What is light?

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csmyth3025

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csmyth3025":crfq00bh said:
This may not be the correct thread, but I'm wondering if someone has calculated the Swarzschild radius for the event horizon of all the matter (visible and dark) and energy (known and dark) currently estimated to be in the universe. This is, of course, theoretical since - by definition of the problem - there wouldn't be anyone outside the event horizon to appreciate how big it is. Still, the first moments of the Big Band are described as starting from a point of (almost) infinite density and temperature. That sounds a whole lot like a singularity to me.

Chris

First, a caveat: "...the first moments of the Big Band..." is a typo and doesn't refer to our musical past.

I've been trying to answer my own post (above) using the information readily available to me (Wikipedia). As I understand it the diameter of the volume of matter we can observe today (the observable universe) is ~93 x 10^9 light years (~8.8 x 10^26 meters) and the average density (in terms of the equivalent mass of 73% dark energy, 23% cold dark matter, and 4% ordinary matter) is ~9.9 x 10^-30 gm/cm^3. I found this information here:

http://en.wikipedia.org/wiki/Universe#S ... C_and_laws

The formula for the Schwarzchild radius of an uncharged, non-rotating object is : r = 2Gm/c^2 where the value of 2G/c^2 = ~1.48 x 10^-27 m/kg and m is given in kg. I found this information here:

http://en.wikipedia.org/wiki/Schwarzschild_radius

Converting gm/cm^3 for the average density into kg/m^3 gives me 9.9 x 10^-42 kg/m^3 if my math is correct.

Using the formula 4/3*pi*r^3 for the volume of the observable universe and a radius of 4.4 x 10^26 m I get a volume of 8.52 x 10^79 m^3*pi*4/3= ~3.57 x 10^81 m^3

Multiplying this volume by the average density gives me a total equivalent mass for the observable universe of ~3.53 x 10^40 kg. Multiplying this mass by 1.48 x 10^-27 m/kg gives me ~5.22 x 10^13 m for the Swarzschild radius of the entire mass of the observable universe.

There is clearly something wrong with my calculation. This radius is barely larger than the proposed inner radius of the Oort cloud around the sun.

HELP!

Chris
 
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ramparts

Guest
Here's the calculation:

http://www.wolframalpha.com/input/?i=2* ... 289.9+x+10^-30+gm%2Fcm^3+*+4%2F3+*+pi+*+%2813.7+billion+light+years%29^3%29%2F%28speed+of+light%29^2

I'm not sure where you went wrong, although you didn't get the right value of the mass, so it's probably somewhere around there.

The answer is 1.3*10^26 meters, or about 1.4 times the Hubble length (the size of the observable universe). Actually, WolframAlpha seems to have an incorrect value of the Hubble length, but regardless, the answer is about 14 billion light years, so the answer is larger than the size of the observable universe.

Remember this isn't a really meaningful calculation, it's just saying that if you took our observable universe and neglected gravitational effects from elsewhere in the universe (that is, took our observable universe as a standalone sphere), it wouldn't be a black hole.
 
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csmyth3025

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ramparts":3l0crvtj said:
Here's the calculation:

http://www.wolframalpha.com/input/?i=2* ... 289.9+x+10^-30+gm%2Fcm^3+*+4%2F3+*+pi+*+%2813.7+billion+light+years%29^3%29%2F%28speed+of+light%29^2

I'm not sure where you went wrong, although you didn't get the right value of the mass, so it's probably somewhere around there.

The answer is 1.3*10^26 meters, or about 1.4 times the Hubble length (the size of the observable universe). Actually, WolframAlpha seems to have an incorrect value of the Hubble length, but regardless, the answer is about 14 billion light years, so the answer is larger than the size of the observable universe.

Remember this isn't a really meaningful calculation, it's just saying that if you took our observable universe and neglected gravitational effects from elsewhere in the universe (that is, took our observable universe as a standalone sphere), it wouldn't be a black hole.

