B Meaningfulness of the speed of light

[ginevradabenci]

TL;DR Summary

How can the speed of light be constant across the universe when the units (metres and seconds) relate to the Earth? Secondly, how do we know when the speed of light is at the maximum value, given that we do not know the precise contents of space?

Although the speed of light is a 'cosmic speed limit', and is always constant, this seems to be a paradox. Firstly, the units we use to measure it relate to the Earth. How can we measure a metre or a second without the Earth as a reference point? And if we do, what meaning does this have for the rest of the universe, which (as far as we know) is not built with reference to the Earth? Secondly, the speed of light is slower when light passes through substances, so, given that the entire universe is not a vacuum, and we do not know what transparent substances the light is passing through, how can we meaningfully say the speed of light is constant? And when it is at a maximum, how long does this happen for, and how can we know?

 

[phinds]

The speed of light IN A VACUUM is constant.

The fact that our units of measurement were invented by humans has zero to do with their applicability to measuring anything anywhere.

If I decide that I want to define a fribish as the distance from one side of my room in New York to the other side, I can use that metric to measure the size of a football field in France in fribishes. Likewise I could (if I could get there) measure the size of something in the Andromeda galaxy, in terms of fribishes.

 

[Nugatory]

Firstly, the units we use to measure it relate to the Earth. How can we measure a metre or a second without the Earth as a reference point?

The meter is defined to be the distance that light travels in 1/299792458 seconds and the second is defined to be the time it takes for an excited cesium atom to oscillate 9192631770 times, so anyone anywhere in the universe who has a convenient cesium atom can reproduce the units that we earthlings use. But they don’t need to, we or they can do physics in any units we choose - nothing changes if we decide to all our calculations in miles per second or light years per year instead.

Secondly, the speed of light is slower when light passes through substances, so, given that the entire universe is not a vacuum, and we do not know what transparent substances the light is passing through, how can we meaningfully say the speed of light is constant?

Although the math is more than we can go through in a B-level thread, it turns out that there are only two internally consistent possibilities: the speed of light is constant for everyone (so even when you and I are moving relative to one another we will both measure the speed of a passing flash of light to be $c$) or there is a notion of absolute speed (so that if I am at rest and you are moving at speed $v$ relative to me, I will measure the speed of a flash of light moving in the same directIon as you to be $c$ but you will measure it to be $c-v$). Experiments dating back to the 19th century confirm that the first possibility is correct (and if it weren’t the GPS system wouldn’t work).

 

[Orodruin]

the time it takes for an excited cesium atom to oscillate 9192631770 times

It is the time of 9192631770 periods of the radiation emitted by the hyperfine transition in cesium-133. It is not about the cesium atom oscillating.

 

[Orodruin]

there is a notion of absolute speed (so that if I am at rest and you are moving at speed v relative to me, I will measure the speed of a flash of light moving in the same directIon as you to be c but you will measure it to be c−v).

Absolute time. There is no absolute speed in Galilean spacetime nor Minkowski spacetime. That would mean having a universal rest frame.

 

[Herman Trivilino]

Although the speed of light is a 'cosmic speed limit', and is always constant, this seems to be a paradox.

No, it's an assumption. Follow that assumption to various conclusions (there are lots of them) and then test experimentally to see if the conclusions match the way Nature behaves. So far, they all match to an overwhelming precision and in a huge number of different ways.

Moreover, the assumption and its conclusions are all logically self-consistent, so both theoretically and experimentally there are no inconsistencies or paradoxes. That is the best contribution to knowledge that physics can make.

Firstly, the units we use to measure it relate to the Earth.

We don't always do that. For example, often we use a dimensionless (that is, unitless) value of exactly $1$ for the speed of light.

Secondly, the speed of light is slower when light passes through substances,

Yeah, but in this context we are referring to the speed of light in a vacuum.

This is hard to understand, but in relativity when we talk about the speed of light, we are talking about the speed, not the light. If it were discovered that the speed of light (in a vacuum) were something less than $c$ there would be no need to change anything about the theory of relativity. We would simply refer to the speed $c$ by some other name, such as the invariant speed, or the maximum possible speed.

 

[Dale]

Firstly, the units we use to measure it relate to the Earth.

This has nothing to do with anything. We can use Earth based units or natural units as we please. It doesn’t matter.

given that the entire universe is not a vacuum, and we do not know what transparent substances the light is passing through, how can we meaningfully say the speed of light is constant?

We only claim that the speed of light in vacuum is invariant.

