49 minutes ago, KJW said:

but locally it is still c. And considered in terms of proper distance and proper time, regardless of where the observer is, it is still c.

True, up to the point of being a tautology and hence misleading. measuring c locally is leading measurement ad absurdum, since it means measuring it in units of proper length and time, which definition tracks back to the atom, which again is a bound state of the field characterized by c. so it means measuring c in units of itself which always yields exactly 1c, and that is a tautology.

LET interpretation therefore is that c cannot be measured entirely by local means (or at least not utilizing electromagnetic means only).

1 hour ago, KJW said:

Also, have you checked the deflection of light given by the above? Is it the correct value, or half the correct value? If you only consider gravitational time dilation, you'll only get half the correct value. The full value also includes the curvature of space (the Schwarzschild metric).

hmm, the metric i started with has a component for both time dilation and spatial curvature. but with the weak field first order approximation you drop terms here and there, hopefully i didn't drop one too many. but it look fine to me, when i check the result against sources for gravitational lensing.

5 hours ago, Killtech said:

True, up to the point of being a tautology and hence misleading. measuring c locally is leading measurement ad absurdum, since it means measuring it in units of proper length and time, which definition tracks back to the atom, which again is a bound state of the field characterized by c

Repeating this doesn’t make it true.

6 hours ago, Killtech said:

True, up to the point of being a tautology and hence misleading. measuring c locally is leading measurement ad absurdum, since it means measuring it in units of proper length and time, which definition tracks back to the atom, which again is a bound state of the field characterized by c. so it means measuring c in units of itself which always yields exactly 1c, and that is a tautology.

The reason why the speed of light in a vacuum has a value of 299,792,458 metres per second is because we have defined a unit of length called "metre" and a unit of time called "second". If instead we define a unit of length called "metre" and a unit of time also called "metre", then the speed of light in a vacuum would have a value of exactly 1. The constancy and invariance of the speed of light in a vacuum is a consequence of the notion of spacetime. Lightlike trajectories in spacetime satisfy in all coordinate systems the expression:

g_pq dx^p dx^q = 0

This expresses the notion that there is an equivalence between timelike distances and spacelike distances which allows the same unit to be applied to both. But we don't use the same unit for both because a metre of time is an inconveniently small unit of time.

Edited May 3May 3 by KJW

11 hours ago, Killtech said:

the atom, which again is a bound state of the field characterized by c.

How is an atom a bound state of the field characterised by c? It's being used to define time. It should be noted that the choice of the particular atom and the particular transition is for technical reasons and not for anything that could be considered fundamentally theoretical. I'm quite sure that if the gravitational constant could be measured to an accuracy and precision comparable to the Planck constant and the speed of light in a vacuum, then it would also be defined to have an exact numerical value as the definition of the second.

9 hours ago, KJW said:

The constancy and invariance of the speed of light in a vacuum is a consequence of the notion of spacetime.

exactly

9 hours ago, KJW said:

Lightlike trajectories in spacetime satisfy in all coordinate systems the expression:

g_pq dx^p dx^q = 0

This expresses the notion that there is an equivalence between timelike distances and spacelike distances which allows the same unit to be applied to both.

Yes and this is a fundamental aspect of the math used to describe wave physics in general. for example it holds to for acoustics just the same, if you use the acoustic metric (https://en.wikipedia.org/wiki/Acoustic_metric), that is

\[g_{\mu \nu}^{acoustic} = \frac \rho c_s \begin{pmatrix} -(c_s^2-v^2) & -v^j \\ -v^i & \delta_{ij} \end{pmatrix} \]

with that the difference between acoustics and light physics almost vanishes. they do really only differ in interpretation.

apparently this is know and very useful to study astronomical situations, like the situation around black holes in a lab... yes, apparently sonic black holes can be build and are so similar that even the sonic analog of Hawking radiation can be experimentally observed. So much for talking to an AI. I figured previously the similarity between light and acoustics is astounding and the AI immediately understands what i meant and pointed me to sources that do apply that very idea and showed me the exact method how the math between both is made to agree.

5 hours ago, KJW said:

How is an atom a bound state of the field characterised by c? It's being used to define time. It should be noted that the choice of the particular atom and the particular transition is for technical reasons and not for anything that could be considered fundamentally theoretical.

The atom physics is described by quantum mechanics. As you rightly say, the choice of atom does not matter in theory, so is sufficient to constrain to the simple hydrogen model. And hydrogen is a bound state of positive and negative electric charge that gets all its properties from the electromagnetic interaction modelled at quantum level - the very field which core characteristic is c. From here we can deduct it from the math that anything that would affect the speed of light would identically affect the atom. That is for any change of the speed of light there exists a coordinate transformation that undoes it and returns everything to the original situation. So an atom is entirely unable to observe any change in the speed of light at a theoretical level. Any deviations lead to immediate contradictions in the theory. Hence no measure of time or length defined by atoms is suited to measure the speed of light.

This argument becomes weaker if we would chose a transition between bound states of the strong force, since that would at least measure the speed of light in units of the speed of the strong force and therefore have physical meaning as there would at least be a logical possibility of a deviation.

6 hours ago, KJW said:

I'm quite sure that if the gravitational constant could be measured to an accuracy and precision comparable to the Planck constant and the speed of light in a vacuum, then it would also be defined to have an exact numerical value as the definition of the second.

Hmm, it could be but it would require some other constant to lose its definition. The unit of G is composed of units of time, length and mass. It makes no sense to compete for the first two, so its would compete with Plancks constant to define the Kilogramm by its value. As only the value of one of them can be defined, the value of the other becomes a derivative as a consequence.

23 hours ago, Killtech said:

On 5/4/2025 at 1:46 PM, KJW said:

I'm quite sure that if the gravitational constant could be measured to an accuracy and precision comparable to the Planck constant and the speed of light in a vacuum, then it would also be defined to have an exact numerical value as the definition of the second.

