# Physics Question

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Here's a simplified visual representation of the Big Bang and the expansion of the universe:

Each blob represent a galaxy, or if you prefer, millions of galaxies. Whatever. The blobs maintain their size but move away from each other.

Here's a simplified visual representation of a different event:

Again, each blob represents a galaxy, or if you prefer, millions of them. In this case, however, each shrinks in size but maintains its position in space in relation to the others.

My question is this: If in both scenarios, we are basically a tiny speck on one of the blobs, how would we determine which of the two scenarios represented what we were observing from within the system?

If, in the second scenario, we and the instruments that we used to observe and measure relationships were "shrinking" along with everything else, how would we establish that the universe was not expanding, but that we were actually "shrinking" and only misinterpreting the universe as expanding?

J

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What we actually see is that the further away from us an object is, the more its spectrum is red-shifted away from us. That is, because it is moving away from us at a significant portion of the speed of light, the light which reaches us has been shifted to a lower frequency, just as a siren speeding away from you sounds lower in frequency than a siren speeding toward you. This cannot be accounted for by galaxies shrinking, because their shrinking limited to the speed of light would not be suficient over time to account for the distances that the galaxies are apparently moving apart from each other. They could not shrink so small to account for the apparent change in distance between them. The second video cannot be made to fit the data.

Edited by Ted Keer

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In my previous response, I am assuming you keep the wavelength of light constant. If you assume that absolutely everything, including the wavelength of light, is shrinking, while the size of space and the locations of centers of mass in space stay relatively constant, then one could perhaps argue that space is staying constant but things are shrinking ever more rapidly. This seems to involve too many assumptions. The standard big bang model assumes constant entities with an initial velocity away from each other. The shrinking universe model would treat space as a constant, and rather than assuming simply that bodies are moving away from each other (they have to have some initial velocity in any case).

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What we actually see is that the further away from us an object is, the more its spectrum is red-shifted away from us. That is, because it is accelerating away from us at a significant portion of the speed of light, the light which reaches us has been shifted to a lower frequency, just as a siren speeding away from you sounds lower in frequency than a siren speeding toward you.

If we were shrinking rapidly -- including our ears -- wouldn't a stationary siren's sound waves seem to be proportionately larger to us, and wouldn't we therefore perceive them as being lower in pitch? In effect, if we quickly became the size of a mouse, wouldn't our range of hearing alter significantly? Likewise, if our instruments for measuring light were shrinking radidly, wouldn't they measure light waves with a similar difference in proportion?

This cannot be accounted for by galaxies shrinking, because their shrinking limited to the speed of light would not be suficient over time to account for the distances that the galaxies are apparently moving apart from each other. They could not shrink so small to account for the apparent change in distance between them. The second video cannot be made to fit the data.

How would you determine the limitations of achievable smallness and rate of shrinkage? After all, don't theories about black holes posit the condensing of matter to an infinitesimal scale at immensely high velocities?

J

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In my previous response, I am assuming you keep the wavelength of light constant. If you assume that absolutely everything, including the wavelength of light, is shrinking, while the size of space and the locations of centers of mass in space stay relatively constant, then one could perhaps argue that space is staying constant but things are shrinking ever more rapidly.

Right -- what if the wavelength of light, since it lacks mass, is not shrinking along with everything that has mass? Or if it's not shrinking anywhere near the same rate as things with mass?

This seems to involve too many assumptions. The standard big bang model assumes constant entities with an initial velocity away from each other. The shrinking universe model would treat space as a constant, and rather than assuming simply that bodies are moving away from each other (they have to have some initial velocity in any case).

Well, my illustrations are only meant as extreme scenarios which isolate the relevant issues. The blobs wouldn't necessarily have to be perfectly stationary in the second clip. I only made them that way in order to focus on the problem of perspectives.

J

Edited by Jonathan

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If, in the second scenario, we and the instruments that we used to observe and measure relationships were "shrinking" along with everything else, how would we establish that the universe was not expanding, but that we were actually "shrinking" and only misinterpreting the universe as expanding?

There is no such thing as an absolute size. Size is measured with respect to a unit. That can be a platinum bar or a certain number of wavelengths of the light of a certain transition between two levels of a certain atom, or still another definition, but in your scenario the size of a galaxy remains the same, as the relation between the galaxy and the measuring unit doesn't change. On the other hand, when the distance between two galaxies was at first n units, it now becomes m units, with m > n. We call the increase in the number of units an increase in size, and not a decrease of the unit, as the unit is defined to be unchangeable. That we in the course of the history have chosen different units is because the original units were not really constant with respect to more elementary physical phenomena and the increasing accuracy of our measurements made units based on more elementary phenomena necessary.

