Why is the speed of light exactly exactly 299 792 458 meters per second ?

[mgb_phys]

I disagree. The original definition of the meter was inherently faulty in the sense that it was unrealizable and non-standard.

It was good idea in theory!
Obviously nobody intended to measure the actual distance to the pole - all you need to measure is the latitude of 2 points a known distance apart. Measuring latitude accurately is relatively easy.

The intention that any country could establish it's own standard meter without needing diplomatic relations with the country holding the standard (which was a problem for the USA after 1776) and the idea that units should be determined by science rather than length of some part of a king's anatomy were valid.

Completely screwing up the execution while accidentally founding the science of geodesy in the process is just one of those things that happen ;-)

 

[lightarrow]

The usual treatment (e.g., Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is exposed, for example, in the second volume of the Course in Theoretical Physics by Landau and Lifgarbagez), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say, exerts on another can not be transmitted instantaneously. Hence, there exists a theoretical maximal speed of information transmission,which must be invariant and it turns out that this speed coincides with the speed of light in vacuum.

I have that book (Theoretical Physics 2: "Field Theory") but I sincerely have never been able to understand that phrase. While it's an experimental fact that the "influences" we know are not transmitted instantaneously, why do we need to suppose a general validity of it?

 

[jnorman]

of course, if you use the original "cubit" established around 3200BC by Zoser's Chief Vizier and Architect, Imhhotep, the speed of light is exactly 6x10^8 cubits/sec, as it should be.

i thought there was some talk a few years back about defining the speed of light to be exactly 3x10^10 cm/sec, and adjusting the length of the meter accordingly. what happened to that idea?

 

[Dale]

Wow! Go to work and miss a lot on this forum sometimes!

There seem to be a manmade constant at the bottom of this bottle wherever I look ! First, the constant of C, then the constant "permittivity and permeability" related to the medium of space, and now the value of "ampere" which is a consequense of the "magnetic constant", also known as the permeability of free space, measured at exactly 4 x 10–7 henries per metre, 0 = 4 x 10–7 H/m.

Yes, there is always at least one arbitrary man-made convention at the bottom of any dimensionful physical constant.

There has to be an underlying reason why light speed is what it is, regardless of units chosen...

How can you even express a dimensionful quantity like the speed of light without choosing units (let alone answering questions about why it is what it is)? Do you understand the difference between dimensionless and dimensionful quantities?

Your discussion of a "theory of everything" possibly leading to a greater understanding of what these "magic numbers" are is, as far as I know, only applicable to dimensionless fundamental constants. This is not the same situation at all as it is with the speed of light. The operative words in the OP's original question were why is the speed of light exactly what it is in metres per second?

This is exactly correct, and is precisely why I explicitly limited my comment to dimensionful physical constants only. As you mention, a complete Theory Of Everything would eliminate the current http://math.ucr.edu/home/baez/constants.html" . That does not apply to dimensionful physical constants like c, which would still be defined by arbitrary man-made conventions even within a complete Theory of Everything.

 

[neopolitan]

Anybody know what the above text says about WHY the speed of information transmission must be invariant?

Hi Naty1,

I'm going to conveniently ignore the context of your question (ie in terms of the text you quoted) and provide my explanation of why the speed of information transmission must be invariant.

I put it down to the structure of spacetime. If there is a quantum unit of time and a quantum distance, then there is going to be a maximum distance something can travel in a minimum amount of time. Such granularity of spacetime will result in a universal speed limit.

Proving that might not be easy. I think of it this way: any particle can conceptually have a minimum distance traveled (in a given frame), that would be not moving at all - being at rest, v=0. (Note that such a frame may not be strictly valid.)

Otherwise, a particle could move one quantum distance in one quantum unit of time. I would argue that in one quantum unit of time, a particle could not move more than that because it would imply two "location changes" in one quantum unit of time, and further imply that the quantum unit of time is divisible.

