Wikipedia:Reference desk/Archives/Science/2024 June 30

= June 30 =

Where does USA show its non-lawsuit certified 30yr station pressure averages?
I know at least 1 free commercial site lets you find hourly pressure since long enough ago but 30yrs would be manually averaging many thousands of numbers on 10,958 webpages one per day. I just want the regular $0 version not the paid certificated version for lawyers, bridge engineers etc Sagittarian Milky Way (talk) 15:26, 30 June 2024 (UTC)


 * By "station" do you mean "weather station" and by "pressure" do you mean "atmospheric pressure"? (If so, I don't know the answer, but I was struggling to understand the question, so perhaps others were also.)
 * Is the mention of bridge engineers pertinent to your reason for asking, or an inadvertent red herring? 151.227.226.178 (talk) 09:57, 1 July 2024 (UTC)
 * Weather station, atmospheric pressure. On one of the government weather/climate websites I saw a link to certified super-duper extra-checked data intended for lawsuits etc but presumably anyone can pay. Sagittarian Milky Way (talk) 12:50, 1 July 2024 (UTC)
 * And a specific weather station, not all of them averaged together (the only weather textbook I was lucky enough to have read (an undergraduate weather 101-level covering all meteorology) just called them stations) Sagittarian Milky Way (talk) 13:00, 1 July 2024 (UTC)

Is there any difference between, what "no rest-mass" means, and what "zero rest-mass" means?
1. Some authors write "light has no rest-mass", whereas others write "light has zero rest-mass".

2. There are some arguments against ascribing any rest-mass, even a zero rest-mass, to the light, e.g.
 * First, The formula of relativistic momentum may collapse once any value, including any zero value, is substituted for the rest-mass in that formula.
 * Second, light cannot be at rest, hence - logically - it cannot carry any rest-mass. That said, and bearing in mind - that although (for example) the function $$f(x)=1/x$$ has no value at $$x=0$$ this does not mean that the value of the function $$f(x)=1/x$$ at $$x=0$$ is zero - and more generally: when we don't ascribe "any value" to a property we don't mean the value of the property is zero, the same must be true for what we (don't) mean by "light has no rest-mass".
 * Third, from a logical point of view: Any sentence, whether true or flase, may be substituted for A in the true sentence "If light is at rest then A". Hence, for any value X, we will always get it right saying "If light is at rest then its mass will then be X". Hence for any value X, we will always get it right saying "if light has a rest mass then its value is X". Hence we would collide with a contradiction, if we assumed light carried any rest mass - even a zero one only.
 * Third, from a logical point of view: Any sentence, whether true or flase, may be substituted for A in the true sentence "If light is at rest then A". Hence, for any value X, we will always get it right saying "If light is at rest then its mass will then be X". Hence for any value X, we will always get it right saying "if light has a rest mass then its value is X". Hence we would collide with a contradiction, if we assumed light carried any rest mass - even a zero one only.
 * Third, from a logical point of view: Any sentence, whether true or flase, may be substituted for A in the true sentence "If light is at rest then A". Hence, for any value X, we will always get it right saying "If light is at rest then its mass will then be X". Hence for any value X, we will always get it right saying "if light has a rest mass then its value is X". Hence we would collide with a contradiction, if we assumed light carried any rest mass - even a zero one only.

3. On the other hand, there is a well known argument in favor of ascribing a zero rest-mass, to the light: This is actually a direct consequence, of combining the formulas $$E^2=m_0^2c^4+p^2c^2$$, and $$E_{light}=p_{light}c.$$

4. To sum up: Bearing in mind the pros and cons for/against ascribing a zero rest-mass to the light, I wonder if light, has no rest-mass at all, even not a zero rest-mass, or it still has a zero rest-mass.

