[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....

[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. 

[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 4375 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 4421 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'.
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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.

[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.
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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.

[yor_on]

Not when looked at from the standpoint of relativity Halc, for that you need three objects to prove it to yourself. With two objects in relative motion you're free to associate any speed you like to yourself from a total standstill to the other object being the one unmoving. But put in one more and it becomes different, then you can prove that different speeds exist even if looked at as relative. Which is weird in one way, in another perfectly fitting to the way we normally look at motion. We do find different speeds to exist every day in our life.

the first one is also about 'potential energy'. In the two body system I described the combined kinetic energy in a collision doesn't change but the 'potential energy' of one or the other becomes diffuse. It's a matter of choice, and not locally measurable.
=

Actually that holds for the three body system too :)

[yor_on]

Not sure how you think there Halc. With two objects in relative motion you are free to associate this 'relative speed' to any of those objects. That's what changes when you introduce a third object. Even though the motion still is 'relative' for each one you now can prove that different speeds exist. May not seem important , but if you combine it with the fact that your potential energy is a fluid expression depending on frames of reference, and that you locally have no way of measure any of this possible energy it becomes interesting, at least to me :)

and it's not about accelerations at all Halc, it's about relative motion, and what it might mean. To it you can add that locally defined there is no way to differ Earths 'relative motion' from Earth being unmoving (black box scenario) the only thing measurable should be the spin. There is some subtlety to the proof in that you still will be unable to give yourself a definite 'speed', even though you now can prove different speeds to exist.
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spelling

[yor_on]

Maybe I should fill in some background to it. Accelerations becomes GR in relativity, 'relative motion' as in a uniform is SR. Accelerations are intrinsic, there will be a measurable force to it locally (weight by scale) also defined as 'gravity' when discussing uniform accelerations.. Relative uniform motion has no such coupling, and can't even be locally defined. And it is weird when you think of it in those terms, at least I find it so. Almost as if they were two disconnected phenomena
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I'll give you another thought experiment. Take those two rockets again, one going in the 'motion' of Earth, the other against that 'relative motion'. Then accelerate Earth at some meaningful number, to then to 'coast' again, uniformly moving. Let the rockets leave Earth. Will they measure any difference locally from the former 'lift of', before that Earthly acceleration?

Will it cost any of them more (or less:) energy?

I would say no, all uniform motions are (locally) equivalent. If they weren't we would have a way to measure it locally.
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If that is correct, how will you measure yourself gaining  'c' in your rocket?
Your relative motion (Earths) at lift of not meaning a thing?

this one included a acceleration, but for the relative (uniform) motion before and after it didn't change a thing.

Another thing worth noticing is that even though we can assume that Earths acceleration had a vector, it didn't change the way Earth in its relative motion still don't have any preferred direction, locally measured.

[yor_on]

A third example: Imagine a rocket constantly accelerating through a space. The idea is that as it gets closer to 'c', it will cost it more energy right, fuel spent etc? Now stop the acceleration, let it coast for a while, then start accelerating again. Will it now draw more fuel than when it once started its journey? (assume that to have been in space too)

Now, if the postulate I presented before where an acceleration didn't change a thing is correct. What do you think will happen in this circumstance?
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Now, what does this remind me of ?
'c'. 

It becomes just as weird, thinking of it in those terms :) I call it 'potential energy', but then you could also include the stress energy tensor acting on you with different 'relative motions' as well as accelerations.

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So to summarize.
I can prove different uniform motions to exist.
I can not prove my own uniform motion though.

All uniform motions must be equivalent, or we would be able to measure a difference locally.
We can't

Equivalent, but still having different speeds, although not possible to define locally.

Now the question becomes, how get those to fit each other :)
Either they do, or they don't.
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Actually I don't see how to understand the stress energy tensor here? If the postulate is correct in where there is no possibility for me to measure locally, and if you simultaneously can prove different 'uniform speeds' then you either gain such or you don't. Reason seem to argue that you can, as with earths 'acceleration' in the above example, but if there is no way to define a 'cost' for those rockets? The last example is just naturally following, a extreme of it.

The other way to see it is that there will be a cost. If that is true then relative motion isn't relative anymore.
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The easiest way to prove that all uniform motions are the same (equivalent) is to use red and blueshifts. With Earth accelerating to a higher 'speed' you could expect a blue respectively redshift to show itself, and it will under the acceleration. But not before, and neither after it.
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there are some 'outlandish' possibilities to it. You might want to assume that accelerations are all there is for example. Just as some argue that a 'real' time dilation only can exist with accelerations.  'gravitational time dilation's' 'Earths spin' all fall under the category 'accelerations' in relativity.

Against that one you have the proof that different uniform motions can be proven to exist.