Thanks ramparts,

I was unable to follow your link but I rechecked my calculation using WolframAlpha (a very useful site, by the way):

Using 4.4 x 10^26 meters as the radius of the presently observable universe I got a volume of 3.568 x 10^80 m^3. this value is smaller by a factor of ten than my original calculation (mistake #1). The WolframAlpha web site indicates that this corrected number is equal to 1.0005 x volume of the observable universe so I feel pretty good about it.

I then took the Wikipedia value for the average density of the universe (9.9 x 10^-30 gm/cm^3) and converted it to kg/m^3. This comes out to 9.9 x 10^-27 kg/m^3. This number is 10^15 larger than my original calculation (big mistake #2). Interestingly, the WolframAlpha site indicates that this corrected value in kg/m^3 is ~10 times larger than the average density of the universe. Upon closer inspection I found that the WolframAlpha site is using the same g/cm^3 value as Wikipedia. By my reasoning the average density in kg/cm^3 should be 1/1000 that given for gm/cm^3 and this would give me 9.9 x 10^-33 kg/cm^3. Since 1m=100cm, 1m^3 should equal (100 cm)^3 or 1 x10^6 cm^3. Using this conversion factor, I come up with an average density of 9.9 x 10^-27 kg/m^3 - which is the same calculated value that the WolframAlpha site produced. I don't know why the site is saying that this is ~10 times the value of the density of the universe.

Taking these corrected results, the WolframAlpha site calculates that the mass of the universe is ~5.5 x 10^54 kg. Here, again, the site indicates that this is ~120 times the mass of the universe - which it cites as being ~3 x 10^55 gm (~3 x 10^52 kg).

Taking the above calculated value for the mass contained in the observable universe and plugging it into the formula for the Swarzschild radius of an uncharged, non-rotating black hole I get 5.245 x 10^27 m (~554.4 Billion LY, or about 6 times the 93 billion LY diameter of the observable universe - according to Wikipedia - that I started with). Since this final calculated value is a radius, the diameter of the "event horizon" of the mass in the observable universe would be twice this, or 12 times the diameter of the observable universe.

If I use the WolframAlpha cited value for the mass of the universe (3 x 10^52 kg) I get 4.455x10^25 m (4.709 billion LY, or about 1/20 the diameter of the observable universe. Again, since this calculated value is a radius, the diameter of the "event horizon" of the mass in the observable universe would be about 1/10 that of the presently observable universe.

The meaning of these numbers perplexs me. Whether my calculated value for the Schwarzschild radius of the mass contained in the observable universe (~6 times the diameter of the observable universe) or the Schwarzschild radius of the mass contained in the observable universe (~1/20 the diameter of the observable universe) according to the WolframAlpha site is more probable, I'm left scratching my head.

In the first case (my calculation), it seems that an event horizon for the mass contained in the observable universe already exists at a distance (from Earth) of 554.4 billion LY. If there is mass beyond our observable universe, it will serve only to shrink this distance.

It's my understanding that the reason our present-day observable universe is described as having a diameter of ~93 billion LY is that objects (stars and such) beyond 46.5 billion LY from us are moving at superluminal velocities due to the expansion of the intervening space. The light from these objects will never reach us. If the expansion of space is accelerating then the diameter of our observable universe will shrink accordingly. For my present calculation, however, there appears to be sufficient mass in our observable universe to create an event horizon.

If this is the case, then my question would be: If we're living in a black hole with an event horizon, can the expansion of space push matter and energy past the event horizon to the "other side"?

In the second case (WolframAlpa's value for the mass of the universe), it would seem that the mass contained in our present-day observable universe would have to be concentrated in a volume within ~4.7 billion LY from where Earth now is in order to form a black hole with an event horizon. According to the currently accepted cosmological model, this was the case at some point in the past. Since our present-day observable universe stretches beyond this limit by a factor of ten, the answer to the question I posed above seems to be that, yes, the expansion of space can push matter and energy beyond an event horizon.

