Q: What happens to the speed of light if it's velocity is decreased?

Okay, first things first: Why is the speed of light the speed it is?

The answer is, because it must be. The oscillating magnetic and electric fields that constitute a lightwave inherently propagate (at c) perpendicular to the fields’ collapse. They are precisely at the correct energy level to be mutually self-sustaining; as the electric field collapses it produces a magnetic field that when collapsed produces an electric field of the same intensity as before. Continue ad infinitum. That is just the way it is.

Now if c was “slowed down” that means that either the magnetic field or the electric field had lost energy. That in turn would cause a decrease in the other field, which would cause further decrease in the first field, ad mortem.

Basically, if light were to fundamentally slow down, it would continue to slow down until it completely ran out of energy and stopped.

None at all. the value, in meters per second, is completely an artifact of our arbitrary choices of denominating length in meters and time in seconds; we could choose other basic units for length and time and the value of c would appear to be different.

What *is* of fundamental importance is that the nature of spacetime is that there exists some special speed which is independent of choice of inertial frame, and almost as important, that electromagnetic (and other massless field) waves travel at that speed in a vacuum. In fact, it is completely common for physicists to work in a system of units in which the speed of light is exactly 1 by definition, and neither length nor time are treated as basic units.

We don't.

No, seriously, we don't measure the speed of light (which always refers to the speed in a vacuum).

We know exactly what the speed of light is.

It is:

[math]c = [/math][math]299792458[/math][math] ms^{-1}[/math]

And that is absolutely 100% accurate, with no measurement errors.

But Jack, I hear you say, what the bloody hell are you talking about?

The reason we know that that's exactly the speed of light, is that we defined it to be that number.

We then take our definition of a second (the length of time for a certain number of periods of the radiation emitted in hyperfine transitions in caesium-133), and from that we define a metre.

So the thing we would be measuring is what a metre is!

We use the speed of light as a fixed velocity, from which all observers can define their own length scale.

To measure the speed of light would require an external definition of what a metre is - and since about the 1970s, we don't have one!

And if you did want to measure the speed of light using this external distance reference, it's easy to test - you just release a light pulse at t=0, towards a mirror - and then time how long it takes to get back to you. This is the exact principle that Radar/Sonar work on (although again, they measure the distance knowing the speed - but it works either way round).

Some background:

The metre was originally defined after the French Revolution, in about 1799. It was defined as [math]\frac{1}{10,000,000}[/math] the distance between the equator and the pole.

The “metre” was formally defined from 1889 as the length of a platinum rod, held in a vault in Paris.

From this definition of a metre (and an old definition of a second - I forget what that was), we measured (using the mirror-timing method, or based on astronomical observations) the speed of light to be about [math]299792458[/math], plus a non-integer bit, and error bars from the measurement errors.

Eventually, we realised that having a metre defined by something there was only one of was a bit annoying. So, we attempted to define it in a way that anyone could replicate - without having to refer to a “standard object”.

Therefore, we redefined the metre - using the speed of light.

The official definition of a metre today is:

[math]\frac{1}{299792458} [/math]of the distance travelled by light in a vacuum, in 1 second[math].[/math]

Using the caesium definition of a second.

Therefore, this was exactly equivalent to defining the speed of light to be the number given above.

We chose that number (and not a more convenient number like 300,000,000), because that number changed the definition of a metre by only a fraction of a fraction of a percent - but made everything all nice and integer-y.

A consequence of using this definition is that any attempt to measure the speed of light is cyclical - you must use a “metre” to measure it at some point - which relies on the speed of light.

Therefore what you actually do now, when you “measure” the speed of light (in a vacuum), is actually “measure how accurate your measuring instruments are”!

An interesting documentary on that topic on Netflix, called “Einstein’s Greatest Blunder”.

It is a heretical thought, but it discusses that the speed of light may vary of huge, cosmological intervals. An increase in C would explain why the universe is accelerating. A decrease would take energy out of the universe. I'm too dense to think it all through, but the documentary does a nice job of “dumbing it down”.

