Correction:
should have been
But that statement is just a way of thinking about it, trying to provide an intuition for a 4 dimensional space that we humans can’t really visualize. Light cones are useful because although the points don’t map to flat space every event on a hyperbola is “simultaneous” for that observer. Those cones aren’t really cones but I can’t figure out words to describe geometry on a saddle like surface like I use in my head for my own intuitions.
Because one, you wouldn’t reconstruct like that. You would build an Android body out of plastic or whatever and drive it with a powerful enough computer to emulate the neural map. This is straightforward known physics and even rat avatar should admit this would work. Or two, you build each organ - concept demonstrated on Earth already - except for the brain and again, drive the body with a nerve stimulating interface. All very feasible stuff.
Antimatter production is feasible with vacuum boiling lasers and orders of magnitude more efficient. Rat avatar always picks the worst possible numbers. The handwavy part is no one has trapped sufficient antihydrogren in an apparatus to attempt to form anti deuterium. So we don’t know if the laws of physics really allow anti elements. They probably do but it hasn’t been verified. We know 99.9999 percent that the laws do permit brain emulation. The remaining decimal is left for magical deities.
Edit - just checked, anti deuterium has been produced. So really the thing to argue is how efficient can a vacuum boiling free electron laser be in practice? Even a tenth of a percent in net antiproton production would be more than usable. Rat avatar, know anything about it?
Much discussion about the arrow of causality uses circular reasoning.
It seems to me that once you link the arrow of causality to the thermodynamic arrow, you’ve given up on an “absolute” arrow. Stephen Hawking once thought that time’s arrow would reverse during a contraction to the Big Crunch. Although he may have revised this opinion, the fact that he once believed it makes one skeptical of overly-glib refutations. (And he revised his opinion not out of a belief in a fundamental Time’s Arrow but because his calculations showed him entropy would continue to increase during the contraction.)
The Second Law is closely related to the Law of Large Numbers — a container with trillions of molecules will move toward equilibrium. But what if the container has only 2 or 3 molecules? It’s almost as likely to lose entropy as to gain entropy. If it loses entropy for a few seconds, would you say that its local arrow of time reversed?
Entropy is not “disorder”, microstates are what matters, orderly patterns of the molecules don’t matter at all.
Even with a container with 2 or 3 molecules the entropy remains the same or goes down. Another way to consider it is that those 2 or 3 molecules will have a greater difference in momentum in the start, but assuming a ideal container without gravitational red-shift or heat transfer those molecules momentum will get closer to each other with each interaction. As there is less difference in their momentum there is less of a differential to do “work”. Thinking of entropy as that loss in differences of energy levels over time also helps.
Maxwell’s demon is an apparent paradox that is not exactly related but may help with the concepts.
The reality is that the numbers involved with macrostates and microstates are too big for us to have good intuition with. In a non-ideal thought experiment energy would be lost to the containers sides etc…
But the number of particles in your ideal box is immaterial to the question, entropy will stay the same or go up.
Suppose an atom of hydrogen and an atom of tritium travelling at the same speed collide head-on; assume perfect elasticity.
The tritium will come to a standstill, while the hydrogen rebounds at twice its initial speed. Correct so far?
We’re not talking about statistical averages involving large numbers of particles and large numbers of collisions. Neither the Law of Large Numbers nor the empirical fact that we see lower entropy in the past is in dispute. The question involves the Arrow of Causality, if any, at the most microscopic level.
You are probably hitting the Gibbs paradox which is cased by not using the more correct formulas or if you move past superseded classical theories.
Note that the tritium wouldn’t stop, and even in your example one really needs to involve phase space. I get the feeling you are trying to set up a one dimensional example of an ideal gas, that phase space would be a circle for two monotonic particles.
The paradox you are seeing is completely an artifact of oversimplifying the math and sticking to superseded classical theories.
Here is a paper that will walk you through more correct extensible formula for your thought experiment to get you past this apparent paradox while still staying in the classical domain.