That would mean that the maximum speed for a particle is one quantum distance over one quantum unit of time, and that just happens to be the speed of light, and the speed of information transmission.

A final option is for a theoretical particle to move, but at rate less than one quantum distance per quantum unit of time. Here is where the movement would be statistical, you'd never know precisely which quantum cube a subluminal particle is in. However, when the positions are averaged out and the time elapsed measured you would end up with x quantum distances traveled in t quantum units of time (where x < t).

Since this sort of subluminal motion pertains to masses, you would really average out the positions of a large number of particles to find that the mass as a whole moves at less than one quantum distance per quantum unit of time. I suspect that at the quantum level the basic constituents of the mass would move at lightspeed, but not consistently in one direction as photons tend to.

cheers,

neopolitan

 

[Haelfix]

You can go about this in so many ways, its easy to get confused. Keep in mind science involves a lot of intrinsically circular reasoning, the big difference from usual propositional logic is that at the end of the day we have experiment to ensure the consistency of the model.

Its really no different than picking an axiomatic system, and then choosing extra axioms that are really related by theorems to former ones, eg they are not necessarily independent.

In the original work of Einstein, the constancy of the speed of light/information is an axiom. You are of course free to not do this and pick another axiom as fundamental, and for instance classical field theory (Landau/Lifschitz) more or less does this and instead rederives the former as a theorem.

 

[Phrak]

The value of the permeability of free space is a result of the http://www.bipm.org/en/si/si_brochure/chapter2/2-1/ampere.html" . And then (together with the definition of the meter which defines the speed of light) the permittivity of free space is also defined exactly.

Dale. I took a look at your web link and found this:

"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 Newton per metre of length."

Did I understand you correctly that the velocity of light is defined in terms of the permeability and permittivity of the vaccum? If these a dependent upon the ampere we seem to have circular standards.

But you bring up a nice topic: The pedigree of standard units--dependencies, basically. I have never seen it sorted out. For instance, does permittivity depend on constructing two plates of known dimensions, etc?

 

[D H]

Did I understand you correctly that the velocity of light is defined in terms of the permeability and permittivity of the vaccum?

The velocity of light and permeability of space are numerically-defined constants. The vacuum permittivity is defined to be 1/(\mu_0c^2).

 

[Naty1]

The purpose of physics is to both explain how things work (say via math) and also why they work. We are not so good at the latter as the former, I think.

This is a lay mischaracterization of science.

Maybe in the opinion of some, yet I just finished reading a Nobel Prize acceptance speech a few days ago...that was part of the physicsts comments addressing the audience...

 

[Naty1]

Lightarrow posted:

one supposes that the influence that one particle, say, exerts on another can not be transmitted instantaneously. Hence, there exists a theoretical maximal speed of information transmission,which must be invariant and it turns out that this speed coincides with the speed of light in vacuum.

I have that book (Theoretical Physics 2: "Field Theory") but I sincerely have never been able to understand that phrase.

Before Maxwell's equations and Einsteins relativity such a "supposition" would have been deemed rather radical I think.

Thanks for the background but, darn, I was really hoping there was a rational reason... interesting question...

 

[neopolitan]

Hi Naty1,

I'm going to conveniently ignore the context of your question (ie in terms of the text you quoted) and provide my explanation of why the speed of information transmission must be invariant.

I put it down to the structure of spacetime. If there is a quantum unit of time and a quantum distance, then there is going to be a maximum distance something can travel in a minimum amount of time. Such granularity of spacetime will result in a universal speed limit.

Proving that might not be easy. I think of it this way: any particle can conceptually have a minimum distance traveled (in a given frame), that would be not moving at all - being at rest, v=0. (Note that such a frame may not be strictly valid.)

Otherwise, a particle could move one quantum distance in one quantum unit of time. I would argue that in one quantum unit of time, a particle could not move more than that because it would imply two "location changes" in one quantum unit of time, and further imply that the quantum unit of time is divisible.

