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{{Spoken article requested|] (])ScientistBuilder] (]) 17:18, 29 January 2022 (UTC)|The speed of light is central to physics fields including the Big Bang Theory, special relativity, general relativity, spectroscopy, optics, as well as real world applications such as signal processing and GPS networks}} {{Spoken article requested|] (])ScientistBuilder] (]) 17:18, 29 January 2022 (UTC)|The speed of light is central to physics fields including the Big Bang Theory, special relativity, general relativity, spectroscopy, optics, as well as real world applications such as signal processing and GPS networks}}
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== Speed of causality? == == Is this part accurate in History? ==


Quote:
"The speed of light is not about light" or so I've seen youtube video titles ( https://www.youtube.com/watch?v=msVuCEs8Ydo ). IIRC I've seen it called "speed of causality". Can/shall we include something like this? ] (]) 10:04, 18 February 2022 (UTC)
:The article already says that anything else massless will also travel a the speed of light, and that ''c'' {{tq|is the upper limit for the speed at which ... any signal carrying information can travel through space.}} I don't think we need to say more than the article already does, but that's just my take. ] (]) 19:19, 18 February 2022 (UTC)
::Maybe specifying that light only moves at c when in a vacuum would be better. There are lots of cases where photons move slower than c due to a medium or gravity or whatever, from my understanding. ] (]) 22:02, 30 June 2022 (UTC)
:::This is already explained at the end of the intro. ] (]) 22:17, 30 June 2022 (UTC)
::::oh yeah, it does, my bad lol ] (]) 16:25, 1 July 2022 (UTC)
:::::No worries! :-) ] (]) 16:31, 1 July 2022 (UTC)


'''Connections with electromagnetism'''
== Which units need to be in the infobox? ==


In the 19th century ''Hippolyte Fizeau'' developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of 315000 km/s (''704,634,932 m/h'').
Bearing in mind that an overlong infobox means more for mobile users to scroll past, which units and numerical values should we report? The case for the exact SI value is pretty obvious, but "astronomical units per day" feels more like trivia. Does it provide additional insight to say that ''c'' is roughly 0.307 parsecs per year as well as saying that light takes about 3.26 years to travel one parsec? ] (]) 22:33, 16 June 2022 (UTC)


His method was improved upon by ''Léon Foucault'' who obtained a value of 298000 km/s (''666,607,015 m/h'') in 1862. ] (]) 01:06, 18 November 2023 (UTC)
:Trivia multiply on WP like a disease. Some sort of guideline or criterion to restrict this should be in the MoS, IMO. Here, as you point out, reciprocals are trivially redundant and hence space-wasters. In general, we should avoid illustrative stuff in infoboxes: this is not their function, so the entire "Approximate light signal travel times" list should be removed or moved into the article. Some of the signal travel time entries have essentially no merit anyway, such as "from geostationary orbit to Earth", "the length of Earth's equator" (the person who wants this would relate better to "7.5 times around the Earth in one second"), "one light-year" (we do not need to be reminded in an infobox about the obvious), "one parsec" (the speed in parsecs per year gives this), "from the nearest galaxy to Earth" (worse than bad; whether it is a galaxy is disputed and it is unrelatable, since almost all readers will have to research what is meant by this). ] (]) 15:30, 7 August 2022 (UTC)


:Are you suggesting our article may not be correct or proposing that it include conversions to km/h at that point, and in either case, why? ] (]) 11:07, 18 November 2023 (UTC)
== Descartes' eclipse argument is nullified by Bradley's discovery of aberration -- should this be noted? ==


::There's a definite discrepancy in number of significant digits between the quoted metric and traditional measurements... ] (]) 13:10, 18 November 2023 (UTC)
Descartes' oft-cited argument, that any propagation delay of light would result in a misalignment of Sun/Earth/Moon during a lunar eclipse, has an oft-overlooked flaw that is evident in retrospect since Bradley's time -- that the supposed misalignment would be cancelled by aberration of light, so that the alignment would appear straight regardless of light speed. <ref>Sakellariadis, S. Descartes' experimental proof of the infinite velocity of light and huygens' rejoinder. Arch. Hist. Exact Sci. 26, 1–12 (1982)</ref> Thus, the absence of discernible misalignment does not impose a lower limit on light speed, but instead has no bearing on the matter.
:::Indeed, but the values in parentheses aren't in the article. If we wanted to include them, we could use {{tl|Convert}}, which would probably round them appropriately automatically, and wouldn't abbreviate miles to "m" either, but I don't see why we'd want to include such conversions in that part of the article anyway. ] (]) 13:46, 18 November 2023 (UTC)
::::I added the parenthesis. It's just a conversion to m/h that I made, just to show how different they are & to convert it into U.S. terms. ] (]) 00:15, 24 December 2023 (UTC)
::I'm not sure if 315000 or 298000 km/s is correct. I feel it's 315000 km/s, but I'm not sure. ] (]) 18:04, 25 November 2023 (UTC)


== Why not also include an accurate description of c in miles per second? ==
A note about this has been added to the page on ]. Should a brief note be given here also? (There may be some value in pointing this out, as an online search on this point turns up more confusion than clarity -- some students and even professors seem to think that such misalignment is still present, and inconspicuous only because of the short timescale, not absent altogether.)


186282.3970512 mi/s, to be fairly accurate.
If the above considerations are deemed convincing, please consider augmenting your historical section, excerpted below, with a brief note along the lines of the new sentence in parentheses there.


== Speed of light in vacuum ==
[If unconvinced, or if the cited reference is difficult to access or follow, perhaps the following approximate ''gedanken'' experiment will help:
Imagine yourself (like Gamow's Mr. Tompkins) in a world where lightspeed is much slower, say only about 10 times as fast as you can run. Suppose you are on a flat field facing due North, while on your left the Sun is just setting due West, and on your right, your shadow is visible on some white fence (Tom Sawyer memorial) that runs north/south. Standing still, you see your shadow perfectly abreast of you, but if you start running North, your shadow begins to fall behind a little, as Descartes would have expected. After you have been running at a steady 0.1c for a bit, an overhead observer (in the Goodyear Blimp high above you and your shadow and roughly equidistant from both) would see your shadow lagging you by about 0.1 radian. Since your view of your shadow involves a round trip, you might expect to see a lag of 0.2 radian instead. But since you are moving North at 0.1c, the aberration of light will make the sun and your shadow each appear to be 0.1 radian north of their "geometric" locations, thereby cancelling out the lag effect, so that your shadow still appears diametrically opposite from the sun after all.]


Misplaced Pages should get rid of all occurrences of the phrase "speed of light in vacuum". There is only one speed of light, which is a universal constant. Also the speed of light doesn't change if not in vacuum. ] represents the real speed of a photon, and that doesn't change. Only ] is changing, causing the optical effects that mislead people. But this very article is explaining the same in the section ]. ] (]) 13:24, 20 May 2024 (UTC)
---------
Present text excerpt (with proposed new note in parentheses):


