# We all accept/believe in $c$. But what happens when light travels away from the center of gravity of a heavy star? Does it slow down?

I'm basically trying to understand a mysterious characteristic of the universe. Why light has to travel at $$c$$? I understand and accept that from experiment. Not arguing that it does not. Just saying that there must be something mysterious that we don't understand that leads to that constant speed $$c$$.

Remember there is no medium. In theory, light could travel at different velocities, as long as it is below $$c$$, but nature chose not to allow that. Why? Not looking for a mathematical proof. I'm looking for a physical explanation of why the universe chooses to be that way. What prevents/enforces/make it a wholly and divine law that light will always travel at $$c$$ in vacuum period. Why can't it travel at $$c/2$$? The mathematics can confirm/predict that, but it cannot explain why things had to be that way, in other words, what mysterious characteristics of the universe demands that this constant $$c$$ be so.

One more observation... I'm trying to make sense of the constant velocity $$c$$ which is always the same (same magnitude) no matter if you are not moving at all or if you are traveling very close to the speed of light. Of course a photon reaches the speed of light and for us it is simply frozen in time. Time does not exist for the photon relativily for us who are at rest observeing the photon passing by. For the phonton time is as normal, without running slowly.

Why does light travel at $$c$$? This comes from Maxwell's equations. The explanation is not trivial and you'll need some background in calculus and E&M to understand it. The upshot is that one can construct a wave equation from Maxwell's equations (which in turn are derived from experiment). The speed of this wave is (it can be read directly from the electromagnetic wave equation):

$$c = \frac{1}{\sqrt{\mu \epsilon}}$$

In a vacuum, we use the values of the permittivity of free space ($$\epsilon_0$$) and the value of the permeability of free space ($$\mu_0$$) (which are in turn both measured experimentally)*, and get the speed of light: about $$3 \times 10^8$$ meters per second. Note what this depends on - only on the properties of free space. If all observers see free space as free space (and they do), they should also get this speed for an electromagnetic wave. That's why the speed of light is constant for all observers.

I'm looking for a physical explanation of why the universe chooses to be that way.

That's more of a philosophical question than a physics one. Physics does not usually seek to explain why the laws of physics are the way they are. They just are. They are what experiment tells us. We don't ask nature why they make the experiment do what it does, we just take it as an axiom.

*Technical note - which physical constants are measured, which are defined, and which aren't, is a subtle question. It's also varied in history, most recently in the 2019 redefinition of SI units. For example, the speed of light in a vacuum is defined to be exactly $$299,792,458 m/s$$. In turn this makes the length of a meter dependent on the definition of a second, etc. Wikipedia's article on vacuum permittivity says that $$\epsilon_0$$ used to be an exact defined quantity, but since the 2019 redefinition it's no longer exact and depends on the permeability $$\mu_0$$. In turn, $$\mu_0$$ depends on the experimentally-measured fine structure constant $$\alpha$$.

• "Physics does not usually seek to explain why the laws of physics are the way they are." One big reason for this is that it is nearly impossible to perform experiments that test the 'why' :) – Marius Ladegård Meyer Oct 16 '19 at 5:32
• Laws, postulates, principles are the axioms physics theories have to pick up from the general mathematical solutions those that fit the data, and very important, are predictive ( if they just fit the data, they are maps , not theories) – anna v Oct 16 '19 at 6:02
• "That's more of a philosophical question than a physics one" That is discutable. I get the point and it is valid, but i feel like this answer is overused nowadays. Searching for why can lead (and in history it a lot of time did) to finding some deeper underlying theory that explains "why" using more fundamental assumptions. Of course you need to start with something and that starting point will always be empirical, but physically it makes always sense to seek some deeper underlying principles. – Umaxo Oct 16 '19 at 6:21
• @safesphere hmm I've understood these numbers as measured - for example for the permittivity, we set up an experiment to measure the forces between charges, and that gives the permittivity. However it seems the 2019 redefinition of SI units screwed this picture up. I'll add a technical note, but leave it at that. – Allure Oct 16 '19 at 7:08
• @Umaxo yes, there is some work on why the laws of physics are the way they are (e.g. as I understand it, part of the point of the string theory landscape is to "explain" why we measure this amount of dark energy). However to my knowledge most of the basic laws - Maxwell's equations certainly qualify - are simply taken as axioms. They work, they're backed by experiment, they make testable predictions that are verified in new experiments, so we believe them ... and don't ask why. – Allure Oct 16 '19 at 7:10

Most of your questions were answered pretty well already, but there are few points that were left out.

For the phonton time is as normal, without running slowly.

That is not so. Relativity cannot give any sense to concept of time or space for the photon. In relativity the notion of space and time are relative, they are just different view on one entity that is spacetime. The spacetime is the mathematical object that describes the "stage of our universe" on which things are happening. We, as subluminal observers, can (artificially, albeit the construction is physically meaningfull) separate spacetime on time and space, but photon can not. But that is nothing to be worried about, because separation to time and space is only, as i said, artificial.

