Is the speed of light a degree of freedom?

[Killtech]

The speed of light is postulated to be constant in all inertial frames. but why is it called a postulate actually?
looking at the SI definition of the meter that is specifically defined by the propagation of light i notice it makes it constant by definition. so isn't this actually just a choice, a fixing - like a coordinate system - rather then a physical fact?

i mean one could define a meter via propagation of sound waves instead (a bat could come up with that) - just for the sake of showing its possible (at least here on earth) rather then for any practical purpose. such a definition has a major impact on the speed of light obviously and for the space time geometry.

So aren't the speed of light, the meter and second actually simply degrees of freedom that can be fixed at each point of space differently?

 

[stoomart]

The speed of light is the constraint here, time and distance can be measured in whatever units you like.

Edit: The meter was redefined in 1983 to be how far light travels in 1/299 792 458 of a second.

 

[Drakkith]

The speed of light is postulated to be constant in all inertial frames. but why is it called a postulate actually?

Because it is the starting point for essentially all of special relativity and, as far as I know, it can't be derived. If you take the premise that the speed of light is the same in all inertial frames, you naturally arrive at most, if not all, of special relativity.

looking at the SI definition of the meter that is specifically defined by the propagation of light i notice it makes it constant by definition. so isn't this actually just a choice, a fixing - like a coordinate system - rather then a physical fact?

This definition of the meter is an arbitrary choice that makes things convenient. Instead of having as a reference a bar of metal that can change based on temperature, moisture, etc, we have a non-changing reference to go by.

i mean one could define a meter via propagation of sound waves instead (a bat could come up with that) - just for the sake of showing its possible (at least here on earth) rather then for any practical purpose. such a definition has a major impact on the speed of light obviously and for the space time geometry.

No it doesn't. It just changes the units and makes things horribly complicated since the speed of sound is not invariant.

So aren't the speed of light, the meter and second actually simply degrees of freedom that can be fixed at each point of space differently?

To be honest, I'm not sure what this means. The speed of light is a natural constant that cannot be changed just because we change our units of measurement. I could define the meter to be twice the length that it currently is, but that changes nothing other than the numbers we use in our calculations. In fact, a popular system of units sets the speed of light to be exactly 1.

 

[Dale]

So aren't the speed of light, the meter and second actually simply degrees of freedom that can be fixed at each point of space differently?

Not in SI units, but you certainly could pick some strange units such that the speed of light in those units varies across space.

such a definition has a major impact on the speed of light obviously and for the space time geometry.

It doesn't change the spacetime geometry at all. The crucial geometrical concept is that the invariant speed is finite. Its numerical value is not physically important. All of the physics is in the dimensionless constants (e.g. the fine structure constant), not the dimensionful constants (e.g. the speed of light).

 

[strangerep]

[Constancy of light speed] is the starting point for essentially all of special relativity and, as far as I know, it can't be derived.

That's the old SR derivations (or the modern lazy ones).

With a bit more work, one can derive SR from little more than the relativity principle and spatial isotropy (plus some technical assumptions about Lie groups of transformations). One discovers that a universal constant limiting relativity velocity is admitted, though its value must be empirically determined.

Actually, one can do a bit better by deeper analysis of the transformation properties, and study of the associated quantum (unitary, irreducible) representations, which makes it pretty obvious that the constant should be identified with light speed in vacuum.

 

[Killtech]

Not in SI units, but you certainly could pick some strange units such that the speed of light in those units varies across space.

out of curiosity i am looking for such units where the speed of sound becomes constant (ignoring here that it depends on the frequency but not its other dependencies like e.g. air pressure).

It doesn't change the spacetime geometry at all. The crucial geometrical concept is that the invariant speed is finite. Its numerical value is not physically important. All of the physics is in the dimensionless constants (e.g. the fine structure constant), not the dimensionful constants (e.g. the speed of light).

well, i am looking for more then a change of units. rather a change of the definition of distance and my proposed definition of meter should already change it: sound doesn't exist outside of our Earth's atmosphere and therefore the space associated with that definition is necessarily not connected (i.e. there is no connection from moon to earth). also sound wave propagation depends on air pressure and due to fermant's principle it will follow an curved trajectory in inhomogenous air where light (in vacuum) would go in a straight line. now i want a geometry that simply defines that trajectory as a straight line, a geodesic if you want.

that's basically my question. is the geometry and space i use to describe physics in not just a degree of freedom?

