# Do we also travel at a fixed velocity?

## Main Question or Discussion Point

Since, light is always travelling at a constant velocity with respect to everything else, does it also mean that everything else is also travelling at a constant velocity with light?

As in, since light is always travelling at C irrespective of our velocity, then does it not also mean that we are also travelling at a constant fixed velocity with respect to light? Is our velocity then taken as 0? If that is the case what does velocity actually mean?

With respect to one photon, what would be the velocity of another photon that is travelling towards it?

Sorry about these basic questions, I am just a fan pf physics and don't really know anything much about it in detail.. Related Special and General Relativity News on Phys.org
JesseM
Since, light is always travelling at a constant velocity with respect to everything else, does it also mean that everything else is also travelling at a constant velocity with light?
When physicists talk about the speed of one object "with respect to" another, they usually mean the speed of the first object in the inertial rest frame of the second ('rest frame' is a coordinate system where the object is at rest, and 'inertial' means the coordinate system is moving at constant velocity, not accelerating), but light doesn't have its own inertial rest frame in relativity--see this post for a little more info.

DaveC426913
Gold Member
... light doesn't have its own inertial rest frame in relativity...
Yes, and in this is the answer to your question. You cannot pretend to "stand next to a photon" and measure the speeds of other objects. It is meaningless.

russ_watters
Mentor
Actually, I think the main question was asking it from the other direction. That makes this the answer:
the speed of the first object in the inertial rest frame of the second
In other words, the OP asked the speed of "everything else" -- but since the speed of light is measured from our rest frame (and not the other way around), the answer [to a slightly different question maybe] is zero.

A.T.
Since, light is always travelling at a constant velocity with respect to everything else, does it also mean that everything else is also travelling at a constant velocity with light?
If you consider traveling trough spacetime, instead of space only, then everything is traveling at a constant velocity c, just in different directions:

JesseM
If you consider traveling trough spacetime, instead of space only, then everything is traveling at a constant velocity c, just in different directions:
The statement that everything moves at c spacetime is only true if you adopt a weird mathematical definition of "speed through spacetime" (which isn't a term used by most physicists), see my post #3 on this thread.

A.T.
The statement that everything moves at c spacetime is only true if you adopt a weird mathematical definition of "speed through spacetime" (which isn't a term used by most physicists), see my post #3 on this thread.
I don't find it that weird. It a consequent extension of the classical "speed through space" by the adding the time dimension.

JesseM
I don't find it that weird. It a consequent extension of the classical "speed through space" by the adding the time dimension.
But nothing actually "moves" in a spacetime diagram, spacetime is just a fixed 4-dimensional structure with worldlines embedded in it, so this terminology tends to be confusing to people who haven't learned to take this geometric perspective on spacetime. What you're really doing when you talk about "speed through spacetime" is taking the spacetime interval between two events on the object's worldline and dividing by the proper time experienced by the object between those events, so it's really quite trivial that this will equal c since the spacetime interval is essentially defined as c * proper time (with the c there just to ensure that the spacetime interval has units of distance rather than time).

A.T.
But nothing actually "moves" in a spacetime diagram,
Yes it does! Just press "play" http://www.adamtoons.de/physics/relativity.swf" [Broken] and see it move. ;-)
spacetime is just a fixed 4-dimensional structure with worldlines embedded in it, so this terminology tends to be confusing to people who haven't learned to take this geometric perspective on spacetime.
The picture of objects moving along their worldline doesn't seem confusing to me. It is a way to visualize the meaning of spacetime diagrams.
so it's really quite trivial that this will equal c since the spacetime interval is essentially defined as c * proper time.
The nice thing about these space-propertime diagrams is that you directly see all the quantities (space, coordinate time. proper time) as geometrical lengths. And the fact that everything "moves" with c trough this diagram is a nice simple rule.

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DaveC426913
Gold Member
The picture of objects moving along their worldline doesn't seem confusing to me.
But they don't move. In these diagrams time is fixed and unmoving.

To set anything moving is to introduce an additional component that doesn't exist.

JesseM
The picture of objects moving along their worldline doesn't seem confusing to me. It is a way to visualize the meaning of spacetime diagrams.
But what "meaning" is that? If you adjusted the animation so that objects traveled twice as fast along their worldline, or twice as slow, these types of "changes" would not seem to have any physical meaning, since the worldline itself would be unchanged. And to make sense of anything moving through spacetime, it seems you must implicitly be imagining a second time dimension, no?

Since, light is always travelling at a constant velocity with respect to everything else, does it also mean that everything else is also travelling at a constant velocity with light?

As in, since light is always travelling at C irrespective of our velocity, then does it not also mean that we are also travelling at a constant fixed velocity with respect to light? Is our velocity then taken as 0? If that is the case what does velocity actually mean?

With respect to one photon, what would be the velocity of another photon that is travelling towards it?

