Proof Minkowski Spacetime is Poorly Conceived

[danshawen]

Finally, if

c = omega1 x r, and
-c = omega2 x r,

divide both sides of both equations by r (distance = light travel time)
Then multiply them together and for a simple case, omega1=omega2:

1/t^2 = omega^2

1/t = +/- omega

And we finally have the identity involving time Minkowski was missing. Notice that the speed of light isn't even involved unless we know that photons of sufficient energy can combine in this way to form matter. Time is always positive (one direction) no matter which direction omega (or light) propagates. The rest can be taken care of using the results of the Lorentz transformations. Be careful how you treat time dilations. They are just as valid for circular paths as they are for linear ones. In this way, you understand that time has two components. One is energy-like, and one is matter-like, but in both cases, space is simply light travel time and has no inertia until or unless it is bound, and by that we mean 'spinning'. Time literally is inertia.

Triple sizing your soft drinks and French fries probably won't help extend your life by means of time dilation, unless you eat enough to become a black hole, that is. Yeah, that would work. Don't you just love physics that has real, practical applications? Minkowski didn't.

 

[The God]

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.

Well, I will let you do the honors with some basic googlee on history of E = mc^2......

 

[The God]

Finally, if

c = omega1 x r, and
-c = omega2 x r,

divide both sides of both equations by r (distance = light travel time)
Then multiply them together and for a simple case, omega1=omega2:

1/t^2 = omega^2

1/t = +/- omega

And we finally have the identity involving time Minkowski was missing. Notice that the speed of light isn't even involved unless we know that photons of sufficient energy can combine in this way to form matter. Time is always positive (one direction) no matter which direction omega (or light) propagates. The rest can be taken care of using the results of the Lorentz transformations. Be careful how you treat time dilations. They are just as valid for circular paths as they are for linear ones. In this way, you understand that time has two components. One is energy-like, and one is matter-like, but in both cases, space is simply light travel time and has no inertia until or unless it is bound, and by that we mean 'spinning'. Time literally is inertia.

Well, it is not that you need my endorsement, it is also not the case that I am fan of some of these guys...... I would be the first one to cheer any worthy alternative, but man this is no Physics.

 

[danshawen]

Well, I will let you do the honors with some basic googlee on history of E = mc^2......

And for anyone who thought that last post was 'trivial':

Et (time for energy)/mt (time for matter) = c^2 x (t/t)

 

[danshawen]

Well, it is not that you need my endorsement, it is also not the case that I am fan of some of these guys...... I would be the first one to cheer any worthy alternative, but man this is no Physics.

And,

t is proportional to ict

which was Minkowski's assumption about time vs the speed of light when he created the interval using simultaneity and the Lorentz transformation, which he used inappropriately

That's 'physics' in your book?

I have just shown a reciprocal temporal relationship for bound energy (matter), vs. time as an uninverted form for unbound energy like a beam of light. No wonder he got so confused.

Bound energy is permanent (time dilation and inertia is large, travels at speeds <c). Unbound energy dissipates, (time dilation is large, inertia is zero, energy propagates at c). I just explained the invariance of the speed of light, rest mass, mass/energy equivalence, and the origins of time in only two relations.

You want more? Didn't think so.

 

[danshawen]

No one flinched when Minkowski posited a hyperbolic rotation different to every observer, but when I suggested an even more fundamental reciprocal-temporal relationship between time as experienced by energy vs. time experienced by matter, everyone balks at it.

I don't care. What is it you believe powers your nuclear reactors or weapons? Magic?

 

[Ophiolite]

No one flinched when Minkowski posited a hyperbolic rotation different to every observer, but when I suggested an even more fundamental reciprocal-temporal relationship between time as experienced by energy vs. time experienced by matter, everyone balks at it.

1. That simple fact should give you pause for thought. I have seen evidence of only the shortest of pauses and no evidence of any thought.
2. Several people have explained to you carefully why they "balk at" your suggestions.
Despite this.....

I don't care.

That is not something to be proud of.

