Wikipedia:Reference desk/Archives/Science/2023 November 18

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November 18

Follow up: Here I'm strictly disproving the claim about the immeasurability of distances shorter than the Planck length. Am I right?

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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I rely on three well known and accepted formulas:

1. The Planck formula of the relativistic momentum: $p={\frac {m_{0}v}{\sqrt {1-v^{2}/c^{2}}}},$ where $m_{0}$ is the rest mass, $v$ is the velocity, and $c$ is the speed of light.

2. The De Broglie formula of the wavelength: $\lambda ={\frac {h}{p}},$ where $h$ is the Planck constant, and $p$ is the relativistic momentum.

3. The Planck length: $L={\sqrt {\frac {hG}{2\pi c^{3}}}},$ where $h$ is the Planck constant, $G$ is the gravitational constant, and $c$ is the speed of light.

From the combination of all three formulas mentioned above, it algerbraically follows that any object, whose rest mass is $m_{0}$, and whose wavelength can't be shorter than the Planck length, can't move faster than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$

Substituting the actual values for the constants indicated in the last formula, and substituting $m_{0}=1$ (i.e. one kg), it arithmetically follows that any object, whose rest mass is one kg, and whose wavelength can't be shorter than the Planck length, can't move faster than (approx.) - a third of a millionth of a meter - per second. But this conclusion contradicts the facts. Hence, a given object whose rest mass is one kg, can have a wavelength shorter than the Planck length. QED.

Am I right? If I am, then should this seemingly important information be added to our aticle in the chapter about the Planck length?

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 10:08, 17 November 2023 (UTC)

You're assuming an object whose mass is larger than the Planck mass — by assuming a limit on the Planck length while ignoring possible limits on the other quantities you are inviting inconistencies. And yes, that mass needs to be concentrated in a volume $\sim l_{P}^{3}$, so I'm not available as a counterexample. --Wrongfilter (talk) 11:49, 17 November 2023 (UTC)

I suspect I didn't understand your point. Actually, I didn't assume anything about the Planck mass, which does not appear in my proof. Let's ask you directly: Which step you don't agree with? Is it the three formulas mentioned in the beginning? Or is it the algebraic paragraph following them? Or the following arithmetic paragraph? Or what? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 12:01, 17 November 2023 (UTC)

You assume that a particle with a mass of 1 kg can exist. --Wrongfilter (talk) 12:05, 17 November 2023 (UTC)

By "a particle", do you mean an elementary particle? Does the De Broglie formula refer to elementary particles only? I was referring to a given body whose rest mass is one kg. Doesn't it exist? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 12:10, 17 November 2023 (UTC)

Yes, I mean elementary particles. That's why I wrote that the mass needs to be concentrated within $\sim l_{P}^{3}$. Take a composite particle like the neutron for instance: at moderate energies we can assign neutrons a de Broglie wavelength to describe neutron diffraction. But at the energies you're talking about you won't see the neutron, you'll see its constituent particles (Deep inelastic scattering), so those are relevant, not the composite neutron. --Wrongfilter (talk) 12:21, 17 November 2023 (UTC)

Does the De Broglie formula refer to elementary particles only? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 12:25, 17 November 2023 (UTC)

It can be applied to composite particles in situations where the inner structure is not important. --Wrongfilter (talk) 12:47, 17 November 2023 (UTC)

Besides the De Broglie fromula, is there a more general formula for calculating a wavelength of "regular" objects, like a simple ball made of metal, like that used in shot put and likewise? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 13:04, 17 November 2023 (UTC)

For what purpose??? That thing has a size that is many orders of magnitude larger than the Planck length that you want to probe. Do you think you can somehow magically shrink it down? --Wrongfilter (talk) 13:08, 17 November 2023 (UTC)

Now it's off topic, and I don't want you to search for such a more general formula, if it's not a well known one. But yes, now I'm just curious about whether one can calculate the wavelength of a "regular" object (like a simple regular ball made of metal and likewise), by a general well known formula, if the De Broglie formula is not applicable for "regular" objects. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 13:20, 17 November 2023 (UTC)

I already told you twice that you can use de Broglie in situations where it is appropriate. For more generality, use the equations of Schrödinger or Dirac, or the full apparatus of quantum field theory. And that's enough now. --Wrongfilter (talk) 13:24, 17 November 2023 (UTC)

Anyway, do all those physicists who accept the Planck length as a limit of all measurable lengths, actually impose a new upper bound - being $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}},$ for all velocities possible in nature - as long as elementary particles are concerned, whereas this limit is actually lower than the speed of light - as long as this elementary particle is a massive one? I'm just asking, not claiming anything. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 17:41, 18 November 2023 (UTC)

Yes one can associate a tiny wavelength less than the Planck length with a shot putt using the equation. But how are you going to measure it? In Quantum Mechanics you really have to talk about things that are observable. Or if you can think of a really nice theory that explains things better people can live with that and maybe someone in the future can think of a test. But you're not talking about anything like that. NadVolum (talk) 21:53, 17 November 2023 (UTC)

When you measure the ball's velocity, and then calculate its wavelength by the De Broglie formula, you actually measure the ball's wavelength. Just as, when you measure the length of the path traveled by a photon, and then calculate the time it took the photon to travel this path (by using the well known value of speed of light), you actually measure the time it took the photon to travel the path.

