# Relativistic speed wrt light

## Main Question or Discussion Point

I have a simple question on the relativistic view point with regard to light.

From wiki, "All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration."
Simply I understand if a physical object keep the motion unchanged in time o uniform velocity, then it is considered as the IFR. Also I think that light itself is IFR because it moves in the empty space with constant velocity. In Einstein's relativistic view, I have learned that the velocity can be only defined with regard to other reference. And between two IRFs(A and B), either side can claim to be at rest or moving so that A is at rest but B is moving and vice versa. So assuming that I and a quanta of light are both the IFRs, I would like to ask a question to you.

By definition of IRF, light is also IRF. So let me describe my velocity with regard to light.
It will be common sense to say that I am at rest and light is moving at c. But problem is that I can take another view point that I am moving at c and light is at rest. If the latter is valid, then it seems that I am mass-less because I am moving at c. It seems to be a problem to say that I am moving at c.

I believe that every physical raw must be consistent with no exception. A massive object under a uniform motion and light both must be treated as IRF by definition. If an IRF can be treated as resting or moving upon choice between two massive IRFs, same rule must be applied between a massive IRF and light and even further a massive IRF can have the velocity of light c.

So my question is what follows:

Is it safe to say that a massive physical object can have a relativistic velocity same to c and zero (relativistic) mass with regard to the light moving in empty space?

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light is also IRF
No it is not.

Stephanus
Nugatory
Mentor
So assuming that I and a quanta of light are both the IFR.....,
That assumption is your problem. There is no inertial reference frame in which a flash of light can be at rest.

For any massive object, I can always find a frame (which really just means "choose a convention for assigning space and time coordinates to every point in spacetime") in which that object is at rest. All other massive objects will be moving at less than the speed of light relative to that object, and a flash of light will be moving at speed ##c## relative to that object. I cannot, however, find a frame in which a flash of light is at rest and some massive object is moving at speed ##c## relative to it.

Ibix
An object isn't a reference frame. What is true is that for all unaccelerated massive objects you can define an inertial reference frame in which the object is at rest.

The same is not true of light. There is no frame in which light is at rest, by the postulates of relativity - light travels at c in all inertial reference frames.

Edit: beaten to it by Nugatory, I see.

Dale
Mentor
Simply I understand if a physical object keep the motion unchanged in time o uniform velocity, then it is considered as the IFR
Not quite. Any two IFR are in constant rectilinear motion, but that does not imply that anything in constant rectilinear motion with respect to an IFR is alsoan IFR.

The comment in wikipedia that you are referring to is a property of pairs of IRFs, not a definition of an IFR

Weirdoguy is right. This question comes up often enough that it is a FAQ entry. There's a list of all our relativity FAQs here and the one for this question is https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/
Thanks for the link. It gives me one more doubt. In the link, "The rest frame of a photon would require the photon to be at rest (velocity=0) and moving at c(velocity=299792458 m/s). That of course is contradictory. In other words, the concept doesn't make sense."

Hmm. Lets assume that there are two flashes of light. At t0, first flash of light moves along positive x direction and At t1>t0, second flash of light is emitted and follows the first flash of light along same direction. In such case, the distance between two flashes will not be changed forever so that the first flash of light will be at rest second flash. This gives me the impression that there exists the case that "the photon to be at rest (velocity=0) and moving at c(velocity=299792458 m/s)" because all flash of light moving at c(the second hypothesis of special relativity and at the same time at rest with regard to other flash of light. It does not seem to be contradictory to me if I interpret this observation as that light has relativistic velocity (dependent on observer) and absolute velocity (independent on observer) at the same time.

Dale
Mentor
You are confusing the separation velocity with the relative velocity, and neither is what is described in the FAQ.

The FAQ is talking about the velocity (no "relative" or "separation") of a single pulse of light in a single reference frame. That single quantity cannot both be c and 0.

A.T.
same rule must be applied between a massive IRF and light
Then apply the rule (Lorentz transformation) to light, and see if you get a valid reference frame.

You are confusing the separation velocity with the relative velocity, and neither is what is described in the FAQ.

The FAQ is talking about the velocity (no "relative" or "separation") of a single pulse of light in a single reference frame. That single quantity cannot both be c and 0.
The link says that the concept for the rest frame of a photon does not make sense and I argue that the rest frame of a photon makes sense as I wrote in #7. I also mentioned that when viewed in the position of second flash which is a single reference frame, the velocity of the first is zero, not c.

