Wikipedia:Reference desk/Archives/Science/2023 November 12

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November 12

Unconventional metro train

Are there any metro systems where, instead of conventional flanged wheels on conventional rails, the trains run on diagonally-inclined wheels in matching grooves in a concrete trough-shaped guideway? If so, how do they switch trains between different tracks? What kinds of advantages and disadvantages would such a system have? 2601:646:9882:46E0:C195:DC40:D019:40A6 (talk) 07:47, 12 November 2023 (UTC)

No. You may be thinking of a guided bus which is not generally considered a metro system. They use a concrete guideway so that they can switch to normal road running, not a different type of track. I've never heard of any of these using diagonally-inclined wheels, which would defeat the object. Shantavira|^{feed me} 09:18, 12 November 2023 (UTC)

You may be thinking of a monorail, some designs of which do indeed use a V-rail. Martin of Sheffield (talk) 10:43, 12 November 2023 (UTC)

Well, I was thinking of a kind of inside-out monorail, where instead of the V-rail being between the wheels, the inclined wheels are between inclined rails set into the walls of a concrete trough. (I take it there aren't actually any examples of this kind of system?) 2601:646:9882:46E0:14C6:F9B5:5479:2A27 (talk) 03:13, 13 November 2023 (UTC)

I've a vague recollection of having seen what you describe in a suspension-type monorail. Can't give you a reference of any sort though, sorry. Martin of Sheffield (talk) 10:54, 13 November 2023 (UTC)

A disadvantage of slanted wheels is the torque caused by the base of the wheel not being directly below its centre, which will demand much more from the bearing.  --Lambiam 11:59, 12 November 2023 (UTC)

Plank length: Why is it impossible to measure a length shorter than the Planck length?

From our article discussing the Plank length, I understand the following: theoretically, for measuring a length shorter than the Planck length, there is no choice but to create a high-energy collision between particles, which is actually supposed to create a black hole [whose radius is shorter than the Planck length, while it is not possible to measure the internal event horizon of a given black hole - and therefore also the internal event horizon of the aforementioned tiny black hole].

In the previous paragraph, the addition in the brackets is not indicated in the article, but is an addition of my own.

Did I understand correctly, why it's impossible to measure a length shorter than the Planck length? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 14:19, 12 November 2023 (UTC)

(BTW, it's Planck, not Plank as in your links). No. I think you are mistaken. As I understand it, and interpret the whole of the sub-section from which you have excerpted (and I may well be wrong), 'space' is quantised and there cannot be a length smaller than the Planck length (not just that one cannot measure any smaller). Trying to create conditions in which a smaller length could be 'created' and measured will instead create a singularity/black hole, not smaller than a Planck length, distorting space to the extent that meaningful lengths and measurements would be respectively meaningless and impossible. In effect, one would destroy the space one was trying to measure.

Of course, all this is trying to describe in macroscopic 'classical' terms (which is how our minds work) things that can really only be realistically described by esoteric mathematics. Maybe someone else can do a better (and more accurate) job? {The poster formerly known as 87.81.230.195} 94.2.5.208 (talk) 15:11, 12 November 2023 (UTC)

Please notice I had typed "Planck" four times. "Plank" was typed only twice, but it was a typo. Anyway, I still didn't understand why there cannot be a length smaller than the Planck length. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:30, 12 November 2023 (UTC)

To a chemist like me the crucial problem is the measurement part. What would you use to measure such a small length? At 10^-20 the size of a proton, you're going to find it difficult to construct anything! We can imagine things that small or smaller but we are unlikely to be able to build them. Mike Turnbull (talk) 15:48, 12 November 2023 (UTC)

Per our article mentioned in the title, one can prove that it's impossible to build any object (e.g a photon or an electron) whose wavelength is shorter than the Planck length. Is there really such a proof? If there is, what is it exactly? Our article intends to present such a proof, but I didn't understand it well (if at all). 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:23, 12 November 2023 (UTC)

Shorter wavelengths are equivalent to higher energy, and energy is equivalent to mass, if that helps. Remsense聊 16:27, 12 November 2023 (UTC)