:If you have a reference for your point of view please share it. ] (]) 15:15, 20 May 2024 (UTC)
'''Early history'''
::@] shouldn't this work the other way around? I don't want to add anything. I want something to be removed which has no reference. ] (]) 15:52, 20 May 2024 (UTC)
…
:::The article has rather a lot of mentions of the speed of light in vacuum that are supported by references to ]. Merely in ], we have {{tqb|Sometimes {{Math|''c''}} is used for the speed of waves in any material medium, and {{Math|''c''}}<sub>0</sub> for the speed of light in vacuum.<ref name=handbook>See, for example:
In the early 17th century, Johannes Kepler believed that the speed of light was infinite since empty space presents no obstacle to it. René Descartes argued that if the speed of light were to be finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. (Although this argument fails when ] is taken into account, the latter was not recognized until the following century.) Since such misalignment had not been observed, Descartes concluded the speed of light was infinite….
* {{Cite book
|last=Lide |first=D. R.
|year=2004
|title=CRC Handbook of Chemistry and Physics
|url=https://books.google.com/books?id=WDll8hA006AC&q=speed+of+light+%22c0+OR+%22&pg=PT76
|pages=2–9
|publisher=]
|isbn=978-0-8493-0485-9
}}
* {{Cite book
|last=Harris |first=J. W. |year=2002
|title=Handbook of Physics
|url=https://books.google.com/books?id=c60mCxGRMR8C&q=speed+of+light+%22c0+OR+%22+date:2000-2009&pg=PA499
|page=499
|publisher=Springer
|isbn=978-0-387-95269-7
|display-authors=etal}}
* {{Cite book
|last=Whitaker |first=J. C.
|year=2005
|title=The Electronics Handbook
|url=https://books.google.com/books?id=FdSQSAC3_EwC&q=speed+of+light+c0+handbook&pg=PA235
|page=235
|publisher=CRC Press
|isbn=978-0-8493-1889-4
}}
* {{Cite book
|last=Cohen |first=E. R. |year=2007
|title=Quantities, Units and Symbols in Physical Chemistry
|url=https://books.google.com/books?id=TElmhULQoeIC&q=speed+of+light+c0+handbook&pg=PA143
|page=184
|edition=3rd
|publisher=]
|isbn=978-0-85404-433-7
|display-authors=etal}}</ref> This subscripted notation, which is endorsed in official SI literature<ref name=BIPM_SI_units>{{SIbrochure8th|page=112}}</ref> ....}} I find the idea that we would deny the current definition of the metre rather disturbing. ] (]) 16:20, 20 May 2024 (UTC)
::::This is what I was talking about from the beginning. You are confusing two different concepts as well. ''c''<sub>0</sub> has a place in physics. In one place. Optics. In case of refraction the phase velocity is used for calculations, because the phase of light is shifting constantly if travelling in a medium which is not vacuum. Every other area of physics is using the universal constant ''c'', which can be calculated using ]. By the way the ] article also says "Photons are massless particles that always move at the speed of light when in vacuum." which is plain wrong. Photons are unable to travel slower then ''c''.
::::If you think that Misplaced Pages is correct in its current state, than I won't say anything more. ] (]) 16:58, 20 May 2024 (UTC)
:::::I fixed the ] article thanks. ] (]) 20:20, 20 May 2024 (UTC)
:::@] You asked that all occurences across Misplaced Pages to be changed. I think we better discuss a reference for your claim first. You pointed to one section, ], but it has sources so you need to explain why they should be removed. ] (]) 16:58, 20 May 2024 (UTC)
::::Understanding should be the key here. Please look at this . After watching it you will have the urge searching for references, too. ] (]) 17:10, 20 May 2024 (UTC)
:::::That's a great video. But it's not news, sorry. It explains the atomic model of the index of refraction. Based on this video I recommend no changes. ] (]) 17:58, 20 May 2024 (UTC)


* In the literature:
---------
::{| class="wikitable" style="text-align: center"
DAL47 ] (]) 00:22, 27 June 2022 (UTC)
|-

! Google Search !! Scholar !! Books
: Good addition. I did not know that. ] (]) 17:56, 27 June 2022 (UTC)
|-
| "Speed of light in vacuum"
|
|
|-
|}
: Getting rid of the term would be spectacularly against Misplaced Pages's mission. - ] (]) 19:41, 20 May 2024 (UTC)


{{reflist-talk}} {{reflist-talk}}


:If the speed of light is always the same, then ] shouldn't exist. ] (]) 09:24, 21 May 2024 (UTC)
== Semi-protected edit request on 8 July 2022 ==

{{edit semi-protected|Speed of light|answered=yes}}
विश्वमा भासिरोचनम ] (]) 12:26, 8 July 2022 (UTC)

:]&nbsp;'''Not done:''' it's not clear what changes you want to be made. Please mention the specific changes in a ] and provide a ] if appropriate.<!-- Template:EIp --> Also, any requested edits to the text must be in English. ] (]) 13:00, 8 July 2022 (UTC)

== Grammar fix (request for semi-protected edit) ==

{{edit semi-protected|answered=yes}}
Please insert a word: "one can thus a standard for the metre" should be "one can thus '''define''' a standard for the metre" (or any similar correction). ] (]) 19:01, 1 August 2022 (UTC)
:{{Done}} I went with "'''establish''' a standard for the metre", which is equivalent to "define the metre", also noting that "define" is used in the previous sentence. Thanks for catching this! <sup>]</sup>/<sub>]</sub> 19:51, 1 August 2022 (UTC)

:::It would be better English to say "thus, one can..." than "one can thus...". Also, "thus" itself is usually a very pedantic and amateurish word. Try and make a sentence without "thus". cheers ] (]) 05:17, 16 August 2022 (UTC)

== Esplaining in Plain English ==

It would be great if a physicist with some teaching chops could put some real world examples here, for instance "the Lorenz Factor means that a person travelling headlong at 85% of the speed of light would be 100 feet tall", or that if a space ship travelled away from Earth at 50% of the speed of light for a year its clocks would be six months ahead of Earth clocks, but if it returned to Earth at the same speed for a year, the clocks would re-synchronise. Thanks ] (]) 05:15, 16 August 2022 (UTC)

: The idea is introduced in a section (''{{section link|Speed of light#Fundamental role in physics}}''), but to get further detail like this is beyond the scope of this article. The link at the top of the section (to '']'') is sufficient: that is where detail of this nature belongs. ] (]) 11:38, 16 August 2022 (UTC)

== Definition ==

"Its exact value is defined as 299792458 metres per second"

That's the wrong way around really. C is an absolute constant - you can't define it in terms of metres and seconds. Indeed the metre is defined in terms of c, so that would be a circular definition. I think it should just say something like "It's value is 299792458 m/s" ] (]) 14:15, 16 August 2022 (UTC)

:Maybe I'm missing something, but isn't that what the article already explains? The note at the end of the line goes into more detail; the point is that the value is exact by definition. ] (]) 14:24, 16 August 2022 (UTC)

::Maybe this is an opportunity to consider the wording, so that more people read the intended meaning into the statement: what is being defined might be made clearer. What is being defined is a relationship between units (the second and metre) through the choice of a numeric value for the physical quantity when ''c'' is expressed in terms of those units. The footnote does a good job of explaining it, but the sentence could be revised. I'll give thought to a rewording. ] (]) 15:00, 16 August 2022 (UTC)
:::I made a to it. ] (]) 15:10, 16 August 2022 (UTC)
::::I'm not going to fight this corner - it's probably a bit too pedantic. But I would nevertheless suggest that this still implies that the speed of light is what it is by definition. This is not so - c is a fundamental constant, you can define units in terms of it, but not the other way around.] (]) 15:31, 16 August 2022 (UTC)
:::::It is that value by definition of the meter. &#32;<span style="font-variant:small-caps; whitespace:nowrap;">] {] · ] · ] · ]}</span> 15:33, 16 August 2022 (UTC)
::::::So maybe the article can avoid all confusion by saying "by the definition of the metre" instead of just "by definition". <span style="box-shadow:2px 2px 6px #999">]]</span> 16:44, 16 August 2022 (UTC)
:::::::I think "by definition" is good enough, what with the elaboration in the endnote and later. ] (]) 18:18, 16 August 2022 (UTC)
::::::::ByThis is the lead and that is not how readers might first interpret it. Since we do not say by definition of what, I think the footnote is sufficient and we should just omit any mention if "by definition" in that sentence. That is, I would suggest "Its exact value is {{val|299792458|u=metres per second}} ...", along the lines suggested by Bagunceiro. What are we actually adding by including "by definition"? Only this who know already will understand from the sentence what it is saying. ] (]) 19:13, 16 August 2022 (UTC)
:::::::::I was about to suggest dropping 'by definition' in the lead myself. As long as we state it's an exact value, that's all that matters for the lead IMO. &#32;<span style="font-variant:small-caps; whitespace:nowrap;">] {] · ] · ] · ]}</span> 19:59, 16 August 2022 (UTC)
::::::::::I'm not convinced that "by definition" is confusing or that dropping it would be clarifying (sometimes those lay readers just glide past the things that I, in my boundless wisdom, think would trip them up). But I have no strong feelings about it. ] (]) 20:18, 16 August 2022 (UTC)
:::::::::::OK, I will say that "The speed of light defines the metre such that by definition" is more awkward than either what we started with, what we had before (with just "by definition"), or just "The speed of light is exactly". ] (]) 12:00, 17 August 2022 (UTC)

== BC or BCE ==

I see an from 2007 used BCE. Is there a reason it was changed to BC? Great article, by the way. ] (]) 16:15, 16 August 2022 (UTC)

