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- Classical mechanics: Basically views time as another spacial axis. In classical mechanics bodies can be viewed as being a 4D extrusion of their 3D shape along

- Classical mechanics: Basically views time as another spacial axis. In classical mechanics bodies can be viewed as being a 4D extrusion of their 3D shape along a 1D time path. High precision simulation of classical mechanics does not model time as steps / frames in a movie, but as a continuous 4D geometry. - Relativity: Builds on classical mechanics idea that time is a geometric axis and using a 4D coordinate system. What is further added is the possible distortion of that 4D spacetime. - Quantum mechanics: Strictly speaking quantum mechanics does not model time at all. It is more like algebra. It only describes equivalences / transformations which can occur. When we reformulate some algebraic expressions we don't think of the steps we take as time steps. It wouldn't work anyway because there are many possible paths not one. It is not a 1D sequence but a graph, which can even contain cycles. - Thermodynamics: None of the other areas of physics make time "pass", because to them time is symmetric and past and future might as well be swapped. Only thermodynamics introduces an asymmetry by coupling it to information theory: On the macroscopic average, entropy can not decrease, only increase. Thus, we get a global gradient form low to high entropy, which is what makes time irreversible on a large scale.

creata 2y ago
> High precision simulation of classical mechanics does not model time as steps / frames in a movie, but as a continuous 4D geometry. What is this sentence referring to, if you don't mind me asking? I know that some implementations of collision detection use volumes swept over time, but that's the only link I'm aware of.
- Lichtso 2y ago
  Yes exactly, continuous collision detection (CCD) is what I am referring to. https://scholar.google.com/scholar?q=continuous+collision+detection https://scholar.google.com/scholar?q=continuous+collision+de...
plaidfuji 2y ago
Congratulations, you’ve just explained relativity, QM and thermo more clearly and concisely than years and years of other courses and literature. Thank you.
oezi 2y ago
> On the macroscopic average, entropy can not decrease, only increase. The reason or physical principle from which this law of thermodynamics originats has always escaped me. Why can't there be a way to decrease entropy?
- paulnpace 2y ago
  My layperson's understanding of entropy is energy that cannot be used. If something cannot be used, it also cannot be made smaller.
- IsTom 2y ago
  In QM information can be created (by measurements), but not destroyed* (no-deletion/no-cloning theorem). To "store" that information you need to have enough possible physical quantum states (the kind bounded in Bekenstein bound) which is thermodynamic entropy. [*] what made blackhole information paradox controversial
- af3d 2y ago
  I think it originates from the observation that all machines "leak" power in the process of performing work. Vibrations, thermal conduction, infrared radiation, etc all tend to decrease efficiency and hence increase entropy (in the form of heat loss, mostly). Entropy can of course be lowered by bringing a measure of order to a given "isolated" system. At much larger scales however the vast number of possible microstates dominate, and thus the "inevitable march toward disorder". Also bear in mind that "entropy" itself is a fairly general concept which can be applied to just about any field. Information, for example, can expressed in terms of entropy. (Which obviously has nothing to do with the "thermal entropy" of physics.)
- Jensson 2y ago
  > Why can't there be a way to decrease entropy? It is like asking "why can't things go faster than the speed of light", this is an observation of all known processes, not an absolute law. It is possible there are things we haven't observed that will change this.
- BobaFloutist 2y ago
aredox 2y ago
Note that thermodynamics may be kind of a "meta" or "supra" theory: other areas of physics don't have a concept of entropy or direction of time because it is an emergent property of a great number of particles following more "basic" rules. The same way the game of go doesn't have a concept of "immortal shapes", those are just a consequence of its rules.
max51 2y ago
>High precision simulation of classical mechanics does not model time as steps / frames in a movie, but as a continuous 4D geometry. Strong disagree on that part. High precision numerical analysis is always done with discrete time steps. It has been this way since the Finite Element method was invented. Anything non-linear (eg. collisions, large displacements, non-linear material behavior, non-linear boundary conditions, etc.) requires discrete steps to be calculated accurately. The CCD research you linked below has very good uses cases (eg. robot control systems) but predicting the collision time and location of two simple solid shapes in a linear domain is absolutely not a "High precision simulation". There could be ways to use it to make a complex simulation more efficient (eg. dynamically adjust the steps to make them shorter right before a collision, densifying the mesh where you predict a collision, etc.) but at the end of the day your simulation is solved using discrete time steps.
- creata 2y ago