Hmm, it could be but it would require some other constant to lose its definition. The unit of G is composed of units of time, length and mass. It makes no sense to compete for the first two, so its would compete with Plancks constant to define the Kilogramm by its value. As only the value of one of them can be defined, the value of the other becomes a derivative as a consequence.

No.

Considering the dimensions of the fundamental constants, [math]c[/math], [math]h[/math], and [math]G[/math], one has the following system of equations:

[math]c = \dfrac{L}{T} \ \ \ \ \ ;\ \ \ \ \ h = \dfrac{M L^2}{T} \ \ \ \ \ ;\ \ \ \ \ G = \dfrac{L^3}{M T^2}[/math]

Inverting this system of equations, one obtains expressions for the individual dimensions in terms of the fundamental constants:

[math]L = \sqrt{\dfrac{h G}{c^3}} \ \ \ \ \ ;\ \ \ \ \ M = \sqrt{\dfrac{h c}{G}} \ \ \ \ \ ;\ \ \ \ \ T = \sqrt{\dfrac{h G}{c^5}}[/math]

Therefore, specifying the numerical value of each of the three fundamental constants, [math]c[/math], [math]h[/math], and [math]G[/math], is sufficient to define the units of each of the three dimensions, [math]L[/math], [math]M[/math], and [math]T[/math]. Mathematically, it doesn't matter that none of the units are defined in isolation of the others. That is because the three fundamental constants are independent, and thus their expressions in terms of the three dimensions are invertible. However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument.

[Note: If the LaTex above doesn't render, please Refresh this page]

In your example you have only 3 constants left, hence you eliminated the 4th \( \Delta \nu_{Cs} \) constant which currently servers to define the second. If that was your intension, that i misunderstood your statement. But yeah, come to think of it, this one is indeed lacking fundamental physical meaning, hence it is a very fair point to wanting to eliminate it. i did not have that in mind when i answered your post, hence did not consider to contest it. So fair point, i do agree with you.

9 hours ago, KJW said:

However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument.

No, there is no such problem as the fundamental constant cannot be measured in this situation and therefore must be defined. This is fine because the constants - or more precisely the core physics they originate from - serve as the rulers to measure everything with. for example the speed of light together with the other constant allows you to construct a real photon emission which wavelength is fully determined by the constants and this base wave lengths servers as a ruler to compare any other real length to. For this we only need to know the defined values of the constants instead of measuring them. The definition via constants has the nice advantage that we have some freedom in constructing the ruler we use - yet all the different rulers constructed in this way will still agree (if the physical laws underlying them use are indeed correct).

In this situation the "true" value of the constants remains unmeasurable, or if the constants are even constant at all. As all measurement is fundamentally relative, that is a comparison of e.g. a length vs a reference length, hence absolute length independent of the reference cannot be determined. It is a bit like asking for my absolute velocity - but we can only meaningfully measure my velocity relative to some point of reference.

The definitions of the constants are instead always chosen to ensure maximum continuity and consistency with the previous older definitions of the SI system rather then for physical reasons. So this is why we first need to measure G to high accuracy in the old system before we can define it anew in a new SI iteration.

11 hours ago, KJW said:

However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument.

One problem is that G isn’t determined to a very high precision

6.67430(15)×10^-11 m^3/kg s^2

The limitations on that would affect any system relying on it.

1 hour ago, Killtech said:

In this situation the "true" value of the constants remains unmeasurable, or if the constants are even constant at all.

You can measure dimensionless constants, such as the fine structure constant, to determine that

On 5/6/2025 at 7:45 AM, swansont said:

On 5/5/2025 at 8:22 PM, KJW said:

However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument.

One problem is that G isn’t determined to a very high precision

6.67430(15)×10^-11 m^3/kg s^2

The limitations on that would affect any system relying on it.

Yes. But what I said was a continuation of the hypothetical notion mentioned earlier of being able to measure G to an accuracy and precision comparable to that of h and c. Indeed, one of the reasons I said I don't know how to design the measuring instrument is because I don't know how to measure G to the required accuracy and precision. Bear in mind that the reason for replacing Δν_Cs with G, apart from philosophical ideality, was to address the concern raised by @Killtech that the current definition of the second is based on an electromagnetic notion (the Cs atom).

On 5/6/2025 at 6:14 AM, Killtech said:

On 5/5/2025 at 8:22 PM, KJW said:

However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument.

No, there is no such problem as the fundamental constant cannot be measured in this situation and therefore must be defined. This is fine because the constants - or more precisely the core physics they originate from - serve as the rulers to measure everything with. for example the speed of light together with the other constant allows you to construct a real photon emission which wavelength is fully determined by the constants and this base wave lengths servers as a ruler to compare any other real length to. For this we only need to know the defined values of the constants instead of measuring them. The definition via constants has the nice advantage that we have some freedom in constructing the ruler we use - yet all the different rulers constructed in this way will still agree (if the physical laws underlying them use are indeed correct).

I take responsibility for the possible misunderstanding here. Even though the fundamental constants are defined to have definite numerical values, measurements of the dimensions still require physical access to the fundamental constants. Therefore, all the issues associated with measuring the fundamental constants in the past when the fundamental constants were measured still apply to the measurement of the dimensions in terms of the numerically defined fundamental constants today. In particular, the accuracy and precision of measurements of the dimensions is limited by the accuracy and precision of measurements of the fundamental constants even though they are not being measured in the same sense that they were in the past but as a standard of comparison.

On 5/6/2025 at 6:14 AM, Killtech said:

In this situation the "true" value of the constants remains unmeasurable

Why do you think that there is a "true" value of the fundamental constants? Yes, the Planck length is a definite interval of spacetime, but without a unit of length to compare it with, the Planck length can't be specified. And if the Planck length is the unit of length, then the Planck length has a value of 1, but its interval of spacetime remains unspecified. At least with the old one metre platinum-iridium rod, one could look at it and see what the length of one metre looks like.

