Relativity and speed of light basics

[starstruck_]

I decided to read up on the chapters we didn’t cover in first year Physics from my textbook, and decided to start with general relativity since it was in the same section of the textbook as the last topic we covered (that topic was physical optics - not lenses- photons and the double slit experiment and so on).

I 100% do not understand the whole speed of light light portion of it// why all observers observe it at the same speed.

From previous knowledge, I know that the velocities we have dealt with were relative to something. If we were moving within our frame of reference then the velocities would change accordingly.

Light doesn’t follow that. No matter whether the observer is moving or not, the speed of light remains constant in a constant medium.

So does that mean that the speed of light is relative to the medium it is traveling through and not to objects traveling to or away from a source of light? ((I think I’m understanding this wrong))

Also does it have anything to do with the amount of medium between the object and the light source.

If the speed of light depends on the medium it is traveling through, then only a certain number of photons could exist within a given volume of the medium at a certain time, right? Or is that wrong?

If a car is moving toward the light source, then the amount of medium between the light source and car is reduced but so is the number of photons there so the light that is still approaching the car would be approaching it at a constant speed?

I don’t really know what I’m talking about, I’m just trying to make sense of this. I watched a video on it that seemed helpful but I’m a little slow so it hasn’t made any sense.

If someone could explain this from scratch (sorry if it’s asking for a lot) that would be extremely helpful!

 

[ZapperZ]

Just so you are aware of it, this is not General Relativity, this is Spacial Relativity.

Zz.

 

[Orodruin]

From previous knowledge, I know that the velocities we have dealt with were relative to something. If we were moving within our frame of reference then the velocities would change accordingly.

This is the expectation from classical mechanics and its corresponding Galilei transformations. (Also note, you are not moving "within your reference frame". The more correct statement would be that you are moving relative to some reference frame.) That does not mean that it must be correct and in fact it is not what is observed for light.

Light doesn’t follow that. No matter whether the observer is moving or not, the speed of light remains constant in a constant medium.

There is no medium. The statement that the speed of light is invariant is in regards to the speed of light in vacuum. If you have a medium, then there will be a certain drag coefficient. One of the deeper insights from SR is that there need not be a medium for light to propagate, which led to the idea of a luminiferous aether being scrapped.

Also does it have anything to do with the amount of medium between the object and the light source.

Again, there is no medium

If the speed of light depends on the medium it is traveling through, then only a certain number of photons could exist within a given volume of the medium at a certain time, right? Or is that wrong?

I don't know where you got that from. It is certainly wrong. I also strongly suggest that you leave photons out of it for the time being. It is not worth thinking about photons unless you start doing quantum field theory.

I don’t really know what I’m talking about, I’m just trying to make sense of this. I watched a video on it that seemed helpful but I’m a little slow so it hasn’t made any sense.

Unless you tell us which video you watched, how are we to know what you saw or whether the problem is in your interpretation or in the video itself? Please provide appropriate references.

If someone could explain this from scratch (sorry if it’s asking for a lot) that would be extremely helpful!

Explaining from scratch would entail effectively writing a textbook on relativity. This has already been done and there are several good textbooks available. It is not what forums are for. If you have specific questions regarding what you read in those textbooks, please feel free to ask for clarification.

 

[sophiecentaur]

100% do not understand the whole speed of light light portion of it// why all observers observe it at the same speed.

There isn't an answer to any of the "why" questions that people ask about Science. Without going into details , all we can say is that assuming the invariant speed of light fits the evidence of experiments (not under normal conditions).
Try this link and avoid skipping too much. It could help. It is not intuitive stuff, remember.

 

[Nugatory]

Light doesn’t follow that. No matter whether the observer is moving or not, the speed of light remains constant in a constant medium.

The speed of light in vacuum is the same for all observers. The speed of light in a medium is not. You should concentrate on the vacuum case because it's much easier and you have to understand it before you can take on the more complicated problem of the behavior of light in a medium.

