[geordief (OP)]

Suppose I am washing my face some time tomorrow.

Within my body there will be many events occurring during that time.

I am no chemist but one might be that there is a reaction  between an atom of carbon and an atom of iron in my hand.

Whatever the particular reaction (and I assume there will also be reactions within that reaction) there will be a previous event that can be said to have "immediately" preceded or caused that iron/carbon event.

Will that earlier event be distinct from the (iron/carbon) event that followed or are these two events  connected in a continuous way?

I understand that particles are now modeled as being properties of an underlying field.Are these fields  believed to be continuous or discrete in nature?(in the model,I suppose I should say)

[Halc]

Whatever the particular reaction (and I assume there will also be reactions within that reaction) there will be a previous event that can be said to have "immediately" preceded or caused that iron/carbon event.

I think the answer to this is dependent on your interpretation of quantum mechanics.
Assuming a local one (one that disallows effect before cause for instance), then the previous event probably cannot immediately precede the interaction effect. Hard to see that with the hand washing example, but imagine a photon emitted by a distant galaxy and exciting some electron of some atom here on Earth. That's a very long time between cause and effect, and there are no intermediate events between the two.
A different (non-local) quantum interpretation might assert that the photon propagates along the way, forming a series of arbitrarily small steps along the way. Hence my saying that it is interpretation dependent.

I understand that particles are now modeled as being properties of an underlying field.Are these fields  believed to be continuous or discrete in nature?(in the model,I suppose I should say)

There is a level below which differences cannot be measured, even in principle, and therefore one can argue for discreetness, but it's not like there are pixels or ticks lined up at regular intervals. Not an expert, so take my reply to this part with a grain of salt.

[evan_au]

At this point in time, nobody knows whether time is quantised at some very fine level.

Relativity and quantum theory assume time is continuous. Our experiments to date have not revealed any quantisation of time. But perhaps such a thing might resolve some of the infinities around black holes (just like quantisation of electron orbitals resolved some infinities around atomic energy levels).

Stephen Wolfram is trying to develop a computational Theory of Everything; if I've understood his intent, it appears to assume quantised time (at least for local interactions). But the timescale is very small.

See: https://www.preposterousuniverse.com/podcast/2021/07/12/155-stephen-wolfram-on-computation-hypergraphs-and-fundamental-physics/

[geordief (OP)]

At this point in time, nobody knows whether time is quantised at some very fine level.

Relativity and quantum theory assume time is continuous. Our experiments to date have not revealed any quantisation of time. But perhaps such a thing might resolve some of the infinities around black holes (just like quantisation of electron orbitals resolved some infinities around atomic energy levels).

Stephen Wolfram is trying to develop a computational Theory of Everything; if I've understood his intent, it appears to assume quantised time (at least for local interactions). But the timescale is very small.

See: https://www.preposterousuniverse.com/podcast/2021/07/12/155-stephen-wolfram-on-computation-hypergraphs-and-fundamental-physics/

Is it fair to say that there is no need to actually  find evidence  to show quantization of time or spacetime?

If we postulate continuity of spacetime at the finest detail it seems to me that that may  pose more  problems than to postulate discreteness.

If matter creates it's own space  would the smallest size of matter (matter =fields?)  place a limit on the smallest region of space  or spacetime?

[Colin2B]

Hi geordief

To clarify the specific case above, if she took ,say 5 minutes extra to do the shopping on a day before I was born ,I am saying that that extra 5 minutes would have changed the course of the universe and my  life (and all others ) would be included in that changed universe.

So her shopping and my , say fit of coughing would be connected events  but only in the direction of her to me .

So to my mind all events in the universe are connected but sometimes only  in one direction.

You also have to consider the sphere of influence of such ripple effects. Imagine a probability tree branching out at each effect of that cough. Some will be dead ends having no effect, but very few will have any likelihood of affecting, say, events on the moon let alone the universe.

Is it fair to say that there is no need to actually  find evidence  to show quantization of time or spacetime?

I don’t understand what you are saying. Can you clarify why no evidence is required?

If we postulate continuity of spacetime at the finest detail it seems to me that that may  pose more  problems than to postulate discreteness.

Such as?
The energy of a free electron is not quantised and that doesn’t cause any problems, you can give it any ke you want. Electrons energies are only quantised when they are constrained eg in an atom orbital, or ejected as part of a quantised process.
What @evan_au quotes as a theory which assumes quantised time is that it would give an inherent constraint that might result in quantisation, but might only show at very high energies or extreme spacetime curvature (my speculation).

If matter creates it's own space  would the smallest size of matter (matter =fields?)  place a limit on the smallest region of space  or spacetime?

There is no evidence that matter creates space. Matter occupies space.
The Planck length is likely to be the smallest dimension we are able to see/measure, but that doesn’t exclude things being smaller.

