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07 Nov 2018 19:40

Gnargenox wrote:
Source of the post Knowing what we know, what can we rule out? Knowing what physics allows, what could we expect in the realm of normal things? Can we hear a light bulb 5 light years away? 50, 500, 5000, (5^(n!)!)? Knowing what we know, what could ET know about us? How far back in time do we want to search, because we don't see things as they are now. If intelligence tends to wipe itself out or hides how far away should we be looking based on the age of the universe and the window of time life usually last? Should we just set a telescope on a swivel and throw darts?

A good summary of the problem Mr. G! I only wish more people considered this when they blabbered their opinions in 'news' articles or presentations.

As for the analogy - I say again: I DID find gold dust near where I live... :lol:.  
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07 Nov 2018 19:55

I'll give you RNA for the gold dust
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08 Nov 2018 23:55

Gnargenox wrote:
Source of the post I'll give you RNA for the gold dust


I'm sorry, I'd only accept quadriplicate-form DNA. The market nowadays for anything gold is crazy, y'know?
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09 Nov 2018 06:18

Gnargenox wrote:
Source of the post A new method of determining this probability came to the conclusion we are alone in our galaxy, and perhaps even in our observable universe (53%–99.6% and 39%–85% respectively). New Model Predicts That We’re Probably the Only Advanced Civilization in the Observable Universe

What the authors did was reference the various factors of the Drake equation used in previous studies, made some assumptions about what the uncertainties (in the form of probability distributions) might look like for each of those factors, and then propagated those uncertainties through the equation.  In other words, they applied the rigorous techniques of error analysis to the problem.  But those techniques are not new either; the study of error analysis has existed for over a century.  It's just that nobody had previously bothered to assume probability distributions on top of already assumed values for the factors themselves.

The media, as usual, largely missed this nuance and instead focused on the most profitable headline.  The study is important because it shows that the form of those probability distributions has a big effect on the final result, which isn't obvious if they're just treated as pure numbers with no uncertainty.   But its flaw, and the reason the conclusion "we are probably alone in the observable universe" is too strong, is that it still requires a number of assumptions for what those probability distributions for the biotechnical factors are.  Nobody knows what they are.  


I look forward to a new study that takes it a step further by quantifying what are the uncertainties of the uncertainties of the values of the factors used in the Drake equation, and seeing what that does to the "final answer". :P
 
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10 Nov 2018 14:41

Watsisname wrote:
Source of the post But its flaw, and the reason the conclusion "we are probably alone in the observable universe" is too strong, is that it still requires a number of assumptions for what those probability distributions for the biotechnical factors are.  Nobody knows what they are.  

Exactly.
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20 Nov 2018 14:54

Watsisname wrote:
That makes more sense. :)  Yes, it is nice that the Alcubierre drive, being within the realm of general relativity, can be described mathematically.  The equations work both ways, so on one hand you can take a given distribution of matter and energy and predict how space-time behaves around it, or in this case you start with the behavior of space-time that you want and the equations tell you what sort of mass-energy would create it.  Of course solving the equations in that direction easily leads to unphysical situations or impossible mass-energy requirements, but if you take those as given then the math still lets you describe it, as in if you did have an Alcubierre drive, then what would it look like?  

For a "ZPE device", I think describing how it would work (in even the impossible sense) would be up to what kind of assumptions someone wants to use to model it.  Zero-point energy is a real thing, but there isn't a clear physical framework to describe how you would power something with it.

Wat do you think humanity will survive long enough to develop something as magnificent as this?  Exotic matter would be a necessity, I would think, but I dont see why that wouldn't be possible, our uni/multi/omniverse seems to be symmetric on various levels.
 
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20 Nov 2018 14:58

Watsisname wrote:
Gnargenox wrote:
Source of the post A new method of determining this probability came to the conclusion we are alone in our galaxy, and perhaps even in our observable universe (53%–99.6% and 39%–85% respectively). New Model Predicts That We’re Probably the Only Advanced Civilization in the Observable Universe

What the authors did was reference the various factors of the Drake equation used in previous studies, made some assumptions about what the uncertainties (in the form of probability distributions) might look like for each of those factors, and then propagated those uncertainties through the equation.  In other words, they applied the rigorous techniques of error analysis to the problem.  But those techniques are not new either; the study of error analysis has existed for over a century.  It's just that nobody had previously bothered to assume probability distributions on top of already assumed values for the factors themselves.