All of this may seem like idle speculation, but to me it seems that the rules that apply to black holes within our universe should also apply to our universe in total. If there's a mechanism by which matter and energy can be forced out of the event horizon of a black hole encompassing all the matter in our observable universe, then there must be a lower limit of mass within which this mechanism can't prevail against gravity. This seems likely since there's ample evidence that black holes do, in fact, exist in our universe. My question then becomes: Is there a certain maximum mass beyond which a black hole cannot exist due to the expansion of space contained within its event horizon?

Chris
 
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ramparts

Guest
Hi Chris - WolframAlpha is useful because it cuts out a lot of the intermediate steps where one can make mistakes. SDC screwed up the link - try http://bit.ly/pkQ7a.

csmyth3025":2c9plgwz said:
The meaning of these numbers perplex me. Whether my calculated value for the Schwarzschild radius of the mass contained in the observable universe (~12 times the diameter of the observable universe) or the Schwarzschild radius of the mass contained in the observable universe (~1/10 the diameter of the observable universe) according to the WolframAlpha site is more probable, I'm left scratching my head.

These sound like the same thing - "the Schwarzschild radius of the mass contained in the observable universe." Can you explain (briefly) what you did differently to get those two numbers?

In the first case (my calculation), it seems that an event horizon for the mass contained in the observable universe already exists at a distance (from Earth) of 554.4 billion LY. If there is mass beyond our observable universe, it will serve only to shrink this distance.

Well, we're taking the size of the observable universe as our radius, so if we consider mass beyond the observable universe, then we also have to expand the radius we consider.

Anywho, I got a little suspicious that our answers are coming out so close to 1 Hubble length (the age of the universe in light years), so I just ran through the math and it turns out that we're considering a tautology, albeit a somewhat interesting one. Turns out, the answer should be a Hubble length. If you take a universe at the critical density (that is, a flat universe) and calculate the Schwarzschild radius for all the matter inside the Hubble length, the answer is that the Schwarzschild radius is the Hubble length (the math actually isn't too difficult, if anyone is curious). Now, if the universe were denser than that, we know we would live in what's called a closed universe - a universe with negative curvature that expands and then eventually stops, and contracts. In that case, the Schwarzschild radius would be greater than the size of the observable universe, and you could think of the "big crunch" as being analogous to the universe living inside a black hole. But at the critical density, we're just barely not dense enough to avoid that, so the size is exactly equal to the Schwarzschild radius.

Again, though, don't read too much into all this. There is matter outside the sphere we're considering, and that will counteract the effects we're talking about. In reality, a sphere the size of our visible universe would not act like a black hole, since there's stuff pulling from the outside.
 
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csmyth3025

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Again, though, don't read too much into all this. There is matter outside the sphere we're considering, and that will counteract the effects we're talking about. In reality, a sphere the size of our visible universe would not act like a black hole, since there's stuff pulling from the outside.

This is an interesting concept. Is it really possible that a black hole can be in proximity to a large enough distribution of mass outside its event horizon that the external gravitational fields can enable matter and energy within the event horizon to escape the event horizon and return to the visible universe?

I realize that the source numbers we're using for the mass of the universe differ. These numbers are, at best, educated guesses by researchers and theorists who utilize different criteria and modeling to arrive at their estimates. By any calculation it seems the the mass contained in our presently observable universe is sufficient to create a black hole with an event horizon, either now or at some time in the past when this matter was contained in a smaller volume.

You're correct that any mass outside our observable universe, but within an event horizon that lies beyond would, in fact, increase the volume contained in the event horizon. My opposite conclusion is just another example of my following a line of logic and then inexplicably getting derailed into a totally illogical conclusion at the last minute.