 

[Nugatory]

The speed of light is postulated to be constant in all inertial frames. but why is it called a postulate actually?
looking at the SI definition of the meter that is specifically defined by the propagation of light i notice it makes it constant by definition. so isn't this actually just a choice, a fixing - like a coordinate system - rather then a physical fact?

You are overlooking the history here.
The SI definition of the meter in terms of the propagation of light only works if you are already absolutely certain that the speed of light will be constant for all inertial observers. That light-speed postulate was proposed by Einstein in 1905 when the meter was still defined by a metal bar in a vault in Paris; nothing in that definition makes Einstein's postulate obvious. The SI definition of the meter was settled in 1983; that's 78 years later, and most of that time was spent convincing ourselves that the light speed postulate is so solid that we can depend on it to define the meter.

 

[Dale]

i am looking for more then a change of units. rather a change of the definition of distance and my proposed definition of meter should already change it

The meter is a unit, it isn't "distance". Changing the definition of the meter only changes the definition of a specific unit, not the definition of distance in general.

It is rather strange to say "I am looking for more than a change of units" and then do nothing more than propose a redefinition of one specific unit.

that's basically my question. is the geometry and space i use to describe physics in not just a degree of freedom?

I think that I already answered that in post 4.

 

[Mister T]

The speed of light is postulated to be constant in all inertial frames. but why is it called a postulate actually?

Because of the way the notion entered our body of knowledge. The guy who introduced it called it that because that was the way he was using the notion in the paper he wrote. It caught on and as it turns out, he got the consequences right.

looking at the SI definition of the meter that is specifically defined by the propagation of light i notice it makes it constant by definition. so isn't this actually just a choice, a fixing - like a coordinate system - rather then a physical fact?

It doesn't mean anything that profound. It's a metrological choice, a convention carefully chosen to be useful.

So aren't the speed of light, the meter and second actually simply degrees of freedom that can be fixed at each point of space differently?

I believe the way the metrologists view it there are only two degrees of freedom there because choosing any two to define implies the third. Previously the meter and second were defined, which implied a specific value for the speed of light. Currently the second and the speed of light are defined, which implies a specific value for the length of a meter.

It doesn't change the physics.

And by the way, this same scheme, defining things by assigning exact values to fundamental constants, is about to expand. Last I heard it's likely to happen in 2018.

out of curiosity i am looking for such units where the speed of sound becomes constant (ignoring here that it depends on the frequency but not its other dependencies like e.g. air pressure).

I think you'd have to define this yourself. It's hard for me to imagine a use for that definition so it's hard for me to imagine a definition exists. I could be wrong, though. The usual criteria for making the choice is utility.

 

[Ibix]

An easy way to show the problems with an invariant speed of sound is to have a region of still air containing a tube in which air is flowing. A reference frame attached to the air outside the tube will see a direction-dependent velocity of sound inside the tube and an isotropic one outside. Vice versa for a reference frame attached to the air inside the tube. A reference frame defining both volumes as stationary would be discontinuous at the boundary, and hence spectacularly non-inertial.

The point is that the invariance of the speed of light in inertial frames is a consequence of the geometry of spacetime, not your unit choice.

 

[Killtech]

You are overlooking the history here.
The SI definition of the meter in terms of the propagation of light only works if you are already absolutely certain that the speed of light will be constant for all inertial observers. That light-speed postulate was proposed by Einstein in 1905 when the meter was still defined by a metal bar in a vault in Paris;

the SI definition of meter indirectly specifies a measurement method for distance and thus defines more then just a unit. as for the meter-bar: its made out of atoms which core property like size are totally determined by the electromagnetic force. changing a property like the speed of light will therefore also change the bars size as well but without a reference to compare it to you are unable to detect that. hypothetically: assuming that changing that property would make the bar - and matter in general - shorten by the very same size as the travel distance of light in vacuum then it becomes impossible to detect that effect at all. therefore it would be a degree of freedom - a choice that can be made.

The meter is a unit, it isn't "distance". Changing the definition of the meter only changes the definition of a specific unit, not the definition of distance in general.