 

[jbriggs444]

given that the entire universe is not a vacuum, and we do not know what transparent substances the light is passing through

We know that the overwhelming majority of the entire universe is approximately a vacuum. We also know that substances slow light down. They do not speed it up.

The light we see from distant stars, novas and such got here at a very very close approximation to light speed. In addition to being a prediction of our models, we have direct experimental evidence confirming this, e.g. supernova 1987A.

 

[ginevradabenci]

The speed of light IN A VACUUM is constant.

The fact that our units of measurement were invented by humans has zero to do with their applicability to measuring anything anywhere.

If I decide that I want to define a fribish as the distance from one side of my room in New York to the other side, I can use that metric to measure the size of a football field in France in fribishes. Likewise I could (if I could get there) measure the size of something in the Andromeda galaxy, in terms of fribishes.

The speed of light IN A VACUUM is constant.

The fact that our units of measurement were invented by humans has zero to do with their applicability to measuring anything anywhere.

If I decide that I want to define a fribish as the distance from one side of my room in New York to the other side, I can use that metric to measure the size of a football field in France in fribishes. Likewise I could (if I could get there) measure the size of something in the Andromeda galaxy, in terms of fribishes.

Thank you for this. I see the logic, in relation to Earth, but if we use earthly measurements for other parts of the universe, wouldn't they be affected by relativity? One part of the equation, the unit, would be clearly defined, but surely the other part, some distance in distant space, would depend on the movements of everything else in space?

 

[jbriggs444]

Thank you for this. I see the logic, in relation to Earth, but if we use earthly measurements for other parts of the universe, wouldn't they be affected by relativity?

The theories of special relativity and general relativity say not. [I am assuming that this question is not a veiled reference to the idea of "parallel transport" under general relativity].

One part of the equation, the unit, would be clearly defined, but surely the other part, some distance in distant space, would depend on the movements of everything else in space?

What is this equation you speak of? What is this "other part" you speak of? You are going to have to be a lot more specific if you want us to debunk your reasoning.

Perhaps you could consider asking different questions. Like "how is velocity defined relative to a coordinate system"? Or "how can velocity relative to one coordinate system be converted to velocity relative to a different coordinate system"? Or "how can one theoretically compare velocities across an expanse of curved space time"? Or maybe even "what sort of coordinate system do we use to describe the entire universe"?

 

[ginevradabenci]

The theories of special relativity and general relativity say not. [I am assuming that this question is not a veiled reference to the idea of "parallel transport" under general relativity].

What is this equation you speak of? What is this "other part" you speak of? You are going to have to be a lot more specific if you want us to debunk your reasoning.

Perhaps you could consider asking different questions. Like "how is velocity defined relative to a coordinate system"? Or "how can velocity relative to one coordinate system be converted to velocity relative to a different coordinate system"? Or "how can one theoretically compare velocities across an expanse of curved space time"? Or maybe even "what sort of coordinate system do we use to describe the entire universe"?

Yep, those are all better ways of phrasing my question. It's probably quite a big job to answer them, I assume.

 

[jbriggs444]

Yep, those are all better ways of phrasing my question. It's probably quite a big job to answer them, I assume.

All of those questions have reasonably simple answers. All are covered in text books and university courses in a fair bit of detail.

 

[ESponge2000]

What if we say we don’t know what the speed of light does in a vacuum for all things we can’t test but we have the following :

1) the theory of GR and SR for all testing we’ve done is endlessly consistent with the speed of light being what we measure it to be ,

2) that the Maxwell equations unchanged regardless of a rest velocity

3) that we measure a time interval using a discreet atomic pulse count and observe the atomic activity obeys the same relationship in any rest frame it is at rest with …. So we have “clock” and then we have the construct of SR theory length and SR theory time and no Change in electromagnetic travel in vacuum after endless testing …

Is science that we “know nothing to be 100% confirmed true” , But we have “all testing confirms same result consistent with a theoretical framework, contested in and re-contested for a discrepancy is a Yes-able extraction, that’s how science says something must be true, down to 1+1=2 we have no disagreement in all human observation, guaranteed that’s true we still can’t say because we can’t rule out what our brain sees as 2 is something other than 1 more than 1 but with overwhelming near 100% weight of scientific evidence 1+1 proves to be 2 …. Science is perception is reality and perception of identical results to expected outcomes across all observations among all variations means, it is 2 not something other than 2. What else do we have? Science is about using only what we have and determining the evidence sufficient to call it.