HOTmag (talk) 16:37, 30 June 2024 (UTC)


 * To me, this relates more to semantics than physics. "Zero rest-mass" implies a countable quantity, as if it could be measured; "no rest-mass" suggests that rest-mass is not necessarily measurable.  My understanding (based on knowledge from c.1980s) is that photons do not have a defined mass in a stationary state; and, "zero" is useful as a construct.  --136.54.106.120 (talk) 18:02, 30 June 2024 (UTC)
 * As to your last word: I suspect zero can't be a construct. For more details, see my previous response, in its section 2, against ascribing any rest mass to the light, even a zero rest mass only. HOTmag (talk) 10:43, 1 July 2024 (UTC)
 * I was thinking of the noun "construct" referring to using "zero" as a logical placeholder for the absence of anything, nonexistence or "nothing" -- rather than a cardinal number. --136.54.106.120 (talk) 17:58, 1 July 2024 (UTC)
 * See my first response. Its section 3 gives an argument for ascribing a zero rest-mass to the light, zero being a cardinal number. On the other hand: section 2 gives three arguments against ascribing any rest mass - including a zero rest-mass - to the light, zero being a cardinal number. That's why I asked my question indicated in section 4. HOTmag (talk) 18:34, 1 July 2024 (UTC)
 * The concept of "zero" overlaps mathematics and philosophy. One could say that there are varying forms of nonexistence (?)  — Preceding unsigned comment added by 136.54.106.120 (talk) 18:53, 1 July 2024 (UTC)
 * It seems you didn't get my point. I'm focusing on the contradiction between section 2 and section 3, both referring to zero as a cardinal number. The implicit question was: Can anyone remove the contradiction? HOTmag (talk) 20:32, 1 July 2024 (UTC)
 * Okay, shifting focus from philosophy to physics:  quantum electrodynamics and the Standard Model of particle physics treat photons as massless particles, providing theoretical support for zero rest mass.   Nevertheless, a photon at rest is a non-entity. --136.54.106.120 (talk) 22:08, 1 July 2024 (UTC)
 * A. Re. your first source: It claims light has a non-zero rest mass.
 * B. Re. your second source: Why didn't you provide also my section 3 as an additional "theoretical support for zero rest mass?"
 * C. However, please notice my section 3 contradicts my section 2. Also your second source contradicts my section 2. The implicit question was: Can anyone remove the contradiction?
 * D. Re. your last sentence. From a logical point of view, saying that "a photon at rest is a non-entity", is the same as saying that "light cannot be at rest". So, not only do I know that a photon at rest is a non-entity, i.e that light cannot be at rest, I also use this fact for establishing my section 2 (in its "Second" and "Third" paragraphs).
 * HOTmag (talk) 22:47, 1 July 2024 (UTC)
 * The real numbers are a field, which implies it has both an additive and a multiplicative identity, traditionally denoted by $0$ and $1$. These elements are true real numbers, not cardinal numbers.
 * There is a traditional embedding of the finite cardinal numbers in the real numbers which sends the cardinal number $0$ to the real number $0$ and the cardinal number $1$ to the real number $1$, but this fact does not turn these real numbers into cardinal numbers.
 * Since 0 kg = 0 μg = 0 oz = 0 Da, there is no need to specify the unit; "zero mass" is unambiguous. --Lambiam 23:43, 1 July 2024 (UTC)
 * As to cardinal numbers: Please notice I hadn't been the first to claim that zero was a "cardinal number". The anonymous user I responded to had, and I only followed them, adopting the term "cardinal number" they had already used, so your response should have responded to them rather than to me.
 * As to your last sentence: Did anyone claim there was a need to specify the unit? I only claimed there was a contradiction between sections 2,3 in my first post, and I asked if anyone could remove the contradiction. If you think there is anything wrong in my arguments in section 2 against attributing a zero rest-mass to a photon, please specify - both the wrong argument - and what's wrong in it. HOTmag (talk) 11:37, 2 July 2024 (UTC)
 * There is a traditional embedding of the finite cardinal numbers in the real numbers which sends the cardinal number ᙭᙭᙭ to the real number ᙭᙭᙭ and the cardinal number ᙭᙭᙭ to the real number ᙭᙭᙭, but this fact does not turn these real numbers into cardinal numbers.
 * Since 0 kg = 0 μg = 0 oz = 0 Da, there is no need to specify the unit; "zero mass" is unambiguous. --Lambiam 23:43, 1 July 2024 (UTC)
 * As to cardinal numbers: Please notice I hadn't been the first to claim that zero was a "cardinal number". The anonymous user I responded to had, and I only followed them, adopting the term "cardinal number" they had already used, so your response should have responded to them rather than to me.
 * As to your last sentence: Did anyone claim there was a need to specify the unit? I only claimed there was a contradiction between sections 2,3 in my first post, and I asked if anyone could remove the contradiction. If you think there is anything wrong in my arguments in section 2 against attributing a zero rest-mass to a photon, please specify - both the wrong argument - and what's wrong in it. HOTmag (talk) 11:37, 2 July 2024 (UTC)
 * As to your last sentence: Did anyone claim there was a need to specify the unit? I only claimed there was a contradiction between sections 2,3 in my first post, and I asked if anyone could remove the contradiction. If you think there is anything wrong in my arguments in section 2 against attributing a zero rest-mass to a photon, please specify - both the wrong argument - and what's wrong in it. HOTmag (talk) 11:37, 2 July 2024 (UTC)


