Post by: geordief on 11/06/2022 11:30:59
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?)
Post by: evan_au on 11/06/2022 13:30:28
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/
Post by: alancalverd on 11/06/2022 13:30:42
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.
Post by: Eternal Student on 11/06/2022 14:27:25
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.
Post by: Colin2B on 11/06/2022 14:58:17
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.
Post by: Eternal Student on 11/06/2022 17:52:45
@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 agreeWe'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.
Post by: Dimensional on 11/06/2022 19:27:15
I think about this question from time to time. It is quite interesting.
(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?)
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.
Post by: geordief on 11/06/2022 20:26:05
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.I think about this question from time to time. It is quite interesting.
(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?)
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.
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.
Post by: Halc on 11/06/2022 20:28:54
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.
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SR predicts length contractionLength 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.
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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.
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Now someone else can be moving past the table at a constant speed, say half the speed of light. They should see that rod contractedYea, 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.
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which means that in their reference frame there exists lengths that are less than LThat'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.
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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'.
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there is one frame of reference that is different and special compared to others ...There is no CMB predicted under SR, which is why SR cannot be a model of the universe.
- it's the one where the CMB is isotropic.
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.
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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.
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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.
Post by: Eternal Student on 11/06/2022 23:22:24
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.
Post by: Colin2B on 11/06/2022 23:44:03
@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.
Post by: Eternal Student on 12/06/2022 00:10:08
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.
Post by: Colin2B on 12/06/2022 08:48:06
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?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.
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.
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 ???
Post by: alancalverd on 12/06/2022 11:37:17
What is a "law of physics"?A mathematical description of an extremely consistent observation.
Post by: Eternal Student on 12/06/2022 13:55:15
(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.
Post by: Halc on 12/06/2022 14:58:24
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 (..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.
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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.
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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.
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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.There would be no fixed minimum length, just a sort of average one.That is complicated and difficult to develop. An average over what?
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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.
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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.
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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 (http://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.
Post by: alancalverd on 12/06/2022 17:08:10
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)
Post by: geordief on 12/06/2022 17:52:36
. I suspect geordief likes these continued discussionsYes 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?
Post by: Eternal Student on 12/06/2022 23:57:15
@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.
Post by: Eternal Student on 13/06/2022 01:11:26
(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.
Post by: alancalverd on 13/06/2022 10:14:52
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!
Post by: Eternal Student on 13/06/2022 18:18:50
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.
Post by: Eternal Student on 14/06/2022 03:58:27
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
Best Wishes.
Post by: evan_au on 14/06/2022 06:50:14
Quote from: Halc
Sprinkle events like dots almost at random on a piece of paperThe 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
Post by: paul cotter on 14/06/2022 09:30:18
Post by: evan_au on 14/06/2022 10:01:17
Quote from: paul cotter
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...
Post by: alancalverd on 14/06/2022 13:45:50
(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!
Post by: Eternal Student on 14/06/2022 17:16:09
(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.
Post by: alancalverd on 14/06/2022 18:26:31
(1) the human species is very likely to go extinct before reaching a “posthuman” stage;Species evolve, survive, or extinguish. So what?
Quote
(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!
Quote
(3) we are almost certainly living in a computer simulation....Non sequitur ex nihilo
Post by: Halc on 16/06/2022 00:39:23
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.
Quote
This is roughly what you seemed to be suggesting:I said that. In reality, a Lorentz transform must be used to rotate the paper. It isn’t Euclidean like paper is.
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.
Quote
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.
Quote
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.
Quote
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.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.
How finely? As much as you like, just not so much it becomes continuous.
I kind of lost you after that, but it already seems to doom the dot idea.
Post by: evan_au on 16/06/2022 22:55:20
Quote from: 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.
- 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...
Post by: Halc on 18/06/2022 06:06:41
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:Quote from: Halca 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
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.
Quote
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.
Post by: alancalverd on 18/06/2022 17:25:32
Post by: geordief on 18/06/2022 20:25:54
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.
Post by: Eternal Student on 18/06/2022 23:06:28
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.
Post by: alancalverd on 18/06/2022 23:14:30
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 17:25:32QuoteIf 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.
Post by: evan_au on 19/06/2022 09:29:37
Quote from: Halc
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
Quote
Faster-than-light causality. Objective state. All the things I detestHowever, 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.
Post by: geordief on 26/06/2022 14:50:22
The idea of quantisation of photon energy arose from a need to explain observations and is frequently misinterpreted.I remembered your post just now and want to ask you how it can be known that the energy levels can take any value?
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.
How is it required that some discreteness is not also embedded into that seeming continuum?
Post by: Deecart on 26/06/2022 21:07:43
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.