[alancalverd]

F1   =   -F2      doesn't tell you what  F1    and   F2    are supposed to be.

forces. Or do you dismiss E = mc² because the terms are not explicit? Heck, now I'm not sure whether 1 + 1 = 2 applies to cows or universes, because you didn't say!

As for le Chatelier,

2H₂ + O₂ ↔ 2H₂O + 122MJ

says it all, rather succinctly, for a single case, or

nX + mY ↔ nXmY + Z (moles being implicit in chemistry and implicated in my garden)

for the more general case.

Now you might argue that I haven't said what Z means, but that's a bit circular because the general definition of energy is "one of the conserved parameters of change".

In short, beware of philosophy - it causes wars and doesn't save lives!

[Eternal Student]

Hi.

   There's a lot you could say about the description of  Le Chatelier's principle but I'm not going to do that.  Instead I'll just thank you ( @alancalverd ) for your time.
    A description or definition of what a "law of physics" is,  is not in my power to change or influence.   These things can usually be expressed with equations but there is no demand or requirement for that.  That's my bottom line.   

     I have tried to see it differently,  I used Google and tried to find definitions for a "law of physics" in several places.   In all of those the demand for the thing to be expressed in mathematics is not there.

Best Wishes.

[Eternal Student]

Hi again.

    It's taken me a while to re-read some of these posts, especially @Halc 's longer posts.  I've started and scrapped so many posts.    Overall, I don't think there's too much value in criticising the idea, despite Halc putting his hands up and asking to be shot.

...so shoot me to pieces.

    I think Halc has already spotted one important issue,  does Physics still rely on the existence of some ledger (or an array of variables set aside for the task, if you put it into terms of a Simulated universe running on a computer)  which still keeps track of where things are actually supposed to be as if space and time were continuous?   That ledger is the important feature that drives the rest of physics.   If that ledger is required to hold continuous (rather than discrete) values, then there's no change in the way physics behaves.  So a discrete nature to space and/or time doesn't have to mean anything more than physical limitations on being able to measure a location precisely or identify a moment in time when something happened precisely.   Practical limitations already do that.   Quantum mechanics also puts absolute theoretical limits on it.

    It's not a bad idea, @Halc and I've enjoyed spending a bit of time thinking it over.   I'll put one comment about your (Halc) random sprinkling of events on paper under a spoiler instead of discarding it.  It's not short and there's no need to clog up the entire thread for everyone else.

Spoiler: show

Your proposed construction of discrete events for a discrete spacetime by randomly sprinkling them like dots onto a piece of paper is a little awkward and I'm not sure it achieves very much.   This is roughly what you seemed to be suggesting:
     Sprinkle events like dots almost at random on a piece of paper and (just for good measure?) also hold the paper at some random angle to randomise it a bit more, then have time up the vertical and space on the horizontal.
1.   Those "times" and "space" are, presumably just for construction purposes,  the observer can't observe those continuous values.
   How you then proposed to identify the discrete values of space and time that correspond to those events is more problemantic and awkward than it might have seemed.
2.   You suggested trying to start with horizontal lines across the page that are representative of lines of constant time.   However the events don't usually lie nicely on a straight line, so you allow some wiggling up and down to make sure you pass through the nearest dot to what would be a horizontal line.   If you did this nearest dot finding at every value of x along the page you could have a real mess, the wiggling up and down could become a continuous block of colour.  So presumably that wasn't what you had in mind.   Instead you seem to need to know in advance how finely you would like to divide the space axis.   That's OK, let's shift our attention to that axis across the page.
3.    For the "for-construction only" continuous x-axis running across the page you might suggest cutting the axis up as finely as you can.   How finely can it be divided?  Well very finely indeed.   If you start by drawing a straight vertical line off the x-axis and running up the page that passes through any dot (event) on the page, then that is one x-axis location you can have.   Any vertical line that passes through a dot is an x-axis location we can have.   Now we see a problem...  Assuming the sprinkle remains of consistent density and random across every time slice, and time extends up the page indefinitely, then we will always be able to find another possible x-axis location as close as we like to the first one we started with.   Overall the entire x-axis could be divided up into so many lines that it is just a continuous range of possible x-values again.    That's no good, we want some discreteness in our spacetime.   So we're not going to divide the x-axis up as finely as we can... we're just going to do it fairly finely.
    How finely?  As much as you like, just not so much it becomes continuous.  At least that's done, now we can almost go back to step 2. and sort out how we will chop up the vertical time axis.   I said almost... there's been quite a few dots (events) whose x-axis values weren't along a line of constant x-axis value.   I wonder what we will do with those and what value of x will be assigned to those events, never mind that's a later problem.