That would mean that the maximum speed for a particle is one quantum distance over one quantum unit of time, and that just happens to be the speed of light, and the speed of information transmission.

A final option is for a theoretical particle to move, but at rate less than one quantum distance per quantum unit of time. Here is where the movement would be statistical, you'd never know precisely which quantum cube a subluminal particle is in. However, when the positions are averaged out and the time elapsed measured you would end up with x quantum distances traveled in t quantum units of time (where x < t).

Since this sort of subluminal motion pertains to masses, you would really average out the positions of a large number of particles to find that the mass as a whole moves at less than one quantum distance per quantum unit of time. I suspect that at the quantum level the basic constituents of the mass would move at lightspeed, but not consistently in one direction as photons tend to.

cheers,

neopolitan

woops,

I obviously have too much hassle going on the background.

This was not so much about why the speed of information is invariant and more about why there is an upper limit to the transmission of information.

There is a further step you have to take to explain why information travels at that upper limit.

If you look at galilean relativity, if you want to call it that, you can see that there is also an assumption of invariant speed of information transmission. It just that in the galilean boosts information is assumed to be transmitted instantaneously. If you remove that assumption, you can arrive at the Lorentz transformations.

You have to keep the assumption of invariant speed of information transmission and I suppose you might want to explain it. I do think that people probably thought about it another way. Information travels really fast, not instanteously, even though it might seem like it. So, they would then be looking for what holds the transmission of information back. Well, we found something in the upper speed limit inherent in the universe.

The only reason then that information would _not_ be invariant would be if there were to be some reason why information doesn't travel at the upper speed limit. I don't have such a reason, they didn't and I don't think anyone else has either (if I recall correctly even the "in a vacuum" is a bit of a misnomer, because photons do travel at c whenever they travel, but they get slowed down when not in a vacuum because they tend to get absorbed and reemitted.)

cheers,

neopolitan

 

[Strangerone]

Wow, this debate was very good and interesting! :-)

Now a little on the side of what this debate is about:

For 2.5 months ago I sent an article to the AstroPhysical Journal. The article is a summary of my research last 10 years. The respons so far from the editorial board is that it is in progress. But is it usual that the treatment at the APJ takes so long? If they conclude that my findings are completely wrong, they should be able to reject it immediately! Here is something going on, I believe :-))))))))

 

[Alfi]

Hi Naty1,

I'm going to conveniently ignore the context of your question (ie in terms of the text you quoted) and provide my explanation of why the speed of information transmission must be invariant.

I put it down to the structure of spacetime. If there is a quantum unit of time and a quantum distance, then there is going to be a maximum distance something can travel in a minimum amount of time. Such granularity of spacetime will result in a universal speed limit.

Proving that might not be easy. I think of it this way: any particle can conceptually have a minimum distance traveled (in a given frame), that would be not moving at all - being at rest, v=0. (Note that such a frame may not be strictly valid.)

Otherwise, a particle could move one quantum distance in one quantum unit of time. I would argue that in one quantum unit of time, a particle could not move more than that because it would imply two "location changes" in one quantum unit of time, and further imply that the quantum unit of time is divisible.

That would mean that the maximum speed for a particle is one quantum distance over one quantum unit of time, and that just happens to be the speed of light, and the speed of information transmission.

A final option is for a theoretical particle to move, but at rate less than one quantum distance per quantum unit of time. Here is where the movement would be statistical, you'd never know precisely which quantum cube a subluminal particle is in. However, when the positions are averaged out and the time elapsed measured you would end up with x quantum distances traveled in t quantum units of time (where x < t).

