Understanding the Invariant Nature of the Speed Of Light

- E: The speed of light is invariant!

- M: So what? A car travelling with a constant speed also has invariant speed.

- E: But the speed of light is invariant for any observer.

- M: What difference does that make?

- E: Let’s imagine that you are standing by the road with a speed radar and measure the speed of a car going with a constant speed as 50 km/h. Is that ok for now?

- M: As long as you give me the radar.

- E: Alright, now you get into another car which goes with a constant speed of 30 km/h. If you measure the previous car with the same radar once more, what speed will it show?

- M: 20 km/h of course.

- E: Ignoring the minor relativistic effects, you are absolutely correct.

- M: Smarty-pants.

- E: What if I tell you that this simple everyday logic doesn’t work for the light?

- M: What do you mean?

- E: The speed of light is invariant.

- M: For any observer?

- E: Now we are talking.

- M: Even if I travel with half the speed of light?

- E: That would be utterly difficult but even if you could, yes. You would still measure that the light has the same speed.

- M: Even if I travel with the speed of light?

- E: No, you can’t go with the speed of light.

- M: Why not?

- E: You will need infinite amount of energy.

- M: So, there is still a possibility?

- E: No!

- M: Meeh, whatever.

As I tried to explain in this probable conversation, the speed of light has a very strange feature called the invariance. It doesn’t fit into our intuition about the relative speeds of everyday objects as you already read. This feature has appeared in Maxwell’s equations first and has started the relativity era by being the main inspiration for Albert Einstein. Any person who is interested in theoretical physics cannot escape its dazzling temptation and probably tried to find reasoning about what kind of circumstances can lead light to have such a feature.

Obviously, I also did. I have written it as a Quora answer previously but this horizon analogy meant so much to me that it still guides me to reach new answers about the mysteris of the universe and it probably is much more than an analogy, so I wanted to share it once again in my blog. Here is my answer for the quora question;

What is the speed of the light?

This is a question which you will get numerous replies.

To be precise, it is the speed amount that is equal to 299279458 meters per second (Actually, the metric system now gives the definition of 1 meter as the distance covered by light in 1/299279458 seconds in vacuum. So light speed is not that many meters but meter is that many light seconds, which means it is the other way round but who cares about that).

Some will also say that it is the universal speed limit which all the electromagnetic radiation and massless particles are traveling with.

Some will add that it is the conversion factor called c which you can use to convert temporal dimension into the spatial one by multiplying the time amount with it.

Some will even say that it is not possible to reach to this speed rate for the massive objects and it is not possible to exceed it for any object.

It is also known as being measured always the same (called invariant), independent from your own speed, so this will probably also be mentioned.

But all this information is available in many sources and was discussed for the zillionth of time even in Quora, so I assume that you are not looking for these answers, otherwise you could reach them with a simple search.

Therefore, I find it reasonable to add my own non-scientific layman view on this subject hoping that it may give you or to the others some new look.

In my opinion, the key point to solve the mystery of speed of light is to understand its invariant nature. Under which circumstances will you measure the speed of something always the same, independent from your own speed. What kind of setting can cause such result? Let’s start some reasoning on our own.

If you try to catch something which is connected to your body with a length of stick which is longer than your arms, it will keep the same distance from you, doesn’t matter how much you move towards or away from it. This could be a starting point but we face the invariant speed of light phenomena with speed of any light not only with the ones which we are at their source. We face it even if it comes from distant stars. So it must be something else. What always keeps its distance from us all the time, independent from our motion?

There is one similarity between the speed of light and the horizon of the earth. If you measure the distance from the horizon and try to reduce this distance by moving towards it, doesn’t matter how much distance you have covered, how fast you move or accelerate, your distance to the horizon will always be the same. Very similar to invariant speed of light. (To make it a perfect analogy, let's assume that we are travelling in sea where there is no land in our sight, there is no wave or wind, the sky is clear and the sun is just above our head.)

But there is also one problem with this analogy. The example we have given is a displacement based one (distance to horizon) and the one we seek for similarity is velocity based (light speed). Let’s replace every displacement related terms in our first sentence with the velocity based ones in our scenario and see if it fits. Check the below version with the parenthesis and replace them with the bold ones to see the equivalence.

There is one similarity with the horizon of the earth (speed of light). If you measure distance (speed) from (of) horizon (light) and try to reduce this distance (speed) by moving towards it, doesn’t matter how much distance (speed) you have covered (gained), your distance to (speed from) the horizon (speed of light) will always be the same.

So, it seems like it works. This tells me that, if we somehow change our displacement based perception with the velocity based one, in a sense that, if we can take the time derivative of our reality and start to replace the distances with velocity (just like the photons do) maybe, only maybe then we can relate with this example.

