Relativity Theory is THEORETICALLY wrong!

[przyk]

martillo,

I accept the change of the minus sign in the equation. You would have it in that way if you had started with the equation cos(kx-wt) for the wave.
I must recognize you have found a very good point with your reasoning.
This will make me think more about.

Happy thinking

I'd just like to point out something: The Minkowski product of any two four-vectors is invariant (this is why you'll sometimes hear Lorentz boosts called "rotations" in space-time), so you can see immediately that a relation like $$\Psi = e^{i \vec{k} \cdot \vec{r}}$$ is Lorentz invariant. This is why Minkowski's formalism is so popular - it allows laws to be expressed in a form that emphasizes their invariance using terms that are Lorentz scalars. There are also invariant equivalents to the classical gradient, divergence, and laplacian operators.

I still wonder: if the wavelenght is a lenght (a distance) in the x axis why it does not transform as a normal lenght contraction λ=λ'/γ? I think that in principle it should do.

You can derive the length contraction formula from the Lorentz transformation by considering the worldlines of two objects stationary in one frame.

If you have an object at rest at the origin in $$K'$$ ($$x_1' = 0$$) and another at $$ x_2' = L'$$, then for object #1:

$$x_1' = \gamma ( x_1 - v t ) = 0$$​

$$\Rightarrow x_1 = v t$$​

For #2:

$$ x_2' = \gamma ( x_2 - v t ) = L'$$​

$$\Rightarrow x_2 = vt + \frac{L'}{\gamma}$$​

The difference $$L = x_2 - x_1$$ gives:

$$L' = \gamma L$$​

I'm sure you can extend this reasoning to see what happens to the relationship between $$L$$ and $$L'$$ if objects #1 and #2 are not stationary in $$K'$$.

Returning to other subject:

But the concept of the "fictitius"forces enables for exmple the motion law: F=dp/dt have the same form. Is just that the forces are different when seen from different frames.
This is why I asked for an example. In which cases a law would take different form?
Note that if this is the case you are pointing to a possible inconsistency in Relativity Theory.

On its own $$\vec{F} = \frac{d \vec{p}}{d \tau}$$ has no predictive power. To make real predictions you need another law that determines $$\vec{F}$$ (electromagnetism, gravity, etc.). While it's true that you can introduce centrifugal forces and the like to keep $$\vec{F} = \frac{d \vec{p}}{d \tau}$$ invariant, this comes at the expense of making the laws determining the force variant.

 

[martillo]

przyk,

Thanks to our discussion I got deeper in De Broglie wave features and I have found that I had a different concept of the matter-wave.
I used to think it was a real wave but now I see it is not!
I realize now that the De Broglie waves seen by different frames are not geometrically the same wave in the space! The limit case is that while in the "fixed" frame is a periodic wave with λ=h/p in the "moving" frame it is a straight line (λ=infinite) moving at infinite velocity (actually not a wave)!
So it is stated by current Physics that for any massive object exist a wave associated to it but it is frame dependent! Different frames see different waves!
This is too strange...

 

[przyk]

martillo,

Thanks to our discussion I got deeper in De Broglie wave features and I have found that I had a different concept of the matter-wave.
I used to think it was a real wave but now I see it is not!

Ironically, I thought this in your "Classical Physics is coming back, RELOADED!!!" thread, and have since realized that it is the same wave in both frames!

I realize now that the De Broglie waves seen by different frames are not geometrically the same wave in the space! The limit case is that while in the "fixed" frame is a periodic wave with λ=h/p in the "moving" frame it is a straight line (λ=infinite) moving at infinite velocity (actually not a wave)!

It's the same wave, in the sense that any two observers will agree on the value of $$\Psi$$ at any given point in space and time. The strangeness is all in the phase velocity being greater than $$c$$ and the Lorentz transformation (specifically, relativity of simultaneity). An infinite wavelength corresponds to an infinite phase velocity, and the Lorentz transformation allows a velocity to be infinite in one frame and finite in another. Velocities transform according to:

$$u' = \frac{u - v}{1 - \frac{u v}{c^2}}$$​

$$u'$$ can be infinite if the denominator $$1 - \frac{u v}{c^2} = 0$$, or rearranged:

$$u = \frac{c^2}{v}$$​

This is the phase velocity you derived earlier!