2.. revisited..  We now have the x-axis divisions and some vertical running lines running up from them.   Start from the left, find an event, mark that corresponding time axis value as something we can have and proceed to move right.  Every time we cross a vertical permitted x-axis location line, we must find the nearest event along that line to a horizontal.  We allow our line of constant time to wiggle up and down a bit to pass through those events.    That's OK and that's done.   (Goto step 4).

4.  Sadly, since the sprinkling of events was quite random,  there have been some events that aren't passed through by a line of constant x-axis value and also a line of constant time.   They just were never the closest to a horizontal line when we crossed over the vertical lines.   Come to think of it some of the events that we did pick weren't on a line of constant x-value we were permitting anyway.   Of course, there were some events that weren't on a line of time or a line of x.   We seem to have a lot of events without an assigned (X,T) co-ordinate for them.   Obviously that's no good, events are supposed to be just points in spacetime so they must have assigned X and T ordinates.   We can try and fix this.    We'll need to go back to step 3,  identify all the lines of constant x and immediately pick out and throw away all the dots that weren't included on a line.   Then do step 2, identify lines of constant time and throw away all events that don't get on a line.
    OK....  overall the sprinkling of events onto the page can't be as "random" as you would have liked.   Some of the randomness had to be thrown away.   It must always be possible to put an event on a line of constant permitted discrete x value and onto a wiggly line of constant permitted discrete time.  We can't have unassigned events floating about between permitted values.

   Now....  don't forget that the observer in the real-life discrete spacetime can't see or observe the vertical time axis on the page or the horizontal axis on that page.  Those continuous vertical and horizontal axis on the page were only for construction purposes.   Overall, I'm not sure the observer cares or can tell that their lines of constant permitted discrete time actually wiggle up and down a bit relative to some continuous time axis that was only for construction anyway.    We can deform the page of paper instead and do it in exactly the right way that the lines of constant discrete time are straight.   
   Anyway... I'm not convinced that the random sprinkling of events onto a page of paper has achieved very much,  we have a representation of spacetime with a perfectly conventional and regularly spaced grid and precisely one event on each point of intersection of those grid lines.   Possibly, just possibly you were imagining a situation where the distance up the construction only time axis affects the spacetime interval (or since it's at constant space, just "the time interval").   However we can achieve that just by assigning a certain metric to the discrete spacetime we plotted on a conventional regular grid with everything equally spaced and co-ordinates just marked 1,2, 3, 4,....   We can assign a metric where co-ordinate units of separation aren't always worth the same amount of metric distance.   Anyway, that sort of mathematical machinery is already available - General Relativity is basically this.  There's discrete metric space theory in mathematics if the restriction to discrete values only for the co-ordinates becomes important.

Best Wishes.

[evan_au]

Sprinkle events like dots almost at random on a piece of paper

The advantage of these hypothetical random dots (in time and/or space) is that you don't need to track how far you are from the grid and then suddenly jump to the next grid point.
- This conceptual tracking mechanism is creating conceptual "intermediate" points between the grid points (which contradicts the initial assumption that these grid points were some minimum quantum of time and/or space).

When you measure some quantum object, there is a certain probability that it will be found at one position or another (or one time or another), according to Heisenberg's uncertainty principle. The randomness of the dots becomes one component of the uncertainty.

Presumably, this speculation would be testable - does a distribution of dots predict the Heisenberg result, with events being observed at the "nearest" point in time and/or space?