No. My example involved two distinguishable particles. This has nothing to do with Gibbs Paradox. I think you are deriving erroneous conclusions from what I write and then debating those strawman conclusions. In my previous post I intended only the obvious:
(a) With the exception of 2nd LoT and a weak-force peculiarity which is probably of minimal relevance, the laws of physics are time-reversible.
(b) The Second Law of Thermodynamics is a statistical law, not a dynamical law.
Do you agree with these? Then we can move on.
Or better yet, since there are dozens on the Board who know far more physics than I do, we can hope a 3rd party comes along and arbitrates our “dispute.” Be aware that I am not proposing anything novel; I’m obviously not expressing my point(s) with adequate clarity but there’s nothing I’m trying to say that can’t be found — were I inclined to search for it, which I’m not — in the writings of famous physicists.
Entropy is statistical mechanics in modern theories. The incorrectness of classical thermodynamics has been known for a long time.
It is useless to discuss what is now merely a superseded phenomenological theory when trying to discuss our current understanding of the universe if you want to apply it to actual observations.
Note you ignored my cite too, which did show that:
I can’t format the math on this board to show it, feel free to explain why you think my cite is wrong.
Hello Mr. Avatar. This whole discussion is very reminiscent of another recent thread where we talked past each other. Not mentioning specific names, one of us seemed unwilling to acknowledge what the other said, preferring to debate strawmen of choice.
Nobody’s seeing a paradox. Somebody is testing to see if you understand the statistical nature of the 2LoT.
At this point, all I can do is repeat my effort to keep the dialog on-track, using larger and larger fonts until it appears you’ve caught up.
As momentum and kinetic energy conserved as you defined it as “perfect elasticity”. In classical head-on elastic collisions of equal masses, the velocities will always exchange. Both your particles were moving, and have unequal masses.
Assuming by hydrogen you mean protium or [sup]1[/sup]H
[sup]1[/sup]H: ~1.007825 u
[sup]3[/sup]H: ~3.016049 u
# Elastic Headon Collision
from mpmath import mpf, mp
mp.dps = 100
# Mass of protium (Hydrogen) in KG
m_1 = mpf(1.660539040e-17 * 1.007825032241)
# Mass of tritium in KG
m_2 = mpf(1.660539040e-17 * 3.01604928199)
# starting velocity protium
v_1 = 1
# starting velocity tritium
v_2 = -1
v_1_prime = v_2*((2*m_2)/(m_1 + m_2)) + v_1*((m_1 - m_2)/(m_1 + m_2))
v_2_prime = v_1*((2*m_1)/(m_1 + m_2)) - v_2*((m_1 - m_2)/(m_1 + m_2))
Will show:
v_1_prime ~ -1.99815456096
v_2_prime ~ 0.00184543903
And so yet as you are trying to stay classical and offered a false claim I will not move forward.
As this is GQ how about just providing me with a cite as you are edging between the micro and the macro world and the postulate that will be accepted vary dramatically based on the domain you are trying to make the claim in.
The limitations of classical few-particle microcanonical ensembles is well known, and I am guessing that is where you are trying to establish your apparent paradox but given an ideal non-interacting box the above two particles would tend to having equal momentum over time with more interactions under the classical model. As you don’t have enough particles for heat flow this perfectly elastic “work” is the only statistical mechanics analog you have for entropy.
Please let me know what domain you are arguing from, but as you suggested the microscopic level I would mention that the field of quantum thermodynamics is in it’s early stage and mostly at the stage of finding violations.
But the cosmological arrow of time which are from thermodynamics of large ensembles which do not hit this limit aren’t dependent on a theory replacing the known-incomplete standard model although a validated theory for quantum gravity may enough. But we won’t know that until we get there.
As our best quantum theory, QFT, only uses special relativistic concepts it will not scale outside of the local context in a way to describe the arrow of time as related to this threads subject which is at the interstellar travel scale.
