The Fundamental Postulate Of Special Relativity Is Self-Contradictory

[StarThrower]

And another nifty thing about degenerate coordinate systems; even if you could convince me that a photon-centered inertial reference frame exists, there is no contradiction between the assertion "The speed of the photon is c" and "The photon is at rest" because the worldline of the photon is a single point.

That isn't a way out.

Postulate: The speed of a photon is 299792458 m/s in ANY inertial reference frame.
The postulate is either true or false.

The postulate is false provided there is at least one inertial reference frame in which the speed of a photon isn't 299792458 m/s. In a photonic reference frame (reference frame in which a photon is at rest), the speed of a photon is 0. Thus, if a reference frame in which a photon is at rest is an inertial reference frame, then the postulate is false.

A reference frame in which a photon is at rest will be an inertial reference frame if Newton's first law of motion is satisfied. Newton's first law of motion is that an object at rest will remain at rest unless acted upon by an outside force, and an object in motion will remain in motion in a straight line at a constant speed, unless acted upon by an outside force. This is precisely the case with reference frame F1 in this thread.

We are standing on top of the whole issue. Will a clock traveling along with a photon tick. The answer is either yes or no. You say no. That is what I have a huge problem with, and won't ever believe.

Kind regards,

The Star

 

[Hurkyl]

I deleted that post because upon reflection, I didn't think it made sense (because, as is brought up, you can't really define speed)

 

[StarThrower]

I deleted that post because upon reflection, I didn't think it made sense (because, as is brought up, you can't really define speed)

To me, this is all a matter for binary logic, and its not really even so hard.

There is one statement we are all investigating, and that statement is world-famous. The statement I am challenging is the fundamental assumption of the special theory of relativity.

Fundamental postulate of SR: The speed of a photon is 299792458 meters per second in any inertial reference frame.

Using nothing more than binary logic, the statement is false provided there is at least one reference frame which is an inertial reference frame, in which the speed of a photon isn't c.

Clearly, a reference frame with a photon at the origin is a reference frame in which the speed of a photon isn't c. The question now is whether or not such a frame is an inertial frame.

We have a definition for an inertial reference frame. Hence regardless of your intelligence and mine, the answer is decidable. I am trying to show you that Newton's first law is satisfied in a photonic frame.

Kind regards,

The Star

 

[Hurkyl]

Will a clock traveling along with a photon tick. The answer is either yes or no. You say no. That is what I have a huge problem with, and won't ever believe.

The problem is that science doesn't conform to what people want to believe.

Incidentally, I can't imagine how one would go about making a clock that can travel at light speed anyways. If light speed clocks don't exist, then it is vacuously true that all light speed clocks don't tick, and also true that all light speed clocks do tick.

 

[Hurkyl]

We have a definition for an inertial reference frame. Hence regardless of your intelligence and mine, the answer is decidable. I am trying to show you that Newton's first law is satisfied in a photonic frame.

We do have a definition. We haven't discussed if that definition is valid in SR, and we don't even seem to agree on what the definition says.

 

[StarThrower]

The problem is that science doesn't conform to what people want to believe.

Incidentally, I can't imagine how one would go about making a clock that can travel at light speed anyways. If light speed clocks don't exist, then it is vacuously true that all light speed clocks don't tick, and also true that all light speed clocks do tick.

If the number of light speed clocks that exist is zero, then the number of light speed clocks that tick is equal to zero.

SR argument for why there are no light speed clocks:

\Delta t = \frac{\Delta t^\prime}{\sqrt{1-v^2/c^2}}

suppose v=c, then we have division by zero error unless \Delta t^\prime = 0

In a case where v=c what we get is this:

\Delta t = \frac{0}{0}

The RHS is in an indeterminate form, but not so for the LHS.

delta t is the amount of time passing on a clock in a frame in which the photon's speed is c.

delta t` is the amount of time passing on a clock at rest with respect to the photon.

The conclusion is that there are no light speed clocks.

But this conclusion is not, epistemologically speaking, absolute knowledge; rather it is contingent knowledge. Logically, all we know for certain is this:

If \Delta t = \frac{\Delta t^\prime}{\sqrt{1-v^2/c^2}} then there are no light speed clocks.

