[geordief (OP)]

I understand that we have no answer as yet and my intimation  is that we may never know (although "we" may build a satisfactory model based on either supposition.)

In the meantime, what indications are there that one of these two paths might eventually bear fruit?

Is it all going to boil down    to some clever person devising an experiment that more or less rules out one of the options or  can some possibilities already be ruled out on the basis of existing understandings?

Suppose ,say one was investigating a possible discreteness, at what level might that be conjectured to occur -and would some mechanism be required to cause this or would  we reach the end of the chain of causality at that point?

(as an aside  ,does the thinking process have to follow the same laws and are our minds forbidden to imagine possibilities  at some deep physical level no matter how unrestrained our imagination can appear to us? Even imagination would be tethered?)

[evan_au]

If the level of discrete jumps were sufficiently fine, we would not be able to distinguish them from continuous values.

However, consider electromagnetism as another phenomenon over which debate raged for centuries as to whether it was continuous or discrete.
- Einstein's explanation of the photoelectric effect showed that there was a discrete element to the energy of electromagnetism (what we now call a photon)
- The concept of discrete electronic orbitals explained why there would be discrete energy levels in an emission or absorption spectrum
- Suddenly, it was realized that this discreteness was absolutely necessary for the existence of matter as we know it.
- If the photons could be generated at all energy levels (instead of discrete levels*), the electrons would spiral into the nucleus in nanoseconds, leaving only something like the matter of neutron stars. This would happen in a blaze of radiation dubbed "the ultraviolet catastrophe".
-  Everything we see and take for granted is there because of discreteness in electromagnetic radiation and atomic orbitals.
https://en.wikipedia.org/wiki/Ultraviolet_catastrophe
*Black-body radiation does generate a continuous spectrum, but the discreteness of photons impacts the high-frequency end of the spectrum.

One day, we may discover some discreteness in time and/or space. And we may discover that this discreteness may be so fundamental as to explain everything we see and take for granted.

But for now, it's pure speculation.
- People who speculate that we may live in a simulation are motivated to test for any discreteness in time and/or space
https://en.wikipedia.org/wiki/Simulation_hypothesis#Testing_the_hypothesis_physically

- One speculator with another perspective is Stephen Wolfram, who is working on a cosmology based on discrete computation on an extremely fine scale
See: https://www.preposterousuniverse.com/podcast/2021/07/12/155-stephen-wolfram-on-computation-hypergraphs-and-fundamental-physics/

[alancalverd]

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.

[Eternal Student]

Hi.     (A couple of other posts have appeared since I started writing - but I've tried to adjust this to compensate, hopefully there's no repetition).

In the meantime, what indications are there that one of these two paths might eventually bear fruit?

    There's at least one thing suggesting space (and time) could be either way:

1.   Special Relativity (SR) opposes the idea of discrete space.
     SR predicts length contraction but also asserts that the laws of physics are the same in every inertial reference frame.    Suppose there is a minimum length,   let's call it  L.   We can (theoretically even if not practically) put down a rod of length L on the table.    Now someone else can be moving past the table at a constant speed, say half the speed of light.   They should see that rod contracted, which means that in their reference frame there exists lengths that are less than L - the minimum length that should exist.     So the minimum possible length is not consistent across all frames of reference,  which contradicts the idea that the laws of physics are the same in every inertial reference frame.

2.   Quantum Mechanics would have a lot less problems with re-normalisation if space was discrete.   This will take a bit longer to explain and assumes some appreciation of what a re-normalisation problem is.   This article explains it as well as I could:   https://medium.com/starts-with-a-bang/even-in-a-quantum-universe-space-and-time-might-be-continuous-not-discrete-f38a34f9aa8c

Is it all going to boil down    to some clever person devising an experiment that more or less rules out one of the options or  can some possibilities already be ruled out on the basis of existing understandings?

     There are already some proposed experiments that might do this.
One idea, usually attributed to Jacob Berkenstein, is to have a crystal and fire individual photons of light into it (of different wavelengths).   Those photons should transfer a tiny amount of momentum to the Crystal which reduces as you reduce the frequency of that light.    There should come a point where the photon is unable to deflect the crystal and cause it to creep through one small unit of space.   (This is also discussed in the previous article linked to:  https://medium.com/starts-with-a-bang/even-in-a-quantum-universe-space-and-time-might-be-continuous-not-discrete-f38a34f9aa8c )

Suppose ,say one was investigating a possible discreteness, at what level might that be conjectured to occur ?

