1

Physics, Astronomy & Cosmology / Re: How does special relativity explain dimensional components ...

« on: Today at 02:29:15 »

Hi again.

I would like to know how the components of time vs space work in SR.  It seems, from where I am at in my knowledge, that the temporal component and the spatial component can swap, aka fabric of spacetime.

   It is a fascinating topic and I'm glad you're interested.  I'm sure people can recommend references and texts.    We might need a little more guidance as to what your current level of experience is.   It doesn't matter, by the way, none of us were born knowing anything about SR.  More-over, you're going to need to be the one giving me some good references in a few years, please.

Here's an example:
 
Pre-requisite:   Someone who studied some Maths and Physics at school to about age 17.    For example a United Kingdom AS level.

The resource:   Freely available YT videos of lectures presented by Prof. Leonard Susskind of Stanford University.     

Time required:    There are many (I think 10)  lectures although much more than just SR is covered.   Each lecture is about 1.5 hours.    You could sensibly skip some introductions (you won't care about essay deadlines etc.),   however, realistically you should expect to watch several hours of lectures and give yourself some extra time to think through and try some problems yourself.

Alternatives include some good textbooks.   Much faster alternatives include assorted "Pop Sci" videos which will race over the topics in under 20 minutes - but that's never going to offer the full understanding.

Anyway.... the main point is that I couldn't present SR any better than the existing texts and resources for the topic and I'm also fairly sure a forum is not ideal for the task.   However, if there were some specific issues you wanted to discuss then I'm sure people on this forum will try and help.

Best Wishes.

2

Physics, Astronomy & Cosmology / Re: How does special relativity explain dimensional components ...

« on: Today at 01:39:42 »

Hi.

If both answers are correct, then doesn't that mean that 2 different universes can exist depending on which object you choose to be at rest?

    Does there need to be two universes just because there's two different ways of describing it?

You can go outside and measure your bicycle and find it's 1 metre long.
I can go outside and measure your bicycle and find it's 39 inches long.

Presumably, you wouldn't have thought that there must be two different universes, one where the bicycle is 1 metre and the other where it is 39 inches.   You'd probably be quite happy to accept that I was using inches and you were using metres, we were just using different measurements to describe the same physical thing.

    However, if what you meant was that (for at least some things) there's no objective reality, then I'd agree with you. 
None-the-less, at the moment (as described by Colin2B) you haven't really described a situation that required much more than simple Gallilean relativity and it might be best to just push complications from special relativity to one side for a moment.   It's not important here.

More specifically, if A is chosen to follow the direction of the time dimension, or, "be only in time" (I can't remember the proper wording; it's been a long time since I took linear algebra)

    I think this could be a problem or misunderstanding.   You could choose to make object A stationary and that would make the spatial component of its 4-velocity 0.   However  0  is something, it is a numerical value.   The object still has an ordinary spatial velocity, it's just that the magnitude of that velocity is 0.   I probably need to rephrase this - the object is always found somewhere in space it doesn't vanish and exist "only in time" or anything weird like that.    The object is found at the same place in space at all times, it has 0 velocity which just means it's location doesn't change with time.   
    The spatial 3-velocity is  (0, 0, 0)      it is not   ( n/a,  n/a,  n/a )

Best Wishes.

3

New Theories / Re: How Many Numbers Exist?

« on: Yesterday at 14:25:44 »

Hi.

Here are what I  got after go down the rabbit hole.

    Seems reasonable.   For whatever it's worth I didn't know all of the classifications you've managed to find.  I have no doubt that there's more ways you could divide up the real numbers.   There should be loads of sets of numbers that someone has given a name to and had some passing reason to want to study them.

    If you were studying the Real numbers as part of a structured course in Real Analysis,  then at about this point people would push your attention to the remarkable facts that do seem to appear:
1.    It's very difficult to construct the Real numbers by algebraic methods.   (Conventional wisdom is that you can't).
2.    However techniques from Real Analysis allow the construction of an object (a complete, totally ordered field extension of the Rationals) that we can call the real numbers.
3.     Furthermore, accepting certain axioms, we have a uniqueness property:  Any complete totally ordered field extension of the rationals is the same field (up-to isomorphism).