But the time dilation formula is derived using the main postulate of SR, which is that the speed of a photon is c in any inertial reference frame. So this centers the issue on whether or not the rest frame of a photon is an inertial reference frame.

Theorem to prove: Suppose F1 is an inertial reference frame. Let V denote a vector in another reference frame F2. If all the points of V move in a straight line at a constant speed in F1, then F2 is also an inertial reference frame.

This theorem is mathematically provable. Hence the main postulate of SR is false.

Kind regards,

The Star

 

[StarThrower]

We do have a definition. We haven't discussed if that definition is valid in SR, and we don't even seem to agree on what the definition says.

Not agreeing on what the definition says might be a problem.

An inertial reference frame is a reference frame in which all three of Newton's classical laws are satisfied.

In particular, the classical form of his second law is:

F = dP/dt


Kind regards,

The Star

 

[Hurkyl]

Actually, there's more to the proof than that (it's easiest to use the differential formula for proper time), but the details are irrelevant since it's still a consequence of the assumption of a constant speed of light.


Anyways, I'm now convinced that the definition you are using is a bad one, because it doesn't even work for classical mechanics; boosts preserve straight lines, even in classical mechanics, but no inertial frame of classical mechanics is a boosted frame.

 

[Severian596]

StarThrower is beating around the bush without offering answers to his own questions. The title of this thread is "The Fundamental Postulate Of Special Relativity Is Self-Contradictory." If you want to convince anyone of this other than yourself StarThrower, I suggest you at least attempt one of the following:

1) Show the mathematical proof that "F1 is an inertial reference frame. Let V denote a vector in another reference frame F2. If all the points of V move in a straight line at a constant speed in F1, then F2 is also an inertial reference frame." I suspect that 1 will require you to
1.1) Prove that the reference frame of a photon has points.
1.2) Prove that the reference frame can travel at the speed of light and still have meaningful coordinates.
1.3) Do not assume it's given (as you've been doing)

2) Describe the reference frame of a photon in more detail. If an inertial reference frame exists at v=c in your thought experiment, what are its properties?

3) Perphaps approach it from a different angle...assume you're correct. What are the implicaitons?

 

[Severian596]

StarThrower, this is my plea that you provide some concrete information. Some concrete conclusions. Yes I understand your logic:

(1) SR states that photons travel at c through a vacuum in all inertial reference frames.
(2) Photons have inertial reference frames.
(3) Photons do not travel through their own inertial reference frames at c.
(c) Therefore SR is incorrect/inconsistent.

I can accept the first premise because it reflects our current understanding of the universe, and there has been substantial evidence (and the support of uncounted professionals and scholars) to back up. So you don’t have to convince me—or anyone else—of statement one.

So that leaves you with statements (2) and (3). Proving one or both of these is not trivial, and thus far the most I’ve seen from you on proving their truth are comments like these:

"A reference frame in which a photon is at rest happens to be an inertial reference frame, so the whole theory is self-contradictory."

"Clearly, a reference frame with a photon at the origin is a reference frame in which the speed of a photon isn't c. The question now is whether or not such a frame is an inertial frame."

"A reference frame in which a photon is at rest will be an inertial reference frame if Newton's first law of motion is satisfied. Newton's first law of motion is that an object at rest will remain at rest unless acted upon by an outside force, and an object in motion will remain in motion in a straight line at a constant speed, unless acted upon by an outside force. This is precisely the case with reference frame F1 in this thread."

You make assumptions. You assume that photons are blessed with frames of reference, and in fact that they are inertial in nature! If Newtonian physics break down at near-light speeds why should they all of a sudden apply to a reference frame that is traveling at c? And how can you conclude that Newton’s first law applies in such a frame? You’re going to have to convince us of that, because we’re not biting yet.

If you manage to prove (2)—the more difficult in my opinion—then it seems to make sense that concluding (3) shouldn’t be as difficult. But then again who knows. You haven’t proven (2) yet so that’s down the road.

