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I know that the speed of light remains constant irrespective of whether the light source is moving or not. But it's very difficult for my brain to visualize it. Light has dual characteristics, i.e. of both waves and particles, thus how can it be possible if a light source is moving near the speed of light that its emitted light will not reach more than $c$? (I know, as per Einstein, time slows down for moving objects.)

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  • $\begingroup$ This might be helpful: physics.stackexchange.com/q/230703/249968 $\endgroup$ – Johan Liebert Jan 14 at 1:29
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    $\begingroup$ One way to help visualize it, is to think of the photons being taken away instead of being emitted. No matter how fast the source is moving, all the photons are carried away at the same speed in every direction. $\endgroup$ – Bill Alsept Jan 14 at 2:06
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    $\begingroup$ Does this answer your question? Why and how is the speed of light in vacuum constant, i.e., independent of reference frame? $\endgroup$ – Alfred Centauri Jan 14 at 2:16
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    $\begingroup$ ARPAN, I've downvoted your question for the "does not show any research effort" reason. There are quite a few similar if not exact duplicates of your question here but you do not mention why none of these sufficiently address your concerns. $\endgroup$ – Alfred Centauri Jan 14 at 2:20
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    $\begingroup$ You have to give up the idea of invariance of simultaneity. The property of two events being simultaneous is depend on your speed and what direction you are moving in relative to those events. This is the key step to being able to visualize special relativity... but it is very hard. The invariance seems pretty hardwired in our brains. Einstein was the first to see it even if the math had been around already for awhile. And giving it up allows your question to be answered in a visual way. $\endgroup$ – Mike Wise Jan 14 at 10:19
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Why is the speed of light independent of the speed of the source?

There is nothing peculiar at all here. This is not where special relativity or quantum mechanics comes in. This is, in fact, the standard behavior of all wave phenomena, i.e., the speed of a wave depends only on the medium and not on the source. For example, the speed of the sound wave from a loudspeaker traveling at $50 \text{ m/s}$ and that of the sound wave from a loudspeaker at rest are both the same. This is just plain old wave mechanics, nothing peculiar here.

This is very intuitive to understand too. The propagation of a wave is a mechanism that takes place in the medium. The source only initiates the disturbance, the propagation of that disturbance is what the wave is. This process of propagation happens in the medium and thus, the speed of this propagation (i.e., the speed of the wave) depends entirely on the medium.

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    $\begingroup$ ... except there is no medium for the light. Aether-related theories failed long ago. That's what is counter-intuitive in light. $\endgroup$ – fraxinus Jan 14 at 10:43
  • $\begingroup$ Apparently @Dvij Mankad supports Lorentz Ether Theory, which is empirically equivalent to SR and assumes existence of medium or Ether. in which light propagates. +1. Indeed it is not quite clear how light can propagate in nothing, that’s why there are so many upvotes. $\endgroup$ – Albert Jan 14 at 11:00
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    $\begingroup$ I'm not supporting Lorentz ether theory (which, by the way, is not equivalent to SR in any shape or form). Light propagates in vacuum. It doesn't need a material medium. That is the whole point. That electromagnetic waves do follow wave mechanics but they don't need a material medium to propagate. $\endgroup$ – Dvij Mankad Jan 14 at 12:19
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    $\begingroup$ The electromagnetic field is the "medium" and the wave propagates according to the Maxwell equations. This is quite similar to air being the medium of sound and sound propagating according to equations that describe how air molecules interact. You could say that in Newtonian world, the Maxwell equations have a preferred reference frame. However, SR actually tells that the Maxwell equations do not have a preferred reference frame, so I don't quite agree with this answer. $\endgroup$ – JiK Jan 14 at 13:27
  • $\begingroup$ @JiK The question of a preferred frame is a different one. It has nothing do with the dependence of the speed of light on its source. It has to do with the dependence of the speed of light on the frame of reference. $\endgroup$ – Dvij Mankad Jan 14 at 13:34
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You can see the mathematics about the velocity addition formula and say, wow this is how it works. But you are asking why?

We use mathematics to describe the real world, and not the other way around. And you are correctly asking for a down-to-earth explanation why reality is like that. Your intuition tells you that if the light source moves in space at speed let's say 0.9 c, then the emitted light from the source should move at a speed that adds the speed of the lightsource (that sped up to 0.9 c) and the speed of light, because the light already has a headstart.

