21

New Theories / Re: What is the real meaning of the most-distant-quasar/galaxy?

« on: 19/05/2022 23:38:38 »

Despite this being a reply to Dave, I am posting this mostly to readers who actually care about what some of these numbers mean. I know that Dave will continue to post things that conveys a lack of reading comprehension of this information.

Yes, we can measure the Hubble constant.
and it is constant everywhere.

It is not constant anywhere. It is approximately 1/t where t is cosmological time, and being a function of time, it is continuously changing, not a constant at all.

https://www.researchgate.net/figure/The-Hubble-diagram-or-the-velocity-distance-relation-plot-for-type-Ia-supernovae_fig1_331983227
The Hubble diagram or the velocity-distance relation plot for type Ia supernovae

They don't say how they measure distance in that graph. There are many ways to do so, and they're approximately the same only for nearby objects. That graph goes only to about 2 billion light years away, so yea, it doesn't matter much. But we see galaxies much further away than that, and distances become meaningless without specification of coordinate system used.  My example object is GN-z11, a very distant galaxy. Some typical choices:

1) Inertial coordinates: Only in inertial coordinates is light speed a constant c, and the coordinate system only applies to space that is more or less Minkowskian (flat), which is not true at large scales. In such coordinates, light can get from anywhere to anywhere else given enough time. There are no event horizons. The Milne solution uses such coordinates. Using such coordinates, the current size of the entire universe (relative to the inertial frame of Earth) is a sphere of radius about 13.8 BLY. Distances are measured along lines of simultaneity in the chosen frame. GN-z11 is about 13.5 BLY away, and the light we see now was emitted 6.7 BY ago.

2) Proper distance, comoving coordinates: This is the only coordinate system where H0 is meaningful. There is no maximum speed for anything, so there is no problem with objects at arbitrarily large separations after finite time. Distances are proper distance (measured by adjacent comoving rulers at a given time) traced on lines of constant cosmological time.
GN-z11 is a proper distance of about 31 BLY away and the light we see now was emitted 13.2 BY ago from only about 2 BLY away. Light from sufficiently distant events will not reach us due to acceleration of expansion forming event horizons.

3) Comoving distance/coordinates: In these coordinates, light speed is a function of time (c/scalefactor). Most objects (galaxies) are reasonably stationary and their distance is fixed since the big bang. Distances are proper distance (measured by adjacent comoving rulers at the current time) traced on a line of 13.8 BY cosmological age.
GN-z11 is a proper distance of about 31 BLY away and the light we see now was emitted 13.2 BY ago from a comoving distance of about 31 BLY.  Light from sufficiently distant events will not reach us due to dark energy slowing light speed to the extent that it can never reach us.

4) There is also the dubious light-travel distance, which isn't a valid coordinate system at all, but declares the distance to objects to be c/t from emission event. Light from GN-z11 was emitted from about 13.2 BLY away as measured by light travel time.

The velocity-distance relation plots for freely expanding gas molecules (Figure 2 to Figure 6) are exactly like the velocity-distance relation plot for the receding large-scale structures according to the Hubble diagram; the molecules receding slowly are closer to us whereas the molecules receding faster are further away from us.

That's nice, but the model is Newtonian and doesn't work at all at scales approaching visible universe distances, let alone distances beyond that.

Hence, at any distance and at any direction from us the Hubble constant is always 70 (km/s)/Mpc.

No. Only at events at similar cosmological time to us, which reduces the applicability of the value to coordinate systems 2 and 3 above.

Therefore, the value of Hubble constant should exists at any location in the entire infinite universe.

Again, no. Only to events at similar cosmological time to us.

Hence, if we could jump to a point that is located at 10BLY from us

Ambiguous statement without coordinate system. Using for instance inertial coordinates, jumping to a point located 10 BLY away gets you to a galaxy where the Hubble constant is currently measured at perhaps 100 km/sec/mpc, not 70. This is why choice of coordinate system matters.

we would find that any galaxy that is located in the visible universe of that point has exactly the same Hubble constant.

If you used comoving coordinate system, then you can choose a galaxy a trillion LY away and H0 will currently be measured at 70 there, just like here. There are no galaxies that far away in the inertial coordinates, not in our frame anyway. In a different inertial frame, yes, you can get galaxies at any distance you want, but H0 will not currently be 70 there.

1 Trillion years away and even in the infinity LY away

Infinity is not a distance or a size or a number. Much of your nonsense assertions stem from using it like it was a number. BC has pointed this out. Yes, you can talk about a galaxy a trillion LY away, at least if you use an appropriate frame.

