B Thought experiment: Beyond the slowest measurable speed?

[CelestialAeon]

I had this thought experiment when I ran into a cog system that had a simple idea behind it: Each cog in the system completes one turn only after the previous one has completed ten turns. If you chain let's say 40 such cogs, the last one is already rotating so slow that not even the time until heat death will be enough to have it rotate.

However, because the system is rigid and completely classically mechanic, there is no question about the forces / chain of transferred energy that is going on in the system, so it should be measurable and predictable, if we just would be able to take snapshots of the system throughout the aeons and see that each cog moves as presumed.

This made me question that how does this kind of steady, stable, predictable movement work in the universe, if the movement is so slow that it's past all the lowest observable limits, like Planck length? Somehow the accumulated movement is "there", hidden in time, but after enough time has passed, it should follow the theoretical model and eventually turn into actual observable miniscule movement.

This also brought to my mind the simulation hypothesis - if the Universe was a simulation, how would the underlying simulation logic model this? It should have a system in place that would allow arbitrarily small amounts of detail that would accumulate on hilarious timespans and still end up fulfilling the required models.

This is a humoristic scifi idea, but let's say that some alien civilization would be able to build such cog systems and spend unimaginable amount of years following them, just to see if the last cog actually moves as it should, or will it turn out that past certain speed limit, the "Universe just can't model it properly"? :)

I guess I'm interested mainly in this basic question that what does physics state about this kind of thought experiment and the lowest possible limit of speed that the system defines exactly and absolutely, yet makes it hard to observe?

 

[fresh_42]

This is, at its kernel, a philosophical question: what does infinity or its reciprocal mean in reality? I just watched a Veritassium video about AC. I think your question is along these lines. The concept of a point has a flaw. I have also read these days that an electron decays in $10^{35}\,s.$ I thought it was stable, but even if not, where is the difference? A professor of mine once said, "Reality is discrete." I admit that this can be discussed endlessly, but it remains a philosophical question. If you asked this in the classical physics forum, and I do not see the relevance of this question to quantum mechanics, I would have referred to the pitch drop experiment.

As long as we use continuous paths to model physics, as long as there will be infinitely slow processes.

 

[CelestialAeon]

Thank you for your answer! The main reason about this specific setup that made me curious was that for every second the gears turn, we can calculate the exact theoretical turn the last gear should have turned, no matter how small. So it is very concrete "thing" and not just philosophical. And as it can be built by trivial materials and make it work, we can with our own eyes look at the last gear while the first one revolves. So at the same time yes, it is a philosophical thought experiment, but on the other hand very concrete buildable system we can see without any intricate instruments.

 

[Dale]

The lowest speed is 0. The lowest speed that is distinguishable from 0 depends on your measuring device and experimental setup.

 

[PeroK]

I had this thought experiment when I ran into a cog system that had a simple idea behind it: Each cog in the system completes one turn only after the previous one has completed ten turns. If you chain let's say 40 such cogs, the last one is already rotating so slow that not even the time until heat death will be enough to have it rotate.

However, because the system is rigid and completely classically mechanic, there is no question about the forces / chain of transferred energy that is going on in the system, so it should be measurable and predictable, if we just would be able to take snapshots of the system throughout the aeons and see that each cog moves as presumed.

The motions of cogs are ultimately limited by the micoscopic size of atoms and by the laws of quantum mechanics.

 

[PeterDonis]

what does physics state about this kind of thought experiment

That depends on what physical model you use to describe it. You referred to a classical model in which each cog is perfectly rigid--but in relativity there is no such thing as a perfectly rigid body. I suspect there are probably other issues lurking beneath the implicit assumptions you are making.

the lowest possible limit of speed that the system defines exactly and absolutely, yet makes it hard to observe?

In our current physical theories, there is no such lower limit.

 

[PeterDonis]

it can be built by trivial materials and make it work

I am not at all convinced that this is actually true. You are talking about 40 cogs with a 1 to 10 gear ratio between each successive pair. That means a ratio of $10^{40}$ between the first and the last cog. Have you thought about what that implies about the size of this apparatus?