[evan_au]

The discussion of "continuous" vs "discrete" has been going on for millennia.
- Greek philosopher Democritus assumed that there must be some indivisible particle of matter that he called an "atom". He assumed this with absolutely no physical evidence. (Since the 1900s, we have proof that an atom is made of even smaller things...)
- Zeno, another Greek philosopher produced some paradoxes, some of which assume quantized time or quantized space, again with no physical evidence. (Some of his paradoxes were just a mathematical error that assumed an infinite series cannot have a finite sum.)

See: https://en.wikipedia.org/wiki/Democritus#Atomic_hypothesis
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Arrow_paradox

[Halc]

Not sure what this has to do with the continuity of spacetime, but:

Imagine a probability tree branching out at each effect of that cough. Some will be dead ends having no effect, but very few will have any likelihood of affecting, say, events on the moon let alone the universe.

I must disagree here. Chaos theory says that the slightest change anywhere will have a macroscopic effect eventually (and not a long time) anywhere in its future light cone. The moon is a pretty static place, chaotic only at the microscopic level, so the only changes will likely be things like a completely different set of photons being emitted by the moon. We don't have access to both outcomes (the moon photons with and without the cough), so it doesn't really qualify as an empirical difference. No, the cough isn't going to rearrange the craters or anything, but it will completely change the weather on Venus in a month.

The energy of a free electron is not quantised and that doesn’t cause any problems, you can give it any ke you want. Electrons energies are only quantised when they are constrained eg in an atom orbital, or ejected as part of a quantised process.

Even then, the energy is frame dependent and probably expressed in the proper frame of the atom, which is becoming complex enough to have a classic property like KE.
I have a rough time giving KE to a free electron when (per Heisenberg uncertainty) such a thing doesn't really have a velocity until measured, and that measurement does not preserve the velocity, so you only know what it was, not what it is. For the same reason, it doesn't have a location, and it having neither of these properties kind of puts a dent in the model of continuous spacetime.

[geordief (OP)]

Hi geordief

To clarify the specific case above, if she took ,say 5 minutes extra to do the shopping on a day before I was born ,I am saying that that extra 5 minutes would have changed the course of the universe and my  life (and all others ) would be included in that changed universe.

So her shopping and my , say fit of coughing would be connected events  but only in the direction of her to me .

So to my mind all events in the universe are connected but sometimes only  in one direction.

You also have to consider the sphere of influence of such ripple effects. Imagine a probability tree branching out at each effect of that cough. Some will be dead ends having no effect, but very few will have any likelihood of affecting, say, events on the moon let alone the universe.

Is it fair to say that there is no need to actually  find evidence  to show quantization of tim
e or spacetime?

I don’t understand what you are saying. Can you clarify why no evidence is required?

If we postulate continuity of spacetime at the finest detail it seems to me that that may  pose more  problems than to postulate discreteness.

Such as?
The energy of a free electron is not quantised and that doesn’t cause any problems, you can give it any ke you want. Electrons energies are only quantised when they are constrained eg in an atom orbital, or ejected as part of a quantised process.
What @evan_au quotes as a theory which assumes quantised time is that it would give an inherent constraint that might result in quantisation, but might only show at very high energies or extreme spacetime curvature (my speculation).

If matter creates it's own space  would the smallest size of matter (matter =fields?)  place a limit on the smallest region of space  or spacetime?

There is no evidence that matter creates space. Matter occupies space.
The Planck length is likely to be the smallest dimension we are able to see/measure, but that doesn’t exclude things being smaller.

Thanks very  much.I know you deserve a response to  your reply  but I feel embarrassed to spell out  what I was thinking as it might seem that I was trying to back up my opinions.(or that I understood what I was saying;)  )

But just to attemt to clarify the point you were asking directly,I had  in mind that there might be a discreteness at levels unattainable of detection either practical or theoretical such that we would have to simply assume it to be the  more likely case out of intellectual preference (if such a concept is valid).

I guess I just  anticipate  that it will be entirely impossible to find evidence one way or the other but you seem to be suggesting that evan_au 's link contains an avenue of attack that may bear fruit at some stage.(I had better attempt to have a look at it even it is probably too hard for me to understand)

[TommyJ]

To add all of the above.

Today physics doesn't tell us that time is discrete. Maybe in the future quantum mechanics will tell us about quants of time. Time and space quantization will give both of them in a discrete packets.

Time has rules of what comes one after the other.
The laws of physics start from a moment (a state of a system at one instance of time), then tell what happens next, using the patterns, using the physics (laws) to tell what happens to the next subsequent moment.

One good embracing example would be The Nyquist–Shannon sampling theorem [...] ‘which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.’

The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity [...] that no actual information is lost in the sampling process. (Wikipedia)

The theorem used a lot of works and notion given by Whittaker, Borel, Kotel'nikov.

In simpler words, we consider time as continuous in a certain system with pre-conditions, using small enough quanta of time to sample a physical quantity, so that it can be reconstructed without loss of information.

