[Waste of Time (OP)]

   The following scenario utilizes events that are applicable to Einstein’s Special Relativity Theory. What follows requires further analysis regarding application of the first postulate WRT SRT. For information with images, see http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/5916 [nofollow].

- Definitions; (Beta) β = v/c, (Gamma) γ = (1-v^2/c^2)^-1/2.
- Electromagnetic relations (second postulate); x = cΔτ, x’ = cΔτ’.
- There are two parallel linear events (A and B) with uniform velocity along the positive x-axis.
- Event A is an electromagnetic event (velocity = c) following the path from point x = 0 to x.
- Event B is an inertial body event (velocity = u) following an identical and parallel path from point x = 0 to x.

EVENTS OCCURRING IN REST FRAME (v = 0)
- These events now occur within a reference frame considered to be at rest (rest frame).
- The event time for A is; Δτ = x/c.
- The event time for B is; Δt = x/u.
- The ratio of these event times gives us the relationship between their event times;
Δτ/Δt = (x/c)/(x/u) = u/c.

EVENTS OCCURRING IN INERTIAL FRAME (v)
- These events now occur within a reference frame considered to be in uniform motion (inertial frame).
- The SRT event time for A is; Δτ = (Δτ’+vx’/c^2)γ. Applying the second postulate;
Δτ = (Δτ’+vx’/c^2)γ, x’ = cΔτ’
Δτ = (Δτ’+v(cΔτ’)/c^2)γ
Δτ = (Δτ’+vΔτ’/c)γ
Δτ = Δτ’(1+ β)γ
- The SRT event time for B is; Δt = (Δt’+vx’/c^2)γ.
- The ratio of these event times gives us their the relationship between their event times;
Δτ/Δt = [Δτ’(1+ β)γ]/[(Δt’+vx’/c^2)γ]
Δτ/Δt = [Δτ’(1+ β)]/[(Δt’+vx’/c^2)]
Δτ/Δt = [Δτ’(1+ β)]/[Δt’(1+vx’/(c^2)Δt’)]
Δτ/Δt = [Δτ’(1+ β)]/[Δt’(1+ βx’/cΔt’)]

   In order to satisfy the first postulate, the relationship between their event times must remain unchanged in order to prevent one from ascertaining the motion of the inertial frame utilizing this scenario. As we can clearly see, the relationship between their event times can only be regained by allowing an electromagnetic relation (x’ = cΔt’) to be utilized to reduce the Δt relation to (1+ β) in order to regain equality for these events.
Δτ/Δt = [Δτ’(1+ β)]/[Δt’(1+ βx’/cΔt’)], x’ = cΔt’
Δτ/Δt = [Δτ’(1+ β)]/[Δt’(1+ β)]
Δτ/Δt = Δτ/Δt
   If we were to allow this substitution, then we would have to admit that in order for the first postulate to remain valid, then the Lorentz transformations (in their current format) could only apply to electromagnetic events. It appears that the only recourse would be to reformat the Lorentz temporal transformation to;
***Δτ = Δτ’(1+ β)γ

[jeffreyH]

http://en.wikipedia.org/wiki/Principle_of_relativity

Principle of relativity

"In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

For example, in the framework of special relativity the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell equations or the Einstein field equations have the same form in arbitrary frames of reference.

Several principles of relativity have been successfully applied throughout science, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein's special relativity and general relativity)."

Now I haven't even had the time to read carefully through your post but are you saying this is not correct? Are you saying it needs to be modified?

[jeffreyH]

So what you are saying is that light is intrinsically linked to gravitation.

[Waste of Time (OP)]

All that I show is that the current format of the Lorentz temporal transformation complies with the first postulate for round-trip events, but not one-way events. We can either choose to accept this as a limitation of STR, or choose a format for the temporal transformation that does comply with the first postulate for one-way events.

[Colin2B]

All that I show is that the current format of the Lorentz temporal transformation complies with the first postulate for round-trip events, but not one-way events. We can either choose to accept this as a limitation of STR, or choose a format for the temporal transformation that does comply with the first postulate for one-way events.

Hi Robert
Hadn't come across this argument before, and as this is not my subject area I, like Jeffrey, will need to read though a few times. But a couple of initial observations:

I can't see why what you've written applies to one way events and not to round trip events.
Some of the reasoning in your gsjournal paper is a little obscure and it's easy to lose track of what you are saying.
In your uniform motion frame you appear to apply dilation to the time of travel of the EM wave, have I misunderstood?
In your paper you say

"Since the principle of relativity requires that the laws of physics remain valid for all
reference frames, then the resulting measurements of the two events must be identical in a state of motion as they were observed at rest."