So…regardless of ticking clocks at light speed, or proper time, you have the responsibility of proving that statements (2) and (3) are true. You’ll also have to do this without the benefit of using any equations of SR, since those equations are based on your conclusion being FALSE. You’re trying to prove otherwise.

If you have anything substantial or compelling I suggest you present it now. And two or three catch phrases won’t cut it.

 

[StarThrower]

StarThrower is beating around the bush without offering answers to his own questions. The title of this thread is "The Fundamental Postulate Of Special Relativity Is Self-Contradictory." If you want to convince anyone of this other than yourself StarThrower, I suggest you at least attempt one of the following:

1) Show the mathematical proof that "F1 is an inertial reference frame. Let V denote a vector in another reference frame F2. If all the points of V move in a straight line at a constant speed in F1, then F2 is also an inertial reference frame." I suspect that 1 will require you to
1.1) Prove that the reference frame of a photon has points.
1.2) Prove that the reference frame can travel at the speed of light and still have meaningful coordinates.
1.3) Do not assume it's given (as you've been doing)

2) Describe the reference frame of a photon in more detail. If an inertial reference frame exists at v=c in your thought experiment, what are its properties?

3) Perphaps approach it from a different angle...assume you're correct. What are the implicaitons?

It is impossible to answer all your questions simultaneously. This particular post of yours practically begs the question, "how do you know space is three dimensional?"

You ask: 1.1) Prove that the reference frame of a photon has points.

Set up a rectangular coordinate system with a photon fixed at the origin. This coordinate system assigns 3 numbers to each point in real space. Photons exist somewhere in real space. In principle, this reference frame has as many coordinate assignments as there are point in real space. Real space consists of an infinite number of places. Your question has been answered. Since real space consists of more than one point, a coordinate system with a photon at the origin will consist of a plurality of points.

You ask: 1.2) Prove that the reference frame can travel at the speed of light and still have meaningful coordinates.

I am not sure what you mean by "meaningful coordinates."


You ask: 1.3) Do not assume it's given (as you've been doing)

Do not assume (what) is given?

You ask: 2) Describe the reference frame of a photon in more detail. If an inertial reference frame exists at v=c in your thought experiment, what are its properties?

A rectangular coordinate system consists of three infinitely long straight lines that meet at a single point, such that the three straight lines are mutually perpendicular. The lines are number lines, with units that correspond to some chosen standard of distance. Points in space are assigned three numerical coordinates which have meaning in this system and no other. No two points in a coordinate system can move relative to each other. Thus, the distance between any two points in a system is constant.

Kind regards,

The Star

 

[Severian596]

The lines are number lines, with units that correspond to some chosen standard of distance.

Your definition for a coordinate system is correct as long as our common sense idea of space applies. In this case you are asserting that our common sense idea of space must apply to a frame traveling at c.

Why?

Our common sense idea of space does not apply at relativistic speeds.

 

[Severian596]

And let me ask this. If considering two frames of reference S and S', observerations in one frame must exactly coincide with observations made from the other. This means the frames are interchangeable (that is we could call S the frame "in motion" relative to S', or we could call S' the frame "in motion"), and that neither frame is preferred over the other.

So how can we assert that a photon in "rest frame" S' be at rest and that S be moving at the speed of light?

 

[Severian596]

Finally, I found this concise quote that reflects my thoughts:

"Things traveling at the speed of light don't have rest frames the way that other things do. The Lorentz transformation equations that relate coordinates in different frames are singular if the relative velocity of the two frames is c."

This summarizes my point earlier, about the nature of space and transforming coordinates as your velocity increases.

 

[StarThrower]

StarThrower is beating around the bush without offering answers to his own questions. The title of this thread is "The Fundamental Postulate Of Special Relativity Is Self-Contradictory." If you want to convince anyone of this other than yourself StarThrower, I suggest you at least attempt one of the following:

1) Show the mathematical proof that "F1 is an inertial reference frame. Let V denote a vector in another reference frame F2. If all the points of V move in a straight line at a constant speed in F1, then F2 is also an inertial reference frame."

Let F1 be a rectangular coordinate system that is also an inertial reference frame.
Let F2 be a rectangular coordinate system.