Ever had your science teacher tell you that we’re seeing the past of distance stars? The light a far away star emits that reaches is not of its current state.

if the speed of light were to decrease this effect would be amplified where you could see where someone was. If it were decreased so drastically, the world would seem laggy:

If the SoL were 2’/sec and you were to pick up a glass off the table (that was 2’ away) you would feel the glass in your hand but would only see yourself pick it up 1ish second later.

Disclaimer: I have nothing to truly back that up besides common sense, it’s just how’d I’d imagine the world would seem. Scientific Community don’t chew me a new one for my theory, it’s my 2 cents.

Relativity defines the speed of light as an absolute constant. However, the apparent speed of light is not. For example, if light is climbing out of a gravity well of a black hole, it will take it longer than what we calculate for the radial distance at the speed of light. This is the combined result of gravitational time dilation and length expansion.

But here is the thing. If you were to measure the beam of light passing any point along its path we would measure the exact same constant of c.

Is there something that shifts frequency without changing distances? Yes. If I shine a laser beam from the top of the mountain to the ground it will be blue shifted. And if I shine a laser from the bottom of the mountain to the top the light arrives redshifted. Now gravity causes both time dilation and length expansion. But that length expansion is a constant. If I measure the height of the mountain that will not change over time.

But how would we make distant galaxies mountain tops? The easiest I can think of is to add an extra dimension of height. The galaxies were all initially on mountain tops but have been settling ever time. This gives redshift like Hubble’s law, and an apparent reduction in the speed of light.

This of course defies Occam’s razor and ignores the fact CERN has been unable to find evidence of extra dimensions and but constraints that would prohibit this model.

But if I want to do something that we don’t observe nor predict with known laws of physics I have to thing outside the box.

So the answer is if the apparent speed of light decreases we get a redshifted universe that somewhat resembles our own. But needs mathematical tricks like extra dimensions that are somehow hidden from particle physicists.

Surprisingly though the Freidman’s field equations are general enough you could define a function that would accommodate such a wild model.

This question is more subtle than may appear at first glance, and it has to do with what you mean by "measuring a speed." You might say that you pick a unit, say meters per second, and then you measure how many times bigger the speed of light is than a meter per second. Seems simple enough. Except...

What is a meter? And what is a second? Well, you might pull out your meterstick and tell me that there, that's a meter. As for a second, that's easy: Everyone knows what a day is, so just split that up into 24 hours, split each of those up into 60 minutes, then split each of those into 60 pieces, and that's what a second is. And, frankly, that's what people did for a while. Here is the official meterstick of the International Bureau of Weights and Measures, which defined the meter up until 1960.

But what happened in 1960? Was there a distortion in the space-time continuum that changed the length of a meter? Sadly, no. All that happened was that a lot of folks started wanting to measure distances precisely, and sometimes they didn't happen to have their copy of the International Prototype Metre with them, or maybe it got bent. Also, by that time folks had invented Interferometry which let them measure very precise distances with a lot less squinting at tiny lines on a meterstick. In fact, all this had happened many decades before 1960. 1960 was just the year when the International Bureau of Weights and Measures finally got fed up with all the complaints and decided to replace the international prototype metre with...

The Krypton Standard. Rather than being a code of behavior followed by Superman, the krypton standard redefined a meter in terms of a property of the element krypton. Sometimes krypton gets excited, and when it settles back down it releases orange-ish red light. The meter was then defined as 1,650,763.73 wavelengths of this light. Great, now that you've settled on what a meter is, you can do science.

Oh, but the wavelength of light is different between air and vacuum, so you have to make sure to measure the krypton wavelengths in a vacuum. Oh, and also there are five different stable isotopes of krypton, and each of them releases light at slightly different wavelengths. You sigh, get out your centrifuge, spin up some krypton gas to separate out the isotopes of krypton, take the heaviest one, krypton-86, and measure the wavelength of that. OK, now that you know what a meter is, you can measure the speed of light.

