Invariance of c

[Mordred]

14 hours ago, YaDinghus said:

I think it's about the propagation speed of the waves. I'm not entirely sure since I've never done the kind of math required to describe a change in c in physics. Photons as massless particles aren't inertial, which is why they 'can' go the speed of light in the first place, but they can't go any slower, either. Rather than c being slower at the instance of the big bang, I would guess that if it changed at all, it would be higher, maybe even infinite, but that is not anything I could hope to provide evidence or even a sound theory for

At higher energy levels the photon frequencies increase but the invariance still applies. Massless particles have no invariant/rest frame so its wavelength strictly depends on the momentum components [latex]e=pc^2[/latex] of the energy/momentum equation [latex]E^2=(pc^2)+(m_0c^2)^2[/latex]. As you mentioned the photon frame is invalid as an inertial frame. This is seen by the null separation distance [latex] ds^2=0 [/latex].

 Markus mentioned already mentioned the fine structure  constants would vary and we have looked into this possibility but have never found any evidence to support a varying c at any time in the past. A varying c over universe time would cause several detectable effects. The temperature of the CMB would also be affected and this can be compared by the BAO acoustic oscillations looking at the rate of infalling/expanding  matter and comparing how the temperature measurements vary. If c had a different value then the ratio of change would not follow the ideal gas laws we have today. In particular the Bose-Einstein formulas would not work properly as the Boltzmann constant would also change.

 The Boltzmann constant provides a correlation between the average kinetic energy of a multiparticle system under ideal gas law treatments to the temperature measurements.

 

Edited June 2, 2018 by Mordred

[swansont]

7 hours ago, AbstractDreamer said:

 Is this the kind of forum where everyone has to get familiar with a subject before asking a question or face being scorned?  Does my complaint carry less weight because I'm a novice?

Asking questions and making assertions are different situations. When you assert that something about mainstream physics is wrong, then yes, it is assumed that you know something of mainstream physics, and you aren't going to be treated with kid gloves when it turns out that you aren't.

7 hours ago, AbstractDreamer said:

 

While the people answering me have spent more time on the subject, they seem more intent to focus their attention on telling me how wrong I am on some irrelevant point, or how its not science, or how i need to come up with a theory, or that I cant accept some answers, or missing my point, not reading my posts, asking me define something I already defined, jumping to an absurd conclusion about me wanting to test every electron in the universe, accusing me of random ideas, resorting to ridicule using analogies of flying unicorns; instead of actually answering any of my questions.

And you seem very focused on these responses rather that the reasons behind them, and the science that has been offered up to you.

We don't know what you don't know. So when someone tells you that science doesn't prove things, it really doesn't help for you to get hot under the collar because you know that already. And if they tell you that you have missed the point, then maybe you should consider that you have missed the point.

As for testing every electron, you did in fact complain that SR had not been tested at all points and all times.

7 hours ago, AbstractDreamer said:

 

Having read a little on fine-structured constant and spectral emission lines of hydrogen, I now understand it something to do with the how the energy levels of an elementary particle such as an electron may be excited and jump to a level above ground state due to spin orbit interactions between the electrons magnetic dipole and the magnetic field created by its orbit around a positively charged nucleus; and in doing so release mission spectra lines that are very close but separate.

α=e(2)/ℏc4πϵ0=μ0ce22h

 

It's more than that, even. It reflects the strength of the electromagnetic interaction. So if it changes, all photon interactions change energy. In certain interactions the energy scales with Z, so you would expect a certain pattern to a shift in frequencies from different atoms.

If c changes, all interactions change energy as well, because E=mc^2. This will be more apparent in nuclear interaction. Fusion would occur differently, as would radioactive decay. And - the kicker here — since the energy depends on c^2, this will not behave the same as an effect that depends linearly on c.

 

7 hours ago, AbstractDreamer said:

It would be far more sensible to change the value of the reduced Planck's constant seeing as it is related to the porportionality between  a quantum particle's energy and frequency, or momentum and wavelength.   On a new-magical note, if ℏ is also a function of time or space, or time is a function space, wouldn't c necessarily be variable?
 

That changes photon energy as well as other things. You have to account for them all. Hence my comment about having other changes that exactly cancel.