It is rather strange to say "I am looking for more than a change of units" and then do nothing more than propose a redefinition of one specific unit

then how is the distance between two points in space defined? as i see it the definition of meter not only provides a unit fixing but also specifies a method how to measure distance: evacuate the space between then and send a light from one point to another measuring its time. of course using our knowledge of physics we can find alternative equivalents to this method (like keeping the air as it is but applying a factor for how light is slowed by matter).

but yeah, why not try a different definition of distance instead: don't evacuate the space in between the points and send a sound wave instead and measure its time. that's what i implied with the definition of a meter via sound waves.

besides in mathematics i can change the definition of distance (metric, or even a norm) at will if i want to. i can even define metrics it in such a way that things that are local for one aren't for another. why then should physics have only a single way to define distances? i agree that other definitions won't be very useful but this isn't the point of the question.

An easy way to show the problems with an invariant speed of sound is to have a region of still air containing a tube in which air is flowing. A reference frame attached to the air outside the tube will see a direction-dependent velocity of sound inside the tube and an isotropic one outside. Vice versa for a reference frame attached to the air inside the tube. A reference frame defining both volumes as stationary would be discontinuous at the boundary, and hence spectacularly non-inertial.

The point is that the invariance of the speed of light in inertial frames is a consequence of the geometry of spacetime, not your unit choice.

you are absolutely right, but your observation only holds in the default definition of distance and space. redefining it is the key here. if you measure distances via sound you have to consider that they will be deflected by the air flow and thus give you a different space. maybe try to imagine how a bat (which perceives the world around it via sound waves rather then light) would see your air tube? for the bat an object fixed to the inside of the tube not flowing with the air would look like it was in an accelerated frame or sitting in a weird gravity-like field.

besides, you need to realize one thing though: try to measure the speed of sound with using measurement methods for length that are based on the acoustic wave propagation. in that case you are trying to measure the length of a rule with itself so don't expect to yield anything other then the speed of sound being constant.

 

[Killtech]

hypothetically:
if the speed of light was slowed down by a factor in a one part of the space then
1) wouldn't also change the impulse & energy carried by a photon as well?
2) wouldn't therefore all interactions with the EM field be affected too? more precisely wouldn't the Coulomb force be scaled by the same factor?
3) wouldn't that change the QM solution of hydrogen atom (and others)? specifically wouldn't it alter its size by the same factor?
4) wouldn't that directly affect the size of all crystals, liquids and so on? wouldn't they change their properties like volume by the same factor?
5) couldn't the definition of the meter via light propagation in vacuum and via a bar being affected in the same way?
6) what would be left unmodified such that one could use it to measure the change?

 

[Ibix]

besides, you need to realize one thing though: try to measure the speed of sound with using measurement methods for length that are based on the acoustic wave propagation. in that case you are trying to measure the length of a rule with itself so don't expect to yield anything other then the speed of sound being constant.

You might want to look up Fizeau's experiments with light in flowing water. That it doesn't behave like sound was a key piece of evidence for relativity.

Also, what is the speed of sound in a vacuum?

 

[Killtech]

You might want to look up Fizeau's experiments with light in flowing water. That it doesn't behave like sound was a key piece of evidence for relativity.

Also, what is the speed of sound in a vacuum?

the speed of sound is explicitly bound it its medium - which is exactly what i want for my alternative definition of distance. sound does not exist in vacuum and therefore any space defined via this distance definition will be unable be applied in vacuum. you could say that vacuum simply doesn't exist as space from the perspective of a bat. you should notice that using the topology defined by sound waves the resulting space is necessarily not connected i.e. there exists no connection between moon and Earth within that topology exactly due to your remark (the distance between them can be arbitrarily set to infinity if it needs to be set at all). so it should be clear that this is an entirely different geometry then what relativity theory uses.

and of course sound doesn't behave like light, but the way how you measure distances and therefore how you track the propagation speed of waves has a huge impact on that behavior that you seem unwilling to consider.

I'll try to make an analogy for Fizeu's experiment but with light: let's assume we have a tube but instead of a medium it is evacuated yet there is an (hypothetical) external constant force present in the entire tube. this force is meant to be indistinguishable from gravity such that the equivalence principle applies. in an accelerated frame the propagation of light should be depending on how it is aligned to the direction of acceleration i.e. the special force. this is how i suppose the sound experiment could look like in the bats topology but using sound waves instead of light.

 

[Mister T]

the SI definition of meter indirectly specifies a measurement method for distance and thus defines more then just a unit.

Correct. The metrologists would, I believe, make that distinction by calling the meter a dimension. It is also a unit. The radian is an example of something that's a unit but not a dimension. Dimensions are also units, but not all units are dimensions.

but yeah, why not try a different definition of distance instead: don't evacuate the space in between the points and send a sound wave instead and measure its time. that's what i implied with the definition of a meter via sound waves.

