Proof Minkowski Spacetime is Poorly Conceived

[el es]

From post #198:

"You will be needing an understanding of what time is,...."

The nature of time is a subject for philosophy.

In physics, measurements of time are useful. Agreed upon increments of duration can be represented as lengths and used as a dimension.

 

[danshawen]

Using the Lorentz transformations, rpenner proved that the interval is invariant when you change reference frames. He did it right here in this thread.

He did no such thing.

Minkowski didn't "prove" that t = sqrt(-1) x ct either, which was where Minkowski began his development of an invariant interval and the static geometry that goes along with it to replace the speed of light. Simultaneity was simply the cheat he used to make things appear static and mathematically consistent with a static geometry. And you all fell for it.

Whenever your mathematics considers an instant of time and equivocates that with an interval of time, that is a cheat, the same way that dividing by zero is. You are only fooling yourselves.

You can't "prove" something that is an assumption to begin with.

Minkowski didn't understand what "time" was. Neither do you, or rpenner.

 

[James R]

He did no such thing.

Sorry, my mistake. It was przyk, here:

http://sciforums.com/threads/proof-...s-poorly-conceived.156114/page-9#post-3378873

Please read this post and get back to me as to whether you will now admit that the invariance of the space-time interval follows form the Lorentz transformations.

The proof has been given to you. Will you accept the logical conclusion, or stay in denial?

Minkowski didn't "prove" that t = sqrt(-1) x ct either, which was where Minkowski began his development of an invariant interval and the static geometry that goes along with it to replace the speed of light.

It doesn't matter how he got to the invariance of the interval. If you accept the Lorentz transformations, you must logically accept the invariance of the interval. You have been given the proof.

Do you agree?

Simultaneity was simply the cheat he used to make things appear static and mathematically consistent with a static geometry. And you all fell for it.

That is a separate matter. Let us deal with the matter of the invariance of the interval first, then we can move on to other issues.

Whenever your mathematics considers an instant of time and equivocates that with an interval of time, that is a cheat, the same way that dividing by zero is. You are only fooling yourselves.

In my post before this one, I showed you a proof that time intervals transform in the same way as time coordinates.

Do you deny that proof or accept it?

You can't "prove" something that is an assumption to begin with.

Correct.

So, let's be clear about what you accept or do not accept.

Do you accept the Lorentz transformations are correct?
Do you accept that the invariance of the interval follows logically if the Lorentz transformations are correct?
Do you accept that time intervals transform the same way as time coordinates, according to the Lorentz transformations?

Minkowski didn't understand what "time" was. Neither do you, or rpenner.

We can get to discussing my understanding of time once we sort out this matter of your acceptance of mathematical proof.

I look forward to your answers to the above questions.

 

[danshawen]

Please read this post and get back to me as to whether you will now admit that the invariance of the space-time interval follows form the Lorentz transformations.

The "proof", which I said was "good", as in "good math", is only valid if you buy into its underlying assumptions. I don't.

Here are some assumptions that I DO buy into:

I buy into the assumptions underlying the Lorentz transformations which includes solid geometry that can easily be implemented on a long straight solid road on which things have the freedom to move along a single linear dimension, and time dilation is (macroscopically, at least), is uniform along the entire road. These assumptions were never explicitly stated in any derivations I have ever seen, but PERHAPS THEY SHOULD HAVE BEEN.

I buy into the assumption that the universe is an arena of energy transfer events and time and nothing else physically exists there.

I buy into the assumption of the invariance of the speed of light in all inertial reference frames, and that space itself is light travel time in all three dimensions, in any direction in which energy may propagate along a directed path.

I buy into the invariance of rest mass.

I buy into the assumption that no luminiferous aether is required for the propagation of unbound energy or for the bulk transport of bound energy.

I buy into the assumption that energy is an excitation of an underlying quantum field, and that underlying field possesses no linear or rotational inertia not associated with the presence of the bound energy form we know as matter, and that every point within that quantum field is quantum entangled with every other point. It is not appropriate to perform geometry or math on the quantum field that is consistent with those calculated using solid matter with inertia UNLESS IT IS DONE ON SOLID MATTER WITH INERTIA.