But wait! What about the second? But didn't we already settle that with defining it as a certain fraction of a day? Unfortunately, it turns out that the rate of the Earth's rotation changes, so using it to define a second is no good. The rate of rotation gradually slows due to the tidal forces from the Moon, and it also changes sporadically due to the rearrangement of the mass of the Earth, sort of like a figure skater moving their arms in to spin faster except with earthquakes and volcanic explosions.

Well, crap. So you think bigger and decide to use the revolution of the Earth around the sun to define a second. But, alas, it turns out that, like a day, a year isn't as constant as you'd think. The tug of Jupiter and the other planets on the Sun is enough to move it off course a little bit, which can change the length of a year slightly in a way that's hard to predict. Alas, the time intervals that you thought were constant have all betrayed you.

But all hope is not lost! The Atomic clock comes to the rescue. Just like your friend krypton-86, the atom cesium-133 atom also releases light in particular frequencies when it settles down after getting excited. An atomic clock can measure this frequency very precisely, which lets you define the second as the time it takes for there to be 9,192,631,770 oscillations of the emitted light.

After all your hard work in nailing down a meter and a second, you can finally measure the speed of light like you wanted all along. But what's this? The International Bureau of Weights and Measures redefined the meter in 1983 to be the length that light travels in 1/(299,792,458) seconds. The speed of light is thus exactly 299,792,458 meters per second, to arbitrary accuracy, by definition. But that's cheating!

On the other hand, from a physics perspective, using one unit to measure length and another unit to measure time makes about as much sense as using miles to measure horizontal distances and feet to measure vertical distances. Yes, going 100 miles north is very different from going 100 miles up, but if you insist on using different units for horizontal and vertical lengths, boy are you going to have a fun time setting up ladders.

Or playing with lasers, if you break out of the metaphor. In fact, if, instead of using the wavelength of light from krypton-86 to define a meter and the frequency of light from cesium-133 to define a second, you had picked the same atom for both, then you'd wind up with the same sort of cheating for speed of light. The wavelength of that light times its frequency is the speed of light, so if you fix the wavelength by definition and you fix the frequency by definition, then you end up fixing the speed of light by definition. It's a very unsatisfying answer.

However, the case isn't closed, and there's still a very reasonable question to ask: How accurately can you measure speeds, at least theoretically? If you see a thing that's moving, how accurately can you measure its speed in terms of the speed of light? Or, if you like, how accurately can you measure the speed of light in terms of the thing's speed?

Heisenberg's Uncertainty principle doesn't actually pose a problem for you. The principle says that you can't know both a particle's position and momentum: If you want more accuracy in measuring one quantity, you have to give up accuracy in the other quantity. However, if you know the particle's rest mass, then you can compute the particle's velocity knowing only its momentum, and you can know the momentum as accurately as you like, provided you give up all hope of ever finding where the particle is.

There is also something to be said about the Planck length. However, it's not currently clear what, if any, physical significance the Planck length has. If you believe that the Planck length is the smallest measurable length, then the smallest theoretically measurable velocity is the Planck length divided by the lifetime of the universe. So, if you want to measure the velocity of a moving particle, you won't be able to compute it to greater accuracy than the Planck length divided by the lifetime of the universe. Tough luck, I know. Of course, if the universe will go on for ever, as is currently believed, then there is no limit to your accuracy.

• Whenever we are in motion there is some change in mass but due very very low speed as compared to speed of light ,this change is neglible and v/c ratio approches to zero.
• According to einstein equation , if speed of light decrease then there is significant change occur in our mass , because v/c ratio is compareble. and for a given velocity of an observer if speed of light decrease then there will some increase in mass .
• There are many things change in our surrounding eg length contraction , there is significant change in energy mass relation. But i am discussing only variation of mass wrt speed of light

Does the speed of light change depending on who is measuring it?

Who? Where? While possibly relevant we should look at special relativity. Its major precept is the invariant speed of light (in a vacuum). In this special case, it depends on neither who nor where. Everyone, everywhere measures the speed of light the same.

Where the difference comes in is frames of reference. If you are going the speed of light one way and I am going the speed of light the opposite way and we look at each other’s clocks we see they are both stopped. Our relative speed is still the speed of light.