It would be a far less precise definition, and therefore far less useful. To put it bluntly, scientists, engineers, and technicians doing work where a more precise definition is required would make up a new one and use it. That is in fact the way new definitions get created.

why then should physics have only a single way to define distances?

It makes the definition more useful. And technically, the science is not physics, it's metrology. As I said in Post #9, this issue is nowhere near as profound as you seem to think it is. It's merely a matter of convention.

 

[Killtech]

It would be a far less precise definition, and therefore far less useful. To put it bluntly, scientists, engineers, and technicians doing work where a more precise definition is required would make up a new one and use it. That is in fact the way new definitions get created.

It makes the definition more useful. And technically, the science is not physics, it's metrology. As I said in Post #9, this issue is nowhere near as profound as you seem to think it is. It's merely a matter of convention.

i completely agree that my proposed definition would be totally unpractical and horrible to use. but that is not the point of it - it's for theoretical considerations to get a new perspective on some things.

and i think you're making a mistake by calling a measurement via sound waves less precise. yes, the distance measured between two buildings at high pressure days will vary from that measured during low pressure. but this deviation is not meant to be an imprecision that needs to be corrected but rather a feature that i explicitly want to have! yes, it means that distance between objects that appear for us to be stationary will suddenly vary and thus the entire space will easily get quite distorted. i mean relativity theory says space deforms due to large masses. but in the sound metric space also deforms already at good weather days! and this is what i want to understand: how are the properties of space (e.g. like curvature) dependent on the original definition of the meter (or the dimension as you call it).

 

[stoomart]

it means that distance between objects that appear for us to be stationary will suddenly vary and thus the entire space will easily get quite distorted. i mean relativity theory says space deforms due to large masses. but in the sound metric space also deforms already at good weather days! and this is what i want to understand: how are the properties of space (e.g. like curvature) dependent on the original definition of the meter (or the dimension as you call it).

My understanding is light travels the same speed around massive objects, regardless of how distorted it appears to an external observer. What I find interesting is the trip takes longer for light to travel from point A to point B when a massive body is between the two points, than if the massive body was not present:

A -----<O>----- B vs A ---------- B

https://en.m.wikipedia.org/wiki/General_relativity#Light_deflection_and_gravitational_time_delay
https://en.m.wikipedia.org/wiki/Schwarzschild_geodesics#Bending_of_light_by_gravity

 

[Killtech]

My understanding is light travels the same speed around massive objects, regardless of how distorted it appears to an external observer. What I find interesting is the trip takes longer for light to travel from point A to point B when a massive body is between the two points, than if the massive body was not present:

A -----<O>----- B vs A ---------- B

https://en.m.wikipedia.org/wiki/General_relativity#Light_deflection_and_gravitational_time_delay
https://en.m.wikipedia.org/wiki/Schwarzschild_geodesics#Bending_of_light_by_gravity

whether light travels the same speed along a path elongated by geometry or whether it travels the flat path but at a slowed down speed may be the very same thing but looking at if from two mismatching definitions of distances and geometries. Note that a mutable wave speed in any wave equation bends these waves in the direction of the gradient of the wave-speed-scalar-field c(x,t) described by Fermat's principle too. if you now happen to define your distance and geometry by such a wave propagation (e.g. defining the curved trajectories of your wave front as geodesics) you get a curved space. at least that's what i am trying to achieve by using sound waves for my definition of distance/meter.

 

[stoomart]

That sounds above my head.

 

[PeterDonis]

how are the properties of space (e.g. like curvature) dependent on the original definition of the meter (or the dimension as you call it

They aren't, at least not when the former are defined properly.

First, in GR, we are talking about the geometric properties of spacetime, not space.

Second, as @Dale pointed out, all of the actual physics, including the geometric properties of spacetime, is contained in dimensionless constants like the fine structure constant, or dimensionless observations, which are just numbers. So, for example, the SI meter is defined as the distance traveled by light in vacuum in 1/299792458 second; if we substitute in the SI second definition, we get that the meter is the distance traveled by light in vacuum in 9192631770/299792458 periods of the radiation from a particular hyperfine transition in the ground state of the Cesium-133 atom. So we can measure a meter by just counting periods of radiation that we know how to make in the lab. And we can define, for example, the curvature of spacetime in terms of the same measurements (that's what the SI system of units does). The end result is that we can reduce anything that has units to a dimensionless number with no units, that expresses ratios between the direct results of actual physical processes that involve nothing more that counting. Those ratios obviously cannot depend on our choice of units. Systems of units are just a convenience to make this process easier.

