Defining c

[throng]

Hello everyone,

 

I wonder how to define light speed.

 

Imagine a solitary particle. It isn’t moving toward or away from anything so it “looks” like its still. There is no way to ascertain if it is moving or how fast. Movement and inertia are the same.

 

Is this the nature of light speed?

 

I was kicked off a physics forum for twice posting this notion, so they see it as crackpottery. A generous compliment, I think.

[ajb]

As we are talking about light speed I assume we are talking about special relativity?

 

The way I think of c, is not as the speed of light but as a fundamental constant that defines the causal structure on space-time. It only "happens" to be the universal speed of light in vacuum.

 

Another way I think of it is as the fundamental constant that allows us to "mix" space and time, i.e. [distance] = [time] [speed] = [time][distance]/[time]. (These two ideas are not really independent)

 

As we now have all the same units for space and time we can have transformations that mix the two. These are the Lorentz transformations.

 

I think this is the "correct" way to view c.

[swansont]

Part of the issue is that it doesn't make much sense to describe a situation in which there is but one particle. As you seem to state, a solitary article is assumed to be at rest, because there is nothing to which one might compare to determine relative motion. Including light.

[traveler]

No need to compare, we are talking about reality.

 

If you tell me a particle traveled 10 feet, I know exactly how far that is.

 

If you tell me observer A views the particle as having traveled 20 feet, and observer B views the particle as having traveled 5 feet, then I know for a fact that one or both observers are wrong.

 

The particle traveled a specific distance, whether there is something to measure it against or not, regardless of how many different observations are made of the particle from different angles and distances in the universe.

 

And rest doesn't mean zero velocity, it means zero acceleration.

[ajb]

That is just completely wrong traveler.

 

Swansont has correctly stated that without something to measure motion with respect to the notion of motion becomes lost. This is also why in my first post I don't say anything about particles moving. I point to the geometric significance of c, which we can discuss without particles moving or anything like that.

[traveler]

That is just completely wrong traveler.

 

Swansont has correctly stated that without something to measure motion with respect to the notion of motion becomes lost. This is also why in my first post I don't say anything about particles moving. I point to the geometric significance of c, which we can discuss without particles moving or anything like that.

 

Can you name a place in this universe that has no reference to measure motion, or are you thinking in terms of text books?

 

The universe exists, or?

[ajb]

You want to measure motions in the universe with respect to the universe? Please explain this.

[traveler]

You want to measure motions in the universe with respect to the universe? Please explain this.

 

If I am not there to measure the motion, does that mean the particle doesn't travel a specific distance?

[ajb]

Please just read up on special relativity before you enter a thread on the subject and attempt to argue that it is wrong.

 

Lets try not to get distracted by metaphysical and philosophical issues for now.

[traveler]

Please just read up on special relativity before you enter a thread on the subject and attempt to argue that it is wrong.

 

Lets try not to get distracted by metaphysical and philosophical issues for now.

 

I never mentioned relativity. I merely expressed the idea that there is no such animal as a place in this universe that doesn't have a reference to measure motion.

[ajb]

Maybe not, but the rest of us did. How does what you said help with throng trying to understand the importance of c in physics?

 

The point is no absolute frames of reference exist. The idea that at every point in the universe you can always see something to measure motion with respect to does not imply a global reference frame.

[traveler]

The point is no absolute frames of reference exist

 

A frame of reference has no time, therefore no motion.

[insane_alien]

err, traveler, it would be wise to go and learn what you are talking about before you continue to make yourself look rather foolish.

[Klaynos]

A frame of reference has no time, therefore no motion.

 

Urmm yes they do...

 

I think there's some confusion here.

 

A universe in which there is only one particle, has only one useful frame of reference that at rest with the particle, there's nothing to compare it to to say it's moving with respect to that.

 

Once you introduce an observer "I can see if it moves" you have introduced another rest frame, the frame of some observer, which can be treated as a second particle.

 

So you now have two particles with which you can compare the velocity of one of them with respect to the other. There's nothing else to compare it to.

 

The universe has no absolute rest frame.

 

I'd suggest going and reading about special relativity a bit... and possibly even classical relativity first...

[ajb]

You have lost me now.

 

An inertial reference frame (in special relativity) is just a choice of coordinates on Minkowski space-time [math]\mathcal{M}[/math] (from a particular family of coordinates). That is any point in Minkowski space-time is described by 4-numbers [math]x^{\mu} = \{ct, x,y,z\}[/math].

 

 

"Motion" should be understood as a path in Minkowski space-time. A path is a map [math]\gamma : I \subset \mathbf{R}\rightarrow \mathcal{M}[/math] which can locally be described as [math]x^{\mu}(\lambda)[/math] where [math]\lambda[/math] is a coordinate on [math]\mathbf{R}[/math].

 

Proper time is only defined for time-like paths, which describe the motion of massive particles. Basically, you can pick [math]\lambda[/math] such that it describes the passage of time of a clock being carried by the particle. This is not quite the same thing as the first coordinate [math]ct[/math], think about it. It can't be as this is just a choice of coordinate.

 

So, please explain your last comment. No proper time or no first coordinate? (both make no sense to me)

[traveler]

So, please explain your last comment. No proper time or no first coordinate? (both make no sense to me)

 

My comment, "A frame of reference has no time, therefore no motion" means that there is no relative motion between two objects unless you observe an interval of time. A frame of reference has no interval of time, therefore there is no motion. No change occurs in a zero interval, so there is no relative motion during a zero interval.