The media, as usual, largely missed this nuance and instead focused on the most profitable headline.  The study is important because it shows that the form of those probability distributions has a big effect on the final result, which isn't obvious if they're just treated as pure numbers with no uncertainty.   But its flaw, and the reason the conclusion "we are probably alone in the observable universe" is too strong, is that it still requires a number of assumptions for what those probability distributions for the biotechnical factors are.  Nobody knows what they are.  


I look forward to a new study that takes it a step further by quantifying what are the uncertainties of the uncertainties of the values of the factors used in the Drake equation, and seeing what that does to the "final answer". :P

"we are probably alone in the observable universe"

I find this conclusion ridiculous and very anthropomorphic.  There are galaxies that have existed billions of years longer than ours has, as a matter of fact a few months ago there was an article about unexplained signals coming from a galaxy 3 billion light years away, thousands of them.

Thinking that humanity is alone or special in any way violates every facet of the Copernican principle.  We have no concept of what exotic life might even be like- it could even exist in interstellar space, consist entirely of energy or on the quantum level.  The fact that we have found none only highlights our own limitations, nothing else.
 
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20 Nov 2018 15:03

I guess the cup is half full.
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20 Nov 2018 15:06

Stellarator wrote:
Gnargenox wrote:
Source of the post Have YOU, personally, ever found a 15lbs nugget of gold laying on the beach?

Heh, I did find lots of gold dust around where I live - does that count? Would that be a metaphor for unicellular life hiding under Europa's ice?

Anyway, I didn't mean to sound rude with my question, I'm just curious to hear what people have to say about "The Paradox" (yes, pretty much a misnomer) and their reasons for believing it. My stance is at this point: it's too early in the game to make any definite claims about anything. We honestly don't know enough about exoplanets, or even our own solar-system, for that. Reckless optimism only hurts this area of study, just as much as defeatist cynicism masquerading as honest skepticism. The annoying thing about a lot of these ETI-absence papers and articles is that they just address the uncertainties of the mathematical model with our current understanding of the universe, which is far from complete and no doubt subject to real changes next year or even next day. None of them really consider the sheer infancy of our observations, the age of the entire universe (so far!) and it's entailed sheer vastness. This may come across as a weak counter-argument, but when entire theories are completely dashed for the sake of brand-new, but better ideas with a greater pool of evidence to pull from, it makes more sense. So with that, we must resort to that tried-and-true Sagan quote (which somehow I knew I could use on this forum at some point  8-)):

"Absence of evidence is not evidence of absence"

Cliche but true until we have the Final Answer, even if that is an impossible dream. 

It's also possible that detection of life is complicated by the fact that we assume that it's going to be like us- it could be completely different from us and not even experience space or time in the same way we do.
 
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20 Nov 2018 15:11

Watsisname wrote:
Stellarator wrote:
Source of the post For the sake of argument, FTL is possible. You just need to be inventive about it and read between the lines of your physics textbooks. The Alcubierre drive is proof of this.

How is something that does not exist 'proof' that it is possible?  Just because the Alcubierre drive is a solution to the field equations does not mean it is physically valid.  It violates several energy conditions and introduces causal paradoxes.  Similarly, white holes are very simple to describe in general relativity, but there are deeper principles for why they don't exist.

It's possible that causality no longer is valid on those scales.  I've always had a problem with causality because it doesn't seem like a natural law, but rather something we created to make understanding the universe more simple.  On the quantum level causality is violated on a regular basis.  Kip Thorne, the noted physicist, explained how traversable wormholes would be possible (I think we've talked about this before lol.)  You do need to have exotic matter, which might be possible since it would fix another symmetry problem.
 
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20 Nov 2018 15:22

Stellarator wrote:
FastFourierTransform wrote:
They create a mathematical model for Von Neuman self-replicating probes expansion in the galaxy

An'shur wrote:
Source of the post We now have a bacteria/nanobot like growth rate doubling the numbers every 15 minutes!