There is no requirement that the position of the dots appears the same to all observers.
- Some experiments (eg LIGO) use squeezed quantum states to put most of the uncertainty in one dimension, and minimal uncertainty in the other dimension (LIGO wants minimum uncertainty in the length dimension, but is not so concerned about the time dimension).
- Observers in a different relativistic frame of reference may see the dots being squeezed in space and/or time because of relative velocity, or relative gravitational potential

See: https://en.wikipedia.org/wiki/Uncertainty_principle

[paul cotter]

Fascinating discussion, love it. I have my own theory(speculation) on space and time but until I can make it consistent with known facts I won't disseminate it. A quick question for the simulation theorists: who is on the other side writing the code and tapping the keyboard??

[evan_au]

who is on the other side writing the code and tapping the keyboard??

According to the simulation theorists, probably someone/something in a higher-level simulation...

[alancalverd]

(a) what are we a simulation of?

(b) why?

And just to tease ES, can you define any mathematical construct, say set, integer, or addition, without using words? We've touched elsewhere on the use of "symmetry" as a rigorous argument which allows such statements as A ≡ -B: the equivalence is only valid with that qualifying word!

[Eternal Student]

Hi.

(a) what are we a simulation of?

      It can't be possible that you haven't heard of the simulation hypothesis.   It's been discussed in various versions on this forum before.
     Some basic references:
1.   https://en.wikipedia.org/wiki/Simulation_hypothesis
2.   This is generally considered to be the seminal paper about the topic:
Bostrom, Nick (2003). "Are You Living in a Computer Simulation?". Philosophical Quarterly. 53 (211): 243–255
    I think this is an accurate pdf of that paper and it's freely available on the internet:
https://www.simulation-argument.com/simulation.pdf

   Here's some of the abstract from Nick Bostrom's paper:
This paper argues that at least one of the following propositions is true:
(1)  the human species is very likely to go extinct before reaching a “posthuman” stage;
(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
(3) we are almost certainly living in a computer simulation....

   From which possibility (3) is the one everyone has run away with and continued developing into what is now genrally put under the category or description of being "simulaton theory."    Meanwhile the the concept of being "posthuman" doesn't get a lot of good press these days.

    Anyway, in the early,  Nick Bostrom style versions of the theory, it's assumed there would be an interest in running ancestor simulations,   i.e.  simulations to model what it would have been like for your ancestors or what else could have happened if the initial conditions had been slightly different etc.     The term "ancestors" could be your mum and dad but more generally it's an intelligent civilisation that existed before your own   (recall that Bostrom was throwing the term "post-human" around as if we might have evolved or moved on quite a lot).
    Modern versions replace ancestor simulations with anything similar - for example scientists running simulations, much as we do currently to model stuff in science;   or computer gamers playing a good simulated reality game   etc.

(b) why?

   ... hopefully already hinted at in the above discussion.   Let's say there's an interest in science and/or ancestor simulations.   There might have been someone interested to see how aeroplanes were used and first developed, for example.

...can you define any mathematical construct, say set, integer, or addition, without using words?

    Possibly not but that might be a limitation of my own mind.   I do tend to be one of those people who has an inner voice in my head,  so I will often "read out" a mathematical expression to myself etc.   Some people who have studied another language for years can start to think and dream in that language.  Much the same will happen with mathematics.   However, it's all still some sort of language or symbolic representation of objects that is used, that's what seems to convey meaning and existence especially to things that are fundamentally abstract instead of some solid thing you can point at in reality.
    Once you've got that notion, it's then less obvious which language was the one that intrinsically provided the meaning and granted exitstance of the idea or concept.      Is the phrase  "A is equivalent to negative B" the language which gives it meaning or     "  A ≡ -B  "   ?
    There you go,  a bit of philosophy about language, the meaning of existence and symbolic representation.   I know that's the sort of thing you love.

Best Wishes.

[alancalverd]

(1)  the human species is very likely to go extinct before reaching a “posthuman” stage;

Species evolve, survive, or extinguish. So what?