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> I am assuming you keep the wavelength of light constant. If you assume that absolutely everything, including the wavelength of light, is shrinking... [Ted]

Ted, would the idea of the speed of light decreasing over interstellar distances be the same as what you are saying? We know that the speed of light alters based on medium (through water, through glass) and that it is bent when passing through different mediums (refraction).

What if the alternative hypothesis is not shrinkage but variable light speed, in other words?

If light slows down at greater distances than we can currently measure (intergalactic), would that explain the red shift and offer an alternative to the idea that everything is flying away from everything else and so there must have been an initial explosion (or massive and rapid expansion) fourteen billion years ago?

Then you have to look for causes. So as not to violate Newton's first law, ask what force(s) might cause a slowdown in velocity.

The usual explanation for slowing on earth is 'friction', interaction with entities along the way that cause a degree of bleeding of energy. That might be the case with electromagnetic energy (light) if space is not entirely empty. Which takes us back not necessarily to the ether. Not necessarily to a 'plenum', but very scattered and weak distribution - as is the case with interstellar gas.

The only additional idea would be that there is weak interaction with light as it passes through. Sort of like 'friction' on a macroscopic scale. To me, that would be plausible. At least as a hypothesis.

It seems as if "Phil's physics" might explain the red shift. Yes? No?

Edited by Philip Coates

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There is no such thing as an absolute size. Size is measured with respect to a unit. That can be a platinum bar or a certain number of wavelengths of the light of a certain transition between two levels of a certain atom, or still another definition, but in your scenario the size of a galaxy remains the same, as the relation between the galaxy and the measuring unit doesn't change.

Are you saying that our description of the universe depends on which unit of measurement we arbitrarily choose? In my shrinking galaxies scenario, if we choose the length of a specific platinum bar as our unit, and we, and it, and everything in our galaxy is shrinking, then, when we measure relationships in the universe with that unit, we will conclude that our universe is expanding? But if we instead choose as our unit of measurement the distance between the centers of any two galaxies (or between several of them), we would conclude that the universe is not expanding but that each galaxy is shrinking?

On the other hand, when the distance between two galaxies was at first n units, it now becomes m units, with m > n.

That would depend on what you mean by "distance between two galaxies." Do you mean the distance from one galaxy's perimeter to another's, or do you mean the distance from one galaxy's center to another's? In my second animation clip above, the distance between perimeters increases, but the distance between centers does not. So, again, if we arbitrarily choose either the distance between perimeters or the distance between centers as our unit of measurement, that arbitrary choice will determine which description of the universe we end up with.

(And now might be a good time to confess that the first animation clip doesn't actually show an expanding universe either. It shows the same blob-center-based-shrinkage as in the second clip. The only significant difference between the two clips is that in the first one, I put the viewer a greater distance away from the blobs and moved closer as time progressed, which only gives the appearance of an expanding universe.)

J

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I am having a hard time wraping my head around what would happen to light in transit between galaxies in a constant-spcae/shrinking galaxy model of the universe. Would it make sense to say that the photons would shrink? Would they be losing energy? If they weren't losing energy, then old photons would impact electrons with a much higher proportional energy, and we should notice this. In the standard expanding spacetime model, nothing happens to photons traveling between galaxies, only the distance they travel increases.

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I am having a hard time wraping my head around what would happen to light in transit between galaxies in a constant-spcae/shrinking galaxy model of the universe. Would it make sense to say that the photons would shrink? Would they be losing energy? If they weren't losing energy, then old photons would impact electrons with a much higher proportional energy, and we should notice this.

And what would the effect be? What would our noticing a higher proportional energy consist of? Would we perceive it as more intense light? Would we perceive it as a spectral shift?

Would non-shrinking, non-energy-losing photons necessarily impact smaller particles (which had also become more dense) any differently than they'd impact larger, less dense particles?

In the standard expanding spacetime model, nothing happens to photons traveling between galaxies, only the distance they travel increases.

And that might be true of a shrinking galaxy model, and it might not. I don't know. It's something to think about.

Btw, the distance that light travels from galaxy to galaxy in a shrinking galaxy system would increase. As I mentioned in my post to Dragonfly, although the distance between centers of galaxies would remain the same, the distance between galaxy perimeters would increase.

