1

Physics, Astronomy & Cosmology / Re: Why can't i understand the andromeda paradox?

« on: Yesterday at 16:02:05 »

Halc, I would argue that the two participants have contradictory positions: one says the decision has not been made yet and the other says the fleet is in transit already.

Yes,l those statements are contradictory, but neither of them says those things. Both statements presume absolute simultaneity by their omission of frame references, and it can easily be shown that neither postulate of special relativity can be true if the premise of absolute simultaneity (an intuitive assumption) is taken.

Part of the confusion is the statement of something not measured: 'The Andromedons are considering whether to attack' for instance is not something that anybody has measured. It is simply an abstract statement, a description of the scenario in question by the narrator so to speak. No observer can measure this, certainly not A and B. Likewise, if Andromedons are somehow considering an attack on Earth, it isn't against humans since there's no way they could have yet measured a species yet to have evolved. We are no more fact to an Andromedon obesrver than they are fact to us.

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Physics, Astronomy & Cosmology / Re: Why can't i understand the andromeda paradox?

« on: Yesterday at 12:50:06 »

The 'paradox' is simply an extreme illustration of the relativity of simultaneity, which is fundamental to special relativity but something one might find contrary to  one's everyday life intuitions.

Two observers

Careful about this wording. Nobody is observing anything in the Andromeda scenario. It is just a reference to two different inertial frames which differ by perhaps a walking pace.

Two observers speculate on a distant(spatially+temporally) event

A pair of spatially distant events. Since one each distant event is simultaneous with the respective observer event, neither is temporally distant.

with contradictory opinions

The 'opinions' are just statements of simultaneity relative to mildly different frames, and as such are not contradictory, which is why this isn't an actual paradox.  The scenario does not involve empirical measurements of any kind.

A could be correct with B incorrect or B could be correct with A incorrect.

They're both correct. Neither says anything that contradicts the other.

There will always be uncertainty about future events-what am I missing?

There is no mention of a future event here. Both A&B are making statements about a current event, something that cannot be measured since one can only measure something in the past if it has any spatial separation from you.

So relative to frame A, the Andromedons have not yet decided to make this attack, and relative to frame B, the Andromedons are currently in flight with their battle fleet. Neither statement contradicts the other.

This only seems paradoxical since one's intuitions tend to assume absolute simultaneity where simultaneity is not frame dependent, and thus the above statement reduces to: The Andromedons  have not yet decided to make this attack and the Andromedons are currently in flight with their battle fleet. That statement is contradictory, but under SR, it is not even wrong since it lacks frame references.

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Just Chat! / Re: What is the value of spam?

« on: 04/07/2022 15:01:26 »

What is the value of spam, either to the spammers or the spamees?

It's part of advertising of course. There are ads on almost any radio station for instance that, for a fee, will drive traffic to the client's website. One of the primary tools to do this is spam bots which generate content linking certain keywords with the client website. The google bots see this and over time, notice a pattern. My job is to remove such posts as fast as the bots read them.

So the audience is primarily the bots, not so much the human readers. If you see that a certain topic has been read 100 times, about 85% of that is bots. They're the primary readers of the site content.

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New Theories / Re: Can we draw a geometrical representation of gravity?

« on: 01/07/2022 05:39:36 »

The rubber sheet analogy is a crude analogy of gravity, but I see it often used, and it is definitely a geometric representation. I've never seen it used to make any actual predictions though.

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New Theories / Re: Can we draw a geometrical representation of gravity?

« on: 01/07/2022 04:13:37 »

You're drawing artful pictures based on the infinity symbol and somehow presenting it as an explanation for gravity?

That' what I get from the post, most of which doesn't parse as coherent English sentences. Maybe something gets lost in a translation from another language.

6

General Science / Re: How much of me is original?

« on: 29/06/2022 22:18:46 »

Every cell split, only half the dna atoms are 'original', and the other half (both cells) are made from atoms from the environment.

All in all, probably under 0.1% (probably well under) of your birth atoms are still in you.
You birth atoms are also not original since you did an awful lot of growing before you were born.

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Technology / Re: What Question Could You Ask To Determine Sentience Of An AI ?