In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.

https://en.wikipedia.org/wiki/Velocity-addition_formula

You are thinking about this the wrong way. First, after the big band, there were only massless particles (sea of photons), all moving at speed c in vacuum. This was the only speed.

Now to slow down from this speed in the spatial dimensions, you need to gain rest mass. Some particles (and objects) gained rest mass and their spatial velocity decreased to slower than c.

Now in your case one of these objects moves at let's say 0.9 c, so relative to the only speed for massless particles, it is 0.9 times slower.

This object emits light. These massless particles as they are emitted, start moving at the only allowed speed they can, c.

In this case, there is no wrong intuition. The massless particles that are emitted cannot go faster than c, since this is the only speed. Everything else (that has rest mass) moves relative (slower) to them.

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    $\begingroup$ You make an excellent presentation of what science does. Describe rather than explain. But as far as the question is concerned, you only "kick the can down the road". Why was $c$ the only speed in the early universe? Why must the emitted photons travel at that speed? The truth of the matter is: nobody can answer the question. Physics does not address the question "why". One of the few things that we can say for certain is that our intuition and common sense does not apply to things that move very fast, or things that are very small. $\endgroup$ – garyp Jan 14 at 3:32
  • $\begingroup$ @garyp yes you are correct. $\endgroup$ – Árpád Szendrei Jan 14 at 3:34
  • $\begingroup$ @garyp "Why must the emitted photons travel at that speed? The truth of the matter is: nobody can answer the question." - Not at all. The answer is actually very simple. In hyperbolic geometry of spacetime, space and time are related in such a way that the speed of time can be defined. Photons don't move in time, they move with time at the speed of time. We call this speed "the speed of light" historically, but it really is the speed of time. It is unity in natural units, e.g. one lightsecond per second and is constant since your time rate measured by your own clock is always the same. $\endgroup$ – safesphere Jan 14 at 8:03
  • $\begingroup$ @safesphere Good comment. Let me ask you a question: why is the geometry of time and space hyperbolic? $\endgroup$ – garyp Jan 14 at 11:22
  • $\begingroup$ @garyp In space you can move forward and back. In time you can move only forward, because moving back in time would violate causality. This fact makes spacetime hyperbolic. When you derive coordinate transformations using a very simple math and obvious assumptions, you get 4 possible choices of the structure of spacetime defined by the speed of time: Eucledian (imaginary $c$), Galilean (infinite $c$), dual to Galilean (zero $c$), and hyperbolic Minkowskian (finite $c$). These are the only 4 choices mathematically available. Then we simply test experimentally to see that the first 3 don't work. $\endgroup$ – safesphere Jan 14 at 14:58
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Please note that I have limited scientific knowledge. This is only a popularized explanation that helped me understand that concept. Take this for what it is, it may be inaccurate or very simplified.

The problem is that our real life definition of "speed" is flawed when talking about photons.

Space-time has 4 dimensions, time being one of them. Every single object (not only photons !) in this space-time moves at the same speed, c. What this means if that the length of the vector used to represent this speed is always c. Its direction varies, though. So the length of its components in each dimension vary. Let's call these x, y, z and t. What is really important here is the value of t.

For all real life objects, t values are extremly similar and extremly close to c. They "move" at almost full speed in time, but very slowly in space. That's why it makes sense to consider "time speed" as a constant and measure how x, y and z vary depending on the position in time. That's what our real life definition of speed is. That's why we get the illusion that objects can move at different speeds. They do, but in 3D space, not in 4D space-time.

This definition of speed does not make any sense for photons, because in their case t = 0 ! Our definition considers the position of photons in the 3 dimensions of space depending of their position in time. But their position in time never changes ! The idea of "speed of light" based on what we usually mean by "speed" is absurd, that's why it seems incoherent.

Here is my source, it's a video in french but has english subtitles : https://www.youtube.com/watch?v=kELX0GEQ0H0

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Imagine people flying over a lake, tapping the water quick enough so only a ripple emanates from it. It doesn't matter how fast or slow people are going, the speed of the ripple stays the same. You are in the lake's frame, other people would see it from their own lake's frame, everyone has their own lake that they see others touch (this may seem weird but relativity describes reality for us, not the other way around). And if you want a particle representation, you can think of dividing the ripple into wave packets (again, this may seem weird but quantum mechanics gives us a new picture of reality, what we see is described by it, not the other way around).