 

7 hours ago, AbstractDreamer said:

Doesn't everything matter if you're trying to accurately model quantum physics?  Or is it safe to assume nothing happens whatsoever while in transit over billions of years light years for billions of years, through numerous quantum fields that mutually interact , other than redshift from expansion and lensing from gravity?

Yes. And you aren't the one modeling physics. You're taking a stab in the dark, without knowing how anything differs if the constants change.

We "assume" that nothing happens because there is no evidence that it does, and there is no valid theory that would allow for it. IOW, that assumption is repeatedly tested.

7 hours ago, AbstractDreamer said:

What kind of consequences? What kind of implications?  How would the universe look if c was constant, but a different value?  How would the universe behave if c was not constant?

Those are good questions but with very complicated answers. Or possibly no answers at all; one implication is that the laws of physics would be changing, and if you don't specify how they would be changing, you can't hope to have an answer. 

7 hours ago, AbstractDreamer said:

Is it not possible for there to be a reasonably simple solution to balancing all the equations to consider a variable c that varies only in special situations, yet only alter the consequence in those special circumstances?

There is no reason to think that it would in free space, since something has to be different about a region in time or space where the values are different. Light speed does differ in non-inertial frames or in a medium. We know about these effects.

 

[studiot]

I too welcome Markus back and his first post shows he was thinking somewhat along the same lines as myself.

However the world has moved on since Einstein and much of Markus’ material is post Einstein and I have promised the basic breakthrough in thinking which was due to the great man himself.

So to start with a quote from what he actually said (the 1905 SR paper)

Quote

 It is known that Maxwell’s electrodynamics… when applied to moving bodies leads to asymmetries which do not appear to be inherent in the phenomena……

 

Examples of this sort, together with unsuccessful attempts to discover any motion of the earth relatively to the “light medium” suggest that the phenomena of electrodynamics as well as mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereinafter be called the “Principle of Relativity”) to the status of a postulate and also introduce another postulate, which is only apparently irreconcilable with the former, namely that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies.  ………..

 

I will try to explain just how well thought out and put together these few words are and that they really do justify the claim in the final line that these two postulates are in effect all you need to know.

1)

First note that Einstein acknowledges preceding work and that a weaker Principle of Relativity (for mechanical systems) was already known.

His first Postulate extends this to non-mechanical ones.

2)

He recognises that further postulates must perforce be compatible with the first.
Since there are only two postulates this means that they must be compatible with each other.

3)

He then posits his second postulate which introduces the speed of light as c but note that he does not say this is constant, just definite. Note also that he does not say explicitly that c is the same for all observers.

 

These are the three key steps that must be taken as a whole to understanding SR.

 

The rest of the paper is devoted to the consequences of these three steps taken together. It is here he develops the ad hoc Lorenz equations, the equality of the c for all observers and other important things, which includes the constancy of c as a necessity built into the mathematical model developed.

The constancy of c is the subject of this thread and swansont has already observed that the mathematics of Physics would be (very) different if this were not so.

I propose to examine more closely how this arises in my next post.

 

 

 

Edited June 2, 2018 by studiot

[beecee]

9 hours ago, AbstractDreamer said:

Anywhere within a BH is not empty free space and therefore not a valid  spatial frame of reference to test invariance of c, irrespective of whether or not the theory is valid.  Only at the EH and outside can there be empty space between which light can pass at invariant c for the 2nd postulate to hold and for it still to be a valid frame of reference, and also a point where the theory fails.

GR tells us that once the Schwarzchild radius is reached, that further collapse is compulsory. Therefor ignoring other infalling matter/energy, the interior of any BH should be nothing but critically curved spacetime, at least up to the quantum/Planck level where GR fails us.

Quote

Your first post was about time dilation as evidence that c must be invariant.   Now you're saying of course its an approximation. Had you actually read my #1 post and listened, we could have saved 3 pages of missing the point.   Given that there a limits at where GR/SR fails, is it not scientifically valid to question the postulates as the reason why it fails?

I have never hinted or said that GR is not an approximation. As I see others have told you, all theories are approximations...even a future validated QGT would probably be an approximation. That does not mean that it is wrong. And more importantly, it does not suggest that "c" is not invariant.

