Big Crunch or Big Rip?

[dipayankar]

It would be interesting to find out how a continuous field can propagate in a discreet spacetime abric.

Actually I think both are continuous Dip. I don't think it matters, it is what it is. The real question that Antonio suggested, is the space/time field continuous or discreet? That I am having a more difficult time researching the answer.

Best,

Pat

[Profpat]

It would be interesting to find out how a continuous field can propagate in a discreet spacetime abric.

I'm not sure space time is discreet, however, if the quanta was small enough, like a Planck length, I don't think the waves would have trouble propagating. I view spacetime to be quanta but but layed out in a continuous field.

Though I'm not sure and I'm still researching the topic.

Does anyone know if spacetime is discreet or continuous?

Best,

Pat

[Profpat]

It appears the jury is still trying to decide the question of discreet vs continuous.

I found this on the internet:


"According to Ashtekar, space-time is not a continuum as physicists once believed. Instead, it is made up of individual building blocks, just as a piece of fabric, though it appears to be continuous, is made up of individual threads. "Once we realized that the notion of space-time as a continuum is only an approximation of reality, it became clear to us that singularities are merely artifacts of our insistence that space-time should be described as a continuum."

AND:


Are space and time infinitely divisible?

Given the above analyses, a rather straightforward solution to some of the paradoxes is to deny that space and time are infinitely divisible. Just because our number system enables us to give a number between any two numbers, it does not necessarily follow that there is a point in space between any two different points in space, and the same goes for time.

Indeed, physicists talk about Planck length and Planck time as the smallest meaningful, measurable units of space and of time, thus making measurements of both time and space discrete rather than continuous.

Of course, whether or not space and time are measurable with infinite precision is ultimately irrelevant to the paradoxes and their resolution: what we as humans can know about the world is a different matter from what is or is not true or possible in the world.

That is, quantum mechanics may prevent us from making infinitely precise measurements, but if time and space are continuous, the paradoxes still apply. However, if time and space are discrete, one avoids obtaining the infinite series that underlies most of the paradoxes.

WHAT DO YOU THINK?

[SteveA]

Will the Universe end in a Big crunch or a Big RIP? Or is there other means that the Universe will end in??

It's interesting to consider that neither would appear much different from the other as there isn't an outside perspective that can see it and whether or not space becomes compressed and accelerates time relative to that "objective" view or the opposite occurs and times slow until they stop, internally the relative rates could remain at one observation = a unit of time.

Notice that if a black hole continually "sucked" objects into an inescapable virtual singularity, the density of interactions within this space would expand and allow for an equivalent of an infinite amount of time in an equivalent blink of an eye to an external observer - the perceived internal distance would not depend upon an external observers perspective but instead upon the properties of the interactions approaching a singularity, so an infinitesimal could appear infinitely vast and complex in that respect.

[SteveA]

It appears the jury is still trying to decide the question of discreet vs continuous.

I found this on the internet:


"According to Ashtekar, space-time is not a continuum as physicists once believed. Instead, it is made up of individual building blocks, just as a piece of fabric, though it appears to be continuous, is made up of individual threads. "Once we realized that the notion of space-time as a continuum is only an approximation of reality, it became clear to us that singularities are merely artifacts of our insistence that space-time should be described as a continuum."

AND:


Are space and time infinitely divisible?

Given the above analyses, a rather straightforward solution to some of the paradoxes is to deny that space and time are infinitely divisible. Just because our number system enables us to give a number between any two numbers, it does not necessarily follow that there is a point in space between any two different points in space, and the same goes for time.

Indeed, physicists talk about Planck length and Planck time as the smallest meaningful, measurable units of space and of time, thus making measurements of both time and space discrete rather than continuous.

Of course, whether or not space and time are measurable with infinite precision is ultimately irrelevant to the paradoxes and their resolution: what we as humans can know about the world is a different matter from what is or is not true or possible in the world.

That is, quantum mechanics may prevent us from making infinitely precise measurements, but if time and space are continuous, the paradoxes still apply. However, if time and space are discrete, one avoids obtaining the infinite series that underlies most of the paradoxes.

WHAT DO YOU THINK?

Excellent post!

From my perspective, whether or not space is continuous is rather irrelevant to social institution of science as it relies upon physical communication to exchange knowledge/evidence/proofs etc. and as long as physical methods of communication appear to be limited to finite quantities of information over finite periods of time, then the only potential infinity that exists is time (and if you look at the manners in which the most rigorously defined mathematical relationships are constructed, they'll only contain a single largest "infinite" value in the limit - adding a second infinite dimensions allows for indeterminism in the results and a free will in the selection of a desired result if the relative ratios of these infinite quantities influence the result).

Notice that in Zeno's paradox, if we truly decided to see if the arrow traversed all locations in space, and we looked at it very closely as a true physical object and not initially make the assumption that it is already infinite in some respect, then we see the granularity arise from individual photon detections and if we shrink the frame down to miniscule femtoseconds of time, we may not even detect a single photon in that period of time, much less enough information to hypothesize about precisely where a macroscopic object exists at that moment.