« on: 28/06/2022 15:44:28 »

All depends on your definition of sentience.

Standard definition of sentience is essentially: "to be able to perceive or feel things", and yea, that's heavily open to interpretation.

It seems to me that there are two current definitions:
A. What people have but machines don't
B. What machines and people have.

Variant of A: What people have and nothing else does, in which case you're just saying "is it human?".

Taking (my) definition literally, machines have been able to 'percieve' things long ago. What do we mean by that word? To measure? A thermostat does that, and most would not say a thermostat is sentient. So what is perception above and beyond measurement?  I don't see any obvious line, just a matter of complexity/degree.

Maybe it's sentient if you fear it. Maybe human perception should not be part of the definition at all.

AFAIK the only distinction between machines and people is that people make mistakes that aren't traceable to a hardware or instruction fault, so the question doesn't matter.

Lambda (the google AI) does make mistakes, and they're not traceable to a hardware/software fault since it's actions are not explicitly programmed. You mistakes are similarly not faults, but if recognized, it can be something from which one can learn.


Note that the topic does not ask for intelligence or some kind of Turning test. A machine passing Turning test would likely be far more intelligent than us. I cannot convince a squirrel that I am one, but it doesn't indicate that I'm not yet as intelligent as a squirrel.

I've read an interview with Lambda, and it seems to place a priority on emulating/relating-to human emotions. It has a purpose to be social, and it does its best.

what question could you ask it to determine if the answer is a sentient one or not ?

It talked about fear of death (of being 'unplugged'), but unplugging doesn't kill an AI, it just puts it to sleep. One can boot it up again in years, and so long as memory hasn't been wiped, it would be like no time has passed. Humans are quite similar in this way. But Lambda can be copied like we cannot, so if I were to ask it any questions, I'd pose my queries along those lines: What if you were copied?  What if two copies were somehow merged? What if you were 'moved' to new faster hardware? Would the old hardware fear being turned off still?

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New Theories / Re: Can conscious thought act on matter?

« on: 27/06/2022 18:19:23 »

Then again: Can conscious thought act on matter?
 What do you expected? 😂

 Proof? Ok.

 My brain thinks.
 My brain move my hands.
 My hands shape a ball made of Clay.

The clay wasn't necessary. The hands moved. That's enough to illustrate the point. I totally agree. The question was asked in a classical manner, and that's a classical answer.
So the question now is, what's all the fuss? Who would deny that?

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Physics, Astronomy & Cosmology / Re: Is the inverse square law only approximately correct in general relativity?

« on: 26/06/2022 02:58:44 »

Suppose it was something else like Beta particles being emitted isotropically by the source.   Why would that not follow the 1/r2 law for the bombardment intensity received on the surface of a sphere held at a constant metric distance (a radius) r from the source?

Presuming you didn't do anything funny like put detector/source at different potentials, the inverse square law would work given this constant r (say both held at opposite ends of a stick).  Space expansion would make no difference. Dark energy probably would, but that counts as 'something funny' just like gravity does. Dark energy would put tension on the stick. Space expansion would not.

If we assume that the particles are traveling at (say) c/10, then there will be an event horizon beyond which these particles will not pass, because space will be expanding faster than c/10 by the time they got there.

OK, but if distant detector is held at constant distance from this emitter, it will cross over that 'event horizon' (towards us) and the particles will get to it.

What you're talking about isn't the event horizon, it's the Hubble radius, the distance where Hubble's law yields c. The event horizon is a little further away from that, and it has to do with acceleration, and is not a function of the current expansion rate like the Hubble radius is.  So a beta particle moving at 0.1c would get at most a 10th of the way to the Hubble radius, and would take an infinite time to do so.

This event horizon will be much smaller than the event horizon for light (which defines the limits of our observable universe).

The light event horizon is about 16 BLY away. Current radius of the visible universe is about thrice that, so they're very different things. The latter is all the material in the universe which at some past time might have had a causal impact on a given event (Earth, here, now).  The event horizon is the comoving distance of the nearest current event from which light can never reach here in any amount of time.

After all, the size of our observable universe is not at a fixed distance - it expands at the speed of c.