Since this sort of subluminal motion pertains to masses, you would really average out the positions of a large number of particles to find that the mass as a whole moves at less than one quantum distance per quantum unit of time. I suspect that at the quantum level the basic constituents of the mass would move at lightspeed, but not consistently in one direction as photons tend to.

cheers,

neopolitan

Just to say, Thank you. As an educated layperson, I really liked the explanation.
I like the 'if / then / otherwise, approach at the options when the base unit is Plancks quantum. It seems a very Integer based scaling system.
- as an aside and a follow up question;
I remember an article in Sci Am a few years ago about the Planck scale and how there was a gap in the scale from quark to atom ( ?? hazy memory - If anyone knows the issue, a link or pointer is most welcome, and would save me a search ) something like that.
The question is.
Is this gap in the spectrum, a lack in theory or a gap in measurement technology?
Just curious.

 

[Dale]

For 2.5 months ago I sent an article to the AstroPhysical Journal. The article is a summary of my research last 10 years. The respons so far from the editorial board is that it is in progress. But is it usual that the treatment at the APJ takes so long? If they conclude that my findings are completely wrong, they should be able to reject it immediately! Here is something going on, I believe :-))))))))

I don't know APJ's usual timeline, but 2.5 months is not unusual for most of the journals where I have had manuscripts published. Even much longer is not unusual if the first two reviewers disagree and it has to be sent to a third reviewer. I wouldn't make any assumptions at this point.

By the way, the likely best response is that it needs significant revisions before it is accepted. Don't argue the point, just make the requested revisions. That is a normal part of the peer-review process.

 

[Naty1]

Dalespam posted:

As you mention, a complete Theory Of Everything would eliminate the current 26 fundamental dimensionless constants. That does not apply to dimensionful physical constants like c, which would still be defined by arbitrary man-made conventions even within a complete Theory of Everything.

And since I believe Cephid and Me Jennifer agrees, looks like Strangerone and I have some "adjustments" to make in our thinking...at least I do...

Now I understand the distinction that was being made, but not quite it's significance...

Wikipedia does cover this..for starters, Dimensionless Quantity...
http://en.wikipedia.org/wiki/Dimensionless_quantity

http://en.wikipedia.org/wiki/Dimensionless_physical_constant


but "bells" of insight did not sound as I skimmed ...

be back after some reading...have to take my new dog to the vet for a checkup first.

Thanks, guys,girls!

 

[Strangerone]

I don't know APJ's usual timeline, but 2.5 months is not unusual for most of the journals where I have had manuscripts published. Even much longer is not unusual if the first two reviewers disagree and it has to be sent to a third reviewer. I wouldn't make any assumptions at this point.

By the way, the likely best response is that it needs significant revisions before it is accepted. Don't argue the point, just make the requested revisions. That is a normal part of the peer-review process.

Okay, thank you for a good and detailed response.

I apologize if my English is not so good. (I'm not from an English-speaking country)

Have a nice evening :-)

 

[HallsofIvy]

Well, yes, of course. The precise value of any constant depends upon the units in which you are measuring. The "physical" information, from experiment rather than simply "made up" is that the speed of light is independent of the speed of the one observing the light, not the specific value in a given system of units.

 

[Dale]

Dale. I took a look at your web link and found this:

"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 Newton per metre of length."

Did I understand you correctly that the velocity of light is defined in terms of the permeability and permittivity of the vaccum? If these a dependent upon the ampere we seem to have circular standards.

But you bring up a nice topic: The pedigree of standard units--dependencies, basically. I have never seen it sorted out. For instance, does permittivity depend on constructing two plates of known dimensions, etc?

It is not circular, but I think the "pedigree" is an appropriate description. The http://www.bipm.org/en/si/si_brochure/chapter2/2-1/" explicitly.

Finally, it should be recognized that although the seven base quantities – length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity – are by convention regarded as independent, their respective base units – the metre, kilogram, second, ampere, kelvin, mole, and candela – are in a number of instances interdependent. Thus the definition of the metre incorporates the second; the definition of the ampere incorporates the metre, kilogram, and second; the definition of the mole incorporates the kilogram; and the definition of the candela incorporates the metre, kilogram, and second.