Edited May 9May 9 by KJW

On 5/9/2025 at 11:59 PM, KJW said:

Why do you think that there is a "true" value of the fundamental constants? Yes, the Planck length is a definite interval of spacetime, but without a unit of length to compare it with, the Planck length can't be specified. And if the Planck length is the unit of length, then the Planck length has a value of 1, but its interval of spacetime remains unspecified. At least with the old one metre platinum-iridium rod, one could look at it and see what the length of one metre looks like.

No, it's not what i think. i used the quotes for a reason. so i think we are in agreement here. i was just confused because you highlighted that your instrument would have to measure these constants - which made little sense to me, once they are defined. i suppose you meant to measure them according to previous definitions in order to establish an accurate redefinition?

On 5/9/2025 at 11:59 PM, KJW said:

Bear in mind that the reason for replacing Δν_Cs with G, apart from philosophical ideality, was to address the concern raised by @Killtech that the current definition of the second is based on an electromagnetic notion (the Cs atom).

My concern lies not with the definition of time itself but with the miscommunication of the nature of light as represented by the constancy of c. We look for new physics by making hypothesis extending our current laws of physics and can put those new theories to the experimental test. GR was discovered this way. but when it comes to the speed of light, the situation is fundamentally different. we cannot even hypothesize it to vary due to how it is tied to both the definitions of time and space. It should be highlighted that the problem remain the same, even when we go back to the previous definitions, simply because how the behavior of the atom is tied to c.

My concern is that we do not distinguish between laws of physics which are implied by the definitions of time and space to laws of physics which behavior shows some degree of independence from them. The latter can be approached making new assumptions and theories, while it is not possible for the prior because such assumptions result in contradiction to the core definitions. I understand that looking for contradicting assumptions in a theory instead of experimental verification is not how physicist think - yet it is a step that cannot be avoided when discussing the nature of c.

Looking back at the definition of T, L and M that you proposed, it of course makes perfect sense if we could get G with high accuracy. But it also defines a spacetime where c is perfectly fixed since you use it as a basis for your definitions, right? Yet unlike laws of physics, definitions are conventions that are judged by practicality. I argue that there might be some purposes for which a different definition of spacetime which allows for a varying c is more advantageous. But this does not mean that we have to pick one over the other. I propose to treat the definition of spacetime similar to how we treat coordinates: accept that there are multiple possibilities and we choose the one most suited for the problem.

Edited May 11May 11 by Killtech

2 hours ago, Killtech said:

we cannot even hypothesize it to vary due to how it is tied to both the definitions of time and space. It should be highlighted that the problem remain the same, even when we go back to the previous definitions, simply because how the behavior of the atom is tied to c.

I must be hallucinating this, then

https://en.m.wikipedia.org/wiki/Variable_speed_of_light

There’s an item in there that points out that dimensionless constants are not dependent on your choice of unit systems, which is one reason they are investigated.

On 5/11/2025 at 9:17 PM, Killtech said:

On 5/10/2025 at 7:59 AM, KJW said:

Why do you think that there is a "true" value of the fundamental constants?

No, it's not what i think.

You say that, but then you say things like:

On 5/11/2025 at 9:17 PM, Killtech said:

I argue that there might be some purposes for which a different definition of spacetime which allows for a varying c is more advantageous.

The notion of a variable c might seem reasonable from a superficial perspective, but when one considers it more deeply, it becomes clear that it is really quite meaningless, in the "how long is a piece of string" territory.

On 5/11/2025 at 9:17 PM, Killtech said:

i suppose you meant to measure them according to previous definitions in order to establish an accurate redefinition?

No, that's not what I meant. Suppose that in the past, before the standard of length was defined in terms of the speed of light in a vacuum, one performs a measurement of the speed of light in a vacuum. One can do this by measuring the time it takes for light to travel in a vacuum the distance of the standard of length and return. From the measured time and the known distance, the speed of light in a vacuum is determined. Now consider that currently, with the standard of length defined in terms of the speed of light in a vacuum, one performs a measurement of a given length. One can do this by measuring the time it takes for light to travel in a vacuum the distance of the given length and return. From the measured time and the known speed of light in a vacuum, the given length is determined. But note that the same experiment is performed in both cases. That is, in both cases, one is measuring the time it takes light to travel some distance in a vacuum... a measurement of the speed of light in a vacuum. To make this more explicit, consider in the second case that one can define the given length as a temporary standard of length with the unit of "tmpstd". Then one is measuring the speed of light in a vacuum in units of tmpstds per second. Dividing the defined speed of light in a vacuum in units of metres per second by the measured speed of light in a vacuum in units of tmpstds per second gives a value in units of metres per tmpstd corresponding to the length in metres for the given length.

On 5/11/2025 at 9:17 PM, Killtech said:

My concern lies not with the definition of time itself but with the miscommunication of the nature of light as represented by the constancy of c.

I agree that the speed of light in a vacuum is conceptually distinct from c. The speed of light in a vacuum is a property of light or electromagnetism in general, whereas c is a value that relates units of length and units of time with regards to the equivalence of length and time in spacetime. Whereas one can use the same ruler to measure lengths in the east-west, north-south, and up-down directions by simply rotating the ruler, one can't rotate the ruler to the past-future direction. But relativistic effects do provide a way to determine the equivalence between length and time in spacetime. For example, one can measure c by measuring the velocity of light in water at rest and in water moving at velocity v. From the three velocities, the value of c can be obtained by rearranging the relativistic velocity-addition formula. Note that the length standard used to measure the three velocities is based on the speed of light in a vacuum, not c, so the measurement of c is a truly independent measurement. However, it is unfortunate that the length standard is based on the speed of light in a vacuum, and not on c, given that it is c that is about the equivalence of length and time in spacetime.

On 5/11/2025 at 9:17 PM, Killtech said:

I argue that there might be some purposes for which a different definition of spacetime which allows for a varying c is more advantageous.