Maxwell's equations predict a speed of light from a source, and Einstein showed that the laws of physics are the same for any inertial frame, thus the speed is the same for everyone, no matter how fast or slow they are moving.

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    $\begingroup$ A nice image. A key point is that light emitted is not being pushed by the source or by later light emitted. Once emitted, it just travels at the speed physics requires. $\endgroup$ – Paul Sinclair Jan 14 at 14:57
  • $\begingroup$ This example seems pretty non-intuitive to me. The ripple only stays the same in a frame stationary to the ripple. For a moving observer, the ripples would have a different relative speed depending on the observers velocity, which is where it really starts to fall apart from the speed of light analogy IMO. $\endgroup$ – JMac Jan 14 at 15:04
  • $\begingroup$ @JMac it's never going to be that intuitive without the math explaining things (which when people say intuitive, they seem to want to avoid), I edited it. Though one could say the speed measured within the lake would be the same for everyone, moving or not, this would imply a medium for light. So lets just give everyone their own lake. $\endgroup$ – user234190 Jan 14 at 15:15
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It is one of Einstein postulates.

Scientific answer on your question based on velocities additional formula: $$ V^\prime = \frac{V+u}{1+Vu/c^2} $$

If $V=c$ then $V^\prime = c$.

To understand more deeply you need use Maxwell theory. As convenience of this theory, speed of light is constant in any system frame. This laws was discovered experimentally.

Some physical phenomena have not daily-life analogue, we only try to describe nature around us.

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The wave-particle duality of photons (or other particles) is I think not relevant for this question.

I won't try to answer the 'why' part of your question, but I will give a description that should help you intuitively grasp how it is possible that light emitted from a moving source appears to travel at the speed of light in any frame of reference.

description 1:

Say there is an observer standing on earth and standing still. A starship flies past, at a speed of 0.9 c, i.e. 90% of the speed of light. Define $T_0$ as the moment that the starship is exactly overhead. At that moment $T_0$ the starship fires a laser pulse forward.

Now, at $T_0 + 10$ seconds, in the reference frame of the observer, the starship will have traveled 9 light seconds, and the laser pulse, traveling at the speed of light, will have traveled 10 light seconds.

As you mentioned, time passes more slowly for an object traveling at high speed. Therefore, when according to the observer 10 seconds have passed, according to the starship pilot only 1 second will have passed. The distance between the starship and the laser pulse at that moment is one light second, which is exactly what the pilot would expect, having fired the laser (in his frame of reference) 1 second ago.

This description probably does not match entirely with the numbers that the equations of relativity would give you, but it gives an intuition.

Apart from time passing more slowly for a fast moving object, you may know that a fast moving object also becomes smaller in the direction it is traveling in. This allows for a different description of the above situation.

description 2:

We have the same situation as in description 1. A starship flying at 90% of the speed of light passes by the observer at $T_0$ and at that moment fires a laser pulse forward. After 10 seconds, according to the observer, the starship has traveled 9 light seconds and the laser pulse 10, so all is fine.

The starship is nominally 300 meters long, or 1 millionth of a light second. However because it is traveling very fast, it appears compressed in the direction of travel, so to the observer the starship only looks like it is 30 meters long. At $T_0 + 10$ seconds the laser pulse looks like it has traveled 10 light seconds according to the observer, or ten million times the nominal length of the starship. According to the pilot of the starship, the laser pulse has also traveled ten million times the length of his ship (which does not appear compressed to him), and therefore the laser pulse has traveled 10 light seconds in 10 seconds, so it is moving at the speed of light just fine.

The observer will agree with the pilot that the distance between the ship and the laser pulse is ten million times the currently observed length of the starship, but according to the observer that works out to 1 light second. Both the pilot and the observer thus agree that the pulse is traveling at the speed of light relative to them.

The two descriptions don't agree with each other, and if you apply them to more complicated situations they will break down. In the actual physics of relativity both effects play a role (as far as I know). But these descriptions may give you an intuition on how it is possible for observers in different frames of reference to all observer light as traveling at the speed of light.

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