 * Re:
 * A) First source: I only read the abstract and noted This review attempts to assess the status of our current knowledge and understanding of the photon rest mass, with particular emphasis on a discussion of the various experimental methods that have been used to set upper limits on it. [And, yet]: failure to find a finite photon mass in any one experiment or class of experiments is not proof that it is identically zero and, even as the experimental limits move more closely towards the fundamental bounds of measurement uncertainty, new conceptual approaches to the task continue to appear.


 * B) Your #3 section does indeed support zero rest mass; otherwise, particles with non-zero rest mass cannot travel at the speed of light, as it would require infinite energy. Since photons always travel at the speed of light in vacuum, they must have zero rest mass.
 * ... To be continued? (gotta go now) --136.54.106.120 (talk) 00:03, 2 July 2024 (UTC)
 * It is (I think) conceivable that not all photons travel at exactly the same speed; if the slowest photons move at a fraction of 10−80 slower than the fastest ones, we would not be able to detect that experimentally. Photons traveling in vacuum are traveling through quantum foam. It is presently unclear if that affects their speed; see  --Lambiam 10:51, 2 July 2024 (UTC)
 * A) See p. 81 in your first source: In section 2, we introduce the theoretical foundation for massive photons, via a discussion of the Proca equations... Using the Proca equations as a starting point, several possible observable effects associated with a nonzero rest mass of the photon are developed in section 3.
 * B) You are actually repeating what I'd claimed in section 3. However, my question, was not about section 3 you're repeating, nor about my section 2 whose consequence actually contradicts the opposite consequence of my section 3, but rather about whether this contradiction could be removed. For it to be removed, one should show what's wrong in my argument in section 2 or in section 3. For showing what's wrong in such an argument, one should quote the wrong step in that argument and then explain why this step is logically wrong. HOTmag (talk) 11:37, 2 July 2024 (UTC)
 * "Rest mass" is just another term for "invariant mass", a property of a physical object that is not dependent on the coordinate system of an observer – in contrast to its relativistic mass, which can be different for different observers. When no confusion is possible, physicists will use just "mass" instead of "invariant mass" and describe the photon as a massless particle. This has the same meaning as saying that photons have zero invariant mass, or equivalently that they have zero rest mass. It is pointless to seek more behind this expression. --Lambiam 18:46, 2 July 2024 (UTC)
 * Re. your first sentence: Yes, this is a well known fact.
 * Re. your second sentence. Those who use the term "massless" don't recognize the relativistic mass. But if you're among those who do, then you should avoid the confusing term "massless", because any particle (e.g. a photon) carrying no rest mass does carry a non-zero relativistic mass.
 * Re. your last two sentences: I guess you want to claim that the term "a photon's rest mass" doesn't mean "a photon's mass when at rest". But if so, then "a photon's rest mass" must mean "a photon relativistic mass", whereas this kind of mass is non-zero, so how does this interpretation of "rest mass" relate to my question about those authors who claim that a photon carries a zero rest mass? HOTmag (talk) 20:29, 2 July 2024 (UTC)
 * This thread reminds me of Codd's Null (SQL). A null indicates a lack of a value, which is not the same thing as a zero value. "No rest mass" seems pretty like the null case. Mike Turnbull (talk) 10:50, 3 July 2024 (UTC)
 * Yes, Just as the function $$f(x)=1/x$$ at $$x=0$$ is a null case.
 * So, combining the formulas $$E^2=M_0^2C^4+P^2C^2$$, and $$E_{light}=P_{light}C,$$ does not let us conclude that a photon carries a zero rest mass $$M_0,$$ because the first formula $$E^2=M_0^2C^4+P^2C^2$$ only refers to bodies carrying a rest mass $$M_0,$$ while a photon's rest mass is a null case - because a photon can't be at rest. HOTmag (talk) 19:07, 3 July 2024 (UTC)