What we are all forgetting here is that self-replicating machines (especially in swarms) cannot replicate exponentially (or even at the speed a lot of people think they can). There is a hard limit to how fast you can do something without causing so much friction that you just explode. Complexity as you might find in such nano-swarms will require a fair bit of energy to replicate. Complexity also will cause the machine to take longer to self-replicate, unless they replicate faster, which would then make them explode again. But the idea of self-replicating swarms is very complex and more then we are asking for here. Suffice to say it is not possible to colonize the entire universe (I know it was an exaggeration An'shur) with them. There are extremely intricate engineering hurdles to overcome even if they are tasked with just traveling around a few light-years and terra-forming and/or exploring and passively replicating. But we were talking about FTL here, so to continue:

An'shur wrote:
Source of the post 1) FTL travel is not possible. Simple as that.

For the sake of argument, FTL is possible. You just need to be inventive about it and read between the lines of your physics textbooks. The Alcubierre drive is proof of this. Its dynamics do not violate general relativity. Yes there are those 'minor' complications like requiring negative mass and so on, but certain designs can minimize the requirement. My point here is that the laws of physics do not say you cannot travel faster then light. The term itself is a misnomer anyway. It is the maximum speed at which massless particles (including photons, but also gluons and theoretical gravitons) can travel to maintain electromagnetic casualty between points in the universe as determined by the Lorentz Transformation in relation to the famous Maxwell equations of field electromagnetism. I would suggest to anyone wanting to understand this type of things to learn more about the work of Lorentz, Maxwell and other pre-Einsteinian physicists (maybe not you guys on this forum, you seem to know a lot about this science :)).

Naturally, to go faster then other matter, you must have negative matter or negative mass. No Mass (or neutral mass) = limit of casualty, and (positive) mass = impediment to motion. It stands to reason that negative mass is the opposite of positive mass and makes things go faster then mass-less matter, which acts as a speedometer in this case. Essentially the only thing standing in our way of building a Alcubierre warp-ship is this negative matter. For the moment we will ignore the other complications that will arise as a result of FTL travel like paradoxical phenomena. We can`t find negative matter, don`t know how nature could make it now and we cannot manufacture it like we can heavy elements.

An'shur wrote:
Source of the post 2) FTL civilizations don't exist. Less advanced civilizations don't get past the great filter, succumbing to the internal struggles we face on Earth today. If life in basic principles works the same as on our piece of rock (survival of the fittest), then I am afraid that extraterrestrial life would be territorial, power-mongering and domineering, both internally and externally to other aliens. If FTL was as easy as to allow aliens to spread faster than evolution could rid them of the aforementioned animal traits, they would just bring the problems of their home world out into space with them.

3) Which brings us to another possible solution. There may be countless FTL-capable civilizations, which wage wars of hardly imaginable proportions among each other, throwing death stars at one another as if they were merely cannon fodder. This would definitely slow their expansion rate, since it would not be safe to spread and no aliens would be able to reign across the universe.

5) Universe may be full of life and chaotic, but we don't matter, so they ignore us, which goes hand in hand with point 4. We are unable to communicate with them and vice versa.


These are probably the most likely, just based off of what we know about our universe. I omitted point 4 because it is only partially correct. I said earlier that we would ignore the actual effects of FTL travel. Now I would like to address it here in relation to your fourth point.

DoctorOfSpace wrote:
Source of the post     An'shur wrote:
   4) The universe is radio-silent because if civilizations were capable of FTL travel, they would most certainly be capable of FTL communication. EM spectrum would be ridiculously ineffective and slow as means of communication.


That's how it is in Star Trek, they use extra-dimensional space to communicate and if you have FTL travel you can probably crack FTL communication.
There was a paper I read before about sending compressed FTL messages in pulses through distorted space, will have to see if I can locate that.

As mentioned earlier, the speed of light is actually the maximum speed at which points in the universe can `communicate` (i.e. maintain casualty) to each other, and be seen communicating to one another by any other point in the same universe. As soon as one area of the universe (say, a space ship) transcends that speed (going faster then mass-less matter), it starts to `communicate` backwards in time relative to it`s origin and it`s relative speed. If the space-ship travels twice the speed of light (2c), to a destination 2 light years away from its origin, but then travel an extra year beyond that point from its origin`s point of view, beaming out homeward-bound messages, at some point these start arriving at its origin before the ship was even launched! This would be.. interesting to say the least. You could plan out entire expeditions via listening to the reports of your future self aboard the ship. Cool. All right maybe not, because this would cause paradoxes and all those bad things that you see happen in time travel movies will happen to you. The very fact that mass-less particles exist as the limit to casualty in the universe suggests that the laws of physics convene to prevent such disastrous things from breaking spacetime. The weird thing is that the messages sent from the traveling space ship in the example are not being sent FTL, they would be relativistic, at the speed of c. If you want to know how terrible FTL communication would be, check out the Tachyonic anti-telephone thought-experiment devised by Einstein and Arnold Sommerfield and later explored by Richard Tolman in his Tolman`s Paradox.

