[Joe L. Ogan (OP)]

Is the speed of light constant?  Did Einstein assume that the speed of light is constant when he devised the formula E=MC2?  If the speed of light is not constant does this cast doubt on the formula E=MC2?  Is it possible that Einstein was just looking for the largest number he could find to justify his opinion that there is a lot of energy in any mass?  Thanks for comments.  Joe L. Ogan

[syhprum]

The speed of light in a vacuum is influenced by the strength of the gravitational field where the measurement is made,the fields encountered in the region of the Solar system have only a tiny effect but close to Neutron stars and black holes the effect is considerable.

[Joe L. Ogan (OP)]

The speed of light Is influenced by the strength of the gravitational field where the measurement is made,the fields encountered in the region of the Solar system have only a tiny effect but close to Neutron stars and black holes the effect is considerable.

I believe that I read an article awhile back about a woman stopping light in cold sodium and then restarting it again with a shot of laser.  If this is true, light is certainly not a constant as Einstein stated.  That leads me to question the validity of E=MC2.  Thanks for your comments.  Joe L. Ogan

[JP]

The speed of light is constant in a vacuum.

The vacuum part is important because when light interacts with matter, it can slow down due to that interaction.  That's what happens in the sodium gas you're referencing. 
 

[Farsight]

Is the speed of light constant?

The modern interpretation of general relativity is that it is constant. See this article for more. Note the General Relativity section where it refers to Einstein in 1916 and says this:

"Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so.  This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity." 

Personally I prefer Einstein's original version wherein the speed of light varies with gravitational potential. 

Did Einstein assume that the speed of light is constant when he devised the formula E=mc²? If the speed of light is not constant does this cast doubt on the formula E=mc²? Is it possible that Einstein was just looking for the largest number he could find to justify his opinion that there is a lot of energy in any mass?

Yes. He wrote Does the Inertia of a Body Depend Upon its Energy Content? in 1905, when he had adopted the postulate of the constancy of the speed of light. But it doesn't cast doubt on E=mc². It's just that things get a little more complicated when you start taking gravity into account.

[yor_on]

Well MD

What can I say? Seen any two-dimensional 'systems' recently?
Passing you by?

Kindly refer me to them if so. That you see the vocabulary used by scientists doesn't mean that they have proofed the existence of such situated inside 'SpaceTime'. It's only about how the properties of some 'system', like a lattice one atom thick may act, that makes them define it as 'constricted to two dimensions.'

If we have a two-dimensional origin then it have to be quite 'metaphysical', and a philosophical reference to a kind of system that I easily can proof you never been experimentally verified inside SpaceTime.

Or?
Can you prove it otherwise?

[yor_on]

Looked up your reference Farsight and saw this "This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c."

How, relative what?

As I understands it the speed of light is invariant, meaning that from any frame it will be measured as having the exact same speed relative that frame of reference in a vacuum? To say that a accelerating system would present a different answer when measuring light-speed seems to imply that motion then exists as some sort of 'instants'?

What I would ecpect from measuring inside an accelerating frame is that to a far observer 'at rest versus both origins (Earth)' the light would increase its frequency, nothing more? And that when measuring it inside that accelerating frame the light still would come out as being at 'c', as tested by letting it meet a sink, either inside that frame, or reflected from something 'being still' relative the accelerated frame, like a 'unmoving' mirror hanging in space relative our rocket.

Am I wrong there?
Why?

[yor_on]

It might fall back on how you define 'SpaceTime'?

If you look at SpaceTime as I do, as a block of jello, distance and time redefined by each frame then I think I'm correct? If you instead define it as having some sort of 'objective' properties, then depending on your choice of 'objective frame' accelerating or not accelerating you will get a difference, although then, ignoring the effects from acceleration? Awh, this one is confusing.

It all seem to come back to what 'frames of reference' means in form of time intervals/motion/acceleration. (and mass of course)

Let me put it this way: if I'm accelerating, and then measure a photon I send a hundred meters (as defined inside that rocket) the rocket being at 99.999% of light speed in that moment, relative some predefined 'inertial frame/common origin' like Earth.

What will I measure?
Will that light be at 'c' relative me?

Compare that to doing the exact same, but after stopping the 'hyper-engine' now coasting.
Being in a free fall? Will the results I see for the lights speed differ?

Then take the third case.

Same rocket at the same speed,doing the same measurement. Only thing differing is that its acceleration have been 'linear', being at a constant one G all the way up to the same velocity, as observed inside that rocket, and then make the measurement.

Will the readings differ for the speed of light?
How? and why?
==

I am using the word 'free fall' for defining a uniform motion here, aka coasting..
Strictly looked on you might want to define a 'free fall' as following a predefined geodesic due to the way SpaceTime 'wrinkles' under mass and motion. But on the other hand, when 'moving uniformly' no matter my former acceleration, doesn't I follow the geodesics too?