The fundamental questions remain: Does the expansion of space occur within the bounds of an event horizon as it does in our universe outside such objects? Is there a maximum volume encompassed by an event horizon beyond which the evpansion of space within this volume is able to overcome gravity? In effect, objects at or within the event horizon would be moving at superluminal velocities away from the singularity due to the expansion of the intervening space.

Chris
 
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MeteorWayne

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I cleaned up the double post. You can do that yourself, BTW, it's the little "x" box to the right of the "edit" box.- MW
 
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csmyth3025

Guest
MeteorWayne":jwjb7dzm said:
I cleaned up the double post. You can do that yourself, BTW, it's the little "x" box to the right of the "edit" box.- MW

Hmm...
I have a little triangular icon containing an exclamation mark to the right of the edit box (it's for reporting posts).

Chris
 
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csmyth3025

Guest
One of the Mach Principles listed in the Wikipedia article here:

http://en.wikipedia.org/wiki/Mach_principle

Is as follows:

Mach8: Omega=4*pi*p*GT^2 is a definite number, of order unity, where ρ is the mean density of matter in the universe, and T is the Hubble time.

Is this conjecture related to our discussion about the possible existence of an event horizon of the universe?

Chris
 
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SpeedFreek

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Crikey! I wish I had looked at this thread earlier, if the last few pages are anything to go by... ;)

Of course the "Schwarzschild radius" of the observable universe is the Hubble distance! Objects have to have an apparent recession speed of c if they are to escape our Hubble Sphere! :lol:

(As an aside, notice how Schwarzschild is german for "black shield"... spooky eh?)

Anyone want to know about the cosmological event horizon?
 
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csmyth3025

Guest
SpeedFreek":10hul3gu said:
Crikey! I wish I had looked at this thread earlier, if the last few pages are anything to go by... ;)

Of course the "Schwarzschild radius" of the observable universe is the Hubble distance! Objects have to have an apparent recession speed of c if they are to escape our Hubble Sphere! :lol:

(As an aside, notice how Schwarzschild is german for "black shield"... spooky eh?)

Anyone want to know about the cosmological event horizon?

Yes SpeedFreek, I'm very curious about the cosmological event horizon. All of the carrying on in my last few posts here has sort of been taking the long way around to ask the question: "Is there a cosmological event horizon?"

My conjecture is that, at a certain cosmological distance from our vantage point in the universe, the expansion of space is carrying objects away from us at superluminal velocities (relative to us). I think this concept is widely accepted in the scientific community.

The part that I'm wondering about is the average density of matter in the spherical volume of space centered on us and extending radially in all directions to that certain distance. Is the average density of matter in that volume sufficient to form an event horizon which, by definition, requires objects with mass to exceed the speed of light in order to achieve an eccape velocity which will propel them outside the evevt horizon?

If this is the case then I reason that there must be some maximum concentration of mass generatig a maximally voluminous event horizon such that the expansion of space itself within the event horizon renders the cosmic censorship principle of the event horizon meaningless from the stanpoint of a distant obserer outside the event horizon.

Any thoughts on this scenario?

Chris
 
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origin

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My conjecture is that, at a certain cosmological distance from our vantage point in the universe, the expansion of space is carrying objects away from us at superluminal velocities (relative to us). I think this concept is widely accepted in the scientific community.

Yes that is correct

The part that I'm wondering about is the average density of matter in the spherical volume of space centered on us and extending radially in all directions to that certain distance. Is the average density of matter in that volume sufficient to form an event horizon which, by definition, requires objects with mass to exceed the speed of light in order to achieve an eccape velocity which will propel them outside the evevt horizon?

No there is not event horizon that is due to gravity (mass).

If this is the case then I reason that there must be some maximum concentration of mass generatig a maximally voluminous event horizon such that the expansion of space itself within the event horizon renders the cosmic censorship principle of the event horizon meaningless from the stanpoint of a distant obserer outside the event horizon.

Any thoughts on this scenario?