At first sight it appears to me that this could be a confusion between who is observing and from which frame, can you make this clearer please?. The introduction of your 'unity' as a physical law could well be compounding this confusion.
As I say these are only my first thoughts and I need to go away and think over. Greater minds than mine may well see instantly what you are saying.

Just a comment, some people here refuse to read non-peer reviewed papers and self published theories, so you might find limited responses to your post.

[jeffreyH]

I will be coming back to this.

[Colin2B]

So what you are saying is that light is intrinsically linked to gravitation.

I thought variability of light was only seen in accelerating frames eg influence of gravity, not inertial frames.
Did I miss something in the arguments?

[PmbPhy]

- There are two parallel linear events

What is "parallel linear events" supposed to mean?

- Event A is an electromagnetic event (velocity = c)...

There is no such thing as an electromagnetic event. What do you mean when you use that phrase?

- Event B is an inertial body event (velocity = u) ...

There is no such thing as an inertial body event . What do you mean when you use that phrase?

EVENTS OCCURRING IN REST FRAME (v = 0)
- These events now occur within a reference frame considered to be at rest (rest frame).
- The event time for A is; Δτ = x/c.
- The event time for B is; Δt = x/u.

What is "x"?

What is the difference between τ and t? Or are those terms defined by those relations?

- The ratio of these event times gives us the relationship between their event times;
Δτ/Δt = (x/c)/(x/u) = u/c.

EVENTS OCCURRING IN INERTIAL FRAME (v)
- These events now occur within a reference frame considered to be in uniform motion (inertial frame).
- The SRT event time for A is; Δτ = (Δτ’+vx’/c^2)γ. Applying the second postulate;
Δτ = (Δτ’+vx’/c^2)γ, x’ = cΔτ’
Δτ = (Δτ’+v(cΔτ’)/c^2)γ
Δτ = (Δτ’+vΔτ’/c)γ
Δτ = Δτ’(1+ β)γ
- The SRT event time for B is; Δt = (Δt’+vx’/c^2)γ.
- The ratio of these event times gives us their the relationship between their event times;
Δτ/Δt = [Δτ’(1+ β)γ]/[(Δt’+vx’/c^2)γ]
Δτ/Δt = [Δτ’(1+ β)]/[(Δt’+vx’/c^2)]
Δτ/Δt = [Δτ’(1+ β)]/[Δt’(1+vx’/(c^2)Δt’)]
Δτ/Δt = [Δτ’(1+ β)]/[Δt’(1+ βx’/cΔt’)]

It's not enough to merely write down formulas. One has to explain exactly what those formulas mean and what they're describing. I can't see that from what you've written down so far.

   In order to satisfy the first postulate, the relationship between their event ..

I don't understand. Who are "they" when you say "their event"?

times must remain unchanged in order to prevent one from ascertaining the motion of the inertial frame utilizing this scenario.

That's not at all what the first postulate means. All it means is that you can't determine an inertial frames absolute motion through space. It doesn't mean that you can't determine its motion relative to another inertial frame.

[jeffreyH]

So what you are saying is that light is intrinsically linked to gravitation.

I thought variability of light was only seen in accelerating frames eg influence of gravity, not inertial frames.
Did I miss something in the arguments?

No you didn't miss anything. It just gave me a thought which I am following up on. I followed his train of thought with difficulty but saw something interesting. It might be garbage but I am following it up.

[jeffreyH]

This is what HeyBert's time dilation profile for one way trips looks like.

Here is the standard plot of time dilation.

http://commons.wikimedia.org/wiki/File:Time_dilation.svg

EDIT: re-uploaded the graph as I forgot the square root in the first one.

[Colin2B]

So what you are saying is that light is intrinsically linked to gravitation.

I thought variability of light was only seen in accelerating frames eg influence of gravity, not inertial frames.
Did I miss something in the arguments?

No you didn't miss anything. It just gave me a thought which I am following up on. I followed his train of thought with difficulty but saw something interesting. It might be garbage but I am following it up.