No, it doesn't help, because I was not asking about the Planck mass. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:33, 12 November 2023 (UTC)

I was not telling you about the Planck mass. I was underlining the connection between distance (wavelengths), energy, and mass. Remsense聊 16:34, 12 November 2023 (UTC)

I'm sure you didn't interpret me well. I hadn't asked about the Planck mass, because it's approximately 20 micrograms, so how can it be of help in our discussion? Are you really claiming that no mass bigger than 20 micrograms can exist in the universe? Of course such a mass can exist, and I had already known that, and that's why I claimed the Planck mass can't be of help in our discussion. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:44, 12 November 2023 (UTC)

I did not say anything about the Planck mass at any point. Remsense聊 16:46, 12 November 2023 (UTC)

The connection between wavelength and mass is well known, but if you didn't intend to use the Planck mass for proving the impossibility of the existence of distances shorter than the Planck length, then how did you think one can use the wavelength-mass connection for proving the impossibility mentioned above? 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 16:51, 12 November 2023 (UTC)

I thought the point was that the density of the mass arising from such short wavelengths, confined in such a small volume, inevitably formed a singularity. However, I may be entirely wrong. Is there a quantum physicist in the house? {The poster formerly known as 87.81.230.195} 94.2.5.208 (talk) 04:44, 13 November 2023 (UTC)

Length and volume are two different things: Geometrically speaking, there can be a length shorter than the Planck length, yet the width can be very long, so the volume can be very big as well. However, your explanaiotn is a bit similat to Gott's explnation, See below. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 07:55, 13 November 2023 (UTC)

The act of measuring requires events which involve elementary particles with a short enough wavelength which implies a large enough energy. It is possible to use statistics with enough lower energy events to infer such things instead but the Planck length is so small even that looks a pretty hopeless undertaking. NadVolum (talk) 12:22, 13 November 2023 (UTC)

Yes, the Planck length is very small, but also $10^{-3}$ mm is very small, and $10^{-100}$ mm is even smaller than each of them, so what's so special with the Planck length, that makes the Planck length the limit of all measurements of lengths? I'm looking for a clear proof, or at least a simple intuition, regarding the Planck length, as that limit.

Additionally, our article mentioned in the title ascribes the Planck length to the creation of a (tiny) black hole, but it's really so tiny (visually) that I can't see it (visually) inside your explanation. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 12:52, 13 November 2023 (UTC)

My (amateur) understanding of this is that you should not think of the Planck length as being any sort of sudden hard limit to measurement, as though you could measure 1.01 Planck lengths but not 0.99. Rather, it's the approximate scale where the techniques we're used to at a macroscopic scale start to break down in ways that are, for fundamental reasons, difficult to work around.

For example, in general, to achieve image resolution on a scale of λ/4, you need to use light with a wavelength of at most approximately λ. The shorter the wavelength, the higher the energy of the photon. When the wavelength gets close to the Planck length, the energy of the photon is getting close to the Planck mass, and you're getting into the regime where if you had a couple of these photons going in different directions within a space that small, their gravitational effect would severely distort the spacetime geometry (maybe making a black hole, maybe not, but in any case making it harder to figure out which space coordinates you're talking about in any given situation).

As to whether space might actually be quantized on that scale, I think that's highly speculative. It's more that we don't have experimental techniques that could confirm it looks like a manifold at those scales. See quantum foam for more. --Trovatore (talk) 20:48, 13 November 2023 (UTC)

Thank you for your detailed response:

You write: "you should not think of the Planck length as being any sort of sudden hard limit to measurement, as though you could measure 1.01 Planck lengths but not 0.99. Rather, it's the approximate scale". If so, then why was it important to calculate the (almost) exact value of the Planck length, being $1.616255\cdot 10^{-35}$ meter? So many digits after the dot, and still not intended to be a limit of anything?