In general relativity, the general metric is expressed succinctly as:

(ds)² = g_pq x^p x^q

How would a variable c even fit into this expression? And what do you think "ds" means in this expression?

On 5/10/2025 at 7:59 AM, KJW said:

At least with the old one metre platinum-iridium rod, one could look at it and see what the length of one metre looks like.

Bear in mind that regardless of what is used to define the standard of length, it will never be possible to determine the "true" value of that length. A length can be measured in terms of another length, but this ultimately leads to an infinite regress. And if a length is measured in terms of itself, it will have a definite value, but that value has no meaning.

Edited May 18May 18 by KJW

16 hours ago, KJW said:

Bear in mind that regardless of what is used to define the standard of length, it will never be possible to determine the "true" value of that length. A length can be measured in terms of another length, but this ultimately leads to an infinite regress. And if a length is measured in terms of itself, it will have a definite value, but that value has no meaning.

well, what is are one and only "true" coordinates? for me conventions like these have no fundamental meaning of right or wrong, but can be exchanged if deemed more practical in a given context. The geometry of a manifold is mathematically similar and can be changed by redefining geometric objects (you just have to make sure to stay in the same differential topology) - it does not affect the predictions you do on it, only the notation of how you describe them. So i do not understand, why you would stick to a singular geometric description of spacetime, if there is no true one. Instead, we could look at all possibilities and check out what advantages they may have. same as we do with coordinates.

15 hours ago, KJW said:

But note that the same experiment is performed in both cases

Yeah, and it is the same two experiments also with the old standard, as the old one standard of length is still based on a derivative of the speed of light and therefore has no potential of deviation. This is my what bothers me.

Maybe you should go through the history of how the speed of light was measured and Poincaré critique of it. Because it turns out astronomers actually did the mistake of using the same experiment to determine distance as they used to determine the speed of light, mistaking that such an arrangement cannot tell if it is constant or not. All later attempts can be reduced to the same problem, even if it is less obvious.

Your line of thought only works if the alternative standard of length used in an experiments can be considered sufficiently independent of c. In the absence of such an option we can however ask another question: what would happen, if the length of a meter or second changed depending on the location? the answer is simple: this produces geometric curvature. We can also ask the question what would happen, if we defined the standard for length and time implicitly or explicitly both via the propagation of some type of wave. it turns out all relativistic effects can be reduced to this relation between the wave propagation and the definitions of time and length.

16 hours ago, KJW said:

But relativistic effects do provide a way to determine the equivalence between length and time in spacetime

and this idea works for any wave, not just light. the acoustic metric is a perfect example of that. it shows that we can treat sound waves identical to light in a vacuum with curvature and using that special definitions of time and space we get all the familiar framework.

16 hours ago, KJW said:

In general relativity, the general metric is expressed succinctly as:

(ds)² = g_pq x^p x^q

How would a variable c even fit into this expression? And what do you think "ds" means in this expression?

yes, and it is the same with the acoustic metric - that is if we change geometry of spacetime just so sound is described analog to light and becomes perfectly constant. you should explore that, if you are not familiar with it. it is a nice learning experience leaving the question how does an acoustic black hole differ from a gravitational one in terms describing the signal propagation around it?

but we can also go the other way around, as we do know a description where the speed of sound is variable. Normally you would start looking for a spacetime definition which is perfectly flat but it that case it is given. However, that alone enforces the propagation speed of your waves to become variable, if spacetime wasn't flat before. of course that produces an issue with the original metric, so you do not want it to have any dependence on it. and if you drop it, you end up with the old Euclidean metric. You lose the entire complexity of a variable geometry but of course this comes at the price of moving the physics previously described by the geometry to other physical entities instead. You get something like a Gravitomagnetic field with the same number of degrees of freedom your geometry had before.

How would that look like? Actually, space agencies like NASA uses effectively that when calculating trajectories of objects in the solar system. they do all calculation in BCRS coordinates. if the geometry becomes more complicated than in the simplistic Schwarzschild case, GR natural representation becomes unsuited for practical calculations. so for many body system we do choose specific coordinates to do calculations or simulations in, but really, these coordinates align with how you would define a flat spacetime framework like LET and hence the coordinate speed of light in such coordinates is never constant.

Edited May 18May 18 by Killtech

2 hours ago, Killtech said:

Your line of thought only works if the alternative standard of length used in an experiments can be considered sufficiently independent of c

Which, of course, it was. People measure length without relying on time-of-flight of light. Meter sticks and tape measures. Surveyors do it over significant distances.

On 5/19/2025 at 6:26 AM, Killtech said:

well, what is are one and only "true" coordinates? for me conventions like these have no fundamental meaning of right or wrong, but can be exchanged if deemed more practical in a given context. The geometry of a manifold is mathematically similar and can be changed by redefining geometric objects (you just have to make sure to stay in the same differential topology) - it does not affect the predictions you do on it, only the notation of how you describe them. So i do not understand, why you would stick to a singular geometric description of spacetime, if there is no true one. Instead, we could look at all possibilities and check out what advantages they may have. same as we do with coordinates.

It would appear that you believe reality has a non-trivial topology. I'm actually quite ambivalent about whether or not spacetime has a non-trivial topology. Anyway, I do consider the question of whether two different descriptions are describing the same reality to be a fundamental question. However, one shouldn't be blasé about what characterises equivalent descriptions. It is something that requires careful consideration. I do believe that reality does have more structure than what is provided by topology.

On 5/19/2025 at 6:26 AM, Killtech said:

On 5/18/2025 at 12:12 PM, KJW said:

But note that the same experiment is performed in both cases

Yeah, and it is the same two experiments also with the old standard, as the old one standard of length is still based on a derivative of the speed of light and therefore has no potential of deviation. This is my what bothers me.

...

Your line of thought only works if the alternative standard of length used in an experiments can be considered sufficiently independent of c.