Therefore, as 1/H0 is the calculated age of the Universe, then the age of the entire infinite Universe is 13.8 BY.
Hence, 13.8 BY ago, just after the Big Bang and the inflation the size of the entire infinite Universe was at the size of "grapefruit".

So very wrong. Nobody said that. You keep (seemingly deliberately) dropping the adjective 'visible' from 'universe'. I have a hard time believing anybody is this stupid, so it just means you're trolling when you make nonsense statements like that.
The visible universe was about the size of a grapefruit shortly after inflation. It was much smaller before inflation, but the Hubble 'constant' is entirely inapplicable until after inflation. The universe expanded at an exponential rate during inflation, but only at an approximately linear rate thereafter.

Therefore, as long as we all agree that the Hubble constant is equal everywhere - the Big bang should create our current infinite universe from a single bang.
There is no other option!

There are other options, which is why these things are 'unknown', and essentially do not matter.

Is it possible for the Big Bang to form Infinite Universe in a single bang that took place 13.8 By ago?

You just said that was the only option, and now you're asking if it's even possible. Go figure...

22

Physiology & Medicine / Re: why is my skin so sensitive when I have a fever?

« on: 19/05/2022 16:14:22 »

Is this a known effect?

Very much so, especially for flu. It is similar to heightened sensitivity to sound and light, especially when feverish.

Is there a known (or likely) mechanism?
Is there anything I can do to limit it while recovering?

Apparently staying hydrated is a good way to limit it. Ibuprofen helps reduce inflamatory related symptoms, including the skin sensitivity. I found that acetaminophen does a nice job on headaches and fever, but not so helpful with the inflamation.

Benefit of covid: Our altered social practices have seemingly prevented about two years of all the common stuff I/we usually contract each year. Sorry this hasn't been entirely true for you.

23

Physics, Astronomy & Cosmology / Re: What happens when photons leave the sun?

« on: 18/05/2022 17:27:55 »

When photons are on their 1,000,000 year journey out of our sun

First of all, it is dangerous/misleading to mix quantum and classic physics. Light might take a million year journey as you describe, but a photon is a quantum object which has no real evidence of existing until it is measured (absorbed) by something. It doesn't take a path. So let's stick with light, or a light pulse, both classic concepts.

are they traveling at 'c'

Light in a vacuum travels locally at c. Open space isn't a perfect vacuum, so it might travel less than c, but not measurably so most of the time. By locally, I mean the speed of a given light pulse is dependent on where it is measured, so relative to say an Earth clock, light leaving the sun travels slower than c and gains speed, surpassing c as it nears the orbital distance of Earth. This is due to changes in gravitational potential along the way. But were you to measure that pulse with any local experiment, it would be c in a vacuum.

are photons slowed by the electromagnetic soup called plasma.

Light generated within the sun (by say some fusion event) is very much slowed the progress of light. A given photon will be absorbed pretty much immediately and be re-emitted in a random direction. This random walk might cause any light generated in the core to take about half a million years to reach the surface and actually be emitted into space.

Also, since it takes energy to escape from the sun's gravity well, do photons lose some of their energy and shift frequency upon leaving the surface of the sun?

Frequency (and direction of travel even) of light is a frame dependent thing. Take a dark star emitting no light, but having the mass of our sun. We put a 580 nm (yellow) laser there and point it outward. If you measure it locally, you will measure 580 nm, but if you measure it at a distance of 1 AU, it will be red shifted to a longer wavelength. You might say that is the light losing energy along the way, or you might say that in the frame of the distant observer, the light was that lower frequency all along since it cannot emit move waves per second at the surface than are received at the distant observation point. There's nowhere for the extra waves to build up since the distance stays constant. So from that point of view, the light doesn't change frequency or wavelength along the way. It's constant, and just measured at a different potential.

How much energy and how much Doppler shift is there?

Doppler is due to the changing distance between emission and detection, so as long as the observer stays at a fixed distance from the sun, there is zero Doppler effect in light emitted from it.

You can calculate the gravitational red shift knowing the sun's surface gravity is about 28g and assuming a massless receiver or one at 1g on the earth's surface.

This is incorrect. Gravitational redshift is a function of difference in gravitational potential, not difference in gravitational force/acceleration.  So for instance, I weigh a lot more on Earth than I do on Mercury, but light from Earth would appear blue shifted (not red shifted as you suggest above) from an observer on Mercury. The gravity is under 0.4 g there, but the gravitational potential well is much deeper than here on Earth.

