An interesting consequence of the closedness of the Cosmos

[bayakiv]

TL;DR Summary

Even if our space-time is flat, it can be closed in augmented space-time in the sense that everywhere it densely fills the compact manifold of our Cosmos.

What then can happen to the radio signal sent into space? It seems to me that after a while our signal will return to us as an echo, but the return period depends on the frequency of the signal. This corollary does not have a rigorous mathematical proof; an analogy is simply drawn with rational windings of a torus.

 

[jbriggs444]

I am having trouble making sense of this.

It seems that you are thinking about a hypothetical space-time that is locally flat everywhere but nonetheless has a global topology which is finite. It loops back on itself. Like a torus.

You go on to speculate that this means that outgoing signals will come back after an interval that depends on the signal's frequency. This appears to stem from a consistency requirement that the peaks and troughs of a wave form that is transmitted must match those of the signal that is received back at the time and place of the original emission.

There are loopholes, of course. The signals might dissipate before making the round trip. Or consistency might simply preclude the transmission of signals that fail to meet the consistency requirement.

One might say that we in our open universe are somewhat spoiled. We can posit a scenario with a radio transmitting an arbitrary signal toward infinity without much concern about how the transmitter came into existence or how the signal was selected. We look at the initial situation and extrapolate to the future. We do not concern ourselves with extrapolation to the past. In particular, we do not concern ourselves with the idea that the extrapolation to the past must be consistent with the extrapolation to the future if the universe is classical, deterministic and closed.

It is far more difficult to invent hypotheticals in a universe that is looped back upon itself. One must accept criticism that a proposed hypothetical could be inconsistent.

 

[PeterDonis]

Even if our space-time is flat, it can be closed in augmented space-time in the sense that everywhere it densely fills the compact manifold of our Cosmos.

Do you have a reference for this? It looks like personal speculation, which is off limits for this forum.

 

[bayakiv]

You go on to speculate that this means that outgoing signals will come back after an interval that depends on the signal's frequency. This appears to stem from a consistency requirement that the peaks and troughs of a wave form that is transmitted must match those of the signal that is received back at the time and place of the original emission.

A bit wrong. I imagined that energy and time are the helical coordinates of the torus, and the radio signal is an arbitrary (rational or irrational) winding of the torus. Then at some frequencies there will be an echo.

 

[PeroK]

I thought it was more poetry than personal speculation:

A signal is sent ...
We hear a distant echo.
The Cosmos is closed.

 

[phinds]

A bit wrong. I imagined that energy and time are the helical coordinates of the torus, and the radio signal is an arbitrary (rational or irrational) winding of the torus. Then at some frequencies there will be an echo.

Scientifically, this is pure word salad.

 

[PeroK]

A bit wrong. I imagined that energy and time are the helical coordinates of the torus, and the radio signal is an arbitrary (rational or irrational) winding of the torus. Then at some frequencies there will be an echo.

Energy and time,
Helical coordinates.
The torus is wound.

 

[Vanadium 50]

A signal is sent ...
We hear a distant echo.
The Cosmos is closed.

Love it - but does it work in Japanese? Can you use Cosmos as a Kigo?

Helix in spacetime.
Radio coordinates.
Words used in salad.

 

[PeroK]

Love it - but does it work in Japanese? Can you use Cosmos as a Kigo?

A signal in spring ...
Distant echo in winter.
The Cosmos is closed.

That adds a seasonal touch. Or:

A spacetime helix,
Round a compact manifold.
Yuletide offering.

 

[phinds]

You guys are killing me here

 

[Vanadium 50]

You guys are killing me here

Seven syllables. It's a start. Two more lines and you're done.

 

[PeterDonis]

Thread closed for moderation.

 

[berkeman]

This very creative thread will remain closed. Thank you for the very entertaining replies!

 

[berkeman]

Update -- At the request of @DaveC426913 and with artistic help from @fresh_42 the closing message is reposted in the spirit of the thread replies...

Very creative,
thread will remain closed, thank you
for funny replies