That one is tricky?

If I assume that I collided with something the 'potential energy' of my rocket would have to differ depending on my velocity, right? And it doesn't really matter from where I defined my velocity, it still would vary with me choosing different speeds. But on the other hand, there is still no way for me to differ the velocity inside a 'black box' from any other velocity, all the way down to free falling on earth, (ignoring spinning effects, tidal forces).

Maybe we should turn that one on its head, and instead ask if I can isolate/define the potential energy to any singular object? I say I can't, it's always a relation. Even though that relation will differ with velocity, it will still only be a 'potential', and inside that black box I have no way of defining it. And the situation is the same with the idea of 'energy' in itself. I do have an 'higher energy' , but only when the relation come true. So the 'energy' observed is an expression of two potentials coincidentally becoming one.

So, where did it 'exist'?

[Farsight]

Looked up your reference Farsight and saw this "This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c." How, relative what?

Relative to itself. You use two light clocks at different altitudes, and one runs faster than the other because the light moves faster. Because clocks clock up motion. At  either location you measure the local speed of light to be the same old 299,792,459 m/s. However the seconds aren't the same so the two 299,792,459 m/s aren't the same either.

As I understands it the speed of light is invariant, meaning that from any frame it will be measured as having the exact same speed relative that frame of reference in a vacuum? To say that a accelerating system would present a different answer when measuring light-speed seems to imply that motion then exists as some sort of 'instants'?

That's the locally-measured speed of light. I'm not sure what you mean about motion and instants, but check out acceleration as per the the rotating earth, where the GPS system makes allowance for the Sagnac effect.   

What I would ecpect from measuring inside an accelerating frame is that to a far observer 'at rest versus both origins (Earth)' the light would increase its frequency, nothing more? And that when measuring it inside that accelerating frame the light still would come out as being at 'c', as tested by letting it meet a sink, either inside that frame, or reflected from something 'being still' relative the accelerated frame, like a 'unmoving' mirror hanging in space relative our rocket.

Yes. It would be like being on the surface of the earth, the principle of equivalence applies. But the light doesn't actually increase its frequency, it's you and your measuring devices changing, not the light.
 

Am I wrong there?

No.

[lightarrow]

Since the context here is GR, which definition of velocity, or of speed, are you talking?
Furthermore, are we talking of the speed in an inertial frame only or even in an accelerated frame?

[yor_on]

Did you mean me Lightarrow?

I thought I gave the definitions?
The speed defined is relative Earth in all cases.

The measurements takes place inside the rocket (frame of reference), relative the person making them.
That same person have his speed checked relative its origin (Earth)

Then you have three scenarios.

accelerating non-linearly (GR)
Coasting, aka uniform motion (SR)
accelerating 'uniformly' at one G. (GR)

As I understands it, this is I expect the light speed to come out the same, relative the measurer?
==

Keep thinking of acceleration as being 'special'
Sorry about that, but to me it is..
==

You can argue that his reference-frame (Earth-rocket) will change with him being accelerating, or not, possibly?
But assuming that there exist a speed, and that there will be a moment when all three scenarios have the exact same speed relative earth, then that's when the measurement is done.
==

You are correct Lightarrow, all three can be seen as GR though.

What I'm thinking there is that when the rocket no longer accelerates and is 'coasting' there will be some object 'somewhere' where you could see it as being still relative. Or you can imagine two rockets instead of one, possibly (This is becoming harder and harder) moving in tandem, with both coasting at the exact same velocity relative each other. But, no matter how we define it, will the measured speed of light differ for the man measuring it? And if you think it would, why?

[yor_on]

Yes Farsight, that's one way of expressing it

"Relative to itself. You use two light clocks at different altitudes, and one runs faster than the other because the light moves faster. Because clocks clock up motion. At  either location you measure the local speed of light to be the same old 299,792,459 m/s. However the seconds aren't the same so the two 299,792,459 m/s aren't the same either. "

Or you can state it like this.

No matter where you measure it, under any circumstance, will that light speed differ relative the guy measuring it. That makes this frame 'invariant' to that guy, no matter where he is. All other frames will differ, depending on speed/velocity and mass, but not the 'intrinsic one' belonging to the guy measuring, if I got it right that is?

So in a way you have an 'invariant frame' in SpaceTime, even though your relations with all other frames differ, if you see how I think of it That is also the frame creating our 'arrow in time' I think. But, even if you look at it that way you will still find it hard to understand how all those different 'frames of reference' in terms of time dilation and contraction can be experienced simultaneously by you seamlessly, never 'coming apart'.