So I would think that communications at interstellar distances would need to be delayed or sped-up en route after being sent to their destination relative to their origin`s position and velocity in timespace to arrive instantly. I don`t know how this could be done.

After all that is said and done, EM might be the only medium in which to communicate effectively - unless the aliens use hypothetical means like neutrinos, quark entanglements or something even more exotic and fantastic that does not lead to paradoxes. But even if the majority of them would use such strange and to us, undetectable ways of talking, there would be those who inevitably do not for whatever reason. We should be able to pick those up at some point. And is my point: we have not been looking for long enough or hard enough to really make dent in this field. That is the attitude of SETI, and although it implores you to ``keep faith``, its really all you can do. Unless you want to be more pro-active and send out messages yourself. We did that a few times and none of them repeated, so I guess those are just another WOW! signal for somebody else. 


FastFourierTransform wrote:
Source of the post There has been some objections to this crazy expansion rate (which I think could be appliet also for your FTL-travel scenarios). It has been shown that only a society that has economic (and ecological) sustainability, with a strict birth control policy and a coherent cautios long term expansion strategy can really accomplish the colonisation of the galaxy. It has also been shown that a society that don't make control policies on its growth would exponentially consume more materials that those available in the increasingly large territory they expand on due to the limits of light speed travel. This would generate in a few millenia an interstellar societal collapse that would limit the "expansion bubble" to a few tenths of light years in what has been called the "ligth cage". So the reality is that no colonisation would occur in 5 million years (at those speeds they would fall in a Malthusian catastrophe quickly and would be limited to a tiny region of the galaxy). Only a very slow and gradual attempt would be victorious in invading the entire galaxy.

Yes, exponentiation tends to be blunted by other overlapping internal systems that arrange for self-regulation. Just take the population crises for example. A few decades ago scientists believed that the population boom of the industrial revolution and exponential growth thereof in the West and in Asia would doom us all to die from over-population difficulties by the 2050s, when humans would number over twenty billion. Now it has been learned that because of the development of first world countries, birth-rates in those countries has dropped. Population growth stabilized. Now the only human growth is from 2nd and 3rd world countries - but the reason why it is from there is because they are making the same industrial-era transition that the first-world countries made. After they pull through and provided we can clean up this planet and curb our excessive consumerist mindset, the population should stabilize overall at around 12 billion. Still a lot people, but technological and sociological innovation that results from the the prevalence of education in developed countries (which will be the ONLY countries by then mind you) should make that sustainable.

Anyway, to tie into what you said here about gradual colonization, I remember reading in Carl Sagan`s book Cosmos that based on the expansion dynamic`s of civilizations here on Earth, if a alien civilization 200 light-years away from Earth using sub-light travel started colonizing the stars around them, only targeting those stars that are suitable for them (Sagan used yellow dwarf stars as an example) in a roughly spherical volume, they would take 2 million years to reach our solar-system with their scouts, assuming they did not make Sol an objective in their missions. A million years per hundred light years. 2 billion years for the entire galaxy (which, as of new research, is around 170,000 light-years across). Bear in mind this is if they only colonize type G yellow dwarf stars.

The take away from all of this is that interstellar expansion is fiendishly difficult even with FTL. It is not a game changer, despite getting so much attention.

midtskogen wrote:
Source of the post There's one possible problem to interstellar travel.  Dust.  Interstellar dust is extremely sparse, but given the distances and the great travel speeds, could it pose a problem?  Has anyone tried to calculate the risks?  A small pebble, even just a gramme, will utterly destroy your spacecraft hits it at 10% the speed of light.  That's nearly half a gigajoule of energy, or the equivalent of more than 100 tonnes of TNT.