Anyway, in the expanding model, there are issues which, as I understand them, have required a lot of "fixes" which potentially present bigger problems than they solve, or which remain unexplained, such as the acceleration of the expansion of the universe, and the proposed theories of dark matter and energy. Might a Shrinking Galaxies Theory (or similar new perspectives based on choosing different, unconventional standards of measurement) eliminate some of these issues -- isn't acceleration of the rate of the condensing of matter, for example, much easier to "wrap your head around" than the acceleration of the dispersal of matter?

J

Edited by Jonathan

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According to Occam's razor coming up with the idea of things shrinking (without any idea of a cause)wouldn't be a likely hypothesis compared to things slowing down since we do know that friction forces are quite prominent in reality.

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Are you saying that our description of the universe depends on which unit of measurement we arbitrarily choose? In my shrinking galaxies scenario, if we choose the length of a specific platinum bar as our unit, and we, and it, and everything in our galaxy is shrinking, then, when we measure relationships in the universe with that unit, we will conclude that our universe is expanding? But if we instead choose as our unit of measurement the distance between the centers of any two galaxies (or between several of them), we would conclude that the universe is not expanding but that each galaxy is shrinking?

If you choose a unit for a measurement, or perhaps I should say a standard on which that unit is based (the unit "meter" is used already for centuries, but the standards have been changed several times, for increasing accuracy), you choose a standard that is as invariant as possible, compared to elementary physical units like the Bohr radius of the hydrogen atom. Therefore the platinum bar that was used first, was kept in controlled conditions at a certain temperature etc. Later more accurate standards were chosen, like a certain number of wavelengths of a particular spectral line. Now there isn't any reason to think that the distance between two galaxies, whether between the centers or the perimeters, has a constant relation to the distances defined in elementary physical systems like atoms (which correspond to our notion of distance that we use in daily life), so such a distance would be a bad unit. We prefer to consider the elementary building blocks of the universe, the atoms and elementary particles, to be constant instead of the whole universe, as that would enormously complicate matters. After all, all hydrogen atoms are equal, as are all iron atoms etc., while stars and galaxies are continuously changing. The galaxies may for example in general move away from us, but some of them are moving towards us.

(And now might be a good time to confess that the first animation clip doesn't actually show an expanding universe either. It shows the same blob-center-based-shrinkage as in the second clip. The only significant difference between the two clips is that in the first one, I put the viewer a greater distance away from the blobs and moved closer as time progressed, which only gives the appearance of an expanding universe.)

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I am having a hard time wraping my head around what would happen to light in transit between galaxies in a constant-spcae/shrinking galaxy model of the universe. Would it make sense to say that the photons would shrink?

What do you mean by a shrinking photon? A really monochromatic photon would be infinitely long (a plane wave), a photon with a finite spectral breadth would have a finite length that depends on its spectral content. Or do you mean a photon with a smaller wavelength? That would in standard theory correspond to a more energetic photon. But the point is of course: smaller compared to what? Length is defined by the wavelength of photons with a certain frequency, so it is meaningless to talk about shrinking photons (or shrinking atoms for that matter).

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What do you mean by a shrinking photon?

Well, exactly.

One thing to consider is that an object moving away from you in a fourth spatial dimension would appear to shrink away from observers three-dimensional observers no matter where they are placed in relation to that object. (Heinlein mentions this in Stranger in a Strange Land.)

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If you choose a unit for a measurement, or perhaps I should say a standard on which that unit is based (the unit "meter" is used already for centuries, but the standards have been changed several times, for increasing accuracy), you choose a standard that is as invariant as possible, compared to elementary physical units like the Bohr radius of the hydrogen atom. Therefore the platinum bar that was used first, was kept in controlled conditions at a certain temperature etc. Later more accurate standards were chosen, like a certain number of wavelengths of a particular spectral line.

Okay, I was wrong to call our choice of standard "arbitrary." It would have been better of me to say "practical."

So, our practical choice of a standard determines which model we end up with as a description of the universe. If we choose a standard that's more difficult to use, we end up with a different model. The problem is that most "practical" standards are probably only practical in the short term. I think it's kind of like early astronomers choosing the Earth as the center of the universe -- eventually you need to construct very complex models to describe entities and motions which are actually quite simple when seen from a different but perhaps less practical standard or perspective.

Now there isn't any reason to think that the distance between two galaxies, whether between the centers or the perimeters, has a constant relation to the distances defined in elementary physical systems like atoms (which correspond to our notion of distance that we use in daily life), so such a distance would be a bad unit.

