Question about Cosmology

[Johnny5]

2 nickels =1 dime, it's all[/b'] about assumptions

 

That's cute, but in the example I provided, the argument goes something like this...

 

2 points = 1 point

 

Therefore, 2=1.

And 2 does not equal 1, hence....

 

 

Regards

[J.C.MacSwell]

That's cute' date=' but in the example I provided, the argument goes something like this...

 

2 points = 1 point

 

Therefore, 2=1.

And 2 does not equal 1, hence....

 

 

Regards[/quote']

 

Assuming no two points can coincide you are correct.

[Johnny5]

Assuming [/b'] no two points can coincide you are correct.

 

Its a conclusion, not an assumption.

 

Set up a three dimensional rectangular coordinate system whose origin is the center of mass of the universe. Let the center of mass of the universe be permanently at rest in this frame.

 

Make this frame a minimum energy frame. That means you don't want the axes spinning wildly relative to the fixed stars.

 

Mathematically this means we want Galileo's law of inertia to be true in this coordinate system.

 

Ok all that being done, consider two locations in space A,B relative to the center of mass of the universe, which is at point C.

 

I say that the distance between A and B cannot change. It is a temporal constant. For suppose not. Let it be the case that A can move relative to B. Let a force act upon A, to give it an impulse in the direction of B, with just the right final speed so that at some point in the future, A coincides with B.

 

At that moment in time, the point A is spatially equivalent to the point B.

 

But the points are different by stipulation.

 

Therefore, point A cannot move through the coordinate system.

 

Regards

 

(If the argument seems corny, that's not my fault. It constantly boils down to not (2=1), because if at any moment in time the point A moved it would be on top of and in (coinciding) with some other distinct point D in the frame. And in a rigid frame such as this, the Pythagorean theorem is a true statement)

[Tom Mattson]

Suppose that space could be created. Therefore' date=' points in a coordinate system could move relative to one another. If a point in a coordinate system could move in a coordinate system, then two points in the coordinate system would simultaneously be located at one point in the coordinate system, whence 1=2.

[/quote']

 

Of course 1 can't equal 2, but that doesn't prove anything even remotely resembling your point. If space is indeed created (or I should say, if the spatial separation of 2 objects is increasing as a result of cosmic inflation), then it is possible to construct a map from a coordinate axis at one time t to the same axis at another time t such that all points from the first map continusously on to the second. A simple such model is:

 

T: R³xR-->R³xR, T(x,y,z,t)=((x+|a|Dt,y,z,t+Dt).

 

This would increase the metric between two points (in the x-direction), and would not lead to "1=2".

[J.C.MacSwell]

That's what I thought. I also think that position is completely untenable.

 

There is no sensible way to talk about locations in space in the absence of physical objects. Take away all physical objects in the universe' date=' and there is no way you can point somewhere and say, "There's where Earth used to be".

 

I think that a much more sensible conception of space is the relational view, which states that space does not exist apart from the spatial relationships which physical objects bear relative to one another. Take away the objects, and you take away their spatial relationship.

 

This is not only more attractive logically, it also has its advantages scientifically, being more in harmony with General Relativity.[/quote']

 

I understand your point but I do not see it as more logical, only plausibly more practical. If you "recreated" all physical objects in the universe there is no way you can point somewhere and say, "There's where Earth is now".

until the light had time to "orient" you in space but you could not say that space does not exist until the light had time to cross it anymore than I can argue that nothing existed before I was born (or conceived).

 

My point is that I am not sure that space "requires" matter, it certainly seems to be able to delay light without matter.

[Johnny5]

If space is indeed created (or I should say' date=' if the [b']spatial separation of 2 objects is increasing as a result of cosmic inflation[/b]), then it is possible to construct a map from a coordinate axis at one time t to the same axis at another time t such that all points from the first map continusously on to the second.

 

In order to mathematically define the "spatial location of an object" one needs to have already chosen some reference frame in which to define that location. The location of the object is to be taken as the location of the objects center of inertia.

 

The spatial separation of two objects would then be measured by a rigid ruler (ruler at absolute zero kelvin) at rest in the measurement frame.

 

Now the location of a center of inertia is just a point in the reference frame.

 

So to say that two objects got further apart we do not mean that two points in the reference frame moved. Instead we mean that there was relative motion of material, and the center of inertia of at least one of the objects, now has a new location in the original frame.