[lightarrow]

Did you mean me Lightarrow?

Not specifically. I'm referring to all the poster in general.

[yor_on]

Ahh..

Cool, you made me think any which way

[yor_on]

Looking at it that way makes for a very 'Aristotelean universe', as you then may define all you see as being uniquely adapted to your 'invariant personal frame'. But at least it's a 'point of stability' in a ever-changing SpaceTime.  But it all falls back to how to define those 'frames of reference' and where their limits are, if there are?
==

In fact I would like to see the universe this way, as I think that is a key to understanding it. But those 'frames of reference' makes it a joke. We define frames macroscopically and they work, and I, I don't understand how they do it? As I as easily can change my perception to a 'smaller' level, and using particles mass and velocities/speeds inside my body find different 'time dilations'. At least I think I can?

How does times arrow do it?

If time dilation exist, and it does, look at our muons f.ex or GPS, then everything must be in a constant 'flux'? We can't measure that small frames of reference for time dilation, but they must still be there, I'm sure of that. So now I start to wonder about what 'super-positions' are? Electrons able to exist at two places simultaneously? Would that include those I 'carry around'? We don't speak of them orbiting, although we expect them to have a restmass, instead we 'find' them by using probability mathematics. So, how 'real' is Heisenberg's uncertainty principle, the one that 'explains' it for us? I think it's very real, and that what it says about our inability to simultaneously measure both a position and momentum must be true. We won't be able to do it, under any circumstances, ever. So, does that theorem touch upon our super-positions too? I don't know, but if we can't define a 'particle' then 'super-positions' seems more probable, if you excuse my expression. So, can we stretch the principle to include 'super-positions' too? (In this case I'm referring the existence of electrons 'existing' at two spatial locations/orbitals simultaneously, not to the QM 'superposition' in where a a particles state still is undefined.)

Can An Electron Be In Two Places At The Same Time   

So, where can we start to define both a position and a momentum to something?
Atoms?
Or?

[Farsight]

Yes Farsight, that's one way of expressing it... Or you can state it like this.

No matter where you measure it, under any circumstance, will that light speed differ relative the guy measuring it. That makes this frame 'invariant' to that guy, no matter where he is. All other frames will differ, depending on speed/velocity and mass, but not the 'intrinsic one' belonging to the guy measuring, if I got it right that is?

I'm not sure whether that's the right way to use invariant and intrinsic, but yes, I know what you mean, and yes, the guy measuring the local speed of light will always measure it to be the same.

So in a way you have an 'invariant frame' in SpaceTime, even though your relations with all other frames differ, if you see how I think of it That is also the frame creating our 'arrow in time' I think. But, even if you look at it that way you will still find it hard to understand how all those different 'frames of reference' in terms of time dilation and contraction can be experienced simultaneously by you seamlessly, never 'coming apart'.

The seamless thing is because a frame of reference don't have any real objective existence. It's just an artefact of your measurement, which is affected by your motion and the gravitational field you're in.   

[yor_on]

Nope, not to me it is

That frame of reference is the only one I can be sure of, all other frames will differ.
Imagine that you're in a rocket, you have no windows and nothing tells you what velocity it has.
Then all frames of reference are unknown to you, except your own 'invariant' one. The others possible 'time dilations' can only become known from some common 'frame of reference', defined beforehand by your 'history' of whatever kind.

In that motto, looking at SpaceTime as a constant 'now' time-dilations disappear as you always need a 'history' to prove their existence. And what you work with making a experiment is the definition of time from your 'frame of reference'. Only theoretically can you define it from some other frame. Which doesn't imply that they're not as 'real' as your own, although taken to its limit you could? But that's philosophy of the more esoteric kind, metaphysics? Well, I need to think about it it's weird..

[Farsight]

It isn't weird yor-on, it's simpler than you think. Set gravity aside for a moment, and take a walk out into the back garden and look up at the clear night sky. You can see the moon, and stars, but you can't see a reference frame. You might adopt your back door as the centre of a coordinate system, and your measurements with a tape-measure or a clock are real enough. But your coordinate system isn't, and nor is your reference frame. Climb into a spaceship and get into a high orbit round the earth, and you might adopt the North Pole as the centre of your coordinate system and thus switch to a different reference frame. Leave the earth way behind and you might adopt the Sun as the centre of your coordinate system, and switch again. Go really fast and leave it all behind, and maybe you adopt the centre of the galaxy as the centre of your coordinate system. Now you've switched to a different reference frame again, so different that you start noticing length contraction, because the stars look flattened. All the while you might think you're "in" a reference frame, but you can't actually observe this thing. It's just an artefact of measurement, a convenience and a convention for the real things you can observe and measure. It as as much real existence as lines of latitude and longitude, or the grid squares on a map or a star chart.   