24

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 17/05/2022 17:37:39 »

Mention a different alternative to "always existed".

This would require one to drop one or more naive bias.

"Always existed" is a phrase only meaningful to objects (a house, galaxy, the weather, etc.) contained by time. So if the universe is not reduced to an object contained by time, but is rather a structure that contains time, then it just exists. This is standard realism, a view held by Einstein and by probably the majority of physics that understand Einstein. If the universe is not a structure that contains time, then all of relativity theory is wrong, and there's not really an alternative thoery that has done its own generalization. So for instance, there's the neo-Lorentian interpretation, which says absurdly that all the equations that Einstein derived in relativity theory can be used to make any prediction, despite the fact that they're all based on premises that are wrong (such as the frame independent constant speed of light). But that's a view (used by nobody that actually has to work with physics) that posits the universe as an object contained by time, and thus is in need of being 'started'.

Dropping the bias of 'universe as an object in time' is not difficult, but if it is for you, then dropping the others will be out of reach, so I'll not go into other alternatives that require more out-of-the-box thinking. This is a science forum. Science is concerned with making empirical predictions, and none of the explanations of the existence of the universe make any empirical predictions, so they're not science.

It's like the question you asked about life elsewhere: If it's beyond the event horizon (which is currently just outside the Hubble radius and well inside the radius of the visible universe), then it cannot be measured by us and by any definition of existence that involves measurability, doesn't exist. That's a very different answer than the mathematical "any nonzero probability multiplied arbitrarily high results in a certainty".

25

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 17/05/2022 03:08:33 »

The other part of my premise is that the universe has always existed.

I might agree with that part, at least so far as to say there is not a time when there was no universe (or anything else), and a later time when there was. But I consider time to be contained by the universe rather than the other way around. The statement above is open to interpretation.

The alternative is "God did it". Is that where you are going with this?

Heh... There are a lot more alternatives than that, and ones that don't involve positing something even less likely than our universe. Getting into philosophy on a science site are we?

26

New Theories / Re: What is the real meaning of the most-distant-quasar/galaxy?

« on: 16/05/2022 16:42:44 »

Based on the BBT the Universe started from "Planck epoch".

This contradicts the quote you gave which says the Planck epoch is "immediately following the initial singularity". So saying it started with the singularity would be closer. But also, time isn't meaningful until the Planck epoch, so in that way you could admittedly argue that it is the 'start' of the universe.

"All matter and energy of the entire visible universe is contained in a hot, dense point (gravitational singularity), a billionth the size of a nuclear particle."

So, how that "gravitational singularity, a billionth the size of a nuclear particle" could suddenly be considered as Infinite space without breaking the BBT theory?

It doesn't say that. It says the visible universe is that size, not the entire singularity, which, being singular, has no meaningful size/temperature/density/energy/whatever. So what was to become our visible universe was contained in this space under a billionth the size of a particle (which also suggests that a unspecified particle has a size, suggesting a non-fundamental construct of multiple things). Hey, it's wiki, hardly an authoritative source of what represents the current details of the theory.

Therefore, if the Universe started off with an infinite size

It started with the singularity, which means it's singular: It has no meaningful size and other things, which is what they mean by time and space having no meaning. Don't confuse a singularity with a point. The latter has a size. The former is just where physics (certainly classic physics at least, which seems to be the level at which your nonsense is staged) cannot describe the situation.

"the theory describes an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity")."
If you start the Bang when the Universe is already infinite

There you go, giving meaning where it says time and space have no meaning. So no, the universe has no meaningful dimensions at the singularity, but it begins to at the Planck epoch.

So, how can we claim about concentrated cosmos while this cosmos is already infinite?

Learn some grade school mathematics. Concentration (or density actually since concentration seems more of a chemical term) is not measured in meters but rather units of stuff/volume which can be the same for different volumes. Hence knowledge of the size isn't necessary if the density has been measured. For instance, rock (the heavy stuff like you get at say the bottom of the Atlantic) is about 6 times the density of water. Knowledge of the size of the specific rock isn't necessary for that to be known.

If you start the Big Bang from "Planck epoch", and you claim that the early universe was compact, then by definition due to the expansion rate there is a limit for the maximal size of the Universe.

Non-sequitur. By definition of what? Compact? The word as used here just means relativity dense, and as pointed out just above, knowing the density of a thing gives you no clue as to the size of it.

Let's assume that the maximal size of the universe after the inflation is X.