I buy into the assumption that time and inertia, both linear and rotational, are intimately related.

 

[danshawen]

Farsight was kind enough to contribute this link:

http://einsteinpapers.press.princeton.edu/vol4-trans/271?highlightText="writer of these lines"

With special emphasis on the section:

Minkowski's Mathematical Treatment of the Theory of Relativity

States that in order to derive his invariant interval, the quantity:



has been set as a quantity that is proportional to time.

If this was an equation of the form:

t = ict, it would imply that
t/t = 1 = ic

Which is a consistent form often used by Einstein himself to explain Special Relativity. But it says more. It says that Minkowski believed the speed of light to be the basis of time itself. This was also consistent with the thinking of the day. In particular, Einstein had often said that if a spaceship were capable of reaching the speed of light in a vacuum, time dilation to an observer on the relativistic spacecraft would be infinite. There are two things wrong with this idea. First, it's never going to happen. The mechanism that gives inertial mass itself has mass and therefore cannot actually reach the speed of light (in linear propagation fashion, at least). Second, when light itself propagates, nothing actually "travels" or transports in the sense that matter does. The mechanism of propagation is a local excitation of a quantum field that chains like a line of falling dominos into the region of the next. The only difference is, this particular process can work even without inertia. So it is impossible for time to actually "dilate" for a moving photon because nothing really moves, it naturally follows that THE SPEED OF LIGHT CANNOT BE THE BASIS OF TIME ITSELF. The chaining into the next region itself happens faster than a photon of light appears to travel. Magnetic fields increase and decrease, and electric fields increase and then decrease, and this all happens on a much finer scale of time than the bulk propagation of light. Relativity must be compatible with Maxwell too.

So Minkowski's fundamental assumption is dead before it even gets started. Complex numbers don't get it any further. Static geometry intended for working with solids at rest is of no use either. The man didn't have a single clue what he was doing math about.

 

[rpenner]

That's atrociously bad reading. As everyone who does physics knows, and as you have been told many times to little effect, quantities in physics are not numbers, but have a magnitude which is a combination of a number and some unit.

So 1 = 100 is wrong, but 1 meter = 100 centimeters is correct.

Likewise 1 meter + 1 kilometer is a sensible sum, as is 1 foot + 12 centimeters is a sensible sum, but 1 kelvin + 1 kilogram is not sensible because the units are incompatible.

As an accident of human designed units, time and space are not measure in compatible units. Thus if one is to relate time and space in a single geometry, it makes sense to use compatible units. That relation renders all velocities as pure numbers as v = [quantity of space in compatible units] / [quantity of time in compatible units] has no net units.

So we go to the test-theory of relativity:

$$ t' = \frac{1}{\sqrt{1 - K \vec{v}^2}} \left( t + K \vec{v} \cdot \vec{x} \right) \\ \vec{x}' = \vec{x} + \left( \frac{1}{\sqrt{1 - K \vec{v}^2}} - 1 \right) \frac{1}{ \vec{v}^2} \left( \vec{v} \cdot \vec{x} \right) \vec{v} + \frac{1}{\sqrt{1 - K \vec{v}^2}} t \vec{v} $$​

And since 1859 we have had experimental evidence that K is a positive (and therefore non-zero) quantity with units of [TIME]² / [DISTANCE]² .

Therefore there must be some physical speed such that $$K v^2 = 1$$.

So K is a physical constant which relates [TIME]² to [DISTANCE]² and so that t is measured in the same units as √K x. Likewise we have for a free particle:

m² = K² E² – K p² ; p = K E v

Now light is just some physical phenomena whose speed is unimportant except that all massless phenomena which convey energy and momentum have to travel at speed 1/√K and light in a vacuum acts like a massless phenomena which convey energy and momentum. Since light, in a vacuum, travels at c, we know what K is.