  And it's not like nonrelativistic quantum mechanics and Newtonian mechanics have that different a conception of time. Both describe the evolution of a system using differential equations in time, both treat the world as having a single shared time (like "frames in a movie"), etc. I think the main differences are what evolves in time, and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens. Also, the idea that "none of the areas of physics make time pass [except thermodynamics], because to them time is symmetric", isn't true, because e.g. the standard model doesn't have time symmetry. Also also, I don't think it's a helpful simplification to say that relativity simply allows for "distortion of spacetime". SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies.
  - Lichtso 2y ago
    > Both describe the evolution of a system using differential equations in time All areas of physics use differential equations, and so does relativity which you are contrasting these two against next. > both treat the world as having a single shared time (like "frames in a movie"), I think you misunderstand what the "frames in a movie" meant. It was about the distinction of time being modeled as discrete or continuous. What you are talking about ("single shared time") is indeed a shared property of all other areas, which are not relativity, by the virtue of not being relativity (which introduces the distortions that make a single shared time impossible). But that is a tautology. > I think the main differences are what evolves in time All four areas are somehow describing the evolution of matter and energy. Again, not a difference. > and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens. Measurement, collapse and conscious observers are unnecessary additions which are not needed for a complete description of quantum mechanics. I would instead argue that the main difference to classical mechanics and relativity is the superposition principle (which has nothing to do with measurement): The idea that the properties of things are not in one state at a time but in a combination of states simultaneously. And that in turn means you can not model time as a simple 1D axis anymore. > because e.g. the standard model doesn't have time symmetry. My point was about flipping the direction of the flow or the role of past and future. The standard model has time reversal symmetry if you also flip matter and anti-matter, which for the sake of the argument makes no difference because you can't tell which one you are made of. From the POV of anti-matter people we are the ones made from anti-matter or matter which moves backward in time. Which strengthens the point that only thermodynamics assigns a clear direction to the flow of time. > SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies. Can you elaborate on that? Are you referring to the free fall equivalence principle?
mensetmanusman 2y ago
On the universe scale, we are about halfway through the ascent from the low entropy beginning to the max entropy end of time.
DHRicoF 2y ago
I think your comment lack a little deep. Quantum mechanics describe the evolution of the state of system given the initial conditions and the hamiltonian describing it. That's exactly what the Schrodinger equation says and why it has a partial derivate of time. Usually in introductory treatments only the "time independent Schrödinger equation" is addressed, but that's a sub product on a common technique used to solve some family of differential equations. In classical mechanics you can interpret time as another coordinate, but with so many privileges that it's a little far reached call it in the same way as space dimensions. Without the metric introduced in special relativity there is no way to justify put them in the same footing. For example, in classical mechanics you cannot rotate in a way that makes the time coordinate fall in a space coordinate, while you can do that in relativity, and it's called a boost.
- Lichtso 2y ago
  Well, the Schrödinger equation only describes the evolution of the wavefunction over time (which is indeed a similarity with classical mechanics). But how the wavefunction then further relates to the actual "state of system" is up to the interpretations of quantum mechanics. And there in lies my point: That because of the superposition the way time works in quantum mechanics (properties are simultaneously in a combination of states) is very different from classical mechanics (properties are in exactly one state at a time), even if both have a "t" in their equations. > For example, in classical mechanics you cannot rotate in a way that makes the time coordinate fall in a space coordinate, while you can do that in relativity That is a good point. Maybe it is fair to say that in classical mechanics we start out with an additional separate geometric dimension (which only translation / shifting is allowed in). And in special relativity it gets promoted to a full spacial dimension, allowing all sorts of transformations.
childintime 2y ago
What do you think about the notion that time as a dimension _competes_ with the space dimensions? So time is not the same thing as space (duh), so no generalized "spacetime" exist. If spacetime is like a wavefront, reconstructing its space dimensions as it goes, we can never get out of it, unless we subside into the underlying (timemore vs timeless) sea. A wavefront has rotation built in, but the wavefront itself could also be rotating, around a center, so you have your entangled oscillator(s) right there.. </agistimulus>