Maybe what you are driving at is the frames of reference at lesser speeds. If I am in a “stationary” frame of reference and you speed by me at half the speed of light I see that your clock is ticking at half its normal rate. Mind you, you always see your clock in proper time. In your frame of reference your ticks as usual.

Then speed (less than light) causes clocks to tick slower from other frames of reference.

The speed of light (in a vacuum) never changes for any observer. If it goes through a prism, well, that’s a different thing.

Actually light does travel at different speeds in medium with different refractive index. What you ask is reducing the speed of light in vacuum from 186K mi/sec. Speed of light is constant in any given medium so is not possible to change that, however it would be possible to achieve this by increasing the refractive index of the medium through light is travelling. Now to achieve this you would need to make the space denser but that would result in increased temperature of the vacuum and thereby of whole of universe - degree of this increase in temperature will depend on how dense the medium you have made. Not sure if that hot dense universe will be able to sustain life. These may very well have been the condition soon after the Big Bang. Hot dense universe with no life!

A2A The only way to slow light is by sending it through a material. In vacuum, light always has the same speed which can’t be reduced.

The velocity of light in water is for instance less than the velocity of light in vacuum. Current physics research tries to find materials for which the velocity of light is reduced as maximum as possible while keeping the interesting aspects of light for data transmission intact. Such experiments are known as “slow light”. Using specially prepared optics, one can slow down a light pluse to a few meters per second and even stopping it, while keeping the exact shape of the pulse intact.

One practical purpose of slow light is in telecommunications where much more effcient internet switches could be created. Switches can only process one light pulse at a time. When the internet traffic is high one gets data contention. Buy storing data in slow light channels a much more efficient switching can be achived under high traffic.

There is another question really similar to this one What would happen if the speed of light suddenly reduced to half its current value? and others that are similar in theme but varying on the specifics:
How would everyday life change if the speed of light were twice what it is now? What if it were half what it is now?
If the speed of light changed in the universe is there any way we would possibly know?
If the speed of light changed in the universe, why would everything fall apart/die?
If I could change the speed of light instantly and universally from c to c * 1.000000001, what would be the result?
Is it possible to detect any change in the speed of light over time? (Traveling through a vacuum with no gravitational influence.)

My initial thoughts were that cutting the speed of light in half would seem to essentially cut the rate of flow the passage of time in half. But your clocks that you are using to measure time would be running at half the speed, so how would you know? I find that the third question above has an answer with some interesting thoughts on that.

We don’t. Since 1983, it’s been impossible to measure the speed of light; the speed of light is defined as exactly 299792458 meters per second.

“But, but,” (you say) “what am I measuring if, for instance, I measure (somehow) exactly how far light travels in 1 second?” The answer is that you’re measuring the length of the meter: in 1983, the 17th General Conference on Weights and Measures changed the definition of the meter (the internationally-agreed-on unit of length) from a fixed length to “the distance light travels in a vacuum in 1/(299,792,458) seconds.”

That said, how do we measure the length of the meter? Generally by measuring the wavelength [math]λ[/math]of light from a particular spectral line emitted by an excited atom, where the frequency f of the light is exactly known, using the relationship [math]λ=c/f. [/math]Spectral lines are used because they can be reliably generated anywhere or any time and always have the same frequency. The frequency can be measured in various ways, although the best current way uses very short laser pulses to generate exact integer multiples of a known frequency (a “frequency comb”) that extend all the way from microwave frequencies (which we can measure very accurately) to visible-light frequencies. The wavelength is measured by interferometry: basically, arranging optics so that light is split into two beams that travel two different paths and are combined again. The combined beam will show “fringes” of light and dark areas, and each fringe corresponds to one wavelength difference between the two paths. By deliberately changing one path (say, by moving a mirror a known distance) and counting the fringes that go by as you make the change, you can count the number of wavelengths in that known distance — to a tiny fraction of a wavelength, if you do it right. From 1960 to 1983, the meter was defined this way, as 1 650 763.73 wavelengths of the orange-red emission line of Krypton 86 (a nice inert gaseous element) in a vacuum. So technically, the speed of light was fixed by definition and couldn’t be measured ever since 1960 — but it wasn’t quite so obvious as with the newer definition of the meter in 1983.