You write: "When the wavelength gets close to the Planck length, the energy of the photon is getting close to the Planck mass". Let me just remind, that according to the well known formula $m=h/\lambda c$ (where $m$ is the mass, $h$ is the Planck constant, $\lambda$ is the wavelength, and $c$ is the speed of light), a given photon whose wavelength is the Planck length, carries energy equivalent to a mass of 0.13675 milligram, i.e. more than six times as heavy as the Planck mass, being 0.02176434 milligram only.

You write: "you're getting into the regime where if you had a couple of these photons going in different directions within a space that small, their gravitational effect would severely distort the spacetime geometry (maybe making a black hole, maybe not, but in any case making it harder to figure out which space coordinates you're talking about in any given situation)". According to this explanation, why does our article (equipped with reliable sources) mention a creation of black hole? Additionally, as far as I know, there does exist a limit of length (being the Schwarzschild radius) for which any black hole can be created, so according to our article it seems that also the Planck length is intended to reflect a limit (besides the argument mentioned in the first paragraph of my current response), don't you agree?

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 10:44, 14 November 2023 (UTC)

Let me put it very bluntly and with a touch of exaggeration: The Planck units are basically numerology, and nobody knows what they mean and whether they have any meaning at all. These values come about by combining powers of the fundamental constants $\hbar$, $c$ and $G$ such that the result has dimensions of length, mass, time, etc. These combinations are unique, and computing the exact values is the simplest thing in this business — it can be done, therefore it is done. At the same time these exact values are somewhat ludicrous. Take the case of Planck's constant: the definition of the Planck length uses the reduced constant $\hbar$, you use $h$ in your 'well-known formula'. The difference is the factor of more than six that you correctly notice in your second point. We see that there is some arbitrariness in the definition of the Planck units. This is actually well reflected in the term "units" here. The original goal was to come up with a set of base units that was motivated by nature to replace the common set of m, kg and s, that we use in everyday life. Many people speculate that these units might be of fundamental significance in some form or another, not necessarily the precise values that we can easily compute but rather the scales, the orders of magnitude associated with those values. Arguments have been given in this thread, but it is important to realise that these are essentially plausibility arguments, which you may or may not buy. No proof can be given for anything because there simply is no theory that can be applied reliably at these physical scales. We do not know how nature behaves at these scales. The article states this quite clearly as it uses formulations such as speculations about quantum gravity, conjectured and it is possible. --Wrongfilter (talk) 16:35, 14 November 2023 (UTC)

Right. Let me pull out an important point from the middle of Wrongfilter's comments: The reason to want to know the Planck units to high precision is not for their posited fundamental physical significance, but as a possible system of units, somewhat less arbitrary than SI. As it stands, there are three main reasons to use SI instead of Planck units, from less to more fundamental:

1. Cost of switching. This can't be ignored, as metric advocates have found.
2. Planck units have inconvenient size. This could be worked around by multiplying by powers-of-10 or something but then you lose some of the aesthetics.
3. The hardest one to work around: We don't know very accurately how big the Planck units are, relative to actual objects of everyday experience, and therefore can't measure those objects very precisely in Planck units.

The first two problems mean that probably we're not going to try very hard to switch to Planck units, as SI, though less amazing than its fanboys seem to think, is perfectly serviceable. But the dream remains, and that's why people might try to get as many significant figures as they can. --Trovatore (talk) 18:26, 14 November 2023 (UTC)

Nuances, but I think you're misrepresenting my point: I don't think anybody has ever seriously proposed using the Planck units as a practical system of units. It's also not about wanting to know the Planck values precisely, rather we do know them accurately because we want to and do know the values of the fundamental constants accurately — those are important because they are the fundamental constants of our physical theories. As a matter of fact, the recent reform of the SI unit system has brought those even closer to the constants (the value of the speed of light was already defined in a previous reform), but that is still an entirely different matter from using the Planck units directly. That is more of a theoretical game. But the significance of the Planck units is vastly overrated. --Wrongfilter (talk) 19:26, 14 November 2023 (UTC)

Hmm, well I certainly thought at some point that the Planck units were cooler than SI. Actually I still do. They would be better than SI if not for the three points I laid out. (As for accuracy, the limiting factor is G, which is known only to four significant digits.) --Trovatore (talk) 19:39, 14 November 2023 (UTC)

Now, you are referring to a question I didn't ask: "Why were the official Planck units chosen as a system of units". I agree with your answer to this question, but it has nothing to do with my main question about, why no length shorter than the Planck length can be measured, according to the conjecture mentioned in our article which gives an argument involving a "black hole".

