Speed of light relative to observers?

[dayalanand roy]

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I am not a physicist, so I cannot make a comment. I can only put my doubts and views.
In most of the explanations or examples of time dilation given on internet, the source of light and the ray of light emitted from it travel in the moving ship/carriage/rocket itself. In this condition, should the light source not suffer from inertia itself? And does the ray of light moving in the ship actually exhibit the peculiar behavior of the constancy of light's speed? To clarify this doubt, I consulted the Einstein's book-'Relativity- the special and general theory'. In unit VII, Einstein uses a somewhat similar example, that of a railway carriage, but his ray of light is not propagating inside the railway carriage. Instead, it is traveling on the embankment. I think it to be the more suitable example, as the source of light will not suffer from inertia here, and the constant value of c, when measured from the carriage and the embankment both, will show the real peculiar behavior of light speed and time dilation.
However, I agree that even in the example given in this post, when the time taken by light is measured by two different observers located in two different reference frames, time dilation effect will be exhibited.
regards

 

[mfb]

What does "suffer from inertia itself" mean?

And does the ray of light moving in the ship actually exhibit the peculiar behavior of the constancy of light's speed?

It does not matter where it moves and who measures its speed, the result is always c (as long as it moves in vacuum).
Why do you expect a difference between "moving on top of the train" and "moving inside the train" as long as it does not have any physical connection to the train? What does "inside" even mean if we remove windows, the ceiling, walls and so on? Remember: all those thought experiments happen in vacuum. We do not need the train, floating light sources would work as well.

 

[HallsofIvy]

[Mentor's note: Split off from this thread]
Distinguished members
I am not a physicist, so I cannot make a comment. I can only put my doubts and views.
In most of the explanations or examples of time dilation given on internet, the source of light and the ray of light emitted from it travel in the moving ship/carriage/rocket itself. In this condition, should the light source not suffer from inertia itself?

No, it doesn't.

And does the ray of light moving in the ship actually exhibit the peculiar behavior of the constancy of light's speed?

Why do you refer to this as "peculiar" behavior?

To clarify this doubt, I consulted the Einstein's book-'Relativity- the special and general theory'. In unit VII, Einstein uses a somewhat similar example, that of a railway carriage, but his ray of light is not propagating inside the railway carriage. Instead, it is traveling on the embankment. I think it to be the more suitable example, as the source of light will not suffer from inertia here, and the constant value of c, when measured from the carriage and the embankment both, will show the real peculiar behavior of light speed and time dilation.

Again, that behavior is not "peculiar" and I don't see what time dilation has to do with this example.

However, I agree that even in the example given in this post, when the time taken by light is measured by two different observers located in two different reference frames, time dilation effect will be exhibited.
regards

If object B is moving at speed u relative to observer A and object C is moving at speed v relative to object B then A will observe object C moving at speed $$\frac{u+ v}{1+ \frac{uv}{c^2}}$$ relative to himself. If object C is a photon, so that v= c, then that reduces to $$\frac{u+ c}{1+ \frac{uc}{c^2}}= \frac{u+ c}{1+ \frac{u}{c}}= \frac{c(u+ c)}{u+ c}= c$$. Light moves at speed c relative to any observer. There is nothing "peculiar" about that.

 

[Dale]

And does the ray of light moving in the ship actually exhibit the peculiar behavior of the constancy of light's speed?

Yes. That is the second postulate, and it is well established experimentally.

 

[albert36]

The New Yorker magazine, of all places, had some keen insights/descriptions on special [and general] relativity that were recently featured in these forums: http://www.newyorker.com/tech/elements/the-space-doctors-big-idea-einstein-general-relativity. Light does have momentum/inertia. Always.

 

[dayalanand roy]

What does "suffer from inertia itself" mean?
It does not matter where it moves and who measures its speed, the result is always c (as long as it moves in vacuum).
Why do you expect a difference between "moving on top of the train" and "moving inside the train" as long as it does not have any physical connection to the train? What does "inside" even mean if we remove windows, the ceiling, walls and so on? Remember: all those thought experiments happen in vacuum. We do not need the train, floating light sources would work as well.

.Thanks for the reply.

 

[dayalanand roy]

Yes. That is the second postulate, and it is well established experimentally.