creata 2y ago

> High precision simulation of classical mechanics does not model time as steps / frames in a movie, but as a continuous 4D geometry. What is this sentence referring to, if you don't mind me asking? I know that some implementations of collision detection use volumes swept over time, but that's the only link I'm aware of.

Lichtso 2y ago
Yes exactly, continuous collision detection (CCD) is what I am referring to. https://scholar.google.com/scholar?q=continuous+collision+detection https://scholar.google.com/scholar?q=continuous+collision+de...

plaidfuji 2y ago

Congratulations, you’ve just explained relativity, QM and thermo more clearly and concisely than years and years of other courses and literature. Thank you.

oezi 2y ago

> On the macroscopic average, entropy can not decrease, only increase. The reason or physical principle from which this law of thermodynamics originats has always escaped me. Why can't there be a way to decrease entropy?

paulnpace 2y ago
My layperson's understanding of entropy is energy that cannot be used. If something cannot be used, it also cannot be made smaller.
IsTom 2y ago
In QM information can be created (by measurements), but not destroyed* (no-deletion/no-cloning theorem). To "store" that information you need to have enough possible physical quantum states (the kind bounded in Bekenstein bound) which is thermodynamic entropy. [*] what made blackhole information paradox controversial
af3d 2y ago
I think it originates from the observation that all machines "leak" power in the process of performing work. Vibrations, thermal conduction, infrared radiation, etc all tend to decrease efficiency and hence increase entropy (in the form of heat loss, mostly). Entropy can of course be lowered by bringing a measure of order to a given "isolated" system. At much larger scales however the vast number of possible microstates dominate, and thus the "inevitable march toward disorder". Also bear in mind that "entropy" itself is a fairly general concept which can be applied to just about any field. Information, for example, can expressed in terms of entropy. (Which obviously has nothing to do with the "thermal entropy" of physics.)
Jensson 2y ago
> Why can't there be a way to decrease entropy? It is like asking "why can't things go faster than the speed of light", this is an observation of all known processes, not an absolute law. It is possible there are things we haven't observed that will change this.
BobaFloutist 2y ago

aredox 2y ago

Note that thermodynamics may be kind of a "meta" or "supra" theory: other areas of physics don't have a concept of entropy or direction of time because it is an emergent property of a great number of particles following more "basic" rules. The same way the game of go doesn't have a concept of "immortal shapes", those are just a consequence of its rules.

max51 2y ago

>High precision simulation of classical mechanics does not model time as steps / frames in a movie, but as a continuous 4D geometry. Strong disagree on that part. High precision numerical analysis is always done with discrete time steps. It has been this way since the Finite Element method was invented. Anything non-linear (eg. collisions, large displacements, non-linear material behavior, non-linear boundary conditions, etc.) requires discrete steps to be calculated accurately. The CCD research you linked below has very good uses cases (eg. robot control systems) but predicting the collision time and location of two simple solid shapes in a linear domain is absolutely not a "High precision simulation". There could be ways to use it to make a complex simulation more efficient (eg. dynamically adjust the steps to make them shorter right before a collision, densifying the mesh where you predict a collision, etc.) but at the end of the day your simulation is solved using discrete time steps.