Because in the m=0 case, we have K E² = p² = K² E² v² so 1 = K v².

So K > 0 which relates to the nature of how space and time are one thing, means ct and x are measured in the same units in the only way that makes sense in relativity. Light isn't special to space-time, but the speed of light in vacuum, c, is a physical quantity which relates to the physical nature of space-time.

 

[paddoboy]

Light isn't special to space-time, but the speed of light in vacuum, c, is a physical quantity which relates to the physical nature of space-time.

Interesting.....Are you suggesting that spacetime could be inferred as the ether?
"A rose by any other name"quote comes to mind.......
[Actually I have also mentioned this to Schmelzer in some debates re his ether paper.

 

[danshawen]

That's atrociously bad reading. As everyone who does physics knows, and as you have been told many times to little effect, quantities in physics are not numbers, but have a magnitude which is a combination of a number and some unit.

So 1 = 100 is wrong, but 1 meter = 100 centimeters is correct.

Likewise 1 meter + 1 kilometer is a sensible sum, as is 1 foot + 12 centimeters is a sensible sum, but 1 kelvin + 1 kilogram is not sensible because the units are incompatible.

As an accident of human designed units, time and space are not measure in compatible units. Thus if one is to relate time and space in a single geometry, it makes sense to use compatible units. That relation renders all velocities as pure numbers as v = [quantity of space in compatible units] / [quantity of time in compatible units] has no net units.

So we go to the test-theory of relativity:

$$ t' = \frac{1}{\sqrt{1 - K \vec{v}^2}} \left( t + K \vec{v} \cdot \vec{x} \right) \\ \vec{x}' = \vec{x} + \left( \frac{1}{\sqrt{1 - K \vec{v}^2}} - 1 \right) \frac{1}{ \vec{v}^2} \left( \vec{v} \cdot \vec{x} \right) \vec{v} + \frac{1}{\sqrt{1 - K \vec{v}^2}} t \vec{v} $$​

And since 1859 we have had experimental evidence that K is a positive (and therefore non-zero) quantity with units of [TIME]² / [DISTANCE]² .

Therefore there must be some physical speed such that $$K v^2 = 1$$.

So K is a physical constant which relates [TIME]² to [DISTANCE]² and so that t is measured in the same units as √K x. Likewise we have for a free particle:

m² = K² E² – K p² ; p = K E v

Now light is just some physical phenomena whose speed is unimportant except that all massless phenomena which convey energy and momentum have to travel at speed 1/√K and light in a vacuum acts like a massless phenomena which convey energy and momentum. Since light, in a vacuum, travels at c, we know what K is.

Because in the m=0 case, we have K E² = p² = K² E² v² so 1 = K v².

So K > 0 which relates to the nature of how space and time are one thing, means ct and x are measured in the same units in the only way that makes sense in relativity. Light isn't special to space-time, but the speed of light in vacuum, c, is a physical quantity which relates to the physical nature of space-time.

Deep enough to satisfy even someone as skeptical as me. There is ample to ponder here, at last.

 

[rpenner]

Using the Lorentz transformations, rpenner proved that the interval is invariant when you change reference frames. He did it right here in this thread.

He did no such thing.

Sorry, my mistake.

Actually, you will want to consult post #194 where I demonstrated:

$$ \left( (A' - B') \right)^{\textrm{T}} \eta (C'-D') = \left( (\Lambda A - \Lambda B) \right)^{\textrm{T}} \eta (\Lambda C- \Lambda D) = \left( \Lambda (A - B) \right)^{\textrm{T}} \eta \Lambda (C-D) = (A - B)^{\textrm{T}} \Lambda^{\textrm{T}} \eta \Lambda (C-D) = (A - B)^{\textrm{T}} \eta' (C-D)$$

With $$ \eta' = \dots
\\ = \eta + 0
\\ = \eta $$

Because $$ \begin{pmatrix} 0 & \vec{\rho}^{\textrm{T}} \\ K \vec{\rho} & 0 \end{pmatrix} \eta + \eta \begin{pmatrix} 0 & K \vec{\rho}^{\textrm{T}} \\ \vec{\rho} & 0 \end{pmatrix} = 0 $$ as you may verify.