At subrelative speeds, even the hydrogen gas is deadly. It depends what your space craft is made out of. You would obviously have a curved shield of some strapped on the front of your ship (which some of the SE ships have, if you are curious). The shields would have to be hard but also rather absorptive and flexible, possibly made out of a aerogel, metamaterial or something similar. As they get bombarded, the shocks of kinetic energy are absorbed and redistributed evenly - maybe even powering internal mechanisms as a opportunistic generator. We must also understand that things in space do not blow up in the same way they do on Earth. Most if not all of the force an explosion makes up there is kinetic and hence easily manageable.  Something bigger heading your way would need to be detected beforehand and vaporized by lasers into smaller chunks.

That being said however, At superluminal speeds, nothing will save you (unless you have FTL lasers :P). The Alcubierre drive works around this problem because it does not travel through space, space carries it in a bubble of negative matter. Hence gas, dust and bigger chunks might be deflected by the negative matter or even annihilated. I`m not entirely sure what effect a bubble of spacetime would have on a asteroid.

Ahhh, nothing like a FTL alien discussion get those synapses firing :D...

I like number 4 myself, but to have FTL communication you have to think beyond our universe and beyond our space-time, it's the only way that would be possible.  Consider a universe with an arrow of time opposite to ours, whose matter would be considered exotic to us and ours would be exotic to them.  They would have a forward arrow relative to themselves so to them we would be the ones who seem to be going "backward."  So each universe would be like a conveyor belt with everyone on each belt facing forward (towards the future) but each belt would itself be going in different directions relative to the other belts (universes.)  To achieve FTL communication or travel or time travel to the past (or to another past as per the multiverse) you would have to jump to a universe with a different arrow of time and jump back into ours (like jumping from one conveyor belt to another.)  The other intriguing aspect of this is if we had a counterpart universe with an opposing arrow of time, ours would expand while the other contracts and vice versa, and both would eternally big bounce (or at least the value of the cosmological constant reaches 0.)  At the singularity level gravity ceases to be an attractive force and expansion/inflation occurs again.   Deflation would happen when the universe exists inside a black hole inside a larger universe and reaches its maximum potential.  We would seem superluminal to the other universe and they to us and rather than speed of light being a limit it would be an asymptote (like absolute zero temps are.)  There is such a thing as below absolute zero temps and that is what this other universe would be like to us (and us to them.)  Asymptotes can't be crossed directly but can be jumped over.


The other possibility is the sterile neutrino, which has been hypothesized to travel back in time because gravity is the only force that it is affected by.
 
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20 Nov 2018 16:15

A-L-E-X wrote:
Source of the post  I've always had a problem with causality because it doesn't seem like a natural law, but rather something we created to make understanding the universe more simple.

Causality is deeply woven into relativity, into the very geometry of space-time.  Every event that you can causally influence lies inside your future light cone, and every event that could have causal influence on you lies in your past light cone.  Everything else is "elsewhere", separated from you more in space than in time, and you cannot reach or communicate with it.

The reason causality exists and is so important stems from logic, really.  If you imagine a scenario where you violate causality, then you quickly get into paradoxes.  The classic example in relativity is to imagine making a trip faster than the speed of light, to travel to an event in "elsewhere".  If you do that, then there will exist observers for which your journey was backwards in time.  You could influence your own past.  This is a paradox.

A-L-E-X wrote:
Source of the post On the quantum level causality is violated on a regular basis.

Is it?  Name an example and an experiment to support it. :)
 
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20 Nov 2018 23:30

Well, at the quantum level, events in time occur equally in both directions (forwards and backwards), does that mean that causality still holds at that level?  Perhaps retrocausality?  I know the speculation is that on the quantum level space and time no longer actually exist, so by definition, I would think that means on that level causality no longer does also.  I think that's where the fundamental divergence between relativity and quantum mechanics happen (and the reason why black holes seem like singularities is because they are basically quantum objects on a relativistic/macro scale.)

Based on the above I would think that space/time/causality are emergent phenomena.

I completely agree with what you mentioned about paradoxes, but I feel this is a macro scale phenomenon.  On a quantum scale (if this happens and MWI or one of its variants is correct) you would be going to a different timeline and not actually affecting your own past.  I dont know of any experiment that proves this one way or another, but wasn't the double slit experiment interpreted this way by MWI?  Also things like space entanglement, time entanglement, tunneling, teleportation (all of which occurs instantaneously), nonlocality, etc.
 
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21 Nov 2018 00:45

A-L-E-X wrote:
Source of the post It's also possible that detection of life is complicated by the fact that we assume that it's going to be like us- it could be completely different from us and not even experience space or time in the same way we do.