Understood, sometimes good ideas come from thinking laterally about garbage.
However, I've made my mind up about this one. My gut feeling was right:

At first sight it appears to me that this could be a confusion between who is observing and from which frame, can you make this clearer please?. The introduction of your 'unity' as a physical law could well be compounding this.

Confirmed by PmbPhy - thanks PmbPhy

   In order to satisfy the first postulate, the relationship between their event ..

I don't understand. Who are "they" when you say "their event"?

OK HeyBert, I see what's happened. I will refer to the frames you call 'at rest' and 'moving'.

If we take an observer who was 'at rest' and is now moving, call him RM, at rest he will measure v, u, x, t, T and when moving v', u', x', t', T' and find that v=v', u=u' etc in other words everything appears as it was when at rest. As implied in the first postulate, RM cannot determine from physical laws whether he is at rest or not.

However, you have applied transforms to the moving frame and that is only valid for an observer who has remained, ie still is, at rest (call him RR).
You now appear to try to apply the equality* valid only for RM, to the observations of RR. These two sets of observations cannot be mixed, hence you create a false conclusion. (* what you state as "the relationship between their event times must remain unchanged")

I think you have misled yourself by using lots of ratios using Δ. If you had stuck to plain v, u, t etc for each observer you would have spotted the problem earlier. To be fair, you were rather set up by the paper you quote which makes the same errors.
GIGO

I wish you well in your studies, but would suggest you check out the excellent resources on the net describing relativity, correctly. Your teacher should be able to point out some relevant sites or texts.

[Waste of Time (OP)]

Perhaps we can look at it this way as my original choice of words may have not been understood clearly by all...(τ and t indicate time spans, or time intervals measured by a clock).

In a stationary laboratory frame (considered to be at rest), a photon and electron race each other along the positive x-axis for an identical distance (they both start the race simultaneously at x = 0). Although the photon and electron travel an identical distance along the x-axis, their velocities and time span for traversing this distance will be different. Utilizing the Lorentz transformations with respect to the stationary laboratory frame, calculate the ratio of the time span it takes for the photon to traverse this distance to the time span it takes for the electron to traverse this distance (τ/t).

Now we introduce another inertial frame at uniform velocity (v), relative to the stationary frame, whose x'-axis moves along the stationary frames' positive x-axis. We reproduce the identical photon vs. electron race in the inertial frame at velocity (v), yet we start this race when the coordinate system origins of the stationary frame and inertial frame at velocity (v) coincide. Utilizing the Lorentz transformations with respect to the stationary laboratory frame, calculate the ratio of the time span it takes for the photon to traverse this distance to the time span it takes for the electron to traverse this distance (τ/t).

Does the ratio of these two scenarios mathematically equal each other (same race happening in two different inertial frames)? If so, then how? If not, then what would stop us from determining the velocity of the inertial frame at velocity (v) by conducting such a "race" experiment and measuring how the ratio changes with increasing velocity of the inertial frame?

Fascinating discussions BTW.

[Waste of Time (OP)]

My calculations, where γ = (1-v^2/c^2)^-1/2;

When the race occurs within the stationary laboratory frame (v = 0), no calculation is needed (inverse Lorentz transformation reduces to Galilean format) and the ratio of the photon time span to the electron time span WRT the stationary laboratory frame is simply;

Photon:    τ = τ'

Electron:   t = t'

Ratio #1:  τ/t = τ'/t'

When the race occurs within the inertial frame at velocity (v), the calculation of the ratio of the photon time span to the electron time span WRT the stationary laboratory frame IAW the inverse Lorentz transformation is;

Photon:     τ=(τ'+vx'/c^2)γ
                Since it is a photon, the second postulate gives x' = cτ'
                τ=(τ'+v(cτ')/c^2)γ
                τ=(τ'+v(τ')/c)γ
                τ=τ'(1+v/c)γ

Electron:   t=(t'+vx'/c^2)γ

Ratio #2:  τ/t = [τ'(1+v/c)γ]/[(t'+vx'/c^2)γ]
                τ/t = τ'(1+v/c)/(t'+vx'/c^2)
                τ/t = τ'(1+v/c)/(t'+vx't'/t'c^2)
                τ/t = τ'(1+v/c)/t'(1+vx'/t'c^2)
                τ/t = τ'(1+v/c)/t'(1+(v/c)(x'/ct'))

Clearly these ratios differ. Why?

[Waste of Time (OP)]

What about a round-trip race? Well, let's walk the dog on that one shall we...