So K=0 means relativity of standard of rest gives Galilean Relativity with Galilean transforms, Newtonian velocity composition and absolute time, while $$K=c^{-2}$$ gives Special Relativity with Lorentz transforms, Einstein velocity composition, and an invariant measure of space-time intervals.

This was analogous to proving the invariance of Euclidean geometry dot products under rotations, with a trivial demonstration that the invariant measure of the interval is preserved by Lorentz transforms.

So, let's be clear about what you accept or do not accept.

Do you accept the Lorentz transformations are correct?
Do you accept that the invariance of the interval follows logically if the Lorentz transformations are correct?
Do you accept that time intervals transform the same way as time coordinates, according to the Lorentz transformations?

Good questions for someone who claims to have rational, communicable reasons for accepting one but not the other.

 

[danshawen]

Actually, you will want to consult post #194 where I demonstrated:

​

This was analogous to proving the invariance of Euclidean geometry dot products under rotations, with a trivial demonstration that the invariant measure of the interval is preserved by Lorentz transforms.

Good questions for someone who claims to have rational, communicable reasons for accepting one but not the other.

The Lorentz transformations cannot be rejected without rejecting time dilation. This effect has been experimentally verified well beyond any reasonable doubt. You can't reject that unless you are insane or willfully ignorant. I am neither.

The Lorentz transformations make no attempt to suggest that length and time are covariant (one must change BECAUSE the other changes). If it did, some folks are stupid enough to become double amputees so that they could live longer (shorter means more time dilation, you see?). In a sense, this is what you do when you suppose that time itself is related to a difference in length, or a hyperbolic rotation, OR EVEN THE NOMINAL INVARIANT SPEED OF LIGHT.

Only someone convinced of the absolute supremacy of static geometry would deign think of time that way. Time dilation evidently is all about how fast you go relative to something else, (or spin) relative to EVEYTHING else. But time itself is a combination of the two, and the Lorentz transformations do not even address relative spin at all.

But Minkowski believed in the Lorentz transformations sufficiently to try to extend them to time intervals and the arrow of time, and what resulted was the usual inconsistent fruition of making a load of arrogant gibberish into fundamental assumptions.

If Minkowsi rotations worked the way he calculated them, part of the necessary relativistic hyperbolic rotations of lengths (the parts that are 3D) would be evident in the room in which you are sitting right now. They would not behave the way Einstein's meter sticks on a relativistic train did. Things with inertia would spontaneously start spinning as a result of their passage through time. Do they? How would you know if they were or were not?

Time may be related to the speed of light, but time is not, as Minkowski posited, EQIVALENT TO the speed of light. For one thing, he completely forgot about rotation, and evidently, that can be a little faster. At least now we understand, RELATIVE TO WHAT?

 

[The God]

Time may be related to the speed of light, but time is not, as Minkowski posited, EQIVALENT TO the speed of light. For one thing, he completely forgot about rotation, and evidently, that can be a little faster. At least now we understand, RELATIVE TO WHAT?

1. Relative to what ?

2. How is time related to speed of light ? As long as you are not talking about multiple frames, the dependence of time flow on the speed of light is not established. Relativity brings in...in relation with.

3. We have no pure translational motion in the universe, all objects are curving, no straightline motion. Instantaneous speed is always translational for any object, irrespective of its rotation.

If you are pursuing 'this Physics' in multiple frames with relative space and time, then you cannot chuck Minkowski/Einstein out. Try this you will be forced to get back into relativity.

Unlearn all the other aspects of SR and GR, just focus on equivalence principle...and see how Physics unfolds infront of your eyes. Amazing. You know what, somehow a nonsensical desire to keep SR/GR 100% intact has killed the creativity on this aspect of Physics. Guys have started boasting of their funny manipulations with mathematics, forgot the real Physics.