   Item 3,  the uniqueness property, is oddly reassuring but not necessarily important.   It's psychologically reassuring:   When Mr. Smith thinks of the real numbers they are using the same thing as Monsieur Smithe  except that one says    "one", "two", "three"   while the other calls it  "un", "deux", "trois"   etc.    It's philosophically reassuring in that perhaps the Real Numbers aren't completely arbitrary or abstract things - there is actually only one thing (up-to isomorphism) that they can be.    The uniqueness of the Real Numbers is often the final result or crowning glory presented at the end of an introductory course on Real Analysis,  however, I'm not sure it really matters for the purposes of Mathematics.   (Maybe it just prevents squabbles among mathematicians claiming that their Real Numbers are better than your Real numbers).
   

However, 2^∞ > ∞
(At least for the counting numbers), so this one seems suspect.

   Cardinal arithmetic is what they what they sometimes call this.  Ummm... I have no idea what else to say but just didn't want you to think your post had gone un-noticed.  Thanks @evan_au.

Best Wishes.

4

New Theories / Re: How Many Numbers Exist?

« on: Yesterday at 13:25:05 »

Hi.

If a is an algebraic number that is not zero or one, and b is an irrational algebraic number, is ab necessarily transcendental?

That has a significant copy-and-paste error.    ab should be   a^b =  a^b

Best Wishes.

5

New Theories / Re: How Many Numbers Exist?

« on: Yesterday at 03:26:19 »

Hi.

Is there a set of numbers which contains more than algebraic numbers but less than real numbers?

   If you just want a SET of numbers,  yes,  many of them.
There's an infinite set of distinct transcendental numbers,   T.   These are real numbers that are not algebraic.   Actually MOST of the real numbers are these,   the algebraic numbers are countable so they are a tiny drop in the ocean compared to the transcendental numbers.
   Anyway, you could just keep adding the transcendental numbers one at a time until you got bored.

   You can cut down some of those intermediate sets of numbers if you put more of a restriction on your set of numbers.   For example, instead of just asking for a set of numbers, insist that the new set of numbers is always a proper Field in its own right.   These would be called Field Extensions.   (Example:   If you try to add π,  then the field operations automatically generate  π², π³, ....,  1/π, ...., -π, .... (705 + 3/π), ....   so  to ensure the set really is closed under field operations you'd need all of these numbers added in one go).
  None the less, I still think there's an infinite set of simple field extensions you could find.  (I haven't spent too long thinking about it but I reckon you could try a simple field extension by adding π and show that √π is still missing,  so extend again with √π and show  the √(√π) is still missing..... etc.....    the root of what you've just extended with should always be missing).

Best Wishes.

6

New Theories / Re: How Many Numbers Exist?

« on: 02/07/2022 23:13:29 »

Hi.

We can represent any rational numbers by combining two integers as numerator and denominator.
Some irrational numbers can be stated as a rational number powered by another rational number.  Let's call them power numbers. How many more expansion procedures like that are required to cover the whole real numbers?

   I honestly don't know.    It depends what you consider to be an "expansion procedure like that".

For example, would you allow taking limits?     If   {X_n}  is a sequence of numbers you already admit in your set,  then  why not also include the Real number X whenever the sequence X_n → X.   That seems like a reasonable expansion procedure.    Anyway, that expansion procedure gets you straight from Q  to  R   in one step.

   The old fashioned view is that when trying to build the Real Numbers getting from N to Q is just algebra.  You can indeed go a bit further and include some irrational numbers in a field extension of Q if you tried.    However, crossing that last mile to build the complete, Archimedian, ordered field we call the Reals steps outside the territory called "Algebra" and into "Real Analysis"  (i.e. where things like limits need to be used).   It's a bit arbitrary to draw a line somewhere and say this bit and no further is algebra, while that bit over there is analysis but that's what is generally done.   I'm mentioning this because you might be considering "an expansion like that" to be some procedure involving only algebra and not analysis:   If you denied yourself access to the techniques of Real Analysis then conventional wisdom is that you'll never get to R.   

[However, I don't know if anyone was so worried about not crossing that arbitrary line that they really tried hard.  I do know that they wouldn't have been able to prove they had got to R - which is mildly amusing.   This is because they must demonstrate the field is complete and "completeness" is a property firmly held in Real Analysis territory, so they can't even use those ideas let alone perform some test for it].

Best Wishes.

7

New Theories / Re: How Many Numbers Exist?