I was actually addressing the concern that I was measuring the speed of light using a standard of length based on the speed of light. Anyway, there was a time when the standard of length was based on a platinum-iridium bar. How is the length of a platinum-iridium bar based on the speed of light? Actually, you did suggest that because atoms are based on electromagnetism that their size is based on the speed of light. But you didn't explain precisely how the electromagnetism of the atom leads to the size of the atom being based on the speed of light. On the other hand, given the fundamental connection between space and time that is manifested by the speed of light, it may be that a standard of length that is not in some way based on the speed of light is impossible. That is, you may have a problem with a standard of length being based on the speed of light, but if it is impossible for a standard of length to be independent of the speed of light, then this becomes problematic to your idea that the speed of light can vary.

On 5/19/2025 at 6:26 AM, Killtech said:

On 5/18/2025 at 12:12 PM, KJW said:

But relativistic effects do provide a way to determine the equivalence between length and time in spacetime

and this idea works for any wave, not just light. the acoustic metric is a perfect example of that. it shows that we can treat sound waves identical to light in a vacuum with curvature and using that special definitions of time and space we get all the familiar framework.

One can't replace the speed of light in a vacuum with the speed of sound. One can't even replace the speed of light in a vacuum with the speed of light in water. In the measurement of c based on the measurement of the speed of light in both still water and moving water, the choice of using light in water was merely to provide a speed that is fast enough for the relativistic effect to be significant. In principle, one could choose the speed of any object to apply the relativistic velocity-addition formula. Although like the speed of light in a vacuum, the speed of sound in a medium is constant with respect to the speed of the source, unlike the speed of light in a vacuum, the speed of sound in a medium is not constant with respect to the speed of the observer. The speed of sound in a medium is constant relative to the medium and therefore does not depend on the speed of the source relative to the medium. But the speed of sound relative to the observer does depend on the speed of the observer relative to the medium. The important role played by the medium with regards to sound in contrast to the absence of a medium with regards to light in a vacuum manifest in the difference in the Doppler effect formula for sound and for light in a vacuum.

Edited June 8Jun 8 by KJW

On 6/8/2025 at 6:36 PM, KJW said:

It would appear that you believe reality has a non-trivial topology. I'm actually quite ambivalent about whether or not spacetime has a non-trivial topology. Anyway, I do consider the question of whether two different descriptions are describing the same reality to be a fundamental question. However, one shouldn't be blasé about what characterises equivalent descriptions. It is something that requires careful consideration. I do believe that reality does have more structure than what is provided by topology.

Firstly i do believe that i (and we in general) don't know enough and so i wouldn't trust in any believe, especially my own.

Instead i prefer to switch between believes in figuring out what works best rather then dig myself into one and disregard all else as false. flexibility and open mindedness works better when looking for answers. I also found that this method of thought is significantly more effective to get a deeper understanding of each believe/interpretation, its weaknesses and advantages. In particular you learn so much more by failing starting from a wrong assumption then never straying from the safe path... but it gets you in trouble when you figure out that some alternative assumptions cannot be made to fail.

Don't take this approach as being blasé about it. Its quite the opposite, as this is my way to approach such problems.

On 6/8/2025 at 6:36 PM, KJW said:

Actually, you did suggest that because atoms are based on electromagnetism that their size is based on the speed of light. But you didn't explain precisely how the electromagnetism of the atom leads to the size of the atom being based on the speed of light

I did mention it in my original post and somewhere later as well here, but true, not detailed enough. It was discussed in detail in my conversation with ChatGPT on the topic which link was deleted.

The original question was to take the assumption of a variable c to what it means for atomic physics - but assuming it remains effectively constant over the region covered by an atom.

One way of approaching this is doing quantum mechanics with generalized LET assumptions. Without loss of generality one can do all this with the simple hydrogen atom. And whatever we assume for c (including a ether wind effect), we can find coordinates that undo it to reduce the problem to the original hydrogen, so we don't have that much to solve. Effectively whatever we do, it scales all atomic quantities, including transition frequencies which serve to define the unit of time and the older definitions of length. The latter is because this approach continues to solid state physics affecting the distances between atoms. if we measure time or length by these standards we can conclude all variations to c must cancel out.

Btw. this is also an interesting showcasing the mechanism by which Michelson-Morley must still yield a null result in LET.

On 6/8/2025 at 6:36 PM, KJW said:

One can't replace the speed of light in a vacuum with the speed of sound. [...] Although like the speed of light in a vacuum, the speed of sound in a medium is constant with respect to the speed of the source, unlike the speed of light in a vacuum, the speed of sound in a medium is not constant with respect to the speed of the observer

Now, the last statement depends on you choice of a metric. i know this is not an easy one to understand, especially given out intuition, but with math we can do a lot of trickery that defies intuition.

Let's recall what Lorentz transformation originally are: coordinate transformations. so let's forget all interpretation and look at reality entirely from the perspective coordinates give us. Let's start with sound waves in a frame x at rest to the medium and pick some other frame x' which moves with a velocity v. What would happen if we apply a Lorentz coordinate trafo from x to x' but using c_s, the speed of sound, instead in the transformation? how does the sound wave equation look like in the new coordinates x'? Alternatively we can get the same answers when we start with the sound wave equation and ask ourselves under what kind of coordinate transformations this equation will remain invariant under?

The acoustic metric i mentioned adopts these coordinates and their transformations between frames as the standard - which will be at odds with our intuitive way of looking at these situations but you cannot argue it to be logically wrong. and that metric (or these coordinates if you want) makes it so, that the (coordinate) speed of sound will be constant with respect to the speed of the observer.

And by doing so, it enables us to make a fully analogy between light in general relativity and sound - so that we can study (acoustic) black holes in a lab and find the analogue observations astronomy yields.

But there are better sources on the topic then me, as there has been some research on this. it would be very helpful if you could read up on it so we can discuss this further on a more equal ground.

