[jeffreyH (OP)]

Since motion is relative then in some frames of reference we can be considered to be moving close to the speed of light. Are we actually moving at close to the speed of light?

[geordief]

Maybe "faster" as we are disappearing from view in some FOR's owing to the "pudding sponge" expansion effect.

There is also the hypothetical FOR of a tachyon....

[Halc]

Since motion is relative, then yes, we are moving at any arbitrary speed relative to any arbitrary reference.  There are always objects that are stationary relative to that reference.
As for that being an actual speed, there is no such thing.  Speed is defined as a relation to a reference, not a property of something.

geordief suggests even faster relative to distant things, but we are beyond the event horizon of things stationary in such frames, and thus the relation isn't really there, or at least not the same.  The concept does have meaning.  We are increasing our proper distance from such objects at a rate greater than the speed of light.  The most distant object known is 22 billion light years away and is and always has been moving at well over light speed relative to us, and yet we can see it, so in that sense we exist relative to each other.

[jeffreyH (OP)]

We can select an infinite number of reference frames between stationary and arbitrarily close to the speed of light with reference to some other object. It is not possible for us to be travelling at all those speeds simultaneously. This would mean we are experiencing an infinite number of time dilation effects all at once. With respect to everything else.

[alancalverd]

But we are! We see red and blue shifts out there, which means that, simultaneously, other observers see us as red or blue shifted, and all shades between. 

[Halc]

We can select an infinite number of reference frames between stationary and arbitrarily close to the speed of light with reference to some other object.

A reference frame need not have an object stationary in it, but yes, usually one is used.

It is not possible for us to be travelling at all those speeds simultaneously. This would mean we are experiencing an infinite number of time dilation effects all at once.

We experience our own frame and no other.  We do not experience time dilation, nor does the twin that goes out and back.  Relative to him, while inertial, the twin he left back home is the one slowed down.

With respect to everything else.

That is not a valid reference and does not define a frame.  I am very much travelling all those speeds at once, each relative to a different frame.  That isn't contradictory at all.  It just says that I have different speed relationships with various obects/frames, which is to be expected.

The red and blue shifts observed are due to the high rate of change of distance (going or coming respectively) of other objects relative to the observer.  Yes, in this manner one might determine the mean velocity of everything that can be seen, but for every inertial frame, there is a point in space where that red shift is isotropic, and thus the inertial frame appears essentially stationary.  So no inertial frame is special in a way that might represent a more objective definition of stationary.

[Janus]

We can select an infinite number of reference frames between stationary and arbitrarily close to the speed of light with reference to some other object. It is not possible for us to be travelling at all those speeds simultaneously. This would mean we are experiencing an infinite number of time dilation effects all at once. With respect to everything else.

That's like arguing that because different people would measure the Left-Right distance between the ends of  the red line shown below as being different (as indicated by the distance between the vertical lines), depending on how the line is rotated with respect to them, that the line would have to point in an infinite numbers of direction at once.

rotate.png (5.29 kB . 400x400 - viewed 2165 times)

Time dilation is akin to measuring that Left-Right distance between the end points of the line as done from different orientations to the line..

It like the red and blues lines below comparing each other's respective "lengths" by sighting along lines perpendicular to themselves ( the thin lines in the diagram)

compare.png (2.08 kB . 225x194 - viewed 2134 times)

[yor_on]

The simple answer is. what do you compare it too?
The more difficult one is

can you still accelerate?

[yor_on]

Actually, what you ask is if there is a local speed limit

Or  if it is globally defined.

Pick a sum. or measure your acceleration
I'm proud of you Jeffrey.

Took me some time to wonder about that one
And it's essential to relativity

[yor_on]

So. a 'golden standard'?`
Or purely local

[yor_on]

Jeffrey
I would call it 'local'

[yor_on]

What one has to remember when asking this kind of question is how we define it.
It's a local speed limit, but one that you can translate to other frames of reference.

There is a subtlety to that, purely cerebral.
the question following becomes

What does it mean?

[yor_on]

The point is that it either depends on your frame of reference.
Or if you still find a acceleration.

It's one of those things that made me define the universe as 'locally defined'.

[yor_on]

Also a question that made me take properties and conservation laws seriously :)
Weird as it might sound

[Petrochemicals]

No, because light reaches us. And nothing, NOTHING is allowed to move faster than light. If we where travelling apart from our twin planet at over half the speed of light it would dissapear, but because there are two motions that does not break the nothing rule. Unless light is pre programmed somehow.

[PmbPhy]

Since motion is relative then in some frames of reference we can be considered to be moving close to the speed of light. Are we actually moving at close to the speed of light?

The question is incomplete. You need to ask "are we moving near the speed of light in as measured in frame S." where S is specified by the person asking the question. In our frame (sitting on earth) the answer is no.

[yor_on]

Take two objects meeting each other, both close to the speed of light. As they collide the combined 'potential energy' must become a sum surpassing the potential energy that each one of them have on their own, and that seems allowed? But that sum can't be able to surpass the sum of one of them at 'c' hitting something defined as being 'still' by the ship/object. So there must be a limit to the 'energy' released in a collision, mustn't there?  Any ship defining a speed will need have to arbitrarily choose another frame of reference as its anchor of being at a 'null motion'. And as it accelerates it will be the acceleration (weight) that informs it of it still not having reached 'c'. Not saying that it can of course but just for the fun of it.