    Most people would expect that the discrete nature of space (or time) might be noticeable around the Planck length and more generally the entire Planck scale.      So that's lengths in the region of 10^-35 m.     There's no rigorous reason or theory to suggest that this is exactly the minimum length, there are just some indicators that strange things happen,  for example that many of our favoured theories like General relativity significantly break down, at these scales.    The Planck scale is a set of units for measuring  distance, time and energy that seem to follow directly from some fundamental constants of nature and is discussed further in this Wikipedia article:  https://en.wikipedia.org/wiki/Planck_units .

-and would some mechanism be required to cause this or would  we reach the end of the chain of causality at that point?

    It's unlikely that science or human understanding ever ends.    There's very likely to be a more fundamental model and a deeper level of explanation to everything.
    I would have mentioned ideas about a simulated universe - but it looks like @evan_au  has already done that.

(as an aside  ,does the thinking process have to follow the same laws and are our minds forbidden to imagine possibilities  at some deep physical level no matter how unrestrained our imagination can appear to us? Even imagination would be tethered?)

    Seems like philosophy.    I don't know.    It seems like you are asking what people have asked for many years - are we (human beings) just like machinery?  Are all of your actions and thoughts governed by physical and chemical laws?   What is the nature of free will and do we actually have it?   These issues are discussed in various other places and a Google search will bring up plenty to read about it.

Best Wishes.

[Colin2B]

They should see that rod contracted, which means that in their reference frame there exists lengths that are less than L - the minimum length that should exist.     So the minimum possible length is not consistent across all frames of reference,  which contradicts the idea that the laws of physics are the same in every inertial reference frame.

If you were talking of proper length I would agree, but the laws of physics include relativity and measurements from a non-local frame such as you describe will show contraction. Relativity allows us to understand that the measurements are consistent across all frames.

[Eternal Student]

Hi.

@Colin2B    I'm not certain what you're trying to say there.    Let's see if I can take your comments in a different order:

the laws of physics include relativity and measurements from a non-local frame such as you describe will show contraction

   "The laws of physics" is a phrase that is used but not clearly or consistently defined.   What is a "law of physics"? can take a chapter in a textbook to discuss.    For example, the Cosmic Microwave Background radiation has a dipole anisotropy as measured from planet earth.    If you change frames of reference then the CMB is isotropic.   
   Is it a "law of physics" that the CMB should be isotropic?   After all, if you want the Cosmological principle as a "law of Physics" then it does lean heavily towards suggesting the CMB should be isotropic in every frame of reference.   Is Special relativity in need of minor revision - there is one frame of reference that is different and special compared to others and there is way to identify and pick out that frame of reference - it's the one where the CMB is isotropic.     Perhaps the best choice is to decide that the isotropy of the CMB isn't a "law of physics" but just an observation you can make (and weaken the Cosmological principle slightly - many things about space are isotropic on large enough scales but not all of them).
     This is not a trivial issue,  what makes some things "an observation" or peculiar to a frame of reference and other things a "law of physics"?

If you were talking of proper length I would agree

    We're not though, are we...   We are talking about space being granular in nature.   That there could be a smallest possible length or distance between two objects,  that  objects in motion might "skip" from one discrete location to another and not pass through any location that was in-between those two locations  etc.
     If you decide that the minimum distance or granularity of space is a "law of Physics", it should be the same in all inertial frames of reference.  So, in the second frame of reference the rod cannot be smaller, it was already at the minimum length in the original frame of reference.
      If you don't consider the size of this granularity as a "law of physics" and instead consider the granularity of space to be a frame-dependent observation you can make then the consequences are profound.   Space stops being isotropic, different directions behave differently:   There would be some frame of reference where the granularity of space would be the same in all directions and space was isotropic but then you can consider a boost to a second frame,  with the off-set velocity along the x-axis of the original frame.  In that new frame, space is not isotropic any longer,  the granularity is different in different directions.

Best Wishes.

[Dimensional]

(as an aside  ,does the thinking process have to follow the same laws and are our minds forbidden to imagine possibilities  at some deep physical level no matter how unrestrained our imagination can appear to us? Even imagination would be tethered?)