:I guess it's no big deal. I changed it back per ]. ] (]) 16:49, 16 August 2022 (UTC)

== Tweak: odd use of "%" ==
{{resolved|1=}}
Could we change
:{{xt|1=For example, a time dilation factor of ''γ''&nbsp;=&nbsp;2 occurs at a relative velocity of 86.6% of the speed of light (''v''&nbsp;=&nbsp;0.866&nbsp;''c''). Similarly, a time dilation factor of ''γ''&nbsp;=&nbsp;10 occurs at ''v''&nbsp;=&nbsp;99.5%&nbsp;''c''.}}
to
:{{xt|1=For example, a time dilation factor of ''γ''&nbsp;=&nbsp;2 occurs at a relative velocity of ''v''&nbsp;=&nbsp;0.866&nbsp;''c''. Similarly, a time dilation factor of ''γ''&nbsp;=&nbsp;10 occurs at ''v''&nbsp;=&nbsp;0.995&nbsp;''c''.}}
? I may find excessive parenthetical repetition detracting and think percentages belong mainly on grade sheets more than others do, but I think that the final {{!xt|99.5%&nbsp;''c''}} is just weird &ndash; using a percentage as a coefficient is rather unusual. ] (]) 21:08, 16 August 2022 (UTC)

:This is for the less mathematical readers. 50% of the speed of light is something pretty much everyone understands. ''v'' = 0.5 ''c'' is... much harder for those that struggle with math. &#32;<span style="font-variant:small-caps; whitespace:nowrap;">] {] · ] · ] · ]}</span> 00:22, 17 August 2022 (UTC)

::That does not address my final comment. Your comment would suggest {{xt|1=Similarly, a time dilation factor of ''γ''&nbsp;=&nbsp;10 occurs at 99.5% of the speed of light.}} Do think people who find {{xt|1=''v'' = 0.5 ''c''}} "much harder" will do any better with {{!xt|1=''v''&nbsp;=&nbsp;99.5%&nbsp;''c''}}? ] (]) 01:47, 17 August 2022 (UTC)

== Photons and Perspective ==

The article says (in Faster-than-light observations and experiments​): If a laser beam is swept quickly across a distant object, the spot of light can move faster than c. Shouldn't you say "from the perspective of the observer"?

Another way of looking at it is that each <u>photon</u> cannot move faster than the speed of light. Pretend you have a laser that will sweep across the moon's surface (about one-half an angular degree from Earth) in, let's say, one microsecond (or 1000 nanoseconds). But the "spot" (as observed from Earth) is an illusion.

What we see from Earth may appear to move much faster on the moon than one foot per ns (taking the moon's diameter to be 3500 km diameter). But we're observing the spot <i>from Earth</i>. On the moon, each individual photon (which travels to the moon in about 1.4 seconds and 1.4 seconds back) is independent from all the others. If you had a laser that could emit just 1000 photons in the microsecond that it takes to complete our sweep then, from the moon, you would observe one photon hitting the surface about every 3.5 km (3500 km diameter / 1000 ns).

Do I have it right or have I missed something? -] (]) 21:24, 16 August 2022 (UTC)

: It does not have to be from the perspective of Earth: the "spot" (the point on the surface at which the laser photons are arriving) travels faster than ''c'' from the perspective of any frame of reference or vantage point. You basically have it right, but I see nothing wrong with the statement in the article. ] (]) 21:45, 16 August 2022 (UTC)
::When you say "travels faster than ''c''", what do mean by "travels"? Is there any ''physical object'' (including a single photon) that travels faster than the speed of light? If so, from what vantage point? (Again I'm talking about <u>physical</u> objects. See ] and ].) -] (]) 23:43, 18 August 2022 (UTC)
:::No, clearly there is no physical object travelling. It is just a locus of events (photons colliding with a surface) of which the space separation is greater than the distance that light could travel in the time that separates them (and this remains true in any frame of reference). This is the point that the statement seems to be making: that despite being able to give some meaning to "velocities" greater than ''c'', there is in actuality ''nothing'' "real" (not even information) that is travelling faster than light. All I am saying is that to answer your original question, it is not necessary to add a qualifier about perspective: the calculated "velocity of the spot" in this example is greater than ''c'' from ''every'' perspective whenever it is so from one perspective. I'm not even sure how to make the wording clearer in the article. ] (]) 15:16, 20 August 2022 (UTC)

== False or Undecidable Statement ==
The first paragraph states as its closing sentence, "According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy, and thus any signal carrying information, can travel through space." I originally requested a citation for this but someone removed it. This statement is strictly speaking either false or undecidable. First, it fails to define "conventional matter", so its validity cannot be ascertained in that respect. Second, it fails to define "space". Space as it was conceived of in 1905 was undergoing a major paradigm shift from a nebulous aether, where time is purely parametric, to an idealized vacuum on a hyperbolic spacetime manifold. The working assumption was that "space" as in outer space far from other gravitational bodies was empty and completely devoid of anything. In the original German text, one can read explicitly that Einstein makes no mention of the speed of light being an upper limit on the flow rate of energy. In particular what is written is that, "all observers irrespective of their motion (both mutually and with regards to the light) will measure the speed of light in vacuum as the same number. This simple and seemingly odd pronouncement turned out to mandate the need for the existence of hyperbolic spacetime. But it still does not place bounds on the rate of energy (and hence information) transfer. This is because in the theory of special relativity only the surprising (at the time) facts about light being measured as the same speed whether one is moving toward an incoming light ray or moving away from an incoming light ray. This was in sharp contrast to Galilean relativity.

Fast forward to today. We now know that there is no such thing as an idealized vacuum. Examples include the ] and the ]. Even the farthest reaches of space have a photon flux through their region of about 2K called the ]. In addition, we know that spacetime is expanding at an accelerated rate, this implies there is a whole new notion of energy that we have no idea what it is or how it works/interacts with other forms of energy. Although special relativity does show the need for treating momentum and energy as one just like spacetime, one must not confuse matter and energy. All matter is energy but not all energy is matter. Thus special relativity makes no conclusion about the rate of transfer of energy and hence information. This is because all information is necessarily energy, and more so seldom just matter. In fact, the definition of existence is having the property of energy or the ability to interact as the potential to demonstrate energy.

Consequently, I am changing the sentence so that it is at least factually true. Please do not revert the sentence until having discussed in-depth with me over any objections. ] (]) 21:17, 22 August 2022 (UTC)

:No. The existing text was correct, and in alignment with every standard presentation of relativity. Moreover, the article already explains this, in considerable detail and with a considerable number of sources, and the introduction is there to ]. ] (]) 23:52, 22 August 2022 (UTC)