If A and B are moving relative to one another, then A can consider himself to be at rest while B is moving relative to him, or the other way around. Thus, any time that you say something is moving, you have to say what it is moving relative to. But no matter who you consider to be at rest, the speed of light in a vacuum will be the same relative to that observer.

 

[Dale]

I 100% do not understand the whole speed of light light portion of it// why all observers observe it at the same speed.

I don’t think that there is a good reason why for this in science. (Science is notoriously bad at answering why questions). Relativity does not explain why c is invariant. Instead, it assumes that c is invariant and examines the consequences of that assumption. All of the famous relativistic effects are the result of making that assumption.

 

[Ibix]

@starstruck_ - Maxwell's equations predicted an invariant speed of light in vacuum. That is, the speed of light was always the same, no matter what the emitter or the observer was doing. This was obviously daft, and much of physics in the latter half of the 19th century boils down to trying to spot the problem with Maxwell's work. Presumably it was a special case of something.

This turned out to be completely wrong. Einstein simply took this daft idea that light always moves at the same speed and worked out the consequences if he assumed it was right. That's special relativity, in a nutshell. All the equations reduce to familiar Newtonian forms when everything is moving much slower than light, but that means Newton is the low-speed limit of a more general theory.

The important difference between the two is that relativity doesn't have an absolute notion of time. If we are moving relative to one another we will both determine that the other's clock is ticking slowly, and we will both determine that clocks on the front of the other's vehicle are out of sync with clocks on the rear (note I'm carefully saying "determine" because I'm assuming we're both smart enough to correct what we see for the travel time of light). The first concept (time dilation) is quite famous, but the latter (relativity of simultaneity) is probably more important to get your head around.

That's a very brief intro. It is extremely counter intuitive. May I ask what textbook you are looking at?

 

[jartsa]

From previous knowledge, I know that the velocities we have dealt with were relative to something. If we were moving within our frame of reference then the velocities would change accordingly.

Yes, and that is wrong.

Let's consider Bob, who is swinging in a swing, and Alice who is traveling at speed 0.87 c relative to Bob (I mean relative to the ground that the swing is standing on). Swing's maximum speed relative to ground is 0.5 m/s. So ground's delta v according to Bob is 1m/s.

Oh yes, Bob is swinging along the x-coordinate and Alice is moving along the x-coordinate.

Now we want to calculate how much Alice's speed is changing according to Bob.

First let's calculate how much Bob's speed changes according to Alice: Answer is 0.25 m/s. (Because in Alice's frame Bob is swinging at half rate,compared to Bob's frame, and the swinging distance is halved too, compared to Bob's frame)

So Alice's speed changes by 0.25 m/s according to Bob, because Bob and Alice always agree about their relative speed.

 

[starstruck_]

Just so you are aware of it, this is not General Relativity, this is Spacial Relativity.

Zz.

Ohh sorry, didn’t know, I was assuming this might be a part of a second year course.

 

[starstruck_]

There is no medium. The statement that the speed of light is invariant is in regards to the speed of light in vacuum. If you have a medium, then there will be a certain drag coefficient. One of the deeper insights from SR is that there need not be a medium for light to propagate, which led to the idea of a luminiferous aether being scrapped.

Again, there is no medium

Okay so the medium isn’t a part of this, this only has to do with the speed of light in a vacuum and working under that assumption?

I don't know where you got that from. It is certainly wrong. I also strongly suggest that you leave photons out of it for the time being. It is not worth thinking about photons unless you start doing quantum field theory.

Unless you tell us which video you watched, how are we to know what you saw or whether the problem is in your interpretation or in the video itself? Please provide appropriate references.

Also, sorry, the video didn’t explain the speed of light//observing question I had, it explained time dilation which didn’t answer my question. I was just trying to understand why, please ignore that gibberish.

This is the video:
I understood the time dilation part. It was just the question I had about observing the speed of light part but I guess, looking at other answers, there is no answer to that question.

 

[stevendaryl]

I understood the time dilation part. It was just the question I had about observing the speed of light part but I guess, looking at other answers, there is no answer to that question.