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 17:36, 18 November 2023 (UTC)

Plus see the note under "How can I get my question answered?" at the top of this page. "We don't answer requests for opinions, predictions or debate." Your 'disproving' is original research as far as Wikipedia is concerned and "We don't conduct original research or provide a free source of ideas, but we'll help you find information you need." I'm sure there's lots of places on the web for discussion - this is more akin to a library reference desk. NadVolum (talk) 22:02, 17 November 2023 (UTC)

1. When I asked "Am I right?", I was not asking about opinions, predictions or debate, nor about original reserch. I was just asking about whether my algebraic calculation was correct - algebraically speaking, and whether my arithmetic calculation (following the algebraic one) was correct - arithmetically speaking, and whether my logical conclusion (following the arithmetic calculation) was correct - logically speaking. I don't see any problem with asking questions whose answers are supposed to be clear cut, algebraically speaking, arithmetically speaking, and logically speaking.

2. As for my last question (if "this seemingly important information should be added to our article"), it seems you didn't interpret me well. I meant, that if you were going to answer my first (algebraic-arithmetic-logical) question - with an affirmitive answer, then you should notice that your answer may have consequences as to whether this seemingly important information should be added to our article. That's because, deriving clear cut conclusions - algebraically or arithmetically or logically, is never considered to be "original research" in Wikipedia. For example, adding the claim 2+5=3+4 to our article arithmetic, is not considered to be original research, as long as also the clear cut proof for this identity is added to that article.

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 17:34, 18 November 2023 (UTC)

Nonsense. You are engaging in synthesis and asking for opinion about its relevance and correctness within a specialized domain. Modocc (talk) 17:56, 18 November 2023 (UTC)

My first question ("Am I right?") was not about "opinion", but rather about whether my calculation was correct, algebraically and arithmetically and logically. As for my last question, it seems you didn't interpret me well. For the correct interpretation, please see the second paragraph - of my previoius response you've just responded to. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 18:02, 18 November 2023 (UTC)

Your conclusion: "...a given object whose rest mass is one kg, can have a [De Broglie] length shorter than the Planck length..." is already known. Modocc (talk) 18:16, 18 November 2023 (UTC)

I just remark, that if you think that such an object exists - then your legitimate answer is different from what Wrongfilter thinks - legitimately as well. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 18:24, 18 November 2023 (UTC)

This is clearly going nowhere. The Wikipedia reference desk isn't an appropriate forum to engage in debate as to whether mainstream physicists can't do algebra, or whatever the point is supposed to be... AndyTheGrump (talk) 18:35, 18 November 2023 (UTC)

You titled this thread "I'm strictly disproving the claim about the immeasurability of distances shorter than the Planck length." But obviously you have not. It's pointless Modocc (talk) 20:00, 18 November 2023 (UTC)

You've only quoted a part of the title, without quoting the main question in the title: "Am I right?". Meanwhile, I have received some different helpful answers to my question, including yours. Anyway, you haven't indicated if you think this object exists. Please notice that Wrongfilter thinks it doesn't. Your future answer to this aside question may influence the answer to my main question in the thread. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 20:10, 18 November 2023 (UTC)

Yes you asked that and the answer given is that you are wrong. To be clear, you are conflating measurement of actual lengths with the De Broglie length at those scales.. It's syn. Modocc (talk) 20:19, 18 November 2023 (UTC)

I've received some different helpful answers to my question, including yours. As to your answer: Let me understand you well: In the beginning you responded: "Your conclusion... is already known". So it's not wrong, because it's "already known". But now you're claiming that I'm "wrong". So I guess you're not referring now to what you referred to in the beginning, when you answered that my conclusion is "already known". So, would you like to be clearer, by quoting exactly my conclusion you do agree with (because it's "already known"), and my other conclusion you don't agree with (because it's "wrong")? I only want to understand you well. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 20:47, 18 November 2023 (UTC)

Note that I inserted [De Broglie] into your conclusion because it is entailed. Your algebra is fine. But it is a leap to generalize that to our understanding of Planck scale lengths. Modocc (talk) 20:59, 18 November 2023 (UTC)

Please note that despite the way the first sentence of the title is formulated, the whole title is actually intended to ask the question at the end of the title, rather than to conclude anything. My conclusions are actually intended to be presented under the title only.