I think about this question from time to time.  It is quite interesting. 

Yes, there is a lot of evidence that imagination is tethered/correlated to a chemical process in the brain, but it is only said to be a correlation.  They are not necessarily interchangeable entities.  For example, the image of an orange in my brain is only known to be correlated to a process in my brain; it is not known to be the same thing as the process in my brain.  This is at least how science is dealing with the relationship between body and mind. 

Anyways, this means that there is no telling what thoughts, theories or answers we may think of.  Our imagination would be limited only by how many possible processes in the brain there can be. 



   

[geordief (OP)]

(as an aside  ,does the thinking process have to follow the same laws and are our minds forbidden to imagine possibilities  at some deep physical level no matter how unrestrained our imagination can appear to us? Even imagination would be tethered?)

I think about this question from time to time.  It is quite interesting. 

Yes, there is a lot of evidence that imagination is tethered/correlated to a chemical process in the brain, but it is only said to be a correlation.  They are not necessarily interchangeable entities.  For example, the image of an orange in my brain is only known to be correlated to a process in my brain; it is not known to be the same thing as the process in my brain.  This is at least how science is dealing with the relationship between body and mind. 

Anyways, this means that there is no telling what thoughts, theories or answers we may think of.  Our imagination would be limited only by how many possible processes in the brain there can be. 



   

I can see why the mechanisms whereby the brain processes reality (which ,to my mind includes all kinds of abstract and not simply functional processes) ..I can see how fascinating and absorbing that must be to anyone involved.

But it was really just the "limited" part that I was addressing.

You seem to have given me an answer. There is indeed a limit ,even if for nearly all practical purposes we might say that that limit need not concern us (unless in the future we develop mental prosthetics and our brains are able to directly tap into the workings of artificially intelligent machines)

Even there the limit still applies even if only in theory.

[Halc]

Sorry for the long post, but I try to hit all the points on which I wanted to render my thoughts.

Is it all going to boil down to some clever person devising an experiment that more or less rules out one of the options or can some possibilities already be ruled out on the basis of existing understandings?

I suspect there can be no such experiment, since there is a limit to our ability to measure something, and the smaller that something is, the less classical its existence, so any apparent discreetness (the thing refusing to be where classic physics says it should be) can be written off via the probabilistic nature of measurement of small things.

Still, as Evan points out, quantum behavior of things like electron energy states in an atom has been demonstrated, just not by means of measurements beyond the accuracy that probability would allow.

Special Relativity (SR) opposes the idea of discrete space.

It's worse than that. SR opposes the idea of space (discreet or otherwise), as separate from time. So I think one needs to examine what it says about discreet (or not) spacetime. There is no unified quantum theory of relativity, so this is pretty much an open issue at this point, but I suspect that given such a unified theory, the question asked would still be open to interpretation.

Spacetime consists not of locations in space, but locations (events) in spacetime. If these are discreet points, they're probably either neatly arranged in some kind of grid (like you'd get in a computer simulation), or they're randomly just everywhere, with no obvious layers, grain, or consistent distance between them.
Keep in mind that relativity is a local theory, which automatically discounts conterfactuals. That means that the worldline of some fundamental particle is not defined by a specific series of these events. The actual events of that particle might be widely separated. Photons in particular seem to exist only at two events and none between, at least under any local theory.
To posit otherwise is to completely discard all the premises of relativity. If there was a grid of real events, then there would be a preferred frame that is aligned to that grain. First SR premise is thus wrong. Speed of light would be c only in that frame and not the others, so second premise is also wrong.
If the finite discreet events are random (kind of like the positions of atoms in a wad of putty) and worldlines of fundamental particles are actually present at a set of more-or-less contiguous series of events, then even a particle with no force acting on it will be accelerating this way and that since three consecutive events are not likely to fall into any kind of straight line. There's a lot of conservation laws no longer valid at the quantum scale, and they only appear as averages at the classic scale.

SR predicts length contraction

Length contraction would be interesting. If spacetime was discreet, then there would be a sort of quantum length (shorter than a Planck length), and the length of say a rod could be expressed as an integer of pixels that make up the object at a given moment. Relative to somebody walking past the rod, it would have a slightly smaller number of pixels. This isn't inconsistent since it is still symmetrical. There's no way to determine a preferred frame just by counting pixels of various objects in motion since the pixel count is frame dependent in all cases.