So there are really 3 "great-grandparent units": the second, the kilogram, and the kelvin. These units are completely independent of the others. Then there are the "grandparent units": the meter (child of the second), and the mole (child of the kilogram). Finally there are the "parent units": the ampere and the candela (children of the meter, kilogram, and second). Then all of the remaining SI units, like the watt or the Newton are children of these "fundamental" units.

 

[Dale]

Now I understand the distinction that was being made, but not quite it's significance...

Wikipedia does cover this..for starters, Dimensionless Quantity...
http://en.wikipedia.org/wiki/Dimensionless_quantity

http://en.wikipedia.org/wiki/Dimensionless_physical_constant


but "bells" of insight did not sound as I skimmed ...

be back after some reading...have to take my new dog to the vet for a checkup first.

Congratulations on your new dog!

Please read up a bit until you get some concrete questions and then don't hesitate to ask. I think this topic is reasonably important to understand, so I am glad to follow-up as best as I can since I am sure that this initial exposure is not self-explanatory.

 

[fluidistic]

Hi,
I don't know if it can help but I've asked the same question there : https://www.physicsforums.com/showthread.php?t=260923&highlight=uncertainty+speed+light.

 

[Naty1]

Fluidistic: Thanks for the thread referenced in post #50 here...I found something, which if accurate, was a big help.

there, HallsofIvy posted:

(And lightarrow seems to have said the same thing here in post # 25)

To clarify- it is NOT the "speed of light" that has been "defined"- as you say that is a constant of nature and we cannot just "define" it to be a specific value.

(my boldface)

This is all I was trying to say here in earlier posts. It seems self explanatory enough for me as long as the current posters in this thread agree its correct. Whether it's quoted in km/sec or mph or any other units makes little difference to me as long as both the magnitude and units are given.

Light is not instantaneous for a reason; it is constant for a reason, and it propogates at a given value for a reason (pick any unit in which you want to measure)...

For my own interest I'm going to read further about dimensionless and dimensionful constants but right now the distinction sounds like one some math wizards concocked during a binge! but maybe there are subtlies I'm missing...wouldn't be the first time!

As a matter of interest, if a theoretical foundation were found for all the "fundamental constants" in the standard model (currently independent inputs) and also for gravity (if there are any) and some/any were found to be different, (say, for example, in the twentieth decimal place beyond current measured accuracy) I'd be interested if any would then cause the speed of light to be ever so slightly refined.

 

[matheinste]

Hello all

This extract is taken from Rindler – Relativity, Special,General and Cosmological. Second Edition. Page 41. I do not know if this is still the current situation but it is interesting nontheless.

-----First of all, we need universal units of time and of length. In this age of atoms it makes good sense to fall back on atomic frequencies and wavelengths to provide these units. Thus in 1967 the (international) General Conference of Weights and Measures (CGPM-1967) defined the second as follows: ‘The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom’. The international standard of length had been defined back in 1960 in terms of the wavelength of a certain line in the spectrum of krypton-86. More recently, however, it has become clear that the precision available from the kryrton-86 line is surpassed by the precision with which, on the one hand, the second, and, on the other hand, the speed of light are determinable. Thus, demonstrating its complete confidence in special relativity, CGPM-1983 re-defined the meter as the distance traveled by light in vacuum in a time interval of 1/299792458 of a second. Note that, consequently, the speed of light is and remains precisely 299792458 meters per second ; improvements in experimental accuracy will modify the meter relative to atomic wavelengths, but not the value of the speed of light!-----

This is, i hope, relevant to Naty 1's last line of the last post #51

Matheinste

 

[Naty1]

Cepheid posted

Huh? Okay, first of all your analogy is flawed, because scientists don't accept that it is not possible to cure the common cold in principle, they only accept that it is not possible to cure it in practice, given our current level of scientific understanding.

My analogy is 'flawless'...you need to reread it...we, in fact, agree completely (i concur with your statement and was using analogous faulty logic to illustrate the faulty logic of the original post.)

 

[Naty1]

In post # 19 Strangerone repeated his original question:

What is the exact physical reality behind these observed constants. There is, as far as I know, no published theory that can tell this. There is only math related to these observed constants. But why does scientists accept this?