« on: 02/07/2022 15:06:05 »

Hi.

Apparently, the complex numbers have the same cardinality as the reals and I'm tempted to assume that the hypercomplex ones do too.

   Yes, that's correct.
The usual proof uses interleaving of decimal digits to generate a unique real number.  Here's an extract that explains it with minimal distraction:

To show this (a bijection exists between C and R )  you need to show every real number maps to a unique complex number and that every complex number maps to a unique real number. The first part is easy -- every real number already is a unique complex number. So let's concentrate on the second part, mapping the complex numbers to the reals.

Each complex number a+bi, a and b real, may be mapped to a unique real number as follows: Expand a and b as decimals, taking care not to end either in repeating 9s for uniqueness. Then you can interleave the digits of the two decimal expansions so, e.g, the even numbered digits are from a and the odd from b. Start at the decimal points and work out in both directions. Call the result of this interleaving c.
So you now have a real number c  from which you can recover a and b, and thus the original complex number a+bi.

Since you did this mapping both ways, by the Cantor-Bernstein theorem (or common sense) the cardinality of the complex numbers and real numbers are the same.

[Quote taken from:  https://www.quora.com/Do-the-complex-numbers-have-a-greater-cardinality-than-the-real-numbers ]

The proof requires something like the Schröder-Cantor-Bernstein theorem which means that you do require some of the higher axioms of set theory   (e.g. the Axiom of Choice or axioms of logic such as the principle of excluded middles).   Wikipedia has some discussion:  https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem#Prerequisites .    To say that a simpler way,  in some systems of mathematics you would not be certain that C and R have the same cardinality.

    Anyway,  with  |R X R| = | R |   it would be simple to generalise and show  | R^k | = |R|  for any natural number k.     Since the hypercomplex numbers are elements of a finite dimensional algebra over R,  we have that any algebra of hypercomplex numbers would have the same cardinality.

There are as many real numbers in a set of complex numbers where imaginary parts is 0. Like wise, there are as many real numbers in a set of complex numbers where imaginary parts is 1. You can change the imaginary part with any magnitude. Each of them contains a whole set of real numbers. How can we say that they have one to one relationship?

    Indeed it is weird.   It follows from a set of abstract axioms.    "Intuitionists" would not accept many of the results concerned with cardinality of infinite sets.   As already mentioned, there are systems of mathematics (or axiom schemes) that would not conclude  |R| = |C|.   If I recall correctly, you ( @hamdani yusuf  ) have an interest in Philosophy.   You might understand the Wikipedia description of Mathematical Intuitionism  better than I do:   https://en.wikipedia.org/wiki/Intuitionism.

Best Wishes.

LATE EDITING:  Sorry for the overlap.  Several new posts have appered since I started writing this.  I'll read those in a moment.

8

New Theories / Re: Origin of magnetic force

« on: 02/07/2022 11:58:26 »

Hi.

Have you tried to calculate the repulsive force when v is 1 mm/s?
What happens to the force if the velocities are doubled?
What must be done to make the force attractive instead of repulsive?

   No.  I'm also sorry if the previous reply wasn't all that well structured.   I seem to have CoVid and can't concentrate.  I'll be handling light topics for a few days.

Best Wishes.

9

New Theories / Re: Origin of magnetic force

« on: 01/07/2022 17:57:37 »

Hi.

    Sometimes I hate making replies, especially when they just aren't likely to say what the original poster wanted to hear.   I don't know what I can do about that, sorry.   Let's just start by saying that Magnetism is complicated and not entirely understood.   I don't claim to understand all of it.

If I assume that translation to the frame of the electrons is symmetrical to translation to the frame of the wire atoms anyway

    Why or how could you do this?   In what way is the situation symmetric or the same?