The paradox arose from assuming we're already witnessing infinite quantities instead of seeing that these are only constructed relationships over time from a single largest source of information as the totality of the memory and experiences etc. that construct the perception of that moment.

[dipayankar]

Its interesting prof. One clarity still remains. Are the threads of spacetime made of strings? If yes then we are returning to the dreaded string theory.

It appears the jury is still trying to decide the question of discreet vs continuous.

I found this on the internet:


"According to Ashtekar, space-time is not a continuum as physicists once believed. Instead, it is made up of individual building blocks, just as a piece of fabric, though it appears to be continuous, is made up of individual threads. "Once we realized that the notion of space-time as a continuum is only an approximation of reality, it became clear to us that singularities are merely artifacts of our insistence that space-time should be described as a continuum."

AND:


Are space and time infinitely divisible?

Given the above analyses, a rather straightforward solution to some of the paradoxes is to deny that space and time are infinitely divisible. Just because our number system enables us to give a number between any two numbers, it does not necessarily follow that there is a point in space between any two different points in space, and the same goes for time.

Indeed, physicists talk about Planck length and Planck time as the smallest meaningful, measurable units of space and of time, thus making measurements of both time and space discrete rather than continuous.

Of course, whether or not space and time are measurable with infinite precision is ultimately irrelevant to the paradoxes and their resolution: what we as humans can know about the world is a different matter from what is or is not true or possible in the world.

That is, quantum mechanics may prevent us from making infinitely precise measurements, but if time and space are continuous, the paradoxes still apply. However, if time and space are discrete, one avoids obtaining the infinite series that underlies most of the paradoxes.

WHAT DO YOU THINK?

[dipayankar]

In a big crunch, the material might be reused, whereas in big rip the material might be destroyed.

It's interesting to consider that neither would appear much different from the other as there isn't an outside perspective that can see it and whether or not space becomes compressed and accelerates time relative to that "objective" view or the opposite occurs and times slow until they stop, internally the relative rates could remain at one observation = a unit of time.

Notice that if a black hole continually "sucked" objects into an inescapable virtual singularity, the density of interactions within this space would expand and allow for an equivalent of an infinite amount of time in an equivalent blink of an eye to an external observer - the perceived internal distance would not depend upon an external observers perspective but instead upon the properties of the interactions approaching a singularity, so an infinitesimal could appear infinitely vast and complex in that respect.

[SteveA]

Its interesting prof. One clarity still remains. Are the threads of spacetime made of strings? If yes then we are returning to the dreaded string theory.

Any system of deterministic description to physical states in the physical sciences should derive the existence of strings because of the underlying logic to such a thought.

Notice that for a deterministic system, if we know the current state, we can predict all future states. So if the system is currently in state "A", there will be a transition determined by those rules of change to some other state, let's call it "B" and from there to some other state, etc.

This results in the underlying descriptions of all such deterministic objects as acting 1 dimensionally over time (the foundation of a string).

Now consider that if the system is finite, and the physical sciences appear limited to analyzing finite quantities of information, can at most traverse through every one of those finite states before ultimately being required to return to the beginning of its state (a closed loop).

This also gives the object an equivalent wavelength of repetition over time and so the "string vibrates in a loop".

These strings arise from logic and knowledge and are not inherently physical objects. They describes the dynamic properties of all forms of deterministic knowledge regarding finite objects.

Of course, my statements here are not direct rehashes of string theory.

Most string theories that are currently being worked on are flawed in their initial presupposition that these strings exist in a some specific space with 10 or 11 dimensions.

Those assumptions arise from beginning with the assumption that spacetime already fundamentally possesses 4 dimensions - but how did we get the appearance of 4 dimensions to spacetime? Most string theories skip what should be one of their most important insights.

No matter what scientist is performing their experiments, there's only one timeline they're following in their experimentation and they're only seeing the equivalent of a single string over time (1-D).

How do we get from 1-D to 2 or 3 or 4 etc. dimensions?

The locations of objects in space are determined by where we believe them to be and those beliefs are constructed from the content of our perceptions so we can analyze this similar to reading some letters of an alphabet to a language that possesses various rules in its construction that we do not yet understand.

Now imagine that you were just born and experiencing "existence" via various forms of (currently) novel sensations.

If none of these ever repeated in any predictable pattern, there would exist no coherent form of space that you would experience and it would be like trying to understand a language in which the letters meant nothing specific because they never repeated and no correlations between them could be found (so in that case, to make a physical correlation, you'd be effectively travelling through time without any relationship to the past and this would like an informationally maximal and highest possible velocity - light speed).

Now let's instead say that you witnessed events that repeated every 2 cycles, such as "I see a tree thing" and then "I see a rock thing" and then "I see a tree thing" etc.