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 22:12, 14 November 2023 (UTC)

As for the difference between $\hbar$ and $h,$ it seems that you didn't interpret me well: The "official" Planck length can be defined, either by $\hbar$ as ${\sqrt {\frac {\hbar G}{c^{3}}}},$ or equivalently by h as ${\sqrt {\frac {hG}{2\pi c^{3}}}}.$ Anyway, the result is always the same result: $1.616255\cdot 10^{-35}$ meter. I agree you could theoretically define another concept, let's call it the "quasi-Planck length", as ${\sqrt {\frac {hG}{c^{3}}}},$ but it's not the concept of the "official" Planck length.

Whether this "official" concept is too arbitrary, is another issue, but this another issue has nothing to do with my (second) point to Trovatore with regard to the relation between the "official" Planck length and the "official" Planck mass. Anyway, my (second) point to Trovatore was, that a given photon whose wavelength is the "official" Planck length, i.e. $1.616255\cdot 10^{-35},$ carries energy equivalent to a mass of 0.13675 milligram, i.e. more than six times as heavy as the "official" Planck mass, being 0.02176434 milligram only. Actually, the same is true for - the quasi Planck units - being the "official" Planck units multiplied by ${\sqrt {2\pi }}:$ a given photon whose wavelength is the quasi Planck length, being the "official" Planck length multiplied by ${\sqrt {2\pi }},$ carries energy equivalent to a mass which is more than six times as heavy as the quasi Planck mass, being the "official" Planck mass multiplied by ${\sqrt {2\pi }}.$

As for your main point regarding numerology: I agree, but your point about numerology has nothing to do with my main question about, why no length shorter than the Planck length can be measured, according to the "conjecture" mentioned in our article which suggests - no numerology - but rather a strict argument involving a "black hole".

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 22:11, 14 November 2023 (UTC)

J. Richard Gott gives the following argument why no clock can measure a time shorter than the Planck time: the clock needs to involve a photon that moves to and fro within the time Δt to be measured, in which time the photon can at most traverse a distance of c Δt, which is also a limit on its wavelength; as we shrink the clock to make Δt smaller and smaller, the wavelength of the photon goes down and so its energy goes up and thereby the mass of the clock, until "it falls within its own Schwarzschild radius and forms a black hole."^[1] That limiting time is the Planck time. He then points out that when Δt equals the Planck time, c Δt equals the Planck length, adding that it is "the shortest distance one can measure". Gott does not present an argument for thus claim, but somehow I think a similar argument can be made for incredible shrinking rulers, something like that in order to ascertain the ruler is lined-up with the distance to be measured, a signal has to be sent between the end points.  --Lambiam 09:51, 16 November 2023 (UTC)

Oh, this sounds a more reasonable argument to me, for clarifying our article's explanation which involves a black hole. Thank you for your efforts to find out this source.

As for your additional explanation about why a distance shorter than the Planck length is immeasurable, why don't you say simply, something quite analogous to what Gott has claimed, i.e.: For a photon's wavelength to be shorter than the Planck length, the photon must have energy equivalent to a mass by which, the photon will "fall within its own Schwarzschild radius and form a black hole", right?

Additionally, I'm not quite sure I've fully understood the "black hole" argument (Gott's argument): If a given photon's wavelength had been shorter than the Planck length, then this photon would have to have energy equivalent to a mass by which - the photon will "fall within its own Schwarzschild radius and form a black hole" (as Gott put it). The shorter its wavelength is, the longer its Schwarzschlid radius is. All right. But what's bad with a tiny black hole, whose wavelength is shorter than the Planck length, and whose Schwarzschlid radius is longer than the Planck length? Where is the contradiction, whose existence proves that no photon's wavelength can be shorter than the Planck length?