Well, if light has a constant speed in one frame, then time dilation would insure that it also has the same constant speed in every frame. That's sort of the reverse of the usual logic, which derives time dilation from the constancy of the speed of light.

 

[ZapperZ]

@starstruck_ : I started a thread on MinutePhysics videos on Special Relativity. It also include videos on the same topic by Fermilab's Don Lincoln. Maybe you should start with those videos first.

https://www.physicsforums.com/threads/minutephysics-special-relativity-series.938686/

Zz.

 

[starstruck_]

Well, if light has a constant speed in one frame, then time dilation would insure that it also has the same constant speed in every frame. That's sort of the reverse of the usual logic, which derives time dilation from the constancy of the speed of light.

Sorry, I’m probably uh understanding this wrong ((again)), so we’re just going backwards and saying that since time dilation is a thing and the time observed for either observer is different, the speed of light is constant?

 

[ZapperZ]

Sorry, I’m probably uh understanding this wrong ((again)), so we’re just going backwards and saying that since time dilation is a thing and the time observed for either observer is different, the speed of light is constant?

We are not mixing the chicken and the egg.

Time dilation concept is a consequence of light having the same speed in all inertial reference frame, not the other way around.

Zz.

 

[stevendaryl]

We are not mixing the chicken and the egg.

Time dilation concept is a consequence of light having the same speed in all inertial reference frame, not the other way around.

Zz.

Well, if light has a constant speed in one frame, then you'll have time dilation for light clocks that are moving with respect to that frame. For light clocks, you don't need to assume that light has the same speed in every frame. Of course, you don't get (without further assumptions) that every physical process experiences the same time dilation.

 

[stevendaryl]

Well, if light has a constant speed in one frame, then you'll have time dilation for light clocks that are moving with respect to that frame. For light clocks, you don't need to assume that light has the same speed in every frame. Of course, you don't get (without further assumptions) that every physical process experiences the same time dilation.

Actually, to get time dilation for light clocks, you need to assume something about how lengths transform between frames. So I guess time dilation doesn't just pop out.

 

[ZapperZ]

Well, if light has a constant speed in one frame, then you'll have time dilation for light clocks that are moving with respect to that frame. For light clocks, you don't need to assume that light has the same speed in every frame. Of course, you don't get (without further assumptions) that every physical process experiences the same time dilation.

But SR did not start with "time dilation".

We all need to go back to the SR postulates, which are the starting point of SR.

https://www.nobelprize.org/educational/physics/relativity/postulates-1.html

Without those postulates, we do not have SR. Time dilation is a consistent outcome of the postulate that c is a constant in all inertial frame. Otherwise, we will be doing Galilean transformation.

Zz.

 

[Dragon27]

It's just a way to construct a theory through logical reasoning. We can also start with space-time with certain properties and derive everything from there (including the constancy of the speed of light). It doesn't matter. What matters is the resulting theory and its logical consistency, non-self-contradictiveness (is that a word?). Time dilation and light-speed invariance are both part of it at the same time.

 

[ZapperZ]

What matters is the resulting theory and its logical consistency, non-self-contradictiveness (is that a word?).

Actually, for science, what matters the most is that it matches experimental observations. A theory can be as logically consistent and esoterically beautiful, but it is useless if it doesn't match empirical evidence. History of physics is littered with such theories that failed this criteria.

Zz.

 

[jtbell]

I decided to read up on the chapters we didn’t cover in first year Physics from my textbook,

Which textbook is this? Title and author(s)? Someone here might actually be acquainted with it or have a copy, and can help with specific rough spots in it.

 

[vanhees71]

It's just a way to construct a theory through logical reasoning. We can also start with space-time with certain properties and derive everything from there (including the constancy of the speed of light). It doesn't matter. What matters is the resulting theory and its logical consistency, non-self-contradictiveness (is that a word?). Time dilation and light-speed invariance are both part of it at the same time.