::At risk of belabouring a point, isn't there a slight non-sequitur here? I accept that it is a pretty standard presentation to make this connection, and (from the reference in the article) it is clear that experimentation fairly firmly supports the conclusion, but this does not necessarily imply that the conclusion (no energy or information faster than light) follows from the premise (special relativity). The causal structure derivable from QFT (which incorporates special relativity) also no doubt allows a mathematical proof of the conclusion, but this uses a lot of structure that is not present in special relativity on its own. Special relativity on its own trivially does show that acceleration of an object from below to above ''c'' is impossible, but not that no energy or nonstandard massive object can do so: it seems pretty clear that special relativity ''on its own'' does not prohibit energy-carrying ]s, notwithstanding the resulting destruction of the accepted causal structure and the experimental evidence to the contrary. That is, you need special relativity + ]) ''or'' QFT ''or'' experimental evidence].
::The article body (§ Upper limit on speeds) seems to be comprehensive in this respect. The lead's "According to the special theory of relativity, ''c'' is the upper limit for the speed at which energy, and thus any signal carrying information, can travel through space" might be an oversimplification, though, and I think misleads the less sophisticated reader. It would be nice to work in something along the lines of "According to the special theory of relativity with a reasonable causality assumption, ..." to better summarize the content in the article. ] (]) 01:36, 23 August 2022 (UTC)
:::I think separating "causality" from the theory of relativity is both nonstandard and an excessively fine point for the introduction of this article. ] (]) 01:42, 23 August 2022 (UTC)
::::My example is not a good way of resolving the problem. SR has strong implications on causality, and I agree that my suggestion, verbatim, would not be great in the lead. All that I am trying to do at this point is to establish the realization that the current sentence in the lead does not summarize the body, is not logically correct, and misleads readers in a nontrivial important way. Removal of the sentence, for example, would IMO be preferable to leaving it as is. Alternatively, it could be qualified in any number of interesting ways, such as by saying "for known physics". SR, strictly speaking, is about ] in physics. It permits counterintuitive results, such as the superluminal transport of electric charge (still, naturally, without violating causality). To reiterate: causality is not a direct consequence of special relativity without additional assumptions. ] (]) 12:55, 23 August 2022 (UTC)
:::::How causality relates to the geometry of Minkowski spacetime is part of the bundle of ideas that go under the heading "special relativity"; one learns about it in a special-relativity course. I'm open to phrasing adjustments, but this seems like going down the path of an artificial distinction, or at least a distinction that is not universally agreed upon as a standard in the physics community about how to organize ideas. It's like saying thermodynamics is, strictly speaking, about the Laws of Thermodynamics, so a statement about Carnot engines has to be extra-qualified with "According to thermodynamics and the definition of a Carnot engine...". (That's a pre-coffee analogy, but maybe it helps illustrate where I'm coming from.) If there's a lack of clarity here, I think we're looking in the wrong place. ] (]) 13:26, 23 August 2022 (UTC)
:::::To say it another way, I think that "according to special relativity" (or "according to the special theory of relativity") already covers the cases that are mathematically consistent with Lorentz invariance but physically inconsistent with relativistic causality. Moreover, the idea of {{mvar|c}} as a speed limit is important enough that we need a line on it at about that spot. Is there a better way to express that idea in that location? Well, I've seen this article so many times that by now I hate all of the words in it, so I'm inclined to say "probably". But I am concerned that we might fall into the habit of inventing an imaginary reader who we imagine is confused in a very particular way and acting on their behalf. ] (]) 14:21, 23 August 2022 (UTC)
::::::We seem to be missing each other on something. I do not wish to push a debate that does not appeal to you at this point. ] (]) 17:02, 23 August 2022 (UTC)
::::@] How is it possible that "separating 'causality' from the theory..." constitutes an excessively fine point when all of special relativity relies heavily upon whether a system is timelike or spacelike separated? With spacelike separation, there is no notion of causality. This is one of the core cruxes of the theory. ] (]) 19:29, 23 August 2022 (UTC)
:::::I had hoped my later comment would have clarified this, but apparently not. I was responding to 172.82.47.242's argument about what "special relativity on its own" implies. My reaction was that trying to separate out the mathematics of Poincaré symmetry and call that "special relativity on its own" (or "special relativity in a strict sense", etc.) was splitting hairs. ] (]) 19:38, 23 August 2022 (UTC)
::::::@] But that's exactly the point, namely, that SR does not contain sufficient information by itself to conclude that the speed of light is a limit on energy or information transfer. SR simply states that all observers irrespective of their motions will measure a ray of light traveling through an idealized truly empty vacuum as the same exact number. A corollary is that an idealized point mass obeying nonquantum (ie classical+SR) mechanics would require an infinite amount of energy to reach the speed of light. As to experimental facts that demonstrate an incomplete picture here, more than 50% of the rest mass (energy) of a proton is from its gluons and not the 3 quarks that comprise it. From a classical perspective this is astonishing, from a quantum perspective this is obvious because the QCD vacuum is even more exotic and QCD calculations are only valid at high energies. A cooled proton at rest will not fulfill the high energy requirements of asymptotic freedom. ] (]) 20:25, 23 August 2022 (UTC)
:::::::So far, you've invoked asymptotic freedom, the EPR paradox, the quantum measurement problem, Dirac delta functions, and the definition of "existence", but I'm still not sure what you're trying to say about the last sentence of the first paragraph of this Misplaced Pages article. In fact, I'm more confused than ever about what point you're aiming for. On the one hand, you take a highly circumscribed view of what counts as "special relativity", a view that excludes concepts of causality. On the other hand, one statement up, you say that some notions of causality are among "the core cruxes of the theory". ] (]) 20:45, 23 August 2022 (UTC)
::::::::@] I may be premature in this conclusion but it seems like I am trying to be drawn into a straw man argument whereupon one confuses spacelike separation with timelike separation. Is this the intent? If so, it may be the source of the confusion. If not, one ought to be careful as to take words within their context. Hint: there are many contexts occurring in this multibranched/multiperson discussion simultaneously (in the standard frame).
::::::::The flat fact remains, one cannot conclude that the speed of light is a limit on energy/information transfer from special relativity, or any other physical theory for that matter because the few experiments that tried to probe this got mired in controversy for no particular reason other than choices made in signal processing matter. There is an easy Gedankenexperiment that clears this up. If I had a rigid stick (which maintained its structure and rigidity) that was about 1 AU in length I could tap Morse code into the surface of Mercury while a light signal would take a few minutes to arrive. To refute the thought experiment one needs to a) argue that no such structure is possible and b) that the nonexistence of such a structure is somehow fundamental to the universe. Neither is true and several experiments tried to establish this except instead of a rigid body they utilized quantum lattices over extended physical distances. In principle, if a LIGO arm was outfitted with a long enough quantum lattice that remained cooled and coherent throughout the length of the arm, and the adjacent region was vacuum, then one could explicitly test whether information can arrive at a location faster than the speed of light. Aside from this being an expensive experiment, I think that it is well worth it considering the controversy this topic has brought up throughout my career as a scientist. It would be nice to finally settle the issue once and for all. So all the talk about quantum this and quantum that is because quantum mechanics is the counter example to the claim that the speed of light is a limit on information transfer. Consequently, the conclusion that has been reached repeatedly is that the theory of special relativity places no bound on the rate of transfer of energy/information. Moreover, quantum theory's nonlocality suggests that such superluminal transfer is possible. ] (]) 22:02, 23 August 2022 (UTC)
:::::::::No, quantum theory does not suggest that superluminal transfer of information is possible. The article already explains this. ] (]) 22:14, 23 August 2022 (UTC)
::::::::::I am sorry but the nature of a nonlocal theory that only conditionally obeys causality absolutely implies the possibility of superluminal information transfer. Not a single claim refuting this statement draws rigorously on all known mathematics and physical experiment. There are so many obviously false statements. For example, it is often claimed that a projection does not transfer information. This is clearly false. Yes there is some information loss but not a 100% loss. In fact, if the argument were true, one would not be able to calculate the height of an unseen object from its shadow. But one can, so objections based on poo-pooing projections as sources of information are obviously invalid. Other erroneous arguments include claiming that the phase velocity is somehow some pale informationless counterpart to the group velocity, and then declaring by fiat that the phase velocity cannot carry information. This is not so. In fact, research by D. Carfi has shown that the phase velocity must be incorporated into mathematically rigorous relativistic quantum theory in order to assure positive probabilities and consequently the phase velocity necessarily carries critical information about a general relativistic quantum state. The list of endless nonsensical objections is exhausting and I have refuted enough erroneous claims in this talk section to award a savvy reader a PhD. I will brook no more whining about wanting something to be true so therefore it must be true. The facts speak for themselves. ] (]) 03:49, 24 August 2022 (UTC)
:::::::::::You're welcome to argue uphill against the entire literature on quantum entanglement, but neither this article nor this Talk page is the place to do so. (There are plenty of cases where I personally believe that people are thinking about such-and-such in quantum mechanics the wrong way, but I don't argue about those on Misplaced Pages. It's ], and speaking egotistically, I wouldn't get credit if I proved myself right.) How much "whining" you will personally "brook" is immaterial; what matters is whether you can get a consensus of editors to support the changes you wish to implement. ] (]) 14:48, 24 August 2022 (UTC)
::::::::::::So you are explicitly announcing that truth is relative to the consensus of editors. This has no place in science and it is not the spirit of Misplaced Pages. Factual arguments do matter. They matter in real life and they matter on Misplaced Pages. ] (]) 19:01, 24 August 2022 (UTC)
:::::::::::::Please see ]. If your position were the mainstream view, broadly represented in reliable sources on the subject, I'm sure you would have no trouble assembling a consensus in its favor. Factual arguments matter precisely so far as they are effective at getting other people to agree with you; you appear to have failed at that here. ] (]) 19:48, 24 August 2022 (UTC)