2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 13:03, 16 November 2023 (UTC)

I don't buy these black hole arguments... The reason is the principle of relativity: for any reference frame in which the photon has an energy (I avoid the term "mass" because photons have no mass) large enough for it to form a black hole there's an equivalent frame where the energy is not large enough for it to do so. Of course it's possible that the principle of relativity does not hold on small scales. Another reason is that this type of argument freely mixes classical objects (black holes) with quantum objects (photons) and there is no theory of how one might or might not turn into another. Also, what about the uncertainty relation? Anyway, my reservations are not particularly relevant, but my point remains that these types of arguments are not solid, they are more or less hand-waving plausibility arguments that one may or may not believe. --Wrongfilter (talk) 13:15, 16 November 2023 (UTC)

There would be a measurement event and the energy would be enough there. It would be interesting to know if lots of lower energy probes in lots of different experiments could measure something smaller. But we're nowhere near that at the moment. NadVolum (talk) 13:54, 16 November 2023 (UTC)

Those two words "measurement event" club me right out of my comfort zone, excellent point, thanks. I'll have to think about that and see whether that'll win me over. --Wrongfilter (talk) 14:03, 16 November 2023 (UTC)

As for your aside claim that a given photon has no mass. Well, all agree that a given photon doesn't have a rest mass, which must equal zero as far as a photon is concerned. But it is only semantically debatable among physicists whether a given photon has a relativistic mass. All depends on whether the momentum p of a given body should only be defined by the formula $p=\gamma m_{0}v$ (whereas $v$ is the velocity of the given massive body slower than light - and $m_{0}$ is the mass of that massive body when at rest), or the momentum can also be defined by the simpler formula $p=m_{rel}v$ (whereas $v$ is the velocity as before, and $m_{rel}$ is the relativistic mass which can actually be obtained - either from the formula $m_{rel}=\gamma m_{0}$ if the body is slower than light - or from the formula $m_{rel}=h/\lambda c$ if the body is a photon). Anyway, I was aware of this semantic debate among physicists - about whether the photon's momentum can also be defined by the photon's (relativistic) mass (and not only by its wavelength), and that's why I'd written that the photon "carries energy equiavalent to a mass" (i.e. to a relativistic mass), instead of writing directly that the photon "carries a mass" (i.e. a relativistic mass). This semantic debate among physicists is not that important, though, because it's semantic only.

As for your main point: Well, it can be used as an additional argument - actually as a proof by contradiction - for why no photon's wavelength can be shorter than the Planck length. For, if - as an initial assumption - a given photon's wavelength had been shorter than the Planck length, then this photon would have to have energy equivalent to a mass by which - the photon will become a black hole, but this is impossible - because of your current argument: A black hole is an absolute phenomenon, while energy is a relative one. Hence, we've reached a contradiction, because of our initial assumption - that a photon's wavelength can be shorter than the Planck length. Conclusion: no photon's wavelength can be shorter than the Planck length. QED. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 15:06, 16 November 2023 (UTC)

A while back on this desk a physicist stated that a black hole's Schwarzschild radius will vary only with its invariant mass and thus one should not or cannot expect to create black holes simply by accelerating matter in one direction. Perhaps they are correct, nevertheless, suppose one accelerates and collides matter into each other from opposite directions, then their combined kinetic energy counts towards the system's rest mass in its zero-momentum frame. In fact, apparently the creation of unstable micro black holes might be feasible with current technology, see Micro_black_hole#Feasibility_of_production. Likewise, for two photons moving away from each other, there is no theoretical reason that I'm aware of that their zero-momentum frame rest mass cannot be part of a black hole, perhaps when they are created when high-velocity matter and antimatter annihilates each other. Modocc (talk) 18:59, 16 November 2023 (UTC)