I was assuming that the proportionality constant of Hubble's Law applied to distances between galaxies would be a good reason to think that the distance between galaxies has a constant relation just as in elementary physical systems like atoms.

We prefer to consider the elementary building blocks of the universe, the atoms and elementary particles, to be constant instead of the whole universe, as that would enormously complicate matters. After all, all hydrogen atoms are equal, as are all iron atoms etc., while stars and galaxies are continuously changing. The galaxies may for example in general move away from us, but some of them are moving towards us.

Sure, some galaxies are drifting a bit here and there, and that would present difficulties if we chose to focus on them as our standard rather than on the general relationships of most galaxies, but the same is true of rogue atoms or subatomic particles, no? There are various atomic states of flux, or whatever, which, if we chose to focus on them, could enormously complicate matters just as easily as a rogue galaxy, no?

J

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Okay, I was wrong to call our choice of standard "arbitrary." It would have been better of me to say "practical."

So, our practical choice of a standard determines which model we end up with as a description of the universe. If we choose a standard that's more difficult to use, we end up with a different model. The problem is that most "practical" standards are probably only practical in the short term.

I don't see why. Measuring rods and tapes are still widely used, even if they're not good enough for high accuracy measurements that you for example need for certain scientific experiments. That we have changed the standards in the course of time is because the newer standard was more accurate than the old one, but, once we had abandoned those standards that were based on the length of human body parts like the cubit or the ell, which had the disadvantage of having a large variability, the basic principle has always been the constancy of atomic structures and elementary physical phenomena. For an ordinary measuring rod it doesn't make any difference if the standard is a platinum rod or a certain number of wavelengths, it's too inaccurate for that anyway.

I was assuming that the proportionality constant of Hubble's Law applied to distances between galaxies would be a good reason to think that the distance between galaxies has a constant relation just as in elementary physical systems like atoms.

That relation is an average relation with a fairly low accuracy, no more than 2 digits (moreover, it also changes in the course of time), while the elementary physical relations of atoms and subatomic particles are known with an accuracy of 9 to 12 digits, so it would be a poor substitute. But the biggest objection is that if you could describe the expanding universe in terms of a constant total size with shrinking constituents (with a simple homogeneous isotropic model that would be possible, I'm not sure about more complex models), you wouldn't get any new physics, as all the physical laws are based on the constant size of size of atomic and subatomic systems and wouldn't change at all as all elementary building blocks would shrink equally. It would merely be a substitution of words (Hubble expansion → constancy, constancy → Hubble shrinking), the same as if we would agree that from tomorrow the new meter equals two old meters. It would change a lot of numbers but every mathematical relationship between length measurements would remain the same, just as when we switch from inches to centimeters. So the only effect would be that we substitute a very precise standard with a rough and still rather poorly understood one.

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In the standard expanding spacetime model, nothing happens to photons traveling between galaxies, only the distance they travel increases.

And that might be true of a shrinking galaxy model, and it might not. I don't know. It's something to think about.

Btw, the distance that light travels from galaxy to galaxy in a shrinking galaxy system would increase. As I mentioned in my post to Dragonfly, although the distance between centers of galaxies would remain the same, the distance between galaxy perimeters would increase.

I'm suspecting you wouldn't get enough distance for the cosmic red shift. How large are you picturing the starting size as being?

Anyway, in the expanding model, there are issues which, as I understand them, have required a lot of "fixes" which potentially present bigger problems than they solve, or which remain unexplained, such as the acceleration of the expansion of the universe, and the proposed theories of dark matter and energy. Might a Shrinking Galaxies Theory (or similar new perspectives based on choosing different, unconventional standards of measurement) eliminate some of these issues -- isn't acceleration of the rate of the condensing of matter, for example, much easier to "wrap your head around" than the acceleration of the dispersal of matter?

I don't see it as any easier to understand, and how are you addressing certain issues which the big bang theory at least provides some basis for explaining, such as the cosmic microwave background radiation, the proportion of elements, the formation of galaxies?

(I suspect big bang theory is wrong, but an alternate theory is going to have to attempt to explain, and in a way which either unifies with the rest of physics or shows errors in the rest of physics, issues which big bang theory addresses.)

Ellen

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What if the alternative hypothesis is not shrinkage but variable light speed, in other words?