::::::::::::::Your summary of the events here are not accurate. I have provided numerous verifiable references as the necessary but not sufficient conditions. Moreover, the stubborn refusal of a single individual is not a measure of lack of consensus, or any failure on my part on a planet of 7 billion humans. The problem with WP:TRUTH is that it is designed as a broad policy across all human endeavors including politics, history, arts and literature just to name a few. In such areas there is no real notion of truth. This is in sharp contrast to science where a testable claim can be explicitly verified. Consensus is not the measure of scientific validity. To this end ignoring sources that are reliable by Misplaced Pages standards is tantamount to cherry picking content. This is surely against the spirit and intent of Misplaced Pages. It also dangerously invites folklore to displace scientific rigor.
::::::::::::::Here is a precise example. It is generally believed by most physicists that a self-adjoint operator, a Hermitean operator and a symmetric operator are all equivalent. But this is mathematically false and there are myriad of sources that demonstrate this. The sources are not only reliable in the sense of Wiki standards but they are fundamental in the sense of understanding the underlying mathematical logic of quantum theory. In the realm of science there is no room for folklore beliefs and indeed science is the very endeavor to free the human species of superstition and folklore. Yet in every technical field folklore exists because it is a natural human tendancy, one that should be discouraged. ] (]) 20:15, 24 August 2022 (UTC)
:::@] It turns out that causality is a purely classical phenomena. One does not need QFT, simply quantum theory will do. In addition, there are no rigorous proofs in QFT (the "proofs" are empirical experimental verification). This is because the rigorous mathematics of QFT is nonexistent. Ritualistically moving symbols around a page is not mathematics nor constitutes a logical proof. Also, the quoted text "As a result, if something were travelling faster than c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated. In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone.", is plainly false for space like separation, since in such instances there is no notion of global causality and hence the perspective of one frame looks exactly like an observer traveling backward in time. In particular, there is no need for tachyonic anything. Tachyons are as their name suggests, tacky. Antimatter is a perfect example of an electron particle perpetually moving backward in time. The problem most scientists face is that they are unable to make the careful distinction of the 3 distinct notions of time. There is time as a spacetime coordinate on a hyperbolic space, which allows for the definition of a "proper time"; there is the time as it appears in Newton's equations as a purely parametric independent global variable for all dynamics; finally, there is the notion of time as it appears in the Schrodinger equation and all other time dependent partial differential equations where time is not parametric and not hyperbolic, rather it is Euclidean and it commutes with all other partial spatial derivatives. Clearly, we do not understand time or causality as we should. The missing pivotal connection is in the breaking of unitarity in quantum statistical mechanics and its mathematical foundations. Until the master equations are fully justified this will remain an open problem. I have my own resolution to this issue but it would constitute original research and not be appropriate for Misplaced Pages. ] (]) 17:03, 23 August 2022 (UTC)
::::Perhaps I am missing something, but this doesn't seem to indicate deficiencies in the explanations the article already includes. For example, antimatter is not "a perfect example of an electron particle perpetually moving backward in time". Such language oversimplifies the mathematics; a closer verbal approximation would be along the lines of, "The probability amplitude for a positron to do something is the same as the amplitude for an electron to do the reverse." You can't build a ] out of positrons. ] (]) 17:16, 23 August 2022 (UTC)
:::::@] The statement refining from the particle to the probability amplitude is also false. This is because all time evolution in a quantum system is handled by the unitary operator. Such operators are always invertible operators and moreover, time reversal, operator inversion and complex conjugation are all the same thing for time evolution. Clearly complex conjugating the probability amplitude does not accomplish this. ] (]) 17:42, 23 August 2022 (UTC)
::::::Yes, time evolution is unitary (presuming that we are ], et cetera), and time-reversal would amount to an anti-unitary. But that doesn't make "positrons are electrons going backwards in time" any better of an oversimplification. ] (]) 17:50, 23 August 2022 (UTC)
:::::::@] Have you calculated the spectrum and resolvent operator of the Dirac equation? If so, the statement is self-evident. However, if not, I highly recommend Bernd Thaller's book called "The Dirac Equation". It makes explicit exactly how and why a positron is an electron moving backward in time. ] (]) 22:07, 23 August 2022 (UTC)
::::::::I've read Thaller's book. It explains how time reversal is an anti-unitary operator (section 3.4.2), but not that the oversimplified metaphor of "positrons are electrons moving backward in time" is anything other than, well, an oversimplified metaphor, just like the "sea of negative-energy electrons". (See in this regard chapter II.2 of Zee's ''Quantum Field Theory in a Nutshell.'') ] (]) 22:48, 23 August 2022 (UTC)
:::::::::Zee is a terrible source for anything. Also, there is no such thing as an "anti-unitary" operator. An unitary operator is one in which its adjoint (complex conjugate transpose) is equal to its inverse. The adjoint of an unitary operator is called an inverse unitary operator, also sometimes the forward and backward unitary operators for unitary and inverse unitary, respectively. However, the order of attribution is immaterial owing to the fact that it is merely human convention to choose the minus sign as the forward time evolution. The distinction in nomenclature matters because "anti" and adjoint are not the same. For example, the adjoint of a vector may be a co-vector but not an anti-vector, or the adjoint of a vector may be a linear functional but not an anti-linear functional (which has a completely different meaning and definition). I also strongly doubt you have read Thaller's book and if you did, obviously you did not understand it. The existence of negative spectral values does not imply a sea of magic (because positrons are in fact stable and are not scarce due to being "bound up" in the sea). Rather it implies the time reversal of positive energy values, which corresponds literally to an electron with its positive energy moving in the opposite direction in time, backward rather than forward. It's not a metaphor, it is rigorous mathematics combined with sensible logical thinking. ] (]) 03:01, 24 August 2022 (UTC)
::::::::::Zee is a standard reference, your personal opinions notwithstanding. "Anti-unitary" is also established terminology, as witnessed by the title of section 3.4.2 in Thaller's book, "Antiunitarity of the Time Reversal Operator". If you have a problem with it, get it changed. When I said I read Thaller's book, I said the truth, and ] is rather impolite. ] (]) 14:46, 24 August 2022 (UTC)
:::::::::::Zee is not a "standard reference" for those that are serious learners. The book is terse and filled with hand wavy nonsense. Moreover, it completely lacks rigor and precision. It is not a suitable reference and every professional I know agrees with me. So this is hardly my personal opinion.
:::::::::::Also I concede that it may be impolite to imply you were not truth full. But sadly as I suspected, I uncovered a piece of misunderstanding. When Thaller writes "anti-unitary", he is talking about a specific type of isometry on the Hilbert space one which acts anti-linearly as opposed to linearly. He then uses unitary to mean the isometries that are linear. This is because of the Wigner-Bargmann theorem which states that all such isometries that are either linear or anti-linear are unitary or anti-unitary (up to an overall U(1) character). This is the correct meaning and usage of "anti-unitary" because it is linked through the symmetry transformation of the action of a linear operator (as opposed to an anti-linear operator).
:::::::::::Also the specific section you reference has an important conditional, which is "if" one wants invariance under the Poincare group for both H_pos and H_neg then one must make the choices as such regarding the pi operators and their unitary/antiunitary behavior. The fact of the matter is that the Poicare invariance is not likely true or necessary. For a reference on a theory which takes this idea and modifies it to get to operators that are not self-adjoint but have real eigenvalues, see Carl Bender's theory on PT-Symmetric quantum mechanics. So when I said there is no such thing as an antiunitary operator, it was because I was speaking about the standard Schrodinger theory where there are no spinors and no relativistic invariance. It turns out one does not need spinors to have relativistic quantum theory, a fact that I think is not so well known.
:::::::::::Finally since you are familiar with Thaller's book, what is the reaction to the sections 1.8.1 "Superluminal Propagation" with its theorem 1.6 and section 1.8.2 "Violation of Einstein Causality". Thaller hand waves away the inevitable conclusion that quantum phenomena is nonlocal and acausal and can furnish a method of superluminal information transfer, by simply saying "we expect these effects to be immeasurably small". It turns out that as humans have studied quantum mechanics, we realized we can take the statistically improbable and in the laboratory set up conditions that make these tiny probabilities near certainty. This is what is down in laboratories that work on quantum phenomena around the globe. Yet you still seem to refuse to acknowledge that quantum phenomena absolutely gives a window into superluminal information transfer and acausality. Moreover, nothing in the theory of special relativity contradicts this. QED ] (]) 17:47, 24 August 2022 (UTC)
::::::::::::] describes Zee's book as {{tq|Packed with wisdom told in a charmingly informal manner}} though {{tq|not the best way to learn how to calculate stuff}} . I've never met a physicist who substantially disagreed with that overall take. Since the point at hand is not about {{tq|how to calculate stuff}} but rather on a more conceptual level, it's fine. {{pb}} What Thaller meant by antiunitary is what I meant by antiunitary. {{pb}} As the opening to chapter 1 and the recapitulation in 1.8.4 of Thaller make clear, those are difficulties introduced by the artificiality of a single-particle theory, which inevitably leads to trouble when squeezed too hard. Trying to crowbar a relativistic notion of localization into a single-particle theory will cause problems to manifest in one way or another. What Thaller is talking about are pathologies that show the limitations of the theory that Thaller is exploring. See section 1.3 of ]'s ''Quantum Field Theory Lectures'', for example. ] (]) 18:28, 24 August 2022 (UTC)
:::::::::::::Where did you get that quote by John Baez? I do not see it on the webpage. Also John may have said that before he met me and noted my and all my colleagues objections to Zee. What Zee is doing is sweeping under the rug all the mathematically invalid ritualistic symbolic manipulation of field theory and simply summarizing the results of calculations and how they agree with experiment. This in itself is not very useful since any reference book on QFT and comparison with the PDG's RPP values accomplish the same. If some how there were a group of physicists that have never heard of QFT then Zee might be a nice primer to ease into the topic.
:::::::::::::It's ironic you bring up Coleman because his theorem states that in d<= 2 long range fluctuations are favored for, and continuous symmetries cannot be broken for, short range interactions. Because vacuum fluctuations can be controlled and stabilized (nature does this in the hydrogen atom in the form of the Lamb shift), it is the case that information can be garnered from them, just as the Lamb shift is an universal indicator of hydrogen. ] (]) 19:31, 24 August 2022 (UTC)
:::::::::::::As for your claims about Thaller, firstly the Dirac equation is not a single particle equation. It is, was and always will be the theory of relativistic leptonic matter with its antimatter pair. Thaller attempts to wave away the meaning and interpretation by essentially making the same erroneous argument all physicists make-- that try desperately to cling to classical thinking, in the sense of locality and causality. The argument is that some how magically by adding more moving parts all the inescapable conclusions go away. That is they essentially claim without a viable mechanism that second quantization magically preserves local causal structure. Nothing could be further from the truth. For more on this topic, see any of NIST's BEC precision tests, aggregated multi-atom single particle behavior and their work on artificial gauge fields.
