Minkowski Space Time Briefly Revisited

Throwing links around isn't analysis. You claim that the world is an absolute space with an absolute time. You never talk about the arguments that Einstein and Minkowski had against this position. You haven't bothered to learn the science of either. It's sad.

 

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For the record, I say space exists and that at the fundamental level I can't distinguish it from energy. And that spacetime is not space, and instead is an abstract thing. For example it's space around the Earth, not spacetime.

Your motion changes how you measure something else, but it doesn't change that something else.

Actually I think it's better to start with curvature. See post #2 where I was talking about a photon and potential. I think this is "more fundamental" than a charged particle.

 

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What the above really shows is that you are confused and sounds like your argument is really about reasserting the existence of the aether.

Point of information, the Leyden address was in 1920, the quote being examined and your interpretation questioned, is from 1929.., and yet you believe that the uncertainty in the second is clarified by the earlier? You think Einstein forget something, in those 9 years? The truth is that you do not understand even his 1920 dumbed down Leyden address.

About the Laughlin quote, he was wrong in a historical sense. Laughlin's comment was based on what became an interpretation of Einstein's 1905 introduction of special relativity. Yes for the most part it did overturn the old concept of the aether as representing a fixed and preferred frame of reference.., but that was how it came to be interpreted and understood. He (Einstein) specifically stated in that first paper that his intent was, that the idea of an ether was not needed to explain reality.., which implies that his intent was not to discard it.., at least overtly. Though that is what happened, it did not really occur until Einstein introduced general relativity. It was at that point the Lorentz Aether Theory, which stood side by side with special relativity, failed to make the transition to a gravity model.., and even Lorentz was won over.

Einstein was not attempting to prove that the ether does not exist. He was demonstrating that you did not need it to explain reality. It was how others interpreted and then incorporated and applied what he presented that pushed the old concept of the aether aside.

Farsight, you really have to spend some time trying to understand CONTEXT. And by that I mean the context that is evident in the times and the audience that a speech or publication is intended for. For the most part the audience at Einstein's Leyden address had a similar physics background as his. They all had been brought up with the concept of the aether, as it was understood at the time from a Poincare-Lorentz perspective. Even Maxwell's work was developed with an understanding that the aether exists. Einstein was a little brighter than you are. He understood that to win over the masses he had popularize his explanations. Thus you find lay oriented books and public addresses, that don't reject popular beliefs out right, while introducing new ideas.

It always looks like you read things, many times historical references, having already decided what you believe.., which leads to an inability to understand what was actually being said.

 

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I'm not confused. Einstein reasserted the existence of the aether in 1920.

I understand it and the 1929 essay. The bottom line is that space isn't nothing. It sustains waves and fields. A field is where space has some particular state.

No, he wasn't.

You really take the biscuit. I give you the references and the quotes, and you airily dismiss what Laughlin and Einstein and others said on specious pompous grounds like "context" and "the masses". LOL, your ignorance is only exceeded by your arrogance.

 

That should be true if there is no dispersion as in vacuum.

But it is not 1 meter long in every inertial frame of reference, nor does it obey the same law of length contraction that an at-rest meterstick would.

For our purposes a (unidirectional) pulse of light 1 meter long in the rest frame has two sources in the past: A, the source event where the light starts, and B, the source event where the light stops. We also have to simultaneous "now" events of where the pulse is: C, the head of the pulse and D, the tail.

Assuming the pulse propagates in the +x direction then we have in the rest frame a space-time trapezoid with parallel sides:
\(x_D - x_B = c (t_D - t_B) \\ x_C - x_A = c (t_C - t_A) \) Because \(x_C - x_D = 1 \, \textrm{m}\) and \(t_C = t_D\) describes the side of the "now" we can write:
\(x_D - x_B = c (t_D - t_B) \\ 1 \, \textrm{m} + x_D - x_A = c (t_D - t_A) \) which gives this relation \(1 \, \textrm{m} + x_B - x_A = c (t_B - t_A) \) for the side of the source. A physical source will also have \((x_B - x_A)^2 < c^2 (t_B - t_A)^2 \). The special case of \(x_A = x_B\) gives \(t_B - t_A = \frac{1 \, \textrm{m}}{c}\) but that is not required by your description.