If light slows down at greater distances than we can currently measure (intergalactic), would that explain the red shift and offer an alternative to the idea that everything is flying away from everything else and so there must have been an initial explosion (or massive and rapid expansion) fourteen billion years ago?

There are physicists who propose "tired light" as the explanation for the red shift. I think this theory is mostly thrown out of court -- Scientific American, for instance, won't even consider papers proposing that idea. But then Scientific American won't consider anything countering the idea of anthropogenic global warming. Likewise with some other "reputable" journals. I don't know if there might be good reasons for the "tired light" hypothesis or not.

Phil, again, really, ixnay on the "explosion." "Massive and rapid expansion" isn't an alternate way of saying "explosion." An explosion is a forceful spewing out of stuff into a surrounding area. With big bang theory, there wasn't any surrounding area -- like a surrounding container of space -- for stuff to be spewed out into. There was no "out there" surrounding. All the "there" was compressed in the initial super-massive "singularity."

Ellen

Edited by Ellen Stuttle

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I'm suspecting you wouldn't get enough distance for the cosmic red shift.

I'm thinking that there's no reason that the distances couldn't be the same as in the expanding universe model. Particles which were in contact with each other at the beginning of the Big Bang, and which are now, say, 200 lightyears apart, would have also been in contact with each other under the shrinking galaxies model, and would also now be 200 lightyears apart. And that's what my animation clips show. As I've mentioned, although the distances between centers of galaxies remain constant, the distances between perimeters increases.

How large are you picturing the starting size as being?

I'm picturing the starting size as being freaking huge. Instead of everything in the universe starting out compressed into a tiny, centralized location, everything would be roughly in the same position that it is now, except it would be multiple-times larger and multiple-times less dense.

...isn't acceleration of the rate of the condensing of matter, for example, much easier to "wrap your head around" than the acceleration of the dispersal of matter?

I don't see it as any easier to understand...

Really? I've heard quite a few scientists talking about how acceleration would make sense in a contracting system as opposed to an expanding one (which is the reason that they find acceleration in an expanding model perplexing, and which still needs an explanation). And as I mentioned earlier, black holes would be just one example of contraction and acceleration. Another would be the simple fact that objects which are attracted to each other in space accelerate as they near each other. Although the specific mechanics of such examples may not be precisely the same as what might happen in a shrinking galaxies model, it seems to me to be at least intuitively easier to grasp the idea of contraction of entities resulting in acceleration than it does to grasp the idea of expansion resulting in acceleration.

...and how are you addressing certain issues which the big bang theory at least provides some basis for explaining, such as the cosmic microwave background radiation, the proportion of elements, the formation of galaxies?

I don't know for sure. That's why I started this thread. I wanted to see if people who have a much deeper understanding of physics than I do would see any benefits or drawbacks in viewing the universe from a different perspective. The purpose of this thread is to ask: "As a thought experiment, does assuming constant distances between the centers of galaxies solve any problems that physicists currently face when dealing with the expanding universe model? And/or does a shrinking galaxies model lead to problems that the expanding model lacks?"

Now, as for background radiation, I see no reason that a shrinking galaxies model couldn't have started out as hot plasma, which, as it cooled, began shrinking into separate galaxies or galaxy clusters, and when the universe cooled enough, the radiation could no longer be fully absorbed.

Basically, where the Big Bang is often seen as an explosion (or at least somewhat like an explosion), a shrinking galaxies model would be seen as being akin to a cloud of gas condensing into millions of separate droplets of liquid, and then eventually solidifying into smaller bits.

Btw, as I said earlier, my intention here was to contrast the expanding universe model against a shrinking galaxies model. That doesn't mean that I'm advocating or opposing one or the other, or that they are necessarily mutually exclusive of each other. I think that in theory, parts of both could exist at the same time -- galaxies could be shrinking while moving away from each other.

J

P.S. Ellen, you probably remember the seed of this discussion. We had once had a few e-mail exchanges about how your husband helps people to visualize the expansion of the universe, and when I played around with the concept in one of my 3D animation programs, I realized that from within any system, universal expansion would look the same as individual galaxies contracting. Recent physics discussions here on OL reminded me of our exchanges, and I thought that the issues of perspectives and appearances might be worth exploring further.

Edited by Jonathan

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The starting size wouldn't particularly matter in regards to the rate. The rate of shrinking would (I believe) be exponential. But that is another problem, isn't it? Growth from a point expanding at the speed of light is well defined. Shrinking from an arbitrarily large size at an arbitrary rate is arbitrary. Basically a division by zero, no?