:::::::::::::Secondly, nothing in 1.8.4 amounts to your claim or summary of its content. He simply outlines 2 unavoidable consequences and makes no claim about "squeezing the Dirac theory too hard". In fact, his comment on the infinite energy barrier is actually not true. In NIST laboratories as well as many others, one can fine tune lasers to pulse at the right frequency which can give the effective result of 'barriering' an ensemble or single atom into localizing where and how one wants. It is then possible to add the right environmental factors (boundary behavior and counter-lasers) to simulate relativistic and gauge field conditions. This is not unlike how graphene transport is governed by the Dirac equation with effective covariant derivative. ] (]) 19:52, 24 August 2022 (UTC)
::@ ]- Agreement with every published textbook, especially low level ones that over simplify the points are not an acceptable standard for scientific fact. Furthermore, the article does not explain the point I make and the high level summary is thus misleading at best. Please show me where in the article my technical point is already elaborated on. Even if such text exists in the article, it does not preclude a more honest and accurate summary, as I have written. I will politely await your reply before reverting your unjustified changes and specifically you did not engage me in discussion prior to reverting the text. This is not only unprofessional but violates the agreed standards and protocol of Misplaced Pages. ] (]) 16:44, 23 August 2022 (UTC)
:::Actually, the common (though not universal) practice is to ]. The technical matters are covered in the "Upper limit on speeds" section and later passages. ] (]) 16:52, 23 August 2022 (UTC)
::::FWIW, I am in agreement with XOR&#39;easter that the reverted edit does not belong: there are style and other reasons (even though I was suggesting a qualification, it is not the same). ] (]) 17:02, 23 August 2022 (UTC)
:::::@] I did exactly the same. I added qualifiers and removed erroneous words. However, I would like to hear more on the issue of style that you mentioned. ] (]) 17:16, 23 August 2022 (UTC)
::::::For example, you added a reference to a talk page from article space. You also added a qualifier "classical idealized empty", without support from the body. This qualifier is also unnecessary with the classical assumption of flat space. ] (]) 17:22, 23 August 2022 (UTC)
:::::::@] I agree on all your style points. The redirection to a talk page was a temporary condition and I would have removed it if the edit remained untampered with. About the descriptors, "classical idealized empty", I agree they may need qualification but "idealized empty" and "vacuum" (as it was understood by Einstein and a few others in 1905) are interchangeable, if and only if the historical context is made clear for the word "vacuum". The term "classical" is a reference to the fact that the human species' notion of vacuum has drastically changed since 1905. So by classical one means non/pre-quantum thinking. Recall Einstein's difficulty with quantum theory and patently false arguments made in the <s>1932</s> 1935 EPR paper. I cannot say I know of a better way of taking all this information and distilling it down further, which is why I used the triple adjective to form a strong qualifier. But as you say, it may be possible with direct linking to the body. Though, the body fails to make the critical key points and generally just regurgitates a historically false perception of special relativity. ] (]) 17:34, 23 August 2022 (UTC)
::::::::The ] was published in 1935, not 1932. It was mostly written by Podolsky, not Einstein, and I doubt that either its argument or Einstein's own would be called "patently false". Yes, they're unpersuasive if you don't accept their premises, but that's something else. Einstein's own thinking on quantum theory was . ] (]) 17:46, 23 August 2022 (UTC)
:::::::::Yes you are correct that the paper is 1935 and not 1932. That's what I get for going from memory rather than turning 90 degrees and double clicking a few times. Nonetheless, my error in the date does not invalidate the point, which is that the equations in the EPR 1935 paper, though few, are incorrect because they get composed in a way that is not consistent with the handling of generalized functions. This error is not surprising because it was not until the years 1939-1950 that the mathematics for composing such equations was rigorously worked out. Therefore, in hindsight, it is completely reasonable to state that the content of the article is "patently false", both mathematically and physically. You are also quite correct that the article was not written by Einstein, in fact he required some cajoling to attach his name to it. Nonetheless, the quality of an article, which argues by authority, and has incorrect mathematics is the prototypical example of scientific content, which has lost merit through the test of time. Also, Einstein's troubles with quantum theory are well documented historically and he did not need to be the author of the 1935 EPR paper for this statement to be true. ] (]) 18:07, 23 August 2022 (UTC)
::::::::::I think you're getting pretty far into ] territory with those claims. ] (]) 18:14, 23 August 2022 (UTC)
:::::::::::@] I'm sorry but I cannot and will not agree that well documented historical fact is original research. If you like I can give you a whole host of references regarding a) the mathematical errors and b) the evidence that Einstein struggled with quantum theory. ] (]) 19:14, 23 August 2022 (UTC)
::::::::::::The mathematical statements in the EPR paper are the application of standard quantum theory to an entangled pair of particles. Nothing about "the handling of generalized functions" invalidates that. Einstein's insistence that quantum theory is incomplete is indeed well-documented, but his arguments to that end are neither "patently false" nor germane to this article. ] (]) 19:18, 23 August 2022 (UTC)
:::::::::::::Again this is not true. If one looks carefully at equation (14) on page 780 of the 1935 EPR paper, one finds a false statement that is in no way indicative of "standard quantum theory". Specifically, it is false that Dirac delta can be an eigenfunction. Eigenfunctions live on Hilbert spaces and there is no known Hilbert space for the Dirac delta. In addition, the Dirac delta cannot have an eigenvalue of multiplication as simply the spatial variable because there is no known linear operator that operates on Dirac delta returning simply the support of the Dirac delta function (except for the only 2 trivial choices of juxtaposition with x and Schwartz pairing with x). The Schwartz pairing fails because x is not a test function, and although the juxtaposition looks like it works, it is a distributional identity, which actually constitutes an infinity (with cardinality of the continuum) of distributionally equivalent but pointwise inequivalent equivalence relations.
:::::::::::::To attempt to draw these false conclusions, one must appeal (without regard to rigorous mathematics) blindly to the so-called Dirac calculus. The Dirac calculus is mathematically incorrect and decades of research have gone into trying to establish it on solid mathematical footing to no avail. Significant forward progress has been made by I. Gelfand, G. Shilov, A. Bohm, M. Gadella and more recently D. Carfi. But there still is no full description. Part of the issue is that the de Broglie pure wave states are not square integrable but do form an abstract basis in a Frechet space. However, the Frechet space has no inner product and therefore the Max Born probability interpretation does not follow in an obvious manner. By the by, this work dates back to the 1960s and is more history than original research with the exception of the more recent pioneering work by D. Carfi.
:::::::::::::As to the germane nature, the point is that unless something is a collection of bosons which can literally all stack on top of each other, everything we know about physical reality involves spacelike separation, which implies that causality is a local classical notion and quantum theory is inherently nonlocal. Due to the high precision in which quantum theory is known to be true, together with its inherent nonlocal nature (For example, see ] and ].) implies that physicists' insistence on locality and causality are just desperate attempts to cling to the classical world, despite our best experiments telling us that the strange exotic nature of the quantum world is here to stay and closer to reality on a fundamental level. Ergo, one cannot conclude that energy or information is constrained by the speed of light through just special relativity alone. ] (]) 20:11, 23 August 2022 (UTC)
::::::::::::::Working with position "eigenfunctions" that are Dirac delta distributions is a standard part of quantum theory, covered in probably any text at the Cohen-Tannoudji level, and in a more sophisticated way in the books of Peres, Holevo, etc. Everyone knows they don't fit into the Hilbert space of square-integrable functions, but ordinary manipulations suffice to handle that. It's not consequential for analyzing EPR. From where I sit, it looks like you're taking what is at most a general complaint about physicists' attitude toward mathematical rigor, making like that applies to the EPR paradox more than to any other application of the same theory, turning that into an "Einstein was obviously wrong" assertion, and from there saying that this article needs to be changed. I'll say, with all honesty and every attempt at cordiality, that this is a hard argument to follow. ] (]) 21:31, 23 August 2022 (UTC)
:::::::::::::::If this is your take away, I seriously wonder if you have actually read and understood anything I have written. In your so-called standard treatment, how do you reconcile the following distributional identity:
:::::::::::::::<math>x\delta(x-\lambda) \,\dot{=}\, \lambda\delta(x-\lambda) \,\dot{=}\, x\cos(x-\lambda)\delta(x-\lambda) \,\dot{=}\, \lambda\delta(x-\lambda),</math>
:::::::::::::::and which is the operator of multiplication <math>X</math> or <math>X\cos(X-\lambda)</math>, both, or neither? By the way in considering your answer, be aware that there is an infinite continuum of possible other so-called "operators of multiplication". Hint, that cardinality really messes with operator algebra, which ruins both Stone-von Neumann and Gelfand-Naimark. ] (]) 03:20, 24 August 2022 (UTC)
::::::::::::::::Oops, missed this comment down at the bottom here. (This is what we get for having {{mvar|N}} conversations simultaneously.) But now that I've seen it ... what? I figure the typical physicist response would be, "Why are you throwing an extra factor in there? Is the potential not what you said it was before?" In other words, not all mathematical manipulations make sense physically; expressions that look equivalent in the abstract may be limiting cases of situations that look very different physically. But again, this looks like {{tq|a general complaint about physicists' attitude toward mathematical rigor}}, which either applies or doesn't apply equally well to ''any mention of a "position operator"''. It's multiple stages removed from the purpose of this Talk page. ] (]) 15:41, 24 August 2022 (UTC)
::::@] They are not covered in the upper limit section as my reply to @] indicates for myriad of reasons. But you mention other places where the technical issues I have brought to light are already delineated. Where/which sentences? ] (]) 17:08, 23 August 2022 (UTC)
::::@] you are correct regarding the bold cycle but I specifically requested the opposite direction because I knew a bunch of people with strong opinions and insufficient education would object. One shall not let ignorance and persistence substitute for scientific fact. ] (]) 17:13, 23 August 2022 (UTC)
:::::Time for a break? Talk page discussion is not helpful when emotionally laden wording creeps in. ] (]) 17:41, 23 August 2022 (UTC)
::::::@] I believe there is a misunderstanding between a statistical qualifying statement of a large group of humans with "emotionally laden wording". I assure you, I place no emotion in my factual statements. Whether another human decides to attribute emotion to stated fact is beyond my control and not entirely relevant. ] (]) 17:49, 23 August 2022 (UTC)

