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What Makes a Valid Law of Nature

What Makes a Valid Law of Nature
Posted by Randy on August 10, 2023 at 8:19 pmIs the relativistic equation, (0)(x^2 – c^2 t^2) = 0, a valid law of nature? Why or why not? Is there any equation outside of relativity that essentially multiplies both sides of an equation by zero.
For those not familiar with the equation, it is the results of taking Einstein’s equation (8), the Lorentz transformation for x’ and t’, and substituting them into his equation (8a), x’^2 – c^2 t’^2 = x^2 – c^2 t^2 from his “Appendix I: Simple Derivation of the Lorentz Transformation” in his book “Relativity: the Special & the General Theory”.
Copies of the book/appendix are online at the Gutenberg Project and Bartleby’s.
Marco replied 10 months, 3 weeks ago 4 Members · 18 Replies 
18 Replies

I am not sure about the equation above. What I know is observed in the natural world is this: x^2+y^2+z^2(v*t)^2=0 are lengths when v is not equal to 0. If v=c they are still lengths. To change the 0 on the right side and say it equal 1 or 1 is a grave error because it deviates from the Pythagoras Theorem which is for the real dimension of length.

The Lorentz condition ( x’^2 – c^2 t’^2 = x^2 – c^2 t^2 ) is obtained from the spherical equations x^2 + y^2 + z^2 – (c*t)^2 = 0 and x’^2 + y’^2 + z’^2 – (c*t’)^2 = 0 by setting y’^2 + z’^2 = y^2 + z^2 and replacing them with their equalities (i.e., x^2 – c^2 t^2 = y^2 + z^2). The claim that the speed of light is the same in all reference frames is satisfied by the Lorentz condition because the final relationship [(0)(x^2 – c^2 t^2) = 0] is true regardless of the inputs. For example, let x = 50ct; substituting this into the Lorentz condition works because (0)(50^2(ct)^2 – ct) = 0. It is not the speed of light that is the same in all directions but that zero is zero in all directions. Essentially, the Lorentz condition is a tautology that works regardless of the inputs.
Are the laws of nature based upon tautologies?

Hi. I’m unfamiliar with much “high level” math. Doesn’t the Lorentz Transformation mathematically slow down objects that would (linearly) reach or exceed the velocity of light?

What of a hypothetical scenario of how there’s two objects that travel in opposite directions, at almost the velocity of light, say each 98% c, relative to an observer? Wouldn’t the combined velocity of the objects almost reach double the velocity of light? or 196% c? Of course, the Lorentz Transformation is said to reduce the linear velocity of objects that exceed c, to under c. So if the math of the Lorentz Transformation is applied to the example I just mentioned, how much would it reduce almost 2c, to under 1c?
 This reply was modified 11 months, 1 week ago by Jerry.

Hallo @jerry ,
looking for https://en.wikipedia.org/wiki/Rapidity we can calculate the sum of velocity in relativistic field.
tanh( 2*atanh( 0.98)) =0.9998 cRegards Ing_mm

Thanks, Marco.
You know how at least one aspect of the Lorentz Transformation reduces the velocity of an object that would linearly exceed the velocity of light? That’s what I want to specifically ask about. How much is the velocity of an object lowered when its linear velocity highly exceeds c? Say even almost double c?

You know, would it subtract the higher percentage number to, say, almost the velocity of light (that is almost 1c) or would it go down to say, half c, or even lower?

Hallo @jerry,
the rule is tanh (v) , described in the link above of rapidity.
For a real velocity of the object =1c, the velocity seen by the static obserber is tanh(1)=0.762c
for a velocity of 2c, the velocity appear of tanh(2)=0.964c and so on.
For low velocity th difference rapidly vanish and for 1/2 c the measured velocity became 0.462c with a difference <10%, it became 2% at 1/4 c and 0.1% at 1/16 cRegards Ing_mm

Thanks, Marco.
So did you mean to say that even already lower than c velocities also involve the Lorentz Transformation?
Also, you wrote, “for a velocity of 2c, the velocity appear of tanh(2)=0.964c and so on.”
If the velocity of 2c is also possible “linearly”, and affected by the Lorentz Transformation to lower to under 1c, then how high up could you go? If 2c is reachable, what of 4c or even up to a million c? At what point (if any) is the linear velocity too high?

Hallo @jerry,
thanks for your question, I wrolte fastly and I made some little troubles in my explanetion.
I wrote velocity instead rapidity and the correct phrase was:
For a real rapidity of the object =1c, the velocity seen by the static obserber is tanh(1)=0.762c
for a rapidity of 2c, the velocity appear of tanh(2)=0.964c and so on.
For low rapidity the difference rapidly vanish and for 1/2 c the measured velocity became 0.462c with a difference <10%, it became 2% at 1/4 c and 0.1% at 1/16 c 
Sorry for the trouble, but this make me think on super luminary speed…
Unfortunately we have only few example of super luminary speed like https://en.wikipedia.org/wiki/Cherenkov_radiation because the particles came from a medium with highest speed of light.
In this case the observer in the medium with a super luminary particle can’t see the particle until it surpasses the observer but it see only a little pulse in direction of emission angle, when the particle had already surpasses the observer and never again see after this moment.
When the speed of an object is higher of c, the rapidity isn’t defined.
We can calculate the sum of speed of object with rapidity formula, and for rapidity of high value this mean that real velocity is near to c ( for rapidity of 4 the velocity is 0.9993c).
I can made you another example:
we see 2 object with velocity 50% c and the other 80% c,
the objects sees reciprocally move at + and – 50% c ( v/c =atanh( tanh (0.8) – tanh(0.5))

Have you ever considered the possibility that the Lorentz Transformation was just a mathematical loophole to disguise the detectable inconsistencies of Special Relativity? I’ve heard it was invented before Special Relativity though. Why would Lorentz (and other possible founders of the theory) want to provide a way to observe a universal limit of velocity (c) that wasn’t yet established (at that time)?