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P.S. Ellen, you probably remember the seed of this discussion. We had once had a few e-mail exchanges about how your husband helps people to visualize the expansion of the universe, and when I played around with the concept in one of my 3D animation programs, I realized that from within any system, universal expansion would look the same as individual galaxies contracting. Recent physics discussions here on OL reminded me of our exchanges, and I thought that the issues of perspectives and appearances might be worth exploring further.

Jonathan,

Yes, I remember the e-mail exchanges, and I wondered if those were "the seed" of your suggestion.

A problem I'm having visualizing is a continuation of the same problem I was having then, which is, that I don't think the appearance of the animations captures what I understand is supposedly proposed in big bang theory. As I understand the supposed "image," from the perspective of any galaxy in the universe, that galaxy would be experienced as itself the "center" of the expansion with basically the same "distribution" being seen as extending in all directions around with quasars and the CMBR appearing as if around a circumference of a surrounding circle. (DF and Ba'al, please comment, if this is your understanding of how the situation is conceived of.)

However, with your animations, what I get in both cases is the image of a center of reference which isn't the vantage point of a particular galaxy but instead is the center of a large spherical shape either from the center of which the galaxies are expanding or by reference to which the perimeters are shrinking. Thus I don't see that from the perspective of any particular galaxy, the distribution seen would be basically the same as from that of any other particular galaxy.

I have this same difficulty with the visualization examples Larry uses. I think the one I described in our exchange several years back was the one of dots on the surface of a balloon being blown up. Another he uses is raisins in a bread loaf being baked -- as the dough expands, the distance between raisins increases. But in each case, the "picture" wouldn't be the same from the vantage point of any particular dot or raisin. For example, a raisin near the center of the bread loaf would see raisins all around, but a raisin at the edge wouldn't. There would be a direction -- toward the edge of the loaf -- where there weren't raisins to be seen.

Which produces another visualization problem for me: Although I can imagine that the balloon surface expanding is all there is, as if it isn't expanding into surrounding area, I can't imagine no surrounding area with the loaf example. Likewise with your animations.

Ellen

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Which produces another visualization problem for me: Although I can imagine that the balloon surface expanding is all there is, as if it isn't expanding into surrounding area, I can't imagine no surrounding area with the loaf example. Likewise with your animations.

Ellen

Visualization IS the problem. Differential manifolds that could be embedded in a higher dimensional space can also exist by and of themselves. There is a theorem in differential geometry that says an n-dimensional differential manifold could be embedded in a 2*n + 1 Euclidean space. But the existence of the embedding space is not logically required by the existence of the manifold. Do not let the visual intuition limit the mathematics. What physicists are dealing with are mathematical objects which can be used to describe physical entities.

Ba'al Chatzaf

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> Differential manifolds that could be embedded in a higher dimensional space can also exist by and of themselves.

There are no "higher dimensions" in physical space that we can speak of with certainty. We only know that there are the three dimensions our senses give us evidence of. Nor is there such a thing as 'curved space-time' that Dragonfly posted about on another thread.

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> Differential manifolds that could be embedded in a higher dimensional space can also exist by and of themselves.

There are no "higher dimensions" in physical space that we can speak of with certainty. We only know that there are the three dimensions our senses give us evidence of. Nor is there such a thing as 'curved space-time' that Dragonfly posted about on another thread.

Dead wrong. Without the space-time manifold we would have no explanation for gravity. The Newtonian force at a distance hypothesis has been falsified for over 150 years. Spacetime is curved by the presence of mass and energy. Gravitation is essentially curvature of the space-time manifold.

Turn in your GPS. You are not worthy of it.

Ba'al Chatzaf

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> Differential manifolds that could be embedded in a higher dimensional space can also exist by and of themselves.

There are no "higher dimensions" in physical space that we can speak of with certainty. We only know that there are the three dimensions our senses give us evidence of. Nor is there such a thing as 'curved space-time' that Dragonfly posted about on another thread.

Dead wrong. Without the space-time manifold we would have no explanation for gravity. The Newtonian force at a distance hypothesis has been falsified for over 150 years. Spacetime is curved by the presence of mass and energy. Gravitation is essentially curvature of the space-time manifold.

The only things that can be curved--acted upon--by mass and energy are mass and energy. Time is a measurement of motion and space of distance and they are only concepts referencing mass and energy which is the only physical stuff of existence. Spacetime is an explanation of something else--not itself. It cannot be curved or bent.

--Brant

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