[EvaH (OP)]

David asks:

Why is the speed of light the speed that it is in a vacuum (186,282mph)?

Can you help?

[Halc]

Why is the speed of light the speed that it is in a vacuum (186,282mph)?

There is no one speed of light since it is variable, depending on coordinate system of choice and on the refractive index of the medium through which it travels.
But the constant c is a constant inherent in the geometry of spacetime. In such spacetime, time is another dimension just like space and c happens to be the ratio between time and space.
Light and other particles with no proper mass just happen to move at this speed in a Minkowskian coordinate system and not in all others.
So think of it not as c being the speed of light, but rather that light in a vacuum just happens to move, relative to one coordinate system at least, at this universal constant c which means so much more.

[alancalverd]

Easier to think of the principles behind Maxwell's equations.

A changing magnetic field produces an electric field and  vice versa. You can measure the constants of proportionality, symbolised by μ and ε, for a medium including a vacuum, and the solution to the simultaneous equations is a wave propagating at a speed equal to 1/√ε₀μ₀.

[yor_on]

I would put it this way.

Defined from main stream physics the speed of light in a vacuum is known, and experimentally confirmed in f.ex 'two way mirror experiments'. We define it as a 'global' constant coming from the only way we can test it, locally, loosely described as with me and my experiment being 'at rest' within a same 'frame of reference' (a coordinate system more or less)

That is, as far as I know, the exact same way we define 'repeatable experiments' proving our physics. So yes, the 'speed of light' is as you say 186000 mi/s and it is a constant.


syntax

[RobC]

Minkowski, Einstein's teacher and a better mathematician, understood the underpinnings of special relativity and the fundamental explanation of why we can't travel faster than light but Minkowski did not explain why we only move at one speed through spacetime.
Nobody else has explained either.

[Eternal Student]

Hi.

Minkowski, Einstein's teacher and a better mathematician, understood the underpinnings of special relativity and the fundamental explanation of why we can't travel faster than light but Minkowski did not explain why we only move at one speed through spacetime.
Nobody else has explained either.

   I like the Minkowski reference and most of what you've said.  However, I think a few people have tried to explain why we only move at one speed though spacetime.
    Whether they did it well is a slightly different matter....

Half the problem is the audience.  They hear words like "speed" and start thinking of 3-dimensional space.  It's then quite difficult to think of movement through spacetime which is 4-dimensional.

The other half of the problem  is the person doing the explaining.  They shouldn't be using words like "speed" or trying to make analogies to 3 dimensional space.

Minkowski didn't have either of these problems when he was explaining the situation to himself.

If you want an explanation, say something here.  I'm sure there's several people who will try.  I might return here myself a bit later and risk boring people to death with some Mathematics if I can get the LaTex Math editor to work.

[Halc]

However, I think a few people have tried to explain why we only move at one speed though spacetime.
...
Half the problem is the audience.  They hear words like "speed" and start thinking of 3-dimensional space.  It's then quite difficult to think of movement through spacetime which is 4-dimensional.

Speed is by definition dx/dt, that is the change in space (not spacetime) over time. Say I am in London at noon. Then I am at spatial location London and not in Paris. 43 minutes later I'm in Paris and not in London, which might result in an average speed of about 8 km/min relative to at least the coordinate system in which London and Paris define spatial locations. This is a change in 3D spatial location over time.
But spacetime isn't something through which one moves. The same trip as expressed in spacetime is nothing but a worldline with a frame-dependent slope. That worldline is present at both London and Paris, so there is no travel through the spacetime involved at all. The frame-dependent slope of the line is the equivalent to speed, but nothing 'moves' along this line.

The other half of the problem  is the person doing the explaining.  They shouldn't be using words like "speed" or trying to make analogies to 3 dimensional space.

The word is entirely appropriate. Speed has a defined meaning in both 3D space and 4D spacetime. It is a coordinate value, not a physical one, so speed is always a relation between an object and a coordinate system, never a property of the object.

[Eternal Student]

Hi Halc.

Speed is by definition dx/dt,

   Which is precisely why it's not a good term to use in the comment made earlier by RobC.

Minkowski did not explain why we only move at one speed through spacetime.
Nobody else has explained either.

