How can a big bang expand to an infinite size?

[Genady]

5 hours ago, zapatos said:

Precisely how fast is 'fast enough'?

The reply was:

3 hours ago, Boltzmannbrain said:

I already posted it.  It's a simple equation of many to choose from.  Something like 1/(1 - t) would work.  

It does not actually answer the question, "how fast". To answer this question, one needs to take the derivative, \( (\frac 1 {1-t})' = \frac t {(1-t)^2} \).

This grows infinitely when \(t \rightarrow 1 \).

Thus, the answer to the question "how fast is 'fast enough'?" is, "infinitely fast".

Edited December 27, 2023 by Genady

[zapatos]

1 hour ago, Genady said:

The reply was:

It does not actually answer the question, "how fast". To answer this question, one needs to take the derivative, (11−t)′=t(1−t)2 .

This grows infinitely when t→1 .

Thus, the answer to the question "how fast is 'fast enough'?" is, "infinitely fast".

Thanks!

[Airbrush]

On 12/27/2023 at 1:40 PM, Genady said:

The reply was:

It does not actually answer the question, "how fast". To answer this question, one needs to take the derivative, (11−t)′=t(1−t)2 .

This grows infinitely when t→1 .

Thus, the answer to the question "how fast is 'fast enough'?" is, "infinitely fast".

There are many functions that head for infinity as a numerator approaches zero.  Try to apply that math to the actual big bang.  Look at the biggest picture possible, the observable universe.  It resembles a homogenious sponge-like structure of galaxy clusters.  If you had to bet on only one or the other, what would you bet on? 

1 That homogenious, isotropic structure extends like that all the way to infinity? 

Or 2 That structure changes over distance, becoming scarcer or denser?

Edited January 2 by Airbrush

[Genady]

1 hour ago, Airbrush said:

If you had to bet on only one or the other ...

... I'd toss a coin.

[sethoflagos]

5 hours ago, Airbrush said:

1 That homogenious, isotropic structure extends like that all the way to infinity?

You've framed this discussion so far in terms of the (understandable) difficulty in envisaging a spatially infinite universe. Do you have the same difficulty in envisaging temporal infinity? If the expansion of our universe has (as seems likely) no means of reversing then how can time (in the forward direction) be anything but infinte? And if so, that sounds like a good prima facie case for the infinity of space-time in at least one dimension.

But if space-time is only infinite in OUR time dimension what impact would this have on far distant observers for whom our time axis is transformed into the spatial axes of their local coordinate system? We must all agree on the observed spacetime interval between two events (because causality) and while I'm admittedly no mathematical expert and speak with only some slim understanding of SR, it does appear that an infinity in any one dimension of spacetime implies infinities in all.

5 hours ago, Airbrush said:

Or 2 That structure changes over distance, becoming scarcer or denser?

Is the 'fade to grey' option on the table? The impression I get is that the boundaries of spacetime are either infinities or singularities.

Taking the time dimension again, but this time in the reverse direction, when we run the film backwards we end up in a singularity and all hell seems to break loose. Same deal with black holes. I'm not saying that our squeamishness towards infinity is akin to a fear of sailing of the edge of the world into the bottomless abyss. But it might be. A bit.

Personally I experience less angst over infinity than I do singularities. Not that counts as evidence for one or the other.

4 hours ago, Genady said:

... I'd toss a coin.

I'd say the balance of the argument is a bit better than 50:50 subject to whether or not you can give my spacetime interval argument a good caning.

Edited January 2 by sethoflagos
bra but no ket

[Genady]

8 minutes ago, sethoflagos said:

far distant observers for whom our time axis is transformed into the spatial axes of their local coordinate system

Unfortunately, I don't understand what you mean here. (Each observer has their own proper time.)

[sethoflagos]

28 minutes ago, Genady said:

Unfortunately, I don't understand what you mean here. (Each observer has their own proper time.)

Yes - and each observer has their own world line which is typically rotated from the other's point of view according to their relative velocities such that the proper time interval of one is seen at least in part as part of the space interval of the other. Does that help? 