(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);

Indeed - what would be the point? Is there any evidence of any species even being interested in doing that? Archaeology and biochemistry satisfy most people's curiosity. The reason for constructing a simulation is normally to predict behavior under altered conditions or to analyse a failure, and it is never as accurate as actual experiment, which in this case will have already been done!

(3) we are almost certainly living in a computer simulation....

Non sequitur ex nihilo

[Halc]

About the dots. I’ve had little time to respond to all that’s been said, but here I go.

I mentioned all the dots being sort of ‘socially distant’ so no pair of them was too close to each other, but it would be better if it was truly random. If we did the nice even but not regular distribution, then a significant Lorentz transform of the dots will bring some dots into far closer proximity. So we once again have a preferred frame where this does not occur, and the point of the random dots was to avoid the preferred frame. So true random, not just somewhat random like the pattern of sheep on your pajamas.

And then there’s the counterfactual thing. The dots (occupied by something or not) seem to be something that exists entirely absent any measurement. This goes against everything I normally prefer. It totally violates locality. I brought up a computer simulation simply because implementing one would typically need to implement a state to keep track of. That means no spacetime. Presentism. Faster-than-light causality. Objective state.  All the things I detest.
I don’t think a convincing computer simulation could ever be done, at least not implemented with the physics we know. So if it’s done, it’s done via higher (more powerful) physics than we can know.

When you measure some quantum object, there is a certain probability that it will be found at one position or another (or one time or another), according to Heisenberg's uncertainty principle.

The principle allows arbitrarily high precision to say position, but at the expense of knowing its momentum. It’s not something you can measure twice if you got it really precise the first time. Then again, I think Planck (not Heisenberg) put hard limits on this precision, and that precision is probably far more coarse than these ‘dots’.

Your proposed construction of discrete events for a discrete spacetime by randomly sprinkling them like dots onto a piece of paper is a little awkward and I'm not sure it achieves very much. 

I actually agree with this. I was just tasting the idea mostly.

This is roughly what you seemed to be suggesting:
     Sprinkle events like dots almost at random on a piece of paper and (just for good measure?) also hold the paper at some random angle to randomise it a bit more, then have time up the vertical and space on the horizontal.

I said that. In reality, a Lorentz transform must be used to rotate the paper. It isn’t Euclidean like paper is.

You suggested trying to start with horizontal lines across the page that are representative of lines of constant time.   However the events don't usually lie nicely on a straight line, so you allow some wiggling up and down to make sure you pass through the nearest dot to what would be a horizontal line.

Sure. ‘Nearly simultaneous’ (if that has any possible meaning) relative to this local frame. Gets pretty ambiguous. How do you decide which dots are near enough and which are at different times? The more picky you get about that, the more distant the possible spatial locations available at that ‘time’, and as time progresses not a whole dot forward, some dots are no longer close enough to the new ‘time’, but others still are. Event A simultaneous with B (in this given frame), and B with C, but A not simultaneous with C. All very contradictory.

Any vertical line that passes through a dot is an x-axis location we can have.

Eventually. Technically dots and lines have no width, so it will be an arbitrarily long time before a random line drawn anywhere ‘hits’ anything. So now we need a ‘close enough’ value that is less than the minimum distance. Another contradiction.

Now we see a problem...  Assuming the sprinkle remains of consistent density and random across every time slice, and time extends up the page indefinitely, then we will always be able to find another possible x-axis location as close as we like to the first one we started with.   Overall the entire x-axis could be divided up into so many lines that it is just a continuous range of possible x-values again.    That's no good, we want some discreteness in our spacetime.   So we're not going to divide the x-axis up as finely as we can... we're just going to do it fairly finely.
    How finely?  As much as you like, just not so much it becomes continuous.

Say it’s a meter apart (a min distance). Sprinkle dots a meter apart (in a grid or randomly) and draw lines randomly through each one perpendicular to a random time axis. It will still be sliced up arbitrarily fine as there is nowhere you can choose an x that doesn’t get arbitrarily close to some dot somewhere. So don’t know where you’re going with this. Only way to avoid this is a flat regular grid perfectly lined up (the preferred frame), in which case you can walk between the trees indefinitely without every getting close to one.

