Given complete knowledge of the precise state of every property of every particle and energy phenomenon existing in our universe for a given infinitely small frame of time, is it possible to completely determine the status of every property of every particle and energy phenomenon existing in the succeeding time frame?  This situation assumes that there are no restrictions towards the access of any information, particularly particle states, existing in the universe.  How can this situation be mathematically modeled?
77589
What are the main problems that we need to solve to prove Laplace's determinism correct and overcome the Uncertainty principle?
107185
My question pertains to a possible inconsistency between the first law of thermodynamics and the general expansion of space itself.   First, the knowns:   Space itself has, and continues to expand - the acceleration aspect is not relevant to the discussion Empty space in a vacuum has intrinsic energy - some refer to this as dark energy Energy cannot be created or destroyed as per the first law of thermodynamics   Concisely, what is the source of energy that is imbued into this "new" space?  A few speculations:   The energy for this process is taken from something other source that already exists inside or outside the known universe. The energy for this process is created from nothing, thus violating the first law. If space itself is quantized, perhaps the planck length itself is expanding across the universe, giving the appearance that new space is created, but actually it is just the space "particles" themselves that are expanding.  At some critical point this expanding space would have observable consequences for our own scale of existence.   These ponderings can also be applied to the big bang theory - either energy was created at some point (from nothing) or existence of anything has been an infinite cycle into the past. Either way we are dealing with infinites. Create something from nothing and you will find infinites cropping into your calculations.
77985
Phase space theory suggests that the largest course-graining region, $p$, in a phase space, $P$, is the point in the phase space with the highest entropy. As such, it is in thermal equilibrium with the course-graining regions surrounding it.   Now, when an intensity vs frequency graph is obtained for the CMB (Cosmic Microwave Background), a curve almost identical to Planck's curve representing black-body radiation is seen. The temperature of the CMB is observed to be almost uniform across the universe, and the curve of black-body radiation represents a point of thermal equilibrium for a system. Since the CMB has the same curve as black-body radiation, this would suggest that at the birth of the cosmic microwave background, the universe was in a state of thermal equilibrium.  Referring back to the phase space spoken of in the first paragraph, since the universe was in a state of thermal equilibrium, it was at a point of highest entropy.   However, surely due to the Second Law of Thermodynamics, the entropy of the universe would need to decrease - so it wouldn't be possible for the entropy of the universe to be in such a high state so soon after its birth - so it should surely begin in a low state of entropy.  So what's the deal here? Did the universe begin in a really low state of entropy, or a really high one? Are all my explanations here logical or quite inaccurate?
20305
Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and so far I understand most of general ideas he has talked about. Or at least, I think I understand them :-)  There is however one part, at the end of chapter 6 that I can't grasp.  It is about entropy and the state of the universe a few minutes after the big bang.  On page 171 he says:     Our most refined theories of the origin of the universe -our most refined cosmological theories- tell us that by the time the universe was a couple of minutes old, it was filled with a nearly uniform hot gas composed of roughly 75 percent hydrogen, 23 percent helium, and small amounts of deuterium and lithium. The essential point is that this gas filling the universe had extraordinarily low entropy.   And on page 173-174:     We have now come to the place where the buck finally stops. The ultimate source of order, of low entropy, must be the big bang itself. In its earliest moments, rather than being filled with gargantuan containers of entropy such as black holes, as we would expect from probabilistic considerations, for some reason the nascent universe was filled with a hot,   uniform, gaseous mixture of hydrogen and helium. Although this configuration has high entropy when densities are so low that we can ignore gravity, the situation is otherwise when gravity can't be ignored; then, such a uniform gas has extremely low entropy. In comparison with black holes, the diffuse, nearly uniform gas was in an extraordinarily low-entropy state.   In the first part of the chapter Brian Greene explains the concept of entropy with tossing the 693 pages of War and Peace in the air.  At first, the pages are ordered. The specific order they are in make sense and are required to recognize the pages as a readable book called War and Peace. This is low entropy. It is very highly ordered and there is no chaos.  Now, when you throw the pages in the air, let them fall and then pick them up one by one and put them on top of each other, the chances you get the exact same order as the initial state are extremely small. The chance you get another order (no matter what order, just not the one from the beginning) is extremely big. When the pages are in the wrong order, there is high entropy and a high amount of chaos. The pages are not ordered and when they are not ordered you would not notice the difference between one unordered state and another one.  However, should you swap two pages in the ordered, low entropy version, you would notice the difference.  So I understand low entropy as a highly ordered state with low chaos in which a reordering of the elements would be noticeable.  I hope I'm still correct here :-)  Now, what I don't understand is how a uniform mixture of hydrogen and helium can by highly ordered? I'd say you wouldn't notice it if some particles traded places. I'd say that a uniform mixture is actually in a state of high entropy because you wouldn't notice it if you swapped some hydrogen atoms.  Brian Greene explains this would indeed be the case when gravity plays no important role, but that things change when gravity does play a role; and in the universe right after the big bang, gravity plays a big role.  Is that because a reordering of the particles would change the effects of gravity? Or is there something else that I'm missing here?