On 6/8/2025 at 6:36 PM, KJW said:

The important role played by the medium with regards to sound in contrast to the absence of a medium with regards to light in a vacuum manifest in the difference in the Doppler effect formula for sound and for light in a vacuum.

Within the acoustic metric, the formulas become identical. That's the gist of it.

This shows that we can interpret special relativity as a general mathematical methodology for removing the background dependence for any wave equation.

Of course the big difference is that for general relativity we have clocks that directly correspond to time coordinate as produced by the Lorentz trafos, but for acoustics, while we could construct such devices that behave analogous, they won't be considered natural in any way... although maybe a for a bat, they will be as it sees the world though acoustics instead of light.

Edited June 9Jun 9 by Killtech

On 6/10/2025 at 7:31 AM, Killtech said:

the assumption of a variable c

The defining feature of a lightlike trajectory in spacetime is that at all points along the trajectory, in all coordinate systems:

g_uv dx^u dx^v = 0

That is, g_uv dx^u dx^v is a constant over the lightlike trajectory and invariant with respect to coordinate transformations. And because the chosen lightlike trajectory is arbitrary, g_uv dx^u dx^v is also constant over all possible lightlike trajectories. g_uv dx^u dx^v can't be non-zero because that would mean the trajectory is either timelike or spacelike, depending on whether g_uv dx^u dx^v is greater than or less than zero. Quite simply, spacetime does not admit the notion of a variable c, and this has nothing to do with how units of time and length are defined.

Furthermore, for g_uv dx^u dx^v ≠ 0, the magnitude of an interval on the trajectory depends on the chosen endpoints of the interval. This is not the case for a lightlike trajectory, for which the magnitude of the interval is always zero regardless of the chosen endpoints. This makes the speed of light in a vacuum quite special compared to other speeds (even superluminal speeds).

On 6/10/2025 at 7:31 AM, Killtech said:

Effectively whatever we do, it scales all atomic quantities, including transition frequencies which serve to define the unit of time and the older definitions of length. The latter is because this approach continues to solid state physics affecting the distances between atoms. if we measure time or length by these standards we can conclude all variations to c must cancel out.

One thing you seem to be overlooking throughout this entire discussion is that one can't directly compare two arbitrarily chosen spacetime intervals. To perform an indirect comparison, one uses a physical object such as a clock or ruler to transfer the magnitude from the location of one interval to the location of the other interval. This relies on the magnitude not changing during the transfer from one location to the other. In the case of a clock or ruler being based on the laws of physics, it relies on the laws of physics not changing during the transfer from one location to the other. Thus, the first postulate of special relativity states that the laws of physics take the same form in all inertial frames of reference. (Note that in general relativity, local physics is special relativity).

On 6/10/2025 at 7:31 AM, Killtech said:

On 6/9/2025 at 2:36 AM, KJW said:

One can't replace the speed of light in a vacuum with the speed of sound. [...] Although like the speed of light in a vacuum, the speed of sound in a medium is constant with respect to the speed of the source, unlike the speed of light in a vacuum, the speed of sound in a medium is not constant with respect to the speed of the observer

Now, the last statement depends on you choice of a metric. i know this is not an easy one to understand, especially given out intuition, but with math we can do a lot of trickery that defies intuition.

Let's recall what Lorentz transformation originally are: coordinate transformations. so let's forget all interpretation and look at reality entirely from the perspective coordinates give us. Let's start with sound waves in a frame x at rest to the medium and pick some other frame x' which moves with a velocity v. What would happen if we apply a Lorentz coordinate trafo from x to x' but using c_s, the speed of sound, instead in the transformation? how does the sound wave equation look like in the new coordinates x'? Alternatively we can get the same answers when we start with the sound wave equation and ask ourselves under what kind of coordinate transformations this equation will remain invariant under?

I think I understand what you are saying. You are saying that because the wave equation for sound is the same as the wave equation for light but with the speed of sound replacing the speed of light, the wave equation for sound will be invariant to Lorentz transformations with the speed of sound replacing the speed of light, and all of relativity will apply with the speed of sound replacing the speed of light. This would be true except that your initial premise is not true. The wave equation for sound:

∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z² − 1/c_sound² ∂²φ/∂t² = 0

is incomplete. It is incomplete because there is no mention of the speed of the medium. Thus, the equation only applies to the frame of reference in which the medium is at rest. Therefore, the above wave equation is not invariant to Lorentz transformations with the speed of sound replacing the speed of light, and the rest of relativity doesn't apply either.

On 6/10/2025 at 7:31 AM, Killtech said:

On 6/9/2025 at 2:36 AM, KJW said:

The important role played by the medium with regards to sound in contrast to the absence of a medium with regards to light in a vacuum manifest in the difference in the Doppler effect formula for sound and for light in a vacuum.

Within the acoustic metric, the formulas become identical.

But they are not physically identical. Consider the transverse Doppler effect. For sound, there is no transverse Doppler effect, whereas for light in a vacuum, there is a Doppler effect corresponding to time dilation.

On 6/10/2025 at 7:31 AM, Killtech said:

This shows that we can interpret special relativity as a general mathematical methodology for removing the background dependence for any wave equation.

An important property of tensors is that a tensor that is zero (or non-zero) in one coordinate system is zero (or non-zero) in every coordinate system. A corollary of this is that a tensor equation that is true in one coordinate system is true in every coordinate system. Ideally, the laws of physics are tensor expressions. This makes sense because physical reality doesn't come with a coordinate system, and therefore the behaviour of physical reality is independent of any coordinate system. General relativity is explicitly about tensors. The idea of removing a background indicates the background is not a tensor and therefore goes against the spirit of relativity. As I said above, the above wave equation for sound is incomplete and valid only in the frame of reference in which the medium is at rest. This also means that the complete equation that reduced to the above equation is not a tensor equation (three-dimensional velocity is not a tensor).

