Attention Paid To Accelerating Reference Frames Overthrows SR

[Hurkyl]

Ok, so that's speed in an inertial frame. What's relative speed?

 

[StarThrower]

Ok, so that's speed in an inertial frame. What's relative speed?

Suppose that two objects are not moving relative to each other.

The distance between them in any frame is unchanging.

In this case, the relative velocity v is zero.

Case II: not (v=0)

Suppose that two objects are in relative motion. Thus, the distance between them is changing.

Choose one object to be at rest, at the origin of its own frame of reference, say F1. Since the two objects are in relative motion, the distance between them is changing. Thus, the coordinates of object 2 are changing in F1.

Let the position of object 2 at the current moment in time, in F1 be denoted by (x,y,z).

Define the position vector of object 2 in F1 as follows:

$$\vec{r} = xi + yj + zk$$

Let there be an infinite number of clocks in F1, one at every point. Let all the clocks be synchronized.

Let (x1,y1,z1) be the position of object 2 in F1, the moment when all clocks read 1. Let (x2,y2,z2) be the position of object 2 in F1, the moment when all clocks read 2, and so on.

The relative speed of object 1 to object 2 can be defined as follows:

$$|\vec{V}| = \frac{|\vec{r2} - \vec{r1}|}{2-1}$$

Or we can define time of travel using arbitrary clock readings. Let object 2 be located at (x1,y1,z1) when all clocks read A, and later, let it be located at position (x2,y2,z2) when all clocks read B. The clocks increase in their readings, tick at the same rate (by hypothesis), hence B>A. The relative speed of object 2 to object one is the magnitude of the objects velocity vector which is:

$$\vec{V} = \frac{\vec{r2} - \vec{r1}}{B-A}$$

Kind regards,

StarThrower

Keep in mind, that the above definition is only useful when the relative speed is constant in time. If the objects are accelerating relative to each other, then the denominator must be vanishingly small.

 

[Hurkyl]

Suppose that two objects are in relative motion. Thus, the distance between them is changing.

According to some reference frame, I presume you mean?

Choose one object to be at rest, at the origin of its own frame of reference, say F1.

This doesn't apply to photons. Would you care to provide a definition of relative speed that does work for photons?

 

[StarThrower]

Choose one object to be at rest, at the origin of its own frame of reference, say F1.

This doesn't apply to photons. Would you care to provide a definition of relative speed that does work for photons?

Yes it does.

Kind Regards,

StarThrower

P.S. Certainly you can analyze the motion in a reference frame in which the photon is at rest. Whether or not that frame happens to be inertial is a totally separate issue.

 

[quantumdude]

So this is what this thread has boiled down to?

OK, fine.

Yes it does.

No, it doesn't.

There is no reference frame in which the photon is at rest.

 

[Hurkyl]

Yes it does.

This definition requires one of the objects in question to have a rest frame. Since photons don't have rest frames, this definition does not work.

 

[StarThrower]

So this is what this thread has boiled down to?

OK, fine.



No, it doesn't.

There is no reference frame in which the photon is at rest.

Incorrect Tom. You can choose any object in the universe you wish, and fix a rectangular coordinate system to it.

What you are concerned about is whether or not such a reference frame is an inertial reference frame, well I have news for you... if the photon isn't being subjected to a force, then it is.

Kind regards,

The Star

 

[quantumdude]

Incorrect Tom.

You can choose any object in the universe you wish, and fix a rectangular coordinate system to it. Makes sense to place the object at the origin of the system/reference frame. Then you get to the concept of "worldline" but I'm not going there.

Whatever. If you fix a rectangular system to a photon, then that rectangular coordinate system will be moving at the speed of light in anyone's frame.

What you are concerned about is whether or not such a reference frame is an inertial reference frame, well I have news for you... it is.

If you consider an inertial reference frame to be one that can always be brought to rest by a change of coordinates, then I have news for you: A photon cannot be placed at the origin of such a frame.

 

[StarThrower]

:

If you consider an inertial reference frame to be one that can always be brought to rest by a change of coordinates, then I have news for you: A photon cannot be placed at the origin of such a frame.

Notice I changed that post slightly. It now reads:

If the photon isn't being subjected to an outside force, then that photon is in an inertial reference frame.

Kind regards,

StarThrower

 

[quantumdude]

Notice I changed that post slightly. It now reads:

If the photon isn't being subjected to an outside force, then that photon is in an inertial reference frame.

So? What does that have to do with the fact that you cannot consider the photon as the origin of a stationary frame?

 

[StarThrower]

This definition requires one of the objects in question to have a rest frame. Since photons don't have rest frames, this definition does not work.

Well then Hurkyl, that's really what it all boils down to huh?

A photon placed at the origin of a frame is at rest in a frame. It's in a rest frame, regardless of whether or not that frame is inertial. I mean we can view life from a photon's point of view.

It all boils down to this:

Is a photon which isn't being subjected to a force in an inertial reference frame?

The answer of course is yes.

Kind regards,

StarThrower

 

[Hurkyl]

A photon placed at the origin of a frame is at rest in a frame.

Too bad that the time axis of such a coordinate chart is a null vector, and thus can't be considered a frame.

Is a photon which isn't being subjected to a force in an inertial reference frame?

The answer of course is yes.

Why of course?

 

[Hurkyl]

And no I'm not getting sloppy.

Earlier on, you insisted on long, detailed proofs, even of elementary facts (though, admittedly, you were making tons of implicit assumptions).

Now, your assertions are backed up with phrases like "of course it's yes".

That's what I call getting sloppy. You were only interested in proving the things with which you know I'll agree; once we get to points of debate, you have lost all interest in proof.

 

[russ_watters]

Well, what a nice thread. Scrolling back a little, I found this gem:

I did not "assume" the speed of light depends upon inertial frame, in fact, I assumed the exact opposite (that it doesn't), and subsequently arrived at a contradiction.

Translation: I assume SR to be wrong, therefore SR is wrong.

Hmm...speaking of contradictions.

If you consider an inertial reference frame to be one that can always be brought to rest by a change of coordinates, then I have news for you: A photon cannot be placed at the origin of such a frame.

We've discussed this one too.

Essentially guys, StarThrower bases his beliefs here on several basic assumptions that are contrary to accepted physics. I honestly don't know how to fix that: like he said, "you can lead a horse to water..."