We will utilize the same photon/electron race scenario as before, only now we add the requirement for the photon and electron to be reflected (after traveling an identical distance along the positive x-axis) and travel an identical distance back along the negative x-axis. The new round-trip times will be reflected as rτ for the photon and rt for the electron.

When the race occurs within the stationary laboratory frame (v = 0), no special calculation is needed (Lorentz transformations reduce to Galilean format) and the ratio of the photon time span to the electron time span WRT the stationary laboratory frame is (1/2 the trip is in the positive x-axis direction, the other 1/2 of the trip is in the negative x-axis direction, where both photon and electron end up returning to their perspective points of origin);

Photon:    rτ = τ'+τ'
               rτ = 2τ'

Electron:  rt = t'+t'
               rt = 2t'

Ratio #1:  rτ/rt = 2τ'/2t'
                rτ/rt = τ'/t'

When the race occurs within the inertial frame at velocity (v), the calculation of the ratio of the photon time span to the electron time span WRT the stationary laboratory frame IAW the Lorentz transformations is;

Photon:     rτ = (τ'+vx'/c^2)γ + (τ'+v(-x')/c^2)γ
                rτ = (τ'+vx'/c^2)γ + (τ'-vx'/c^2)γ
                Since it is a photon, the second postulate gives x' = cτ'
                rτ = (τ'+v(cτ')/c^2)γ + (τ'-v(cτ')/c^2)γ
                rτ = (τ'+v(τ')/c)γ + (τ'+v(τ')/c)γ
                rτ = τ'(1+v/c)γ + τ'(1-v/c)γ
                rτ = τ'γ+τ'(v/c)γ+τ'γ-τ'(v/c)γ
                rτ = 2τ'γ
                *NOTE: (2τ'γ) was expected as this is the same round-trip time that would occur for the photon if the race occurred along the y-axis (reference "http://en.wikipedia.org/wiki/Michelson [nofollow]–Morley_experiment", 'Length contraction and Lorentz transformation' section). See also "http://www.people.fas.harvard.edu/~djmorin/chap11.pdf [nofollow]".

Electron:   rt = (t'+vx'/c^2)γ + (t'+v(-x')/c^2)γ
                rt = (t'+vx'/c^2)γ + (t'-vx'/c^2)γ
                rt = t'γ+t'(vx'/c^2)γ+t'γ-t'(vx'/c^2)γ
                rt = 2t'γ
                *NOTE: (2t'γ) was expected as the same relativistic delay (γ factor) encountered by the photon would also be expected to affect the electron in order for the measured race results to appear the same to the inertial frame at velocity (v) as when the race occurred within and was measured by the stationary laboratory frame.

Ratio #2:  rτ/rt = (2τ'γ)/(2t'γ)
                rτ/rt = τ'/t'

The ratios are identical as expected since "The laws of physics are the same in all inertial frames of reference." This means that the race results measured by the stationary laboratory frame when the race occurs within the stationary laboratory frame as well as the race results measured by the inertial frame at velocity (v) when the race occurs within the inertial frame at velocity (v) will be identical. This is Einstein's first postulate in action!

Why are the ratios equal for the round-trip races, yet unequal for the one-way races?

[Colin2B]

OK, things are staring to look clearer, but before we confuse ourselves with maths let's be really clear that we are talking about the same things.

Perhaps we can look at it this way as my original choice of words may have not been understood clearly by all...(τ and t indicate time spans, or time intervals measured by a clock).

Which clock? Sorry to labour this but there are 2 clocks, one in the rest frame and one in the moving frame.
For the observer in the moving frame the moving clock measures the same time intervals as when he made the same measurements in the rest frame so T/t is the same. So by doing a physics experiment he sees no difference between the frames. From his point of view he is stationary (because he is moving with the frame) and no Lorentz transforms are required.

For the observer in the rest frame observing the moving frame, he sees the clock in the moving frame measuring time more slowly than the one he has next to him in the rest frame. So the T/t is not the same and this difference is calculated using the Lorentz transforms.

Does the ratio of these two scenarios mathematically equal each other (same race happening in two different inertial frames)? If so, then how? If not, then what would stop us from determining the velocity of the inertial frame at velocity (v) by conducting such a "race" experiment and measuring how the ratio changes with increasing velocity of the inertial frame.