Edited to add: Brett Buckland correctly notes that I used the phrase a ‘known distance’ which implies that I already have a standard of length when I make an interferometric measurement of wavelength. That was the case before 1960, but to be strictly correct now, I should have said a ‘fixed distance’ or something similar; it’s only a known distace after you’ve measured how many wavelengths it’s equal to.

In the early 17th century, many people believed that speed of light is infinite. Galileo Galilei disagreed. In 1638, he tried an experiment in which he and another person each took a shutter lantern and walked miles apart. The rule was, as soon as one of them flashes lantern, the other one will flash back. Then Galileo just divided the distance by time. He found that speed of light was atleast 10 times greater than the speed of sound(3.4 km/s). The problem with this experiment was that he couldn't include their reaction time and the speed of their arms. But at least he provided a lower bound for the speed of light.

In 1675, the Danish astronomer Ole Roemer noticed, while observing Jupiter's moons, that the times of the eclipses of the moons of Jupiter seemed to depend on the relative positions of Jupiter and Earth. If Earth was close to Jupiter, the orbits of its moons appeared to speed up. If Earth was far from Jupiter, they seemed to slow down. Reasoning that the moons orbital velocities should not be affected by their separation, he deduced that the apparent change must be due to the extra time for light to travel when Earth was more distant from Jupiter. Using the commonly accepted value for the diameter of the Earth's orbit, he came to the conclusion that light must have traveled at 300,000 Km/s.

In 1728 James Bradley, an English physicist, estimated the speed of light in vacuum to be around 301,000 km/s. He used stellar aberration to calculate the speed of light. Stellar aberration causes the apparent position of stars to change due to the motion of Earth around the sun. Stellar aberration is approximately the ratio of the speed that the earth orbits the sun to the speed of light. He knew the speed of Earth around the sun and he could also measure this stellar aberration angle. These two facts enabled him to calculate the speed of light in vacuum.

In 1849, a French physicist, Hippolyte Louis Fizeau, shone a light between the teeth of a rapidly rotating toothed wheel. A mirror more than 5 miles away reflected the beam back through the same gap between the teeth of the wheel. There were over a hundred teeth in the wheel. The wheel rotated at hundreds of times a second; therefore a fraction of a second was easy to measure. By varying the speed of the wheel, it was possible to determine at what speed the wheel was spinning too fast for the light to pass through the gap between the teeth, to the remote mirror, and then back through the same gap. He knew how far the light traveled and the time it took. By dividing that distance by the time, he got the speed of light. Fizeau measured the speed of light to be 313,300 Km/s.

In 1862, another French physicist, Leon Foucault, used a similar method to Fizeau. He shone a light to a rotating mirror, then it bounced back to a remote fixed mirror and then back to the first rotating mirror. But because the first mirror was rotating, the light from the rotating mirror finally bounced back at an angle slightly different from the angle it initially hit the mirror with. By measuring this angle, it was possible to measure the speed of the light. Foucault continually increased the accuracy of this method over the years. His final measurement determined that light traveled at 299,796 Km/s.

As of now, astronauts have attached a mirror to a rock on the moon. Scientists on earth can aim a laser at this mirror and measure the travel time of the laser pulse(about 2.5 s) for the round trip. The British National Physical Laboratory considered the speed of light to be 299792.4590 ± 0.0008 km/sec and US National Bureau of Standards considered it to be 299792.4574 ± 0.0011 km/sec.
299,792.458 km/s is the adopted value for speed of light at the General Conference of Weights And Measures, 1983 Oct 21.
Since 1983, the meter has been internationally defined as the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second.

You can do it in the comfort of your own home! Do you have one of these?

That’s right, all you need is a microwave and something that melts kinda easily..let’s say one of these:

The next thing you will need to know is the frequency of microwave radiation - there is a good chance it is written somewhere on your microwave. The standard is usually 2.45 GHz (gigahertz).