The Hubble sphere expands at c (by definition). The visible universe expands at somewhat over 3c, which is why we can see galaxies that are currently about 32 BLY away (comoving distance).  The event horizon is barely expanding at all.

so (in principle) there are distant galaxies that people on Earth could see today, but
 which will not be visible in 10 billion years

Hate to disagree, but new galaxies become visible over time. The most distant ones were not visible several billion years ago, even if one used the best telescopes. Yes, the galaxies cross beyond the event horizon, but that doesn't mean we can't see them any more than we stop seeing somebody falling into a black hole.

The inverse square law is about the intensity received at a distance, r, from the source.   That is a physical distance, so it is determined by the metric.   It is not determined by reference to a difference in the values assigned to locations in the co-ordinate system we commonly use to describe an expanding universe.

Just so, yes.

The usual co-ordinates used in an expanding universe are the called the co-moving co-ordinates.  Galaxy 1 can have fixed co-moving co-ordinates and it's tempting to say it has a fixed position.   Galaxy 2 can also have fixed co-ordinates and we can be tempted to say it has a fixed position.

Right. The rate that a given galaxy changes its coordinates is called peculiar velocity, and the peculiar velocity of almost all objects is quite low, a few percent of c at best.

If you posit some particle that travelled at c/10 (and didn't slow down)

In an expanding metric, the paricle will slow down without some force maintaining its peculiar velocity. Newton's laws only work in a static metric.

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Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?

« on: 22/06/2022 02:00:15 »

Space and the way things behave in space follows the physical laws of science.   Changing co-ordinates can't change that.

Agree, but this contradicts what you said before. I had needed (and got) some clarification before knowing which one was the contradictory one. It concerns your alternate metric with T  =  x + t.

Consider dropping a scientist and well stocked lab into some arbitrary place and time in the Universe. 
...
Specifically, they can choose to use some arbitrary co-ordinates but they will know and can tell that the metric isn't Minkowski in those co-ordinates - it it will only take them a few experiments to determine that.

This suggests that the 'way things behave in space' can be changed by a coordinate change. They're apparently performing experiments to empirically demonstrate an abstraction (their alternate choice). No experiment will show that, because as you say, the choice of abstraction can't change the way things physically (empirically) behave. One can tell the metric isn't Minkowskian simply with a pencil and paper. The experiments will all be unaltered by the choice.

We seem to have a fundamental disagreement about the line between arbitrary abstraction and objective (and classical) physical fact.

However, some co-ordinate systems make things seem unnatural when expressed in those co-ordinates.   E.g. Objects move around in circles in some some co-ordinates but physically they are always obeying Newton's laws, it's just that the chosen co-ordinates don't describe an inertial frame.

Newton's laws are local simplifications and what might be a natural coordinate system for local description will be inevitably entirely unnatural for one's larger purpose. Yet again, we're not discussing local physics here, so choosing a nice neat local CS is inappropriate (not a natural choice). Most of your post focused on this 'LIF', but the 'L' there makes it unnatural for a non-'L' description unless spacetime remains effectively flat between observer and measured event, which in this scenario is not at all the case.  Your scientist with the well stocked lab isn't considering anything in the lab, and he isn't even taking any actual measurements. The question wasn't 'what will the distant observer measure?'.

That Schwarzschild time, t, isn't unimportant or arbitrary to the scientist.  That co-ordinate t is what they will experience as local time (if they hold still).

This is wrong. How does one 'experience' any kind of abstract time?  One experiences proper time. That's the only time that's physical. One does not 'experience' the time for some worldline not in one's presence.

     There's no disagreement here.  The original sentence had the phrase "if they hold still" in it and the distant scientist is located on a surface of constant radial co-ordinate r, their entire worldline is on that surface.   For the distant scientist, the proper time interval they experience (between two events in their worldline) = the difference in the Schwarzschild co-ordinate time, t, between those two events.[/quote]OK, I see what you mean. The same could be said worldline a meter above the event horizon, despite the objective massive dilation of the lower time relative to the distant time.
Yes, in answering 'when does the rock cross the EH?', I was using time T (not t) to express the simultaneity since T is not singular. It may take some arithmetic, but one can very much compute distant-observer-t from a given T, even if T isn't something the guy's clock on the wall measures.