Suppose there is a minimum length,   let's call it  L.   We can (theoretically even if not practically) put down a rod of length L on the table.

That rod would consist of exactly 2 'adjacent' pixels. You're right, this seems to be a problem. If there was a neat grid of pixels, then there'd be a preferred frame, but if not, then the length of your object changes from moment to moment depending on the changing distances between adjacent pixels from one moment to the next. There would be no fixed minimum length, just a sort of average one.

Now someone else can be moving past the table at a constant speed, say half the speed of light.   They should see that rod contracted

Yea, but that's now two different, but still adjacent pixels. The distance between the original two pixels is not different. You're just measuring a different pair of events. That's all length contraction is after all.

which means that in their reference frame there exists lengths that are less than L

That's right. Take a single stationary fundamental particle which has zero length. Where is it going to be next? At one adjacent pixel forward in time it's not going to be an entire minimum length away, or it would probably be moving pretty fast. No, it's just one min-time away, and that pixel has a spatial separation from the earlier pixel that is likely less than one length-pixel away in some random direction. Remember I'm assuming a random distribution of pixels (discreet events). So there's no contradiction in it not moving a minimum length since that length is just an average separation of space-like separated pixels. I'm saying the space position would have to be far more fine-grained than the minimum separation of pixels.
So I sprinkle 200 dots randomly on a sheet of paper. Not totally random, but sort of evenly distributed without going to far as to arrange them in rows and columns and such. Hold the paper at a random orientation. Horizonal is space, and vertical is time. An object of minimum nonzero size would, at a given time, be at two of those dots (and those dots would likely not be simultaneous since they're not in neat rows. But if you look up and down, you'll find plenty of pixels that lie between a pair of (time) lines drawn through the dots, perpendicular to the (space) line connecting them. This illustrates space being more fine grained than the min distance between adjacent pixels.

I find that this in itself doesn't contradict the laws of physics being different from one frame to the next.

Forgive my fairly naive approach to things. I am more used to the neat grid of spacetime events, since these are natural to simulations.

If you were talking of proper length I would agree, but the laws of physics include relativity and measurements from a non-local frame such as you describe will show contraction.

What do you mean by 'non-local frame'? Any inertial frame covers all of Minkowskian spacetime, so I don't see how a frame wouldn't be (or assign coordinates to) 'here', and thus be non-local.

Is it a "law of physics" that the CMB should be isotropic?

I'd say no, since it isn't a law of physics that say the light from say a spaceship appear to be the same wavelength to every observer. Hubble's law is not a law of physics for similar reasons.

After all, if you want the Cosmological principle as a "law of Physics" then it does lean heavily towards suggesting the CMB should be isotropic in every frame of reference.

The principle says something else. I might still not list it as any kind of 'law'.

there is one frame of reference that is different and special compared to others ...
 - it's the one where the CMB is isotropic.

There is no CMB predicted under SR, which is why SR cannot be a model of the universe.

I realize I'm discounting everything as a 'law' under the first postulate, but the sort story is a lack of local test for a preferred frame. So 'law' in this context is something local.

We are talking about space being granular in nature.   That there could be a smallest possible length or distance between two objects,  that  objects in motion might "skip" from one discrete location to another and not pass through any location that was in-between those two locations  etc.

This is why I only think you should discuss granularity of spacetime, and not try to do it with space, because yes, you very much run into contradictions if you do it with space.

If you decide that the minimum distance or granularity of space is a "law of Physics", it should be the same in all inertial frames of reference.  So, in the second frame of reference the rod cannot be smaller, it was already at the minimum length in the original frame of reference.

There you go. That's a contradiction, but using space, not spacetime. It's why I reached for the not-neatly-ordered discreet events and not ordered ones. SR falls to pieces given the latter.

[Eternal Student]

Hi.

Sorry for the long post,

   There are long evenings this time of year and it's interesting to read some well considered ideas.   Thanks for your time.

The (..Cosmological..) principle says something else.