I agree,,,no theory I have seen either...it's not really "accepted", just the best we can do so far.

Having reread all the posts here I am led to the conclusion we did not provide a direct answer to Strangerone's question very well, or maybe it would be better to say we sure took a round about way. What someone asks "Why does a baseball fly off a typical major league hitter's bat at about 98 mph?" getting into a discussion of dimensions is not the way to go to aid the questioner.

At least I found the Wikipedia result I quoted was misleading at best.

HallsofIvy, Dalespam, and Lightarrow I think helped clarify what was for me the subsequent confusing dialogue among posters about units/dimensionlesss/dimensionful but the language can sure be confusing.

I think Lightarrow posted:

To clarify- it is NOT the "speed of light" that has been "defined"- as you say that is a constant of nature and we cannot just "define" it to be a specific value.

and that's enough clarification for me.

Seems maybe had the original question been something like "Is there a theoretical reason the experimentally measured value for the speed of light is 300K m/sec instead of, say, 400K m/sec"...we might have been more succinct in replies.

 

[Dale]

Hi Naty1,

Sorry about the delay. I wanted to explain in more detail why the dimensionless quantities are considered more fundamental than the dimensionful quantities. I thought it might help to see an example of what it would mean to change a dimensionful quantity without changing any of the dimensionless quantities, and it took a while to work it out. Specifically, I wanted to work out what would be the experimental result if the speed of light doubled but the fine structure constant was unchanged.

The fine structure constant \alpha =\frac{e^2}{2 h c \epsilon _0} has several terms, but if we suppose additionally that mass and charge do not change then we see that if c is doubled then the vacuum permittivity must be halved. And since c^2=\frac{1}{\epsilon _0 \mu _0} the vacuum permeability must also be halved. So, basically we have just c doubling and the permittivity and permeability halving and no other changes.

Now, let's determine what we measure. The http://en.wikipedia.org/wiki/Hyperfine" energy is proportional to c² which is quadrupled. So, if E for the Caesium hyperfine transition goes up by a factor of 4 then by E=hf the frequency also goes up by a factor of 4 meaning that our new seconds are a quarter of our old seconds.

Now, our new meters are equal to the distance that light travels in 1/4 of an old second and since c is doubled that distance is 1/2 of an old meter. Note that this definition of the meter leaves the numerical value of c in new meters per new seconds unchanged. This is not terribly surprising because it is a direct result of the definition of the meter, but let's use our new meters to measure the length of a bar that was 1 old meter long prior to the change in c.

Due to the doubling of c, the Bohr radius a_0=\frac{h}{2 \pi m_e c \alpha } is halved. This means that our 1 old meter bar has shrunk to 1/2 of an old meter. As we discovered above this is also the length of our new meter. In other words, a bar that was previously measured to be 1 old meter is now measured to be 1 new meter, despite the fact that c doubled and our new meter is defined based on this doubled c.

So, although our new seconds reduced by a factor of 4 and our new meters reduced by a factor of 2 when c doubled, we cannot tell any difference. Things that used to be 1 old meter long are still measured to be 1 new meter long even though all of our measurements are now distorted as are the objects themselves. This is why dimensionful parameters are not considered fundamental. A change in c (without a change in the fine structure constant) wouldn't change any physical measurement we could make. Only changes in the dimensionless parameters have physical significance.

 

[neopolitan]

First I would like to say well done to Dale, that was a brilliant, cogent approach to a deceptively simple topic.

Then my two cents.

I think the simplest way to explain that light has a specific speed, and not another (I gather that this was the OP's thrust, rather than why the defined speed is a round number), is to point out that the speed of light is a really the ratio between one fundamental division of space and one fundamental division of time. We could say it is 1:1 or one Planck length per Planck time, or one light year per year, or 299792458 m/s depending on the units we find most convenient to work with.