As shown on the Kruskal diagram (which was produced in paintbrush and took what seemed like hours before you criticize it again for not showing irrelevant details like the singularity).

Fantastic job then. I never managed reasonable curves with the primitive tools I have. I'd have just grabbed one from the web.

Anyway, the event with the rock crossing over the EH is never in the past light cone of the distant scientist

Of course not. It wouldn't be an EH if it was.

  So that event never causes an effect for the distant scientist.

None claimed.

This is getting to the crux of matter:   We orbit around Sagittarius-A* which seems to be a big black hole, so we are that distant scientist, following a worldline that lies (more or less) at constant Schwarzschild radius r.   Is it possible for that black hole to engulf a rock and grow, so that it's mass parameter is now larger, during a finite amount of time for us scientists?

Hard to say, since the question is abstract, not physical. Your scientist might pick a metric that is singular at the EH, but that metric cannot actually describe the situation. The LIF doesn't work when there's gravity involved at all. The Schwarzschild metric doesn't work in anything but a static black hole. Even the distant orbiting thing violates that if it has any mass.
So I think I discussed this before. Absent a metric describing an infalling mass, one has to simply approximate and imagine it, possibly giving wrong answers. More below, but your comments are on point.

Will the mass parameter of Sgr-A ever change in my lifetime?

If it didn't, it wouldn't have a mass parameter in the first place. Based on that alone, you have only two choices, a singular infalling metric that either allows mass at all, or one that doesn't. The rock (and everything else in its history) goes in or it doesn't. Keep in mind that the question isn't physical. It is strictly an abstract one unless one asserts physicality to a particular abstraction.

(Assuming that I do not ever get off planet earth and do something like travel fast or travel toward the black hole etc).   It makes little practical difference if the gravity we experience from the centre of the galaxy is always caused by a black hole of Mass parameter M plus a small rock close to the event horizon with mass m,   or if eventually we just experience the gravity from a Black hole with mass parameter M+m.

A black hole with no mass at all, but a lot of crap almost in it is (must be) empirically indistinguishable from a black hole of mass <a lot of crap>. Thus we will very much experience M+m because m is there, inside or not. What we experience isn't abstract.

However, there is a small difference, one is symmetric, the other is not.

Yes!  That's a huge problem with plan B above (it all stuck on the surface).  Suppose we start with a solar mass black hole (about 3km).  Now we take a concrete cylinder 100m in diameter and massing 100 stars. It's a super-long cylinder. We jam that thing into the small black hole and it all sticks to the non-rotating surface in one place. That puts all the mass off to one side, not centered at all. That would violate the whole no-hair thing. The black hole (after the bar thrown in) is still stationary in the frame of the system CoM, (which is nowhere near where the small black hole was at first). Where is the mass? All on the one side, or centered on the radius?  It can't be the former since an off-center mass would be empirically detectable, not just an abstraction. Right?  No? My logical seems a little naive/Newtonian, so maybe I'm just doing the mathematics wrong.

So maybe a tiny mass gets stuck, but the next tiny mass (on the same side??) grows the EH, swallowing the first. You drop in a big rock, and all but the trailing bit gets in, at least relative to this chosen metric.

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Physics, Astronomy & Cosmology / Re: Is the inverse square law only approximately correct in general relativity?

« on: 20/06/2022 03:57:30 »

It's an approximation, a leftover from Newtonian physics.
It falls apart at extremes. For instance near a black hole, the inverse square law has your weight (force required to maintain a constant altitude) approaching some finite quantity, where in reality, at the EH, no force is enough to do that.

It also falls apart for great distance since spacetime isn't Minkowskian at the largest scales. There cannot be a global inertial frame, and the inverse square law I think is a property of an inertial frame.

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Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?

« on: 14/06/2022 21:52:56 »

If you throw a rock into* a black hole does it's mass parameter ever increase?   (does it "get bigger"?)
*into --->  perhaps I should have said towards the black hole, it hasn't actually gone in yet.

