# Speed of light relative to observers?

1. Dec 1, 2015

### dayalanand roy

[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? 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 travelling 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

Last edited by a moderator: Dec 1, 2015
2. Dec 1, 2015

### Staff: Mentor

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.

3. Dec 2, 2015

### HallsofIvy

Staff Emeritus
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.

4. Dec 2, 2015

### Staff: Mentor

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

5. Dec 2, 2015

### albert36

Last edited: Dec 2, 2015
6. Dec 2, 2015

7. Dec 2, 2015

Thanks.

8. Dec 2, 2015

9. Dec 3, 2015

### Mister T

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.

10. Dec 3, 2015

### Staff: Mentor

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.

11. Dec 3, 2015

### Mister T

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.

12. Dec 4, 2015

### 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.[dubiousdiscuss]

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??

13. Dec 4, 2015

### 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.

Last edited: Dec 4, 2015
14. Dec 4, 2015

### Staff: Mentor

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.

15. Dec 4, 2015

### Staff: Mentor

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?

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

16. Dec 4, 2015

### 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.

17. Dec 4, 2015

### Staff: Mentor

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).

18. Dec 4, 2015

### Mister T

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

19. Dec 4, 2015

### Staff: Mentor

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.

20. Dec 4, 2015

### Staff: Mentor

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