Here's a typical electrical circuit:

   
    The conventional current moves anti-clockwise around the circuit, so the electrons move clockwise.
Now if you have a test charge at the bottom of the circuit and you use a frame of reference where the positive charges of the wire are stationary, then the situation looks a certain way.     Neither the top, bottom or side wires in the circuit are moving,  a certain total length of the wire is obtained and the electrons, being free to move, will tend to spread out so as to be uniformly dense throughout the wire*.
    *This is an approximation but a very good one when the electrons have low velocity and the wire is stationary.  The electrons will tend to move to a region of lower electrical potential just by ordinary electrostatics until all regions reach an equi-potential.   In a more thorough treatment we must note that every charge creates both an electric field and, if the charge is moving, a magnetic field.   The total pattern of movement of electrons is not quite as simple as moving so as to spread out uniformly along the wire.  More generally, we actually do think that the electrons distribute themselves to be slightly more dense at the peripheral (outer edges of the wire) and slightly less dense at the core of the wire, that's how a net electric field along the wire is maintained and what drives the electrons along the wire with the usual drift velocity.    The surface density of charge also changes very slightly as you progress along the wire from the +ve end of the cell to the -ve end  -  BUT overall, this is just complicated and not making a significant difference to the overall density of electrons along the wire anyway, it is almost uniform along the wire.     For low electron velocities and a stationary wire, it's a reasonable approximation the electrons are uniformly spread along the wire.   Specifically, by experiment we notice that if we have current flowing in a wire and we bring a test charge close to it (but the test charge has 0 velocity relative to the wire) then there is no electrostatic attraction to/from the wire (no E field exists).  Conversely if we bring a compass close to such a wire then it swings (a B field does seem to exist).

   As it happens there is an overall conservation of charge in special relativity, so the total number of electrons = the total number of positive atoms in any frame of reference you choose.   The atoms weren't moving and so they are equally spread out (indeed their separation is totally determined by the lattice in which they are held anyway) and then we have seen that the electrons will tend to be equally spread out.   Overall the net density of charge in the wire at any small volume element is 0.

    Meanwhile, if you switch to a frame of reference where the electrons were stationary, then the situation looks completely different.    Presumably you meant the electrons in the bottom wire closest to your test charge were stationary because the electrons move in a loop and there's no way to have ALL the electrons stationary everywhere.   Then the electrons in the top wire are moving at almost 2v and in the side wires the electrons have non-aligned but equal valued diagonal velocities of almost √2 v.   The most striking difference is that the wires themselves are moving in this frame.   There is very little about the situation that is the same as how things look in the other frame of reference.   You can "assume symmetry" but it doesn't make it exist.  Nothing much looks the same in this new frame of reference and the approximation about the electrons distributing themselves uniformly (marked with a * earlier) doesn't hold well.
    Overall there tends to be a lower density of electrons in the bottom wire and a correspondingly higher density of electrons in the top wire (so total charge is conserved as it should be in every frame of reference).   While the positive charges were locked in a lattice and can not be re-distributed like this - both the top and bottom wire show the same length contraction and hence the same density of +ve charges is observed.

    I completely agree that this is a bit weird and little hard to believe and any sensible person would want a reference or something to back this up.   Trying to keep things simple, take a look at this video   ("How special relativity fixed electromagnetism",  Science Asylum, available on YouTube)   around time index  7:00 to 7:20 where the unequal distribution of -ve charge density in the top and bottom wires is exhibited and discussed in much the same way as it was done here.   This is an example where observers in different frames of reference disagree about something that might have seemed like it should have been an invariant:  Specifically the density of electrons in the top and bottom wires are not agreed on they aren't always the same in every frame of reference, that is not an invariant.   This could take ages to think about and resolve and I haven't tried to do it myself much.   This is where I would start:   The electrons weren't all at the same place and that's the problem -  you might count all the electrons in the bottom wire at a fixed time t₀ in one reference frame.   By conservation of charge (or just plain old conservation of events),  you'd expect all those events to be mapped to distinct events in the other frame and the total number of them to be the same.  That will happen (hooray!) but, of course, there's a simultaneity problem because the electrons were not all at the same location in space.   In the new frame you have a collection of events you can count but the time co-ordinates are all different.   So you're not counting anything that looks like a density of negative charge at one fixed time (in the new frame) in the bottom wire.  If you did apply equations of motion and determine where all of those electrons would have been at one fixed time in the new frame, then some of them have left the bottom wire and are now in the side wires etc.   Overall, you really do seem to be able to get a different density of -ve charge in the bottom wire in the new frame (compared to the density in the top wire in the new frame).

Final Notes:   
1.  The movement and behaviour of a test charge is never exactly the same as you observe in real life.   This is because in real life, the test charge is making it's own electric field and when it starts moving, then it is making it's own magnetic field.   Trying to solve Maxwell's equations for the real-life situation is then extremely complicated and usually reduced to finding reasonable numerical approximations.