 

Or to put this another way.

 

Take a rigid steel bar, and locate the center of inertia. Now bend the bar into a V shape. The center of inertia no longer lies inside the material, it lies exterior to the material. You did not bend space in order to change the coordinates of the center of inertia... no sir... you bent the bar.

 

Regards

[J.C.MacSwell]

Its a conclusion' date=' not an assumption.

 

Set up a three dimensional rectangular coordinate system whose origin is the center of mass of the universe. Let the center of mass of the universe be permanently at rest in this frame.

 

Make this frame a minimum energy frame. That means you don't want the axes spinning wildly relative to the fixed stars.

 

Mathematically this means we want Galileo's law of inertia to be true in this coordinate system.

 

Ok all that being done, consider two locations in space A,B relative to the center of mass of the universe, which is at point C.

 

I say that the distance between A and B cannot change. It is a temporal constant. For suppose not. Let it be the case that A can move relative to B. Let a force act upon A, to give it an impulse in the direction of B, with just the right final speed so that at some point in the future, A coincides with B.

 

At that moment in time, the point A is spatially equivalent to the point B.

 

But the points are different by stipulation.

 

Therefore, point A cannot move through the coordinate system.

 

Regards

 

(If the argument seems corny, that's not my fault. It constantly boils down to not (2=1), because if at any moment in time the point A moved it would be on top of and in (coinciding) with some other distinct point D in the frame. And in a rigid frame such as this, the Pythagorean theorem is a true statement)[/quote']

 

What you are saying is that in a fixed cartesian coordinate system the points cannot move with respect to each other.

 

But is that the way space "is"?

[Tom Mattson]

I understand your point but I do not see it as more logical' date=' only plausibly more practical.

[/quote']

 

OK, try to envision space devoid of matter, and then try to identify places within that space. With nothing to refer to, you won't be able to do it.

 

If you "recreated" all physical objects in the universe there is no way you can point somewhere and say, "There's where Earth is now".

until the light had time to "orient" you in space but you could not say that space does not exist until the light had time to cross it anymore than I can argue that nothing existed before I was born (or conceived).

 

This isn't the same problem. We can talk sensibly about where the Earth is now if we take into account the finite propagation time for light, which we know how to do. What I'm saying is that it isn't possible even in principle to specify locations in empty space. And this has nothing to do with solipsism or idealism.

 

My point is that I am not sure that space "requires" matter, it certainly seems to be able to delay light without matter.

 

I've never heard of light being delayed between 2 points in space.

[Tom Mattson]

Johnny5, I did not present an argument in favor of expanding space. I presented an argument that expanding space does not imply 2=1 (which was, after all, your original point). Your response, which is an opinion against expanding space, does not address that.

[J.C.MacSwell]

OK, try to envision space devoid of matter, and then try to identify places within that space. With nothing to refer to, you won't be able to do it. .

 

Agreed

 

 

This isn't the same problem. We can talk sensibly about where the Earth is now if we take into account the finite propagation time for light' date=' which we know how to do. What I'm saying is that it isn't possible [i']even in principle[/i] to specify locations in empty space. And this has nothing to do with solipsism or idealism..

 

In principle it's quite easy. Location A (1,2,3) Location B (4,5,6)

 

In practice see above, I agree with you,

 

 

 

I've never heard of light being delayed between 2 points in space.

 

I'm sure you don't believe the speed of light is infinite.

[Tom Mattson]

Tom: What I'm saying is that it isn't possible even in principle to specify locations in empty space.

 

J. C.: In principle it's quite easy. Location A (1,2,3) Location B (4,5,6)

 

That means nothing without specifying the (0,0,0) point. And since (1,2,3) is indistinguishable from (0,0,0) without material bodies to refer to, (1,2,3) cannot mean anything in an empty universe, even in principle.

 

I'm sure you don't believe the speed of light is infinite.

 

No I don't, but accepting a finite speed of light is not the same as accepting that light is "delayed". In order to regard light as delayed, one would have to hold the a priori notion that light should be moving faster than c. I do not hold that notion.

[Deified]

In order to mathematically define the "spatial location of an object" one needs to have already chosen some reference frame in which to define that location. The location of the object is to be taken as the location of the objects center of inertia.

 

The spatial separation of two objects would then be measured by a rigid ruler (ruler at absolute zero kelvin) at rest in the measurement frame.