Despite what the physicist you've mentioned has claimed, I'm not quite sure the Schwarzschild formula refers to the rest mass, rather than to the relativistic mass. If this formula really refers (as an option I still don't rule out), to the relativistic mass of given bodies (and to their wavelength if it really represents their "real radius"), then a given body whose rest mass is half a milligram (i.e. a tenth of an average mosquito's weight), will never reach (approx.) 40% of the speed of light. BTW, an electron has no fundamental difficulty in approaching "almost" the speed of light, because an electron's rest mass "almost" approaches a photon's rest mass (being zero), with respect to the previous massive body I've just mentioned. 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 20:25, 16 November 2023 (UTC)

The details of what happens in these situations are extremely slippery and complicated. I think it's fair to say they are simply not well-understood by anyone (but in any case definitely not by me). That's the basic reason that there's no agreement among physicists about quantum gravity.

Again, the Planck scales are the order of magnitude where they start to be a serious problem, not some sort of hard line where everything's fine above it but impossible below it. Worrying about a factor of $2\pi$ here is almost certainly misplaced. --Trovatore (talk) 20:46, 16 November 2023 (UTC)

At 40% of the speed of light the Lorentz factor is near one and doubles at twice that speed and it limits the velocity of invariant mass to less than c. Yet, you say that "...a given body whose rest mass is half a milligram... ...will never reach (approx.) 40% of the speed of light." Why? Besides relativistic mass, under what assumptions have you reached that conclusion? Modocc (talk) 10:29, 17 November 2023 (UTC)

By algebra. For more details, see my new thread below, under the title "Follow up", in which I calculate the velocity for more regular bodies, whose rest mass is one kg, for which the body's maximal velocity becomes even slower, and actually almost reaches the floor, i.e. the zero... 2A06:C701:7463:9900:11BA:FAE2:6F7E:5413 (talk) 10:40, 17 November 2023 (UTC)

Gott did not argue that the photon would acquire a mass making it collapse into a black hole. He only referred to its energy, arguing that the clock containing the tick-tocking photon would become too massive.  --Lambiam 22:01, 16 November 2023 (UTC)

Low-flying helicopter vibrations

I've noticed that the glassware in our apartment starts clinking whenever a helicopter is flying low to land at a nearby airfield (the helicopters fly quite frequently near us). Is that clinking because of strong air vibrations from blades or something else? 212.180.235.46 (talk) 16:32, 12 November 2023 (UTC)

Does that happen even when the windows are closed? ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:51, 12 November 2023 (UTC)

Identifying the Types and Origins of Helicopter Vibrations and

The science behind helicopter noise — and how the industry is working to reduce it. Alansplodge (talk) 20:20, 12 November 2023 (UTC)

Is it anywhere the glass is or only when it on a particular shelf for instance? It souns like a resonance problem to me. NadVolum (talk) 20:27, 12 November 2023 (UTC)

There's a good chance it's not just sound but actual air motion, see Downwash. Abductive (reasoning) 08:52, 14 November 2023 (UTC)

The downwash is only significant while the helicopter is not only near but almost overhead. Also, a steady airflow will not make the glassware clink, but a frequency pattern of varying pressure imposed on the downward airflow will result in vibration. At 480 RPM with four rotor blades, the frequency will be 32 Hz, possibly with pronounced harmonics. Inside a nearby house, this will produce a standing wave whose strength also depends on the resonant frequencies of the space. Internal reflections may focus the wave and produce some high-intensity anti-nodes, perhaps right where the glassware is situated.  --Lambiam 10:38, 15 November 2023 (UTC)

32 Hz gives a half-wavelength of about 5 m in air, which is also a typical size for a room in a house, so the fundamental frequency of the rotor noise could excite the fundamental frequency of the room. But alongside vibrations of the air in the house, I would also consider vibrations of the house itself. Large surfaces like the walls and roof are better at picking up the low-frequency noise than small glasses and may vibrate in response to the pressure waves, even if not very close to a resonant frequency. These vibrations can then be transmitted to any shelves mounted on the walls and then to glasses on the shelves. PiusImpavidus (talk) 09:53, 16 November 2023 (UTC)