creata 2y ago
And it's not like nonrelativistic quantum mechanics and Newtonian mechanics have that different a conception of time. Both describe the evolution of a system using differential equations in time, both treat the world as having a single shared time (like "frames in a movie"), etc. I think the main differences are what evolves in time, and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens. Also, the idea that "none of the areas of physics make time pass [except thermodynamics], because to them time is symmetric", isn't true, because e.g. the standard model doesn't have time symmetry. Also also, I don't think it's a helpful simplification to say that relativity simply allows for "distortion of spacetime". SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies.
- Lichtso 2y ago
  > Both describe the evolution of a system using differential equations in time All areas of physics use differential equations, and so does relativity which you are contrasting these two against next. > both treat the world as having a single shared time (like "frames in a movie"), I think you misunderstand what the "frames in a movie" meant. It was about the distinction of time being modeled as discrete or continuous. What you are talking about ("single shared time") is indeed a shared property of all other areas, which are not relativity, by the virtue of not being relativity (which introduces the distortions that make a single shared time impossible). But that is a tautology. > I think the main differences are what evolves in time All four areas are somehow describing the evolution of matter and energy. Again, not a difference. > and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens. Measurement, collapse and conscious observers are unnecessary additions which are not needed for a complete description of quantum mechanics. I would instead argue that the main difference to classical mechanics and relativity is the superposition principle (which has nothing to do with measurement): The idea that the properties of things are not in one state at a time but in a combination of states simultaneously. And that in turn means you can not model time as a simple 1D axis anymore. > because e.g. the standard model doesn't have time symmetry. My point was about flipping the direction of the flow or the role of past and future. The standard model has time reversal symmetry if you also flip matter and anti-matter, which for the sake of the argument makes no difference because you can't tell which one you are made of. From the POV of anti-matter people we are the ones made from anti-matter or matter which moves backward in time. Which strengthens the point that only thermodynamics assigns a clear direction to the flow of time. > SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies. Can you elaborate on that? Are you referring to the free fall equivalence principle?

mensetmanusman 2y ago

On the universe scale, we are about halfway through the ascent from the low entropy beginning to the max entropy end of time.

DHRicoF 2y ago

I think your comment lack a little deep. Quantum mechanics describe the evolution of the state of system given the initial conditions and the hamiltonian describing it. That's exactly what the Schrodinger equation says and why it has a partial derivate of time. Usually in introductory treatments only the "time independent Schrödinger equation" is addressed, but that's a sub product on a common technique used to solve some family of differential equations. In classical mechanics you can interpret time as another coordinate, but with so many privileges that it's a little far reached call it in the same way as space dimensions. Without the metric introduced in special relativity there is no way to justify put them in the same footing. For example, in classical mechanics you cannot rotate in a way that makes the time coordinate fall in a space coordinate, while you can do that in relativity, and it's called a boost.

Lichtso 2y ago
Well, the Schrödinger equation only describes the evolution of the wavefunction over time (which is indeed a similarity with classical mechanics). But how the wavefunction then further relates to the actual "state of system" is up to the interpretations of quantum mechanics. And there in lies my point: That because of the superposition the way time works in quantum mechanics (properties are simultaneously in a combination of states) is very different from classical mechanics (properties are in exactly one state at a time), even if both have a "t" in their equations. > For example, in classical mechanics you cannot rotate in a way that makes the time coordinate fall in a space coordinate, while you can do that in relativity That is a good point. Maybe it is fair to say that in classical mechanics we start out with an additional separate geometric dimension (which only translation / shifting is allowed in). And in special relativity it gets promoted to a full spacial dimension, allowing all sorts of transformations.

childintime 2y ago

What do you think about the notion that time as a dimension _competes_ with the space dimensions? So time is not the same thing as space (duh), so no generalized "spacetime" exist. If spacetime is like a wavefront, reconstructing its space dimensions as it goes, we can never get out of it, unless we subside into the underlying (timemore vs timeless) sea. A wavefront has rotation built in, but the wavefront itself could also be rotating, around a center, so you have your entangled oscillator(s) right there.. </agistimulus>