=== This is awkward ===

This article has a certain behind-the-scenes notoriety among Misplaced Pages editors. A very long conflict about the speed of light culminated in an arbiration case (if you're unfamiliar with the process, I'll just say that on Misplaced Pages, arbitration is where we go when all other forms of dispute resolution have been exhausted and the community has been unable to agree on an effective end to disruption). The ruling on that case, ] or ] for short, began by reaffirming pertinent principles and policies, including
<blockquote>'''Neutral point of view'''<br />
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There is a wealth of policy behind each of those links, much of which has developed not in a top-down way but as a documentation of best practice and necessity as the community discovered it. It springs from the fundamental principle that Misplaced Pages isn't written by authorities on subjects; it's written by editors documenting what authorities have written. Much of the above discussion runs counter to that; on Misplaced Pages talk pages, something like (for example) "If one looks carefully at equation (14) on page 780 of the 1935 EPR paper, one finds a false statement" is a big red flag. That is not for us as editors to judge. We merely summarise our sources, giving ].<br />
Arbcom's ruling also affirmed
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7) Misplaced Pages users are expected to behave reasonably, calmly, and courteously in their interactions with other users; to approach even difficult situations in a dignified fashion and with a constructive and collaborative outlook; and to avoid acting in a manner that brings the project into disrepute. In content disputes, editors should comment on the content and not the contributor. Personalising content disputes disrupts the ]-building process on which Misplaced Pages depends. Unseemly conduct, such as ], ] and ], is prohibited. </blockquote>
Then, as so often, some of the harshest things were said by people who were adamant that they were not being in the least emotional, which just goes to show that you don't need to be consciously emotional to overstep the bounds of civility and perhaps provoke emotions in others who, for example, as the only other disputants may quite reasonably take "a bunch of people with strong opinions and insufficient education ... ignorance and persistence" personally. ] describes a different approach. ] (]) 15:59, 24 August 2022 (UTC)

: amounts to ]: insisting that the authors of reliably-published sources must only be giving their personal opinions because they didn't write enough equations (for a point that is more conceptual than technical, so a superfluity of equations would probably be a sign of obfuscated thinking). I'm burnt out on this and don't want to engage any further. Goodbye. ] (]) 18:37, 24 August 2022 (UTC)


:The existence of Cherenkov radiation is already mentioned at the end of {{section link|Speed of light#In a medium}}. <span style="box-shadow:2px 2px 6px #999">]]</span> 10:16, 21 May 2024 (UTC)
::There clearly is ] to remove the properly sourced content. I have restored the content and warned user {{u|MMmpds}} on their user talk page for edit warring. - ] (]) 20:09, 24 August 2022 (UTC)
:::The lack of consensus of 3 people is not a good standard for documenting and neutrally retaining knowledge made freely available to billions of humans. This now requires arbitration. ] (]) 20:58, 24 August 2022 (UTC)
:There is now an issue regarding, "It springs from the fundamental principle that Misplaced Pages isn't written by authorities on subjects; it's written by editors documenting what authorities have written. Much of the above discussion runs counter to that; on Misplaced Pages talk pages, something like (for example) "If one looks carefully at equation (14) on page 780 of the 1935 EPR paper, one finds a false statement" is a big red flag. That is not for us as editors to judge. We merely summarise our sources, giving due weight."
:It is not possible to discuss and resolve disputes without delving into detail. It is not possible to assess due weight without recourse to detail. There needs to be controls in place to prevent famous but out of date references from displacing modern knowledge. In addition, there are missing controls on the quality of sources and their due weight. In essence, the claim is that there is a red flag on account of unavoidable assessment of source quality based upon assessment of content detail. Surely the Wiki policy is not based on assessing weight due to the reputation of the author, the reputation of the publisher and the title on the cover of the book. What is inside the book matters greatly. ] (]) 20:53, 24 August 2022 (UTC)