What is it you believe powers your nuclear reactors or weapons? Magic?

What is it that you believe powers your rhetoric and angst? Delusions?

 

[danshawen]

1. That simple fact should give you pause for thought. I have seen evidence of only the shortest of pauses and no evidence of any thought.
2. Several people have explained to you carefully why they "balk at" your suggestions.
Despite this.....
That is not something to be proud of.

What is it that you believe powers your rhetoric and angst? Delusions?

You probably would have made a decent psychiatrist also, Ophiolite.

No, just an ordinary, garden variety obsession with physics. Don't read any deeper into it than that. I'll be Okay. This has been therapeutic for me, even if not for people here. I'm just glad I was never Minkowski. I can only imagine what he must have gone through.

 

[przyk]

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

Well that's what we've been telling you. I only used one assumption to show the invariance of the spacetime interval: that the coordinates of inertial reference frames are related by Lorentz transformations. That is all. I used no other assumption at all. So your rejection of this result is completely irrational.

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.

Except Minkowski didn't do this or most of the things you are attributing to him. Most of your problems with Minkowski are fictions that you just made up yourself.

You could substitute the name of pretty much anyone else in your rants and they would make no less sense:

Charles Darwin believed that species evolve by natural selection over time. Clearly, Darwin believed that evolution forms the basis of time itself. This was consistent with the thinking of the day. Einstein said that if an animal of a certain species were to travel at the speed of light, then time dilation would become infinite and evolution would stop. But this can never happen because mass is made by a mechanism that itself has mass and light is really an excitation of a quantum field rippling through space. and nothing really moves. Darwin didn't understand the difference between bound and unbound energy. Evolution must be compatible with Maxwell too. Also, a pair of entangled particles can both flip their spins simultaneously even if they're separated by a great distance. How could Darwin's ideas explain this quandry?

So Darwin's fundamental assumption is dead before it even gets started. The man didn't have a clue what he was talking about. Unfortunately, he influenced generations of scientists to adopt his misguided way of thinking, and we still don't have a unified field theory of biology today.

 

[Dr_Toad]

Brilliant!

 

[danshawen]

I do believe in Darwin's Theory of Evolution, so if that theory is correct, then I must be completely wrong.

Thanks for clearing that up! I feel so very silly now. I suppose I owe Minkowski an apology.

So, as a matter of curiosity, why do we measure linear distance in wavelengths per unit time (t), but rotation in unit time per radian or revolution (1/t)? Probably because of something fundamental to rotation that begins with r, which is the only distance that doesn't actually change under Lorentz transformation (yes, there is one, and ONLY one).

Even though, observers at different radii traveling in the same direction will age differently and will not be able to agree with each other on how long it takes to complete a single revolution. That's because the center of rotation and the starting positions can only be communicated to different radii by means of light travel time, you see?

Why no mention of rotational velocity in the Lorentz transformations? A circular path is as good as a linear one for producing both time dilation and length contraction. Any serious takers, or are we permanently derailed to a discussion of something that belongs in a discussion of biological or evolutionary/molecular clocks in biology? Those are fascinating too, I will grant you.

Don't let on like I'm really annoying anyone. I might get the impression that I'm actually onto something that matters. This thread is still in Alternative Theories, right? What did you expect?

 

[rpenner]

I must be completely wrong.
I suppose I owe Minkowski an apology.

Shorter, more correct.

So, as a matter of curiosity, why do we measure linear distance in wavelengths per second (t), but rotation in seconds per wavelength or revolution (1/t)?