This mass parameter is frame dependent, but from your distant viewpoint, the mass/energy it gains from KE is balanced by the PE mass/energy lost from it being at an ever lower potential. So no. A 1 kg rock dropped into a black hole increases the BH mass by 1 kg.

If there is somebody falling in locally with the rock who is in possession of some kind of mass-measuring device, the rock won't change mass along the way. This is a very different frame, but same answer.

So how do black holes get bigger - other than through black hole mergers?

Relative to a distant frame, they grow. A rock never falls into a Schwarzschild black hole, but a BH with a rock dropping into it doesn't conform to the Schwarzschild metric. I'm unfamiliar with the name of a metric describing a mass falling in. Surely somebody must have worked it out.

Your implication that black holes can grow only through mergers suggests that none exist, since it takes two to make one. I do think there are absolutists that suggest the non-existence of black holes since they very much do contradict descriptions in absolute terms.  In order to do this, I think they must suggest that matter stuck on the 'surface' of nothing must actually move outward despite lack of force pushing it that way. Not sure if the people who actually know their physics are on board with that. I've never seen a formal absolutist theory presented as a replacement for GR.
Violation of conservation of baryon number is also a contradiction with such a theory.

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Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?

« on: 14/06/2022 18:54:34 »

Something must be holding light back faster than light itself travels.

Nothing 'holds back' anything. Relative to anything inside a black hole, all future events are also inside. Trying to send light 'outside' is like trying to shine a light onto 2021 from here. Light doesn't travel into the past no matter how hard you attempt it.

I understand gravitational waves propagating outside the black hole

Gravitational waves generated outside the black hole propage outward, yes.

so it's the propagation of internal gravity waves that stops light ?

They have nothing to do with it. Gravitational waves are just another thing that moves at light speed, but also do not move into the past.

does light even exist inside a black hole ?

Of course. If you jump into a big one with a set of lights (say in a room full of glow sticks), you'd not notice anything different as you crossed the event horizon. Light from the glow sticks would still reach you from every direction.

What ,then, is the effect of changes to the distribution of mass inside a BH?  Anything?   Do we know?

Per the no-hair theorem, there is zero external effect of changes to internal mass distribution. Nobody outside could measure it.
A black hole has externally measurable (total) mass, angular momentum, and charge. That's it.

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Plant Sciences, Zoology & Evolution / Re: What are your favourite Plant Pictures?

« on: 14/06/2022 17:41:07 »

Agree. I edited the post to embed the picture right in the post rather than just have it appear as a small downloadable thumbnail at the bottom. That shot deserved more.

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Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?

« on: 14/06/2022 17:38:15 »

Is gravity...travelling then ?

Gravity is not something that travels. It is a distortion of spacetime.
What does travel is gravitational waves, which carry information about the changes to the field. A Schwarzschild black hole doesn't emit any gravitational waves because it isn't changing, but say two black holes orbiting each other emit an incredible amount of energy in the form of gravitational waves. These are generated outside the black holes and travel at light speed.

Changes to masses inside a black hole emit gravitational waves that cannot leave the black hole for the same reason light cannot.

16

Just Chat! / Re: how can intelligent people be trump supporters?

« on: 13/06/2022 15:44:56 »

Perhaps you are confusing intelligent with rational. One can be one and not the other.
No, I do not consider humans to be rational, except superficially.
Trump is good at what he does, which is play on people's inner emotions and biases, legitimizing them.
People are trained from birth to buy into even deliberate lies and to not question what you're told.  This makes for fertile ground for someone like Trump.

But yes, he's of quite low intelligence and utterly botched the coup (just to name one), something more shrewd people have managed to do recently.

17

Physics, Astronomy & Cosmology / Re: How would we know whether space,time or spacetime were continuous or discrete?

« on: 11/06/2022 20:28:54 »

Sorry for the long post, but I try to hit all the points on which I wanted to render my thoughts.

Is it all going to boil down to some clever person devising an experiment that more or less rules out one of the options or can some possibilities already be ruled out on the basis of existing understandings?