Thanks.

 

[dayalanand roy]

No, it doesn't. Why do you refer to this as "peculiar" behavior? Again, that behavior is not "peculiar" and I don't see what time dilation has to do with this example. If object B is moving at speed u relative to observer A and object C is moving at speed v relative to object B then A will observe object C moving at speed $$\frac{u+ v}{1+ \frac{uv}{c^2}}$$ relative to himself. If object C is a photon, so that v= c, then that reduces to $$\frac{u+ c}{1+ \frac{uc}{c^2}}= \frac{u+ c}{1+ \frac{u}{c}}= \frac{c(u+ c)}{u+ c}= c$$. Light moves at speed c relative to any observer. There is nothing "peculiar" about that.

Thanks for this educating reply.

 

[Mister T]

Light does have momentum/inertia. Always.

Momentum is a well-defined concept. Inertia is not. It turns out the concept of inertia is meaningful only in the low speed limit of Newtonian physics. And even then it is not a particularly useful concept.

 

[PeterDonis]

It turns out the concept of inertia is meaningful only in the low speed limit of Newtonian physics.

Do you have a reference for this statement? AFAIK inertia is meaningful in general in GR, though it requires some care in its definition. The physical origin of inertia is still a matter of discussion, but that doesn't make the concept itself invalid.

 

[Mister T]

Do you have a reference for this statement? AFAIK inertia is meaningful in general in GR, though it requires some care in its definition. The physical origin of inertia is still a matter of discussion, but that doesn't make the concept itself invalid.

The references I have are the usual discourses on the abuses of relativistic mass. Usually inertia is used as the constant of proportionality between force and acceleration, but there is no such proportionality in relativistic physics.

 

[albert36]

"It turns out the concept of inertia is meaningful only in the low speed limit of Newtonian physics."

"Do you have a reference for this statement?"

Interesting!

I found some possible 'distinctions' between Newtonian and relativistic inertia described here:

https://en.wikipedia.org/wiki/Inertia#Relativity

"...On the Electrodynamics of Moving Bodies," was built on the understanding of inertia and inertial reference frames developed by Galileo and Newton... in general relativity Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of space-time, instead of the more traditional system of forces understood by Newton.[20]

As a result of this redefinition, Einstein also redefined the concept of "inertia" in terms of geodesic deviation instead, with some subtle but significant additional implications. The result of this is that according to general relativity, when dealing with very large scales, the traditional Newtonian idea of "inertia" does not actually apply, and cannot necessarily be relied upon. Luckily, for sufficiently small regions of spacetime, the special theory can be used, in which inertia still means the same (and works the same) as in the classical model.[dubious – discuss]

Another profound conclusion of the theory of special relativity, perhaps the most well-known, was that energy and mass are not separate things, but are, in fact, interchangeable. This new relationship, however, also carried with it new implications for the concept of inertia. The logical conclusion of special relativity was that if mass exhibits the principle of inertia, then inertia must also apply to energy. This theory, and subsequent experiments confirming some of its conclusions, have also served to radically expand the definition of inertia in some contexts to apply to a much wider context including energy as well as matter.[citation needed]..."

Any further thoughts, insights??

 

[albert36]

For those interested, Roger Penrose has a related discussion, from a more mathematical perspective, about "Newtonian dynamics in Spacetime Terms" in THE ROAD TO REALITY, Pg 388.

Penrose talks about the need for an approrpiate description of spacetime, geodesics defining inertial motions, and that Newtonian forces between particles act simultaneously.

 

[PeterDonis]

Usually inertia is used as the constant of proportionality between force and acceleration, but there is no such proportionality in relativistic physics.

That just means the Newtonian understanding of inertia is incomplete, and the relativistic understanding of it is more complete; it doesn't mean the concept of inertia is no longer valid in relativity.

 

[PeterDonis]

I found some possible 'distinctions' between Newtonian and relativistic inertia described here

This doesn't look like a good source, since several key statements are marked as disputed or needing citations. Do you have any better sources?

Einstein also redefined the concept of "inertia" in terms of geodesic deviation instead

No, he defined spacetime curvature in terms of geodesic deviation. Spacetime curvature and inertia are not the same thing.

