The Nature of the Universe, Time Travel and More...

[Asbo Zaprudder]

I'd instead say some people are just good at making intuitive leaps and filling in the details later. Sometimes it works; often it doesn't. Sometimes we end up with alternate forms of mathematics with different sets of axioms, without infinities of any cardinality, or assuming or not assuming the continuum hypothesis.

The Collatz conjecture or 3x + 1 problem is unsolved and may remain so forever. One counterexample would indeed disprove it, but who's got time to wait around for that? Even though conceptually simple, it was described by Jeffrey Lagarias in 2010 as "...an extraordinarily difficult problem, completely out of reach of present day mathematics." My suspicion is that it is undecidable, although I don't believe it has been shown to be equivalent to the halting problem, for example. John Conway proved in 1972 that a natural generalization of the problem is algorithmically undecidable. More recent work seems largely to be based on establishing probabilistic constraints on stopping time.

The ultimate challenge. The 3x+1 problem.
Document Zbl 1253.11003 - zbMATH Open

 

[Will The Serious]

More recent work seems largely to be based on establishing probabilistic constraints on stopping time.

Can you expound upon this? Is this in reference to 3x+1? I'm curious.

-Will

 

[Asbo Zaprudder]

I'm just going by the Wikipedia article. I assume you know more about the conjecture and theoretical work on it because you first mentioned it. It's not something that interests me particularly.

https://en.wikipedia.org/wiki/Collatz_conjecture

 

[Will The Serious]

<Ha ha ha!
I completely read that wrong. I was thinking you were suggested there was some relationship to Time, not the number of times for an operation to occur.

SomeTIMES, I'm not all there.

-Will

 

[Asbo Zaprudder]

I completely read that wrong. I was thinking you were suggested there was some relationship to Time, not the number of times for an operation to occur.

Yes, time (steps) until iterating 3x+1 or x/2 for arbitrary odd x or even x reaches 1 and halts, not how to stop time itself. Presumably, we'd never be able to tell if time ever stops as we are embedded within it. Whether it is discrete or continuous, I also don't know, but there is the problem of it appearing to run at different rates according to the relative motion of observers. Perhaps there is a way to observe a slowed system tick through time quanta or chronons. Perhaps a chronon is no greater than the Planck time, 10^-43 seconds. If space is similarly quantised, its fundamental discrete unit might be no larger than the Planck length, 1.6 x 10^-35 metres. A related question is whether the Planck length and time or their corresponding quanta are Lorentz invariant - that is, they have the same values when measured in all inertial frames. I believe the fundamental quanta of branchial space aren't invariant - that concept having no meaning at that level - but space-time, general relativity, quantum theory and statistical thermodynamics arise as emergent properties as do presumably Lorentz invariant Planck length and time - the quantisation being effectively much tinier in branchial space than in emergent space-time, although our units presumably have no meaning there. One just hopes it isn't turtles all the way down.

 

[Will The Serious]

Oh no, It's turtles all the way down!

I just hope that all the way down means the bottom turtle is standing on firm footing, or there is no bottom turtle, else we could be in for a very long drop.

Presumably, we'd never be able to tell if time ever stops as we are embedded within it. Whether it is discrete or continuous, I also don't know, but there is the problem of it appearing to run at different rates according to the relative motion of observers.

If time stopped, and by that I mean all time, what could possibly start it back up again?

Varying time or, as my physics professor put it, time being lumpy, might mean it can run or halt in different physical locations such that it moves like a wave across existence. There could be a harmonic aspect to it. It could reflect, refract, or compound its energy, even stop in local space. This would mean that waves of time could allow for restarting a region of stopped time/energy.

-Will

 

[publiusr]

A stasis field

 

[Will The Serious]

A stasis field

Can we differentiate time stopping from a stasis field? Would there be any difference between a localized time stop and a true absolute zero where all change halted?

I suppose you could fill a chamber with a vacuum, somehow introduce a collection of objects that were at 0°Kelvin and bounce them around inside the chamber and claim, stasis and time stop were not the same thing because you observe the movement of the objects within that chamber, even though the objects themselves would experience no change internally. The question would then be, where is the stasis field? Within the chamber movement or change can happen, but within the objects...?

-Will

 

[Asbo Zaprudder]

If the constituent quantum particles of the objects undergo at least zero-point vibration, which they must, they are not in stasis. If you can observe them, they are not in stasis because the EM radiation that you use to probe them must interact with the electron clouds of their atoms. The nearest we can approach objects appearing to be in stasis is to accelerate them to near light speed relative to us or to put them in a deep gravity well.

Time dilation due to gravity makes a clock at the photosphere of the Sun tick slower than a clock on Earth by just over a minute per year, or about 10,000 years for the 4.55 billion years since the Sun was formed.

 

[Will The Serious]

Time dilation due to gravity makes a clock at the photosphere of the Sun tick slower than a clock on Earth by just over a minute per year, or about 10,000 years for the 4.55 billion years since the Sun was formed.