[ajb]

Whatever you are trying to say is not worded very well.

 

I think you are just saying "frame of reference = a point". Which is ok. I usually rather think of a frame as being a coordinate choice in the neighbourhood of a point rather than a point itself. An event is a point which can be described using coordinates.

 

Motion is a path, not an isolated point. Fine.

[throng]

So you now have two particles with which you can compare the velocity of one of them with respect to the other. There's nothing else to compare it to.

 

The universe has no absolute rest frame.

 

...

 

 

Imagine the massless solitary partice splits.

 

Both “move forward” at indefinable “speed” and apart relative to each other.

 

We can’t tell which or if both are moving and only velocity (not speed) is detectable.

 

Line motion is detectable so we have time, distance and velocity.

 

“Space” is expanding in a straight line between two massless particles.

 

I don’t know much math. Am I still in the realm?

Edited September 7, 2008 by throng
Incorrect wording

[ajb]

Think about what "move forward" means.

 

I.e. move forward with respect to/ in what direction?

[throng]

Think about what "move forward" means.

 

I.e. move forward with respect to/ in what direction?

 

I used inverted commas as I understand the solitary partial can neither be inert, in motion nor even exist relative to another thing. How would one describe this state? Inertia is equally inaccurate as motion. Is it c?

 

In observing movement in the two halves we could assume that movement of the primary particle was the cause. It could be potential energy, which in turn must be kinetically derived.

 

For the sake of sanity let’s say the primary particle is potential energy and call it E.

 

It splits and movement becomes observable. The particles move in an expanding line. The observer at a third point of reference can’t tell which or if both are in motion.

 

From a particle’s point of view distance is meaningless. The two halves would appear to have distance of “anything”, for there is no third point.

 

So E is conserved in motion and the two particles move in an indefinable way. The linear universe is only observable from a third reference point. (similar to a point universe)

 

The movement between two reference points is as meaningless as the movement of one. How would one assertain distance or speed? At best it could be said the halves are “relative” to each other.

 

Are my visualisations still in the realm?

Edited September 9, 2008 by throng
multiple post merged

[Klaynos]

I think it best if we use massive particles not massless ones. As massless ones lead to all kinds of questions...

 

So your particle splits into two identical ones that start moving away from each other in the rest frame of the original particle.

 

An independent observer could tell that the particles are moving in relation to himself.

 

You seem to be heading along the right tracks.

 

Speed, distance etc are all relative. What someone measures in one frame is different to what someone else will measure in another frame, and neither frame is absolutely correct, neither is preferred.... On earth we often use the earth as our fixed reference frame because it's easy to do. But if we used the reference frame of the sun it would still be possible to work everything out it'd just be more annoying.

[throng]

I think it best if we use massive particles not massless ones. As massless ones lead to all kinds of questions...

 

So your particle splits into two identical ones that start moving away from each other in the rest frame of the original particle.

 

An independent observer could tell that the particles are moving in relation to himself.

 

You seem to be heading along the right tracks.

 

Speed, distance etc are all relative. What someone measures in one frame is different to what someone else will measure in another frame, and neither frame is absolutely correct, neither is preferred.... On earth we often use the earth as our fixed reference frame because it's easy to do. But if we used the reference frame of the sun it would still be possible to work everything out it'd just be more annoying.

 

 

 

 

ONE PARTICLE:

 

From a second point of reference, motion is anything.

 

From within the point universe, there is nothing.

 

 

TWO PARTICLES:

 

The observer at a third point of reference would see motion as an expanding straight line. He has no perception of “sideways” or orbital movement. He can’t tell which or if both are moving. Only straight relative motion can be observed. The universe is an expanding straight line.

 

From within the linear universe motion remains undetectable, though there is a relative movement.

 

 

Is there flaw in that notion?

[Klaynos]

Why do you think a 3rd observer could only see an "expanding straight line", conversation of momentum would say the two would have to be moving away from each other but relative to the observer there's nothing that says they have to be moving at a given velocity...

[throng]

Why do you think a 3rd observer could only see an "expanding straight line", conversation of momentum would say the two would have to be moving away from each other but relative to the observer there's nothing that says they have to be moving at a given velocity...

 

I never mentioned a "given" velocity. Only that velocity is detectable, and only from a reference point not on the trajectory.

 

From any point on the trajectory no motion is detectable, no line is detectable, no distance is detectable and no velocity is detectable.

 

From within the linear universe the point of observation is the only thing observable. (as opposed to a point universe where only nothing is detectable from within.)

 

Can that be denied? If not, I'd like to expand the concept a little furthur so as to more accurately define c.

 

If I am not there to measure the motion, does that mean the particle doesn't travel a specific distance?

 

 

 

I understand your point.

 

There is an actual distance travelled. The observer would perceive the motion and distance relative to his own perspective.

 

You point out the actuallity that the observer's perception is relative to.

 

It is not included in relativity.

 

This thread is just visual thinking about particles, movement and c so if you can picture it, thats all you need.

 

I appreciate your point that perception seems relative to an actuality and hope you contribute to the thread.

 

Don't be intimididated by the knowledgable. Those who know most know how little they know.

Edited September 11, 2008 by throng
multiple post merged

[uncool]

Guys:

 

One of the assumptions of relativity is that there are such things as inertial paths. Once you assume that, you can take any inertial path. Then anything moving at the speed of light will be moving at the speed of light relative to any other inertial path.

 

You can also get the speed of light from Maxwell's equations, which state how fast an electromagnetic wave moves through space (hint: it's at a familiar speed...)

=Uncool-