 

Quote

Must any future validated QGT also specify that c must be invariant?

I'm not really knowledgable enough to answer that question, other then to say that we have no reason to believe that "c" can be anything other then "c" and plenty of reasons to accept that "c" has always been "c". 

7 hours ago, AbstractDreamer said:

Based on an understanding the laws of physics don't apply beyond the EH.

I don't believe that is true. As I said just above, GR tells us that when the Schwarzchild radius is reached that further collapse is compulsory. It is then reasonably logical for us to then assume that the interior of a BH is just critically curved spacetime. [ignoring infalling matter/energy] At least up to the quantum/Planck region where we know GR fails us. 

Edited June 2, 2018 by beecee

[Markus Hanke]

9 hours ago, beecee said:

I'm not really knowledgable enough to answer that question, other then to say that we have no reason to believe that "c" can be anything other then "c" and plenty of reasons to accept that "c" has always been "c". 

I think, based on several bits and pieces that we already know, it is reasonable to assume that in a region where QG effects are non-negligible, spacetime itself will increasingly cease to be smooth and regular. This means that the notion of “separation between events” will become at best fuzzy, at worst meaningless in such regions. That will also mean that the very notion of “speed” and its invariance will loose its meaning. In short - the very concept of Lorentz invariance will likely not make sense in a QG regime, and neither will things such as speed, duration and distance. 

Note that in the absence of a fully worked out QGT, this is speculation. 

 

19 hours ago, AbstractDreamer said:

I looked for anything that might explain where the limits of SR might be and found

This is indeed a very reasonable and important question to ask! The short answer is that, for a region of spacetime to be considered special relativistic, its geometry has to be Minkowskian - in practical terms this means that any two neighbouring events will always be related to one another in the same way, regardless of where and when you are within the region in question.  This means that a number of restrictions apply:

1. There is no curvature (i.e. the Riemann tensor vanishes everywhere in that region)
2. The temporal and spatial parts of the metric have opposite sign
3. The spacetime is everywhere smooth, continuous, and differentiable

Among some other, more technical ones. Essentially, (1) means that gravitation can be neglected in the scenario in question; (2) means we are dealing with a type of hyperbolic geometry, so inertial frames are related by hyperbolic rotations in spacetime; (3) means that spacetime can be described as a manifold, so it’s a continuum of events, and all world lines are continuous and differentiable everywhere.

Note that there is no mention here of acceleration, because SR is more general than just inertial frames; it can also handle accelerated observers just fine, so long as the above three criteria apply. For a frame to be inertial is a more restrictive condition, because we also need to add the requirement that proper acceleration vanishes everywhere, meaning we consider only geodesics in spacetime, as opposed to just any arbitrary world line.

GR then generalises this by abandoning (1), allowing non-vanishing curvature, and hence non-trivial relationships between events. The limits of GR then would be given by (3) - if we have a situation where energies are so high that spacetime itself becomes subject to quantum fluctuations, we can no longer describe it as a smooth and differentiable manifold, making even simple notions such as distance etc problematic. This is where QG has to step in, then.

[beecee]

2 hours ago, Markus Hanke said:

I think, based on several bits and pieces that we already know, it is reasonable to assume that in a region where QG effects are non-negligible, spacetime itself will increasingly cease to be smooth and regular. This means that the notion of “separation between events” will become at best fuzzy, at worst meaningless in such regions. That will also mean that the very notion of “speed” and its invariance will loose its meaning. In short - the very concept of Lorentz invariance will likely not make sense in a QG regime, and neither will things such as speed, duration and distance. 

Note that in the absence of a fully worked out QGT, this is speculation. 

Thanks for clearing that up Marcus, including also the reply to AbstractDreamer.

[studiot]

3 hours ago, Markus Hanke said:

its geometry has to be Minkowskian - in practical terms this means that any two neighbouring events will always be related to one another in the same way, regardless of where and when you are within the region in question. 

This is the killer step in the theoretical Physics answer to the original question, to come in the next post in my development.

The obvious Physics version of the question is "Why do we want it to be Minkowskian ?"
That was Einstein's breakthrough, which preceded Minkowski. Einstein was a theoretical physicist. Minkowski was a mathematician.