 

Now the location of a center of inertia is just a point in the reference frame.

 

So to say that two objects got further apart we do not mean that two points in the reference frame moved. Instead we mean that there was relative motion of material' date=' and the center of inertia of at least one of the objects, now has a new location in the original frame.

[/quote']

 

 

If we are talking about expanding space, then you're wrong, the points changed. The distance is greater between the objects but neither of them have move in respect to the reference frame. If the objects are pulling each other then then the distance between might change a little bit but would eventually settle into an equilibrium. In this case they move in respect to the reference frame (they are no longer at their original points) but not in respect to each other. (the distance between them remains the same)

[J.C.MacSwell]

That means nothing without specifying the (0' date='0,0) point. And since (1,2,3) is indistinguishable from (0,0,0) without material bodies to refer to, (1,2,3) [i']cannot[/i] mean anything in an empty universe, even in principle.

 

 

 

No I don't, but accepting a finite speed of light is not the same as accepting that light is "delayed". In order to regard light as delayed, one would have to hold the a priori notion that light should be moving faster than c. I do not hold that notion.

 

You do not believe in any "fabric" of space? Is this correct?

 

If it is correct then what do you perceive to prevent light from travelling (say) two light years in one years duration?

 

Maybe a better way of putting it is:

 

What is it that does not allow the light to arrive earlier? What is it that makes it a 2 light year distance instead of just one? You seem to be sure that it is nothing substantial. I cannot prove that it is. But I doubt that you can prove that it is not.

 

Even in principle.

[swansont]

Space isn't a tangible thing to be created.

The big bang was most definitely an explosion in space.

 

The reason I am right has to due with the impedance of the vacuum' date=' it's literally zero. And I don't mean electrical impedance, and I don't mean our local vacuum, which isn't a true vacuum.

 

 

Regards

 

PS: If I'm wrong prove it to me.[/quote']

 

Tom Mattson has already addressed most of this, but let me add that whether your view of the universe is right or wrong, it still does not validly represent the Big Bang model, in which space was created. Your hypothesis is different.

 

Stating what you don't mean by impedance and what you don't mean by vacuum isn't particularly helpful.

 

If you're right, what are some of the predictions you can make about the universe?

[Spyman]

I just want to know whether or not the universe has a center.

In theory if it has dimensions then it must have a center, it does not matter if it is finite or infinite, is expanding, static or retracting and have any number of dimensions.

 

However to prove experimentally that the universe has a center, one must be able to someway point out its direction and distance.

 

Not so easy when positioned someplace inside without knowing where.

 

As far as I know there has NOT been any successful experiment even proving the possibility of a method of how to find the center.

 

[Johnny5]

What you are saying is that in a fixed cartesian coordinate system the points cannot move with respect to each other.

 

But is that the way space "is"?

 

Yes, that's what is being said. That the points in space have a 1-1 mapping to the points in the coordinate system.

[Johnny5]

Johnny5, I did not present an argument in favor of expanding space. I presented an argument that expanding space does not imply 2=1 (which was, after all, your original point). Your response, which is an opinion against expanding space, does not address that.

 

Here was your model for space expansion:

 

T: R³xR-->R³xR, T(x,y,z,t)=((x+|a|Dt,y,z,t+Dt)

 

You have the x axis stretching.

 

Use this model of space expansion to analyze a rigid bar for me, if you don't mind.

 

At some moment in time, let one end of a steel bar have x coordinate 0, and let the other end of the bar have x coordinate 3. So the bar is three meters long presently, at moment in time t=0.

 

Then exactly one moment in time later, let space have expanded in that model. Tell me where the center of inertia is now, and where the ends of the bar are now.

 

One more thing... at moment in time t=0, the temperature of the bar is absolute zero, the density of the bar is uniform, and the bar is at rest in the frame. You can introduce any other physical concepts you need.

 

Regards

[Tom Mattson]

You do not believe in any "fabric" of space? Is this correct?

 

No' date=' I don't believe in a fabric of space. I think that space does not have any independent existence of its own.

 

If it is correct then what do you perceive to prevent light from travelling (say) two light years in one years duration?

 

Maybe a better way of putting it is:

 

What is it that does not allow the light to arrive earlier? What is it that makes it a 2 light year distance instead of just one?

 

I don't know why the speed of light is what it is. No one does.