Now, you ask, what if the speed of light changes? But the speed of light is a dimensionful number; what you should be asking is, what if the fine structure constant changes? That's because the fine structure constant is the dimensionless number that governs the physics of things like atomic hyperfine transitions. But we can measure the fine structure constant too, and we can look for evidence that it changes over time or in different regions of space (so far, all the evidence is that it doesn't). If we found that it changed, we could start looking for another dimensionless constant that didn't change, so we could modify all of our standard unit definitions to use that instead. But no such need has arisen.

 

[Killtech]

Now, you ask, what if the speed of light changes? But the speed of light is a dimensionful number; what you should be asking is, what if the fine structure constant changes? That's because the fine structure constant is the dimensionless number that governs the physics of things like atomic hyperfine transitions. But we can measure the fine structure constant too, and we can look for evidence that it changes over time or in different regions of space (so far, all the evidence is that it doesn't). If we found that it changed, we could start looking for another dimensionless constant that didn't change, so we could modify all of our standard unit definitions to use that instead. But no such need has arisen.

the speed of light is not an independent quantity - so in order to change it a lot of other things need to change with it. what i am asking for is changing the properties of the electromagnetic force such that the speed of light becomes variable. now the hyper fine structure of Cs-133 can be modeled via quantum mechanics using the properties of the coulomb force. but changing the properties of that force will undoubtedly change the solution for the hyper-fine structure and therefore affect your definition. so if all EM-based interactions react in similar fashion to a change to their force then they can become invisible. i mean we are trying to measure EM-properties of matter using the EM-force as the measuring tool - basically trying to measure a ruler with itself. how is one supposed to find out that the ruler got larger when the measure of length scales along with him??

my problem is that the entire space-time geometry seems to be deeply liked with the EM-force alone - so i try to figure out how a geometry would look like that is bound to a different force instead. using weak or strong forces for this is not suitable nor is gravity. and while sound isn't a good candidate either a distance definition using it as a measure is well defined on Earth because two acoustic waves following the same path cannot overtake each other.

 

[Ibix]

my problem is that the entire space-time geometry seems to be deeply liked with the EM-force alone

Not really. You can derive relativity to the point of showing that there are only two options - Newton or Einstein - without mentioning light once. See, for example, https://arxiv.org/abs/physics/0302045. You only then need to see if the velocity composition law matches Newton or Einstein to rule out Newton.

It's then just an experimental fact that light travels at the invariant speed. In fact, there's no problem for relativity if light doesn't travel at the invariant speed. I gather particle physics gets a lot hairier, however.

 

[Killtech]

Not really. You can derive relativity to the point of showing that there's only two options - Newton or Einstein - without mentioning light once. See, for example, https://arxiv.org/abs/physics/0302045. You only then need to see if the velocity composition law matches Newton or Einstein to rule out Newton.

It's then just an experimental fact that light travels at the invariant speed. In fact, there's no problem for relativity if light doesn't travel at the invariant speed. I gather particle physics gets a lot hairier, however.

the transformation laws of inertial frames carries the properties of light waves in it. ANY different/nonequivalent definition for distance will break that behavior. in general inertial frames will have a different meaning in a different metric and the transformation behavior will also change.

 

[PeterDonis]

what i am asking for is changing the properties of the electromagnetic force such that the speed of light becomes variable

That means changing the fine structure constant, as I said in my previous post. And all the evidence we have tells us that the fine structure constant is indeed constant--it doesn't change.

the entire space-time geometry seems to be deeply liked with the EM-force alone

No, it isn't. The fact that EM radiation travels on null curves of the spacetime geometry is a fact about EM radiation. But the fact that the spacetime geometry has null curves is not.

i try to figure out how a geometry would look like that is bound to a different force instead

The geometry is not "bound" to any force, so this is a meaningless effort.

 

[Ibix]

the transformation laws of inertial frames carries the properties of light waves in it.

What is this supposed to mean? Did you read the reference I provided?

ANY different/nonequivalent definition for distance will break that behavior.

You are free to use any coordinate system you like. It doesn't change physics.

in general inertial frames will have a different meaning using a different metric and the transformation behavior will also change.

"Inertial frames" are frames wherein observers considered at rest have zero readings on their accelerometers and have constant separation. Again, changing your distance measurement method doesn't change this.