This assumes that it has a finite size, which seems to contradict your typical assertions. The visible universe was perhaps the size of a grapefruit immediately after inflation. Estimates vary considerably.

We know that the expansion rate is based on Hubble constant  (about 70 (km/s)/Mpc).

No, the Hubble constant is based on the current measured expansion rate. It isn't a constant, and it only tells you approximately how old the universe is since it is in units of t^-1.

Therefore, after 13.8 BY with that kind of expansion rate - there must be a maximal size for the Universe.

This absurdly suggests that expansion must stop now since the universe cannot expand further. Do you read your own comments? There is no maximal size, even for a finite size thing, if it continues to expand forever. The visible universe for instance has grown to about 96 BLY across (proper distance along a line of constant cosmological time) and there is no size of it that will not eventually be reached.

If the real universe is bigger than this maximal estimated size, then there must be an error in the BBT.

Or an error in you postulating this maximal size limit. Hmm, which is it you think?

If you claim that the BBT didn't start from "Planck epoch"

The BBT is a theory that started only about a century ago. Perhaps you mean the universe that started from the Planck epoch.

then our puzzled scientists

I'm not locking the topic, but do stop saying that. It is you that is puzzled, apparently by choce. The people whom you are slandering are far more knowledgeable about the theory than any of us and none of them see problems in the places that you do because that's not where the problems are.

So, how could it be that after observing that quasar for quite long time, we didn't observe even one tinny star as it falls inwards with amazing fireworks?

A quasar is about as fireworks as you can get. They consume stellar masses at an insane rate.
Your comments of black holes is very much along the lines of your prior topics, about which you agreed to desist discussion.

Just tell me to stop the discussion in this topic - and I would stop.

But you don't. You're going on again claiming nothing falling into black holes, even the ones that are visibly doing so at the highest rates. So you don't keep your promises to stop.

27

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 16/05/2022 05:40:00 »

Is this thread in this forum putting me in jeopardy with management?

Not at all. You just don't seem to care that your fantasy cannot possibly work.

28

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 16/05/2022 01:54:46 »

I'm hypothesizing that "big bangs" are not uncommon events in an infinite universe that is filled with matter and energy across its infinite expanse.

Yes, you just said the same thing in the prior post, and it's still wrong for reasons including the one I gave (among others), and not because consensus is otherwise.

Have you contemplated that kind of universe, or do you stop at Standard Theory and generally accepted science?

New theories are fine if they work. This one requires an entire rewrite of the last seven centuries of physics, which I don't see being posted here.

And note that this thread and these posts are in the sub-forum "on the lighter side", and are not intended to be hard science.

Fine, but you don't accept that it cannot work without said total rewrite of new physics that is completely absent.

29

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 15/05/2022 23:53:45 »

I'm going with the idea that there is only one universe, and Big Bang type events occur now and then, here and there, within that one infinite and eternal universe

OK, but why post something like that? It has been explained many times how this contradicts all known laws of physics. Any concentration of mass in one place like a new bang in existing space would be an amazing amount of mass in a tiny space, when it's Schwarzschild radius is far larger. The mass would vanish in an instant into its own temporal singularity. The universe would have nothing but a bunch of black holes in it.

Your name off to the left says "Science enthusiast" but 'going with' something blatantly self contradictory like that is science denialism, not science enthusiasm. Science is about learning, not about blind naive assertions.

30

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 15/05/2022 23:15:49 »

In other words, my question does not even get off the ground if we just assume that GR is correct.

First of all, SR is sufficient for this case since there is no gravity involved. If you're assuming that your assumptions somehow contradict relativity theory, then maybe it's time to rethink your assumptions. Relativity theory does not in any way forbid an object passing in front of another object.

At exactly 6:43, he has the other part of the Minkowski diagram.

6:42 actually is when the nose of the ship is at the event where the rock crosses in front.
atRockEvent.JPG (34.78 kB . 430x267 - viewed 510 times)

The Minkowski diagram still shows the frame of the 'ground'. If in the frame of the ship, the ship would be stationary and not be progressing to the right like they depict. But the animation shows the ship at events that are simultaneous in the ship frame.

Relative to (0,0), where in space and time is the nose of the rocket for the spaceman when the rock rolls in front of the ship?

The event of the rock rolling in front is not present at the origin event, so the spatial location and time of that rock event is frame dependent (per relativity of simultaneity). The physical event is objective, but the abstract coordinates assigned to that event are coordinate system (frame) dependent.