== Speed of light in literature ==
==Photons faster than the speed of light==
Researchers managed the speed limit of light "inside hot swarms of charged particles, fine-tuning the speed of light waves within plasma to anywhere from around one-tenth of light's usual vacuum speed to more than 30 percent ''faster''." (source: ) <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 13:59, 2 September 2022 (UTC)</small> <!--Autosigned by SineBot-->


I think there needs to be a section about speed of light in popular culture somewhere, namely the teleportation gimmick used areas like in Star Wars and Kingdom Hearts. The disambiguation mentions a few examples but not this article. ] (]) 00:00, 15 October 2024 (UTC)
: That source says this is about ], and this Misplaced Pages article already states that group velocities greater than ''c'' are possible, and have been achieved before. --<span style="box-shadow:2px 2px 6px #999">]]</span> 14:24, 2 September 2022 (UTC)
:: Thank you, but the current WP article not the ] affirm that "fine-tuning the speed of light waves within plasma to anywhere from around one-tenth of light's usual vacuum speed to more than 30 percent ''faster''." 30 percent ''faster'' seems to be a relevant experimental result. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 19:21, 2 September 2022 (UTC)</small> <!--Autosigned by SineBot-->
:::This is not a comprehensible use of the English language. Try again? ] (]) 20:48, 2 September 2022 (UTC)
::::Sorry, there was a typo. The current WP article doesn't affirm that "fine-tuning the speed of light waves within plasma to anywhere from around one-tenth of light's usual vacuum speed to more than 30 percent ''faster''.
::::In the same way, nothing similar is said within the article titled ]. To say that someone has achieved a group velocity that is 30 percent faster than the speed of light, seems to be relevant for the WP article. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 15:45, 4 September 2022 (UTC)</small> <!--Autosigned by SineBot-->
:::::We have an entire section on ] and it begins {{See also|Faster-than-light|Superluminal motion}}The experiment you mention is just one instance in a large field of study. ] applies to the continual flow of scientific experiments and demonstrations too. ] (]) 16:08, 4 September 2022 (UTC)
:::::Ok, thanks for your help. I misunderstood that my link was a summary of a peer-reviewed scientific paper instead of a part of a continous flow of scientific news. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 18:06, 4 September 2022 (UTC)</small> <!--Autosigned by SineBot-->


:We already have a page on ] and one on ] and on ]. ] (]) 01:32, 15 October 2024 (UTC)
== Semi-protected edit request on 15 September 2022 ==


:A fairly well-known old science-fiction story where the speed of light plays a prominent role is "]" by Philip Latham. The speed of light actually remains the same, but other things change, resulting in the doom of the universe... ] (]) 07:41, 15 October 2024 (UTC)
{{Edit semi-protected|Speed of light|answered=yes}}
Copying one letter ] (]) 05:45, 15 September 2022 (UTC)
:] '''Not done:''' it's not clear what changes you want to be made. Please mention the specific changes in a ] and provide a ] if appropriate.<!-- Template:ESp --> '']''<sup>]</sup> 05:59, 15 September 2022 (UTC)

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Is this part accurate in History?

Quote:

Connections with electromagnetism

In the 19th century Hippolyte Fizeau developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of 315000 km/s (704,634,932 m/h).

His method was improved upon by Léon Foucault who obtained a value of 298000 km/s (666,607,015 m/h) in 1862. Kailandosk (talk) 01:06, 18 November 2023 (UTC)

Are you suggesting our article may not be correct or proposing that it include conversions to km/h at that point, and in either case, why? NebY (talk) 11:07, 18 November 2023 (UTC)
There's a definite discrepancy in number of significant digits between the quoted metric and traditional measurements... AnonMoos (talk) 13:10, 18 November 2023 (UTC)
Indeed, but the values in parentheses aren't in the article. If we wanted to include them, we could use {{Convert}}, which would probably round them appropriately automatically, and wouldn't abbreviate miles to "m" either, but I don't see why we'd want to include such conversions in that part of the article anyway. NebY (talk) 13:46, 18 November 2023 (UTC)
I added the parenthesis. It's just a conversion to m/h that I made, just to show how different they are & to convert it into U.S. terms. Kailandosk (talk) 00:15, 24 December 2023 (UTC)
I'm not sure if 315000 or 298000 km/s is correct. I feel it's 315000 km/s, but I'm not sure. Kailandosk (talk) 18:04, 25 November 2023 (UTC)

Why not also include an accurate description of c in miles per second?

186282.3970512 mi/s, to be fairly accurate.

Speed of light in vacuum

Misplaced Pages should get rid of all occurrences of the phrase "speed of light in vacuum". There is only one speed of light, which is a universal constant. Also the speed of light doesn't change if not in vacuum. Group velocity represents the real speed of a photon, and that doesn't change. Only phase velocity is changing, causing the optical effects that mislead people. But this very article is explaining the same in the section Speed of light#In a medium. Lustakutya (talk) 13:24, 20 May 2024 (UTC)

If you have a reference for your point of view please share it. Johnjbarton (talk) 15:15, 20 May 2024 (UTC)
@Johnjbarton shouldn't this work the other way around? I don't want to add anything. I want something to be removed which has no reference. Lustakutya (talk) 15:52, 20 May 2024 (UTC)
The article has rather a lot of mentions of the speed of light in vacuum that are supported by references to reliable sources. Merely in Speed of light#Numerical value, notation, and units, we have

Sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This subscripted notation, which is endorsed in official SI literature ....

I find the idea that we would deny the current definition of the metre rather disturbing. NebY (talk) 16:20, 20 May 2024 (UTC)
This is what I was talking about from the beginning. You are confusing two different concepts as well. c0 has a place in physics. In one place. Optics. In case of refraction the phase velocity is used for calculations, because the phase of light is shifting constantly if travelling in a medium which is not vacuum. Every other area of physics is using the universal constant c, which can be calculated using Maxwell's equations. By the way the Photon article also says "Photons are massless particles that always move at the speed of light when in vacuum." which is plain wrong. Photons are unable to travel slower then c.
If you think that Misplaced Pages is correct in its current state, than I won't say anything more. Lustakutya (talk) 16:58, 20 May 2024 (UTC)
I fixed the Photon article thanks. Johnjbarton (talk) 20:20, 20 May 2024 (UTC)
@Lustakutya You asked that all occurences across Misplaced Pages to be changed. I think we better discuss a reference for your claim first. You pointed to one section, Speed of light#In a medium, but it has sources so you need to explain why they should be removed. Johnjbarton (talk) 16:58, 20 May 2024 (UTC)
Understanding should be the key here. Please look at this video. After watching it you will have the urge searching for references, too. Lustakutya (talk) 17:10, 20 May 2024 (UTC)
That's a great video. But it's not news, sorry. It explains the atomic model of the index of refraction. Based on this video I recommend no changes. Johnjbarton (talk) 17:58, 20 May 2024 (UTC)
  • In the literature:
Google Search Scholar Books
"Speed of light in vacuum" 67,400 68,200
Getting rid of the term would be spectacularly against Misplaced Pages's mission. - DVdm (talk) 19:41, 20 May 2024 (UTC)

References

  1. See, for example:
  2. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 112, ISBN 92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
If the speed of light is always the same, then Cherenkov radiation shouldn't exist. AnonMoos (talk) 09:24, 21 May 2024 (UTC)
The existence of Cherenkov radiation is already mentioned at the end of Speed of light § In a medium.  Dr Greg  talk  10:16, 21 May 2024 (UTC)

Speed of light in literature

I think there needs to be a section about speed of light in popular culture somewhere, namely the teleportation gimmick used areas like in Star Wars and Kingdom Hearts. The disambiguation mentions a few examples but not this article. Jordf32123 (talk) 00:00, 15 October 2024 (UTC)

We already have a page on Teleportation and one on Teleportation in fiction and on warp drive. Johnjbarton (talk) 01:32, 15 October 2024 (UTC)
A fairly well-known old science-fiction story where the speed of light plays a prominent role is "The Xi Effect" by Philip Latham. The speed of light actually remains the same, but other things change, resulting in the doom of the universe... AnonMoos (talk) 07:41, 15 October 2024 (UTC)
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