I never understood the time dilation thing. How do we know that the burden of maintaining a constant harmonic state isn't effected by acceleration? Time aside, wouldn't acceleration of a grandfather clock, have an effect on the pendulum and cause the clock to change its harmonic rate? Same with spinning the clock or driving it in a circle. Would that mean time dilation is involved? Or, do we have some way of knowing the difference between a change in time and a change in harmonic energy?

-Will

 

[Asbo Zaprudder]

Gravity is equivalent to acceleration - that's our experience of it! Time is the measurement of things changing - such as atomic clocks. We have demonstrated gravitational time dilation experimentally and it agrees with the predictions of General Relativity. GPS satellites also have to be corrected for both gravitational time dilation and the effects of relative motion. I have no idea what you mean by "burden".

 

[Will The Serious]

What I'm asking is, given that a constant harmonic state either needs some form of driver to maintain it, or there is no energy loss from the steady state system. When we introduce any change (acceleration) to such systems in harmonic motion, the frequency is likely to also be affected by that motion.

If a harmonic state can be equated to a measure of time in the case of atomic particles, can't any regular harmonic system be equated to time? The swing of a pendulum drives a grandfather clock to measure time. Yet, we don't consider affecting the swing of that pendulum, by applying some form of acceleration in an outside frame of reference, as having any effect on the local time of the grandfather clock. So, why would that be different with an atomic particle? Just because we are able to affect the vibrations of an atomic particle, does that mean time has slowed or changed with respect to another atomic particle that has not undergone the same conditions of acceleration? Why do we not just recognize that the frequency is affected and leave it at that? Why are we so sure that is an example of time dilation?

Let's say we have a pendulum in a gravity free field. The behavior of that pendulum would be a free rotation around its fob or pivot point. It has frequency and, in a frictionless world, would be constant. Add a directed gravitational field and no the period slows and accelerates. Without friction, the period is probably unaffected, but what if that system began to accelerate in rotation? There would then be a lopsided application of acceleration upon that system. It the system was to rotate in the direction of the bob's orbit around the pivot point, relative to the gravitational field, wouldn't that mean a greater amount of time, and therefore influence, on the upswing (away from gravity) was allowing gravity to decelerate the bob, then on the down swing (towards gravity).

It would act more like a cork riding a wave. As the wave passes, the cork is lifted, but, then gravity pulls the cork down the forward face of the wave as the wave tries to lift the cork, thus it takes longer for the wave to lift the cork as the cork moves ahead and down the rising, tilting face of water. Once on the back side of the wave, the cork would then be influenced by gravity to move back, towards its original position, but because that is in the opposite direction of the wave's motion, the cork spends much less time on the backside of the wave then it did on the front. The wave isn't trying to lift three cork against gravity, it is setting the cork back down while gravity is pulling the cork down the slope of the receding back of the wave. This means the cork reaches the trough faster then it took to reach the peak when it was being lifted out of the trough. Thus gravity had less time to influence the cork's motion and the result is the cork doesn't return to its original position and is overall movement its in the direction of the wave. Also, the cork's period (movement up and down) would be longer then that of the wave. Each time the cork returned to the bottom of the trough, the wave had moved farther then it does during its own normal period.

-Will

 

[Asbo Zaprudder]

You're thinking classically, where objects lose energy gradually due to friction and the like. No driver required as there is no energy lost or gained except by quantum transitions. That's just the way things behave at the quantum level. Fundamental particles are excitations of quantum fields and effectively have perpetual motion, but that's just as well. Otherwise, electrons would lose energy by Magnetobremsstrahlung (synchrotron radiation) and spiral into the nuclei of atoms. Even if absolute zero were attainable, which it isn't by the third law of thermodynamics, zero-point vibrations would still occur thanks to the Heisenberg uncertainty principle. Unlike on Stargate SG-1, we know of no way to extract this energy as there is no lower state.

Quantum mechanics requires you to abandon your expectations formed from the everyday world.

 

[publiusr]

At the smallest scales, the universe is tweaking worse than any addict.

At our scales, everything seems Victorian.

At the largest scales…it gets a little weirder again—-the farther from our notice, the more it seems to unravel.

https://www.coasttocoastam.com/article/knapps-news-101523/

On time travel
https://theconversation.com/is-time...the-science-behind-the-science-fiction-213836
https://www.bbc.com/future/article/20231113-the-invisible-dangers-of-travelling-through-time

Gravity’s Tree
https://www.thevintagenews.com/2023...alive-and-well-outside-of-his-childhood-home/

 

[Will The Serious]

You're thinking classically, where objects lose energy gradually due to friction and the like. No driver required as there is no energy lost or gained except by quantum transitions.

What I'm asking is, given that a constant harmonic state either needs some form of driver to maintain it, or there is no energy loss from the steady state system(this could be a quantum state or absolute zero or zero entropy). When we introduce any change (acceleration) to such systems in harmonic motion, the frequency is likely to also be affected by that motion<-(Here, I should have written, 'change' or 'acceleration', instead of motion).

