Is it Possible For A Particle To Stay Completely Still in Space-Time?

[OpenSourceArts]

What is the minium velocity that a particle can have through
space-time?

What is the maximum velocity that a particle can have through
space-time?

Thanks!

 

[daniel_i_l]

-The speed of light
-The speed of light

 

[JesseM]

What is the minium velocity that a particle can have through
space-time?

When you say velocity "through space-time", do you mean something different than ordinary velocity through space (ie distance divided by time)? In his explanation of relativity Brian Greene defines his own notion of "speed through space-time", but like I said on the other thread about "speed through time" (what happened to that thread?), Brian Greene's explanation and definitions are different from the usual ones in most textbooks.

If you're just talking about ordinary velocity, keep in mind that all velocities depend on your reference frame, there's no absolute truth about an object's velocity. Relative to a given frame the minimum speed an object can have is zero, but if my speed is zero in one frame, in other frames it will be nonzero. The maximum speed is the speed of light, and if something has the speed of light in one frame, it must have the speed of light in all frames.

 

[daniel_i_l]

An particle will always travel through ST at the speed of light. But exactly how much of that speed is through space and how much through time depends on the frame.

 

[OpenSourceArts]

Thanks for the correct answer daniel.

So then it is impossible to stand still in space-time.

Why is this?

How can it be impossible to stand still in space-time?

What does this imply about the underlying fabric of space-time?

 

[HallsofIvy]

It would help you a heck of a lot to find out what "space-time" means before you use the words.

 

[OpenSourceArts]

Why do you think I don't know what space-time means?

I think I do.

Can you please define it?

 

[quantumdude]

What does this imply about the underlying fabric of space-time?

I don't think it implies anything about the fabric of spacetime, but rather about the definition of velocity that one chooses.

 

[OpenSourceArts]

Isn't it amazing that it is impossible to stand still in the space-time continuum?

Isn't it also amazing that it is impossible to change one's velocity through the space-time continuum?

It seems that the fourth dimension must be expanding relative to the three spatial dimensions.

When we're in the expanding fourth dimension, we are stationary relative to the fourth dimension--time stops.

When we're not in the fourth dimension, we are stationary relative to the three spatial dimensions. Photons can be carried away from us, and we age, or experience time.

 

[quantumdude]

Isn't it amazing that it is impossible to stand still in the space-time continuum?

Maybe if you take that as an isolated axiom and do not consider the rest of what we know about physics. But if you take Maxwellian electrodynamics and impose the eminently reasonable requirement that that theory be invariant under boosts from one inertial frame to another, then the idea that one's 4-speed is always c is not such a "gee-whiz" phenomenon at all.

Isn't it also amazing that it is impossible to change one's velocity through the space-time continuum?

Under the assumptions of SR, you can change your 4-velocity. You just can't change your 4-speed.

It seems that the fourth dimension must be expanding relative to the three spatial dimensions.

When we're in the expanding fourth dimension, we are stationary relative to the fourth dimension--time stops.

When we're not in the fourth dimension, we are stationary relative to the three spatial dimensions. Photons can be carried away from us, and we age, or experience time.

Near as I can tell, none of this makes any sense in the context of Special Relativity. Are these your own ideas you are proposing? Because if it is then I would like to advise you that the Independent Research Forum is the only section of PF in which non-peer reviewed ideas are hosted. That is explicitly stated in our Guidelines, and you agreed to it before you started posting.

 

[OpenSourceArts]

I think Brian Greene said this somewhere. I will check and get back to you.

You write, "Under the assumptions of SR, you can change your 4-velocity. You just can't change your 4-speed."

Where can I find out more about this? Can you give an example of changing the 4-velocity without changing the 4-speed?

Thanks!

 

[selfAdjoint]

I think Brian Greene said this somewhere. I will check and get back to you.
You write, "Under the assumptions of SR, you can change your 4-velocity. You just can't change your 4-speed."
Where can I find out more about this? Can you give an example of changing the 4-velocity without changing the 4-speed?
Thanks!

What he meant here is that different observers moving differently in relation to you will see your 4-velocity differently, but they will all see the same 4-speed. Each will see some particular allocation of value to the time components and the space components but the 4-vector relationship $$vectormagnitude^2 = sizeoftimecomponent^2 - sizeofspacecomponent^2$$ will be true for everybody (everybody inertial anyway).

 

[OpenSourceArts]

So then we are all in agreement that the minimum and maximum value of a particle's velocity through space-time is c. So then it is impossible for a particle to stand still in space-time or ever change its velocity through space-time.

What does this imply about space-time?

 

[pervect]

So then we are all in agreement that the minimum and maximum value of a particle's velocity through space-time is c. So then it is impossible for a particle to stand still in space-time or ever change its velocity through space-time.

What does this imply about space-time?

I see OSA has decided to take a vacation, so I'll point out that "we-all" don't agree that the velocity of a particle "through space-time" is well-defined, the terminology is rather vague.

A minor fix fixes this - the magnitude of the 4-velocity of a particle through space-time is well defined, and is equal to 'c'. This change in wording avoids confusing 4-velocities with ordinary velocities - ordinary velocities only occur through space, not space-time.

The invariance of the magnitude of the 4 velocity is a direct consequence of Lorentz invariance of space-time.

 

[JesseM]

So then we are all in agreement that the minimum and maximum value of a particle's velocity through space-time is c. So then it is impossible for a particle to stand still in space-time or ever change its velocity through space-time.

What does this imply about space-time?

It really just implies that Brian Greene picked a somewhat arbitrary and counterintuitive way to define the term "speed through spacetime", which is not a traditional concept in relativity. See this thread for more on the details of Greene's definitions and some criticisms of it.

 

[Garth]

So then we are all in agreement that the minimum and maximum value of a particle's velocity through space-time is c. So then it is impossible for a particle to stand still in space-time or ever change its velocity through space-time.

What does this imply about space-time?

A particle that appeared and then disappeared instanteously, coming into existence only for an 'instant', might be said to be "standing still" in space-time. In actual fact a massive virtual particle doing just that would nevertheless have a very short life-time, and hence very short world-line.

Of course this is only illustrating the poor terminology being used here. All world lines "stand still" in space-time. A 4-view of the universe is a frozen 'block universe', time is already included within it; it is by trying to envisage this 4-D perspective with language ("speed") that is only appropriate to a 3+1D view of the world that is causing the confusion.

I hope this helps.

Garth