 

[martillo]

przyk,

It's the same wave, in the sense that any two observers will agree on the value of at any given point in space and time. The strangeness is all in the phase velocity being greater than and the Lorentz transformation (specifically, relativity of simultaneity). An infinite wavelength corresponds to an infinite phase velocity, and the Lorentz transformation allows a velocity to be infinite in one frame and finite in another.

Yes, the variation of the time in the different referentials introduce strange features...

I must rethink what I have wrotten.
It is seeming De Broglie law is invariant within Relativity statements.

I give the point for you in this part but not yet in the other two. They involve conceptual subjects (not mathematical ones) in which we probably will not agree:

“ Relativity is inconsistent with the intrinsic property of age of living beings. ”

Therefore, your notion that age is an "intrinsic property" of living beings is inconsistent with reality.

I think that the "intrinsic property" of the age is consistent with reality while Relativity is inconsistent with reality.

“ They "detect an absolute state of rotation" and you think this is irrelevant? ”

As far as special relativity is concerned, yes (I don't really feel like defending a theory like GR that I don't understand).

I'm referring to GR here and its statement that there are no privileged frames.

 

[Singularity]

What do u think will happen to Magnetic Induction if the conductor and the magnetic fields pass by each other at near light speed compared to earth but in opposite directions.


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

Please correct the question if u understood, i am not much aware of what i am quoting here.

 

[martillo]

Singularity,
Your question is out of the topic of this thread. Please open a new thread for it.

 

[przyk]

I think that the "intrinsic property" of the age is consistent with reality while Relativity is inconsistent with reality.

We could go in circles arguing about what nature can and can't do, but in this case I don't think it's necessary. At a first glance, reciprocity (the "each twin ageing slower than the other" claim) seems impossible, but unlike quantum mechanics, relativity doesn't require you to abandon your worldview, provided you are willing to accept contraction and slowing of physical processes relative to an absolute frame. Here's a scenario I think you should consider carefully:

Imagine we have an observer A at rest (let's say at the origin) in an absolute frame, and B in motion (velocity $$+v$$ to the right) in this absolute frame. B's motion results in him ageing slower than A in accordance with the time dilation formula. While A ages $$\Delta t$$ seconds, B ages $$\Delta t' = \frac{1}{\gamma} \Delta t$$ seconds.

The equations of motion for the two observers are:

$$x_A = 0$$​

$$x_B = v t + X$$ (with $$X > 0$$)​

Now suppose A sends two pulses of light out toward B: the first at $$t = 0$$ and the second at $$t = T$$. The equations for these are then:

$$x_{\gamma 1} = c t$$​

$$x_{\gamma 2} = c ( t - T )$$ (with $$T > 0$$)​

The first pulse reaches B when $$x_{\gamma 1} = x_B$$:

$$c t_1 = v t_1 + X \Rightarrow t_1 = \frac{X}{c - v}$$​

The second pulse reaches B when $$x_{\gamma 2} = x_B$$:

$$c ( t_2 - T ) = v t_2 + X \Rightarrow t_2 = \frac{X + cT}{c - v}$$​

then:

$$\Delta t = t_2 - t_1 = \frac{c}{c - v}T$$​

During this time, taking B's slow ageing rate into account, B will age:

$$\Delta t' = \frac{1}{\gamma} \frac{1}{1 - \frac{v}{c}}T = \frac{1}{\gamma} \gamma^2 \left( 1 + \frac{v}{c} \right) T$$​

so:

$$\Delta t' = \gamma \left( 1 + \frac{v}{c} \right) T$$​

Now we repeat the same scenario, but this time it is B who sends the pulses at A.