Even if absolute zero were attainable, which it isn't by the third law of thermodynamics, zero-point vibrations would still occur thanks to the Heisenberg uncertainty principle.

I'm wondering how we know the change in the measured atomic period of motion is not because of the classic mechanical acceleration of the system, instead of a dilation in local time?
Also,
If we are defining time based upon this atomic period of motion, then why would we not include any regular harmonic motion to define time for us?

-Will

 

[Asbo Zaprudder]

You're mixing up frames of reference. The dilation is apparent in the observed frame from the observer's frame, not in the observed frame if it observes itself. For relatively moving observers, each measures the same dilation in the other but not themselves. This is the twin paradox - asymmetry in ageing comes about from one of the observers accelerating relative to the other from the same initial frame of reference. It also appears to occur if the observers are always moving with constant relative velocity and different observers co-ordinate their times on outbound and inbound legs relative to a third observer (such as one who remains on Earth). Special Relativity is applicable here where space-time is considered flat away from gravitational fields. Such non-intuitive aspects arise because there is no absolute "now" and the spacing in time of events can vary between different inertial frames. However, time ordering and thus causality is preserved.

For a gravity well, the observer deeper in the field sees time passing more quickly for an observer higher and the higher observer sees time passing slower for the deeper observer. For the latter case, a deeper pendulum would appear to swing more slowly to a higher observer than classically expected (where frequency is proportional to the square root of acceleration) and one could interpret this as a negative deviation from the expected acceleration for the field strength. The lower observer would measure the expected acceleration in their frame. We need General Relativity to describe such cases as Newtonian gravity assumes there is a universally applicable frame of reference.

I suggest seeking out a dedicated Physics forum if you want to explore this subject. I am too old and ill to discuss this in further detail here. It's something that can't be easily summarised as it requires years of study (and practice) to understand - and my knowledge is very rusty. Frankly, it's exhausting to have to try to explain in words when I'm really not sure what the point being made is. It's very easy to get muddled up by language if you don't define your frames of reference correctly. Mathematics is preferable and even then it's easy to screw up.

"Wovon man nicht sprechen kann, darüber muss man schweigen." - Ludwig Wittgenstein

 

[Asbo Zaprudder]

The gravitational time dilation factor ζ for an object distance r from a non-rotating gravitating mass M that has a Schwarzschild radius R = (2GM/c²) < r as seen from a large distance >> r is ζ=1/√(1-R/r). A pendulums's period t in the object's local frame is approximately 2π√(l/g), where l is the pendulum length and g is the gravitational acceleration (g=GM/r²). The distant observer sees an effective period T = ζt = ζ2π√(l/g) = 2π√(ζ²l/g) and so the apparent acceleration due to gravity as seen by the distant observer would be deduced to be g' = g/ζ² = g(1-R/r). That is, the apparent acceleration is the local frame acceleration g minus g(R/r). For an object falling into the event horizon of a non-rotating black hole, R/r → 1, ζ → ∞ and g' → 0. An object falling into an event horizon appears to freeze there as seen by a distant observer (light from the object gets red-shifted as ζ → ∞ and it dims to invisibility as fewer and fewer photons are emitted per second). As for what the object sees, it's rather complicated and I refer you to the following article:

general relativity - Does someone falling into a black hole see the end of the universe? - Physics Stack Exchange

 

[Kamen Rider Blade]

Spoiler: The Overview Effect - The Locations of Star Trek and Other Sci-fi in Real Space

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The YT vid tries to point out some of the real life star locations that many Sci-Fi franchises talk about.
Nice 3D video pointing out where everything is.

It's NOT comprehensive in any way/shape/form.

But a good starter video.

 

[Asbo Zaprudder]

Yeah, it shows up how some writers really just don't understand just how vast space is and how numerous stars and galaxies are, not to mention that Beyer's designation system (Greek letters combined with the genitive form of constellation names) is only a sensible way of naming stars if you stay relatively close to the solar system. Most stars visible to the naked eye are within a couple of thousand light years of the Sun and most stars in a constellation lie at greatly varying distances. For example, the main stars in Orion lie at distances that range from 250 light years (Bellatrix or γ Orionis) to 2,000 light years (Alnilam or ε Orionis). Relative motions of stars will break up constellations after a suitable passage of time - of the order of 100,000 years.

 

[Asbo Zaprudder]

Interesting video about how the pilot wave theory and the many worlds theory of quantum mechanics are pretty much the same thing, although at first glance they might seem dissimilar. Many worlds appears to be preferable of the two in terms of Occam's razor as it can encompass Special Relativity and it has a natural explanation for the Born rule for calculating the probability of the result of a quantum measurement. Neither interpretation relies on the state-vector reduction or wave-function collapse assumption of the Copenhagen interpretation, which results in somewhat odd implications about the specialness of conscious observers in the universe and simultaneously dead and alive cats until they are observed.

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