is no boundary, thus it is unbounded). The actual shape or size of a Universe that meets all these conditions is not something human minds can grok. We live within the Universe, we are missing a dimension in our experience, this is much harder to visualize than simple Relativity, but it MUST be true, there's nothing else that can be true. The geometry of the Universe is not the same as the geometry of things within the Universe, everything in the Universe has the rest of the Universe to have a boundary with, the Universe cannot have a boundary, there's nothing there to have a boundary with. The Universe has no edge, it only has a center, and every point is at that center from it's own frame of reference, surfing on the leading edge of time.

Grumpy