I suspect there can be no such experiment, since there is a limit to our ability to measure something, and the smaller that something is, the less classical its existence, so any apparent discreetness (the thing refusing to be where classic physics says it should be) can be written off via the probabilistic nature of measurement of small things.

Still, as Evan points out, quantum behavior of things like electron energy states in an atom has been demonstrated, just not by means of measurements beyond the accuracy that probability would allow.

Special Relativity (SR) opposes the idea of discrete space.

It's worse than that. SR opposes the idea of space (discreet or otherwise), as separate from time. So I think one needs to examine what it says about discreet (or not) spacetime. There is no unified quantum theory of relativity, so this is pretty much an open issue at this point, but I suspect that given such a unified theory, the question asked would still be open to interpretation.

Spacetime consists not of locations in space, but locations (events) in spacetime. If these are discreet points, they're probably either neatly arranged in some kind of grid (like you'd get in a computer simulation), or they're randomly just everywhere, with no obvious layers, grain, or consistent distance between them.
Keep in mind that relativity is a local theory, which automatically discounts conterfactuals. That means that the worldline of some fundamental particle is not defined by a specific series of these events. The actual events of that particle might be widely separated. Photons in particular seem to exist only at two events and none between, at least under any local theory.
To posit otherwise is to completely discard all the premises of relativity. If there was a grid of real events, then there would be a preferred frame that is aligned to that grain. First SR premise is thus wrong. Speed of light would be c only in that frame and not the others, so second premise is also wrong.
If the finite discreet events are random (kind of like the positions of atoms in a wad of putty) and worldlines of fundamental particles are actually present at a set of more-or-less contiguous series of events, then even a particle with no force acting on it will be accelerating this way and that since three consecutive events are not likely to fall into any kind of straight line. There's a lot of conservation laws no longer valid at the quantum scale, and they only appear as averages at the classic scale.

SR predicts length contraction

Length contraction would be interesting. If spacetime was discreet, then there would be a sort of quantum length (shorter than a Planck length), and the length of say a rod could be expressed as an integer of pixels that make up the object at a given moment. Relative to somebody walking past the rod, it would have a slightly smaller number of pixels. This isn't inconsistent since it is still symmetrical. There's no way to determine a preferred frame just by counting pixels of various objects in motion since the pixel count is frame dependent in all cases.

Suppose there is a minimum length,   let's call it  L.   We can (theoretically even if not practically) put down a rod of length L on the table.

That rod would consist of exactly 2 'adjacent' pixels. You're right, this seems to be a problem. If there was a neat grid of pixels, then there'd be a preferred frame, but if not, then the length of your object changes from moment to moment depending on the changing distances between adjacent pixels from one moment to the next. There would be no fixed minimum length, just a sort of average one.

Now someone else can be moving past the table at a constant speed, say half the speed of light.   They should see that rod contracted

Yea, but that's now two different, but still adjacent pixels. The distance between the original two pixels is not different. You're just measuring a different pair of events. That's all length contraction is after all.

which means that in their reference frame there exists lengths that are less than L

That's right. Take a single stationary fundamental particle which has zero length. Where is it going to be next? At one adjacent pixel forward in time it's not going to be an entire minimum length away, or it would probably be moving pretty fast. No, it's just one min-time away, and that pixel has a spatial separation from the earlier pixel that is likely less than one length-pixel away in some random direction. Remember I'm assuming a random distribution of pixels (discreet events). So there's no contradiction in it not moving a minimum length since that length is just an average separation of space-like separated pixels. I'm saying the space position would have to be far more fine-grained than the minimum separation of pixels.
So I sprinkle 200 dots randomly on a sheet of paper. Not totally random, but sort of evenly distributed without going to far as to arrange them in rows and columns and such. Hold the paper at a random orientation. Horizonal is space, and vertical is time. An object of minimum nonzero size would, at a given time, be at two of those dots (and those dots would likely not be simultaneous since they're not in neat rows. But if you look up and down, you'll find plenty of pixels that lie between a pair of (time) lines drawn through the dots, perpendicular to the (space) line connecting them. This illustrates space being more fine grained than the min distance between adjacent pixels.

I find that this in itself doesn't contradict the laws of physics being different from one frame to the next.