    It depends which book or text you look in.  Some will limit it to suggesting an even distribution of matter.   Other texts will broaden that idea, sometimes implying that everything about space is isotropic and homogeneous on large enough scales.    A fairly strong version of the Cosmological Principle is what I was using.

SR opposes the idea of space (discreet or otherwise), as separate from time.

   Yes.    The rest of your development of this idea is where it gets interesting.
   The idea of a more random or possibly even a dynamically changing grid of pixels in spacetime,  instead of a rigid and regular fixed grid,  is totally un-orthodox but does make some sense.

There would be no fixed minimum length, just a sort of average one.

    That is complicated and difficult to develop.   An average over what?   It's difficult to make sense of averaging it over time and imagining the length does fluctuate a little as time progresses.   Spacetime has time built in and fixed in with it.   Specifying an event in spacetime has left you no room to vary time.
     You might make progress by considering that there is a certain probability of finding the ends of a rod at "this event",  or "that event"   and then effectively have the rod length behave as the sort of average you seek.   The average or expected observed length can then be a continuous quantity and not imply the ends of the rod are actually in-between the pixel or grain limits.    Very roughtly, this is like quantum mechanics - assigning probabilities to the end of rod being observed at certain pixels and having the rod exist in a superposition of states to achieve the overall typically observed length.
    I'm not going to say more because, as I'm sure you ( @Halc ) have realised, what you have said is already some way off the mainstream view of science.   Some moderator (you know the type) could suggest this moves into the New Theories section  and  it's also someone else's OP and they probably don't want to go too far down this road.
- - - - - - - -

If you ( @Halc ) feel so inclined,  the bit about   "counterfactuals" isn't meaning much to me at the moment.  I'm not sure I've even heard that terminology before.   Perhaps you could say a bit more about that or drop a reference to it.

Best Wishes.

[Colin2B]

@Colin2B    I'm not certain what you're trying to say there.   

Sorry, I was in too much of a hurry to expand.
The laws of physics are the same in all inertial frames yes, but not necessarily between frames. Take conservation of energy, true within any frame but not between frames, we need to take into account of relativity.
So you say “ If you decide that the minimum distance or granularity of space is a "law of Physics", it should be the same in all inertial frames of reference.”
What I would say is yes, assume there is a minimum distance, but don’t assume that specific distance is the same when measured from any other frame.
How are you making the measurements? In your lab frame at rest relative to what you are measuring, you are using one set of clocks and rulers, which you cannot apply to another lab moving relative to you unless you convert using relatively. However, that other lab making local measurements of their ‘at rest’ set up will get exactly the same results as you. So, the laws of physics are the same in all frames.

Of course I may have completely misunderstood what you were saying, so I’ll try to find time to read all the recent replies.

[Eternal Student]

Hi.

   That does make a good deal more sense, thanks @Colin2B .   
   However, there's still a minor issue.   Start with a rod at rest in your lab frame and give it exactly the minimum length, L, which your x-axis supports.   Now get that rod moving along the x-axis relative to your lab frame.   Do you see the rod contracted and having less length in your lab frame?   
     Can it have less than the minimum grain of length that is available in your lab frame?

     The only way to get around this is to assume the minmum length that you measure or observe in your lab frame, is only a minimum length for objects that are also at rest in your lab frame.   That's OK,  that's consistent  - but it means that your idea of a minumum length in the lab frame isn't  my (or most other people's) idea of a minimum length existing.   Some objects do have lengths smaller than your idea of the minimum length (all those which are not at rest in your frame can have smaller lengths).

Best Wishes.

[Colin2B]

However, there's still a minor issue.   Start with a rod at rest in your lab frame and give it exactly the minimum length, L, which your x-axis supports.   Now get that rod moving along the x-axis relative to your lab frame.   Do you see the rod contracted and having less length in your lab frame?   
     Can it have less than the minimum grain of length that is available in your lab frame?

     The only way to get around this is to assume the minmum length that you measure or observe in your lab frame, is only a minimum length for objects that are also at rest in your lab frame.   That's OK,  that's consistent  - but it means that your idea of a minumum length in the lab frame isn't  my (or most other people's) idea of a minimum length existing.   Some objects do have lengths smaller than your idea of the minimum length (all those which are not at rest in your frame can have smaller lengths).

Best Wishes.