But what happens when light travels away from the center of gravity of a heavy star? Does it slow down?

The gravity is described by general relativity. General relativity tells you, that the spacetime i was talking about is curved. The curved spacetime actually makes separation on time and space even more artificial.

The separation to time and space is done through the notion of simultaneity. That is two events that happened simultaneously you say happened at given time. Then space is set of all the events in the universe that are happening at the same time. But because what is called simultaneous depends on who is defining it, so is the separation on space and time observer dependent.

But in curved spacetime there is (in general) no natural way of defining simultaneity. Great examples are black holes. The distant observer is completly separated from the events happening inside the black hole. So how could he determine wheter his clock showing 9am happened at the same time as some unfortunate astronauts clock inside black hole? He has no way of knowing what is happening inside.

You can still separate universe on space and time, but this time it will be more and more just a mathematical trick the stronger the gravity is (and the further away from yourself you are trying to do the separation). This is of course very vague, but i think it conveys the main message.

That being said, the curved spacetime is not curved too strongly. I mean by that, that if you hide yourself inside small enaugh box, you will not see any curvature inside a box. That is similar to Earth - when you consider only small area (especially in the ocean) the Earth will be flat to high accuracy, even though the Earth is not flat at all. So no matter how strong the gravity is, you can always find box so small that the spacetime inside will appear flat with enaugh accuracy. Then general realivity will tell you that the physics inside your box will be same as if there was no gravity at all. So inside the box (and if it is in free fall you have basically inertial system), you can separate spacetime on space and time and measure velocity of light as distanced traveled divided by time passed. And since the physics inside the box is as if there is no gravity at all, the speed of light is always c no matter how strong of the gravity source there is outside of your small box.

So no, the observer inside the box will not see light slowing down.

But what happens if observer is not inside the box? This observer would also need to measure some distance that light traveled and time that passed and divide it to get speed of light. But as we said, the separation on what is space and what is time becomes more and more artificial the further away you are from the spot you are measuring and the stronger the gravity is. And this kind of speed does not need to be c at all. For example the distant observer looking at the light coming radially away from some heavy star and that is in rest with respect to this star, would see the speed of light to be (given by schwarschild metric): $$c_{distant}=c\left(1-\frac{2GM}{c^2r}\right)$$ where $$c$$ is the speed of light, $$M$$ is the mass of the star, $$r$$ is how far away from the star the light is and $$G$$ is gravitational constant. So yes, this observer would see the light slowing down, but that is only from his point of view. From the point of view of the observer that is right near the light it would still be c.

We all accept/believe in c .

There are no beliefs in physics, there are validations and falsifications through observations and experiments. Physics uses postulates, laws, principles as axioms to pick up the correct mathematical solutions from the general solutions mathematically possible. These axiomatic statements are picked using occams razor,i.e. the simplest possible.

The constancy of c is not a law or postulate or principle, it comes out of the solutions used for studying and preding data, and up to now has been validated in all measurements.

But what happens when light travels away from the center of gravity of a heavy star? Does it slow down?

Because the photons that compose light have zero mass, they follow the geodesic of the space time around the star, with velocity c, as all zero mass particles would.

The mathematics can confirm/predict that, but it cannot explain why things had to be that way, in other words, what mysterious characteristics of the universe demands that this constant c be so.

Basic laws, principles, postulates cannot be explained away, other than they are necessary to describe observations and data and predict new situations. So it it the laws assumed in the physics theories that lead to the conclusion c is constant in vacuum. It is constant because of the laws when using the theory's mathematics. So the "mysterious characteristics" are the laws, which leads us directly to observations, those are the mysterious characteristics. Physics cannot answer existential why?s.

The answer to the central question

But what happens when light travels away from the center of gravity of a heavy star? Does it slow down?

is simple. No it does not slow down, but its frequency decreases.

Suppose you have a collection of fixed observers around a heavy star. In order not to fall into the star, they need to fight the star's gravity. But if they are fixed, they cannot orbit the star, so they need to have rockets that balance the attraction. Or they could all be tied to a very long rope which is anchored to some very massive object so far away from the star that its gravity is negligible there, so it stays fixed and keep the whole rope fixed (it must be a very long and strong rope).

Let the lowest observer send a laser beam upwards, of a given frequency. Each observer up the line intercepts a small fraction of the beam and leaves the remainder go up. Each one will find a frequency lower than the observer below him. However the frequency does not keep decreasing indefinitely. Once one is far enough from the star, the frequency is essentially constant.

In fact this experiment can actually be made on Earth.

Mössbauer spectroscopy is so precise that it can show the change of energy (which is proportional to its frequency) of a gamma ray observed a few meters above or below its point of emission.