For me, the most convincing way to "derive" SR is to investigate all spacetimes which obey the special principle of relativity (existence of a class of global inertial frames) and that any inertial observer finds space to be described as a Euclidean affine manifold. From these assumptions you get two basic kinds of spacetime, the Galilei-Newton spacetime underlying Newtonian physics (no limiting speed) and Einstein-Minkowski spacetime underlying special relativistic physics (with limiting speed). Which one of the two possibilities describes the observations better (approximately of course) is then a matter of empirical validation, and it's very clear that the special-relativistic description is way better than the Newtonian one, which is however valid as an approximation for low speeds and accelerations. SR itself is also only approximate, because as soon as gravity becomes important (which due to its weakness is only rarely the case in some sense, which is why we can deal very well with Newtonian physics in everyday life) one has to take into account general-relativistic spacetime.

 

[Mister T]

Light doesn’t follow that.

Don't focus on light. Focus on a speed. There's a speed that's the same regardless of the state of motion of an observer. It's just that we believe light travels at this speed, but even if it didn't nothing would change, there would still be a speed that's the same for all observers.

Philosophically you can ask why this is true, but all we can really do in the way of a response is to look at the implications of it. And then look at Nature to see if it behaves in a way that's consistent with it.

Lots of books have been written explaining special relativity. Find one you like and read it. It's a much more satisfying experience than asking to have it explained. Of course, if you get stuck on something come here to ask about it. That's the best way to do it.

 

[Dragon27]

Actually, for science, what matters the most is that it matches experimental observations.

Yes, of course, though I was talking specifically about that.

 

[pervect]

I decided to read up on the chapters we didn’t cover in first year Physics from my textbook, and decided to start with general relativity since it was in the same section of the textbook as the last topic we covered (that topic was physical optics - not lenses- photons and the double slit experiment and so on).

I 100% do not understand the whole speed of light light portion of it// why all observers observe it at the same speed.

You just stated the basic idea correctly, that the speed of light is constant for all observers. So your difficulty isn't as simple as not understanding it, it's that you're resisting the idea for some reason. It may be as simple a reason as "this isn't the way things used to work", or there may be more subtle reasons why you're resisting the idea.

Your musings about a medium do not seem to be part of the textbook. I would guess that they are a part of you resisting the idea that the speed of light is constant for all observers.

IT's not clear at this point why you are resisting the idea so strongly - it could be as simple as that it's a new idea, but it's probably more complicated than than that. There are many possible sources for your resistance, most of them are common, but they aren't necessarily exactly the same from person to person, so it's hard to guess what they might be in order to address them. There are some common stumbling blocks, it's not clear if you've gone far enough down the road of understanding relativity to stumble over them yet, though.

The main point I want to make is that you seem to understand the basic idea OK (before you start to try to distract yourself with personal musings about a medium, at least). You just don't want to accept it - not even on a provisional basis, which is at this point is all that's required, a very provisional acceptance and a willingness to explore the logical consequences of this strange assumption.

As for the "why" of it all, it boils down to "because it matches observations". At some point you can eventually start looking at some of the experiments that relativity explains, and that classical mechanics does not, such as the Michelson-Morley experiment.

 

[Erribert]

I don’t think that there is a good reason why for this in science. (Science is notoriously bad at answering why questions). Relativity does not explain why c is invariant. Instead, it assumes that c is invariant and examines the consequences of that assumption. All of the famous relativistic effects are the result of making that assumption.

Erribert: I have gone through the derivations of both special and general relativity and too have some questions. Since this is special relativity, I will continue with where you left off. Einnstein’s Second Postulate (since he provides no references in his paper) is that the speed of light is constant in a vacuum. Einstein did not have access to satellite data we have today.

According to articles I have read from NASA and others, there appears to be a lot of plasma in our solar system. There is also “dust”. Could these act as mediums? If so, wouldn’t the speed of light vary.

I am far from well educated in this, and am not a physics experimentalist in this area. What would be the impact of plasma, solar winds, and dust on the speed of light. Why did Einstein like the idea of it being constant? Have experiments in earthly laboratories confirmed this?

Cheers

 

[jbriggs444]

Have experiments in earthly laboratories confirmed this?