I'm sort of uncomfortable trying to explain the mechanics of coordinate transformation to a mathematician 🤨

[Genady]

5 minutes ago, sethoflagos said:

Yes - and each observer has their own world line which is typically rotated from the other's point of view according to their relative velocities such that the proper time interval of one is seen at least in part as part of the space interval of the other. Does that help? 

I'm sort of uncomfortable trying to explain the mechanics of coordinate transformation to a mathematician 🤨

Right, no need to do this.

We can transform from one coordinate system to another. Such transformations transform coordinates of events. Axes do not transform. That's why I don't understand the meaning of 

1 hour ago, sethoflagos said:

our time axis is transformed into the spatial axes of their local coordinate system

 

[sethoflagos]

8 minutes ago, Genady said:

That's why I don't understand the meaning of 

Substitute axis/axes with interval/intervals. Are we good now?

[Genady]

18 minutes ago, sethoflagos said:

Substitute axis/axes with interval/intervals. Are we good now?

No. Timelike intervals in SR are timelike in ALL inertial frames of reference. And spacelike stay spacelike as well.

[sethoflagos]

47 minutes ago, Genady said:

No. Timelike intervals in SR are timelike in ALL inertial frames of reference. And spacelike stay spacelike as well.

Say Alice observes a time interval of 1 year and space interval of 1 light year between two events.

If Bob sees a time interval of 1 million years between between those events is the following not true:

Bob's space interval = sqrt (Bob's time interval² + Alice's space interval² - Alice's time interval²) = 1 million light years

Hence, presuming the technology was available to detect CMBR radiation as the age of the universe tended towards infinity would not the source of that radiation tend towards being infinitely distant?

ie infinities in the time intervals spawn infinities in spatial intervals.

 

[MigL]

IOW, Seth, the axis, or principal dimensions, do not change in any way,; the 'projection' of the interval onto the axis, or principal dimensions, is what changes.

Singularities and infinities are essentially the same; a singularity is a point where an infinity arises.

No one needs to consider  the 'fade to gray', or any other kind of 'boundary' to the universe; a finite universe simply 'closes in' on itself, such that, if you 'looked' far enough away, you would 'see' the back of your head.

[Genady]

5 minutes ago, sethoflagos said:

Hence, presuming the technology was available to detect CMBR radiation as the age of the universe tended towards infinity would not the source of that radiation tend towards being infinitely distant?

Yes, but this is not how the age of the universe is defined. In the definition of the age of the universe peculiar motion of the observers is removed. The cosmological time is the time of co-moving observers, i.e., observers for whom the CMBR is isotropic. All these observers find the age of the universe being the same (~13.8 billion years).

[sethoflagos]

20 minutes ago, MigL said:

IOW, Seth, the axis, or principal dimensions, do not change in any way,; the 'projection' of the interval onto the axis, or principal dimensions, is what changes.

Singularities and infinities are essentially the same; a singularity is a point where an infinity arises.

No one needs to consider  the 'fade to gray', or any other kind of 'boundary' to the universe; a finite universe simply 'closes in' on itself, such that, if you 'looked' far enough away, you would 'see' the back of your head.

Thanks, @MigL. Matter of picking the correct wording in the main. Is the end of time a singularity? Have to sleep on that one. That and would we see a step change in CMBR intensity when it comes around for the second time?

14 minutes ago, Genady said:

Yes, but this is not how the age of the universe is defined. In the definition of the age of the universe peculiar motion of the observers is removed. The cosmological time is the time of co-moving observers, i.e., observers for whom the CMBR is isotropic. All these observers find the age of the universe being the same (~13.8 billion years).

Do you mind if I ignore everything after 'but'? It's late and the rest is way off the point I was trying to make.

[Genady]

7 hours ago, sethoflagos said:

Do you mind if I ignore everything after 'but'? It's late and the rest is way off the point I was trying to make.

No problem. However, in this case, my 'Yes', before the 'but', is to a different question, too, and should be ignored as well.

Edited January 3 by Genady

[sethoflagos]

7 hours ago, Genady said:

No problem. However, in this case, my 'Yes', before the 'but', is to a different question, too, and should be ignored as well.