 

[DaveC426913]

What if we say we don’t know what the speed of light does in a vacuum for all things we can’t test but we have the following :

1) the theory of GR and SR for all testing we’ve done is endlessly consistent with the speed of light being what we measure it to be ,

Well, science is about things we can measure.

If we want to talk about what things do when we can't measure them; that would be meta-physics or philosophy, both of which are outside the scope of PF's mandate.

 

[jbriggs444]

3) that we measure a time interval using a discreet atomic pulse count and observe the atomic activity obeys the same relationship in any rest frame it is at rest with

You should read an article about how atomic clocks work. It is not done by counting atomic pulses. It is done by controlling the frequency of microwave radiation to match the period of the radiation corresponding to a particular hyperfine transition. In a Cesium atom, for example. It has nothing to do with how frequently a cesium atom makes such a transition. It has to do with the frequency of the associated electromagnetic radiation.

You are correct that at least two well known experiments involve comparisons of atomic clocks moving at different speeds and/or at different altitudes. Those being the Hafele Keating experiment and the GPS system.

However, there are many many other tests of special and general relativity. A list of them is stickied to this forum. It is not just about comparing clocks.

 

[PeterDonis]

What if we say we don’t know what the speed of light does in a vacuum for all things we can’t test

What things about this can't we test?

 

[DaveC426913]

However, there are many many other tests of special and general relativity. A list of them is stickied to this forum. It is not just about comparing clocks.

:aside: for a moment. Am I interpreting this correctly?

7. Tests of Length Contraction
"If one considers the situation in the rest frame of a charge moving with the drift velocity of the electrons in the wire, the force is purely electrostatic due to the different length contractions of the positive and negative charges in the wire (the former are fixed relative to the wire, while the latter are mobile with drift velocities of a few mm per second). This approach gives the correct quantitative value of the magnetic force in the wire frame. This is discussed in more detail in: Purcel, Electricity and Magnetism. It is rather remarkable that relativistic effects for such a tiny speed explain the enormous magnetic forces we observe."

Is the implication here that when passing a wire through a magnetic field, the current induced in the wire is
a direct product of special relativity i.e. the tiny length contraction caused by the relative motion?

If the answer is more than a simple 'yes' or 'no', I'll move it to its own thread.

 

[Ibix]

Is the implication here that when passing a wire through a magnetic field, the current induced in the wire is
a direct product of special relativity i.e. the tiny length contraction caused by the relative motion?

No, it's an explanation for why you get a purely magnetic field in one frame and a mixed magnetic and electric field in the other - the charge densities of the two species vary differently as you change frames because they have equal densities by hypothesis in the wire frame even though the electrons are moving.

 

[cianfa72]

You should read an article about how atomic clocks work. It is not done by counting atomic pulses. It is done by controlling the frequency of microwave radiation to match the period of the radiation corresponding to a particular hyperfine transition. In a Cesium atom, for example. It has nothing to do with how frequently a cesium atom makes such a transition. It has to do with the frequency of the associated electromagnetic radiation.

As far as I can tell, the fact to employ the elettromagnetic radiation emitted by the hyperfine transition in cesium-133 to define one second (9192631770 periods of such radiation) is just a matter of definition.

Basically what is being defined is the amount of proper time required to get the above number of periods of that specific electromagnetic radiation.

 

[jbriggs444]

As far as I can tell, the fact to employ the elettromagnetic radiation emitted by the hyperfine transition in cesium-133 to define one second (9192631770 periods of such radiation) is just a matter of definition.

It is also a matter of measurement. The definition is chosen so that a measurement is feasible. And reliable, precise, accurate and repeatable.

Basically what is being defined is the amount of proper time required to get the above number of periods of that specific electromagnetic radiation.

Yes. I thought that was obvious.

 

[cianfa72]

It is also a matter of measurement. The definition is chosen so that a measurement is feasible. And reliable, precise, accurate and repeatable.

You mean the measurement of that specific number (9192631770 periods) from that specific electromagnetic radiation. From a pratical point of view, how that measurement is done ?

 

[jbriggs444]

You mean the measurement of that specific number (9192631770 periods) from that specific electromagnetic radiation. From a pratical point of view, how that measurement is done ?

The specific number was chosen so that the new definition of the second matched the old definition of the second to within experimental accuracy.

The measurement is done by constructing a Cesium atomic clock.

At the risk of being glib, "the second is what a Cesium atomic clock measures".