 

[albert36]

whoa,there...that is not me saying those things...I am just quoting Wikipedia.

But I don't think Wikipedia said spacetime curvature and inertia are 'the same thing'.

Like Wikipedia, the Penrose reference also discusses using geodesics in defining inertial motion and seems to me to say pretty much the same thing as Wikipedia, but words mean different things to different people.

Further on in the Penrose book, Pg 394, he notes in connection with the equivalence principle that Newton and Einstein would not always agree on what is 'inertial' motion,,,as standing on the ground for example ...and goes on to say "...This does not actually represent a change in Newton's theory, but merely provides a new description of it..."

Well, that actually DOES sound like a 'change' to me...but 'words' again.

 

[Nugatory]

whoa,there...that is not me saying those things...I am just quoting Wikipedia.

Often a bad idea... There's a reason why wikipedia is not an acceptable source at PF.
(We do make exceptions for specific articles, as some of them are OK. But on balance we spend as much time correcting misconceptions that people have picked up from wikipedia than we gain back by being to able to link to good wikipedia explanations).

 

[Mister T]

That just means the Newtonian understanding of inertia is incomplete, and the relativistic understanding of it is more complete; it doesn't mean the concept of inertia is no longer valid in relativity.

Is it possible to assign a number to an object and say it has this much inertia? And what would that mean?

 

[PeterDonis]

Is it possible to assign a number to an object and say it has this much inertia?

Sure; the object's invariant mass. If you apply a force to the object, and measure the magnitude of the force and the proper acceleration produced on the object, the ratio of the two, which is reasonably representative of the word "inertia", will be the object's invariant mass. Note that I said the magnitude of the force and the proper acceleration of the object; both of these are invariants, so their ratio must also be invariant. Discussions of SR where "relativistic mass" is used, and where the difference in coordinate acceleration between longitudinal and transverse forces is discussed, obscure the actual invariants involved; but the invariants are still there.

 

[mfb]

Usually inertia is used as the constant of proportionality between force and acceleration, but there is no such proportionality in relativistic physics.

F=ma is valid in relativity, but you have to use 4-vectors for F and a.

 

[greswd]

Yes. That is the second postulate, and it is well established experimentally.

Its kinda weird, it is almost as if photons are the kings of all particles, a cut above the rest.

 

[phinds]

Its kinda weird, it is almost as if photons are the kings of all particles, a cut above the rest.

No, just different that the rest, as all the rest are different from each other (which is pretty obvious since if they weren't they wouldn't be different particles). Electrons, after all, pity the poor photons because the photons have no charge.

 

[greswd]

No, just different that the rest, as all the rest are different from each other (which is pretty obvious since if they weren't they wouldn't be different particles). Electrons, after all, pity the poor photons because the photons have no charge.

haha, well photons are the only ones with the license to whizz about at the universal speed limit, so I guess they don't mind.

 

[mfb]

Gluons don't have a mass either.
They just don't exist as long-living stuff we could see going from A to B.

 

[Mister T]

Sure; the object's invariant mass. If you apply a force to the object, and measure the magnitude of the force and the proper acceleration produced on the object, the ratio of the two, which is reasonably representative of the word "inertia", will be the object's invariant mass.

That's precise for the concept of mass. But why the phrase "reasonably representative" for inertia? Do you mean reasonably representative of the Newtonian concept of inertia? Is there something inertia represents in relativistic physics that's useful or helpful in understanding something more so than mass?

The other issue I have with inertia is the way it's used in describing Newton's 1st Law. To call it the law of inertia and say that the reason objects in motion tend to remain in motion is due to a property of the object deflects a true understanding. The law is about frames of reference, The difference between a state of rest and a state of uniform motion is the frame of reference of the observer. It's not some property (called inertia) of an object that keeps it moving as opposed to coming to a stop. It's the frame of reference of the observer and the fact that the frames are equivalent.

I don't see any pedagogical value in the concept of inertia.

 

[PeterDonis]

why the phrase "reasonably representative" for inertia?

Because the usual physical interpretation of "inertia" is "resistance to being accelerated"--the ratio of force to acceleration. (Some sources use "inertial mass" to describe this.)

The other issue I have with inertia is the way it's used in describing Newton's 1st Law. To call it the law of inertia and say that the reason objects in motion tend to remain in motion is due to a property of the object deflects a true understanding.