The Lorentz transform \(\Delta x' = \frac{\Delta x - u \Delta t}{\sqrt{1 - \frac{u^2}{c^2}}} \\ \Delta t' = \frac{\Delta t - \frac{u \Delta x}{c^2}}{\sqrt{1 - \frac{u^2}{c^2}}} \) gives the coordinate differences for any two events in a different inertial frame, but if that frame has relative motion, \(u \neq 0\), in the X direction to our first one, then events C and D will not considered simultaneous in the new frame so \(x'_C - x'_D\) will not be the length of the pulse of light. We must perforce add at least one event, event E, the location of the tail of the light simultaneous in the new frame with event C.

But in the calculation for E, all information about the source events, A and B, disappears. Using coordinates where we use an arbitrary origin but express points relative to event D, we have
\(\begin{array}{l|cccc} & x & t & x' & t' \\ \hline \\ C & x_D + L & t_D & x'_D + \frac{L}{\sqrt{1 - \frac{u^2}{c^2}}} & t'_D - \frac{u L}{c^2 \sqrt{1 - \frac{u^2}{c^2}}} \\ D & x_D & t_D & x'_D & t'_D \\ E & x_D - \frac{u L ( c + u )}{c ( c - u) } & t_D - \frac{u L ( c + u )}{c^2 ( c - u) } & x'_D -\frac{u L}{c \sqrt{1 - \frac{u^2}{c^2}}} & t'_D - \frac{u L}{c^2 \sqrt{1 - \frac{u^2}{c^2}}} \end{array}\)
or specifically:
\(x_C - x_D = 1 \, \textrm{m} \\ t_C = t_D \\ x_D - x_E = c (t_D - t_E) = c (t_C - t_E) \\ x_D' - x'_E = c (t'_D - t'_E) = c (t'_D - t'_C) \\ t'_C = t'_E \\ x'_C - x'_E = \sqrt{\frac{c + u}{c - u}} \times 1 \, \textrm{m} \)
This is different from the formula for length contraction of a physical object which is 1 meter long in its rest frame because even if the source of the light is at rest, a meter-long pulse of light has no rest frame.

 

To quote an expert!

 

The "ends" of a meter stick at rest in the lab frame (and everything in between also) are every bit as much "simultaneous" events as are the beginning and end of a pulse of light.

If it were not so, the end of a very long stick could move faster than light. it can't. Matter IS energy. Bound in time, but otherwise the same.

This math, for all of its impressive rigor, is wrong if it arrives at a different conclusion.

 

Or the idea that, Matter IS energy, is a naive interpretation of a far more complex relationship.

 

That's not the issue at hand. A material meterstick, by definition, has an associated rest frame where its length is exactly one meter. Its length in any inertial frame where its movement has a component parallel to its length is given by \(L_0 \times \cosh \tanh ^{-1} \frac{v}{c} \) where v is the motion parallel to its length.

Therefore it follows that in another frame, related by the Lorentz transform associated with velocity u, this length is in ratio to the first by the factor
\( \frac{ \cosh (r + \tanh ^{-1} \frac{u}{c} ) }{ \cosh r} \)
where r is the value of the above inverse hyperbolic tangent.

As SR is self, consistent, one expects this formula for the length of a moving meterstick in relation to its length in another frame to generalize to a meter-long pulse of light and indeed either does as
\( \lim_{r\to\infty} \frac{\cosh (r + x ) }{\cosh r} = e^x\)
and
\(e^{\tanh ^{-1} \frac{u}{c}} = \sqrt{\frac{c+u}{c-u}}\).

So I have said nothing contradicting SR, and nothing startling. It is not a coincidence that this is the same as the relativistic Doppler formula because the number of wavelengths for the whole pulse is has to be invariant.

This strongly suggests nothing in my math is wrong or contradicts the behavior of phenomena as summarized by Einstein in 1905. What say you?

(Posted and edited from a mobile from a shopping mall car park. Merry Christmas, ugh!)

 

Curiouser and curiouser. Yes, I recognize the Doppler formula.

Granted, you could define the light pulse in terms of a time that it began, and a time at which the source of the EM was cut off. Likewise, after the beam is cut of, after which it contracts at higher relativistic speeds, just as a meter stick, or any two events along the path of propagation would. How could it not? The only real difference here is that the light pulse is already at c (and assume the experiment is done in a vacuum). Therefore, no manner of time dilation of the energy can by definition occur, other than by Doppler shift. I see how this is different, yet the same.