Firstly, what you (Halc) just defined was a velocity (or just the x-component of velocity) and NOT a speed but I'm sure you had good reason (like it's too late in the day to start using LaTex).  This is a minor issue and most of us understood what you meant and how lazy you were not to use LaTex and get the notation right (I was hoping to do the same).

More importantly, if the term velocity is defined and understood as     and we consider speed as we usually do (the magnitude of that vector) then Minkowski (and most others) would not have said "we can only move at one speed".  It's obviously not true, we can move at lots of different speeds (just not exceeding the speed of light).

I think your (Halc) concerns have arisen because you were not focusing on the same section of RobC's comment.

We could use your comments to respond to RobC's comments but it's harder than just starting from scratch...
You said...

But spacetime isn't something through which one moves.

   This is one reasonable way of looking at the situation.  Unfortunately, it's not the way everyone looks at the situation.  Some people, including authors of Physics text books and Youtube content creators do say that you can move through spacetime.
    They can make this sort of statement when it is understood that time (which was a completely free variable in 3-dimensional space) can still be used to measure rates of change of position in 4-dimensional spacetime but it's just unfortunate that it (time) is no longer a free or independant variable.  The time component of the 4-velocity of an object is dependant on (entirely determined by) the 3-velocity.  I'm sure you (Halc) know this.  It's the essence of what you were saying about worldlines on a spacetime diagram - once a worldine is identified then everything about it is established there is no evolution with respect to time that can be ascribed to it.

However, I think it would be easier to make a discussion about objects being said to have a constant speed (the speed of light, c) through spacetime if we started just by recognising that this isn't a Speed as we might usually define it.   It's not the magnitude of a 3-vector, it's the magnitude of a 4-vector.

(It's too late and I'm too tired to continue.  Bye for now).

[Halc]

Which is precisely why it's not a good term to use in the comment made earlier by RobC.

Minkowski did not explain why we only move at one speed through spacetime.

My point was more about the concept of 'motion through spacetime' rather than on the word 'speed' itself.

Firstly, what you (Halc) just defined was a velocity (or just the x-component of velocity)

Indeed. OK, I meant change of spatial location when I said dx, not change along only the x axis. Speed is the magnitude of that change, and I didn't say that. It wasn't my point, which as I said above, was about motion through spacetime.

Minkowski (and most others) would not have said "we can only move at one speed"

Agree. Obviously the speed of our motion through space is variable and very much frame dependent. Speaking of dx/dt being a velocity, that points out that while the speed of light is constant, the velocity of a given photon of light is not and is frame dependent just like a rock's velocity is frame dependent.

It's obviously not true, we can move at lots of different speeds (just not exceeding the speed of light).

This is true relative to inertial frames. Relative to other kinds of frames, there is no such restriction. Hence certain (still visible) galaxies receding from us at a rate far exceeding c.

You said...

But spacetime isn't something through which one moves.

   This is one reasonable way of looking at the situation.  Unfortunately, it's not the way everyone looks at the situation.  Some people, including authors of Physics text books and Youtube content creators do say that you can move through spacetime.

I find that to be sloppy wording that only leads to confusion. There is motion in spacetime, but not motion through it. The latter wording implies a sort of flow that just doesn't exist.

[Eternal Student]

Hi again.

    Well Halc,   there's you and there's me.   There were a few others who posted something here but they have gone quiet.

I have gathered some information from another thread which I will shamelessly advertise here:
Mathematics is a decent science  https://www.thenakedscientists.com/forum/index.php?topic=82507.20
   
Based on this statistical evidence I am going to claim that (at the time of writing) at least 66.7 %  of the audience would not want to see any Mathematics used here.  I suspect the true figure is more like 99 %.  I base this on the fact that there are 1819 people looking at this website today, while there has been a total of 6 people that have used the poll + up to 6 people who have made a comment in that thread.  There's not been a lot of statistical rigour in producing these figures but my point is that it hardly matters.

We could use some Mathematics to discuss the comment made by RobC earlier but there's hardly any point.  The only person who would read it would be me and a few moderators because they feel obliged to do so.    If we did, the entire issue becomes nonsense.  Let's go back and look at RobC's comment again and just use words not mathematics.

Minkowski did not explain why we only move at one speed through spacetime.

  We would be better off just making it clear that Minkowski didn't need to explain this:   The statement is nonsense,  that isn't a "speed" and Minkowski almost certainly never thought that it was.   There is a similar statement that does make sense:   The magnitude of a velocity 4-vector for an object is always constant and it is the speed of light*.