2.   As mentioned before,  by far the best way to consider electric and magnetic fields is just to give up on handling them separately.   A separate E field and B field is a useful way to describe what happens for some situations,  however describing the both of them with a single electromagnetic field strength tensor is by far more consistent.    There really doesn't have to be a magnetic field, it's not fundamental, it's just what the elctromagnetic field looks like in some frames of reference.   Similar comment goes for the Electric field.

3.   You asked this question earlier:

Do we have to also take time dilation into account? why or why not?

    Yes but it makes everything more complicated.   It's best if you use a Lorentz 4-force to describe the effect of an electromagnetic field.   Here you are using derivatives w.r.t. proper time, τ.   So all the effects like time dilation are already built-in and taken as a contribution to the final conventional Newtonian 3-force you would observe.
   See Wikipedia:  https://en.wikipedia.org/wiki/Four-force    especially the short section about the example of the Lorentz 4-force determined from the electromagnetic field strength tensor  F_μν.

Best Wishes.

LATE EDITING:  To try and empahsise that it's not just the density of -ve charges that varies when you change frames, it's the difference in density between top and bottom wires that isn't an invariant.   (The density of +ve charge in the top and bottom wires would also change - but they change in the same way so the difference between +ve charge density of the top and bottom wires remains invariant).

10

New Theories / Re: Origin of magnetic force

« on: 01/07/2022 10:37:38 »

Hi.

Why can't we translate to the frame where the electrons stay still instead?  Will it change the expected result?

    You could but it's harder.  You lose the ability to assume the density of positive charge in the wire ≈ the density of negative charge in the wire in that frame.   (I think I would just keep changing frames of reference in my head so that the wire was stationary).
    No it shouldn't change the overall result, the test charge would still be repelled, just for slightly different reasons.

Best Wishes.

11

New Theories / Re: Origin of magnetic force

« on: 30/06/2022 19:41:24 »

Hi.

Let's make an experiment where the positively charged test particle is at rest, while the electrons in a wire move to the left at v m/s, and the metal atoms move to the right at v m/s. Will the test particle accelerate? In what direction?

   There may be insufficient information here - but here is the standard prediction based on conventional theory:
You said "wire" so we'll assume the positive charges are the metal atoms and they are locked in a lattice.
Translate to another frame where the wire stays sill  <=>  the positive charges stay still.
It's also very hard to give the electrons an arbitrarily high velocity, they tend to have an average velocity that is the drift velocity indicated by conventional theory which is actually a very low speed.   You'd need to maintain a large voltage across the wire if you want a faster dift velocity and that is difficult to do in practice.  We'll assume the velocity of the electrons is low.

   Anyway, making the translation to the frame where the wire is stationary, this leaves the test particle moving at velocity v to the left.   Meanwhile, the electrons are moving with velocity not quite 2v to the left (find the exact velocity by the velocity addition formula).   Where the wire is stationary and the electron velocity is low, then the electrons do tend to be distributed so that    the density of negative charge ≈ the density of the positive charges in the wire.   That leaves us with negligible conventional electric field generated by the charges in the wire.   Indeed in conventional theory, we consider most of what is there and surrounding the wire to be a magnetic field.   So we have a particle with velocity. v to the left in a magnetic field that is going into the page (if the test particle is below the wire,  while it's coming out of the page if the test particle was above the wire).   By the usual Lorentz force law that should be a force pushing the test particle away from the wire.   (The direction of that force is dynamic, it will change slightly as the test particle changes velocity but initially it's directly away from the wire).
    That should happen in any inertial reference frame although in some frames the explanation will be due to some contribution from an Electric field and not just a Magnetic field.
    Going back to your original frame of reference, the distance between the metal atoms would have been contracted slightly while the distance between the electrons would have been increased slightly compared to the frame I have just used.   Overall there would have been a net +ve charge density in the wire and that would have created an Electric field that repelled the test particle.

   However, if it wasn't a conventional wire and the positive metal atoms weren't locked into a lattice then I don't think you have enough information to proceed.   If the positive atoms can move and spread out then you need to know how and that would affect the charge density and hence the electric field you would observe.

Best Wishes.

12

Just Chat! / Re: FAULT on the website?