 

[DaveC426913]

I had this thought experiment when I ran into a cog system that had a simple idea behind it: Each cog in the system completes one turn only after the previous one has completed ten turns. If you chain let's say 40 such cogs, the last one is already rotating so slow that not even the time until heat death will be enough to have it rotate.

Somebody elseweb is two steps ahead of you.

They have constructed such a device. It has 100 step down gears. The claim is that the final gear will take longer than 13.7 billion years to complete one revolution.

[EDIT] Ah. Here. it is.


Gear ratio: 1:Googol. i.e. 1:10¹⁰⁰.

 

[DaveE]

 

[CelestialAeon]

I am not at all convinced that this is actually true. You are talking about 40 cogs with a 1 to 10 gear ratio between each successive pair. That means a ratio of $10^{40}$ between the first and the last cog. Have you thought about what that implies about the size of this apparatus?

The gears I saw were structured with two layers so that all the gears are of the same size and the transfer of ratio works through the smaller layer. Hence material / sizewise there is no issue. This is why I'm calling it a classical system, because you can see all the connected gears with plain eye, and the forces / connections between them are indeed, classically rigid. The only "problem" arises from the scaling down of the transferred movement. All the gears are connected exactly the same.

 

[CelestialAeon]

Somebody elseweb is two steps ahead of you.

They have constructed such a device. It has 100 step down gears. The claim is that the final gear will take longer than 13.7 billion years to complete one revolution.

[EDIT] Ah. Here. it is.


Gear ratio: 1:Googol. i.e. 1:10¹⁰⁰.

Thank you for this, exactly the kind of contraption I was thinking of, and "classical" as the gears are huge and visible for the plain eye. Isn't it weird to think that the last gear is actually turning right now, but how? :) Underneath the Planck length.

 

[DaveC426913]

Isn't it weird to think that the last gear is actually turning right now, but how? :) Underneath the Planck length.

Well, in theory, not in actuality.

For the last gear - in fact for most of them - to be actually turning would require impossible materials, impossible tolerances and cryo temperatures.

The gear is made of atoms. Carbon atoms - and their molecular bonds - are on the order of 10^-8cm.

Atoms bounce around a lot, as do the molecular bonds. That, and the fact that the gears are not infinitesimally in contact with each other. There is plenty of room for slop.

That alone fails the test at the 8th gear or so.

It is left to the reader to calculate how many of the 100 gears can be considered to be actually turning in, say, the one hour demo the guy posted.

 

[CelestialAeon]

Well, in theory, not in actuality.

For the last gear to be actually turning would require impossible materials, impossible tolerances and cryo temperatures.

The gear is made of atoms. Carbon atoms - and their molecular bonds - are on the order of 10^-8cm. They bounce around a lot, as do the molecular bonds. That, and the fact that the gears are not infinitesimally in contact with each other. There is plenty of room for slop.


It is left to the reader to calculate how many of the 100 gears can be considered to be actually turning in, say, the one hour demo the guy posted.

You're absolutely right — from a practical engineering standpoint.

If we tried to physically build this kind of ultra-slow gear chain using real materials, we’d hit hard limits almost immediately: atomic vibrations, mechanical slop, thermal noise, and manufacturing tolerances would completely swamp the minuscule intended motion long before it reached the final gear. We’re talking about rotations so slow that the edge displacement is far smaller than even the quantum 'fuzziness' of atomic positions.

But — my thought experiment is intentionally not about engineering feasibility. It’s about the philosophical and physical implications of ultra-slow, deterministic motion in the most fundamental models of reality.

The core question is this:

If a deterministic process causes a measurable outcome, but its rate of change is smaller than any physical or measurable unit (like Planck length per Planck time), does that motion still “exist” in a meaningful way?
In classical physics, the answer is yes. Motion is continuous and infinitely divisible.

In quantum mechanics, it becomes murky: uncertainty, quantization, and Planck limits suggest a possible breakdown of meaningful motion at extremely small scales — though this is still debated, especially in theories of quantum gravity.

And if we consider the simulation hypothesis — that reality may be underpinned by a computational substrate — then there may be a hard cutoff below which motion is no longer simulated or accumulated. In that context, the gear chain becomes a kind of conceptual “resolution probe.”