*  The only caveat we might place here, is that the 4-velocity must be well defined.  For a photon, the proper time is not a suitable parameter for the path taken, the differential = 0 so that the components of the 4-velocity     are not well defined.   That caveat did involve some Mathematics so no one read it apart from Halc.  Halc, it was only put there because of your passion for repeatedly saying that photons can have arbitrary velocity in non-inertial frames.  I felt the need to point out that this doesn't invalidate the constancy of the magnitude of a 4-velocity.  It doesn't invalidate it because the 4-velocity of a photon never could be defined anyway.

Bye for now and best wishes  (from an old Mathematician, feeling very sad that no one cares for Mathematics).

P.S.   Did I mention that users can comment and support Mathematics here at  https://www.thenakedscientists.com/forum/index.php?topic=82507.20     ?

[Halc]

Based on this statistical evidence I am going to claim that (at the time of writing) at least 66.7 %  of the audience would not want to see any Mathematics used here.

I'm sorry, but the poll question did not ask "Do you want to see any Mathematics used here". It asked if we should have a separate forum section for it. But mathematics is very much used in all physics threads, especially to demonstrate the self-inconsistency of assertions in new theories for instance. I kind of agree with the majority about refraining from a section for it since we have very few if any mathematical experts here who could correctly answer a pure mathematical question like "Is .9999... equal to 1".

I suspect the true figure is more like 99 %.  I base this on the fact that there are 1819 people looking at this website today, while there has been a total of 6 people that have used the poll + up to 6 people who have made a comment in that thread.

So "all the people who didn't vote would have voted the way that supports the point I'm trying to make now". Interesting assertion, and one that might well be a decent topic to discuss in the nonexistent mathematics section.

We could use some Mathematics to discuss the comment made by RobC earlier but there's hardly any point.  The only person who would read it would be me and a few moderators because they feel obliged to do so.

Far more people read the posts than just moderators, and there are plenty of posts that I, as a moderator, never read. There's a counter of how many times a thread is viewed, but not one for each post since there's no way to tell which individual post is being viewed without putting just one per page.

Minkowski did not explain why we only move at one speed through spacetime.

  We would be better off just making it clear that Minkowski didn't need to explain this:   The statement is nonsense,  that isn't a "speed" and Minkowski almost certainly never thought that it was.

It is a speed (a relation with a coordinate system), but it is not 'through spacetime'. That's my stance. The statement is thus worded poorly for starters. The statement is akin to a (not exactly straight) line drawn on a round piece of paper, and then making the statement that "It is unexplained why the line moves at a fixed slope through the paper" which is wrong at at least two levels. 1: The line doesn't move through the paper. It is a static feature on the paper. 2: The slope isn't fixed since it varies along its length and even then depends on how you choose to orient the paper.

Halc, it was only put there because of your passion for repeatedly saying that photons can have arbitrary velocity in non-inertial frames.

On the contrary, I said that rocks can travel faster than c in non-inertial frames, and that the velocity of light is not constant in even inertial frames. A given photon might be heading north relative to one IRF and east relative to another.

I felt the need to point out that this doesn't invalidate the constancy of the magnitude of a 4-velocity.  It doesn't invalidate it because the 4-velocity of a photon never could be defined anyway.

How so? Relative to any arbitrary IRF, how is not defined?
Edit: is defined, but the former references proper time which is meaningless for a photon.
I am admittedly not used to expressing things in terms of 4-vectors.

Bye for now and best wishes  (from an old Mathematician, feeling very sad that no one cares for Mathematics).

I'm no dunce myself. I took a national mathematics test in high-school and placed third in the state of Michigan (population about 10M). That got me nothing except a pin to put on my lapel. Still miffed about that. Just saying that I care about mathematics, but the question in your thread didn't ask that.

[yor_on]

Minkowski, Einstein's teacher and a better mathematician, understood the underpinnings of special relativity and the fundamental explanation of why we can't travel faster than light but Minkowski did not explain why we only move at one speed through spacetime.
Nobody else has explained either.