Sorry about these basic questions, I am just a fan pf physics and don't really know anything much about it in detail.. Either these guys are answering the wrong question, or I am.
Velocities don't add like you would expect in relativity.
30000 km/s combined with 30000 km/s does not equal 60000 km/s.

So, the way I understand what you people have said so far is this:

1) All velocity is judged from an initial rest frame.

2) Light has no initial rest frame, so judging velocity from its perspective is meaningless.

Okay... this is just like another one of those, rules apply to everything, except electromagnetic ray things.

Only EMRs can travel at c. Only EMRs can have no mass yet they can have energy and be affected by gravity. Only EMR's can have no initial rest frame.

Is there any explanation of mass given by SR or GR that explains that light does not possess it yet it can affect things that do possess mass?

Staff Emeritus
Virtually none of what you have just posted is correct. You might want to reread the rest of the thread.

LURCH

So, the way I understand what you people have said so far is this:

1) All velocity is judged from an initial rest frame.

2) Light has no initial rest frame, so judging velocity from its perspective is meaningless.

Okay... this is just like another one of those, rules apply to everything, except electromagnetic ray things.

Only EMRs can travel at c. Only EMRs can have no mass yet they can have energy and be affected by gravity. Only EMR's can have no initial rest frame.

Is there any explanation of mass given by SR or GR that explains that light does not possess it yet it can affect things that do possess mass?
No no; not "initial," "inertial"! Meaning "not accelerating," from the root word "inertia."

A.T.
But they don't move. In these diagrams time is fixed and unmoving.
If you adjusted the animation so that objects traveled twice as fast along their worldline, or twice as slow, these types of "changes" would not seem to have any physical meaning, since the worldline itself would be unchanged.
Yes of course. The whole point of a time axis is to visualize movement in a static diagram. The animation is just meant to help to understand the relationship between the diagram and real world observation. Therefore the animated parameter is the coordinate time expierenced by the observer.
To set anything moving is to introduce an additional component that doesn't exist.
And to make sense of anything moving through spacetime, it seems you must implicitly be imagining a second time dimension, no?
In the case of a space-propertime diagram this "additional component" or "second time dimension" is the coordinate time measured by the observer. It determines how far the objects "move" along their worldlines. And since they all "move" the same "distance" in a given period of coordinate time, you could say: Everything moves at c trough space-propertime in regards to coordinate time.

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If you consider traveling trough spacetime, instead of space only, then everything is traveling at a constant velocity c, just in different directions:
Technically precise or not I have found Brian Greene's explanation a very simple geometric way to think about relativity. It's real easy to visualize how motion in space "diverts" motion in time and linear acceleration becomes curved and rotational acceleration spiral (corkscrew) shaped.

JesseM
Technically precise or not I have found Brian Greene's explanation a very simple geometric way to think about relativity. It's real easy to visualize how motion in space "diverts" motion in time and linear acceleration becomes curved and rotational acceleration spiral (corkscrew) shaped.
But the fact that linear acceleration gives a curved worldline and rotational acceleration gives a corkscrew is just a fact about the shape of the worldlines, it has nothing to do with any notion of "moving" along the worldlines at speed c.

A.T.
But the fact that linear acceleration gives a curved worldline and rotational acceleration gives a corkscrew is just a fact about the shape of the worldlines, it has nothing to do with any notion of "moving" along the worldlines at speed c.
The notion of "moving" trough spacetime is only a visualization, just like the idea of spacetime itself. It is accessible to beginners, because it naturally extends the idea of spatial motion:

space displacement during a period of observers time

by adding a temporal component (proper time period) to the displacement vector, making it:

spacetime displacement during a period of observers time

JesseM
The notion of "moving" trough spacetime is only a visualization, just like the idea of spacetime itself. It is accessible to beginners, because it naturally extends the idea of spatial motion:

space displacement during a period of observers time

by adding a temporal component (proper time period) to the displacement vector, making it:

spacetime displacement during a period of observers time
Mere spatial displacement doesn't specify whose time-coordinate you're using (whether the observer's or someone else's), it just involves the spatial distance between two different events on the object's worldline. Spatial velocity depends on a choice of time-coordinate, but it's not defined as space displacement divided by a period of observers time, it's defined as space displacement divided by a period of coordinate time in the same coordinate system you're using to measure space displacement. There isn't any obvious intuitive reason why it is more "natural" to define an object's "speed through spacetime" in terms of the object's own time rather than in terms of the time-coordinate of some outside observer's rest frame. And if you do choose to define "speed through spacetime" in terms of spacetime displacement divided by the object's own proper time, then as I said, my biggest problem with this is that the statement "everything moves at c through spacetime" is often presented as a significant physical insight when in fact it's basically a tautology given that the spacetime interval which measures "distance" in spacetime can be defined as proper time * c (with the only purpose of the c being to give the spacetime interval units of distance rather than time, c being the only physical constant that has units of distance/time). There's no reason we couldn't define the metric in terms of proper time itself rather than proper time * c, it's just a convention which I suppose owes to the fact that people find it more natural to think of the metric in terms of spatial distances than temporal distances.