So, besides the title, which is too general and asks a question rather than concludes, would you like to exactly quote my conclusion you don't agree with? When quoting, you are allowed to insert into it [in brackets] whatever you want to insert (I will identify it as your addition because it will be in brackets). Again, I only want to understand you well. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 21:41, 18 November 2023 (UTC)

Again you are fine when it comes to computing the De Broglie matterwave wavelengths. This is known. Furthermore, however, that does not preclude any hard limit(s) to the scale(s) we can actually measure to confirm or rule out their existence. In other words you have not proved there isn't such limits. Modocc (talk) 22:05, 18 November 2023 (UTC)

Since you still refrain from quoting any conclusion of mine which you don't agree with, let me ask that from another direction: Do you agree, that whoever accepts the Planck length as a limit of all measurable lengths, actually imposes a new upper bound - being $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}},$ for all velocities possible in nature - of any object (or at least of any elementary particle), whereas this limit is actually lower than the speed of light - as long as this object is a massive one? I'm only asking, not claiming anything. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 22:58, 18 November 2023 (UTC)

I'm not versed in their theories enough to know. Modocc (talk) 23:59, 18 November 2023 (UTC)

Do you agree to my algebraic paragraph (containing the identity of "v=..."), which is presented under the title of this thread? If you don't, please let me know. If you do agree, then this logically entails you agree that whoever accepts the Planck length actually imposes the upper bound mentioned in my previous response you've just responded to. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 00:15, 19 November 2023 (UTC)

You said "...or at least of any elementary particle..." so of course context matters with respect to what lengths one is talking about, and I do not know (and certainly you don't) what I'd agree with. Which is basically what I said already and then some. Modocc (talk) 01:42, 19 November 2023 (UTC)

Let's be more precise, and refer to elementary particles only. So, do you agree to my algebraic paragraph (containing the identity of "v=..."), which is presented under the title of this thread, if all objects are elementary particles only? If you don't agree, please let me know. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 03:20, 19 November 2023 (UTC)

I'd like to respond a little more generally (and hopefully succinctly). In most well-established fields of science, it is rare, to the point of almost never happening, for anyone to come along and upend a core tenant or basic premise of that scientific field. Usually, there are small, incremental advances within those fields. Sure, there are some revolutionary discoveries that drastically change our understanding of the universe, but oftentimes even these don't truly upend the basic premises of their fields. Take the discovery of DNA; this enabled great advancement in our understanding of heredity and molecular biology, but by the time of its discovery, the field of biology generally agreed that there was some sort of genetic material responsible for trait heredity and changing of alleles within populations. We just didn't know what that genetic material was. By discovering DNA, we could explore further and more accurately how things like molecular biology, evolution, etc. work, but biology generally already accepted that they did work with a genetic material.

What you are trying to do here amounts to upending a core premise of modern quantum physics. That type of revolution in a scientific field almost never happens. The discovery of quantum theory itself was such a revolution, and I can't really think of many others. When such revolutions occur, they are never the result of just some thought experiments and thinking "this doesn't make sense to me, I think I know better!" They come about because of some major observable experimental property within our universe doesn't fit with our current accepted scientific models. In the case of quantum mechanics, this was the ultraviolet catastrophe, where while existing classical mechanics correctly described how much energy would be emitted by black bodies at large wavelengths, it failed utterly at shorter wavelengths. We could directly, experimentally observe that our existing classical model of physics was not correctly predicting real world behaviors. That was the motivation for trying to come up with something better; there was a real, observable reason, and the solution to it required an entirely revolutionary view of physics, that being quantum mechanics.

So... what is your ultraviolet catastrophe? What is your physical, observable flaw that does not match the predictions of quantum mechanics. --OuroborosCobra (talk) 22:31, 18 November 2023 (UTC)

Oh, please don't exaggerate. OP is not trying to do anything of the sort. They're just trying to find a flaw in a plausibility argument for the Planck length being some sort of lower limit. This is not an established theory. Their reasoning is not even that bad; it fails because they did not recognise that there is more than assumption in the argument and that they cannot single out one assumption as "disproved" before checking all the others. --Wrongfilter (talk) 22:48, 18 November 2023 (UTC)

At this point, I don't want to disprove anything. I'm only asking if you agree, that whoever accepts the Planck length as a limit of all measurable lengths, actually imposes a new upper bound - being $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}},$ for all velocities possible in nature - as far as the elementary particles are concerned, whereas this limit is actually lower than the speed of light - as long as the elementary particle is a massive one (i.e. is not a photon, nor a gluon, nor a gravition). At this point, I'm only asking, rather than trying to disprove anything. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 23:12, 18 November 2023 (UTC)