Let A, B be points in F2.
Let the vector from A to B be symbolized as: \vec{AB}

Let A be moving in a straight line at a constant speed through F1.
Let B be moving in a straight line at a constant speed through F1.

Theorem: F2 is an inertial reference frame.

Will this theorem be sufficient?

 

[Severian596]

Let F1 be a rectangular coordinate system that is also an inertial reference frame.
Let F2 be a rectangular coordinate system.

Let A, B be points in F2.
Let the vector from A to B be symbolized as: \vec{AB}

Let A be moving in a straight line at a constant speed through F1.
Let B be moving in a straight line at a constant speed through F1.

Theorem: F2 is an inertial reference frame.

Will this theorem be sufficient?

And if the velocity vectors of A and B are not parallel? Not equal in magnitude?

 

[StarThrower]

Your definition for a coordinate system is correct as long as our common sense idea of space applies.

Let N denote the maximum number of infinitely long straight lines that can meet at a point, such that the lines are mutually perpendicular.

The answer is independent of common sense.
The answer is called the dimensionality of space.
The answer is three... i.e. N=3.

There is a unique distance between any two points in space.

Let A denote one point in space, let B denote another point in space. The basic idea of a straight line segment comes from the following distance axiom:

Let |AB| denote the distance from point A to point B.

Let C denote any point on the straight line segment AB.

|AC| is the distance from A to C
|CB| is the distance from C to B.

Notice that |AC|+|CB| = |AB|

Now, suppose that C is off of straight line segment AB. The following is now the case:

|AC| + |CB| > |AB|

Recall: Triangle Inequality

Kind regards,

The Star

 

[Michael F. Dmitriyev]

Michael,
You fail to understand the meaning of postulate. Einstein is not obligated to prove anything about his postulate. That is the nature of a postulate. You most certainly cannot learn anything other then the results of a constant c by studying Relativity. It is after all a development that explores the implications of a constant speed of light.

If you wish to find the roots of the constancy of c you need to study and understand the work of Clerk Maxwell. The origins of a velocity that is independent of the source, is Maxwell's equations cast in the form of the wave equation. When this result was published in the late 1860s the world of Physics was changed forever. How to rectify the source independence of the speed of Electromagnetism with the accepted and well understood precepts of Classical Mechanics was the single largest issue in Physics of that era. Due to that Einstein was able to postulate a constant c. Physicist of that era did not blink an eye at the postulate because they had spend a generation attempting to disprove the constancy of c. They failed.

Excuse me, but I can’t consider your answer differently than pseudoscientific demagogy.
You do not give the concrete answer, except for the general reasonings.
Do you have the answer to a question – why?

 

[Severian596]

Let |AB| denote the distance from point A to point B.

I will not ask how we define distance, but rather I'll ask you directly if the spacial distance between points A and B is absolute to all reference frames.

EDIT:
In addition you have not accounted for time in your coordinate system. Is the distance \Delta t between two events in one frame absolute--that is, equal in all frames in motion with respect to events' frame?

If this isn't so, and if time is not absolute, how can you define absolute space?

 

[Severian596]

The answer is called the dimensionality of space.

This is not fully understood. The nature of space and time (and how they are related) is more complex than length, width, height, and how long it takes me to go to the bathroom. Furthermore to fully understand their relationship I believe it takes general relativity...but I don't know anything about GR.

 

[StarThrower]

I will not ask how we define distance, but rather I'll ask you directly if the spacial distance between points A and B is absolute to all reference frames.

Yes, the distance between two points is absolute.

Regards,

The Star

 

[Severian596]

Yes, the distance between two points is absolute.

Well, we can stop talking now. I'll keep an eye out for your "StarThrowerian Physics" publication, if it ever hits the shelves.

In relativistic mechanics, there is no such thing as an absolute length or an absolute time since length and time depend on the frame of reference of the observer.

 

[StarThrower]

Well, we can stop talking now. I'll keep an eye out for your "StarThrowerian Physics" publication, if it ever hits the shelves.