In my previous post, I linked to a description of the mechanism used by atomic clocks. Here it is again:

Clock mechanism​

[edit]
An atomic clock is based on a system of atoms which may be in one of two possible energy states. A group of atoms in one state is prepared, then subjected to microwave radiation. If the radiation is of the correct frequency, a number of atoms will transition to the other energy state. The closer the frequency is to the inherent oscillation frequency of the atoms, the more atoms will switch states. Such correlation allows very accurate tuning of the frequency of the microwave radiation. Once the microwave radiation is adjusted to a known frequency where the maximum number of atoms switch states, the atom and thus, its associated transition frequency, can be used as a timekeeping oscillator to measure elapsed time.[35]

and

Microwave atomic clocks​

[edit]

Caesium​

[edit]
Main article: Caesium standard
The SI second is defined as a certain number of unperturbed ground-state hyperfine transitions of the caesium-133 atom. Caesium standards are therefore regarded as primary time and frequency standards.

Caesium clocks include the NIST-F1 clock, developed in 1999, and the NIST-F2 clock, developed in 2013.[63][64]

Caesium has several properties that make it a good choice for an atomic clock. Whereas a hydrogen atom moves at 1,600 m/s at room temperature and a nitrogen atom moves at 510 m/s, a caesium atom moves at a much slower speed of 130 m/s due to its greater mass.[65][10] The hyperfine frequency of caesium (~9.19 GHz) is also higher than other elements such as rubidium (~6.8 GHz) and hydrogen (~1.4 GHz).[10] The high frequency of caesium allows for more accurate measurements. Caesium reference tubes suitable for national standards currently[when?] last about seven years and cost about US$35,000. Primary frequency and time standards like the United States Time Standard atomic clocks, NIST-F1 and NIST-F2, use far higher power.[34][66][67][68]

Block diagram​

[edit]
In a caesium beam frequency reference, timing signals are derived from a high stability voltage-controlled quartz crystal oscillator (VCXO) that is tunable over a narrow range. The output frequency of the VCXO (typically 5 MHz) is multiplied by a frequency synthesizer to obtain microwaves at the frequency of the caesium atomic hyperfine transition (about 9192.6317 MHz). The output of the frequency synthesizer is amplified and applied to a chamber containing caesium gas which absorbs the microwaves. The output current of the caesium chamber increases as absorption increases.

The remainder of the circuitry simply adjusts the running frequency of the VCXO to maximize the output current of the caesium chamber which keeps the oscillator tuned to the resonance frequency of the hyperfine transition.[69]

The simple version that I take away from this is that an atomic clock is pretty much the same thing as an electronic wrist watch. It is based on counting the oscillations of a quartz crystal.

It is just that the atomic clock has an extremely fancy way of controlling and stabilizing the oscillation frequency of that quartz crystal.

 

[Dale]

You mean the measurement of that specific number (9192631770 periods) from that specific electromagnetic radiation. From a pratical point of view, how that measurement is done ?

Usually you use a counting circuit. Basically, it is a digital circuit where each bit flips when the next lower bit goes from 1 to 0. The lowest bit is attached to the oscillator that generates the Cs hyperfine frequency, and is triggered when that goes from positive to negative or vice versa.

 

[cianfa72]

Usually you use a counting circuit. Basically, it is a digital circuit where each bit flips when the next lower bit goes from 1 to 0. The lowest bit is attached to the oscillator that generates the Cs hyperfine frequency, and is triggered when that goes from positive to negative or vice versa.

Ah ok, so the digital circuit's lower bit flips whenever the electromagnetic radiation/signal generated by the oscillator based on cesium-133 hyperfine transition crosses the zero from positive to negative (or the other way around).

 

[jbriggs444]

Ah ok, so the digital circuit's lower bit flips whenever the electromagnetic radiation/signal generated by the oscillator based on cesium-133 hyperfine transition crosses the zero from positive to negative (or the other way around).

For me as a digital software type, the mystery is in how one can take an analog signal (a noisy sine wave) and convert it reliably to a square wave without generating extraneous output transitions at the moment an input threshold is crossed. My EE prof (one quarter hour total for my career) made a point of the fact that analog signals are dirty.

Once one has a clean digital signal in hand, daisy chaining flip flops is the easy part. Though the same EE prof also warned us about the reliability of asynchronous circuitry.

 

[Dale]

For me as a digital software type, the mystery is in how one can take an analog signal (a noisy sine wave) and convert it reliably to a square wave without generating extraneous output transitions at the moment an input threshold is crossed

Yes. That is more difficult. It helps that the specific analog signal in question is not very small so it isn’t very noisy. The signal comes from a tunable oscillator circuit. It is tuned to the hyperfine frequency, but the signal itself is generated by circuitry rather than by the hyperfine transition.