Is it this you refer to RobC?

https://physics.stackexchange.com/questions/112038/minkowski-metric-why-does-it-follow-from-the-constancy-of-the-speed-of-light

[yor_on]

Yeah, the speed of light is a weird thing. But so is Plank scale. And when we put it into SpaceTime terms it becomes even weirder.
=

I'll add this one.  https://www.forbes.com/sites/startswithabang/2019/08/27/this-is-why-time-has-to-be-a-dimension/

But all of that belongs to what I call a global abstract definition, not local. Locally defined the speed of light is a observable and of a constant invariant speed, experimentally defined. Just as your wrist watch always keep a perfect time. And I think you have to expect those kind of equivalences presuming a underlying logic for relativity. That one can also be expressed as us expecting there to be a logic to our universe, which then special relativity base on a postulate of lights speed in a vacuum being a local invariable, no matter your relative motion. Moving from that to general relativity it becomes different, depending on definitions, either you look at your local measurement as proving varying speeds, or you include lights path 'bending' due to the gravity of f.ex the sun as a explanation to speeds differing from special relativity.

And that is actually something I feel missing, this connection between a global description of a SpaceTime and the local, That it comes together logically does not explain how it exist, our 'commonly agreed on' universe. You can get to a infinity of geodesics through a same 'point' just by varying relative speeds and mass (and of course accelerations) for example,and with it different local definitions of a universe and of time, using SpaceTime terms, the way I see it. And that one becomes true locally as well as globally, as long as you also use that abstract global definition while you observe.

What it means is that you use your 'perfect wristwatch', and your 'perfect measuring stick' as your anchor defining everything else from, at the same time as you, using four velocity, defines yourself to have f.ex 'a slowed time'. It makes for a very strange universe.

Furthermore, you can't even define your relative motion, from that follows that you can't define your 'time' either.

That's one of the things fascinating me with 'frames of reference'. That we can define it as 'synchronized' just by joining a same 'frame of reference'. If you do you get a automatic 'clock synchronization' with the other observer, and all other measurement will be the exact same, ideally defined.

[Colin2B]

from an old Mathematician, feeling very sad that no one cares for Mathematics).

I can’t agree with this statement.
As a practicing physicist I care a great deal about maths and use it daily, seeing it as an essential tool. I lean more towards the applied rather than pure and if faced with the eg @Halc gave (does .9999..... = 1) I would tend to look at the application and ask what difference it would make in that situation.
There are quite a few here (regular and occasional) who have very advanced maths skills, even working at the very top level in physics. However, given the target audience of this forum, the podcasts and articles, we don’t immediately reach for the maths explanation as first choice. That doesn’t mean we don’t care.

P.S.   Did I mention that users can comment and support Mathematics here at  https://www.thenakedscientists.com/forum/index.php?topic=82507.20     ?

I don’t see how this thread ‘supports’ mathematics.
It raises some questions on classification, which is valid, but more akin to pigeonholing than asking a serious question such as ‘is maths important’ - to which I would answer ‘essential’.
The poll could be taken many ways; I might feel that I don’t want maths separated from the physics section (or whichever the question occurs in) and so vote No, whereas someone else might not want to see it discussed there and vote for a separate section where it is more easily ignored.

[yor_on]

ES, Collin is right, nobody here dislikes or disrespect mathematics. And it is actually used at times to prove a statement, still, if one can explain without, then it becomes easier assimilated for those of us without that extensive mathematical knowledge. And as this sites primary direction today is to answer questions from anyone curious about something? Being what we are we still keep getting sidetracked, especially me :)

If you want to use mathematics to prove a statement you should ES, but be very clear about what it says.



syntax

[RobC]

Is it this you refer to RobC?

I had been to the Forbes site.

[yor_on]

Yeah. Four velocity is a abstract description of the universe in where we have four dimensions that constantly adjust themselves relative the observer. In that description nothing is static. In the local description your clock never lies, neither does your measurements. But it doesn't tell you what your 'time' is even then, as you can't define your motion. That's relativity as I see it.

That is me differing a clock from 'time', and it's confusing. Your clock can locally defined become a equivalence to 'c' thinking my way, (splitting it) all the way down to Planck scale. That actually should give it a defined amount of 'ticks' scaling it up.

Or you can define it as speeds doesn't matter locally defined, the 'ticks' are the same no matter your speed. It's the interaction with the rest of the universe that distorts (change) other observers definitions of your 'ticks'. And thinking that way it places time dilation's as a result of a relation.  Just as you need two objects to define a relative motion, 'speeds' from.