But also not the reversibility, where a dropped coffee cup wold seem normal when it spontaneously becomes a whole coffee cup, is probably tied to our perception of time. For General Relativity and the speed of causality and shape of causality you are not restricted from going into your own past because of thermodynamics but because close space like curves would require faster than light travel. The speed of light is the speed of causality in GR and cosmology.
New physics may change this but as QFT and GR are some of the best tested theories in human history the replacing theories aren’t likely to change this much. But they are both incomplete so there is something to discover. Due to what we can observe those replacements are most likely going to confirm the arrow of time and exclude mathematical anomalies like worm holes.
But as I said there is fast movement here, if you have experimental proof that these issues have implications in the real world provide a cite please.
I share your skepticism about the motives for our alien friends. It seems to me that smallish self replicating space probes would be the way to go. Or remote viewing with technology beyond ours. (I could jabber about quantum entanglement or universal waves, but honestly I may as well appeal to crystal balls or Mirrors of Galadriel.) The industrial revolution is only some 200 years old after all and we haven’t even experienced an AI singularity yet.
The Fermi paradox presents the outcome of a test on a number of joint hypotheses, which makes it conceptually unwieldy. Might it rule out some scenarios though? Sure, there could be thousands of active civilizations in the galaxy, but I WAG that a 1/50 star ratio is unlikely. There are apparently 33 stars within 12.5 light years of us and 1400 star systems within 50 light years. Sure, I Love Lucy might be difficult to detect, but we have radar systems for defensive purposes in Alaska which apparently leak out radio/micro? waves at higher energies. Some imply that technological civilizations will abandon radio waves, but I find that unlikely. It’s a resource: I suspect it would be used for something, albeit something of lower value than we use if for now. Canals didn’t just disappear once railroads undercut them in cost. They went bankrupt, but shipped items for years. Today they are used for recreation and waterfront property.
I also wonder whether we would find evidence of small self replicating alien probes orbiting around Sol if we looked for them.
Here’s a question. I had understood that a civilization could easily make its way through a galaxy with self replicating probes in a relatively short period of (geologic) time. Is that really the case though? What are the numbers and implied rate of spread? I attempted a back of the envelope calculation and the galaxy seemed bigger than I thought.
If the galaxy were a sphere of uniformly distributed stars, you could colonise every one of the 400 millon stars in 38 doublings (so that each colony produces two, and only two, daughter colonies). If each replication took 25,000 years, you could colonise the whole galaxy in a million years.
But the galaxy isn’t a sphere of stars, so you’d have to allow a bit longer to colonise the extended thin disk. Maybe ten million years, tops. Less than a thousandth of the age of the galaxy.
No, I think you have it wrong. I get 1.68179~.
show your work, dumbshit
OK, The diagonal of one face of the cube (s is the length of one side) is
__d = sqrt(2s[sup]2[/sup])
or 1.41421~
That forms one side of the diagonal bifurcating square of the cube, so corner-to-opposing-corner would be
__c = sqrt(2d[sup]2[/sup])
The Milky Way is 100,000 light years across. If it takes 1 million years, alien expansion would be occurring at 1/10th of the speed of light if it went from one end of the galaxy to the other. That’s quite fast - about 18,600 miles per second. New Horizons, by contrast, putters along at 8.3 miles per second. And it neither zig-zags nor stops for self-replication.
Shift an order of magnitude and our aliens are expanding at 1,860 miles per second over 10 million years. Now the hop to Alpha Centauri takes 400+ years rather than 40. I’m not saying these numbers are impossible, but they are more challenging than I had understood. While anti-matter engines and a matter repellent shield might be sufficient, I’d recommend Harry Potter brooms instead. Humor self-directed.
Also remember that:
The Earth is at the bottom of the range in planetary masses that can maintain an atmosphere.
The Earth may only have enough iron for it’s side to have an effective magnetosphere due to a large collision.
A planet the same density but twice the radius would have almost 8 times the mass and would require a rocket larger than the Atlas V to even put a fairly light communications satellite up in geosynchronous orbit.
This (fun to read) paper will go over it in detail.