I realise that the OP is wandering between SR, GR, cosmology and even quantum developments, but the basics should come first and the chain of physical reasoning that leads to modern relativity should lead the mathematics, not the other way round.

Edited June 3, 2018 by studiot

[Mordred]

 One of the tricks to realize is that the invariance of c has far reaching implications beyond the speed of light. It also relates to the maximal rate of information exchange between any two states. The speed of light is simply the most commonly known consequence of the maximal information exchange rate. This ties incredibly well to causality laws, and how one measures time in causality related interactions.

As Hanke mentioned Minkowskii, under the Lorentz transforms constant velocity is used to match the laws of inertia. Acceleration itself is handled through rapidity which is a type of symmetry rotation.

 Studiot you mentioned the problem of bouncing between theories, this is a particular difficult endeavour if one doesn't pay close attention to the mathematical treatments in each theory. Far too often confusions arise simply from switching between metric coordinate systems ie classical to quantum to commoving under FRW. Its great to study every theory but one has to pay close attention that any theory is specific to the system state it is describing and how it describes those states.

@Hanke its particularly nice having you back for me as your one of the few posters on this forum that can check my replies and answers (particularly when I'm describing gauge groups) so its nice to get that safety net back lol. I can and often do make mistakes so its good to have another set of eyes watching out for them

Edited June 3, 2018 by Mordred

[Markus Hanke]

13 hours ago, Mordred said:

@Hanke its particularly nice having you back for me as your one of the few posters on this forum that can check my replies and answers (particularly when I'm describing gauge groups) so its nice to get that safety net back lol. I can and often do make mistakes so its good to have another set of eyes watching out for them

Well thank you, I shall do my best

It must be said though that I am only an amateur/hobbyist, and that my main area of “expertise” (if you can call it that) is really GR and gravitational physics. I know about gauge theories etc, but not on an in-depth level.

[StringJunky]

38 minutes ago, Markus Hanke said:

Well thank you, I shall do my best

It must be said though that I am only an amateur/hobbyist, and that my main area of “expertise” (if you can call it that) is really GR and gravitational physics. I know about gauge theories etc, but not on an in-depth level.

You know more than many of us and your input is welcomed by me and I'm sure others. You have a good way of explaining quite difficult ideas.

[AbstractDreamer]

 

On 6/3/2018 at 7:49 AM, Markus Hanke said:

for a region of spacetime to be considered special relativistic, its geometry has to be Minkowskian - in practical terms this means that any two neighbouring events will always be related to one another in the same way, regardless of where and when you are within the region in question.  This means that a number of restrictions apply:

1. There is no curvature (i.e. the Riemann tensor vanishes everywhere in that region)
2. The temporal and spatial parts of the metric have opposite sign
3. The spacetime is everywhere smooth, continuous, and differentiable

Among some other, more technical ones. Essentially, (1) means that gravitation can be neglected in the scenario in question; (2) means we are dealing with a type of hyperbolic geometry, so inertial frames are related by hyperbolic rotations in spacetime; (3) means that spacetime can be described as a manifold, so it’s a continuum of events, and all world lines are continuous and differentiable everywhere.

Note that there is no mention here of acceleration, because SR is more general than just inertial frames; it can also handle accelerated observers just fine, so long as the above three criteria apply. For a frame to be inertial is a more restrictive condition, because we also need to add the requirement that proper acceleration vanishes everywhere, meaning we consider only geodesics in spacetime, as opposed to just any arbitrary world line.

GR then generalises this by abandoning (1), allowing non-vanishing curvature, and hence non-trivial relationships between events. The limits of GR then would be given by (3) - if we have a situation where energies are so high that spacetime itself becomes subject to quantum fluctuations, we can no longer describe it as a smooth and differentiable manifold, making even simple notions such as distance etc problematic. This is where QG has to step in, then.

Given observers in an Minkowskian volume of empty space, are there any limits to how large this volume is or how much time this volume exists for before one of the three restrictions that define such a space is violated?

What if this volume of space was so large such that observers on opposite sides of this volume are moving away from each other at superluminal speeds due to expansion?  What if this volume of space is not so large, but over eons grew via expansion to such a size that observers on opposite sides of this volume are moving away from each other at superluminal speeds?