Edited June 21Jun 21 by KJW

5 hours ago, KJW said:

The defining feature of a lightlike trajectory in spacetime is that at all points along the trajectory, in all coordinate systems [...] Quite simply, spacetime does not admit the notion of a variable c, and this has nothing to do with how units of time and length are defined.

Indeed, the spacetime as used in relativity does not admit a variable c, but i did account for that. But you are right in that there are many traps even thinking about the issue.

Consider something historic like the Maxwell equations and its treatment in both LET and relativity spacetime, which are both equivalent. LET uses a Galilean spacetime, hence there are no restrictions on c. Furthermore there is always one frame where both descriptions will yield the identical from for Maxwell - the preferred frame - and this is the frame where we start our considerations from. This is a very important for the next part:

6 hours ago, KJW said:

One thing you seem to be overlooking throughout this entire discussion is that one can't directly compare two arbitrarily chosen spacetime intervals. To perform an indirect comparison, one uses a physical object such as a clock or ruler to transfer the magnitude from the location of one interval to the location of the other interval. This relies on the magnitude not changing during the transfer from one location to the other. In the case of a clock or ruler being based on the laws of physics, it relies on the laws of physics not changing during the transfer from one location to the other. Thus, the first postulate of special relativity states that the laws of physics take the same form in all inertial frames of reference. (Note that in general relativity, local physics is special relativity).

I very much have accounted for that. What you overlook is that your approach ends in a unresolvable circular reference that renders you unable to approach the question at all.

Any assumption of a variable c requires letting go of the relativistic spacetime (see OP "A Need for a Counterhypothesis"). But: as with LET (or sound equation) we know there exist one preferred frame where the equations in LET and SR spacetimes will be identical. In this frame we can make the assumption of a variable c and admit that the new assumed equation is one relative to a abstract theoretical clocks and rules defined by the assumption that they remain invariant under any changes of c. We do not need to know what these abstract clocks and rulers are - because the very next thing we do is to use these equations with a variable c and use them to model what defines our actual clocks and rulers - e.g. the Cs atom. From there we can deduct how the theoretical abstract c-invariant clock and rulers relate to our SI clocks and rulers.

I have mention this already in my opening post that the assumption of a variable c still leads to c being constant if we remain with the standard clocks and rulers and instead it will manifests as curvature of spacetime identical to gravity.

But now that you mention it, it may be complicated to understand that, as it effectively requires to jump between different spacetime models and the same equations written in those different spacetimes.

6 hours ago, KJW said:

It is incomplete because there is no mention of the speed of the medium. Thus, the equation only applies to the frame of reference in which the medium is at rest. Therefore, the above wave equation is not invariant to Lorentz transformations with the speed of sound replacing the speed of light, and the rest of relativity doesn't apply either.

You are getting there :). Of course you are right to mention that my proposition does not work in any frame - but i did mention explicitly that this construction requires to start from the preferred frame i.e. where the medium is at rest.

Now, if we have an equation in one frame and need it in another, we can do the corresponding transformation. For the sound equation we would normally do that by Galilean trafos and hence get additional terms for the medium, right? But starting from the base frame we can now apply also a Lorentz trafo and get an equation without a medium - but in different coordinates. So for one frame where the medium is not at rest we have two equations with two different coordinates sets. We can do a sanity check and calculate whatever physics example to notice that both give identical predictions (if we account that the Lorentz variant requires us to transform time and lengths calculated in a frame from coordinate units to SI units).

With the Lorentz trafo we therefore got the same shape of the sound equation in any frame as in the preferred frame where the medium is at rest. So in the acoustic spacetime, the sound equation maintains its original form in every frame! And suddenly the mediums is gone from the equation - instead it moved into the geometry of spacetime.

7 hours ago, KJW said:

An important property of tensors is that a tensor that is zero (or non-zero) in one coordinate system is zero (or non-zero) in every coordinate system.

But we are not just transforming between coordinate systems. the coordinates serve as a first step of construction.

But the big step to special relativity was elevating these coordinates to a new and fundamentally different definition of spacetime. But this idea is not exclusive to light and can be applied mathematically to any other wave.

Now, tensors are sensitive to the geometry and hance a zero tensor may be non-zero ins the same frame in a different geometry. best example: the medium terms in a frame is a tensor in LET which is 0 only in the preferred frame and nonzero everywhere else. In SR it is always zero.

On 6/22/2025 at 7:01 AM, Killtech said:

On 6/21/2025 at 11:47 PM, KJW said:

It is incomplete because there is no mention of the speed of the medium. Thus, the equation only applies to the frame of reference in which the medium is at rest. Therefore, the above wave equation is not invariant to Lorentz transformations with the speed of sound replacing the speed of light, and the rest of relativity doesn't apply either.

Of course you are right to mention that my proposition does not work in any frame - but i did mention explicitly that this construction requires to start from the preferred frame i.e. where the medium is at rest.

Now, if we have an equation in one frame and need it in another, we can do the corresponding transformation. For the sound equation we would normally do that by Galilean trafos and hence get additional terms for the medium, right? But starting from the base frame we can now apply also a Lorentz trafo and get an equation without a medium - but in different coordinates.

Before my previous post, as well as since your last post, I had spent considerable time over this issue. I must say that what you are saying here is correct. I had been misled by the known physics into believing that one required the complete wave equation in order to apply your modified Lorentz transformation. But in fact, your modified Lorentz transformation, as a coordinate transformation, can be applied to the incomplete wave equation that is valid in the particular coordinate system to which the modified Lorentz transformation is being applied. And in the new coordinate system, the incomplete wave equation is valid due to the invariance of the incomplete wave equation to the modified Lorentz transformations.

But we know that for observers in frames of reference in which the medium is not at rest, the incomplete wave equation is not valid and that the observed speed of sound will depend on the speed of the medium relative to the observer. Thus, we can conclude that the new coordinates produced by the modified Lorentz transformations do not represent the space and time of any observer. The space and time of observers is governed by the speed of light in a vacuum. Also, it may be concluded that the principle of special relativity only applies to space and time and not to the coordinates produced by your modified Lorentz transformations.