In relativistic mechanics, there is no such thing as an absolute length or an absolute time since length and time depend on the frame of reference of the observer.

Relativistic mechanics is wrong, hence I fail to see your point.

Regards,

The Star

 

[StarThrower]

And if the velocity vectors of A and B are not parallel? Not equal in magnitude?

A,B are points in F2. Therefore, the distance from A to B is constant.

If the velocity of A in F2 is different from the velocity of B in F1, then the distance from A to B would vary. In other words, the vector from A to B is rigid.

Regards,

The Star

 

[Severian596]

Hence, I'll leave you to your theories and wait for your work to be published by the experts. I'm tired of comparing apples to oranges.

You're entitled to believe what you like, and so am I.

The conversation was stimulating...

 

[Severian596]

If the velocity of A in F2 is different from the velocity of B in F1, then the distance from A to B would vary. In other words, the vector from A to B is rigid

You didn't stipulate this, which didn't account for any possible rotation or stretching of F2 in comparisson to F1.

 

[StarThrower]

In order to understand the concept three dimensional Euclidean space, one has to understand the definition of a straight line segment. In order to understand this, one needs the axioms of the Euclidean distance function.

Here they are for convenience.

Euclidean Distance Function

Let x,y,z denote arbitrary points in a coordinate system.

Definition: For any points A,B in a coordinate system, |AB| denotes the distance from A to B.

Let x,y,z denote arbitrary points in some coordinate system.

Axiom I: |xy| \geq 0
Axiom II: |xy|=0 \leftrightarrow x=y
Axiom III: |xy| = |yx|
Axiom IV: |xy|+|yz| \geq |xz|

The straight line segment from xy consists of all points c, such that:

|xc|+|cy| = |xy|

Keep in mind that in principle, the distance from one point to another can be measured by a device called a ruler. Thus, distance doesn't need to be defined logically, instead it can be defined operationally.

 

[Severian596]

In order to understand the concept three dimensional Euclidean space...

It's too bad that because we don't live in Euclidean space your efforts are wasted.

I'm curious how you, StarThrower, explain the fact that every other galaxy is redshifted if you also believe in absolute space. Oh and you never answered my question about absolute time, do you also hang on to that?

PS I'll wait for a new-age Newtonian purist physics system from you, if that's the case. I assume you're hip with the ether, too then.

 

[StarThrower]

It's too bad that because we don't live in Euclidean space your efforts are wasted.

I'm curious how you, StarThrower, explain the fact that every other galaxy is redshifted if you also believe in absolute space. Oh and you never answered my question about absolute time, do you also hang on to that?

PS I'll wait for a new-age Newtonian purist physics system from you, if that's the case. I assume you're hip with the ether, too then.

Absolute space, absolute time, yes that's me. Redshift and Blueshift can be explained by Newtonian mechanics.

Kind regards,

The Star

 

[StarThrower]

Once you are armed with the concept of a straight line segment, it is easy to generalize that concept to an infinite straight line.

The straight line segment from A to B consists of all points C, such that:

|AC|+|CB|=|AB|

Now, consider THE infinite straight line through A,B.
It will consist of the straight line segment from A to B, and also, it will consist of all points D such that:

|AB|+|BD| = |AD| or |DA|+|AB|=|DB|

So in principle, the concept of the distance from one point to another has been made as intuitive as possible.

Next comes the notion of two infinite straight lines that contain one point in common.

Any two such lines determine a unique plane.

In Euclid it is proved that vertical angles are congruent. And when all four angles are equivalent, each is a right angle, and the lines are said to be perpendicular.

Now, suppose that we have two infinite straight lines that meet at right angles.

Now, send a third infinite straight line through the intersection point of the first two, such that all vertical angles are congruent. There is one and only one infinite straight line which can meet the other two, such that all three lines are mutually perpendicular.

Thus, real space is three dimensional Euclidean.

Anyone who wants a fancier proof of this is welcome to try.
The fact that space is three dimensional was known by the ancient greeks.

I find it surprising that this fact was ever doubted.

Kind regards,

The Star


P.S. At this point, it is a hop, skip, and a jump to a rectangular coordinate system.