 

[yor_on]

You're missing my point. If time is invariant from my 'frame of reference' then it is.
That time then defines all other relations I observe, even when looking up at the starry sky.
Consider yourself the definition of 'times arrow' Farsight, then enjoy 

The radiation you receive looking up will adapt itself to your 'frame' uniquely. The reason it does so is the way SpaceTime wrinkles and bends. That idea of two mirrors and a light-corn 'bouncing' inbetween describes time dilation as a effect of the distance created by the mirror-pairs motion, forcing the light-corn to take a longer path between the two mirrors. I'm not entirely sure if that's the way to see it but it makes a interesting thought in that you then could use it to describe all time dilation as an effect of space's 'geometries'. So what do we make of gravitation when looked at it that way? Well, mass 'bends' space right? And most of an atom is space too Not that it matter, it's all about geometries now, and particles take place in space. So what is matter? Assume that all is my beloved surface

Then particles must be a lot of that 'surface' wrinkled together. And it somehow makes sense, in a weird way, but he*, whenever have the universe ever been anything else than weird? And what does it make of 'times arrow'? Something that travels at a 'constant speed' in more ways than Einsteins description. To make sense of that idea I will have to assume that there actually is something resembling a 'universal distance' existing on its own, represented by that unwrapped 'surface'. When I wrap it up/in I get SpaceTime.
==

Eh, I'm not saying that it have to be this way though
For example we have motion, as discussed above, how would that fit?
Uniform motion might, as all 'speeds' are the same in a relativistic sense, but acceleration?
Still, I like to play with it
==

I better point out that as we define distance as something 'traveled/propagated' in time then distance as used here would be time too, and that's one reason why I differ the idea of 'time' and 'times arrow'. Hey, it's just an idea )
==

Also, it doesn't explain the concept of consciousness and free will, but maybe(?) 'super positions' as in an undefined state  and the idea of entanglements might have something to do with that? As if we have this surface, that in reality is 'nowhere' where 'mass' offer us our arrow and 'distances'.

I really need to do something else huh

[yor_on]

So what is this 'surface' of mine, if it now would exist?

Well to get to that we might look at the gluon/quark interface, in Quantum Electro Dynamics (QED), those seem to sort of replace, or at least complement, our ideas of 'virtual photons'. First of all we might look at the State of Matter. In it you can find references to the states we discuss here. To me it's also a question of 'sizes', like a fractal behavior of space and I also expect that what we have macroscopically is an expression of what exist at those most 'fundamental sizes'. There have to be a 'likeness', at least as I suspect. The LHC found some surprising results earlier this year when they created proton-proton collisions.

"In the new experiment, the CMS team took data on the charged particles produced in hundreds of thousands of collisions. The team observed the angles the particles’ paths took with respect to each other, and calculated something called a “correlation function” to determine how intimately the particles are linked after they separate. The plot of the data ends up looking like a topographical map of a mountain surrounded by lowlands and a long ridge behind it. In the most basic case the data looked exactly like the physicists expected it to. But in cases where at least 110 charged particles were produced, the team saw a funny ridge-like structure extending away from the mountain peak.

That ridge essentially means that particles in some pairs are flying away from each other at close to the speed of light along one axis, but are oriented along the same angle in the other axis. It’s as if two particles somehow talked to each other when they were produced, the physicists said. This phenomenon has never been seen before in proton-proton collisions, though it resembles something seen at RHIC (the Relativistic Heavy Ion Collider) at Brookhaven National Laboratory in New York. That effect was interpreted to be from the creation of hot dense matter shortly after the collisions." Journal of High Energy Physics.

So, what do we see there?

Well,I have problems with the idea of 'string theory' but that comes from the proposed one-dimensionality it seem to build on. In my imaginary 'surface' I like to think that what we call 3D already are there being present, as 'properties'. You need to understand that I look at it as properties, and as such just as 'real' as the photons 'masslessness' should be That is, very real but in form of 'ethereal structures'. So i would like to see the definitions of what makes a 3D + time in reality only as 'two' definitions, one containing the three properties we call length, width and height. The other containing two, 'time' and 'times arrow' with the arrow being the way that surface treat us.

It solves two problems for me, the question about what the 'interfaces' should be seen as between strings and forces, also it allow time to be a whole 'surface' where what we call 'times arrow' becoming the expression time gets as it gets 'wrinkled'. And I like that

First we should look at an experiment done in Finland. It's from 1996 and is very interesting. Take a look here Liquid Universe and after reading that read this from 2004 Liquid Universe Then read this The String Net Liquid Theory

As for my expected 'fractality'
That's just the 'simplest' way nature seems to treat 'growth' and i see no reason why it shouldn't do the same here.