« on: 30/06/2022 15:09:23 »

Hi.

Reply # 31   on this thread:   https://www.thenakedscientists.com/forum/index.php?topic=67448.20
   I wouldn't have thought that was too large.

   As I mentioned the problem is intermittent and I'm prepared to ignore it.

best Wishes.

13

Physics, Astronomy & Cosmology / Re: What is a black hole made of?

« on: 30/06/2022 14:27:05 »

Hi.

    There's been some reasonable replies but many of them are focusing on what is at the centre of a black hole and I've got to ask why?
    By convention "a Black Hole" is the region of spacetime bound by the Event horizon (EH), usually including the EH itself.
So most of a black hole is just nothing, no material of any kind,  it's just a region of space and time.
   As @evan_au suggested, if there is some matter at what we'll call the centre of the black hole then it has retreated well inside the Event Horizon and by our very best theores it is either:
   (a)   An extremely dense material, occupying a small portion of the region inside the EH.      OR,
   (b)   A genuine singularity,  a point of infinite density.

In either case, most of a black hole is not this stuff.  Most of it is just the spacetime bounded by the EH.

The original question was:

Is it possible Black Holes could be made from sub-atomic particles?

   A reasonable answer is:   No,  most of it is nothing, no material of any kind.
That may change if we discover that gravity can be modelled with force carrying particles,  e.g. we develop a good quantum theory of gravity - but at the moment that is the best answer we can give (I should think).   
    The Scwarzschild solution of the Einstein Field Equations is our best approximation to describe what a black hole is and in that solution,  the region of spacetime we call "the black hole" is a vaccum.   To phrase this another way, a Black hole is not a solid thing of any type, it is just a region of spacetime with extreme spacetime curvature.   The bit of it that might be some material is likely to be so small we can ignore it.
   However, if you (David) were asking what the core or central part of a black hole is made of, then you've already got some answers and replies that are reasonable.

Best Wishes.

14

Just Chat! / FAULT on the website?

« on: 30/06/2022 13:42:03 »

Hi.

The spell check feature seems to be freezing up and timing out.   Is that just me and my computer?

Best Wishes.

LATE EDITING:    It seems random or intermittent.   If you're persistant it will work.

15

New Theories / Re: Origin of magnetic force

« on: 30/06/2022 13:40:36 »

Hi.

The problem identified here is the asymmetric response between the movement of positive and negative charges in the wire.

    Is it a problem?   It's often required that the positive charges don't and can't spread out despite a Lorentz contraction.   The positive charges are the metal atoms and they are locked into a lattice.    Even when Lorentz contraction puts them closer together and suggests there should be increased repulsion between them, the metal atoms cannot move apart.
     However the electrons are not like that, they are free to move around and can spread out.

Here's a 3 minute 40 sec. video from  Science Asylum  available on You Tube  that explains the general idea:

    There are many other videos such as a later video where Science Asylum explain electromagnetism again and Veritasium have quite a nice video about Magnetism.
    Alternatively you can see a textbook describing General relativity like  Spacetime and Geometry, Sean Carroll.   Where the basic approach is to say:   There's an electromagnetic field strength tensor, F_μν, and that's what's important.   A Magnetic field or Electric field are not fundamental or intrinsically real - they are only things that appear in certain reference frames.

Best Wishes.

16

New Theories / Re: Origin of magnetic force

« on: 29/06/2022 18:45:16 »

Hi.

If I recall correctly this situation is actually quite complicated:



Where the test particle is assumed to be be at rest,   the wire has velocity v as shown.    That's complicated because the positive and negative charges in the wire then suffer a Lorentz contraction and the density of charge is changed.    It's more noticeable for the positive charges in the wire because the electrons  were moving opposite the conventional current shown and so the velocity of the electrons is less than the velocity of the positive charges.   Overall then some of the force on the test particle is due to an Electric field and not a magnetic field when you choose that reference frame.

    This has been the mainstream view of electric and magnetic fields for quite a while:   Changing frames of reference can make an Electric field look like a Magnetic Field and vice versa.

Best Wishes.

17

Physics, Astronomy & Cosmology / Re: How does special relativity explain dimensional components ...

« on: 28/06/2022 01:12:19 »

Hi.

That each scientist is going to end up with a different description of this universe from using special relativity.