@Wrongfilter The idea of a quantized universe in basically all qualities, including dimensionally, is very core to quantum mechanics. I would definitely argue that they are trying to basically upend quantum mechanics, and without a demonstrable reason (like the ultraviolet catastrophe). --OuroborosCobra (talk) 00:01, 19 November 2023 (UTC)

@OuroborosCobra In quantum mechanics (non-relativistic or relativistic) and quantum field theory spacetime is an inert background, the stage on which the fields do their thing, and it is treated as a continuum. Quantization of spacetime is still essentially speculation, there's no full theory (the elusive marriage of quantum theory and general relativity!) and there are few ideas that make predictions that could be experimentally verified. Disclaimer: I'm not following the field closely, so I may have missed some recent developments.--Wrongfilter (talk) 02:55, 19 November 2023 (UTC)

I'm not trying to upend quantum mechanics, but rather to ask you the simple question I've asked you in my first response to you below. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 00:19, 19 November 2023 (UTC)

@OuroborosCobra: I have no ultraviolet catastrophe, nor can I point at any physical observable flaw that does not match the predictions of quantum mechanics. At this point, I'm only asking if you agree with my algebraic conclusion (under the title of this thread), that whoever accepts the Planck length as a lower bound/limit for all lengths possible in nature, actually imposes a new upper bound - being $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}},$ for all velocities possible in nature - as far as the elementary particles are concerned, whereas this upper bound/limit is actually lower than the speed of light - as long as the elementary particle is a massive one (i.e. is not a photon, nor a gluon, nor a gravition). At this point, I'm only asking, rather than trying to present any ultraviolet catastrophe. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 23:34, 18 November 2023 (UTC)

Calculating the wavelength of a kilogram ball using de Broglie's relation is not the same as measuring it. The wavelength of electrons has been measured using crystals which diffract them. Even some quite big molecules have been diffracted and their wavelength can be measured from that. But if there is some problem with very large masses how would we measure the wavelength? We are not talking about all lengths possible but all lengths measurable - and saying it is very possible something strange happens at a length where we know measurement becomes a rather nebulous concept. Information is an actual real thing for quantum mechanics and if information is not needed or is spread around in some strange way at those sizes because theres no good way to measure it then talking about actual lengths of those sizes is not a very well founded idea. NadVolum (talk) 00:49, 19 November 2023 (UTC)

I understand your point regarding the strange things that may happen at a length where we know measurement becomes a rather nebulous concept, as well as your point regarding the information that may get spread around in some strange way at those sizes.

However, can you point at the exact substantial difference between:

1. Measuring the length of the path traveled by a given photon, and then - using the well known value of speed of light - for calculating the time it took the photon to travel this path.

2. Measuring a given ball's momentum, and then calculating its wavelength by the De Broglie formula.

If the first calculation can be regarded as an act of measurement (can't it?), why can't the second calculation be regarded as an act of measurement? Where is the substantial difference?

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 01:22, 19 November 2023 (UTC) 01:22, 19 November 2023 (UTC)

NadVolum gave us examples of the waves' measurements did he not? They have been empirically verified. The same cannot be said for your ball even though its wave possibly exists at all scales. We don't know, but it's unlikely. Modocc (talk) 01:54, 19 November 2023 (UTC)

In my recent question to NadVolum, I asked about the substantial difference between calculating a distance traveled by a photon, and calculating a ball's wavelength. Your point does not refer to this difference, but rather to the examples given by NadVolum, which are not what I recently asked NadVolum about. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 03:20, 19 November 2023 (UTC)

Regarding that "ball". If you're still thinking about that shot-put thingie, that is made up of some 10²³ atoms, which in turn consist of electrons and nuclei, protons, neutrons, gluons, whathaveyer. The ball is an "object" only for low-energy interactions, such as you picking it up. At higher energies the ball dissolves into a bunch of its constiuents. An interaction that would probe structure on the Planck scale would involve a single elementary particle within that ball and it would be ignorant of everything else because everything else would be almost infinitely far away. The de Broglie wavelength of that particle would be relevant, not that of the entire ball. --Wrongfilter (talk) 03:07, 19 November 2023 (UTC)

Now I'm only thinking about elementary particles, rather than about the ball. Do you agree, that whoever accepts the Planck length as a limit of all measurable lengths, actually imposes a new upper bound - being $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}},$ for all velocities possible in nature - as far as the elementary particles are concerned, whereas this limit is actually lower than the speed of light - as long as the elementary particle is a massive one (i.e. is not a photon, nor a gluon, nor a gravition)? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 03:20, 19 November 2023 (UTC)

De Broglie waves smaller than their Planck limit are not modeled, correct? In other words, these forbidden waves are not likely to be relevant to their model and this calculation becomes inapplicable... Regardless, velocities are arbitrarily dependent on one's reference frames, so no there is no new limit. Modocc (talk) 05:56, 19 November 2023 (UTC)

Before I respond to your first point ("De Broglie waves smaller than their Planck limit are not modeled"), let me just present a logical fact (which I guess you agree to): If any situation involving a given assumption is not modeled, and this assumption is algebraically provable from a second condition, then you can algebraically prove that any situation involving the second condition is not modeled. Agree?