 

[danshawen]

Relative to the spin zero boson that is an excitation of the Higgs quantum field, which is the reason the whole universe isn't spinning even if galaxies do. Who says they aren't all spinning around each other also? Who needs dark energy? That spin would cause a Doppler shift also. And how much energy would that be?

What component of time was it that Minkowski missed again?

One of the things that puts me off about Farsight's analysis is that he talks about Einstein and Minkowski as though their intellectual properties were somehow inseparable. This is just not the case. E=mc^2 was Einstein's baby, all the way. So was the photoelectric effect and explaining the import of the Lorentz transformations and the null result of Michaelson-Moreley. They are easily separable.

Credit Minkowski with aborting our understanding of time itself by using photonic simultaneity to propose we use static geometry to understand something dynamic like time. Idiot.

 

[The God]

Relative to the spin zero boson that is an excitation of the Higgs quantum field, which is the reason the whole universe isn't spinning even if galaxies do. Who says they aren't all spinning around each other also? Who needs dark energy? That spin would cause a Doppler shift also. And how much energy would that be?

But what makes you think that we are all not one ? The entire universe is a single entity, and it may be spinning...farther a galaxy higher the redshift due to higher angular speed....that we can adjust with the help of MOND or no MOND, who needs DE and CC..

 

[The God]

E=mc^2 was Einstein's baby, all the way.

No it was not....

 

[danshawen]

You can store more energy in something with inertia that is spinning at c^2 or whatever velocity >c than you can in something with no inertia propagating at the speed of light in a straight line.

In that sense, time could be more closely associated with inertia than the speed of light. It makes sense for time dilation OTHER THAN the Lorentz transformation predictions for dilation that derives of relative motion.

As with any kind of physics, your ability to understand something drops precipitously if you neglect to consider or understand one of its principle relativistic vector components.

 

[danshawen]

No it was not....

It was his derivation, and it was clumsy owing to the lack of sophistication of his Newtonian audience, but it was all his, and there is no doubt that it was his.

 

[danshawen]

The Principle of Equivalence was an assumption (and was not 'proven'). It should have been easy to prove by now, except for all the noise from Minkowski. DO IT. It isn't that hard. But you won't be able to do it using inertialess static geometry.

 

[Ophiolite]

Credit Minkowski with aborting our understanding of time itself by using photonic simultaneity to propose we use static geometry to understand something dynamic like time. Idiot.

On the one hand we have tens of thousands of physicists who have no problem with Minkowski's maths and do not believe him to be an idiot.

On the other hand we have an anonymous internet poster who indulges in rants and rages.

Who to provisionally accept as having the more accurate view of reality? Not such a tough one when you think about it.

 

[danshawen]

On the one hand we have tens of thousands of physicists who have no problem with Minkowski's maths and do not believe him to be an idiot.

On the other hand we have an anonymous internet poster who indulges in rants and rages.

Who to provisionally accept as having the more accurate view of reality? Not such a tough one when you think about it.

That is an accurate picture, yes. I don't care. I've had this itch to get off my back about Minkowski literally for longer than there has been an internet, Ophiolite.

There was an ARPAnet in those days but that was all. I had no access to it.

I carried on the discussion through usenet, when it became available, but very few, if any, there even knew what I was talking about.

This much has gotten decidedly better. And you, as much as anyone else here, are the proof of that. Even if you do not follow all of the mathematical discussion, at least you have a grasp of what is at stake (and also, what is not). Thank you.

 

[danshawen]

I did try to engage the sole surviving college physics professor in a discussion about the discovery of the Higgs boson and the principle of equivalence before joining sciforums, but for whatever reason, he did not respond to my email. He was brilliant when he was my professor, but senility eventually takes its toll on us all.

Eventually, it will doubtless remove any misgivings I have about Minkowski as well. No one will shed a tear about that either, including me. At least, no one will be asking any of my old calculus or physics professors what they think of my theory. Even better. We already know how well that usually goes.