 

[Killtech]

That means changing the fine structure constant, as I said in my previous post. And all the evidence we have tells us that the fine structure constant is indeed constant--it doesn't change.

how are you supposed to measure a change to the constant if the measure you measure it with scales along with it? any change will just cancel each other out.

No, it isn't. The fact that EM radiation travels on null curves of the spacetime geometry is a fact about EM radiation. But the fact that the spacetime geometry has null curves is not.

yes, for the distance measure we use, light travels on null curves - this is an undoubted fact.

look, let's assume we have a two-dimensional manifold in R3 shaped like a 2d-gaussian bell curve and another shaped like two displaced bells (two separate hills) - and maps for both to R2. those two have the space-metric based on the L2 norm of R3 restricted to the respective surface. because of the maps i can map everything happening on one manifold to the other. but since the geometries are different geodesics from one will be totally curved paths for the other and vice versa. so whether a path is a geodesic depends on the geometry/metric you chose to describe your system in. and even it it is extremely complicated and thus useless i could describe everything happening on one manifold on the other using my maps. doing the same game with space-time manifolds and metrics is a bit more complicated but it's still the same concept. and that is what i am trying to do.

"Inertial frames" are frames wherein observers considered at rest have zero readings on their accelerometers and have constant separation. Again, changing your measurement method doesn't change this.

consider a tube with air flowing in it. the air flow is steadily and perfectly-homogeneously accelerated. an observer traveling with the air will of course notice that he is in an accelerated frame. now let's switch the method of measuring distance to sound based. for sound related physics there is no difference between this situation and the air being at rest (an effective force applied to all air particles in identical way doesn't do anything to the interaction between themselves). so within that perspective the frame is at rest.

 

[Ibix]

there is no difference between this situation and the air being at rest

...except for the reading on the accelerometer, which tells you unequivocally that they are different scenarios. Whatever choice of coordinates you want to make.

 

[Ibix]

geometries are different geodesics from one will be totally curved paths for the other and vice versa. so whether a path is a geodesic depends on the geometry/metric you chose to describe your system in. and even it it is extremely complicated and thus useless i could describe everything happening on one manifold on the other using my maps. doing the same game with space-time manifolds and metrics is a bit more complicated but it's still the same concept. and that is what i am trying to do.

This isn't what you're doing, however. You're simply specifying a different set of coordinates on the same spacetime (and not a good set, since you exclude the 99.99999-whatever percent of the universe that is vacuum).

 

[PeterDonis]

how are you supposed to measure a change to the constant if the measure you measure it with scales along with it?

By not using such a measure. See, for example, here:

http://physics.nist.gov/cuu/Constants/alpha.html

for the distance measure we use, light travels on null curves

The fact that light travels on null curves is not dependent on the distance measure we use.

let's assume...

Please review the PF rules on personal speculations. Further posts along these lines will receive a warning.

 

[Killtech]

By not using such a measure. See, for example, here:

http://physics.nist.gov/cuu/Constants/alpha.html

so when EM force is changed such that c is increased by a factor and the effect of charge is reduced by inverse square root of that factor alpha remains unable to detect that change?

 

[Killtech]

The fact that light travels on null curves is not dependent on the distance measure we use.

there is only one 2d-manifold in R3 such that the metric on it is exactly the L2 norm of R3 (apart from displacement) - a metric by which R3 is flat. so your metric defines the geometry of your manifold, its curvature and its geodesics.

and to quote wikipedia on manifolds:
"In 1828, Carl Friedrich Gauss proved his Theorema Egregium (remarkable theorem in Latin), establishing an important property of surfaces. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface."

so changing the metric is not just a change of coordinates. it is a change of geometry, curvature and so forth.

 

[PeterDonis]

changing the metric is not just a change of coordinates. it is a change of geometry, curvature and so forth.

The term "metric" means "the geometry of the manifold" (spacetime in this case), so your statement is a tautology: changing the geometry is changing the geometry.

The term "distance measure" as you have been using it means our choice of units, which can be changed without changing the geometry. Gauss was not saying that French people measuring in kilometers would get a different geometry for the surface of the Earth than British people measuring in miles.

 

[PeterDonis]

when EM force is changed such that c is increased by a factor and the effect of charge is reduced by square root alpha remains unable to detect that change?

I have no idea what you are talking about. There is a large body of literature describing various experiments attempting to detect changes in the fine structure constant. Look it up.

 

[PeterDonis]

Thread closed for moderation.