It's true that, on our current relativistic understanding, objects moving "inertially" (i.e., without having any force applied to change their motion) follow the trajectories they do because of the geometry of spacetime, not because of any property of the objects. (This is why many sources use the term "free fall" to describe this type of motion, instead of "inertial"--to try to help disentangle this issue.)

The old usage of "inertia" to describe "what keeps objects from coming to a stop" was, I think, a holdover from Aristotelian physics--when the Galilean principle of relativity was a new idea, people felt an intuitive sense that there must be something "keeping the object moving", because their intuitions were still Aristotelian and so they intuitively thought the "natural" thing was for objects in motion to come to a stop. Today our intuitions have been extensively retrained, so even lay people understand that the "natural" thing is for bodies in motion to stay in motion--it takes a force, like friction or air resistance, to stop them. So the old usage of "inertia" that you're objecting to is, I agree, way past its expiration date.

 

[Mister T]

Today our intuitions have been extensively retrained, so even lay people understand that the "natural" thing is for bodies in motion to stay in motion--it takes a force, like friction or air resistance, to stop them. So the old usage of "inertia" that you're objecting to is, I agree, way past its expiration date.

Claims of what we see in the classroom are anecdotal. Results of physics education research are open to interpretation. Nevertheless, they both point to the fact that the Aristotelian notion of inertia is something most people have, and that it often persists even after instruction. I don't see any advantage to introducing the concept of inertia. Where does it fit into any scheme? Why is it needed?

You mentioned the use of the term inertial mass. Isn't the equivalence of inertial mass and gravitational mass something that's meaningful only in the Newtonian approximation? My understanding, and it doesn't go very deep, is that the equivalence principle defines inertial motion as free fall, and that that is the better way to express it.

It's true that, on our current relativistic understanding, objects moving "inertially" (i.e., without having any force applied to change their motion) follow the trajectories they do because of the geometry of spacetime, not because of any property of the objects. (This is why many sources use the term "free fall" to describe this type of motion, instead of "inertial"--to try to help disentangle this issue)

Certainly terms like inertial reference frame are needed, but promoting the concept of inertia as a property of an object, even as part of the Newtonian approximation, can foster the misconception that inertial motion has something to do with the object itself rather than the frame of reference used to observe that motion.

 

[PeterDonis]

Isn't the equivalence of inertial mass and gravitational mass something that's meaningful only in the Newtonian approximation?

No. It's exact in GR.

the equivalence principle defines inertial motion as free fall

This, in itself, tells you nothing, because "free fall" is just as much in need of definition as "inertial motion". What, physically, defines "free fall"? In GR, the answer is "zero proper acceleration"--i.e., weightlessness. (This was Einstein's original insight that started him on the road to GR: if a person falls freely, they will not feel their own weight.) So we can use the worldlines of weightless objects to define "straight lines" (geodesics) in spacetime. The EP then says that, locally, if we construct an inertial frame, in the usual SR sense, using the worldlines of weightless objects to define "straight lines", all of the laws of SR will be satisfied, locally, in that frame.

 

[Mister T]

Ok then, this was an argument I never understood before anyway. It was based on the notion that flat spacetime is not possible in GR. As I said, it was something I never really understood anyway.

Setting that aside, then, do you agree that the concept of inertia has a different meaning than it does in the Newtonian approximation? In the Newtonian approximation I see it used two ways, one as an explanation of why the First Law is valid, the second is it's role as a resistance to acceleration in the Second Law. In the former case it's used improperly because the issue is frame of reference and in the latter case it's the same thing as mass. Since mass has has a precise definition, why bother with another term that has the same meaning?

I guess I still don't understand the role inertia plays in general. I take your point that mass is the ratio of the magnitude of the proper force to the proper acceleration, and in that sense mass has a similar meaning to what we think of as inertia in the Newtonian sense. But that's mass, which itself has a different meaning in general than it does in the Newtonian approximation.

I'm talking about the term "inertia", a noun; not "inertial", an adjective.

Anyway, I apologize if this is nitpicking or I'm being dense, but I just don't get it.

 

[PeterDonis]

It was based on the notion that flat spacetime is not possible in GR.