As we can see, it depends who is doing the observing.
For the observer who was stationary and is now moving there is no difference and this is what the postulate is all about. The observer cannot tell by the race experiment whether he is moving or not. He can however, look out of the window and see he is moving away from the rest frame, so would perceive himself as moving.

For the observer who is stationary observing the moving frame, no the ratios are not the same. That's what relativity is all about, frames moving relative to one another.

Again sorry to labour this, but it think there is a confusion of observers.
I hate to say it but I don't think you are comparing light with light!  []

[PmbPhy]

My calculations, where γ = (1-v^2/c^2)^-1/2;

When the race occurs within the stationary laboratory frame (v = 0), no calculation is needed (inverse Lorentz transformation reduces to Galilean format) and the ratio of the photon time span to the electron time span WRT the stationary laboratory frame is simply;

Photon:    τ = τ'

Electron:   t = t'

You keep posting things like this without defining them. What you said tells us nothing about what those quantities are/mean.

[Waste of Time (OP)]

Which clock? Sorry to labour this but there are 2 clocks, one in the rest frame and one in the moving frame.
For the observer in the moving frame the moving clock measures the same time intervals as when he made the same measurements in the rest frame so T/t is the same. So by doing a physics experiment he sees no difference between the frames. From his point of view he is stationary (because he is moving with the frame) and no Lorentz transforms are required.

I use the same definitions for the variable "types" as Einstein within his book "Relativity: The Special and General Theory", i.e. the primed variable is with respect to the co-ordinate system K' and the unprimed variable is with respect to the co-ordinate system K. I use the Lorentz transformations in the same manner as well.

[Waste of Time (OP)]

My calculations, where γ = (1-v^2/c^2)^-1/2;

When the race occurs within the stationary laboratory frame (v = 0), no calculation is needed (inverse Lorentz transformation reduces to Galilean format) and the ratio of the photon time span to the electron time span WRT the stationary laboratory frame is simply;

Photon:    τ = τ'

Electron:   t = t'

You keep posting things like this without defining them. What you said tells us nothing about what those quantities are/mean.

"Utilizing the Lorentz transformations with respect to the stationary laboratory frame, calculate the ratio of the time span it takes for the photon to traverse this distance to the time span it takes for the electron to traverse this distance (τ/t)." Already defined both time variables here.

"When the race occurs within the inertial frame at velocity (v)." Already defined what this velocity is here.

For all the primed variables, the clarification is as follows. IAW Einstein's book "Relativity: The Special and General Theory", the primed variable is with respect to the co-ordinate system K' and the unprimed variable is with respect to the co-ordinate system K.

[Waste of Time (OP)]

I am definitely learning a lot about the specific vernacular used to communicate these physics ideas to others on this forum...thanks for the feedback.

[Waste of Time (OP)]

OK, things are staring to look clearer, but before we confuse ourselves with maths let's be really clear that we are talking about the same things.

Perhaps we can look at it this way as my original choice of words may have not been understood clearly by all...(τ and t indicate time spans, or time intervals measured by a clock).

Which clock? Sorry to labour this but there are 2 clocks, one in the rest frame and one in the moving frame.
For the observer in the moving frame the moving clock measures the same time intervals as when he made the same measurements in the rest frame so T/t is the same. So by doing a physics experiment he sees no difference between the frames. From his point of view he is stationary (because he is moving with the frame) and no Lorentz transforms are required.

For the observer in the rest frame observing the moving frame, he sees the clock in the moving frame measuring time more slowly than the one he has next to him in the rest frame. So the T/t is not the same and this difference is calculated using the Lorentz transforms.

Does the ratio of these two scenarios mathematically equal each other (same race happening in two different inertial frames)? If so, then how? If not, then what would stop us from determining the velocity of the inertial frame at velocity (v) by conducting such a "race" experiment and measuring how the ratio changes with increasing velocity of the inertial frame.

As we can see, it depends who is doing the observing.
For the observer who was stationary and is now moving there is no difference and this is what the postulate is all about. The observer cannot tell by the race experiment whether he is moving or not. He can however, look out of the window and see he is moving away from the rest frame, so would perceive himself as moving.

For the observer who is stationary observing the moving frame, no the ratios are not the same. That's what relativity is all about, frames moving relative to one another.

Again sorry to labour this, but it think there is a confusion of observers.
I hate to say it but I don't think you are comparing light with light!  []

I think we can come to a common interpretation by "walking the dog" if you're up to it...wadda ya say?