To keep it simple, I don't think we have to give numbers, just put if it is =, < or > than 0.

As depicted in the animation, the rock rolling event is after the origin event in the ground frame, and before the origin event in the ship frame. You can see in the picture attached that the rear of the ship (the only part that will be present at the origin event) has yet to reach the origin and is in fact off the edge of the screen still.

And let's assume that the rock rolls in front of the ship at the same event as shown at the nose of the ship on the ground.

There is no ground in the picture. There's a frame where the hypothetical ground is statationary, but no ground appears anywhere. It is presumed to be a long way off, and this ship is just going by the planet at 0.55c

31

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 15/05/2022 00:01:31 »

There's an aerodrome here where they fly vintage planes. One game they play is to throw a roll of toilet paper out at high altitude and then see how many times they can cut it with the plane before the paper reaches the ground. I envision your event something like that, although toilet paper hitting a ship at 0.55c would destroy an actual ship.

But in the ship's frame of reference, his nose is advanced further from the origin (0,0) (that they both agree on) in the x position (because the ship is in its proper length) than where the rock rolls into its path.  The ship has also advanced further in time from the origin than when the rock rolls into its path.

That just means that in the ship frame, the interaction with the object took place before the rear of the ship reached the origin event. The nose is present at every event along the right dotted worldline, so all those event happen in every frame. Ditto with the other dotted line.

32

New Theories / Re: What is the real meaning of the most-distant-quasar/galaxy?

« on: 14/05/2022 17:13:08 »

As long as you don't know and don't care than don't tell that you know and care.

Excellent idea. You obviously don't care to show any knowledge of science and don't care to appear to learn, so per your conclusion above, you shouldn't be telling us that you don't know and don't care.
So one chance: Why shouldn't I lock this topic?

33

New Theories / Re: If there was one Big Bang event, why not multiple big bangs?

« on: 14/05/2022 06:52:40 »

Would you mind posting a few words from your thoughts

For the most part, you seem to have gotten completely off track. None of your recent posts have been about multiple bangs or related theory. To be honest, I have little idea what you're currently proposing. You're just blogging random and mostly unrelated thoughts.

about how unique life is in the universe, given an infinity of time and space.

If life is of any probability greater than zero for any given star system, then given unlimited star systems, there must be life on an unlimited number of stars. Any other possibility is mathematically inconsistent.
This assumes infinite space (and thus infinite star systems), but not infinite time, since any given type of life is only good for a finite region of time: Too soon and there's too much violence and not time to develop stable life. Too late and entropy takes over and there's no energy left to support life. As it is, life has been on Earth about 4-5 billion years and all but the simplest life will be gone here in another billion. The planet will not support eukaryotic life soon, and that includes anything multicellular.

34

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 14/05/2022 06:42:46 »

At the higher of the 3 clocks/events is the nose of the ship according to an observer on the ground and so is the clock/event below it.

This sentence doesn't really parse for me, so hard to figure out what you're trying to say. There seem to be no clocks depicted in the 30 second clip you indicate. The vid around 6:45 shows a spacetime diagram with one event at the rear of the ship and one nose event (the lower one) for the 'ground' frame and another nose event (the upper right one) for the ship frame, each simultaneous with the rear event in their respective frames. Hence the 20m ship is contracted by a sixth in the ground frame. All pretty straight forward SR so far.
Perhaps the 'lower clock

Now my thought experiment is about what might happen if an object moves really fast in front of the nose of the ship where the lower clock/event is.

OK, at some point an object crosses in front of the ship.

To make the object appear in front of the nose almost instantaneously, we will say that it came from another spatial dimension z going into your screen.

Or y, since the diagram only shows the x axis. The vertical axis is t (ground frame).

If an interception between the contracted nose (the lower clock) and the object is possible in the scenario given, it would seem that there would be an interaction with the nose of the ship that will never happen with the nose of the ship in the future (the higher clock).

You're saying the object that crosses in front bumps the nose of the ship as it goes by, but not enough to damage anything. That's an objective event. It must occur in any frame. Perhaps it left a mark. In the ship frame at the time indicated in the video, the bump event you describe has already happened in the past and the mark on the nose is already there. The nose of the ship follows the nose worldline (the dotted green line) and is present at every event along that line. Likewise the tail follows the parallel dotted tail line. Those lines are straight because apparently the ship is not accelerating in this scenario.

35

Just Chat! / Re: A Short puzzle with dogs.