How does volume or time limit the range of Minkowskian geometry around such observers?

[Strange]

1 hour ago, AbstractDreamer said:

Given observers in an Minkowskian volume of empty space, are there any limits to how large this volume is or how much time this volume exists for before one of the three restrictions that define such a space is violated?

No. In fact, as an idealisation, it is infinite in all four dimensions.

1 hour ago, AbstractDreamer said:

What if this volume of space was so large such that observers on opposite sides of this volume are moving away from each other at superluminal speeds due to expansion?

Then it wouldn't be Minkowski space. Once you introduce expansion you are into the territory of GR and pseudo-Riemannian manifolds.

And within the observable universe we see objects moving away at more than the speed of light so there is no essential limit. The universe could well be infinite.

 

[MigL]

Markus seems to have taken a sabbatical, so maybe Mordred can explain some thing to me...

Markus states something which puzzles me...

"Note that there is no mention here of acceleration, because SR is more general than just inertial frames; it can also handle accelerated observers just fine, so long as the above three criteria apply."

because I always thought ( assumed ? ) that SR wasn't applicable to accelerated frames. So, if I've been wrong all this time, and SR is applicable, then, given the strong equivalence principle, should SR then also be able to handle gravitational, or curved space-time ?
This would make the first restriction unneeded.

Surely GR is more than SR with the strong equivalence tacked on ?

[Eise]

3 hours ago, MigL said:

I always thought ( assumed ? ) that SR wasn't applicable to accelerated frames

Why wouldn't it be? It just becomes more complicated, because you have to integrate over the changing velocity.

3 hours ago, MigL said:

So, if I've been wrong all this time, and SR is applicable, then, given the strong equivalence principle, should SR then also be able to handle gravitational, or curved space-time ?

Yes and no. As far as I understood, SR can even handle homogeneous gravitational fields, because the gravitation is the same everywhere. Just integrate again... However, in nature there are no real homogeneous gravitational fields, they have a source. So the tidal effects become a problem. And that is where point 1 of Markus chimes in.

3 hours ago, MigL said:

Surely GR is more than SR with the strong equivalence tacked on ?

Maybe not. However, to describe a real gravitational field (i.e. that has a source), in such a way that the gravitation force 'disappears' and is replaced by geometry of spacetime, is obviously not such an easy task...

[Mordred]

This can get a bit tricky to explain. One of the key distinctions of SR to GR is the rest frame. The rest frame is a Euclidean frame of reference in which within the bounds of that frame of reference the Galilean transformations apply. In essence our Newton laws of inertia as well as Pythagoras theory. This is point 1 Markus makes in the above. One must be able to define within a frame of reference of the event or observer that is approximately Euclid. 

Point two is the symmetry relations between the observer and emitter. A change in observer or reversal of vector direction amounts to a change in sign between the spatial and temporal coordinates. This is easy under constant velocity however tricky to maintain under acceleration. However it can be done by performing a hyperbolic rotation or transformation instead of the linear transform of the Lorentz group. In essence it amounts to a rotation of the Lorentz group. One can find examples of how to apply SR to a constant acceleration of which I will provide here.

http://www.physik.uni-leipzig.de/~schiller/ed10/Uniform relativistic acceleration.pdf

It doesn't get into the groups themselves however gives the transforms which will make it easier to understand rather than trying to explain how its shown in gauge groups.

Point three is well described in Markus post. 

Now where GR handles better than SR is in terms of curvature. It has no requirement of a rest frame that approximates a Euclidean geometry. So in a given volume of strong curvature it is a better tool. However one can restrict the volume of the rest frame under SR to a tight enough region that can approximate the Euclid frame. So SR can be used in much the same way as GR to the same results, however when dealing with curvature it is better to use GR for the reasons above for large regions in particular.

One way to see this is to look at the following.

[latex] g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex] this is a GR class of solution called the weak field limit or Newton limit. Under this SR will work fine. It will handle the vast majority of astronomical events such as freefall towards planets and stars etc. As you can see it applies the Minkowskii tensor that is used in SR.