B ages $$T'$$ seconds between sending out the two pulses (first one at $$t = 0$$). In the absolute frame, the second pulse is emitted at $$t = T = \gamma T'$$. The equations for these two pulses are:

$$x_{\gamma 1} = -ct + X$$​

$$x_{\gamma 2} = -ct + X + ( c + v ) T$$​

(the second having to satisfy $$x_{\gamma 2} = x_B$$ at $$t = T$$)

The first pulse reaches A when $$x_{\gamma 1} = 0$$:

$$- c t_1 + X = 0 \Rightarrow t_1 = \frac{X}{c}$$​

The second pulse reaches A when $$x_{\gamma 2} = 0$$:

$$- c t_2 + X + ( c + v ) T = 0 \Rightarrow t_2 = \frac{X + ( c + v ) T}{c}$$​

So the time A ages between receiving both pulses from B is:

$$\Delta t = t_2 - t_1 = \left( 1 + \frac{v}{c} \right) T = \gamma \left( 1 + \frac{v}{c} \right) T'$$​

so:

$$\Delta t = \gamma \left( 1 + \frac{v}{c} \right) T'$$​

There you go: reciprocity, and we never had to consider B's rest frame!

Hope that wasn't too long.

I'm referring to GR here and its statement that there are no privileged frames.

I don't know GR, so I don't know how justified it would be in claiming all frames are completely equivalent.

 

[przyk]

What do u think will happen to Magnetic Induction if the conductor and the magnetic fields pass by each other at near light speed compared to earth but in opposite directions.


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

Please correct the question if u understood, i am not much aware of what i am quoting here.

I'm not too familiar with electromagnetism, so you'd be better off starting a new thread in the Physics subforum or asking a moderator to split this one.

What's prompting this question, anyway?

 

[martillo]

przyk,

I understand your point but that reciprocity does not applly in my problem.

At the final cross point where the three observers coincide there is only only one state possible for each of the twins. As I said in the page each twin can take photographs of themselves and send them to the others to everybody see what really happen to them at that moment. But note that the problem now is not to choose or determine which prediction would be the right one, the problem is that Relativity gives three different predictions in each frame which are not compatible with each other. They are contradictory. You cannot observe a twin aged with a long bear in one frame and see a half bear or not bear at all in the other frames!
Relativity is inconsistent in this problem.

 

[przyk]

At the final cross point where the three observers coincide there is only only one state possible for each of the twins. As I said in the page each twin can take photographs of themselves and send them to the others to everybody see what really happen to them at that moment. But note that the problem now is not to choose or determine which prediction would be the right one, the problem is that Relativity gives three different predictions in each frame which are not compatible with each other. They are contradictory. You cannot observe a twin aged with a long bear in one frame and see a half bear or not bear at all in the other frames!

Hang on, is it the ages or the ageing rates that are bothering you?

All three observers will agree on their relative ages. At the cross point, the two twins are both the same age, and both are younger than the observer on the mothership. This is true in all reference frames.

 

[martillo]

przyk,

is it the ages or the ageing rates that are bothering you?

One is consequence of the other.

All three observers will agree on their relative ages. At the cross point, the two twins are both the same age, and both are younger than the observer on the mothership. This is true in all reference frames.

Not at all. You must "sit" with each observer to see what they see. You must observe the phenomenon from each of the three frames and all the observations are different.

 

[przyk]

Not at all. You must "sit" with each observer to see what they see. You must observe the phenomenon from each of the three frames and all the observations are different.

The observer on the mothership sees the two twins age slowly as they move away and as they come back, such that they are both the same age as each other and both younger than the mothership observer when they get back.

Each twin sees the mother ship observer and the other twin age slowly while he's moving away from the mothership, age rapidly while he's turning his ship around (accelerating) and sees them age slowly on the way back, such that he sees he's the same age as the other twin and younger than the mothership observer when he gets back.

At the crossover point, they all agree on who has the longest beard.

 

[martillo]

przyk,

The observer on the mothership sees the two twins age slowly as they move away and as they come back, such that they are both the same age as each other and both younger than the mothership observer when they get back.

Each twin sees the mother ship observer and the other twin age slowly while he's moving away from the mothership, age rapidly while he's turning his ship around (accelerating) and sees them age slowly on the way back, such that he sees he's the same age as the other twin and younger than the mothership observer when he gets back.

At the crossover point, they all agree on who has the longest beard.

I'm sorry but this is wrong.
One twin could see the other aging faster while going away and slowler while coming but the age accumulates and at the crossover he will always see the other younger. But exactly the same happens to the other twin seeing the first younger!