Ok, I understand that, but my main concern was the statement that this violates the assumption that the laws of physics are the same in all frames.
My contention is that the laws of physics are the same because using the physical laws of relativity we can understand what is happening. Two people in two labs will measure locally (by which I mean they are colocated, at rest and at the same gravitational potential as the property being measured) the minimum length to be the same - proper length. If someone in a lab moving relative to one of those labs tries to measure that lab’s minimum distance, not only will that distance be contracted (as you rightly say) but the measuring apparatus will also be contracted and when you use relativity to work out what is happening you find they all measured the same distance. All consistent. What would shock me would be if the proper length changed.
We get the same problem when measuring the wavelength of a Cesium clock from a different gravitational potential, but we do understand why and it’s consistent with the laws of physics.

I agree that this does not align with most peoples’ view of a minimum length, but relativity doesn’t align with most peoples’ view of what we should observe 

[alancalverd]

What is a "law of physics"?

A mathematical description of an extremely consistent observation.

[Eternal Student]

Hi.
   

(A Law of Physics is....)  A mathematical description of an extremely consistent observation.

    Does it really need to have a mathematical description?
Is Newton's third law (about equal and opposite forces) not a law because I can't state it without using some words?   What about Le Chatelier's principle (from Physical Chemistry)?

Best Wishes.

[Halc]

The (..Cosmological..) principle says something [other than 'suggesting the CMB should be isotropic in every frame of reference'].

    It depends which book or text you look in.  Some will limit it to suggesting an even distribution of matter.

That's strong enough. Matter is distributed evenly only in one frame, so right there the suggestion doesn't work in any other frame.

The rest of your development of this idea is where it gets interesting.

The rest was just thoughts off the top of my head. Not sure how much water it holds. Love to discuss, yes.

The idea of a more random or possibly even a dynamically changing grid of pixels in spacetime,  instead of a rigid and regular fixed grid,  is totally un-orthodox but does make some sense.

I'm talking about some finite number of events existing in some 4D hypervolume of spacetime. I don't know how that can meaningfully 'change' since that would imply time contained by another kind of time. I think you mean changing locations in discreet space over time, which of course would be necessary if the pixels were not in neat lines. But it would also mean discreet time, which means at most times a particle is not anywhere at all.

There would be no fixed minimum length, just a sort of average one.

    That is complicated and difficult to develop.   An average over what?

You have a 'min length' object of two particles at 'adjacent' locations, whatever that means. Turns out that yes, those same events are arbitrarily closer together in a frame where it moves, so it's hardly a min separation. Moving objects contract by 'being at' pixels that are spatially closer together but temporally further apart. That seems consistent with Lorentz transformations without destroying the symmetry between frames.

You might make progress by considering that there is a certain probability of finding the ends of a rod at "this event",  or "that event"

One only gets to measure position once, and even then, only down to limited precision. Heisenberg uncertainty won't let you do it to the other end or a second time. So talking about 'probability of finding' (a classical measurement) at this sub-Planck scale is inappropriate. We need to find some other empirical evidence.

I'm not going to say more because, as I'm sure you have realised, what you have said is already some way off the mainstream view of science.

But I'm just playing with ideas, not asserting anything. And it's not my topic. Yes, I'm sure I'd get shot to pieces by somebody with better knowledge, so shoot me to pieces.

   Some moderator (you know the type) could suggest this moves into the New Theories section  and  it's also someone else's OP and they probably don't want to go too far down this road.[/quote]If we thought it necessary, we'd split the topic, not move the whole thing. I suspect geordief likes these continued discussions.

If you feel so inclined, the bit about "counterfactuals" isn't meaning much to me at the moment.

All the discussion seems to rely on the classical principle of counterfactual definiteness en.wikipedia.org/wiki/Counterfactual_definiteness (also called the principle of reality), that says one can speak meaningfully of the objective state of things in the absence of measurement. It's incredibly important when discussing quantum things. I choose not to hold to the principle, which means that everything I said about the discreet events is meaningless. I choose instead the classical principle of locality (no faster than light cause/effect). Bell proved that you can only pick one.
A classical computer simulation would have to do the opposite, holding on to a current 'state' while computing the next one. Even then, the algorithm requires pretty much infinite resources to simulate a small finite system.
The simulated universe would indeed have discreet events, but in neat rows and columns. There would probably be some pretty easy tests to find the orientation of said rows and columns and thus the preferred frame.