The special relativity theory have a long story… it is based on observation of some experiment (made on the earth) all convergent to that theory, so the mathematical model reflect the results of experiments (on earth).
Why I write “on earth”? Because the theory is based on 2 hypothesis :
 The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration).
 The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer.
I think the first hypothesis is more theoretical then the second one.
The first hypothesis becams https://en.wikipedia.org/wiki/Equivalence_principle (strong or wake) and it is only demonstrate for wake, and the second one is difficult to prove because super luminary object appear and disappear quickly in our world.

Hi Marco. You wrote,
Why I write “on earth”? Because the theory is based on 2 hypothesis :
 The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration).
 The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer.
I think the first hypothesis is more theoretical then the second one.
I would say the first postulate is theoretical, though easy to apply with real life “experiments”, such as simple as bouncing a ball on the “stationary” ground, and comparing that to bouncing the ball on a bus that travels at a constant velocity. This seems easily demonstrable. My view is that the second postulate seems inaccurate, which is the constancy of c. It is this that leads to inconsistencies that time dilation is said to fix.

Hi Marco.
Is the concept of time dilation accurate in your view? What of the theory of Special Relativity, in General (get it? lol)? Would you completely agree with it?

Thanks again for your question, it is not trivial.
The concept of time dilation in my view is correct, the velocity of atoms within ether deforms the shape of boundary and spin decrease, increasing local time viewed from moving objects, so, for example, pion decay time increase when comes from space instead standing in labs.
“What of the theory of Special Relativity, in General” 😅
<font color=”rgba(0, 0, 0, 0)” face=”inherit”>I think it is a good, but not perfect model of reality, it is equivalent (</font>mathematically<font color=”rgba(0, 0, 0, 0)” face=”inherit”> speaking) with LET (</font><font color=”rgba(0, 0, 0, 0)” face=”inherit”>https://en.wikipedia.org/wiki/Lorentz_ether_theory) in </font>which ether make the medium rule.
Special Relativity not need ether but not denies its existence, only it’s unnecessary.
Time dilatation is an effect of general relativity that emerge in special relativity (unexplained in SR) but translated in formulas by Lorentz according to experiments.
Special relativity is a theory applied in inertial frames but developed in NON inertial frame (due to gravity), and it is the approximation in the 2 directions orthogonal to gravity vector of general relativity.
All this concepts is explained very well by @JoP in his works, he and me differ only for source and sink of ether but not for behavior with matter and light.
Gravity is due to an ether flow, and on earth, it is vertical at 11.4 km/sec and it keep we with (foot 😅) down to heart.
King regards
Ing.__mm

Thanks again for your question, it is not trivial.
The concept of time dilation in my view is correct, the velocity of atoms within ether deforms the shape of boundary and spin decrease, increasing local time viewed from moving objects, so, for example, pion decay time increase when comes from space instead standing in labs.
“What of the theory of Special Relativity, in General”
I think it is a good, but not perfect model of reality, it is equivalent (mathematically speaking) with LET (https://en.wikipedia.org/wiki/Lorentz_ether_theory) in which ether make the medium rule.
Special Relativity not need ether but not denies its existence, only it’s unnecessary.
Time dilatation is an effect of general relativity that emerge in special relativity (unexplained in SR) but translated in formulas by Lorentz according to experiments.
Special relativity is a theory applied in inertial frames but developed in NON inertial frame (due to gravity), and it is the approximation in the 2 directions orthogonal to gravity vector of general relativity.
All this concepts is explained very well by @JoP in his works, he and me differ only for source and sink of ether but not for behavior with matter and light.
Gravity is due to an ether flow, and on earth, it is vertical at 11.4 km/sec and it keep we with (foot 😅) down to heart.
King regards
Ing.__mm

Hi @jerry ,
what you say is correct, but your example is easy while velocity is unrelativistic, but when it become near to c, the experiments becomes very difficult to realize because G field must be neglected and we need extra fast rocket/satellite that must meet in far space.
Already with https://en.wikipedia.org/wiki/Pioneer_anomaly we can feel something is wrong in relativity.
For constancy of c, it “may be” a good approximation in special relativity, (on earth) it is almost always verified in experiments.
In space it give some troubles with GPS satellite and Pioneer_anomaly that can be explained with different c velocity.
That constancy become dubious in general relativity when light travel in the direction of force field (G field for example) due to energy/mass of photons:
photons increase/decrease its frequency/energy in that direction, and, in a classic mechanics view, it’s equivalent to an increase/decrease of c.
The mathematics models of relativity (SR & GR) find correct results in experiments, but they loose the “physical” behavior between fields and matter (due, almost certainly to ether).
Regards
Ing.__mm