Let’s take it a bit further and go into the details of the horizon analogy. If this analogy fits well, then the speed of light shall fit to the other features of the horizon, as well. What are the other features of the horizon? Horizon is actually an illusion created by the intersection of 2 dimensional earth surface with the 3 dimensional space. So if our analogy is correct, then this definition should also fit to speed of light.

Yes, somehow it does. But to see that, we need to change our perception again. You know that if you take the time derivatives of displacement again and again, you will reach to the concepts of velocity, acceleration, jerk, jounce etc. after each derivation (taking its integrals will lead you to absement, absity, abseleration etc., too but it will only make the subject more complicated. So, I will pass that part for now). That means all these concepts are related. Actually they are the same phenomenon derived! from each other. And the common thing among them is time, which is often related with the speed of light. It is not possible to explain all the details here now but if you put all of these and many other thoughts together, you can reach to a conclusion that there is a motion based connection between dimensions, speed of light being the border between them. So according to that, any phenomenon around us which has a constant speed motion (like electromagnetic radiation) has 1 more (4) spatial dimension in addition to the ones that we perceive. You can also take that further and say that any constant acceleration phenomenon has even 1 higher number of (5) spatial dimension than that. If you don’t find out any similar things around you, just think about the gravity causing a constant acceleration all the time. It is also known that the mass is usually referred as the 5th dimension. I don’t know how far can you take this idea since I couldn’t see its limit yet but seems like you can take it further.

If you finally can start to see things around you with those glasses, you will also start to see speed of light differently and your restrictions about speed of light will become different, too. Knowing that it is a horizon, an intersection between the dimensions, you are only able to perceive everything around you up to that speed. Your perception cannot reach beyond it just like the horizon of the earth doesn’t allow us to see beyond it (That can also point out to us that there is a curvature in our universe. But this one is between all spatial dimensions, not limited within the 3 spatial ones that we can perceive). You can keep going towards horizon as much as you want but your distance will stay the same. Similarly, you can increase your speed as much as you want. You can physically pass well beyond that amount defined as speed of light but when you measure the speed of any light around you (like your distance to horizon) you will always get the same value. (This is not my assumption. Any physicist will tell you that it is possible to keep accelerating as long as you have the energy needed for that. They only interpret your speed rate differently and tell you that it will never reach to speed of light. This is due to space-time limiting our perception with horizon of speed of light. After all, what will be your reference at that speed rate? You will keep measuring the speed of any light with the same rate. And that is the same light which lets you to see all the other stars, planets, etc around you which could be a reference to define your own speed. With lack of a good reference, how can you tell what your speed is? This is just like watching an illusion shown to us by the greatest magician of the universe. He is always hiding all the clues away from us. Seems like we are helpless to see beyond that illusion.)

This type of thinking will also tell you that the light and all other electromagnetic radiation are having 4 spatial dimensions as I’ve said before. Just like any intersection between n dimensional object and a n-1 dimensional one, we can only perceive its projection in our 3 dimensional space. This prohibits us from discovering the light’s whole nature. That is also the case with the mass and we cannot perceive the fundamental parts of it since there are barriers made of speed of light between us and them, hiding their big picture. What we see is only the thickness of that big picture’s paper which is its intersection with our dimension.

With this point of view, speed of light is not a feature of the light itself nor a universal speed limit but is the horizon between the curved dimensions of our universe.

8. Using Atomic Clocks to Detect Gravitational Waves

8.  Using Atomic Clocks to Detect Gravitational Waves

(If you somehow have ended up on this page without any background knowledge, before continue, you better know that all below scenario is based on the idea that our universe is expanding in time -4th dimension- direction with the speed of light. You can check the previous 2 posts of: 1. Do We Travel in Time Direction With Speed Of Light and 2. Expansion of the Universe as Travel in Time Direction if you are willing to understand this concept)

Last night I was thinking about gravitational waves while trying to sleep. (thinking about theoretical physics subjects somehow drowse me off, don’t ask me why). As usual, I was using lower dimensional analogies in order to help me visualize the scenario:

In this scenario, A and B are objects which belong to a 1 dimensional world which exists in a 2 dimensional space. That 1 dimensional world is flat by default (1) but it can take a wave form when there is a disturbance like a gravitational wave (2). Since the objects belong to a 1 dimensional world, they can detect the length changes in their own dimension (L) since it extends (i.e. using laser interferometry) but cannot detect the changes in 2nd dimension direction (H). But in the ESOL model which I am trying to figure out in this blog, that direction corresponds to time dimension which I assume we travel with the speed of light. Time dilation happens when 2 objects have different speeds in that direction and 1 of those objects lacks behind the other one. That means, if A and B are no longer on a flat line in that direction, that must correspond to a time dilation effect between those 2, when they are hit by the gravitational wave. If we have atomic clocks, located in the same locations with the laser interferometers and precise enough to detect that time dilation effect, it should provide an evidence for my model.