I guess you accept the previous logical paragraph (don't you?), so now I take your first sentence, and use it for asking you whether you accept the following two claims:

A. It's algebraically provable (by means of the combination of all three formulas appearing under the title), that any elementary particle - whose De Broglie wave is not shorter than the Planck length - moves by a velocity not higher than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$

B. If any elementary particle - whose De Broglie wave is shorter than the Planck limit - is not modeled, then from this assumption - you can algebraicaly prove (by means of A) - that any elementary particle whose velocity is higher than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}$ is not modeled, agree? BTW please notice that this limit (for all modeled velocities) is actually lower than the speed of light, as long as the elementary particle is a massive one (i.e. is not a photon, nor a gluon, nor a gravition).

As to your second point ("velocities are arbitrarily dependent on one's reference frames"), let me just remind you the correct formulation: Almost every velocity is arbitrarily dependent on one's reference frame, unless this velocity is a limit. By the way, according to Relativity theory, there is one limit only, being the speed of light. What I was trying to ask you in the beginning was whether, accepting the Planck length as a limit of all modeled lengths in nature, algebraically entails a lower limit - but this time it's only a limit of all modeled velocities in nature (hence this is not the kind of limit imposed by Relativity theory).

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 08:43, 19 November 2023 (UTC) 08:43, 19 November 2023 (UTC)

No, it's not "unless it's a limit", it's "unless it's $c$". It doesn't have anything to do with it being a limit (although that is a consequence), it's because the cone of spacetime paths corresponding to speed $c$ is invariant through Lorentz transformations of spacetime. ChaotıċEnby(talk) 09:38, 19 November 2023 (UTC)

Logically speaking, it must be formulated "Unless it's a limit", which is actually C according to Relativity theory which relies on empirical facts - like Lorentz transformations of spacetime - rather than on logical facts. Other theories, actually some wrong ones, may claim that the limit is not C but rather pi, but they will still agree to the previous general concensual formulation: "Unless it's a limit", which is actually pi according to those (wrong) theories, and which is C according to Relativity theory - because Relativity theory assumes Lorentz transformations of spacetime - which are not assumed by those (wrong) theories. Anyway, those pi-theories are only wrong because of empirical facts (like Lorentz transformations of spacetime), rather than because of logics. Logically speaking - they are not wrong. Therefore, Logically speaking, the general concensual formulation must be formulated "Unless it's a limit" - which is actually C according to Relativity theory.

Anyway, this nuance is semantic only. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 09:52, 19 November 2023 (UTC)

This nuance is not semantic if you're literally using it to argue there's another speed invariant through Lorentz transformations. Also, I don't know any theory that claim the limit is pi (or anything else than c), so that's not an argument that really holds.

In any case, if you're suggesting a complete modification to special relativity, getting it on Wikipedia isn't the first step, by far. If it's so logically evident, publishing it in a journal or anything else should be easy, and then it could be sourced back on Wikipedia. ChaotıċEnby(talk) 10:41, 19 November 2023 (UTC)

As for the first sentence of your first paragraph: By "this nuance is sementic" I meant, that even Einstein would agree to the formulation: "Almost every velocity depends on the reference frame, unless this velocity is a limit, which is actually C according to my Relativity theory". Similar formulations appear a lot in his works, something like "if the [Relativity] theory corresponds to the empirical facts then...". So, no: I'm not "arguing" anything. I'm only asking whether, taking the Planck length as a limit of all measurable lengths, necessarily imposes another upper bound for all (modeled) velocities in nature. That's because, it's algebraically provable (by means of the combination of all three formulas appearing under the title of this thread), that any elementary particle - whose De Broglie wave is not shorter than the Planck length - moves by a velocity not higher than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$ BTW please notice that this limit is actually lower than the speed of light, as long as the elementary particle is a massive one (i.e. is not a photon, nor a gluon, nor a gravition).

As for your second sentence of your first paragraph: Me either. All I said was said hypothetically, as I emphasized "logically speaking". Anyway, the formulation "unless this velocity is a limit" is agreed upon by both Relativity theory and by any other (hypothetical) theory, because this formulation says nothing about what this limit really is: Einstein would say this limit is C, but would still agree to this formulation, so I can't see why you don't agree to a formulation to which even Einstein would agree - because it does not contradict Relativity theory.