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

 

[Erribert]

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

Thank you for the link. Most helpful. I will go through it.

 

[Ibix]

Why did Einstein like the idea of it being constant?

The invariance of the speed of light in vacuum was a prediction of Maxwell's equations, and is incompatible with Newtonian mechanics. Everyone was trying to fix Maxwell's equations to be consistent with Newton; Einstein had the idea of replacing Newton with something consistent with Maxwell.

 

[ZapperZ]

The invariance of the speed of light in vacuum was a prediction of Maxwell's equations, and is incompatible with Newtonian mechanics. Everyone was trying to fix Maxwell's equations to be consistent with Newton; Einstein had the idea of replacing Newton with something consistent with Maxwell.

Actually, this isn't true.

Maxwell equation gives "c", but it doesn't tell you that it is invariant. In fact, Maxwell equations at that time were not invariant under Galilean transformation, and that was the impetus for Einstein to come with SR.

Zz.

 

[kent davidge]

and that was the impetus for Einstein to come with SR

I thought it was Lorentz who came up with the theory through his Lorentz Transformations that keep the wave equation invariant.

 

[m4r35n357]

I thought it was Lorentz who came up with the theory through his Lorentz Transformations that keep the wave equation invariant.

As Ibix has pointed out, the transformation was known, but Lorenz was trying to force light and EM to behave in a Newtonian way. These attempts were getting quite silly towards the end, so I'm not surprised that Einstein didn't refer to their work ;)

 

[Mister T]

The invariance of the speed of light in vacuum was a prediction of Maxwell's equations, and is incompatible with Newtonian mechanics.

Actually, this isn't true. Maxwell equation gives "c", but it doesn't tell you that it is invariant.

You also need the assertion that all inertial reference frames are equivalent. That, combined with Maxwell's electromagnetism, gives you invariance of the speed of light. It was Einstein who demonstrated this. Lorentz didn't.

 

[bahamagreen]

My rather blunt understanding is that Galilean thinking was local principles of mechanics would look the same to each individual inertial observer, Maxwellian thinking was that local principles of electromagnetism would look the same for each individual inertial observer, and that Einstein was perhaps the first to realize a choice needed to be made in order to avoid a paradox when attempting to make these local principles look the same when distributed among all possible inertial observers... the dilemma being that either the principles will look different for different inertial observers, or that the principles will look the same for all inertial observers if time, space, and simultaneity are allowed to do something new. This latter choice assumes constant c for all inertial observers and the "something new" being special relativity with all it's consequences.

 

[f todd baker]

Perhaps you would find that the principle of relativity, the laws of physics are the same in all inertial frames of reference, is easier to swallow than the constancy of the speed of light. Maxwell's equations predict the speed of light in a vacuum to be c≈3x10⁸ m/s in my laboratory and I have done every experiment I can think of to verify that Maxwell's equations are correct. Maxwell's equations are laws of physics. Therefore the laws of electromagnetism, including the speed of light, will be the same in any other inertial reference frame. In other words, the constancy of c is a necessary consequence of the principle of relativity.

 

[Orodruin]

Maxwell's equations predict the speed of light in a vacuum to be c≈3x108 m/s in my laboratory and I have done every experiment I can think of to verify that Maxwell's equations are correct. Maxwell's equations are laws of physics. Therefore the laws of electromagnetism, including the speed of light, will be the same in any other inertial reference frame. In other words, the constancy of c is a necessary consequence of the principle of relativity.

This does not logically follow. For example, Maxwell's equations could be the manifestation of the laws of physics in the rest frame of a medium, let us call it aether, where the speed is the same in all directions much like sound waves have the same speed in all directions in the sound medium's rest frame but not in a frame where it is moving. Of course, you then end up with trying to measure your movement relative to the aether and will be surprised to find that you are in the aether rest frame. People tried to do this for a long time before a more elegant solution was suggested, that the reason that we find the speed of light being the same in all directions is that the speed of light indeed the same in all directions in all frames and that there is no need for a medium.