That thought made me excited and ironically, resulted in an extra sleepless hour:( I decided to write about it this morning but right before start, I wanted to give it a search in the web just to see if anybody else came up with the idea before. The search brought many results like this one.  I was disappointed twice by this finding. It didn’t only mean that I am not the first one to figure this out, it also means that the ESOL model wasn’t needed to come up with this idea. After a short evaluation, I figured out that you don’t need a model with motion in time direction. All you need is a perpendicular extra dimension and associate it with time perception. Current physics is already saying that, so no need for ESOL model for this scenario to be valid.

This concludes my short lived excitement and added another point to the discoveries that  I thought I made first.

P.S. While thinking about why laser interferometers like LIGO has L shape, I think I have found out a flaw in their design.

In a 2 dimensional world that exists in 3 dimensional space, observing the distance variations between 2 perpendicular arms can be enough to detect the waves coming from any direction. This setup will avoid both arms to be on top of a wave at the same time and not being able to detect a wave, even if there is one. In that regards LIGO setup is direction independent but only when located on a 2D world in 3D space. But, in a 3D world in 4D space (3D space in 4D space-time, if you will), there is a chance that 2 arms will be on top of a 3D wave at the same time. (It is visually impossible to imagine but can be comprehended if you start thinking from lower dimensional scenarios).

Perhaps, the designers of LIGO and other interferometers already knew about that flaw and this tiny possibility of missing a wave, if it comes at a bad angle. But considering the really low probability of such coincidence (coming at the exact bad angle) and the difficulty of building a costly vertical arm for such long distances, I would certainly cancel the 3rd vertical arm and take the risk of missing that wave, as well.

7. Our Expanding Universe Might Actually Be Contracting

(If you somehow have ended up on this page without any background knowledge, before continue, you better know that all below scenario is based on the idea that our universe is expanding in time -4th dimension- direction with speed of light. You can check the previous 2 posts of: 1. Do We Travel in Time Direction With Speed Of Lightand 2. Expansion of the Universe as Travel in Time Direction if you are willing to understand this concept)

While I was working on the expanding universe model in 4th dimension, I was also thinking about a contracting model and how would it look like. Obviously, the main difference would be; in a contracting universe in 4th dimension, we would not be observing an expansion in 3 spatial dimensions. But when I think about it further, I found out that a contracting universe in 4th dimension shall exactly look like expanding in 3 spatial ones that we observe. This is how it works:

First thing to consider is; in a 4 spatial dimensional universe, the real expansion (or contraction) happens in 4th dimension direction and what we see in our 3 space dimension is the stretching of this 4 dimensional volumes surface. I have tried to explain it in this previous post , if you would like to understand it better.

Second thing is, this real expansion (or contraction) in 4th dimension direction is somehow related with our time perception. I will try to demonstrate my idea with drawings but as always, I will do it in lower dimensional examples, since nobody is able to draw or comprehend 4 dimensional ones.

So let's have a look at the contracting universe model: Each 1 dimensional circle line below represents our 3 dimensional universe. They contract in 4th dimension direction which is inwards . So each circle with different diameter represents a different moment of our universe, as well.

We will observe 3 distant stars in this universe and how they see each other while the time passes and universe contracts. Let's say each one is 1 million light years away from each other.

Before we start, the most important thing to consider is; when we look at distant stars in space, we are not only looking at far distances, but we are also looking back in time. Further the star we look at, the older version of it we see, since it takes time for light to reach us from that star. This is a well known commonsense information in modern science.

When the light of star B reaches star A1, 1 million years will pass (neglecting contraction effect since it can be minor in such distances). So, in a contracting universe, star A1 observes not star B1 but star B2 If we would like to observe star C from star A1, we will not see C1 or C2 but star C3. It is obvious that further the star we look at, it will look like it is getting away from us. Due to simple Pythagorean theorem application.

You might say, alright, but you don't need a circular and contracting universe for this idea to be valid. any flat universe with linear motion in 4th dimension can have the same effect, then why we need it? Because scientists did not only find out that our universe is expanding but its expansion is accelerating. If the universe was not curved and moving on a linear path, its expansion would be constant. But in this model, due to its curved nature and contraction, the further an object is, the faster its expansion seem to be. But actually you are seeing its past version which was even further than it should be due to contraction in this curved geometry.

Actually when I have figured this out, I have also thought about a universe model inside the event horizon of a non-rotating black hole. If everything inside the event horizon is moving towards singularity with the speed of light, length contraction will be infinitely big, allowing such 4 dimensional universe which is consist of infinitely many 3d universes stack onto each other and it is contracting towards its center. If this model would be valid, due to gravity, each layer closer to the center would be faster. This will cause expansion effect to be even bigger.

If any scientist in future will claim that the expansion of the universe is not only accelerating but this acceleration is even getting faster and faster (having a jerk), then we may start to consider that our universe is only a layer inside the event horizon of a black hole.