So, while I fully agree with your critique in terms of building a physical prototype — that’s not really the point. The question is:

Would the final cog still move — not in steel or carbon, but in physics itself?

Or does reality, at some deep level, round infinitesimal causality down to zero?

Thanks for the thoughtful response — it pushes the discussion in exactly the direction I was hoping: from gears to the limits of what we can meaningfully say about motion, time, and the fabric of reality

 

[CelestialAeon]

I'm also curious about where exactly in that built cog system is the point where the "turning of the cog" doesn't make any sense. It's way before the last one, but there can be found some point where we can still somehow in some realistic timeframe confirm the turn. Then it becomes fuzzy (at least for human timeline)

 

[Nugatory]

but its rate of change is smaller than any physical or measurable unit (like Planck length per Planck time),

You misunderstand what the Planck units are. As far as we we know, they aren't any sort of irreducible minimum size, it's not as if the Planck length is the pixel size of the universe.
https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

 

[lodbrok]

This is a humoristic scifi idea, but let's say that some alien civilization would be able to build such cog systems and spend unimaginable amount of years following them, just to see if the last cog actually moves as it should, or will it turn out that past certain speed limit, the "Universe just can't model it properly"? :)

I'm bemused by the highlighted statement. What do you mean by it? I wasn't aware that the Universe models anything.

 

[PeterDonis]

my thought experiment is intentionally not about engineering feasibility. It’s about the philosophical and physical implications of ultra-slow, deterministic motion in the most fundamental models of reality.

Would the final cog still move — not in steel or carbon, but in physics itself?

Sorry, but the distinction you are trying to draw here is not valid. There is no such thing as "physics itself" outside of actual, real materials doing actual, real things. And you are being given actual, real reasons based on the actual, real behavior of actual, real materials, why the implicit model you have of how your proposed device would work is not correct. It is no answer to that to say that you're asking about "physics itself" instead of an actual device.

 

[DaveE]

my thought experiment is intentionally not about engineering feasibility. It’s about the philosophical and physical implications of ultra-slow, deterministic motion in the most fundamental models of reality.

In which case I think your question is "philosophically" not well posed. Philosophically, we don't have a precise model of the universe. You can never precisely ignore QM (or similar theories). Nor do we have the capability to describe things as big as gears with a virtually uncountable number of QM states. In any case the universe simply isn't deterministic if you look closely enough.

This is a great example of the sort of philosophical navel gazing that physicists tend to dislike. It may be interesting to some, but it's ultimately unsolvable and useless. The extreme complexity does little to improve our understanding of the universe. It's just ridiculously hard for no real gain IMO.

 

[DaveC426913]

You're absolutely right — from a practical engineering standpoint.

Not just from an engineering standpoint. From a physics standpoint as well.

Atoms are physics. Molecules are physics. We did not engineer them. By their existence, they vibrate and slough and spall. Atoms live in the world above absolute zero, so they do this by nature.

Moreso, Einsteinian physics dictates that infinitely rigid materials cannot exist - because it would violate relativity - atoms can only transmit motion at the speed of sound of the material. As far as we now, that tops out at about 12km/s.

So slip and slop are intrinsic to the very nature of the solids of nature. That is encoded in our laws of physics as we know them today. It cannot be waved away by a thought experiment.

But — my thought experiment is intentionally not about engineering feasibility. It’s about the philosophical and physical implications of ultra-slow, deterministic motion in the most fundamental models of reality.

These are the fundamental models of reality. Your thoughts experiment cannot violate the mechanics of nature will-nilly.

Also, we don't do philosophy here.

Would the final cog still move — not in steel or carbon, but in physics itself?

Or does reality, at some deep level, round infinitesimal causality down to zero?

Thanks for the thoughtful response — it pushes the discussion in exactly the direction I was hoping: from gears to the limits of what we can meaningfully say about motion, time, and the fabric of reality

See above.

This thread surely will be locked if you continue down this road. It may be too late already.

 

[berkeman]

Thread is closed for Moderation...

 

[berkeman]

After a Mentor discussion, this thread will remain closed. The Physics questions in the OP have been answered, and we do not discuss the philosophical aspects of the OP's questions. Thanks to all who tried to help the OP.