« on: 12/05/2022 15:27:49 »

you have reached a local minimum not necessarily a global minimum

OK, you wait until a flood occurs and the water reaches just to the straight line between dog and house.
If that's on the table, you might as well wait for the flood to get even worse and perhaps carry the house much closer to the dog, which isn't too far off from my 'riding the raft' idea.

[Spoiler:]

36

Just Chat! / Re: A Short puzzle with dogs.

« on: 12/05/2022 15:01:04 »

Another physical solution:

Spoiler: show

Replace the river 'rod' with a mirror and shine a laser (a surveyors laser that leaves a line on the ground) from the dog to the reflection of the house

[Spoiler:]

37

Just Chat! / Re: A Short puzzle with dogs.

« on: 12/05/2022 14:52:34 »

I'm still working on the circle problem, but have had almost no time to do so. It's coming.

Maybe the dog can shorten the effort by jumping on a board floating on the river, saving steps. I presume such complications are not part of the problem.
This problem has a physical solution:

Spoiler: show

Just put pegs in a board where the house and dog are, and a rod representing the river. Tie a string to the dog and the house looped around the rod and pull it tight. It will move to the shortest path, which momentarily touches the river 4/7th of the way, or ~43 m west of the house.

38

Just Chat! / Re: Too much faith in computers/A.I.?

« on: 10/05/2022 19:57:40 »

Picard: Computer, what is the predominant material in Dyson Spheres?
Computer: Hematite.
Picard: Thank you.

Here's the problem with that: no one ever seemes to ever ask the computer where it gets its facts.

I love how they still name it 'computer' instead of giving it a cute name like Alexa or something. But they don't for the same reason no naming of source of data is involved: It's a fictional show and naming the computer something cute would leave some viewers unaware that it is a futuristic machine being queried, and the data source is not listed since doing so would not add to the plot. Writing for a TV show is very different than an attempt to simulate real discourse on a ship with all the same technology.

BTW, we already have a computer that can answer most questions. OK, it's ability to parse out the actual question being asked is still quite crude, but the answers are most often there.

39

Physics, Astronomy & Cosmology / Re: Does charge contribute to mass?

« on: 02/05/2022 17:48:31 »

For example if two charges are in close proximity, then you can describe the energy as being stored "in" the separated charges.

Anyway, I'm once again interested in where this energy really is and how it behaves:

It seems not to be 'in' any particular place/object/field, similar to the discussion about the mass of an object increasing at higher altitudes. The energy of the rock/Earth system is up, along with the system mass, but that mass is added to the system, not necessarily the Earth, rock, both, or the gravitational field.
Similarly, a system of two stationary protons in close proximity (not too close) has more energy than the same situation with greater separation, but it is probably a mistake to say that energy is in the protons or the field or whatever.

Hence, the main question:   Does charge contribute to mass?

System mass, not field energy or particle energy. Is charge of one particle 'energy'? Only way I can get energy from that is to introduce a 2nd particle, also charged, at which point the energy is a function of their separation.


Didn't yet read the spoiler. Your 'rubbed balloon system' charged with the 1800-1 arguably has more mass because all those extra electrons have been brought into proximity to each other, which is energy that can be harvested. It took work to put them there.

40

General Science / Re: Is 2 really prime? If so, why isn't 1?

« on: 01/05/2022 16:15:12 »

Your definition of a prime (in the OP) includes 1, but the definition asks for 'divisible by 1 and itself' and 1 is not a divisor of 1 in addition to the first 1. That's pretty shaky, but every integer > 1 can be factored into exactly one set of primes, and this would not be true if 1 was a prime. So 6 could be factored into 2,3 or 1,1,1,2,3 and the list goes on.

As for your geometry example just now, besides leaving 2 off the list, your definition as worded doesn't work as worded.
"regular polygons with n sides that can only be divided into n identical portions by connecting vertices to the center"
Take your hexagon. There is only one figure below it that divides it into 6 portions. The others are not divided into 6 so don't count. You might say "regular polygons with n sides that can only be divided into identical portions by connecting vertices to one common additional point".  The mention of the center is unnecessary since I don't see a way to do it without picking that point.  The "one common" part seems necessary since I can happily divide any regular polygon into many identical portions. The pentagon for instance can be slice up into 20 identical shapes, but only with the addition of more than one new point where the lines intersect.

Another possible wording:
"Any n>4 is not prime if a regular n-sided polygon can be divided into m identical portions, with 2 < m < n". Given that wording, my dividing the pentagon into 20 shapes doesn't disqualify it as being prime, and even counting mirror images as identical doesn't trip up the definition.