As for the first sentence of your second paragraph: No, I'm not suggesting a modification to special relativity, I'm only asking whether, taking the Planck length as a limit of all measurable lengths, necessarily imposes another upper bound for all (modeled) velocities in nature, because of the algebraic explanation mentioned above. Please notice, that for accepting an additional upper bound - lower than C, you don't have to disagree with C: You can still agree with Relativity theory, that no object can move by a velocity higher than C, and that every massive object's velocity must be lower than C, and still you can - hypothetically and without contradicting Relativity theory - claim that no elementary particle's velocity can be higher than the new upper bound - which is actually lower than C for massive elementary particles.

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 12:50, 19 November 2023 (UTC)

Op, you asked only about massive particles for which v<c. Neither Point A and Point B are correct. De Broglie waves exceeding the limit imposed by quantization or the Planck length would not imply that the particles (and the waves when they can be shown to manifest at lower speeds) are not modeled anyway near c. It's not inconsistent as long as it mirrors the empirical data. The equation describes only the De Broglie wave length not all lengths. Modocc (talk) 13:34, 19 November 2023 (UTC)

Let's focus on point A: this is actually a fully algebraic argument: It's algebraically provable (by means of the combination of all three formulas appearing under the title), that any elementary particle - whose De Broglie wave is not shorter than the Planck length - moves by a velocity not higher than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$ If you don't agree to A (as you claim now), then could you please give us numerical values of a counterexample, without contracdicting any of the three formulas indicated under the title of this thread? By a counterexample I mean, any elementary particle (e.g. an electron or whatever) - whose De Broglie wave is not shorter than the Planck length - and which moves by a higher velocity, that is: $v>{\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$ 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 14:11, 19 November 2023 (UTC)

Choose a velocity. Any will do. Solve for the particle's mass at your supposed velocity limit. The Planck length formula is perhaps applicable up until that velocity for that mass. If it moves any faster that formula becomes inapplicable with their model (presumably there is no wave above that speed to measure because of the imposed limit). BTW, most mediums in fact do have phase velocity constraints far less than c. Modocc (talk) 14:35, 19 November 2023 (UTC)

I asked for numerical values that don't contradict the three (concensual) formulas mentioned under the title of this thread. You (Modocc) haven't supplied such values. Instead, you (Modocc) said "Choose a velocity...". This is not what I asked for. Your (i.e. Modocc's) expected answer should have been something of the sort: "Here is Modocc's choice: the particle's invariant mass is..., and the particle's De Broglie wavelength is..., and the particle's velocity is...".

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 14:57, 19 November 2023 (UTC) 14:57, 19 November 2023 (UTC)

Can we please stop this now? IP has conclusively shown that in their world, where physics consists of three formulas and the assumption that massive particles can have any velocity <c, there is no lower limit to the de Broglie wavelength. Let IP enjoy their Nobel prize in their world, and let the rest of us move on in our world where physics is a bit more complicated than that. --Wrongfilter (talk) 15:16, 19 November 2023 (UTC)

I didn't understand your point, maybe because I couldn't decipher what IP stands for (I guess you didn't mean Internet protocol). 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 15:23, 19 November 2023 (UTC)

IP means a user identified by their internet protocol address - here that means you. You could also have been referred to as the OP, that stands for original poster. NadVolum (talk) 16:15, 19 November 2023 (UTC)

Thank you for clarifying that by IP they meant internet Protocol, which I thought they didn't. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:52, 19 November 2023 (UTC)

I'm asking if there is any flaw in my algebraic calculation. I can't see here any nobel prize. Only an innocent algebraic question. If I thought my innocent question were worth a nobel prize, I wouldn't present it publically. Again, it's only an innocent question.

Anyway, our world obeys thousands of formulas, including the three presented under the title of this thread, so I see no methodological problem in asking whether our world, which obeys also those three formulas, must obey the conclusion I've algebraically derived from those three formulas. The only question remaining is whether my calculation is correct. This is what I'm asking. The fact that our world obeys also other formulas, does not prevent us from deriving conclusions from any sub-set of the whole set of all formulas our world obeys, so I can't understand your point. Just as I'm allowed to derive the conclusion 2p=2mv from the formula p=mv, even though there are many other formulas I didn't use in this calculation. Not every formula our world obeys must be used when deriving conclusions from a small sub-set of formulas. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:50, 19 November 2023 (UTC) 16:50, 19 November 2023 (UTC)

Your conclusion hinges on the assumption that the de Broglie wavelength of a moving massive object cannot be less than the Planck length. The basis of this assumption is not explained, but under this assumption one may indeed conclude that the Planck length is a lower bound on an object's wavelength, implying some upper bound v_lim on its speed (in some inertial frame). Since velocity is relative, an equally massive observer may be moving with 99% of that speed in the opposite direction, so it then follows that (unless v_lim is getting close to lightspeed) the upper limit is actually more like v_lim/100 in the original inertial frame.  --Lambiam 21:39, 19 November 2023 (UTC)