66015
Sorry if this is really naive, but we learned in Newtonian physics that the total energy of a system is only defined up to an additive constant, since you can always add a constant to the potential energy function without changing the equation of motion (since force is negative the gradient of the potential energy).   Then in Quantum Mechanics we showed how the ground state of a system with potential energy $V(x) = \frac{1}{2} m \omega^{2} x^{2}$ has an energy $E_{0}=\frac{1}{2} \hbar \omega $.   But if we add a constant to $V(x)$ won't that just shift the ground state energy by the same constant? So in what sense can we actually say that the ground state energy has an absolute value (as opposed to just a relative value)? Is there some way to measure it?   I ask this in part because I have heard that Dark Energy might be the ground state energy of quantum fields, but if this energy is only defined up to a constant, how can we say what it's value is?
32942
In popular physics articles and even some physics classes I've been to, the vacuum of space is described as being constantly full of quantum fluctuations.  Supposedly, all sorts of particle-antiparticle pairs at all scales are constantly appearing and disappearing.  We end up with a mental image of the vacuum as a roiling, choppy sea with all sorts of things going on, rather than a calm, placid background.  However, the vacuum, being the lowest-energy state of a theory, should be an energy eigenstate—which means it is time-invariant (except for a physically-irrelevant phase factor).  So it seems the vacuum really should not be seen as a dynamic entity with all kinds of stuff happening in it, as we're led to believe.   that     A “vacuum fluctuation” is when the ground state of a system is measured in a basis that does not include the ground state; it’s merely a special case of a quantum fluctuation.   So it sounds as if the existence of vacuum fluctuations is contingent on measuring the vacuum—in particular, measuring something that doesn't commute with energy (such as, I guess, the value of a field at a point).  How much truth is there to the idea that vacuum fluctuations are constantly happening everywhere, all the time?  Is that really a useful way to think about it, or just a myth that has been propagated by popularizations of physics?
74910
I was looking at a website that claims to generate random numbers from observation of quantum effects. This lead me to question how we know that the numbers are truly random.  When we observe a probability wave and it collapses in one place into a particle, how do we know that the location of the particle is really random?  Do we have any evidence of the randomness, or is it just that no one can predict the location right now?
88405
Has anyone understood the ? What is the current status?  In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's engine) How does one account for thermodynamic concepts applicable to situations involving measurement? What does it mean to reset the state of the apparatus why is free energy expended in the process?
104191
Maybe this is a silly question (I think it is), but it's a question I'm arguing with some of my friends for a long time.  The ultimate question is: Is everything (in our Universe) possible ?  I've read some books (Penrose, Hawking, Greene, etc.) where it was clearly stated several times that quantum mechanics allows any situation to happen (e.g. everything is possible) - even with absurdly tiny probabilities?  Does this mean only physically possible - or "ultimate" possible ?  For example (I know this example seems really absurd, but I'm saying this so you get the idea) what my friends clame it is possible:   If I ask my friend(s): "Is it possible there is a Sun-sized star in my pocket right now?" They will respond: "Yes, there is very very tiny possibility this can be true!" Etc.