Doc Al
Mentor
I also mentioned that when viewed in the position of second flash which is a single reference frame, the velocity of the first is zero, not c.
A "flash" is not a reference frame. It's something that can be observed with respect to a reference frame. There is no inertial reference frame in which either flash has speed zero.

A "flash" is not a reference frame. It's something that can be observed with respect to a reference frame. There is no inertial reference frame in which either flash has speed zero.
Your comment seems that a massless physical object cannot be an observer which can measure other's velocity. I think any physical object including massless photon can measure other velocity. For example, two photon with zero velocity with regard to other will not collide but what the collision of two massless particle means is that they must had non-zero relativistic velocity with regard to other.

robphy
Homework Helper
Gold Member
It seems to me that there is more to being an inertial reference frame than just being a future-pointing causal geodesic... that is, traveling with constant velocity isn't enough to be an inertial reference frame.

Inertial observers Alice and Bob are related by a Lorentz Transformation. However, no Lorentz transformation will boost Alice to light-speed or boost a light-speed object to Alice. (Lorentz Transformations boost light-speed objects to light-speed objects.) So, these are two different groups of objects.

In addition, how would a light-speed object set up a coordinate system operationally [i.e. specified by a physical procedure] in order to define "distance" and "time" in "that" frame?

I think DEFINITIONS are important.

I think this old post of mine is useful

A.T.
our comment seems that a massless physical object cannot be an observer which can measure other's velocity.
It has nothing to do with what a photon can do. The coordinate transformation of SR simply doesn't produce a valid rest frame for them.

Ibix
Your comment seems that a massless physical object cannot be an observer which can measure other's velocity. I think any physical object including massless photon can measure other velocity. For example, two photon with zero velocity with regard to other will not collide but what the collision of two massless particle means is that they must had non-zero relativistic velocity with regard to other.
"They don't collide" isn't enough to define a frame of reference. It doesn't even define a parallel line, since the majority of straight lines in 3+ dimensional space do not intersect, parallel or not. To define a frame of reference you need clocks and rulers, at least notionally. How are you going to build clocks and rulers that move at lightspeed?

Additionally, there's no way to relate what such clocks and rulers would measure to what anyone else measures (see A.T.'s comments), even if it weren't impossible to build them.

Mister T
Gold Member
Lets assume that there are two flashes of light. At t0, first flash of light moves along positive x direction and At t1>t0, second flash of light is emitted and follows the first flash of light along same direction. In such case, the distance between two flashes will not be changed
That is correct. In any inertial reference frame the separation distance between the two flashes will be constant.

Note that if you were to send the two flashes off in opposite directions the distance between them would increase at twice the speed of light, according to the inertial observer who sent them.

forever so that the first flash of light will be at rest [with respect to the] second flash.
It may seem as though this would be true. But, in fact, it is not possible to devise an experiment, even a thought experiment, that could test this assertion. Its validity therefore falls outside the realm of science. In other words, it's a nonscientific claim because there's no way, even in principle, to test it.

Try this one. I send off two rocks, each at a speed of ##0.6c##, in opposite directions. In my frame of reference the distance between the rocks increases at a rate of ##1.2c##. But to an observer moving along side one of the rocks, the other rock will be observed to have a speed of about ##0.88c##.

This is the kind of issue others were referring to when they told you that you are confusing speed with separation rate.

and I argue that the rest frame of a photon makes sense as I wrote in #7
And it is not true as others repeatedly said to you. Just stop and think about it for a while, and then argue.

DrGreg
Gold Member
It's perhaps worth pointing out that it is possible to have coordinates in which light is "at rest", but such coordinates (called "null coordinates") do not behave like inertial coordinates. A null coordinate does not unambiguously represent either time or space.

robphy
Homework Helper
Gold Member
It's perhaps worth pointing out that it is possible to have coordinates in which light is "at rest", but such coordinates (called "null coordinates") do not behave like inertial coordinates. A null coordinate does not unambiguously represent either time or space.
In my earlier post,
I tried to disallow these coordinates by asking for an operational procedure (done by the light speed object) to establish those coordinates.
In addition, how would a light-speed object set up a coordinate system operationally [i.e. specified by a physical procedure] in order to define "distance" and "time" in "that" frame?

Dale
Mentor
I argue that the rest frame of a photon makes sense as I wrote in #7.
Yes, and your argument is wrong. It confuses two different concepts "relative velocity" and "separation velocity" and doesn't even address the concept of "velocity" which is relevant to the FAQ.

I also mentioned that when viewed in the position of second flash which is a single reference frame, the velocity of the first is zero, not c
Then such a coordinate system is not an inertial reference frame, by the second postulate.

Orodruin
Staff Emeritus