I kind of lost you after that, but it already seems to doom the dot idea.

[evan_au]

a computer simulation... implementing one would typically need to implement a state to keep track of. That means no spacetime. Presentism. Faster-than-light causality. Objective state.  All the things I detest.

You seem to be imagining a computer simulation run on a uniprocessor, in which a single processor needs to access the entire state of the universe.
- However, the last uniprocessor to be dubbed "fastest in the world" was the Cray 1, which only held the title until 1982, when it was overtaken by a multiprocessor computer (also from Cray).
See: https://en.wikipedia.org/wiki/TOP500#Systems_ranked_No._1_since_1976

The fastest computer architectures tend to be grid computers, which only have really fast communication with their immediate neighbors,
- A 2D grid CPU has 4 immediate neighbors
- A 3D grid CPU has 6 immediate neighbors
- A 4D grid CPU has 8 immediate neighbors
- And yes, researchers have investigated 5+D grid CPUs with 10+ immediate neighbors

All practical grid computers do have a central communications channel for:
- Loading software into all CPUs in parallel
- Dumping out the state of the simulation at various points in time, enabling construction of a "movie" of the simulation
- But these "central" communication channels are not actually part of the grid computation
- This grid architecture is suitable for a very limited range of applications, which is why they have not been pursued.

General-purpose supercomputers have a more flexible architecture with multi-hop communication for non-local references
- But a pure grid computer does exhibit those properties that you desire in a model of our cosmology...

[Halc]

a computer simulation... implementing one would typically need to implement a state to keep track of. That means no spacetime. Presentism. Faster-than-light causality. Objective state.  All the things I detest.

You seem to be imagining a computer simulation run on a uniprocessor, in which a single processor needs to access the entire state of the universe.
...
The fastest computer architectures tend to be grid computers, which only have really fast communication with their immediate neighbors,
- A 2D grid CPU has 4 immediate neighbors
- A 3D grid CPU has 6 immediate neighbors
- A 4D grid CPU has 8 immediate neighbors
- And yes, researchers have investigated 5+D grid CPUs with 10+ immediate neighbors

I made no mention of an architecture optimized for speed. A simulation has no inherent speed requirement and can be implemented by a guy with pencils and a lot of paper if you want, or worse, by a Turing machine. Even say a 3D grid architecture with millions of processors per dimension would still require a model of:
Presentism. Faster-than-light causality. Objective state.  All the things I detest

It would be interesting to attempt a program that modeled locality, state expressed as entanglement/decoherence, and maybe even a way around the presentism. That last one is admittedly the hardest one to ditch.
 

However, the last uniprocessor to be dubbed "fastest in the world" was the Cray 1, which only held the title until 1982, when it was overtaken by a multiprocessor computer (also from Cray).

For the record, a Cray 1 (I've seen one) was a SIMD machine, which means single instruction but operating on hundreds of data elements at once, so it's very parallel despite apparently being classified as a uniprocessor by somebody. It is thus a fantastic vector processor for crunching simulations of things like the weather, but it would not be particularly good at chess, which would better be served by some sort of cloud configuration.

[alancalverd]

Come to think of it, Heisenberg pretty well contradicts the idea of granular spacetime. As you decrease the uncertainty of your position measurement, so you increase the indeterminacy of your momentum. If both space and time were granular there would only be a finite number of discrete values of both, so indeterminacy would be limited and we'd be back to the impossible orbiting electron model of an atom.

[geordief (OP)]

Come to think of it, Heisenberg pretty well contradicts the idea of granular spacetime. As you decrease the uncertainty of your position measurement, so you increase the indeterminacy of your momentum. If both space and time were granular there would only be a finite number of discrete values of both, so indeterminacy would be limited and we'd be back to the impossible orbiting electron model of an atom.

I hope you are right as that would put my question to bed.
It is nice to occasionally  remove another misunderstanding from one's repertoire.

[Eternal Student]

Hi.

   What notions of "discreteness" are you using @alancalverd ?