Chris

Since there is no huge event horizon that is a result of gravity in our area of the universe your scenario is not valid.
 
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SpeedFreek

Guest
There are two kinds of singularities associated with black holes. The event-horizon is a "coordinate" singularity, whereas the real, honest to goodness, gravitational singularity is at the centre of the black hole. It is unclear if that gravitational singularity can actually form, due to effects at the quantum level.

The cosmological event horizon is a coordinate singularity too, in a certain sense. But as origin said, there is no gravitational singularity associated with the average mass density of the universe. You need an extremely high mass density for a gravitational singularity to form.

The cosmological event horizon is an apparent horizon as, just like the event horizon of a black hole, it is only a horizon relative to a distant observer.
 
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csmyth3025

Guest
SpeedFreek":3cjs8aeo said:
There are two kinds of singularities associated with black holes. The event-horizon is a "coordinate" singularity, whereas the real, honest to goodness, gravitational singularity is at the centre of the black hole. It is unclear if that gravitational singularity can actually form, due to effects at the quantum level.

The cosmological event horizon is a coordinate singularity too, in a certain sense. But as origin said, there is no gravitational singularity associated with the average mass density of the universe. You need an extremely high mass density for a gravitational singularity to form.

The cosmological event horizon is an apparent horizon as, just like the event horizon of a black hole, it is only a horizon relative to a distant observer.

My curiosity concerns the following: "The formula for the Schwarzchild radius of an uncharged, non-rotating object is : r = 2Gm/c^2 where the value of 2G/c^2 = ~1.48 x 10^-27 m/kg and m is given in kg."

As I understand it, this formula says that if you shrink a one kg mass to a spherical volume of radius 1.48 x 10^-27 m, the mass will collapse into a [gravitational] singularity and leave an event horizon of this radius. I hope I've stated this correctly.

Can this formula can be applied to any arbitrarily large mass, resulting in an arbitrarily large radius for the volume contained in the event horizon of the collapsed mass?

The reason I ask this question is that the formula for the Schwarzschild radius presents a linear relationship between mass and radius. The volume contained within the event horizon increases as the cube of the radius, however. So far I'm sure I'm not making any grounbreaking statements here.

This is where things start to get dicey. Origin says: "No there is not event horizon [of the universe] that is due to gravity (mass)." and SpeedFreek says: "You need an extremely high mass density for a gravitational singularity to form."

I can find nothing in the formula for the Swarzschild radius that supports these two statements. As far as I can tell, there is no upper boundary of mass beyond which this formula no longer applies. Additionally, the formula says nothing about the distribution of mass within the volume of the event horizon. It could be a point-like object, or it could be evenly dispersed - the formula makes no distinction between these two possibilities.

In the case of an evenly dispersed mass within the event horizon (the mass of our universe contained within the Hubble volume of our universe, possibly), it seems to me that a theoretical distant observer would only see a rather large black hole "out there".

This possible (to me) scenario leads to an interesting paradox. I believe that the current solutions for the curvature of spacetime within the event horizon results in the timelike metric becoming a spacelike metric pointing towards the [assumed] singularity. In essence, anything within the event horizon is headed for the singularity as surely as night follows day in our more ordinary world. Yet here we are, apparently headed lickety-split away from the singularity that presumably was the precursor of the big bang. Hmm...

I anxiously await being pilloried for the logical errors in my speculation.

Chris
 
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SpeedFreek

Guest
Thank you for that post, I think I can see more clearly what some of the issues are now.

The Schwarzschild solution is an "outside" solution. It deals only with the gravitational field outside of a spherical non-rotating mass. The Schwarzschild radius represents the distance from the centre of mass where, if all the mass of the non-rotating object were inside it, an event horizon would form. Gravitational collapse occurs when an object's internal pressure, energy or forces are insufficient to resist the object's own gravity.

According to your calculations, the Schwarzschild radius of the universe is the Hubble distance, which is currently thought to be a little under 14 billion light-years. The radius of the observable universe however, is over three times larger.