Lambiam, the OP also wrote "...it arithmetically follows that any object, whose rest mass is one kg, and whose wavelength can't be shorter than the Planck length, can't move faster than (approx.) - a third of a millionth of a meter - per second. But this conclusion contradicts the facts. Hence, a given object whose rest mass is one kg, can have a wavelength shorter than the Planck length. QED. Am I right? If I am, then should this seemingly important information be added to our aticle[sic] in the chapter about the Planck length? " The OP is sure to ask if he is right again. Modocc (talk) 00:02, 20 November 2023 (UTC)

We cannot just add this as the fruit of original research, but there are reliable sources that mention that the de Broglie wavelength of a moving massive object can be less than the Planck length, e.g.:

The de Broglie wavelength of a walking human being is actually below the Planck length of 10⁻³⁵ m — and one can currently only speculate about the meaning of any wave physics with dimensions below that scale.^[1]

Note that none of this contradicts the claim that we cannot measure distances shorter than the Planck length, so it does not tell us anything about the Planck length. So while I think this can be added, the appropriate place would be the article Matter wave, since the "important information" is that wave physics then loses the connection with anything that is observable: we enter terrain where its predictions are neither verifiable nor falsifiable.  --Lambiam 10:26, 20 November 2023 (UTC)

The important information, about which I asked whether it should be added to Wikipedia (actually to our article Planck units), was not about waves, nor about wave physics, but rather about measurable velocities (as I have explained several times to user:Modocc), so the question is actually whether our article Planck units should contain the following seemingly important information: Just as Relativity theory imposes an upper bound - being $c$ - for all velocities (whether measurable or not) in nature, so whoever accepts the Planck length as a limit of all measurable lengths - actually imposes an upper bound - being ${\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}$ - for all measurable velocities in nature (An additional fact is, that this upper bound for all measurable velocities is actually lower than the relativistic upper bound for all velocties, as far as the elementary particles referred to are massive). To avoid original research, we can add the algebraic proof for this upper bound, can't we? (Just as, adding the claim 2+5=3+4 to our article arithmetic, is not considered to be original research, as long as also the clear cut proof for this identity is added to that article). This is what I was asking about. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 15:28, 20 November 2023 (UTC)

The title of this question states "Here I'm strictly disproving the claim about the immeasurability of distances shorter than the Planck length. Am I right?" The calculation is right, but the conclusion on measurability of distances shorter than the Planck length is wrong. The de Broglie wavelength of a macroscopic objects can be shorter than the Planck length, but this has no physical consequences, so there's no problem.

Take a visible light microscope. You can use it to see details down to the wavelength of the light. Take an electron microscope. You can use it to see details down to the de Broglie wavelength of the electrons. Take a cannonball scattering experiment. No, you can't see details down to the de Boglie wavelength of the cannonballs, but only down to the diameter of those cannonballs.

That you can calculate something less than the Planck length doesn't mean you can measure it, or that it's physically real. PiusImpavidus (talk) 10:25, 20 November 2023 (UTC)

I think that has already been said enough times but something they can relate to is needed if one is to bother with this. How about this. Suppose you have vehicles going along a road and they make a higher rumbling the faster they go. You calculate the wavelength of a rumbles - does that measure a length along the road? Well no because the road when you look at it finely is all corrugated and the tyres are giving a rumble because of that texture. The distance an ant would have to go along the road would be much greater than the distance a car has to go to get to the same place. Calculating the distance was not the same as measuring it. NadVolum (talk) 11:55, 20 November 2023 (UTC)

See below. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 15:28, 20 November 2023 (UTC)

As I have explained several times to user:Modocc, the question is actually whether, just as Relativity theory imposes an upper bound - being $c$ - for all velocities (whether measurable or not) in nature, so whoever accepts the Planck length as a limit of all (modeled) measurable lengths - actually imposes (does it?) an upper bound - being ${\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}$ - for all measurable velocities in nature (BTW This upper bound for all measurable velocities is actually lower than the relativistic upper bound for all velocities, as far as the elementary particles referred to are massive). 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 15:28, 20 November 2023 (UTC)

The Planck length is not an accepted limit. It is not even the only such unit proposed, see Stoney units. Hence, it or anything added like it requires a reliable source. Modocc (talk) 17:13, 20 November 2023 (UTC)

Sorry, by asking whether "the Planck length actually imposes an upper bound for all measurable velocities", I meant to ask whether "whoever accepts the Planck length as a limit of all measurable lengths - actually imposes an upper bound for all measurable velocities".