Remove the turntable first, place your chocky bar in and after microwaving for a bit - take your chocolate out and measure the distance between two melted spots. Multiplying this distance by 2 will give you the wavelength of microwave radiation (since the microwaves have set up a ‘standing wave’) interference inside the microwave oven.

The product of the wavelength and frequency should give you the speed of light!

The speed of light is constant in all reference of frames ( 299 792 458 m/s),

there are different of ways to calculate the speed of light .. one of the, is The Kerr Cell shutter.. A beam of light is timed between an emitter and receiver while passing through a Kerr Cell.

The Kerr Cell consists of a (A) transparent container filled with (B) Nitrobenzene attached to two electrodes (C and D). A high voltage is passed through the electrodes which causes an electric field perpendicular to the transmitted light beam to be applied..

When the cell is activated the light beam is diverted and takes a different path to the receiver, this time difference is measured and the speed of light is calculated based on knowledge of the expected return time.

Yes, the speed of light is constant, at 186,000 miles per second.

In 1676, the Danish astronomer Ole Roemer became the first person to measure the speed of light. Roemer was not looking for the speed of light when he found it. Instead, he was compiling observations of the orbit of Io. By timing the eclipses of Io by Jupiter, Roemer hoped to find a more accurate value for the satellite’s orbital period. Galileo had suggested that tables of the motion of Jupiter’s satellites would provide a kind of “clock” in the sky. Navigators anywhere in the world might use this clock to read the absolute time (the standard time at a place of known longitude, like the Paris Observatory). Then, by determining the local solar time, they could calculate their longitude from the time difference. This method of finding longitude eventually turned out to be impractical and was abandoned after the development of accurate seagoing timepieces. But the Io eclipse data solved another important scientific problem—the speed of light.

The orbital period of Io is now known to be 1.769 Earth days. The satellite is eclipsed by Jupiter once every orbit, as seen from the Earth. By timing these eclipses over many years, Roemer noticed something peculiar. The time interval between eclipses became steadily shorter as the Earth in its orbit moved toward Jupiter and became longer as the Earth moved away from Jupiter. Roemer estimated that when the Earth was nearest to Jupiter, eclipses of Io would occur about eleven minutes earlier than predicted. 6.5 months later, when the Earth was farthest from Jupiter, the eclipses would occur about eleven minutes later than predicted.

Roemer knew that the orbital period of Io could have nothing to do with the relative positions of the Earth and Jupiter. He realized that the time difference must be due to the finite speed of light. Light from the Jupiter system has to travel farther to reach the Earth when the two planets are on opposite sides of the Sun than when they are closer together. Roemer estimated that light required twenty-two minutes (actually more like 16 minutes) to cross the diameter of the Earth’s orbit. The speed of light could then be found by dividing the diameter of the Earth’s orbit by the time difference.

The Dutch scientist Christiaan Huygens, who first did the arithmetic, set the speed of light to 131,000 miles per second. The correct value is 186,000 miles per second. The difference was due to errors in Roemer’s estimate for the maximum time delay, and an imprecise knowledge of the Earth’s orbital diameter. More important than the exact answer was the fact that Roemer’s data provided the first quantitative estimate for the speed of light.

Of course.

It’s been done many different ways since 1686 when astronomer Ole Roemer deduced the speed of light by observing the eclipses of the Galilean moons of Jupiter. (One of the great deductions in science, in my opinion.) A.A. Michelson’s measurements in the late 1800s were within 0.02% of our current accepted value. And it was consistent with Maxwell’s prediction of the speed of light from his electromagnetic theory - making it clear that what we call light is an example of an electromagnetic wave.

Very often undergraduate physics labs include a speed of light measurement by one or other method.

### Implications of Dark Energy on Distance Measurements

Dark energy, a mysterious form of energy that is driving the accelerated expansion of the universe, has significant implications for distance measurements in cosmology. Here are the key aspects:

#### 1. **Acceleration of the Universe's Expansion**

- **Impact on Distance-Redshift Relationship:** Dark energy affects the relationship between distance and redshift. As the universe expands at an accelerating rate, the redshift of distant objects increases more than what would be expected from a static universe. This complicates the interpretation of redshift data when measuring distances.