A thought experiment, perhaps to drive the pixel concept into the dust bin: You have these pixels (perhaps neatly arranged, perhaps not). You have a fundamental particle with no size, so it is at best present at a single 'line' of those pixels over time. Which pixels are 'visited' by this particle?
Say the pixels are in neat lines and the particle is moving nearly parallel to one of those lines. It is at 1000 pixels in a line (same point in space, different time quanta), and then it drifts far enough to the side that it is now present at some thousands more in the next column. That implies a sort of 'state' that something keeps track of how far off the actual location pixel it is so the jump can happen at the appropriate time. This effect is known as 'jaggies' in computer world, where the location of an object (say edge of a slightly tilted square on a screen of neatly arranged pixels) necessitates occasional jumps, discontinuities in the straightness of a diagonal line.
This all implies internal state that is of higher resolution than that of the spacing of the pixels. How is that not a contradiction with discreet space?

Regards

Two people in two labs will measure locally (by which I mean they are colocated, at rest and at the same gravitational potential as the property being measured) the minimum length to be the same - proper length. If someone in a lab moving relative to one of those labs tries to measure that lab’s minimum distance, not only will that distance be contracted (as you rightly say) but the measuring apparatus will also be contracted and when you use relativity to work out what is happening you find they all measured the same distance. All consistent.

Yes, all consistent. I tried to describe that above. You have this min length for a stationary object, but moving ones will be contracted and can thus be arbitrarily shorter.

All very mathematical and non-empirical, so the presence of a lab and apparatus is meaningless. You're not going to actually measure this object which is far shorter than the published 'size' of any fundamental particle. Fundamental things actually have no physical size, but they have a sort of sphere of influence that can be measured, and that's what is usually referenced when they assign it a 'size'.

Is Newton's third law (about equal and opposite forces) not a law because I can't state it without using some words?

I like Alan's definition. The third law seems mathematical enough. The sum of all the momentum actions must be zero. The law holds only in inertial frames, but it can be expressed mathematically there.

Not sure what you're getting at with the 'without words' bit. Yes, it takes words to convey a concept to somebody else, a concept corresponding to something like a law of physics.

[alancalverd]

Is Newton's third law (about equal and opposite forces) not a law because I can't state it without using some words?

F₁ = -F₂

(bold type indicates vectors)

[geordief (OP)]

. I suspect geordief likes these continued discussions

Yes he does.It takes me a lot of effort to follow the replies ,though after my  question has been answered in the main.

And I may no longer be able to contribute  but  I follow as far as I can.

I find the world as built up of "events" rather than objects /systems evolving in time very interesting  and find the former to be equally acceptable (more so actually) on an intuitive level.

Apparently spacetime is a model  designed to be just a coordinate system (a local one) without any objects  necessarily occupying  any particular location  but I have also wondered if  those  locations could be populated by  real events.(ie if  the real events  could define the location in spacetime)

Seems ,maybe it can be one or the other but not both at the same time?

[Eternal Student]

Hi.

   @alancalverd    and   @Halc , you are glossing over what Newton's laws actually means or tells us.    Of course, you can express a lot of it with mathematics but it's not obvious you convey all of the meaning.

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

Similarly,  Halc's version   ∑ F   =  0   doesn't help much because you'd probably write the 2nd law as   ∑ F  =  m. a.  Those two together would now imply that the acceleration of everything is always 0.

With a great deal of care, there is a fair chance you could formulate all of Newton's laws into statements of mathematics but it would involve more than just equations.   You'd want to be able have full statements written out in something like formal 1st order logic.     For example,
∃F₁ (F₁ ≠ 0)         ∃F₂  ( F₁  =  - F₂ )      as something for Newton's 3rd law.

You'd probably be better off replacing Newton's Laws entirely with a statement about Lagrangian mechanics if you were determined to express all of them in mathematics.

You're all ignoring the other example,  Le Chatelier's principle, which was chosen because it's rarely expressed in anything other than words:
    When any system at equilibrium for a long period of time is subjected to a change in concentration, temperature, volume, or pressure, then
    (1) the system changes to a new equilibrium, and
    (2) this change partly counteracts the applied change

    This might not be possible to express in mathematics and even if you were able to, it would be unwieldy.