Now a situation such as the strong field 

[latex] g_{\mu\nu}=g_{\mu\nu}+h_{\mu\nu}[/latex] notice we have no Minkowskii tensor this is a situation where it is not reasonable to approximate a Euclid rest frame due to extreme curvature such as outside the event horizon of a BH as one example.

On an aside not this is one of the reasons why QFT and String theory uses SR primarily in terms of the Feymann diagrams one has a rest mass for the particle and its locality is easily handled via a Euclid frame. However when dealing with a multi-particle system it oft becomes more convenient to step into the GR methodologies.

In essence GR handles variations in spacetime geometries better than SR

 

Edited January 23, 2019 by Mordred

[Eise]

1 hour ago, Mordred said:

http://www.physik.uni-leipzig.de/~schiller/ed10/Uniform relativistic acceleration.pdf

Right. Last sentence on page 5:

Quote

Note the very important fact that by the equivalence principle this line element gives also the metric for a uniform gravitational field, i.e.  we found a very basic metric without considering the Einstein field equations or even thinking about GRT!

 

[Mordred]

Yes you can find an SR solution in all the examples of that article, however that is under the restrictions mentioned by Markus. If you can keep each reference frame approximately Euclid...

ie at rest example is 

Quote

Note that the proper acceleration is indeed constant since in the moving frame, the observer is at rest

under the Schwartzchild example the key clue is in the term Proper acceleration this correlates to proper as opposed to coordinate time. Proper time is a clock that follows the world-line.

See here on proper time and note the statement

https://en.wikipedia.org/wiki/Proper_time

Quote

This expression generalizes definition (2) and can be taken as the definition. Then using invariance of the interval, equation (4) follows from it in the same way (3) follows from (2), except that here arbitrary coordinate changes are allowed.

In the SR example for Schwartzchild on this link they also mention

Quote

since in the instantaneous rest frame, the particle is at rest

you can see the requirement of maintaining a rest frame is preserved. However that is a different situation than say comparing two coordinate times to one another. https://en.wikipedia.org/wiki/Coordinate_time

 

Edited January 23, 2019 by Mordred

[studiot]

A background note on this.

Mordred (No offence and no suprise) is fond of quoting the Physics definitions he uses every day for some mathematical terms.

Metric is one.

Mathematically, Euclidian space has more than one available metric and results depend upon which one you choose.

So Pythagoras is not the only one.

[MigL]

Thanks guys.
Much appreciated and enlightening.
My apologies for veering off the track of this thread.

[Eise]

<NitpickerMode>

It is Schwartzschild, not Schwartzchild . So not (German) a 'black child', but a 'black shield'

</NitpickerMode>

So funny, I found exactly this error in a book by Jim Baggot The Quantum Story: A history in 40 moments just yesterday. He was consistent in this too. 

[studiot]

1 hour ago, Eise said:

<NitpickerMode>

It is Schwartzschild, not Schwartzchild . So not (German) a 'black child', but a 'black shield'

</NitpickerMode>

So funny, I found exactly this error in a book by Jim Baggot The Quantum Story: A history in 40 moments just yesterday. He was consistent in this too. 

Thanks Eise. +1

A valuable addition to the thread as usual.

Edited January 23, 2019 by studiot

[MigL]

Today I learned...

The meaning of 'child', 'schild' and 'shwartz' in German.

[Mordred]

7 hours ago, MigL said:

Thanks guys.
Much appreciated and enlightening.
My apologies for veering off the track of this thread.

No apology needed it was an excellent question and thanks Eise for the Nitpick lol

8 hours ago, studiot said:

A background note on this.

Mordred (No offence and no suprise) is fond of quoting the Physics definitions he uses every day for some mathematical terms.

 

They are invaluable in understanding the higher physics, helps keep one from travelling endless garden paths

[StringJunky]

3 minutes ago, Mordred said:

No apology needed it was an excellent question and thanks Eise for the Nitpick lol

They are invaluable in understanding the higher physics, helps keep one from travelling endless garden paths

Keeps everyone on the same page.

[studiot]

I just love that quote of Schwartzschild 's

Quote

It's always pleasant to have exact solutions in simple form at your disposal.

Simple exact solutions.

What could be better?