 

You seem to be sure that it is nothing substantial. I cannot prove that it is. But I doubt that you can prove that it is not.

 

Even in principle.

 

I didn't prove that space does not exist, any more than I proved that invisible pink fairies don't exist. What I argued for is that the idea of space existing independently of matter is unintelligble, just as the existence of invisible pink fairies is unintelligible.

[J.C.MacSwell]

No' date=' I don't believe in a fabric of space. I think that space does not have any independent existence of its own.

 

 

 

I don't know why the speed of light is what it is. No one does.

 

 

 

I didn't prove that space does not exist, any more than I proved that invisible pink fairies don't exist. What I argued for is that the idea of space existing independently of matter is [i']unintelligble[/i], just as the existence of invisible pink fairies is unintelligible.

 

I thought that was your position. I do not agree with it but I can see that it is logically consistent based on your assumptions (and lack of assumptions in certain areas)

[Tom Mattson]

Here was your model for space expansion:

 

T: R³xR-->R³xR' date=' T(x,y,z,t)=((x+|a|Dt,y,z,t+Dt)

 

You have the x axis stretching.

 

Actually, I have the x-axis translating. That was my mistake. However, it still has the moving points that you mentioned in your argument.

 

But to really stretch the x-axis, I'd need to multiply the x-coordinate by something, not add something to it. So here's my corrected map:

 

T:R³xR-->R³xR, T(x,y,z,t)=(a(t)x,y,z,t)

 

Use this model of space expansion to analyze a rigid bar for me, if you don't mind.

 

Hold up there, Junior, this is quid pro quo. You have been ducking the issue here for a couple of posts, which is that your argument is bogus. Let's reach closure on that before moving on. So, if you don't mind, let's see you use either of the two above maps (or even the model for expanding space from GR) to derive "1=2".

 

Still waiting...

[Johnny5]

 

T: R³xR-->R³xR' date=' T(x,y,z,t)=((x+|a|Dt,y,z,t+Dt)

 

T:R³xR-->R³xR, T(x,y,z,t)=(a(t)x,y,z,t)

 

...let's see you use either of the two above maps to derive "1=2".

 

Well consider the first mapping... only the x axis moves, and its speed is a.

 

No other points in space move, just the points on the x axis 'move'.

 

So for example consider the origin of the frame initially. Let the origin be the location of the center of mass of the universe, and let no material lie upon the axes of this frame. After time has incremented once, the center of mass of the universe is no longer where it just was, it has moved along the original x axis. Unfortunately, all the material in the universe obeys the laws of physics, hence the center of mass of the universe stayed where it was.

 

So your mapping caused the center of mass of the universe to move .

 

Mapping 1 is physically unrealistic.

 

As for mapping 2...

 

I see no reason not to apply the same argument.

 

Only this time, begin the argument in a frame of reference one meter away from the center of mass of the universe.

 

Let the center of mass of the universe be at (1,0,0).

 

Then magnify all numbers on only the x axis by a factor of five.

 

Therefore, the CMU is now at (5,0,0)

 

But again, there was no material on the axes initially.

 

Hence the center of the universe is still at (1,0,0).

 

Hence the CMU has and hasn't moved, which is absurd.

 

Neither of these mappings is possible.

 

QED

 

Regards

[Tom Mattson]

You have a real knack for missing the point.

 

I never said that either of those mappings are physically realistic. Indeed, neither of them can be because neither of them are identical to the GR model, which is known to be correct.

 

No, what I asked you to do is to show why expanding space of some sort necessarily implies that 1=2. You still haven't given me the answer.

[Johnny5]

Indeed' date=' neither of them can be because neither of them are identical to the GR model, which is known to be correct.

[/quote']

 

Which GR model are you talking about, and known by who to be correct exactly?

[[Tycho?]]

Which GR model are you talking about, and known by who to be correct exactly?

 

GR is presumably General Relativity. Known to be correct by the scientific world.

 

Now, you can't "know" its correct. There still could be a flaw in it. However, the theory has worked amazingly well, and since it was published in 1915 it has stood up to every test people have thrown at it. It is for all intents and purposes correct at this time.

[Tom Mattson]

Which GR model are you talking about' date='

[/quote']

 

I mean GR as applied in cosmology, and described in Chapter 8 of the following book:

 

http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019.pdf

 

and known by who to be correct exactly?

 

Physicists and astronomers.