The key point is that there just is no requirement for laws of physics to be expressed in mathematics:
   Extract of the definition from Wikipedia:
...A law can usually be formulated as one or several statements or equations,...
    A carefull read through the full definition reveals that it is never once demanded that you can always express a law of physics with mathematics.

Best Wishes.

[Eternal Student]

Hi again.

(I'm happy with continued discussions and...)     It takes me a lot of effort to follow the replies ,though after my  question has been answered in the main.

   That's very kind of you @geordief .     Always keep in mind that you are the OP and you can steer the conservation if required.   You can also ask the other participants to start a new post, or get a moderator to enforce a splitting of the post etc.

I find the world as built up of "events" rather than objects /systems evolving in time very interesting  and find the former to be equally acceptable (more so actually) on an intuitive level.

    This sounds like the idea of a "block universe" and you have understood it and expressed it well.
Generalising the idea, events that would be in the future from your current frame of reference often need to exist and could easily be past events in some other frame of reference.  It's one where the existence of "free will" can be seriously challenged.

Apparently spacetime is a model  designed to be just a coordinate system (a local one) without any objects  necessarily occupying  any particular location  but I have also wondered if  those  locations could be populated by  real events.(ie if  the real events  could define the location in spacetime)

    "Spacetime" has a few different definitions.   It could be just the set of all co-ordinate points permitted in the combination of  (Space ,  Time).     Usually this is described as something like a Cartesian product of  (Space) X (Time) but the mathematical terms aren't important and may cloud the issue.   Yes... spacetime can mean just a set of 4-dimensional co-ordinates.
    However, it's also quite common to assume some additional structure exists on that set of co-ordinates.   So some texts will use the term  "Spacetime" to refer to the set of 4-dimensional co-ordinates  WITH  a metric defined on that set.      The most conventional metric would be the Minkowski metric.    Let's re-phrase all of that without the mathematical terms:    "Spacetime" can be used to describe not just a set of 4-dimensional co-ordinates but a set where some notion of distance between those points is defined.   That notion, called the metric, shows how some time will combine with some space to produce a distance (sometimes called a "spacetime interval").
      So, "spacetime" was first used as a term slightly before and also during the time of Newton and then it was just some space with some time, they were just written side by side and produced a 4-dimensional co-ordinate system.   Space and time were just quite separate things and no-one seriously attempted to blend them.   After Einstein, the term is almost always used to convey slightly more meaning than just this - there is a metric defined on that set of 4-dimensional co-ordinates, or to put it in words "space and time are known to combine or blend in a certain way".
      Spacetime isn't just a local thing and unless it is expressly stated that you are confining your attention to a local patch then Spacetime is all of the space that exists in the universe together with all of the time that has existed or will exist.
     Exactly as you stated,  spacetime can be empty, there doesn't need to be any objects in it.   For example, the Minkowski metric only applies in a Spacetime that is empty  (but it holds well enough as an approximation in regions that are just well away from large bodies of matter).     Our actual, real-life Spacetime is evidently not empty - for example, there is planet Earth in it at some co-ordinate values of (Space, Time).
      Finally you mentioned "events".   That's another term that Physicists abuse or vary according to the context.  When discussing Spacetime, an "event" is one specified location in spacetime.   To say this another way it is the set of values   x,y,z,t  in a fixed order,  it's written in round bracketts (x,y,z,t) in conventional co-ordinate notation.     A thing can be "at an event" but it doesn't mean that there is some activity like a house party going on and they are at that party having fun.   It is just a statement about the location of that object in space and at a given time.   "An event" means a grid location (even if it is a 4-dimensional grid you would be using).
     The other way a Physicist can use the term "event" is exactly as we all do in the ordinary English Language.  An event is an activity, process or thing that is happening or has happened.
     If you were using the term "event" in the first sense, then yes... for sure, every location in Spacetime is populated by an event.   Every location in Spacetime is one event.
    So you were almost certainly using the word "event" as per the ordinary English Language.  That's more philosophical and harder to consider.   Arguably everything is an event.   Some events are uninteresting, no matter was there and no interactions took place at that time -  but that is still an event.    Taking this broad definition of what an event is, then yes there is an event at every location in Spacetime.

Best Wishes.