( And the more observers/objects you add and the more speeds you add, the more 'ticks' can we add to this picture, as everyone will define it, and you, differently. And simultaneity doesn't matter for it, they, and you both, will still have different definitions. You can choose freely who you will define your speed from, and so can they.  This is defining it 'globally' and doing so you're either timeless or consisting of all of those definitions, 'simultaneously', when described 'globally'  )

Well, one thing is certain, both globally as locally. The same postulate must hold in both descriptions for it to become true.

 'c'
=

and here's the funny thing about that postulate.                It's locally defined.

And another indicative is the idea of joining a same frame of reference. also local, giving you a 'clock synchronization'
=

both of them states the same, that there is a sort of 'standard' to our universe.

[Eternal Student]

Hi all.  It's been busy here, loads of replies.

To Halc:

in the state of Michigan

   Michigan?  That's a place in America.  You don't sound American when I read your posts, Halc.  You have quite surprised me.
  Anyway, congrats on your school achievement and it's always a pleasure to talk to you.  You don't have to make time to answer posts and the chances are you're a volunteer on this forum.  We appreciate your efforts.

Late editing:   On second reading this looks nasty and I feel obliged to put out a warning.  If there are any children reading this please don't write in and tell us where you live or about your school achievements.  Halc is old enough to make his/her own decisions and stay safe online.

  You also said stuff about the veracity of the statistical evidence that I used....

I'm sorry, but the poll question did not ask "Do you want to see any Mathematics used here"

   Obviously I'm not going to ask that.  People would answer and then we would know.  My way we need only assume they wouldn't want it. 

It is a speed...

   This one is too long to get into but I appreciate the stance you have taken.


 To Yor_on:
     That was interesting to read but I'm going to need to read it again tomorrow after some sleep.
The idea of Planck scales is definitely worth a discussion of it's own.  If lengths and times are discrete rather than continuous quantities then a whole lot of Physics will need to be re-written and re-imagined.  The current thinking (motivated by Quantum Mechanics in particular) is that they may very well be discrete, so there should be some new Physics we can look forward to discovering.
    I know very little about this area and have only seen a few Popular Science videos discussing the idea.


To Colin2B:

I don’t see how this thread ‘supports’ mathematics.

     Seriously, Colin2B, I'm grateful for your concern but the thread was not intended as a plea for help.  There are some phone numbers we can ring when it gets bad and they're listed in the back of most good Mathematics textbooks.
      It's just a thread where people can comment on Mathematics if they want and also it was a convenient place for me to pull some fairly spurious statistics from while I was commenting on this thread.  I know there are reasons why people would vote No to a Mathematics section, I was one of those people:
   Quote from reply #12 of that thread by me:
I've cast my vote already (No).   It's not because I don't think mathematics is a science, I do,  it's just that I wouldn't use such a section much and I remain confident that no one will object to some Mathematics questions appearing in the other existing sections sometimes.

 - - - - -
Thank you and best wishes to everyone.   Bye for now.

[yor_on]

Well yes ES, I find it interesting, or maybe more of a headache :)

As for whether is is discrete or not is indeed interesting, and so is the idea of a defined 'time dilation'. If we take NIST the best they can do if I'm correct is to define a clock synchronization aka the clocks being in a same 'frame of reference' from where they then start to differ gravitationally as one clock f.ex is elevated.  So all time dilatation should, as I see it, consist of comparisons. And the example with different observers avoids 'simultaneity' as no matter how you want to define it they still will give each other different 'time dilation's' depending on each others relative motion, as well as their definition of their own. I'm tired too btw, couldn't sleep tonight, been too hot, and humid, recently. so I'll write instead.

[yor_on]

When it comes to me defining it as us having a regime between Planck scale and 'c' I think that is correct, using the main stream definition in where our known physics 'breaks down' under it, as well as above it. Different situations but equal sort of 'barriers', if one can can express it that way. Which shouldn't be read as I'm prepared to state that the rest of those ideas presented are correct in any way. I keep on swinging between continuity and discrete which easily can be proved by looking at what I used to write about before climate.  And the same can be said about my definition of Planck scale. I don't think that can be tested, as I seem to remember it being at a scale where string theory comes in.