Dale
Mentor
I don't find it that weird. It a consequent extension of the classical "speed through space" by the adding the time dimension.
I don't find it weird either. You are just talking about the proper-time derivative of the spacetime coordinate (ct,x,y,z) which, IMO, is a reasonable definition of velocity regardless of the fact that worldlines don't move.

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A.T.
And if you do choose to define "speed through spacetime" in terms of spacetime displacement divided by the object's own proper time,
You are just talking about the proper-time derivative of the spacetime coordinate (ct,x,y,z)
You both got me wrong, so it must be my fault. With "speed through spacetime" I mean space-propertime displacement divided by coordinate time (the coordinate time derivate of the space-propertime coordinate (ctau,x,y,z)). So it could be called the speed through space-propertime (which is c for all objects).
my biggest problem with this is that the statement "everything moves at c through spacetime" is often presented as a significant physical insight
It's a nice simple rule that helps in geometrical visualizations, of SR & GR.
given that the spacetime interval which measures "distance" in spacetime can be defined as proper time * c
You are thinking about the Minkowski spacetime. In space-propertime the distance is sqrt((delta proper time * c)^2 + (delta space)^2)

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Dale
Mentor
My mistake. I do find it weird after all.

JesseM
It's a nice simple rule that helps in geometrical visualizations, of SR & GR.
How does it "help"? You can't even use the rule until you've already come up with the visualization of the worldlines, and then the only additional thing it does is make you imagine something moving along those worldlines (as in the animation you posted). If you think it actually helps draw the worldlines in the first place, could you give a simple example?
A.T. said:
You are thinking about the Minkowski spacetime. In space-propertime the distance is sqrt((delta proper time * c)^2 + (delta space)^2)
OK, I was going by Brian Greene's definition of speed through spacetime which I quoted in post #3 here, but if you divide your space-propertime displacement by the coordinate time rather than the proper time, your definition works too. The basic point remains the same--the fact that you get a speed of c for everything is not an interesting physical insight, but just a trivial consequence of the way you are defining space-propertime displacement. After all, we know proper time is related to coordinate space and time measurements like so:

delta proper time = sqrt((delta coordinate time)^2 - (delta space / c)^2)
So, naturally (delta proper time * c)^2 = (delta coordinate time * c)^2 - (delta space)^2

Now you plug this into your definition of space-propertime displacement:
space-propertime displacement defined as sqrt((delta proper time * c)^2 + (delta space)^2)
= sqrt((delta coordinate time * c)^2 - (delta space)^2 + (delta space)^2)
=sqrt((delta coordinate time * c)^2)
= delta coordinate time * c.

So, with space-propertime displacement essentially defined as delta coordinate time * c, it's not a great surprise that if you divide by delta coordinate time and call this "speed through space-propertime", you'll find that everything has a "speed through space-propertime" of exactly c!

DrGreg
Gold Member
It's sort of OK to visualise a red dot moving along a worldline in spacetime when there is just a single point-particle being considered. It's problematic if you want to consider two or more particles. If you think of two red dots each moving along their own worldlines there is a problem of how to synchronise the dots. There is no unique solution to that problem, and the danger is you might be misled into thinking in terms of one specific choice of synchronisation to the exclusion of all others. It's better to think in terms of the geometry of the curves themselves and forget the dots.

It's even more of a problem if you want to consider a large object (i.e. with non-zero volume).
You are just talking about the proper-time derivative of the spacetime coordinate (ct,x,y,z) which, IMO, is a reasonable definition of velocity regardless of the fact that worldlines don't move.
I'm sure you know, DaleSpam, but others might not, that the entity you refer to is called "4-velocity". The technical differential-geometrical interpretation is that the 4-velocity is the tangent vector to the worldline, in other words it's the direction in spacetime that the worldline points. As we are only interested in direction, its magnitude is constant.

You both got me wrong, so it must be my fault. With "speed through spacetime" I mean space-propertime displacement divided by coordinate time (the coordinate time derivate of the space-propertime coordinate (ctau,x,y,z)). So it could be called the speed through space-propertime (which is c for all objects)
I've never understood how Euclidean "space-propertime" could make sense. The problem is that each object has its own proper time. Consider, for example, the standard twins paradox. At the end, both twins are at the same event in spacetime, but in a "space-propertime" diagram they would be at two different points (because they have each elapsed a different proper time). This shows there is no one-to-one mapping between points (events) in spacetime and points in space-propertime. Being "at the same place at the same time" is a physical reality independent of any choice of spacetime coordinates, but "space-propertime" seems not to recognise the concept.