7910
It is known that for a system at  described by the , the probability of being in a state of energy $E$ at temperature $T$ is given by the : $$ \tag{1} P(\text{state with energy } E) \propto e^{-E/kT}. $$  I have no problems with the mathematical derivation of this result, but I do wonder if there is a way to understand what (1) means intuitively.  In other words: Is there a way to "guess" that the correct distribution for such a system is given by (1), using solely physical arguments?
781
It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is no experiment that you could perform to prove that you are in motion or at rest. So I have a couple of questions related to this.   Is this still held to be true? I was just wondering if anything in physics has come to light since I learned about this (about 10 years ago) that would allow an observer on the train to tell if they are moving. If this is true, why couldn't you accelerate a particle in different directions to a certain mass and measure how much energy it took to get it up to that mass. If you were moving in any direction, wouldn't you measure less energy in your direction of travel? Would having an outside observer affect the aforementioned experiment in any way?
35930
I was reading  and I got some doubts about a sentence about entropy, specifically when Ethan explains the irreversibility of the conditions of the hot-and-cold room, as in this figure:  In his words:  It's like taking a room with a divider down the middle, where one side is hot and the other is cold, removing the divider, and watching the gas molecules fly around. In the absence of any other inputs, the two halves of the room will mix and equilibrate, reaching the same temperature. No matter what you did to those particles, including reverse all of their momenta, they'd never reach the half-hot and half-cold state ever again.  My question is: Is the spontaneous evolution from the equilibrium temperature (right side of the image) to the half-hot and half-cold state (left side) physically and theoretically impossible/forbidden, or is it simply so astronomically unlikely (from a statistical perspective) that in reality it never happens? The article seems to suggest the former, but I was under the impression of the latter.
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I've heard this pop up in a discussion with my physicist/engineer roommates, but didn't care to ask at the time.  Now I'm mighty curious about it.   doesn't really seem to say much on this issue.  From what I understand about the Uncertainty Principle, it says that there are certain properties of electrons and stuff that cannot be measured, and are therefore uncertain.  Then Wikipedia (under ) states that Sir Arthur Eddington says that the Uncertainty Principle isn't really so because we can't measure these properties, but because turns out nature is indeterministic.  At least that's what I took from those paragraphs.  Even without my biased wording, it sounds more like an assertion than evidence.  I've also read a few things about how other scientific conventions perceive the issue, like how a ball on the peak of a perfect mound might randomly roll down in any direction, and I'm still unconvinced.  My belief of determinism is generally that if you knew every single variable that existed as a factor at the very beginning and birth of the universe, you could correctly determine all properties of any individual particle at any point in time.  Could anyone provide some more background about this?  Especially regarding quantum mechanics?
106669
I was thinking of the noted 1980 paper by Sidney Coleman and Frank de Luccia--"Gravitational effects of and on vacuum decay"-- about metastable vacuum states that could tunnel to a lower energy "true vacuum" with catastrophic results. I suspect the answer is that if our vacuum is a false one, we wouldn't "see" the true one til it hit us.
55273
I was wondering if quantum particles do actually  exists in two different states simultaneously and if it has been proven they do indeed exists in a superposition of states.  How has it been figured out since observing it would collapse the wave-function into one single state (two superposition of states into one ) as it has been mentioned in the Schrodinger's cat experiment?
60340
Is the  a fundamental , or can it be inferred from unitary evolution?
77459
When an excited state couples to the vacuum, it has an infinite number of directions of the quantized electromagnetic field to couple to. Does it evolve into a superposition of all those directions at the same time and only collapses once the photon is measured, or does it couple to only one? (Or, of course, is there no experimental way to tell?)