# I Permittivity/permeability variation in time

#### calinvass

Is it possible to tell with certainty whether μ and ε for vacuum change over time within a very long period of time?
I know that we are measuring a space expansion, and we can tell that not objects are moving away from each other, but the space itself expands.
However, this seems to be similar to spacetime curvature caused by gravity, and this doesn't change the properties of vacuum.

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#### Nugatory

Mentor
Is it possible to tell with certainty whether μ and ε for vacuum change over time within a very long period of time?
I'm assuming from your other threads that you are interested in possible changes in these quantities because that would imply a change in the speed of light in vacuum? If so, the short answer is that is possible to tell, and they do not change over time.

Any discussion beyond this would have to start with a clear explanation of how we could, even in principle, measure/observe such a change. That is much much harder than it looks at first glance: speed is distance over time, right? How do you define and measure either of these quantities? In a way that is experimentally useful?

#### Dale

Mentor
Is it possible to tell with certainty whether μ and ε for vacuum change over time within a very long period of time?
In our current SI units it is certain that it does not change over time

#### calinvass

Thank you.
I'm assuming from your other threads that you are interested in possible changes in these quantities because that would imply a change in the speed of light in vacuum? If so, the short answer is that is possible to tell, and they do not change over time.
Actually, I don't see how these properties could change, but I wanted the know some reasons or ideas that would confirm thiso. I understand that the reason is simply because the speed of light doesn't change.

Any discussion beyond this would have to start with a clear explanation of how we could, even in principle, measure/observe such a change. That is much much harder than it looks at first glance: speed is distance over time, right? How do you define and measure either of these quantities? In a way that is experimentally useful?
No, I don't see how and also there seem to be no reason to believe they would change. Energy and matter curve spacetime and it doesn't affect the speed of light. Dark energy also affects spacetime and naturally, it shouldn't affect the speed of light neither.
But again, I wanted to see a qualified answer.

#### calinvass

In our current SI units it is certain that it does not change over time
Only in the last few years measurements became precise enough so that we could measure a small variation. If presumably the variation is proportional to the age of the universe, I suppose such variation would be very hard to detect.

#### Dale

Mentor
Only in the last few years measurements became precise enough so that we could measure a small variation. If presumably the variation is proportional to the age of the universe, I suppose such variation would be very hard to detect.
No, they are exact defined constants in SI units. There is absolutely no variation of any size by definition.

Experimental precision is not relevant

#### calinvass

Oh, you mean that even if speed of light varies, we keep these properties constant by definition? The variation of c, would automatically imply a change in the properties of free space, I think here is the confusion I've made.

#### Dale

Mentor
Oh, you mean that even if speed of light varies, we keep these properties constant by definition?
The speed of light is also a defined constant in SI units which cannot vary by definition. We have discussed this point with you previously, and we will not discuss it again. Please see the previous closed thread.

#### Baluncore

Everything you question is now locked by definition in SI.
π is defined as the ratio of circumference to diameter of a circle.
The speed of light is defined as an integer, c = 299792458 metre/second.
Absolute permeability, Uo = 4x10-7 * π; henry/metre.
Absolute permittivity, Eo = 1 / ( Uo * c * c ); farad/metre.
The impedance of free space, Zfs = Uo * c; ohms.

#### calinvass

Ok, I understand, in case we make a better measurement and find a different value for the speed of light (say slower by 0.000001%), we adjust the meter unit accordingly.

#### Dale

Mentor
Ok, I understand, in case we make a better measurement and find a different value for the speed of light (say slower by 0.000001%)
You couldn't even do this measurement in SI units. So let's assume for the sake of discussion that we have some other unit system where this could be done.

we adjust the meter unit accordingly.
More exactly, we adjust the conversion factor between meters and the other unit of length. This is all unit definitions, not anything physical.

#### Baluncore

Ok, I understand, in case we make a better measurement and find a different value for the speed of light (say slower by 0.000001%), we adjust the meter unit accordingly.
We cannot measure the speed of light more accurately because it is defined as a constant.

The metre is defined as the distance travelled by light in vacuum in 1 / 299792458 second. And the second is defined as 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. There is no escape, everything tracks and so no change can ever be detected.

All you can do is make a more accurate metre rule and then compare it with one you prepared earlier. Your ability to predict metal creep and to measure temperature is then the limiting factor.

#### Dale

Mentor
@calinvass I will give you a big hint. Almost always when someone is asking about a varying c they actually want to know about a varying fine structure constant. I think that the question that you are hinting at but don't quite understand yet is about the fine structure constant.

#### calinvass

Thank you.
We cannot measure the speed of light more accurately because it is defined as a constant.
This sound like we cannot measure the speed of light anymore since it is established at a fixed value.

The metre is defined as the distance travelled by light in vacuum in 1 / 299792458 second. And the second is defined as 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. There is no escape, everything tracks and so no change can ever be detected.
Yes, I had checked the definitions in the meantime.
All you can do is make a more accurate metre rule and then compare it with one you prepared earlier. Your ability to predict metal creep and to measure temperature is then the limiting factor.
This sound the same thing to me. Either, make a measurement of the velocity and use current standard meter stick. If the meter stick was not accurately measured you will get a different speed of light. Then correct the meter stick. Or you assume from start c is constant and measure the meter stick to determine if it is accurate. Both versions will end with the same conclusion, that the standard meter stick needs to be adjusted based on the new accurate measurement and not that c has changed. But the correct way is to say you are checking the meter stick because c is established as constant.

Now, I have another question.
If the universe expands, can that mean all the objects increase their size over time? Also, clocks frequencies might change compared to current ones. In the case of gravity clock frequencies are influenced by gravity potential. How would universe expansion affect these frequencies? I expect the clock rates will slow down and compensate the effect and we should not notice any change.

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#### Dale

Mentor
This sound like we cannot measure the speed of light anymore since it is established at a fixed value
That is correct. You cannot measure the speed of light in SI units any more.

#### Nugatory

Mentor
If the universe expands, can that mean all the objects increase their size over time?
No. The objects are held together by the intermolecular forces that made them objects (as opposed to clouds of free-floating gas molecules) in the first place. Expansion means that if the molecules at opposite ends of the object were not held together by these forces, they would tend to drift apart while in free fall - but they are held together, so instead of drifting apart they experience a very tiny acceleration towards one another from these forces and they maintain a constant separation. This is why galaxies drift apart with expansion but the galaxies themselves, held together by their gravitational force, don't expand, pull apart, and disintegrate.

For an analogy that helps show how curvature affects force-free inertial motion.... Suppose you and I are standing at the north pole and we start walking south in slightly different directions. Because we're following slightly different longitude lines, we will have drifted many many kilometers apart by the time we reach the equator - that's how longitude lines work. But if we tie ourselves together with a rope one meter long, we'll feel a constant and very gentle tug from the rope all the way south, and we'll still be separated by only one meter when we reach the equator.

#### calinvass

Thank you. It makes sense as long as the expansion rate is constant throughout the Universe and the forces between objects depend on distance.

"Permittivity/permeability variation in time"

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