I'm thunderstruck, as well as dumbstruck, by this revelation, rpenner. Great work.

 

Bound energy can sustain time dilation. No wonder matter exists. Everyone get that? It doesn't matter whether it is a light pulse or some particle of matter like an electron in a bound state. Time dilation affects them all just the same.

 

We only seem to be missing the right equations to correctly describe relativistic "twistyness" for energy, which classical physics dropped with the Ehrenfest paradox and never really returned to the subject. Telling a mathematician that pi is not a constant is like telling a physicist that c is not a constant. Come to think of it, that might be exactly the same problem.

Some people who didn't understand the idea evidently reverted to studying folks like Mach, which was a big mistake. Mach was a gifted natural philosopher, not much else. As bad a physicist as Newton was an Alchemist.

 

So, Minkowski space-time rotation as a mathematical description of length contraction-time dilation effects was ill founded from the get go. Time dilation is just a Doppler shift, in the case of solid objects or energy pulses; not a rotation. Simple.

 

To recap:

We have shown through a thought experiment with a fixed length pulse of light in a vacuum that Doppler shifts and time dilation are allowed, but because the pulse is already traveling at c, NO further length contraction ever occurs, in any inertial reference frame.

By extension, matter is composed of energy and a whole lot of space, so that if a meter stick travels at near relativistic velocity, its length in its direction of motion contracts alright, but there is a limit to the amount of length contraction AND THAT LIMIT is the same as for the light travel time / length it takes a light pulse to travel a distance of 1 meter.

Notice that none of this correction information was ever transferred to the Lorentz transformations you were taught, or at least, that I was taught. Why is that?

 

Minor correction to 2nd paragraph of last post. The limit is obviously not 1 m light travel time (in which case, even a meter stick would't contract). The limit to the contraction is the same as if you removed all of the empty space in the meter stick and concentrated the particles close enough together so that the energy density is comparable to that in the light pulse,and possibly this is also determined by the old saw e=mc^2. I'll bet maximal length contraction happens at some speed less than c for any matter that has atomic structure like a meter stick.

 

except physics IS MATHEMATICS in a form of words without numerical value.
nothing more.
it was just shown ,this is also not understood.

 

I don't think you're quite looking at this right, Dan. Think about pair production where we make an electron and a positron out of light. And about electron diffraction. And electron-positron annihilation, which typically results in two 511keV gamma photons. And take a look at atomic orbitals on Wikipedia. See this bit: "The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves"

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Start with the simplest 1s orbital on the left, then reduce it to a circle to make it even simpler. Now turn it on its side, and take one point on the circumference. Now move the electron, and that point describes a helix. Add in all the other points round the circumference, and the circle becomes a cylinder. Then lets say that you are this electron writ large. You are "smeared out" lengthways in the direction of motion. You don't see this of course, you look normal to yourself. But everything that isn't moving like you looks length-contracted to you. However it didn't change just because you moved fast. Instead you changed.

 

That all sounds like an extremely naive attempt to explain something you don't understand.

Length contraction is a relativistic effect, perhaps even the result of interaction occurring at a quantum level (but that would add a whole new dimension to the discussion),which you are attempting to explain away from a classical frame of reference.

Yes, sometimes things appear length contracted due to the frame of reference they are observed from.., but that is not the same as length contraction, as the subject is generally understood in physics. It isn't smoke and mirrors, which is what the conclusion in your last two sentences implies.

 

I don't see an easy way out of this paradox, if that's what it is. I believe rpenner's equations were correct. It leads to the conclusion that a laser pulse in a vacuum never Lorentz contracts from relative motion, but meter sticks do. It would also mean our calibration standards for length are whacked, because they are based on comparing physical meter sticks to a fixed number of wavelengths of light.

I meant, mc^2 = h * nu = 2 * pi * f * h , to get an equivalent wavelength for the effective rest mass of a meter stick. It can't Lorentz contract shorter than that, because that much of the stick is energy, the same as the pulse.

I'm with krash662 a little bit here. It usually pays to be skeptical of such a surprising result, but I don't see my mistake yet.

 

This would explain (without invoking Higgs) why time doesn't actually stop for energy propagating at the speed of light, any more than it does at the event horizon of a black hole. Conservation of energy alone does not allow time to stop. If it did, any energy associated with it would not be conserved.