No one does that. How are you going to improve physics when you don't understand units.

$$ 1 \, \textrm{second}_{1983} = 9192631770 \times \left[ \textrm{period of radiation of transition between hyperfine levels of the ground state of the cesium-133 atom} \right]
\\ 1 \, \textrm{meter}_{1983} = \frac{656616555}{21413747} \times \frac{ \left[ \textrm{amount of spatial displacement between events A and B} \right] }{ \left[ \textrm{amount of time light needs in a vacuum to travel between events A and B} \right] } \times \left[ \textrm{period of radiation of transition between hyperfine levels of the ground state of the cesium-133 atom} \right]
\\ \quad \quad \quad = \frac{656616555}{21413747} \times \left[ \textrm{how far light will travel in vacuum during one period of radiation of transition between hyperfine levels of the ground state of the cesium-133 atom} \right] $$

Rotation is measured in your choice of radians or degrees or cycles, a quantity which has neither units of time or distance. Rotation rates are measured as radians or cycles per unit of time, just as velocities are measured in terms of distance per unit of time and flow rates are measured in terms of volume per unit of time.

But distance is measured in terms of distance, not time.

 

[danshawen]

Shorter, more correct.
No one does that. How are you going to improve physics when you don't understand units.

$$ 1 \, \textrm{second}_{1983} = 9192631770 \times \left[ \textrm{period of radiation of transition between hyperfine levels of the ground state of the cesium-133 atom} \right]
\\ 1 \, \textrm{meter}_{1983} = \frac{656616555}{21413747} \times \frac{ \left[ \textrm{amount of spatial displacement between events A and B} \right] }{ \left[ \textrm{amount of time light needs in a vacuum to travel between events A and B} \right] } \times \left[ \textrm{period of radiation of transition between hyperfine levels of the ground state of the cesium-133 atom} \right]
\\ \quad \quad \quad = \frac{656616555}{21413747} \times \left[ \textrm{how far light will travel in vacuum during one period of radiation of transition between hyperfine levels of the ground state of the cesium-133 atom} \right] $$

Rotation is measured in your choice of radians or degrees or cycles, a quantity which has neither units of time or distance. Rotation rates are measured as radians or cycles per unit of time, just as velocities are measured in terms of distance per unit of time and flow rates are measured in terms of volume per unit of time.

But distance is measured in terms of distance, not time.

omega = 2 x pi x f
f = 1/t.

 

[danshawen]

A very long time ago (30 years) on usenet, together with my physics discussion cohorts there (like Archimedes Plutonium), we beat dimensional analysis, time and clocks to a pulp (and then some) before coming up with the idea that a measurement of velocity or of time, including the speed of light, never physically amounts to anything more complex than a ratio of how fast some difference in time between events occur compared to how fast some OTHER difference in time between different events at a different speed in some other location occur. It helps a little when light is used as one of the clocks, because it is invariant.

If both units of time are in seconds for the propagation of energy or the bulk transport (travel) of matter, and units of 1/seconds is used for rotational kinematics, and matter is a rotational propagation form of energy, what I said follows any way you cut it. Matter experiences reciprocal time compared to unbound energy.

This shows up in a lot of places in physics. Someone else must have noticed, because I saw references to it throughout my physics academic (student) career: 'matter is space-like', or 'energy is time-like'. All of this is old hat. But no one ever said anything like: 'matter is reciprocal time-like'. I would have noticed.

Is it my imagination acting up again, or do mathematicians like Minkowski tend to treat t and 1/t as the same, simply because an inverted ratio has pretty much the same mathematical interpretation? Not so in physics. An inverted ratio in physics can mean the difference between understanding and missing something important by miles, if not the difference between 1/0 and 0/1. See? BIG difference. One is a number. The other is not.
.

 

[Dr_Toad]

As has been pointed out, you are not a mathematician, where the people you continue to misunderstand are. Pretty simple, eh?

 

[przyk]

Why no mention of rotational velocity in the Lorentz transformations?

Because the Lorentz transformation by definition relates the coordinates of inertial reference frames that are in constant, rectilinear motion relative to one another. This is like asking why firefighters don't arrest criminals: it's simply not and never was their purpose.