#### 2. **Modifying the Cosmic Distance Ladder**

- **Recalibration of Standard Candles:** The presence of dark energy necessitates a reassessment of the distances derived from standard candles like Type Ia supernovae. If the universe's expansion rate changes over time, it can affect the inferred luminosity distances of these supernovae.

- **Incorporating Dark Energy Models:** Different models of dark energy (e.g., cosmological constant vs. dynamic dark energy) can lead to varying predictions for distance measurements, requiring careful calibration and cross-checking with other methods.

#### 3. **Influence on Cosmological Parameters**

- **Determining the Hubble Constant:** Dark energy plays a crucial role in determining the Hubble constant, which relates the distance of galaxies to their recession velocity. Accurate measurements are essential for understanding the universe's expansion history and the effects of dark energy.

- **Density Parameters:** The fraction of the universe's total energy density attributed to dark energy influences the geometry of the universe. This affects how distances are calculated and interpreted, particularly for large-scale structures.

#### 4. **Effects on Cosmic Microwave Background (CMB) Measurements**

- **Distance to the CMB:** Dark energy influences the evolution of the universe before the CMB was emitted. Understanding its effects helps in interpreting the CMB data, which is crucial for measuring distances and understanding the universe's early state.

#### 5. **Challenges in Observational Cosmology**

- **Uncertainties in Distance Measurements:** The effects of dark energy introduce uncertainties in distance measurements, making it challenging to establish a clear picture of the universe's expansion history.

- **Need for Comprehensive Models:** To accurately measure distances affected by dark energy, astronomers require sophisticated models that incorporate dark energy's properties and behaviors, complicating the analysis.

### Summary

Dark energy significantly impacts distance measurements in cosmology by altering the relationship between distance and redshift, necessitating recalibration of standard candles, influencing cosmological parameters, affecting CMB measurements, and introducing uncertainties in observational data. Understanding dark energy is essential for accurately interpreting the structure and evolution of the universe.

You can do it in a microwave … sort of.

But there are a number of things you have to know first. Microwaves are just very long wavelenght electromagnetic radiation … just like light, but much lower frequency and much longer wavelength, but they travel at the same speed. That speed is related to the wavelength and frequency by [math]c=\lambda f[/math].

But your microwave oven has a specific frequency at which it operates - about 2.4 Ghz. And that microwave radiation inside you microwave oven sets up standing waves which cause the molecules of the food inside to vibrate - and that increases their temperature. That’s why you can cook food or boil water or melt a chocolate bar.

Oh, wait, that’s it. Melt a chocolate bar. Well not melt the entire thing, that would be a mess (and a tragic loss of a chocolate bar). But if one places a chocolate bar in a microwave oven for just the right amount of time, they can detect where the maximum intensity of the standing wave is by where the chocolate starts to melt. The distance between two of those maxima is just one-half of a wavelength of the microwaves. Measure that separation, double it, then multiply by the frequency of the microwaves to calculate the speed of light. Does it work? Yes. Is it accurate? What do you think? But accuracy and uncertainty are two different things. There is a lot of uncertainty because where the chocolate bar is starting to melt is not well defined, so the wavelength measurement will have only limited accuracy. But still.

There are other ways, of course, including the first way it was measures by astronomer Ole Roemer in about 1676, but observing the orbits of the moons of Jupiter in a very clever deduction. His answer wasn’t right either (about 70% of the accepted value). But there are many other methods that are.

It is certainly possible to measure the speed of light. There are at least a dozen ways to do it. When I was a kid in high school in the UK in the 1970’s - we actually did the experiment to do it in an 80 minute double-Physics lesson.

I don’t recall the exact details.

Anyway with a laser, a mirror, a light sensor and a decent oscilloscope - it’s a simple experiment.

WHAT IF YOU WANT TO DO IT YOURSELF?

I recently answered a similar question - explaining how you can measure the speed of light using some chocolate chips and a microwave oven!

THE TEENIEST-TINIEST DOUBT:

There is a weird problem with measuring the speed of light - and that is that you can only measure the time it takes to go somewhere and come back again…then divide by two to get the one-way time.