I've just fixed it above, in my previous response you responded to. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 18:30, 20 November 2023 (UTC)

And the answer is the calculated de Broglie wavelength does not impose any limit on speed that anyone knows of. But that wavelength may not correspond to a physical length. It is very possible the world gets rather like the tar on the road I was talking about at those type lengths. There's good arguments the three dimensions of the world are in some way constructed from two dimensions, other arguments that space is just a few of the dimensions and others are wrapped up and not visible, and there's physicists who think our space may actually be an emergent quantum phenomenon rather than 'really' existing as a background. What is known is that quantum mechanics is incomplete and there's some problems about space to be solved. NadVolum (talk) 18:05, 20 November 2023 (UTC)

Sorry, by asking whether "the Planck length actually imposes an upper bound for all measurable velocities", I meant to ask whether "whoever accepts the Planck length as a limit actually imposes an upper bound for all measurable velocities".

I've just fixed it above, in my previous response you responded to. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 18:30, 20 November 2023 (UTC)

The answer is even if the Planck length was a physical limit it is quite possible that it would not affect anything at all that we could measure. NadVolum (talk) 18:37, 20 November 2023 (UTC)

Let's try from another direction:

Do you agree to the following:

It's algebraically provable (by means of the combination of all three formulas appearing under the title), that any elementary particle - whose De Broglie wave is not shorter than the Planck length - moves by a velocity not higher than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$

BTW this value is actually lower than c, as far as the elementary particle referred to is massive.

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 18:48, 20 November 2023 (UTC)

You seem to have some idea about the world that I'm not able to engage with so I think it best I not try any further. NadVolum (talk) 21:26, 20 November 2023 (UTC)

Please notice that my last question to you was a purely algabraic one, which has nothing to do with any idea about the physical world. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 21:57, 20 November 2023 (UTC)

The reference desk is not a discussion forum. What we may or may not agree to is irrelevant. If you feel something is worth adding to an article, be bold, but make sure it is not original research but sourceable to a reliable source while not giving undue weight to one particular point of view.  --Lambiam 13:40, 21 November 2023 (UTC)

My comment about whether any addition should be added to articles in Wikipedia, was an aside remark. My main question was an algebraic one, and since I consider you as a very good methematician, I would be glad to receive your proessional answer to this question, which is whether:

A. It's algebraically provable (by means of the combination of all three formulas appearing under the title of the current thread), that any elementary particle - whose De Broglie wave is not shorter than the Planck length - moves by a velocity not higher than $v={\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}.$

B. just as Relativity theory imposes an upper bound - being $c$ - for all velocities (whether measurable or not) in nature, so whoever accepts the Planck length as a lower bound of all measurable lengths - actually imposes (does it?) an upper bound - being ${\frac {c}{\sqrt {1+m_{0}{\sqrt {\frac {Gc}{2\pi h}}}}}}$ - for all measurable velocities in nature (BTW This upper bound for all measurable velocities is actually lower than the relativistic upper bound for all velocities, as long as the elementary particles referred to are massive).

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 14:21, 21 November 2023 (UTC)

With regard to A: Yes, the algebraic calculation is correct. I've verified it.

With regard to B: I will check it out soon, and will try to answer you shortly.

HOTmag (talk) 17:23, 21 November 2023 (UTC)

If the people accepting the Planck length as a limit of all measurable lengths also agree that measuring the speed of a massive object is equivalent to measuring its de Broglie wavelength, you are correct. It is however foreseeable that some will argue that you can measure the speed of a macroscopic object and use the result to calculate its presumed theoretical wavelength, but that this is not the same as measuring its wavelength. (Scientists have calculated that the temperature of the Solar core is 15 MK, but they have devised no way of measuring it.) I also expect that in court, after getting a speeding ticket, your argument that your speed was not measurable will not fly.  --Lambiam 21:59, 21 November 2023 (UTC)

@Lambiam: When I measure the length of a path traveled by a photon, and then calculate the time it took the photon to travel this path - by my using the well known value of speed of light, don't you agree I actually measure the time it took the photon to travel the path? An analogous question can be asked about your example regarding the solar core, as well as about measuring lengths by calculating them. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 17:31, 23 November 2023 (UTC)

By definition, speed equals distance travelled per time elapsed. There is no similar relation between the observable aspects of the Sun and the temperature of its core; the calculation is based on an extrapolation from theoretical models beyond what can be verified or falsified.  --Lambiam 22:30, 23 November 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Cities in the Cold Desert climate BWk

Is there a site where they show the cities or localities that are located in the Cold Desert climate (BWk) areas? Donmust90 Donmust90 (talk) 01:29, 18 November 2023 (UTC)

@Donmust90 You can download good climate maps from this site. The maps don't have geographic features such as cities shown but it should be possible to overlay such data from other sources. Mike Turnbull (talk) 15:17, 20 November 2023 (UTC)