An path of an individual molecule between collisions with other molecules is deterministic.
The overall path of the molecule is simply a combination of the individual deterministic paths.
Sabine Hossenfelder is trying to make sense of quantum mechanics by re-examining the arguments against Superdeterminism.
"Superdeterministic models are deterministic in the usual sense, but in addition they also postulate correlations between the state that is measured and the measurement setting."
https://en.wikipedia.org/wiki/Superdeterminism
This is the first time i've seen the thread, so forgive me if i'm repeating something that has been said many times in the 480 pages over 8 years..
The question itself makes an assumption that the thing something must expand into was there because of a past. This is framing something in terms of what we experience here on earth, how we experience time, at our magnitudes of energy levels etc etc
I'm not even sure "expand " is the right term, even though it is used by physicists to explain things to layfolk and may be the nearest thing of regular human experience that fits..
The question itself makes an assumption that the thing something must expand into was there because of a past. This is framing something in terms of what we experience here on earth, how we experience time, at our magnitudes of energy levels etc etc
I'm not even sure "expand " is the right term, even though it is used by physicists to explain things to layfolk and may be the nearest thing of regular human experience that fits..
That's a strange experiment!
The function of an experiment is to test a hypothesis.
The hypothesis in your example could be that adding more water reduces the crispness of the pizza.
The hypothesis can then be tested by changing the amount of water and observing how it affects the crispness (while keeping the other variables constant).
That's true, and we've given it great thought on this thread.
The universe is not expanding in the sense that we normally understand the word, it is simply that distances between distant points in the universe are getting bigger with time.
In spacetime, distance is not a fixed quantity as we would normally understand it to be, but is a dynamical quantity which changes with time.
Spacetime is described by a metric which defines how the distance between two points is calculated based on their coordinates. The metric is changing with time, and so the scale of spacetime itself is changing.
https://astronomypedia.fandom.com/wiki/Metric_expansion_of_space#:~:text=The metric expansion of space is the increase,expansion whereby the scale of space itself changes.
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But how can you predict it accurately into the future without knowing which other specific molecules will hit it? You can’t because the process is stochastic. Once you have traced the molecules path after the fact of course, then you can say where it was hit, how many times and the forces involved that caused it to prescribe the (complex) path it took. So, there are unknown possible paths in the future, but there is only one path it took when looking back into in the past.
Determinism is progression from past to future - everything that happens follows from what happened earlier.
The outcome of each stage in a progression may be predicted given the initial conditions.
I'm sure the progress of an individual water molecule can be modelled by a computer simulation - which can then be run backwards in time if necessary!
It is the collective motion of liquid or gas molecules that is stochastic. The behaviour of the molecular system as a whole may be analysed statistically, but may not be predicted precisely.
Edit: I made some changes to the final paragraph.
The outcome of each stage in a progression may be predicted given the initial conditions.
I'm sure the progress of an individual water molecule can be modelled by a computer simulation - which can then be run backwards in time if necessary!
It is the collective motion of liquid or gas molecules that is stochastic. The behaviour of the molecular system as a whole may be analysed statistically, but may not be predicted precisely.
Edit: I made some changes to the final paragraph.
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I think you are testing the hypothesis that: Cuisine is not just a matter of mixing edibles.
Here you tried with the major ingredients of pizza, after several tries, the best you got was no better than decent taste, far from a worthwhile pizza.
Similarly:
There are many ways to make bread with results ranging from excellent to terrible.
Is there any evidence the Big Bang ever stopped? I mean, if all we can see is 5% or so, and the rest is dark matter or dark energy, is there any reason to believe whatever caused its creation stopped in the distant past? We don't understand the cause of the Big Bang, so maybe it just keeps spontaneously creating new dark matter and energy, all around us. It's weak effect on light matter might be enough to pull at it along with other dark matter, and look like an accelerating expansion.
It is now hypothesised that the Big Bang was preceded by a period of rapid inflation.
Pairs of particles and anti-particles routinely emerged from the quantum vacuum of the cold, empty Universe that existed prior to the Big Bang, only to quickly annihilate each other and return their energy to the vacuum.
During the inflationary period, however, the particles and anti-particles were rapidly swept apart from each other. Consequently, they could no longer annihilate each other and could not return their energy to the vacuum.
This liberated vacuum energy caused the cold, empty Universe to become a hot, dense one.
That is how inflation ended and the Big Bang (along with cosmic expansion) began, ultimately producing the particles whose names we are familiar with today - including the particles of Dark Matter.
DISCLAIMER: Although there is a good deal of evidence to support the hypothesis of the Big Bang, we are still quite some way from establishing its existence.
I found this definition on the internet which I think captures the essence of the difference between stochastic and deterministic systems.
A deterministic system is non-stochastic. It is not subject to change. A stochastic system is probabilistic. It can change with calculable probability.
An interesting presentation here on how how and when to use deterministic or stochastic systems analysis ‘mix ‘n match’
http://www.dcs.gla.ac.uk/~srogers/teaching/mscbioinfo/SysBio2.pdf
A deterministic system is non-stochastic. It is not subject to change. A stochastic system is probabilistic. It can change with calculable probability.
An interesting presentation here on how how and when to use deterministic or stochastic systems analysis ‘mix ‘n match’
http://www.dcs.gla.ac.uk/~srogers/teaching/mscbioinfo/SysBio2.pdf
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This does not explain a thing.
Stochastic and probabilistic are synonyms, two words with the same meaning.
A system that has its future behavior entirely determined once it's initial present conditions are known is said deterministic.
Questions arise: This assumes one can calculate exactly the future behavior. This assumes the initial behavior is exactly known.
So, I've only 32 pages of a mathematically based presentation on Stochastic Modelling to wade through!
Unless there a particular page on which I should focus?
P.S. At least the paper is from the University of Glasgow.
Nice article here about Newton and Einstein
https://bigthink.com/starts-with-a-bang/another-einstein-or-newton/
https://bigthink.com/starts-with-a-bang/another-einstein-or-newton/
The point I’ve tried to make Galu is you can’t dismiss stochastic systems at their most basic (ie individual component) level as deterministic. These systems only become deterministic when stochastic tools are used to analyze them, and then, the results are still probabilistic. This leads to the observation that in these systems, the individual components behave in a chaotic like manner that becomes deterministic only when their past activity is considered.
That sounds more reasonable than wading through 32 pages of maths!
I think I get it!Allow me to make a distinction between a stochastic system and a stochastic process.
Stochastic processes are widely used as mathematical models of systems that appear to vary in a random manner.
The behaviour of an ideal gas can be described by a stochastic process.
An ideal gas is said to be a stochastic system.
That is, indeed, a nice article from Ethan - "Will physics ever see another Einstein or Newton?"
It gives a neat summary of each scientist's contribution to physics - I'll read it in full later.
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