You can define accelerating and rotating reference frames just fine in relativity, and you can describe how their coordinates are related to an inertial reference frame by a coordinate transformation if you want. But, unlike Lorentz transformations, these are not symmetries in physics and relativity has nothing particularly special to say about them. The significance of the Lorentz transformation and the time dilation and length contraction factors that it implies is that they are universal where rectilinear motion is concerned. Every physical system (clock, human being, etc.) in rectilinear motion will be time dilated and length contracted by exactly the same factor compared with the same system if it were at rest. The same is not true if you compare a physical system at rest to a moving one going around in a circle. This is because a physical system following a circular trajectory will be subjected to additional stresses, like centrifugal pseudo-forces, and these will affect different systems differently. A rigidly built structure would be generally less affected than a squishy human who will be killed by more than a few $$g$$s, for example.

In short, the effect of rotation is different for different physical systems and is much more complicated than the effect of relative rectilinear motion, and it can't be fully described by just a few parameters like a length contraction and time dilation rate.

Is it my imagination acting up again, or do mathematicians like Minkowski tend to treat t and 1/t as the same, simply because an inverted ratio has pretty much the same mathematical interpretation?

It's your imagination.

Your reactions to being corrected here are incomprehensible. Apparently you've gotten worked up for years believing that Minkowski said that time is invariant and everything is static and (now, apparently) $$t$$ is the same as $$1 / t$$, and so on, and how can physicists believe these silly things? So, if anything, you should be relieved to find out that Minkowski geometry does not, in fact, say or even imply any of these things. Surely that's good news for you, no?

 

[James R]

danshawen:

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

There are only two fundamental assumptions that the Lorentz transformations depends upon. And since the invariance of the interval follows from the Lorentz transformations, that also only depends on the same assumptions. The assumptions are:

1. The laws of physics take the same forms in all inertial frames of reference.
2. The speed of light in all inertial frames is the same (i.e. $$c=299792458$$ m/s).

Which of these two assumptions do you reject, and why? Actually, below you say you accept assumption 2, so we only need to sort out whether you accept assumption 1.

I buy into the assumptions underlying the Lorentz transformations ...

You mean the two postulates I've listed here? They are the only assumptions.

...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 have stated the only relevant assumptions here. Do you accept them, or not?

I buy into the assumption of the invariance of the speed of light in all inertial reference frames...

Ok then. So the only assumption you might possibly disagree with is assumption 1, listed above.

Do you accept that assumption or not?

... and that space itself is light travel time in all three dimensions, in any direction in which energy may propagate along a directed path.

That's an assumption that relates to some vague hypothesis that you have. It has nothing to do with Einstein or Minkowski. Let's sort out your points of difference, if any, with Einstein and Minkowski, before going any further with your "alternative" hypothesis.

[Minkowki?] states that in order to derive his invariant interval, the quantity ict 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

You're not making much sense. If $$t=ict$$, then $$t/t = 1$$, not $$ic$$.

Can you do maths at all?

.... 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.

You apparently don't know to divide ict by itself to come up with 1. So, I doubt your qualifications to comment on maths done by Minkowski or Einstein.

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.

Then if you accept the Lorentz transformations, does that mean you accept assumption 1, listed above? Because the Lorentz transformations follow from the two assumptions.

If you accept that, you logically must also accept the invariance of the spacetime interval. The proof has been given to you, based only on the Lorentz transformations.

[snip].... But time itself is a combination of the two, and the Lorentz transformations do not even address relative spin at all.

The Lorentz transformations are coordinate transformations. You are correct that they do not address spin, for the same reason that firefighters don't arrest criminals and for the same reason that you don't carry water in a sieve.

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.

Show me the errors in Minkowski's maths, then. Show me mathematically where the gibberish comes in and explain what went wrong mathematically.

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.

Show me your mathematical demonstration, starting from "Minkowski rotations", that things with inertial would spontaneously start spinning according to Minkowski's flawed theory.

If you cannot do this, please retract your baseless claim.

Time may be related to the speed of light, but time is not, as Minkowski posited, EQIVALENT TO the speed of light.

Please cite the relevant article or source in which Minkowski posited that time is equivalent to the speed of light.

If you cannot do this, please retract your baseless claim.