The unique way they could all agree in time at the crossover point is if they brake and stop the ships at the mothership's place making v=0 but this is not what they do in the proposed problem. The problem is thought with the twins continuing travelling at their constant velocity and interchanging photographs at the crossover point to all see what really happen to all of them.

 

[przyk]

I'm sorry but this is wrong.
One twin could see the other aging faster while going away and slowler while coming but the age accumulates and at the crossover he will always see the other younger. But exactly the same happens to the other twin seeing the first younger!

Each twin ages slower in the other's rest frame when the other is not accelerating. What happens during the acceleration periods (both twins have to decelerate, turn around, and accelerate back toward the mothership) isn't so simple. Just thinking about it, while each twin is accelerating, the other must be ageing much faster than him in his rest (accelerating) frame if they're going to be the same age at the cross-over point. This is General Relativity's gravitational time dilation. You can derive this effect by extending the Lorentz transformation to include accelerating frames, by considering all the rest frames an accelerating object passes through.

The unique way they could all agree in time at the crossover point is if they brake and stop the ships at the mothership's place making v=0 but this is not what they do in the proposed problem. The problem is thought with the twins continuing travelling at their constant velocity and interchanging photographs at the crossover point to all see what really happen to all of them.

This accelerated/gravitational time dilation effect increases with distance. Braking a short distance from the mother ship changes very little.

 

[martillo]

przyk,
Acceleration has nothing to do here. If you look at Lorentz Transform it depends on velocity only, not in the acceleration.
Einstein showed the timing problem in a relativistic train without even mentioning the necessary acceleration to move it at a relativistic velocity.
One twin age less than the other due to its relative velocity, if the velocity returns to zero again the time difference disappear and their clocks are synchronized again.

 

[przyk]

Acceleration has nothing to do here. If you look at Lorentz Transform it depends on velocity only, not in the acceleration.

Both twins accelerate: they move away from the mothership then turn around to get back. If you want to find the relative ages of all the observers as seen by one of the twins, you can't ignore this.

Einstein showed the timing problem in a relativistic train without even mentioning the necessary acceleration to move it at a relativistic velocity.

Do you have a link? I'm not sure which thought experiment you are referring to.

if the velocity returns to zero again the time difference disappear and their clocks are synchronized again.

Who told you this?

 

[martillo]

przyk,

“ Originally Posted by martillo
Acceleration has nothing to do here. If you look at Lorentz Transform it depends on velocity only, not in the acceleration. ”

Both twins accelerate: they move away from the mothership then turn around to get back. If you want to find the relative ages of all the observers as seen by one of the twins, you can't ignore this.

I assume acceleration in neglihible time to have travels with constant velocity.
The time dilation is due to their relative velocity not their acceleration. Look at Lorentz equations.

Do you have a link? I'm not sure which thought experiment you are referring to.

I have an Spanish translation of Einstein's book "Sobre la Teoria de la Relatividad Especial y General".
Here he explain Special Relativity with a relativistic train.

“ if the velocity returns to zero again the time difference disappear and their clocks are synchronized again. ”

Who told you this?

I deduce this from the Lorentz Transform. There is a time dilation while a relative velocity and distance exist between the two frames. When they coincide again in space with zero velocity there is no more time difference. Just look at the equations!

 

[martillo]

By the way I have updated the manuscript in the site taking away the argument of the De Broglie law, rewriting a little of the twins problem and some other minor edition corrections.

 

[przyk]

I assume acceleration in neglihible time to have travels with constant velocity.
The time dilation is due to their relative velocity not their acceleration. Look at Lorentz equations.

Lets assume the acceleration is instantaneous for the moment. If we call the twins "A" and "B", and the mothership observer "S", then twin A's trajectory in S's frame might look something like this:

$$x_s = \left{ \begin{matrix} - v t_s & \qquad t_s < T \\ v ( t_s - 2 T) & \qquad t_s \geq T \end{matrix} \right.$$​

where $$T$$ is the time twin A turns around, as measured by S.