There are no "outside" solutions for our universe as far as I know, nor does general relativity allow the universe a centre in any way that is not arbitrary.

The expansion of the universe is sufficient to resist the gravity of the universe, or perhaps that should be the other way round! The gravity of the universe is insufficient to resist the expansion.

So as far as I can see, even if we ignore that the Schwarzschild solution is only applicable outside the spherical mass, then just as the Schwarzschild radius of the Sun still inside it, so is the Schwarzschild radius of the universe. The Sun is not massive enough to form a black hole and nor is the universe. Rather than any gravitational collapse to increase the density of the mass of the universe until it is within the Schwarzschild radius, the density of the universe is always decreasing and at no time was gravity strong enough to resist the expansion and collapse all of the mass to within required radius - the metric that defines distance has been constantly increasing all along and in the early universe even short distances were increasing faster than light. Gravity didn't stand a chance!

But maybe I am misunderstanding you, or missing something obvious. :?:

However, I do think that if the Schwarzschild radius of the observable universe is the Hubble distance, then this is significant, as the Hubble distance is the place where a galaxy has an apparent recession speed of c. Is this too close to the escape velocity of c at the Schwarzschild radius to be a coincidence?
 
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csmyth3025

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Well folks,
I concocted a lengthy post in which I recalculated the parameters in my previous post using a value of 71(km/sec)/Mpc for the Hubble constant. As fate would have it, I lost the whole thing when I tried to preview it - thus sparing you a lot of boring reading. The bottom line is that I figure that if the estimated equivalent mass of the universe occupied a volume of ~1/1000 the present Hubble volume, it would be sufficiently dense to collapse into a gravitational singularity.

My question now is: What was the age of the universe when it occupied this volume? I ask this question with the following statement in mind: "...According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called the surface of last scattering. This represents the collection of points in space at which the decoupling event is believed to have occurred, less than 400,000 years after the Big Bang...", which can be found in the Wikipedia article here: http://en.wikipedia.org/wiki/Cosmic_mic ... _radiation

A second question also comes to mind: Is the Hubble constant believed to be significantly larger at this [younger] age of the universe than it is today?

Chris
 
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SpeedFreek

Guest
csmyth3025":2ejf3oe9 said:
The bottom line is that I figure that if the estimated equivalent mass of the universe occupied a volume of ~1/1000 the present Hubble volume, it would be sufficiently dense to collapse into a gravitational singularity.

My question now is: What was the age of the universe when it occupied this volume? I ask this question with the following statement in mind: "...According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called the surface of last scattering. This represents the collection of points in space at which the decoupling event is believed to have occurred, less than 400,000 years after the Big Bang...", which can be found in the Wikipedia article here: http://en.wikipedia.org/wiki/Cosmic_mic ... _radiation
http://www.wolframalpha.com/input/?i=redshift+z%3D1089

Your calculations take you to the decoupling epoch, when the CMBR was released, observable to us via the surface of last scattering or particle horizon. This is when the universe was around 1000 times smaller than it is today and is estimated to be at around t=380,000 years. Everything in the observable universe was within a radius of around 42 million light-years at that time and the particle horizon had an apparent recession velocity of over 50 times the speed of light.

csmyth3025":2ejf3oe9 said:
A second question also comes to mind: Is the Hubble constant believed to be significantly larger at this [younger] age of the universe than it is today?

Yes. The Hubble parameter at that time was 1.54x10^6 km/s/Mpc.

I am pretty sure that we have a domain of applicability issue here. Your calculations initially took you to the Hubble horizon and now they have brought you to the particle horizon. You are searching for the event horizons at each end of the universe and you are finding them, but apparently there is no gravitational collapse.

The page below should be of great interest to you!

http://www.mathpages.com/home/kmath339.htm - Black Holes, Event Horizons, and the Universe
 
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csmyth3025

Guest
Thanks for the link SpeedFreek,
It's a bit complicated for my level of understanding, but I think I get the gist of it.