Spacetime is curved in GR; that's why I added the qualifier "locally" in my discussion of the EP above.

do you agree that the concept of inertia has a different meaning than it does in the Newtonian approximation?

I think that, as your comments imply, the term "inertia" does not have a single meaning; it can be used to refer to at least two concepts, which are related but not identical. Of the two, the second, which, as you note, is also called "mass" (more precisely, "invariant mass"), is the one that makes the most sense, physically.

Since mass has has a precise definition, why bother with another term that has the same meaning?

Because the fact that invariant mass = inertia may be telling us something physical, something that isn't just a matter of definition. The invariant mass of a system composed of multiple objects is not necessarily the same as the sum of the invariant masses of the objects; there are kinetic energies, binding energies, etc. involved. Yet the inertia of the system is still equal to its invariant mass--not to the sum of the invariant masses of the components. It's possible that this is telling us something, we just don't understand what--yet.

 

[albert36]

I don't see any pedagogical value in the concept of inertia.

My post #13 [Penrose, Road to Reality] provides some. If I am interpreting them correctly they comply with the comments I also already posted from Wikipedia, but of course the words are different. I'd provide them here, but I don't know how to without the possibility of taking something out of the context which Penrose provides. His discussion seems overly lengthy...maybe eight or ten pages.

The law is about frames of reference, The difference between a state of rest and a state of uniform motion is the frame of reference of the observer.

moving "inertially" (i.e., without having any force applied to change their motion) follow the trajectories they do because of the geometry of spacetime, not because of any property of the objects.

After reading Penrose several times a more precise description I think he provides is that inertial movement is that which follow geodesics. And I think a geodesic the result of local spacetime geometry AND that induced by the object. In other words, don't two objects with different properties in general move along different 'geodesics' because different objects have different gravitational fields of their own?

 

[albert36]

Sounds like I was thinking 'wrong" ...

Crowell says:
"...In GR, the "lines" are geodesics, which are interpreted as the world-lines of particles that aren't subjected to any nongravitational forces. Since a geodesic is uniquely determined by any initial segment, you can't have different geodesics for red and blue light.,,"

Post # 4: https://www.physicsforums.com/threads/are-photons-affected-differently-by-gravity.391798/

 

[dayalanand roy]

Momentum is a well-defined concept. Inertia is not. It turns out the concept of inertia is meaningful only in the low speed limit of Newtonian physics. And even then it is not a particularly useful concept.

Thanks.

 

[dayalanand roy]

Dear all the participants
Thanks for your educating discussion. I am also trying to get something out of it.

 

[PeterDonis]

I think a geodesic the result of local spacetime geometry AND that induced by the object.

In general, this is what GR would predict; but we do not have any way of solving the equations for this in the general case. What we do, instead, is to approximate most objects as "test objects", which are assumed to have negligible effect on the spacetime geometry. Test objects then follow geodesics of the background geometry that is generated by the bodies that are massive enough not to be test objects. This is how, for example, we would model the motion of spacecraft in orbit around the Earth.

What is less obvious, but turns out to be true, is that we can do this same trick even for objects that are clearly not "test objects" in themselves, but which are sufficiently isolated. For example, in modeling the orbit of the Earth and the other planets around the Sun, we can treat the planets as following geodesics of the background spacetime geometry generated by the Sun, while ignoring the effects of the planets themselves. This works because the Sun is much more massive than any of the planets (the most massive planet, Jupiter, is less than 1/1000 the mass of the Sun), and because all of the planets are well isolated, which means that the distance between them is much, much larger than any of their masses (where "mass" here means the "geometric mass" $GM / c^2$, where $M$ is the mass in conventional units). I believe there is a theorem to the effect that, under these conditions, the "self-gravity" of the planets cancels out, and does not affect the geodesics that the planets travel on, as long as we are not concerned with the internal structure of the planets themselves, but only the orbits of their centers of mass.

Sounds like I was thinking 'wrong" ...

Not necessarily. What you quoted assumes that the light itself has no effect on the spacetime geometry, i.e., that the rays of red and blue light are "test objects" in the above sense. More precisely, it assumes that, whatever effect the light has on the geometry, it is the same for red and blue light (which just means the two colors of light must have the same energy density).