 * Maybe you overlooked the statement that "rest mass" is just another term for "invariant mass". So "a photon's rest mass" means "a photon's invariant mass". Maybe you also overlooked the mentioned restriction to cases when no confusion is possible. But I fear that for some people confusion is always a possibility. --Lambiam 18:28, 3 July 2024 (UTC)
 * I didn't overlook the statement that "rest mass" is just another term for "invariant mass". On the contrary, I explicitly pointed out in my last response: Re. your first sentence: Yes, this is a well known fact. So, I already agreed that "rest mass" was just another term for "invariant mass".
 * I also didn't overlook the mentioned restriction to cases when no confusion was possible. On the contrary, I explicitly pointed out in my last response: Those who use the term "massless" don't recognize the relativistic mass. But if you're among those who do, then you should avoid the confusing term "massless", because any particle (e.g. a photon) carrying no rest mass does carry a non-zero relativistic mass. In other words, those "cases when no confusion is possible" are only those cases when the relativistic mass is not recognized.
 * To sum up: there are only two kinds of a given body's mass:
 * A. The body's current relativistic mass. Please notice, the value of this kind of mass is always non-zero, even if the body is a photon.
 * B. The body's invariant mass, i.e. the body's rest mass, i.e. the relativistic mass the body would have carried if it had been at rest. Please notice, the very existence of this kind of mass depends on whether the body is a massive one or is a photon: If it's a photon, which actually can't have a rest, then it can't have a rest mass either, logically speaking.
 * My question was about those authors who claimed that a photon carried a zero rest mass, as opposed to B. HOTmag (talk) 18:56, 3 July 2024 (UTC)
 * From the formula relating relativistic mass to invariant mass, it follows that the invariant mass of a photon must be zero, but its relativistic mass need not be. The phrase "The rest mass of a photon is zero" might sound nonsensical because the photon can never be at rest; but this is just a side effect of the terminology, since by making this statement, we can bring photons into the same mathematical formalism as the everyday particles that do have rest mass. --Lambiam 07:03, 6 July 2024 (UTC)
 * we can bring photons into the same mathematical formalism as the everyday particles that do have rest mass.
 * I have already referred to this kind of argument, in my first post, section 2, paragraphs "First" and "Third". HOTmag (talk) 20:04, 6 July 2024 (UTC)
 * I know, so I don't get why you don't think this solves the issue and get on with your life. --Lambiam 07:39, 7 July 2024 (UTC)
 * What do you mean by "this"? Is "this", this kind of argument you've quoted, or "this" is how I had already refuted it? HOTmag (talk) 08:53, 7 July 2024 (UTC)
 * My question was about those authors who claimed that a photon carried a zero rest mass, as opposed to B. HOTmag (talk) 18:56, 3 July 2024 (UTC)
 * From the formula relating relativistic mass to invariant mass, it follows that the invariant mass of a photon must be zero, but its relativistic mass need not be. The phrase "The rest mass of a photon is zero" might sound nonsensical because the photon can never be at rest; but this is just a side effect of the terminology, since by making this statement, we can bring photons into the same mathematical formalism as the everyday particles that do have rest mass. --Lambiam 07:03, 6 July 2024 (UTC)
 * we can bring photons into the same mathematical formalism as the everyday particles that do have rest mass.
 * I have already referred to this kind of argument, in my first post, section 2, paragraphs "First" and "Third". HOTmag (talk) 20:04, 6 July 2024 (UTC)
 * I know, so I don't get why you don't think this solves the issue and get on with your life. --Lambiam 07:39, 7 July 2024 (UTC)
 * What do you mean by "this"? Is "this", this kind of argument you've quoted, or "this" is how I had already refuted it? HOTmag (talk) 08:53, 7 July 2024 (UTC)