One thing I'm curious about: Is an infinite universe necessarily an open universe?

Chris
 
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SpeedFreek

Guest
csmyth3025":2h58xmkx said:
One thing I'm curious about: Is an infinite universe necessarily an open universe?

Yes, an infinite universe is necessarily open.

But an open universe isn't necessarily infinite!

The Shape of Space
 
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csmyth3025

Guest
SpeedFreek":39wxb2h6 said:
csmyth3025":39wxb2h6 said:
One thing I'm curious about: Is an infinite universe necessarily an open universe?

Yes, an infinite universe is necessarily open.

But an open universe isn't necessarily infinite!

The Shape of Space

Thanks for the link SpeedFreek,

I must admit that the whole 3-torus idea is hard for me to conceptualize. How it is that this geometric construct is topologically flat is particularly puzzling to me. I'll definitely have to add topology to my list of things to investigate in order to understand the cosmological models being discussed in this forum.

Chris
 
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SpeedFreek

Guest
Here are a couple more links on the subject:

Is the universe infinite or finite? (contains book preview of the relevant pages!)

What is the Shape of Space?

(In case anyone is wondering, I don't google these as I go along in a thread, these are "hand picked" from my cosmology bookmarks that I have been collecting for years - it's a big list of the best links about cosmology!)


As a highly simplified view, if you lived on the surface of a 3-torus, you would think your universe was Euclidean (flat). If you drew parallel lines on its surface, they would never meet like they do on a sphere, and if you drew a triangle on the surface of the torus, the internal angles would add up to 180 degrees. (This may not be correct for a normal torus, but it is correct for a 3-torus).

If you take a flat plane you can bend it into a cylinder without distorting the shapes drawn on it. To bend the ends of the cylinder round until they meet and become a torus would distort the shapes drawn on it in 3 dimensions, but it does not distort them in 4 dimensions.

Of course, our universe is not a 2 dimensional surface, but what if it were a 3 dimensional surface? What shape would it make if it were embedded in a 4th dimension?

The easiest way to conceptualise this is to start with the balloon analogy, where the surface of that balloon represents our universe. Here we are dealing with a 2-sphere. Now we jump up a dimension, so that the surface of the 3-sphere is 3 dimensional. You cannot visualise the 4 dimensional sphere itself of course, but you can imagine that, whichever direction you look in across its 3 dimensional surface, what you think of as a straight line would actually be part of a great circle, but raised up a dimension!

(The above is not a rigorous explanation, it is just to get the idea across!)
 
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aphh

Guest
Light is nothing unless it has something to interact with. Only then light manifests itself.

This can be easily demonstrated in a 3D rendering program. Place a lightsource on a scene outside of the cameraview but otherwise leave the scene completely empty. Unless there is nothing else in the scene, the picture will render out black with nothing in it, despite there being a lightsource emitting light placed outside of the cameraview.
 
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hewes

Guest
aphh":34pklid6 said:
Light is nothing unless it has something to interact with. Only then light manifests itself...

The Universe started as nothing but light.
 
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ramparts

Guest
hewes":38dm5kok said:
aphh":38dm5kok said:
Light is nothing unless it has something to interact with. Only then light manifests itself...

The Universe started as nothing but light.

Statements that sound cool but bear no relation to reality: +1
 
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hewes

Guest
ramparts":2xv98p92 said:
Statements that sound cool but bear no relation to reality: +1

Statements like that bear no relation to knowledge or logic: -11
 
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SpeedFreek

Guest
hewes":23olxyj8 said:
aphh":23olxyj8 said:
Light is nothing unless it has something to interact with. Only then light manifests itself...

The Universe started as nothing but light.

Why do you say that the universe started as nothing but light? According to current theory, there is no time in the history of the universe when there was nothing but light.
 
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