Could Galileo have discovered Sepcial Relativity?

[debra]

I have read that if Galileo had included rotational symmetries in his original relativity theorems then a constant turns up in the mathematics. It is the same constant that Einstein concluded was the velocity of light, but has nothing directly to do with light, it just happens that light travels at that same speed. The constant is gained purely from symmetry considerations.
Here is the paper with the mathematics from Mitchell Feigenbaum (of chaos theory fame):
http://arxiv.org/abs/0806.1234

 

[robphy]

In hindsight, many advances could have been made earlier if certain steps were taken... and recognized [including, for example, experimental confirmation]. More recently, it seems that Felix Klein was a step away... but didn't make the step.

There are many of these 1/c^2-type (a.k.a relativity without the speed of light postulate) proofs... of which Feigenbaum's article appears to be another. (I think Ignatowski formulated the first proof.)

To answer the original question, I think it's possible... but I think that Galileo would first have to deduce "c" for his own kinematics... which would be infinite. (Stay tuned for further development of this idea.)

 

[Phrak]

A rotational symmetry in R^3 doesn't involve a forth coordinate. Do you mean a Lorentz boost?

 

[debra]

A rotational symmetry in R^3 doesn't involve a forth coordinate. Do you mean a Lorentz boost?

I read the Feigenbaum paper quoted above and admit that I could not see where the constant arises, but I know that it is due to a rotational symmetry somehow and wish I could visualize why it is necessary. Its not very clear in the paper itself. That's why I posted to this forum. I also emailed Feigenbaum but he has not replied as yet. Galileo did not consider rotation in his original - I believe he did not have the necessary mathematics to analyse that aspect.
I want to know why rotation throws up a constant and what is it? Is it speed of information travel or what? There must be a physical reason with an underlying concept - which is what I really want to know.

 

[Phrak]

I read the Feigenbaum paper quoted above and admit that I could not see where the constant arises, but I know that it is due to a rotational symmetry somehow and wish I could visualize why it is necessary. Its not very clear in the paper itself. That's why I posted to this forum. I also emailed Feigenbaum but he has not replied as yet. Galileo did not consider rotation in his original - I believe he did not have the necessary mathematics to analyse that aspect.

I don't see that this is the problem. Assume Galileo didn't need group theory to envision isotropic symmetry of space.

I want to know why rotation throws up a constant and what is it? Is it speed of information travel or what? There must be a physical reason with an underlying concept - which is what I really want to know.

It doesn't make a lot of sense to me. You have these Newtonian direct products of manifolds, R^3, and T. They're independent. If he has something, he pulled it out of a hat I can't see. But Feigenbaum is so wordy, in English and math, I won't grind through it to see if he makes sense. One expects to see these things up-front, but the crux of his argumnet seems to be buried somewhere in the middle, only to be discovered on the 4th or 5th reading.

 

[Ich]

There are many of these 1/c^2-type (a.k.a relativity without the speed of light postulate) proofs... of which Feigenbaum's article appears to be another. (I think Ignatowski formulated the first proof.)

To answer the original question, I think it's possible... but I think that Galileo would first have to deduce "c" for his own kinematics... which would be infinite. (Stay tuned for further development of this idea.)

Yes, given Homogeneity of space and time and isotropy of space, the Poincaré Group is the general symmetry group of space and time. I don't have any references for this, but that's exactly what Minkowski called the "staircase wit": Mathematicians should have known this by long when the first evidence for a constant speed in the universe emerged, but they left it for a patent assistant to spell it out.
That does not mean that Galileo could (or should) have found SR: with no evidence for a constant speed, 1/c² should be set to 0, as dictated by Occam's Razor.

 

[debra]

Yes, given Homogeneity of space and time and isotropy of space, the Poincaré Group is the general symmetry group of space and time. I don't have any references for this, but that's exactly what Minkowski called the "staircase wit": Mathematicians should have known this by long when the first evidence for a constant speed in the universe emerged, but they left it for a patent assistant to spell it out.
That does not mean that Galileo could (or should) have found SR: with no evidence for a constant speed, 1/c² should be set to 0, as dictated by Occam's Razor.