To analyze this from A's point of view we need to consider two reference frames in addition to S. The first, A[sub]1[/sub], is A's rest frame up until time $$T$$, while A is moving away from S. The transformation from S to A[sub]1[/sub] is:

$$\begin{eqnarray}
t_{a_1} = & \gamma \left( t_s + \frac{v}{c^2} x_s \right) \\
\\
x_{a_1} = & \gamma \left( x_s + v t_s \right) \end{eqnarray}$$​

The second, A[sub]2[/sub], is A's rest frame after $$T$$, when A is moving toward S. It is related to S by:

$$\begin{eqnarray}
t_{a_2} = & \gamma \left( t_s - \frac{v}{c^2} x_s - 2 \frac{v^2}{c^2} T \right) \\
\\
x_{a_2} = & \gamma \left( x_s - v t_s + 2 v T) \end{eqnarray}$$​

(the extra terms ensure $$x_s = v ( t_s - 2T )$$ for $$x_{a_2} = 0$$, and $$t_{a_1} = t_{a_2}$$ for $$t_s = T$$ and $$x_s = - v T$$)

When twin A returns to S, S has aged $$2 T$$. The second set of transformations (for $$x_s = 0$$ and $$t_s = 2T$$) gives $$t_{a_2} = \frac{2T}{\gamma}$$, which is A's age at the crossover point. This is true for all observers.

The interesting thing is what happens to S's age from A's point of view as A turns around. Rearranging the equations for $$t_{a_1}$$ and $$t_{a_2}$$ for $$x_s = 0$$ yields:

$$t_s = \frac{1}{\gamma} t_{a_1} \\
\\
t_s = \frac{1}{\gamma} t_{a_2} + 2 \frac{v^2}{c^2} T$$​

At $$t_{a_1} = t_{a_2} = \frac{1}{\gamma} T$$, the difference between these two is:

$$\Delta t_s = 2 \frac{v^2}{c^2} T$$​

So twin A's infinite acceleration results in S ageing by $$2 \frac{v^2}{c^2} T$$ (infinitely fast) as seen by A.

I expect considerations like these are what led to General Relativity's gravitational time dilation.

I have an Spanish translation of Einstein's book "Sobre la Teoria de la Relatividad Especial y General".
Here he explain Special Relativity with a relativistic train.

Could you could briefly explain it and Einstein's conclusions, if you still think it's relevant?

 

[martillo]

przyk,

The first part of your calculations when you deduce the age of the twin as seen by the mothership seems right to me but the second does not. Observing from the twin's frame the mothership makes a completely symmetric travel! I mean the mothership goes away at velocity V and at time t=T turns back with velocity v and so the calculations should be exactly the same.
The motherships sees the twin exactly the same way the twin sees the mothership. Here reciprocity applies and so the results should be the same but at the inverse: themothership observer younger than the twin.

Could you could briefly explain it and Einstein's conclusions, if you still think it's relevant?

Is a very interesting book for those interested in Relativity. I recommend you to find one copy. You can see in it the real thoughts Eintein had about all Relativity. Some of them are very abstract and need much attention.

He begins talking about the classical concepts of space and time always with the example of frames in a train and in the railways.After he introduce the principle of the relativity as it is applied in Special Relativity and talks about the relativity of distance and simultaneity (much conceptual talk and no math).
Then he introduce Lorentz Transform. He doesn't do all the math. He describe well the problem and finally says that the Lorentz formula is the right answer. He present two frames of reference, one with coordinates x', y', z', t' in the train and the other x, y, z, t in the railways and he states that for them to measure the velocity of light exactly the same the change of coordinates must verify Lorentz equations. After he talks about how that transformation implies in lenght contraction and time dilation and how the experiment of Fizeau agree with the relativistic addition of velocities under some aproximation.
He also talks that the energy of a massive object is E=mc2 (without deriving it) and how an object that absorbs energy E0 by radiation increases its mass in the value E0/c2.
He very briefly mention Minkowsky space-time and after he enters in concepts about General Relativity for which he dedicates more than half of a small book with 142 pages.

I have found this links:
http://www.bartleby.com/173/
http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm

Einstein also wrote another book with a title like "On the electrodynamic of moving bodies".
Links:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
http://www.phys.lsu.edu/mog/100/elecmovbodeng.pdf