For one thing, he completely forgot about rotation, and evidently, that can be a little faster.

So, in one paragraph you talk about the "Minkowski rotations", and then in the next breath you claim that Minkowski forgot about rotation.

Which is it?

 

[danshawen]

Great detailed post James R. This probably wouldn't happen if I did just publish a paper or something.

As I stated, the Lorentz transformations are not in doubt. Neither are the basic assumptions on which they are based.

The sole thing that is at issue here, and upon which Minkowski's invariant interval is based, is the idea that time itself IS PROPORTIONAL TO j x c x t.

Let's examine this a little more closely, because I see something else wrong here. Time seems to be proportional to itself, so evidently he considered c to be only a scaling factor. This is exactly what is wrong, and in a sense, would be wrong in my analysis as well, if I had not explained that:

Omega = angular velocity = 2 x pi x f = (2 x pi)/t, which has the dimensions 1/t.

Two photons, bound by whatever mechanism results in photon-photon creation of a particle of matter, creates a situation internally WHERE THE LORENTZ TRANSFORMATIONS DO NOT APPLY, other than for some sort of time dilation that may be different from the linear case, and an internal spin mode of propagation that >c. It is elementary that if the photons are counter-rotating, the effective value for omega is 2 x omega, and this would mean that TIME BEHAVES VERY DIFFERENTLY INSIDE OF MATTER than it does in linear fashion. Since the fundamental assumption for the Lorentz transformations is that the speed of light can never be exceeded, I suppose that I have broken something.

Indeed I have, because outside of matter, distance = light travel time = c x t, and out here, time is proportional to time. This makes sense if, as Minkowski believed, c is just a scaling factor for time itself. But it is not as simple as that.

I have shown that inside of elementary particles of matter, time is proportional to 1/c, and they propagate >c, and in the domain of bound energy, time is proportional to the reciprocal of the speed of light.

You have admitted that the Lorentz transformations do not apply to uniform rotation. I have just demonstrated, this situation rates more detailed consideration BECAUSE I have BROKEN MINKOWSKI'S basic assumption about his invariant interval. If the speed of light is just a scaling factor, it cannot be proportional to both t AND 1/t.

We aren't talking about simple unity here. If you cannot replace c by 1/c in every equation Minkowski wrote, then his interval does not apply to matter equally as well as it does to energy, the way that E/m = c^2 does.

You are hands down the top expert on dimensional analysis on this forum, or anywhere else James R. If anyone can spot an error in this part of my logic, it is you. Be that as it may, it probably would not rise to the level of an actual paper unless it tore Minkowski's interval to shreds. Does it?

 

[The God]

Omega = angular velocity = 2 x pi x f = (2 x pi)/t, which has the dimensions 1/t.

No, this is wrong......Omega does not have dimension of 1/t.......2 pi has a meaning here, I am sure you know that.

It is elementary that if the photons are counter-rotating, the effective value for omega is 2 x omega,

Yes, it is elementary...elementarily wrong......first of all it is not clear what you mean by 'effective value of omega'.......It is not that you are talking about rotational energy of photon, but even so, then the effective value shall be Sqrt(w) not 2 X w. On the other hand if you are trying some relative omega, then effective value of omega between two counter rotating photons could be anything between 0 to 2w. (w = omega)....as such this effective value makes no sense.

 

[danshawen]

On Einstein's relativistic train, passengers cannot tell without comparing to time or lengths in relative motion that they are moving, and the measurement of the speed of light is the same as it was before they left the station.

If the same experiment is performed with Minkowski rotations, something is seriously wrong. Spinning meter sticks have inertia, so if they start to spin, they must keep spinning. A component of the 4d rotation occurs in 3D, so the rotation will be visible. EVERYWHERE.

It is ironic that Minkowski came up with this using a set of transformations which ARE KNOWN not to have been crafted even to handle relativistic rotations at all.

I will stipulate that I do not rule out the possibility that ther may be deeper meaning I what Minkowski was suggesting, only that there appear to be major flaws in the way he defined an interval.