In that case, the natural interpretation would be of moving between two states, though my description implicitly assumes an external memory is allowing you to add the hidden context that you're seeing "I see a tree thing (again)", due to memory of the prior tree experience.

So you can draw this 1-D "string of pearls" (I like that reference to some ancient beliefs because it shows the discreteness) as looping back on itself into a loop ("necklace") that contains 2 elements and an equivalent wavelength of 2 periods of time.

As you layer up the possible existence of larger periods, you find various natural asymmetries appear to arise due to relatively prime raios between various "wavelengths of experience" and so we already have a natural asymmetry in the process of witnessing the equivalent of a white spectrum of wavelengths of information as the largest non-prime wavelengths mask the information conveyed by their factors.

There is also a natural manner that these can appear to construct virtual spaces larger than they each exist in terms of wavelength, because as they cycle they construct wavelengths that are the products of their lengths (excluding the greatest common divisor).

So, for example, if I was witnessed two closed "strings" vibrating at some specific wavelengths, say at periods of 2 and 3, and one is presenting ABABABA..., whereas the other is presenting CDECDECDE..., together they appear as:

(time moves horizontally here and the vertical direction shows the experiences connected at that time)

ABABABABABABABAB...
CDECDECDECDECDEC...

The resulting combination of the wavelengths 2 and 3 objects encompasses a "space" or volume of time that's larger than both of these together. So we could physically represent these as encompassing 2*3=6 units of time, but if we mentally "factor" the events, we can in a sense compress the representation down to 2+3=5 and some physical observations can be predicted by early factoring.

To find some additional interesting features here, let's assume we have two randomly selected wavelengths (n and m) and analyze the probability of the two appearing to interact in space.

If both n and m are divisible by 2, then they'll share odd and even phases over which they're synchronized and the probability of this binary synchronization is 1/2*1/2=1/(2^2)=1/4.

We then continue on to periods of 3 and find the probability of a 3 phase synchronization is 1/9.

When we get to 4, we find it's redundant as the detection of binary synchronization is already detecting all periods with powers of 2.

We then check 5 and find it to be 1/25.

6 is not prime and doesn't contribute to the sum.

etc.

And what do we end up with?

1/(2^2)+1/(3^2)+1/(5^2)+...+(1/p^2)+...

Where p is any prime number, and the total converges to an approximate 60.8% chance (if I remember correctly) that any randomly selected pair of objects will interact in at least one dimension.

Of course this expression will be familiar to quite a few people as it's one of the most common results of the Riemann Zeta function.

But there's an entire asymmetric space hidden behind it with various distributions of dimensional interactions (that do not specifically stop at 10 or 11 dimension, but are unlimited, though with super exponential decay in their influences).

Anyway, that's not really string theory, but that's my "Theory of The String".

[SteveA]

In a big crunch, the material might be reused, whereas in big rip the material might be destroyed.

Hmmm ... I hadn't considered that before. That's a good insight (If only one of those two possibilities was to exist, and all the laws of physics were deterministic, then I'd have to assume the rip would ultimately occur because the universe could not repeat without some mechanism to denote such repetitions which would not exist unless the current universe is capable of constructing infinite counts, but this would require that it possess the capability of generating infinite forms to represent all these infinite counts and hence it would have to grow to infinite size).

There's some background here with constructing the natural numbers in mathematics. I don't think there is any way to logically define a manner to count to infinity because it requires an infinite quantity of distinct symbols and though we can begin to enumerate a few, such as 1,2,3,n,n+1. There's no way to define an algorithm that can do it for you deterministically and people inevitably result to simply referring to this infinite potential in physical and temporal "next" terms, which don't reference specific quantities.

As a sidenote, oftentimes mathematicians will refer to the list 1,2,3,...n as a set of natural numbers, but that's not actually correct. We do not know specifically what n is, so 1,2,3,...n is actually defining a set of sets of natural numbers, as there is another set generated by each value for n. This is a subtle, but potentially important distinction (a paradox that can be constructed via. the misinterpretation can be shown by asking whether or not the maximum natural number in the set of all natural numbers is finite. Because all natural numbers are finite and the maximum element from a set is one of those elements, then the maximum or largest natural number is finite and because we can match their quantity one for one with the natural numbers themselves, there are only a finite number of natural numbers).

Anyway, again, if the universe is finite and deterministic, then it would have to repeat, but there would be no way to detect it in a repetitive form because there would exist nothing else within the universe that would be left to count repetitions, hence a repeating universe appears to contain a paradox and only something outside it could view it as repeating (I think this digs some into the problem of subjective observations of time).

[Profpat]

In a big crunch, the material might be reused, whereas in big rip the material might be destroyed.

Even with a big RIP or a big Freeze, matter or energy would not be destroyed.

Maybe strinns are both the field ( Lines ) and little strings rolled up into an enegy ball at every corner.