This is perfectly OK - the speed we get from doing that is used throughout physics and things like electronics.

But it is THEORETICALLY possible that light goes a different speed in one direction than when it comes back in the other direction.

There is literally zero evidence that this is true - and it does seem to be MONUMENTALLY unlikely - but there are people who proclaim this to be a major flaw in our knowledge. However, I doubt any serious physicist believes it to be true.

It's Einstein's fault.

The “meter” (or “metre”), and in fact any other unit of length measurement, used to be based on some prototype, whether that's the length of a kings arm, a fraction of the distance between two landmarks, or a physical object like a bar of metal. Because of this definition, you could measure the speed of light with it by timing how long it takes for the light to travel a certain distance (or use wavelength and interference).

But after Einstein discovered relativity, and the fact that speed of light is absolute and invariant, it was no longer necessary to have a separate definition of distance - under relativity, speed of light, time, and distance were inextricably linked and true under all circumstances. The “meter” (or “metre”) was redefined from the inaccurate physical objects of the past to an exact value based on the speed of light in a vacuum.

Because the speed of light (in a vacuum) is taken as a constant, and distances are measured in terms of it; it becomes a chicken-and-egg problem to quantify the measurement - you're measuring the speed of light and quantifying it based on a unit of measurement defined by the speed of light.

That isn't to say you couldn't make the measurement, and use it to compare different measurements of the speed of light in different circumstances - these are the kinds of experiments being used to detect things like gravitational waves, or whether there is an aether. The experiments you do in school are similar - depending on how you look at the problem, you're either measuring the speed of light in air in terms of the definition of a meter based on your instrument (speed will be in your meters per second, and that may or may not match SI meters depending on how good your meter is), or you're measuring your instrument's length using the speed of light in air (this usually means schoolchildren have actually been measuring how good their rulers are, rather than the speed of light)

As long as we hold true that the speed of light (in a vacuum) being invariant, we don't need to measure it, we take it as a universal constant and define other things with it.

It is customary these days to state that we don’t measure the speed of light because it is a standard number, [math]c=299792458 m/s[/math]. This statement is not accurate. That value, [math]c,[/math] is indeed a defined constant of nature called “the speed of light in vacuum” that needs not be measured. It originated from the most accurate measurement of [math]c[/math] with the best definition of the meter [math]m[/math] of that time (1973). Now, that [math]c[/math] is a constant, it is combined with a standard second [math]s[/math] to define the standard meter. It is possible to measure an experimental speed of light [math]v[/math] in various situations and compare [math]v[/math] to the constant [math]c[/math] and look for discrepancies. I will discuss how we measure [math]v[/math] momentarily. Let’s first discuss why we might still need to measure it.

The measured speed [math]v[/math] may vary because of the presence of gases, gravity, quantum fluctuations or even an experimental challenge/validation of relativity constancy of [math]v[/math]. According to relativity [math]v=[/math][math]c[/math] in free-fall vacuum anywhere in the universe and for any light source’s or observer’s velocity. As science and technology advance that error will get smaller. If you measure [math]v[/math] today with the best available tools you’ll find that [math]v = c \pm 1.2 m/s[/math]. If [math]v[/math] is different than [math]c[/math] in ideal vacuum conditions then by our convention [math]c[/math] will remain unchanged and [math]m[/math] will be refined but if for some reason the measurements will find variations of [math]v[/math] vs. [math]c[/math] in different inertial conditions this will force re-examination of relativity or, more likely, will indicate errors in the measurement technique.

To measure [math]v[/math] accurately high stability lasers are used, their frequency [math]f[/math] is calibrated by [math]s[/math] and then the wavelength [math]\lambda[/math] is measured and [math]v=\lambda f[/math]. The wavelengths are calibrated by from the [math]m[/math] which depends on [math]s[/math] and [math]c[/math]. It now remained to be seen whether [math]v=c[/math] using the most refined calibration technique which depends on the constants [math]c[/math] [math]s[/math] and [math]m[/math].