Even if intelligent life does exist in other parts of the universe they may be restricted by gravity and no matter how advanced they may not be be space-fairing due to the costs and efforts.
But even ignoring the problems with reaching 10% of c etc…the growth assumptions assume that these groups have a highly aggressive expansion and resource use pattern to drive the need and to justify the high cost of expansion at those speed.
Slow expanders, who wait until local resources are consumed before making the next trip or if you even consider the time to collect the energy to get a toothpick to 10% of c would dramatically change the time required to spread.
A very interesting paper on the chemistry of life I’ve linked to before mentions possible exotic life forms including
.
But perhaps only life forms satisfying strong constraints would be able to develop high technology.
[quote="eschereal, post:134, topic:827614"]
[QUOTE=Andy L]
I think you mean 1.732 unit diagonal (unless I'm picturing what you mean incorrectly). The length of a cube's diagonal is proportional to the square root of 3 not the cube root of three.
[/QUOTE]
No, I think you have it wrong. I get 1.68179~.
[d =] 1.41421~
That forms one side of the diagonal bifurcating square of the cube ...[/FONT]
[/QUOTE]
I vote with **Andy L**. What is the "diagonal bifurcating square"? Did you mean "diagonal bifurcating rectangle"?I should clarify again,
I realize what I have been offering are what people working on the problem call “soft filters” which mean they reduce the chances.
A “hard filter” would be a single issue that explains everything in one go and would be what would be required to “resolve” the paradox for many people.
But right now the general fudging numbers with the fuzzy part of the social portion of the Drake equation that most people use put the number of “advanced civilizations” somewhere between none and a ~15,000.
Recent number of powerball tickets sold on one of the big jackpot run ups ($456.7 Million won on 03/17/18).
4.62% chance for 13,498,238 tickets
4.89% chance for 14,293,921 tickets
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5.14% chance for 15,024,559 tickets
4.64% chance for 13,570,900 tickets
5.66% chance for 16,550,828 tickets
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6.28% chance for 18,340,583 tickets
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10.81% chance for 31,595,593 tickets
12.40% chance for 36,246,189 tickets
15.33% chance for 44,791,214 tickets
In total they sold 425,165,694 tickets for a ~ 1:292,201,338 chance of win in any one draw.
If you have a ton of “soft filters” that are additive including the chances the chances that Von Neumann nano probes go Skynet or self replicate until life on the planet is killed off, their planet is too heavy for chemical rocket, or the tech required to make small fusion reactors is used to wipe out life with nuclear war it is not hard to reach powerball like odds.
If you see the challenges we have on our own planet trying to get people to agree to limit the avoidable effects of climate change it is clear that we are at risk of not making it past “The Great Filter” ourselves. The Cuban missile crisis also almost ended the world too.
We need to have people thinking about this problem, but once again we don’t know enough to say the lack of observations of other life is proof we are alone, we are just narrowing where we need to keep looking. Just like powerball example above our short time looking and we may not be lucky enough to be in a time period where we hit the jackpot.
There’s one sub-thread here that left me slightly … flabbergasted.
The Law of Large Numbers (closely related to the Second Law of Thermodynamics) does not apply to Small Numbers! I think we all know that, but one of us seemed almost confused on the point. I spent a minute with a simple exercise from high school physics trying to make the point absolutely clear by showing two particles moving away from “equilibrium”:
I could have written “almost a standstill” I suppose (or better yet “at almost the same speed”), if I wanted to be pedantic. I’m sure I seem pedantic at times, but thank God I’m not that pedantic.
But the tritium atom only loses 99.99966% of its kinetic energy — it doesn’t quite come to a complete standstill. Someone thought this “error” was a big Gotcha. Since my claim was “false” he “would not move forward.” Forward on what? On accepting that small numbers are different from large numbers?
Astounding.
You are correct, it would be a rectangle, which means the diagonal of the cube would be
__c = sqrt(d[sup]2[/sup] + s[sup]2[/sup])
putting it closer to 1.5538~ by my figuring. My math skills are rusty, though.