     Yes, exactly this sort of thing does happen.
    There are some questions you can ask which are going to be frame dependant -  they have answers but the answers will depend on the frame of reference you have chosen.
    For example,  the question  "is object A moving?"  is something that the two scientists will not agree on.   Hopefully they will know the answer is frame dependant so they will answer more cautiously:   "Well, no, not in this frame of reference anyway".

    Fortunately, there are some questions that can be asked and answered more objectively:    "Will the two objects collide"  is something that both scientists will agree on.

Best Wishes.

18

Physics, Astronomy & Cosmology / Re: Why do we talk about light cones?

« on: 28/06/2022 00:53:12 »

Hi.

Je ne parle pas bien le français. Je suis vraiment désolé.  ↔  I don't speak French well, sorry.

Look at the image labeled 2.

   Je ne trouve pas d'image 2. Est-ce celle-ci ?    ↔   I couldn't find an image labelled 2.   Was it this one?


  Onde du Choc  ↔  "Shock wave"

Était-ce celui-ci ?   ↔  Was it this one?


  Mur du son  ↔  "Wall of sound"    but probably better translated as  "the sound barrier".


This is the usual sort of image presented for light cones:

[Image taken from Wikipedia article, in English:  https://en.wikipedia.org/wiki/Light_cone ]

An alternative discussion in French:   https://fr.wikipedia.org/wiki/C%C3%B4ne_de_lumi%C3%A8re

Furhermore i dont understand why in this document we are talking about 2D expansion of light when we know that light is expanding in 3D.

    We want a diagram in 3 -dimensions  BUT one of our available directions is taken up by the time axis.
    All we have left is then (at most) 2 other directions.     We show light as something expanding in a 2-dimensional space BUT we are aware that it's happening in 3-D space  - you just can't fit all the information on a simple diagram.
   ↔   Nous voulons un diagramme en 3 dimensions MAIS l'une des directions est le temps. Par conséquent, nous n'avons que 2 dimensions pour l'espace sur le schéma.

But how do this "object" propagate ? (perhaps it is why we just talked about ligth, because if not it would be just nonsens ?)

    If I've understood what you are saying then I think you have got it right and explained exactly why we're interested in light cones in your next quote:

The future light cone at O contains all the events in the spacetime that can be reached from O by future directed timelike or lightlike curves. If we make the usual assumption that all causal processes propagate at or less than the speed of light, we conclude that these are all the events that we can causally affect from O.

    We usually aren't interested in light.  We are interested in how everything else,  every sort of particle, might propagate.   We make the usual assumption that nothing travels faster than light,   so the future light cone shows the maximum (biggest) regions of spacetime that can be influenced by something that happened at a given event.  Meanwhile, the past light cone shows the biggest region of spacetime that could have influenced that given event.
   

Now we think that "possible action" can be analog to light...

    That is not essential.   All we assume is that no particle travels faster than light.

Best Wishes.

19

Physics, Astronomy & Cosmology / Re: What is a black hole made of?

« on: 27/06/2022 19:01:32 »

Hi.

   Is David joining us as a member on the forum?   You could use a false name etc.   Anyway if you aren't, then your answer will be be available in a podcast shortly.   If you are joining us then please say something here and we'll have a discussion.

Best Wishes.

20

Physics, Astronomy & Cosmology / Re: How does special relativity explain dimensional components ...

« on: 27/06/2022 10:54:24 »

Hi.

I don't think my point has come across properly. 

    I think your point has been understood.   It's just not agreed and the difficulty now is only trying to explain why.

Imagine the spatial (x), temporal (y) plane.  Only one of A and B can have 0 velocity in the x direction, and this is true before you choose the reference point.

     Let's just start by saying no:   It's not so much that only one of them can 0 velocity which is important,   instead it's that either one of them could have 0 velocity.   Before you choose a reference frame there's nothing at all that restricts or informs you about the velocity of A or B.   You have completely free choice to assign any velocity you want to A or B,   restrictions for the velocity of the other object don't appear until after you have decided what the velocity of the first object will be.

 

Can someone explain me why we talk about "light cone"  ?

    The original Poster (OP) has requested that you put this question in a new thread.   That may help to avoid confusing the OP.
Mod edit: New topic here https://www.thenakedscientists.com/forum/index.php?topic=85049.0

Best Wishes.