If both space and time were granular there would only be a finite number of discrete values of both,

1.   Who said space or time had to be finite?    Aren't you prepared to accept a set that is infinite as something that can still exhibit discreteness?    For example space and time could take values in  N,   the set of Natural numbers.    That gives you infinite choices and infinite size for space and time but space and time still isn't a continuum, there are discrete jumps between permitted values.

2.   Just to put some more mud in the water,  would you be prepared to accept the set Q  of rational numbers as having the property of discreteness?
    Between any two rationals there is one (actually infinitely many) irrationals.   So, there's some sense of a gap or that the set of rationals does not form a continuum.  (But not easily identified unless you do have access to the Reals - this is too long and so it's not discussed further).
    Q gets really interesting because not only are there infinitely many of them but we can actually find infinitely many of them within a finite interval of the real number line.

    How would you wish to define discreteness?  I think we can proceed by assuming that space and time can be given numerical values, i.e. that they are some subset of the Reals.    (But even that is not certain and could be challenged).   
    For variables that are Real valued, definitions about what is a discrete variable do vary and some aren't even consistent.   For example this is what Wikipedia says about discrete variables:
In contrast, a variable is a discrete variable if and only if there exists a one-to-one correspondence between this variable and N, the set of natural numbers. In other words; a discrete variable over a particular interval of real values is one for which, for any value in the range that the variable is permitted to take on, there is a positive minimum distance to the nearest other permissible value.   

[ https://en.wikipedia.org/wiki/Continuous_or_discrete_variable#Discrete_variable ]

    They seem to have completely overlooked the fact that Q would fit their first description but does not have the property they describe in the second sentence.   There is no strictly positive minimum distance to the next rational.    Some definitions are based on the latter demand (for a strictly positive distance between a given element and its nearest neighbour).

    I very nearly discussed the possibility of space and time having rational values (or any discrete but dense set within the Reals) earlier when replying to @Halc's post - but left it because everything was already getting too long.
   
   Anyway... have a think about space and time being rational valued and see if you can think of way that you could tell it wasn't Real valued (or if it makes any difference).

Best Wishes.

[alancalverd]

What notions of "discreteness" are you using @alancalverd ?

The opposite of continuous,infinitely divisible and differentiable, or smooth. Having calculable but forbidden regions. Having only a finite number of  denumerable steps between any two positions.

Quote from: alancalverd on Today at 17:25:32

If both space and time were granular there would only be a finite number of discrete values of both,

1.   Who said space or time had to be finite?   

My omission ".....between any two points."

Whilst some mathematics necessarily deals with numbers, which are always (if infinitely) granular, a lot of physics is about a notional continuum which is not granular, and is populated by differentials rather than infinitesimals.

[evan_au]

Cray 1 was a SIMD machine... I made no mention of an architecture...

The Cray 1 with its vector processor, interleaved memory banks and individually-measured cables was an innovation.

But the architecture of interest here is the memory architecture.
- If you ran a simulation of the universe on a Cray 1, down to the level of galaxies in some large volume of space, the vector processor has access to all of the memory representing all of the (simulated) galaxies. All of the universe is instantly accessible in this single bank of memory

Faster-than-light causality. Objective state.  All the things I detest

However, in a grid computer emulating (say) a single atom on Earth, the data about what is happening in the Andromeda Galaxy is simply not accessible on this grid processor representing an atom on Earth - because it is on a different processor with a non-accessible memory. And that information won't percolate through for a few million years.

[geordief (OP)]

The idea of quantisation of photon energy arose from a need to explain observations and is frequently misinterpreted.

Our best explanatory model is that charge is indeed quantised, as are the electron energy levels in any given atom, but a different atom can have arbitrarily different energy levels (which is why we can distinguish them spectroscopically) so "energy" is a continuum.

Thus there is no a priori reason to suspect that "space" or "time" is quantised.

I remembered  your post just now and want to ask you how it can be known that the energy levels can take any value?

How is it required that  some discreteness  is not also embedded into that seeming continuum?

[Deecart]

Discretness or continuous is related to theory.
If you have the formula to describe the continuum, it is continuous.
If you dont have (there is some sort of singularity) then you have to agree to some discretness behaviour.