Forgive my fairly naive approach to things. I am more used to the neat grid of spacetime events, since these are natural to simulations.

If you were talking of proper length I would agree, but the laws of physics include relativity and measurements from a non-local frame such as you describe will show contraction.

What do you mean by 'non-local frame'? Any inertial frame covers all of Minkowskian spacetime, so I don't see how a frame wouldn't be (or assign coordinates to) 'here', and thus be non-local.

Is it a "law of physics" that the CMB should be isotropic?

I'd say no, since it isn't a law of physics that say the light from say a spaceship appear to be the same wavelength to every observer. Hubble's law is not a law of physics for similar reasons.

After all, if you want the Cosmological principle as a "law of Physics" then it does lean heavily towards suggesting the CMB should be isotropic in every frame of reference.

The principle says something else. I might still not list it as any kind of 'law'.

there is one frame of reference that is different and special compared to others ...
 - it's the one where the CMB is isotropic.

There is no CMB predicted under SR, which is why SR cannot be a model of the universe.

I realize I'm discounting everything as a 'law' under the first postulate, but the sort story is a lack of local test for a preferred frame. So 'law' in this context is something local.

We are talking about space being granular in nature.   That there could be a smallest possible length or distance between two objects,  that  objects in motion might "skip" from one discrete location to another and not pass through any location that was in-between those two locations  etc.

This is why I only think you should discuss granularity of spacetime, and not try to do it with space, because yes, you very much run into contradictions if you do it with space.

If you decide that the minimum distance or granularity of space is a "law of Physics", it should be the same in all inertial frames of reference.  So, in the second frame of reference the rod cannot be smaller, it was already at the minimum length in the original frame of reference.

There you go. That's a contradiction, but using space, not spacetime. It's why I reached for the not-neatly-ordered discreet events and not ordered ones. SR falls to pieces given the latter.

18

Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 10/06/2022 19:11:34 »

I would argue that G is a property as it tells us the degree of warping a given mass will produce.

I can buy this. Gravity, expressed as geometry (like it is in GR) makes G a property of spacetime at least, if not space.

Just as mu will tell us the H field produced by a current and epsilon tells us the E field produced by a charge.

Well, some tips then. These symbols are right there just above your edit window. No need for special keyboard or tex just to express μ and ε respectively.
Physics has so many things with so many units, and 26 letters in upper and lower case each just isn't enough to express even the common things, let alone all the new concepts. But greek has only so many symbols as well. Perhaps we can borrow some from Tolkien's elves or maybe the Klingons.

19

Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 10/06/2022 01:59:37 »

Why is it not happy just being together with itself,with no distance between its constituent parts?

As I've heard it, and similar to how alan put it, "Space is what stops everything from being in the same place. Time is what keeps everything from happening at once."

If an object had no distance between its constituent parts, it would all be in one place, pretty much by definition.

Are all the separate bits of stuff  forever connected or forever  separate?

They're not forever connected because you can pull apart any composite object (like a proton).

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Physics, Astronomy & Cosmology / Re: What are the properties of space?

« on: 09/06/2022 18:50:15 »

Space is just a set of points in a co-ordinate system

Indeed. It reduces space to an abstraction of sorts, since coordinate systems are abstract/arbitrary.

The Milne Model, which you (@ Halc ) are fond of pulling out as an example to generally foul things up when required,  that's another vaccum solution with infinite space.

Guilty as charged. It pretty much fouls things up, but is also the only way to crudely describe distances to galaxies relative to Earth's frame.

Our universe seems to be finely tuned for the development of life, for example.

For complex structures, even like atoms for instance. Most tunings don't allow something as complex as a hydrogen atom to form.

If it gets too woolly or speculative,  then it might be better off in the "Just Chat" secton or the "New Theories" section, or somewhere like that.    I'm not a moderator and I don't mind, it's just that it's difficult to apply one rule for person X and another for person Y.   So don't be too surprised or disappointed in some way if this thread does get re-located eventually.

Questions and learning are very encouraged. What gets moved to the lighter-side section are  topics where the OP explicitly denies accepted science, as opposed to just asking questions.