Using no mathematics can we get to relativity and c by pure logic? e.g.

After Newton discovered gravity he could say that one mass must be aware of another mass
in space time and there must be some agent connecting the two masses. (eg gravitons)
If a mass were suddenly to appear how long would it take another mass to react to
it? (ie experience a gravitaional pull).
That agent must travel somewhere between 0 and infinite speed between the two masses.
The speed could not be infinite because that would produce cause and effect absurdities.
The speed could not be zero.
So it must have an actual speed value that we could measure.
That speed value must constant in vacuum space otherwise absudities in cause and effect would occur.
That speed must also be relatively constant regardless the frames of reference otherwise
cause and effect absurdities would likewise arise.

So we can say the maximum speed of information travel in the Universe must be
a fixed value determined by the Universe itself and must also also be relatively constant
between allowed frames of reference.
(hence slow clocks, lorentz contractions etc etc)




note: by information travel we mean essentially in vacuum space: bosons: photons
w and Z Bosons, Gluons and the yet to be found graviton-like particles as the
agent for gravity must all travel at this speed - not more, not less. If not not, then cause and effect
absurdities would arise. Nothing carrying information could go faster, even streams of bits with no mass.

 

[robphy]

Using no mathematics can we get to relativity and c by pure logic? e.g.

You might be interested in an old post of mine ( https://www.physicsforums.com/showthread.php?p=946181#post946181 ) which describes AA Robb's approach to special relativity using a partial-order relation "after".

http://en.wikipedia.org/wiki/Alfred_Robb has links to Robb's works archived on archive.org. (By the way, I think Robb (1911,1914) was the among the first [after Minkowski] to develop many ideas used in modern geometrical approaches to relativity: rapidity, radar/k-calculus measurements of intervals, and causal structure.)

 

[jefswat]

I think there is a chance that he could have discovered it although it would have been so ground breaking at the time he problably would have dismissed it as nonsense. I don't think it is possible to have all the symmetries of special relativity without time dilation. It would have just been to outlandish for his time although it would have greatly helped if he had published it and everyone dismissed it. That way someone could just go back and look at it when c was proved to be constant instead of waiting for someone to come with special relitivity, which as far as theories are, I don't think is that complex at all for the most part. Much like Klaun(I think?) that came up with the idea of curled up dimensions. String theory had something to build on when they got to that point

 

[Naty1]

Debra...interesting point regarding the "constant"...unsure what that means...

Separately, the idea that Galileo could have somehow have discovered special relativity is really a stretch.

Einstein had calculus, frames of reference considerations and F= Ma type stuff all from Newton; Poincaire, Lorentz, and Fitzgerald transformations regarding space contraction and time dilation; Precession of planet Mercury; Maxwell's equations...(and likely a few other "tidbits" that did not come to mind)... quite a steep climb for someone starting out from scratch!

 

[debra]

You might be interested in an old post of mine ( https://www.physicsforums.com/showthread.php?p=946181#post946181 ) which describes AA Robb's approach to special relativity using a partial-order relation "after".

http://en.wikipedia.org/wiki/Alfred_Robb has links to Robb's works archived on archive.org. (By the way, I think Robb (1911,1914) was the among the first [after Minkowski] to develop many ideas used in modern geometrical approaches to relativity: rapidity, radar/k-calculus measurements of intervals, and causal structure.)

Its been a revelation to me.

Thanks guys especially Robphy and Ich. I was never happy with
aether, Michelson-Morley, then Einstein claiming velocity of light
is constant. I have read the references and see that its more about symmetries,
causal structure, frames of reference etc. Light need not enter into it!
It makes sense to me at long long last, or at least can I believe it now -
its no longer just magic.

My teachers used to look at me with disdain when I questioned
what underlies Einsteins view. (why light, I used to think).
They viewed me as a stupid girl and went on and on about clocks and
rods that glazed over my eyes, and only proved how clever they were.

I will open a new thread possibly seeking a logical basis for quantum
wave packets. Maybe even that has causal roots too!