But it's also so that you can use the relative motion of Earth. Think of spinning rope with a stone resting in it to see how. Although in this case the spin is a 'acceleration'.
=

another way of thinking of it is to define Earth as moving in one direction (with the solar system/galaxy/whatever) relative some other frame, then testing if that gives you a boost depending on where you place the ship, with the 'motion' or against it. As far as I get it it won't be any energy saved by that approach intrinsically. And that is the most important point of it to me. Because if you find the energy needed differing depending on choice of take off then that motion is not 'relative' anymore, at least not to me.

[Halc]

Take two objects meeting each other, both close to the speed of light. As they collide the combined 'potential energy' must become a sum surpassing the potential energy that each one of them have on their own, and that seems allowed?

Potential energy has to do with the difference of gravitational potential between where it is and where it might fall.  I think you're talking about kinetic energy here.  Yes, each has a kinetic energy, and that sum goes into the collision if they both subsequently stop in the frame in which they were both moving at nearly c.

But that sum can't be able to surpass the sum of one of them at 'c' hitting something defined as being 'still' by the ship/object.

No, it can't.  Nothing can move 'at c', but you can get close.

So there must be a limit to the 'energy' released in a collision, mustn't there?

Yes, the sum of the kinetic energy of the two objects.  That's the limit, but since there is no limit to the kinetic energy of an object, there is no upper limit to the energy released by an arbitrary collision.

Any ship defining a speed will need have to arbitrarily choose another frame of reference as its anchor of being at a 'null motion'.

You can, but the energy released in a given collision is not frame dependent.  You'll get the same answer in any frame.

And as it accelerates it will be the acceleration (weight) that informs it of it still not having reached 'c'. Not saying that it can of course but just for the fun of it.

That's right.  One can be in a ship accelerating at 1g indefinitely.  There's no speed you can go where you can't feel more acceleration.  What you describe (the accelerating guy measuring the g force locally) is called proper acceleration.

another way of thinking of it is to define Earth as moving in one direction (with the solar system/galaxy/whatever) relative some other frame, then testing if that gives you a boost depending on where you place the ship, with the 'motion' or against it.

Testing if it gives what a boost?  What is a 'boost'?  How might one test that?  Are the Earth and a ship on collision course?

As far as I get it it won't be any energy saved by that approach intrinsically.

You're trying to save energy.  Not going to happen.  Considering things in different frames doesn't change what actually happens, just like the energy released in the collision described above isn't different depending on your chosen frame.  The frame choice is abstract, but the collision is real and involves a real quantity of energy.

[yor_on]

Halc, it's a thought experiment. It's not meant to be 'practical', you can also consider it a exercise in logic, depending on if you accept the prerequisites. There seems to me there must be a limit for that potential energy I'm discussing due to relative motion. I call it potential because it's not locally measurable experimentally. What happens as they collide is definitely 'kinetic' though. As for when a acceleration ends if there now was such a possibility :) Nah, it doesn't, the energy needed is 'infinite' if you want to reach 'c'.

But that's not the point of the exercise.
=

Spelling

The last part is about what a 'relative motion' means(?) Three objects in different relative motion in a space is a proof of it being as 'real' a motion as a acceleration is. But when it comes to the idea I discuss in where you measure energy spent by your rocket, going 'against the motion' or with the 'relative motion' of Earth that you 'decided to choose', I don't expect there to be a difference. Could be wrong there but I don't think I am.

What the last part comes down to in my mind is that if there was a difference relative motion would no longer be relative. Thinking of it as 'displacements' you might reach a different conclusion, but it wouldn't be correct as I see it.

[Halc]

Halc, it's a thought experiment. It's not meant to be 'practical'

Yes.  None of my answers were comments on practicality.

you can also consider it a exercise in logic, depending on if you accept the prerequisites. There seems to me there must be a limit for that potential energy I'm discussing due to relative motion. I call it potential because it's not locally measurable experimentally.

That's because velocity is a relation, and thus so is kinetic energy.  The kinetic energy of an object is frame dependent, which doesn't make it potential energy.  The energy released in the sorts of collisions you describe is not frame dependent.

What happens as they collide is definitely 'kinetic' though. As for when a acceleration ends if there now was such a possibility Nah, it doesn't, the energy needed is 'infinite' if you want to reach 'c'.

There is no limit to proper acceleration, but yes, there is a limit to speed, so you can't accelerate any object with mass to c with any amount of energy.  This doesn't mean you can't continue to apply force to the object, just that the force just begins to add more to the objects mass than its speed. 

The last part is about what a 'relative motion' means(?) Three objects in different relative motion in a space is a proof of it being as 'real' a motion as a acceleration is.

Not sure what you're trying to say, but real motion seems to require only 2 objects.  Acceleration is objective (can be locally detected), and so requires only one 'system'.  I call it a system because I cannot think of a way to detect acceleration of my object without using moving parts.

But when it comes to the idea I discuss in where you measure energy spent by your rocket, going 'against the motion' or with the 'relative motion' of Earth that you 'decided to choose', I don't expect there to be a difference. Could be wrong there but I don't think I am.

The rocket spends X amount of energy to properly accelerate it by so much, and that expenditure is unrelated to the relative motion of Earth, so long as you're not dragging it along with you.  So I agree here.

I use proper acceleration here, since it presumes the frame of the rocket.  In other frames, this is not true.  It takes far less energy to accelerate an object from .1c to .2c than it takes to accelerate the same object from .85c to .95c, despite the same speed change.  This is relative acceleration, not proper acceleration.  The latter has no speed, but has a certain g force applied over a certain period of local time.  There is no speed involved since an object (rocket say) is always stationary in its own frame.