A nod's as good as a wink to a blind man 🤐

[Airbrush]

15 hours ago, MigL said:

IOW, Seth, the axis, or principal dimensions, do not change in any way,; the 'projection' of the interval onto the axis, or principal dimensions, is what changes.

Singularities and infinities are essentially the same; a singularity is a point where an infinity arises.

No one needs to consider  the 'fade to gray', or any other kind of 'boundary' to the universe; a finite universe simply 'closes in' on itself, such that, if you 'looked' far enough away, you would 'see' the back of your head.

"If you 'looked' far enough away, you would 'see' the back of your head."

But would you see your back only if you looked in ONE direction, or every direction?  Would all straight lines of sight circle around to you from every direction?

Edited January 3 by Airbrush

[MigL]

8 hours ago, Airbrush said:

Would all straight lines of sight circle around to you from every direction?

Yes that is what 'closed' implies.
A positive curvature will always close on itself.
This can be seen on the surface of a globe, where a ray of light following the curvature will come up behind itself.
Different distances to the 'back of your head', however, may be seen in different directions depending on topology.

[geordief]

13 minutes ago, MigL said:

Yes that is what 'closed' implies.
A positive curvature will always close on itself.
This can be seen on the surface of a globe, where a ray of light following the curvature will come up behind itself.
Different distances to the 'back of your head', however, may be seen in different directions depending on topology.

Did/does Newtonian physics predict something similar?(light returning to sender)

Wasn't there someone before Einstein who also predicted that light would be affected by gravity?

[MigL]

1 hour ago, geordief said:

Did/does Newtonian physics predict something similar?(light returning to sender)

This is an aspect of the topology of the universe, and has nothing to do with bending of light by gravity.
If the universe is 'curved', light has no choice but to follow the 'curvature; it cannot travel 'outside' as there is no outside.
 

[Markus Hanke]

2 hours ago, geordief said:

Wasn't there someone before Einstein who also predicted that light would be affected by gravity?

Newtonian gravity has nothing to say about massless particles, so strictly speaking it makes no prediction here. However, if one assumes that photons have a very small but finite mass, then one can use Newtonian gravity to work out how they are deflected around massive bodies. Turns out that deflection angle doesn’t depend on the exact mass of the photon, so long as it is much smaller than that of the central body.

The result you get is off by a factor of 2 compared to actual observations - to get the correct angle, one must use GR.

[geordief]

7 hours ago, MigL said:

This is an aspect of the topology of the universe, and has nothing to do with bending of light by gravity.
If the universe is 'curved', light has no choice but to follow the 'curvature; it cannot travel 'outside' as there is no outside.
 

is the topology not a function of spacetime curvature? (perhaps the "curvature" description of the topology gave me the wrong idea)

  What might cause different topologies to arise?

[geordief]

8 hours ago, Markus Hanke said:

Newtonian gravity has nothing to say about massless particles, so strictly speaking it makes no prediction here. However, if one assumes that photons have a very small but finite mass, then one can use Newtonian gravity to work out how they are deflected around massive bodies. Turns out that deflection angle doesn’t depend on the exact mass of the photon, so long as it is much smaller than that of the central body.

The result you get is off by a factor of 2 compared to actual observations - to get the correct angle, one must use GR.

Interesting, though that apparently Laplace and Mitchell (1815?) considered the idea of a Black Hole.They must have thought light had some mass,I suppose.

[MigL]

3 hours ago, geordief said:

is the topology not a function of spacetime curvature?

Yes, the topology depends on curvature.
Obviously a universe with a scarcity of mass/energy would have negative, or flat curvature, and could not form a 'closed' topology like a hypersphere or a flat torus.

[Airbrush]

11 hours ago, Markus Hanke said:

Newtonian gravity has nothing to say about massless particles, so strictly speaking it makes no prediction here. However, if one assumes that photons have a very small but finite mass, then one can use Newtonian gravity to work out how they are deflected around massive bodies. Turns out that deflection angle doesn’t depend on the exact mass of the photon, so long as it is much smaller than that of the central body.

The result you get is off by a factor of 2 compared to actual observations - to get the correct angle, one must use GR.

How can one assume that photons have any mass at all?  I thought photons were energy and that is why they travel the speed of light.  How could any mass travel light speed?