On 6/29/2025 at 1:17 PM, KJW said:

Before my previous post, as well as since your last post, I had spent considerable time over this issue. I must say that what you are saying here is correct.

Good. This is though just the formal aspect of separating the mathematical treatment from the interpretation.

12 hours ago, KJW said:

But we know that for observers in frames of reference in which the medium is not at rest, the incomplete wave equation is not valid and that the observed speed of sound will depend on the speed of the medium relative to the observer. Thus, we can conclude that the new coordinates produced by the modified Lorentz transformations do not represent the space and time of any observer. The space and time of observers is governed by the speed of light in a vacuum. Also, it may be concluded that the principle of special relativity only applies to space and time and not to the coordinates produced by your modified Lorentz transformations.

That throws us back to the original question raised in this thread: where do we get the notion what the space and time of an observer is? We usually assume it to be trivially clear - but in fact it is a tricky circular problem that i want to discuss.

When we observe some physical processes, we get a notion of the passing of time by the rate how the process changes. in order to be able to measure it, we therefore have to define some physical reference which we then can use to establish time. The definitions underling the SI definitions of time and length do therefore specify this via emissions of the Cs atom for one and the propagation of light in vacuum for another.

But let's observe that in the general case, there is no mathematical reason that all physical processes have to adhere to the same concept of time. Just to illustrate this let's assume an alternative universe where there are two electromagnetic forces that differ only in their propagation speed. each will be invariant to its own Lorentz transformations around its constant c. All physical processes like atomic emissions build from one or the other variant of the two forces will fit into this invariance but will disagree when observing processes of the other force. This is because there won't exist a totally Lorentz invariant physics. This means that each observer can denote two concepts of time: that related to physical process of one force or the other. Technically there will also exist a preferred frame where both forces take the same shape and this frame provides a third time an observer can use.

Applying this observation back to acoustic physics, we can construct physical processes which rely solely on acoustic interactions and see how the coordinates produced by the acoustic Lorentz trafo fare with describing such a process in different frames:

consider an in infinite grid of tiny flying sound emitters which constantly emit a sine like sound (a bit like mosquitos). As sound waves carry physical energy and momentum, this interaction of sound with the emitters will cause a constant repulsion which grows stronger the closer two emitters get to each other. This is meant to mimics the repulsion between atoms in a solid. in the case the entire grid has a velocity relative to the medium (i.e. it's center of mass CoM), the repulsion orthogonal to the CoM momentum is weakened due to the effectively prolonged distance sound waves have to move through the medium to get from one emitter to another. effectively the grid will see a contraction along this direction. But the formulas describing this contraction will look all too familiar. If we were to apply the weird coordinates produced from acoustic Loretz transformations onto this grid, we will find that these coordinates in the CoM frame make the grid look always the same regardless of how fast it moves relative to the medium.

So, if your observer happens to be a bat which uses its ears to visualize its surroundings instead of its eyes, it will find that at least the spatial part of this coordinates do agree quite well with its perception of the world.

On 3/24/2025 at 4:14 PM, Killtech said:

The constancy of the speed of light is a fundamental assumption in modern physics, built into both relativity and the SI system of measurement. I’ve been wondering: to what extent is this a fundamental property of nature, and to what extent is it a convention tied to our choice of units and measurement definitions? And does our current measurement framework even allow us to establish the possibility of it to vary in the first place?

The Issue of Measurement

• The SI second is defined using atomic clocks based on the frequency of a cesium transition.

• The meter is defined in terms of the speed of light, which is fixed at 299,792,458 m/s by definition.

• Since c is numerically fixed, any potential variation in light’s speed would be hidden within changes in how we measure time and space rather than appearing as an explicit difference in measured speed.

A Need for a Counterhypothesis

• To test for a varying c, we’d need a physical framework where such variation makes sense and is not simply reabsorbed into our measurement definitions.

• But how do we define an operational way to measure a changing c, when our time and length units are already tied to its assumed constancy?

The Variation of c

• The fine-structure constant alpha is given by: e² / (4pi epsilon0 hbar c), meaning that if c varied, so would the constant.

• Since the energy levels of Caesium atoms - and thus atomic clock frequencies - depend on alpha, any variation in c would affect the very clocks we use to define the second.

• This creates a self-referential issue: if we use atomic clocks to measure changes in c, but those clocks themselves change due to variations in c, can we even establish whether c is varying in the first place?

• If c depended on location, it would cause clocks in different regions to tick at different rates.

• Since clocks define proper time, this effectively means that a variation in c would manifest as spacetime curvature.

• How, then, would we distinguish such an effect from gravitational time dilation caused by mass-energy?

Back around 1900, Poincaré already recognized the subtleties in these assumptions and criticized how astronomers arrived at their conclusion that c was constant. In modern physics this consideration is even more interesting to explore. I tried this conversation with ChatGPT, and it was well versed to discuss the topic. Here is a link to that conversation: link deleted; violation of 2.13

I’d love to hear thoughts on whether this is a meaningful issue to explore.

A distance of 186,000 miles is equal to one second of time. Distance and time are combined in a single phenomenon within which their properties are invariant. That is why a light second can simultaneously be a measure of distance, and timing. Light-seconds and light-years are actually examples of what are referred to as space-time intervals, which are good analogies of the relationship between space, and time.

Einstein stated, nothing can happen until something moves, which is one of the wisest things he ever said. Motion itself is the simultaneous traversing of both distance and time, and it is a cornerstone of his theory of special relativity. to traverse a distance at sub light speed, takes time. and the faster any distance is traversed the less time elapses, if an object is accelerated to light speed, all the motion of that object is occurring in the spacial dimension, so time for that object is meaningless. Alternatively, if all an objects motion is through the temporal dimension, no spacial motion can occur, so that object is at rest.

To be continued....