So, the figure we come up with is really more reflective of the number of fundamental units of space that fit in the unit of space we find convenient and the number of fundamental units of time that fit in the unit of time we find convenient.

(Strictly speaking, it is the ratio of those numbers, since while Planck units are certainly convenient, I cannot say categorically that they are truly fundamental.)

cheers,

neopolitan

 

[neopolitan]

Going back to Dale's post: since if we were to somehow change the relative speed of light, by for example, traveling towards a photon, then in the axis of that motion the decreased speed of light would result in the changes you listed such that we would measure the speed of the photon as being c, yes? At the very least, there would be no way to tell if the relative speed of light has been reduced by our motion towards the photon, which admittedly makes it impossible to say that we are moving towards the photon without bringing in another observer who is notionally at rest. But let's say we do that.

What I find interesting is that, because there could be a photon coming at us from behind (according to the introduced observer), the changes you listed would be directional, ie velocity based rather than speed based. Again it would have to be from the perspective of the notionally at rest observer.

I note that this is not what is referred to as "frame drag" but it is a description which came to mind when I thought of it. Basically the observer watching us heading towards one photon and away from another could calculate that vacuum permittivity and permeability are decreased in the direction of our motion (analogous to a fluid's resistance against motion through it?) and increased behind us (analogous to reduced pressure in a fluid behind a vehicle?).

Further, if we were to face "forwards", our time divisions are shorter T_fw=(t.c²/(c+v)²) and our spatial divisions are shorter X_fw=(x.c/(c+v)) - assume we chose dimensions so that x/t=c. This means that in our inertial dimensions the closing velocity according to the observer (c+v) will be X/T according to us. In other words, we won't be able to measure any speed for the photon other than c. If we face "backwards", our time divisions are longer T_bw=(t.c²/(c-v)²) and our spatial divisions are longer X_bw=(x.c/(c-v)) but the closing velocity according to the observer (c-v) will still be X/T according to us.

The overall effect, according to our observer would then seem to be a form of root mean square:

x' = ct' = sqrt (X_fw . X_bw) = sqrt ((x.c/(c+v).(x.c/(c-v))
= sqrt (x².c²/(c²-v²)
= x.sqrt (1/(1-v²/c²)

The figures seem to work out ok.

Is there any validity to them? Perhaps it is all too ethereal?

cheers and Merry Christmas,

neopolitan

 

[Dale]

First I would like to say well done to Dale, that was a brilliant, cogent approach to a deceptively simple topic.

Thanks neopolitan!

What I find interesting is that, because there could be a photon coming at us from behind (according to the introduced observer), the changes you listed would be directional, ie velocity based rather than speed based. Again it would have to be from the perspective of the notionally at rest observer. ...

Is there any validity to them? Perhaps it is all too ethereal?

cheers and Merry Christmas

That is interesting, I hadn't considered that since it took me a couple of days just to work out the part that I did, but you could be right. The thing that would worry me is that the factors are different than the regular relativistic gamma factor, and they are different for time and space. But you are right, it is very much like the Lorentz aether theory in the sense that clocks and rulers change to make a change in c undetectable.

Merry Christmas to you too!

 

[neopolitan]

Just a quick response, note that I used x where x=ct and x'=ct' and the unprimed frame is the notionally at rest frame. I didn't make that clear enough.

If I was deriving the length contraction equation, I would have had to use different notation, probably L and L', and would be using a different frame as my starting point.

The equation I provided could be used for deriving time dilation.

cheers,

neopolitan

 

[Al68]

I think the simplest way to explain that light has a specific speed, and not another (I gather that this was the OP's thrust, rather than why the defined speed is a round number), is to point out that the speed of light is a really the ratio between one fundamental division of space and one fundamental division of time. We could say it is 1:1 or one Planck length per Planck time, or one light year per year, or 299792458 m/s depending on the units we find most convenient to work with.

How about terafurlongs per fortnight? That makes c=1.8, nice easy number to work with.