[alancalverd]

Greek philosopher Democritus assumed that there must be some indivisible particle of matter that he called an "atom". He assumed this with absolutely no physical evidence. (Since the 1900s, we have proof that an atom is made of even smaller things...)

The story I was told was that he observed a worn stone step (solid physical evidence!) and argued that

(a) bits of it must have been carried away on people's feet (by analogy with mud or water)
(b) the bits must have been very small, since nobody saw them go (unlike mud or water)
(c) the bits must have been part of the stone
(d) there was no reason to suspect that they had evaporated into nothingness as bulk stone doesn't evaporate by itself
(e) therefore the bits that disappeared must have been stone
(f) hence stone must be composed of invisibly small particles that do not disintegrate -  a tomos - indivisible.

A deduction made all the easier if there are only four elements, but like all good hypotheses, it started from what was seen (the stone) and current knowledge (the elements), and was consistent with all other observations.

[Colin2B]

Thanks very  much.I know you deserve a response to  your reply  but I feel embarrassed to spell out  what I was thinking as it might seem that I was trying to back up my opinions.(or that I understood what I was saying;)  )

But just to attemt to clarify the point you were asking directly,I had  in mind that there might be a discreteness at levels unattainable of detection either practical or theoretical such that we would have to simply assume it to be the  more likely case out of intellectual preference (if such a concept is valid).
I guess I just  anticipate  that it will be entirely impossible to find evidence one way or the other but you seem to be suggesting that evan_au 's link contains an avenue of attack that may bear fruit at some stage.(I had better attempt to have a look at it even it is probably too hard for me to understand)

No need to feel embarrassed, it’s just a case of my wanting to clarify what you were looking for.
Yes, high energy is likely to be the limit, the energy needed to probe the Planck length is around that which could form a mini black hole, so practicality comes into it. However, any theory ought to have testable predictions that might give some evidence.
I was talking to people recently who are planning high energy projects and there are some interesting directions being explored, including probing whether gravity might be linked to an extra dimension, to date negative, but all very interesting.

Not sure what this has to do with the continuity of spacetime, but:

It was in response to a question from geordief “If we postulate continuity of spacetime at the finest detail it seems to me that that may  pose more  problems than to postulate discreteness” and I assumed he was drawing a parallel between quantum world and spacetime, I was just pointing out that not all the quantum world is discrete.

Even then, the energy is frame dependent and probably expressed in the proper frame of the atom, which is becoming complex enough to have a classic property like KE.
I have a rough time giving KE to a free electron when (per Heisenberg uncertainty) such a thing doesn't really have a velocity until measured, and that measurement does not preserve the velocity, so you only know what it was, not what it is. For the same reason, it doesn't have a location, and it having neither of these properties kind of puts a dent in the model of continuous spacetime.

I agree that the the KE is frame dependent, but that frame is not relative to the atom for a free electron that is not bound to the atom or part of a metal lattice, say, it’s usual to take the frame of the particle accelerator, or even a crt.
In the frame of the accelerator you can give the free electrons as much KE as you want as a continuous variable rather than discrete.
I agree that we don’t know where a particle is until detected and any measurement disturbs it, but that’s not the same as being unable to have a model with position. The current standard model is QFT and in that we have a position operator, we can also derive terms for momentum and velocity and it incorporates Heisenberg; true it’s still a probabilistic model, but it’s a big step forward from the time of the Copenhagen Interpretation. Interestingly, because QFT takes as it’s starting point the Lagrangian it is also possible to have a meaningful discussion of trajectory - most probable path.

[Halc]

- Greek philosopher Democritus assumed that there must be some indivisible particle of matter that he called an "atom".

And he was right, even if his logical was a non-sequitur.

Since the 1900s, we have proof that an atom is made of even smaller things...

This seems to be the mistake of the physics community at large which allowed the word 'atom' to refer to one of the various elements, each made of smaller things, rather than choosing a new word for them and allowing 'atom' to continue its original meaning of 'indivisible'.

Yes, I agree with Alan that he didn't exactly conclude this sans evidence.

The story I was told was that he observed a worn stone step (solid physical evidence!) and argued that
...
(e) therefore the bits that disappeared must have been stone
(f) hence stone must be composed of invisibly small particles that do not disintegrate -  a tomos - indivisible.

That it is made of smaller bits, yes. That those bits are indivisible doesn't follow from his observations. It might be turtles all the way down, with no fundamental thing at the bottom. Science has observed better since, but I'm thinking about his conclusion based on the evidence at the time.

In the frame of the accelerator you can give the free electrons as much KE as you want as a continuous variable rather than discrete.

Point taken.

I agree that we don’t know where a particle is until detected and any measurement disturbs it, but that’s not the same as being unable to have a model with position.

Again agree. Just because you don't know exactly where the unmeasured electron is in your accelerator doesn't mean it isn't in there and not hitting the walls.