This is doesn't have much meaning in the context of SETI. Unless we know exactly what we are looking for out there in the greater universe, we will have no rational framework to use in identifying and studying a supposed ETI civilization - or even just microbacteria-equivalents floating around in an atmosphere/high geyser. Thus we make some assumptions that extraterrestrial life will follow the natural laws we see operating here on Earth within the confines of established science. Such assumptions could be seen as sloppy anthropomorphism on the part of researchers, but within reason it is not.

Life needs a stable planetary environment, the right star to orbit, utilize certain elements and molecules in their environment, have enough time to evolve, survive any extinctions (whether caused by other phenomena, or by their own functions as in the 'Snowball Earth Catastrophe hypothesis') and of course have a sustainable source of energy, food and procreation. Everything must follow thermodynamic and biochemical principles like a valid thalassogen, respiratory (or equivalent) system and viable means of  metabolism.  Outside of these core concepts, any arrangement of variables is game. These assumptions are not chauvinistic (just research "Earth Chauvinism" in the context of astrobiology) and should never be confused with such. All the processes described above will have a detectable impact on their environment. Each process could potentially completely stump the development of life - but what happens on one planet, might not happen on another.

Once life has been established on a planet, the development and detection of intelligent, industrial ET life is comparatively easy. Comparatively. To evolve into intelligence, the ET life on planet must first go through the so-called Great Filters (of which there are many, all equally as valid with our currant understanding of the universe):






(Note:Isaac Arthur is not an authority on these matters, but is a great place to start :). Like Watsisname, I find he has a way with words that makes the science easy to understand and a joy to learn).

In order to become advanced and be potentially detectable by us (or anyone), the emergent intelligent life must develop and learn trial-and-error science. Without it, no advancement to industrial levels is possible. And in order to work, this science must follow the laws of physics and mathematics, since those rules are observably constant throughout the entire visible universe. Beyond the visible universe at the very end or beginning of time, for example, these laws may theoretically bend a bit. But lets not muddy these waters with that right now. No special treatment to a ET civilization can be given by researchers here on Earth by saying that they are "so exotic". If so, they would be in-observable with current scientific methods and just be an anomaly at best, totally invisible at worst. The only concession would be to say that they are many thousands, or millions or even billions of years ahead of us technologically, and just use means of technology that, despite their advanced nature, still operate on the principles of the universe as we know them, with only slight distortions colored by way of a species-dependent view of the universe.

If by "completely different and spatially-unique" you mean that they are some sort of energy-based life-form, then such discoveries are for future scientists and we could not detect those entities anyway. This concept might seem to some like a 'proof-of burden' shift to others, but in truth science operates on a advancement principle of elimination through elementary progress: the low-hanging fruit are first discovered, then as we become better and more specialized at the task, deeper and more complex ideas are pursued. Astronomy is a prime example of this: first the planets were discovered, then we found the laws for their movements, then we learned what they look like and are made of close-up. In all probability, the first ET life we discovery in the universe will be analogs of what we encounter here on Earth for reasons that we are slightly biased in looking for Earth-like things and our methods were engineered to do so. This applies to ETI as well. :)
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21 Nov 2018 01:58

A-L-E-X wrote:
Source of the post Well, at the quantum level, events in time occur equally in both directions (forwards and backwards), does that mean that causality still holds at that level?

No, they occur forwards in time.  A quantum interaction does not affect events in the past, otherwise I could easily use the double slit experiment or any other simple experiment of a quantum mechanical nature to send messages to myself in the past and win the lottery or cheat on exams. ;)

What you are probably thinking is of time symmetry, meaning the equations describing how systems evolve work just as well running forwards as backwards, as long as all the processes involved are reversible (hence the arrow of time and thermodynamics and increasing entropy).  What this means is that if you, say, scatter two particles off of each other, then you can imagine flipping the velocities around and you'll exactly retrace that collision.  Maybe.  Actually that breaks down quantum mechanically, because the results of a scattering in quantum mechanics are probabilistic.

A-L-E-X wrote:
Source of the post I know the speculation is that on the quantum level space and time no longer actually exist

No, that is not true either.  Otherwise the very notion of assigning a wave function (a function of position and time!) to a particle in quantum mechanics would not work.  The Schrodinger equation wouldn't even make sense.  Yet it's the key equation in quantum mechanics!

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