What is Einsteins Paradigm Shift?

[JM]

A search for the term "Paradigm Shift" brings up a definition and a list of examples including Einsteins Relativity. What is it, exactly, about Relativity that constitutes a paradigm shift?
JM

 

[Nugatory]

A search for the term "Paradigm Shift" brings up a definition and a list of examples including Einsteins Relativity. What is it, exactly, about Relativity that constitutes a paradigm shift?
JM

I'd credit him with two:

- The second postulate of special relativity, which could be informally (but with, in my opinion, historical accuracy) paraphrased as "We don't need no steenkin' ether!"

- The equivalence principle that led to general relativity: The effects of gravitational force are indistinguishable from the effects of acceleration in the absence of gravity, so we don't need to treat gravity as a force if we don't want to.

 

[JM]

I'd credit him with two:

- The second postulate of special relativity, which could be informally (but with, in my opinion, historical accuracy) paraphrased as "We don't need no steenkin' ether!"

- The equivalence principle that led to general relativity: The effects of gravitational force are indistinguishable from the effects of acceleration in the absence of gravity, so we don't need to treat gravity as a force if we don't want to.

Thank you Nugatory for your comments. I agree that these two principles were inspired ideas that made major changes in how people thought about things .
But there is another idea, perhaps related to the two mentioned, that lurks in his writing that I haven't seen mentioned.
Before Einstein the custom was to form the coordinates and time and use them as fixed quantities to describe a given physics problem. For example, the position of a projectile could be given as a function of time. The results were considered to be properties of the projectile. The coordinates remained fixed by some condition outside the projectile analysis.
But Einstein turned the relation around. In his analysis of light he also used coordinates and time, but he did not describe his results as properties of light. He didn't say things like 'the light takes more time to reach A than to reach B'. He said things like ' the moving clock runs slow', and 'the moving rod is shorter than the stationary one'. He thus took the light as the fixed quantity and ascribed the results to the coordinates and clocks.
This reversal of the roles of the physics and the coordinates seems to me to be worthy of the term 'paradigm shift'.
What do you think?
JM

 

[Nugatory]

This reversal of the roles of the physics and the coordinates seems to me to be worthy of the term 'paradigm shift'.
What do you think?
JM

I'm inclined to think that it's inextricably intertwined with the second postulate, which we've already counted. Coordinate transforms were already well known and routinely used in physics; the second postulate allowed the development of a new, interesting, and very powerful set of such transforms.

This is something of an aesthetic judgement though (in particular, a preference for being parsimonious with the term "paradigm shift" ), so if you don't see it the same way, that's cool.

 

[TheBC]

The paradigm shift is that since Einstein we moved from a 3D space reality into 4D spacetime reality.

 

[Scherejg]

For me, it was that gravity and geometry are one in the same.

 

[JM]

Thank you all for your comments. I agree that the ideas you mentiioned are 'paradigm' worthy. 4-D space time and gravity are beyond me at the moment. I'm still grapling with the idea that the results of a physical experiment ( on the speed of light ) can be 'blamed' on the coordinates used to measure. Is there some way to think about this to make it more understandable?
JM

 

[Nugatory]

I'm still grappling with the idea that the results of a physical experiment ( on the speed of light ) can be 'blamed' on the coordinates used to measure.

That is, I think, backwards. The results of a physical experiment are objective facts which all observers must agree about. We can describe them without any coordinates at all if we wish, and if we end up confusing ourselves by choosing confusing coordinates, it's our choice that is to blame.

So I'm going to stick with my answer from #2, which doesn't unnecessarily introduce coordinates.

 

[Devils]

Before Einstein the custom was to form the coordinates and time and use them as fixed quantities to describe a given physics problem. For example, the position of a projectile could be given as a function of time. The results were considered to be properties of the projectile. The coordinates remained fixed by some condition outside the projectile analysis.
But Einstein turned the relation around. In his analysis of light he also used coordinates and time, but he did not describe his results as properties of light. He didn't say things like 'the light takes more time to reach A than to reach B'. He said things like ' the moving clock runs slow', and 'the moving rod is shorter than the stationary one'. He thus took the light as the fixed quantity and ascribed the results to the coordinates and clocks.

Didn't this go hand in hand with the development of tensors. The math had to be developed at the same time to model the formalism. Without the math, you can't envisage the problem.

 

[Nabeshin]

Didn't this go hand in hand with the development of tensors. The math had to be developed at the same time to model the formalism. Without the math, you can't envisage the problem.

Indeed, the two are the same. Expressing the equations as tensor equations is equivalent to saying coordinates don't matter. Einstein introduced this general covariance in large part motivated by Mach's principle (he somehow thought the general covariance ensured that Mach's principle was valid in the theory... it's not).

In my opinion though, the great insight of Einstein (which is sort of captured in the above posts, but not quite) is to elevate space and time from passive backdrops upon which physics takes place to actual actors themselves in the game. He saw spacetime as something 'physical', which can be deformed and warped by masses. This is pretty radical in my opinion, since everyone before him just always assumed there was a static background space that was fixed and immutable.

 

[DiracPool]

A search for the term "Paradigm Shift" brings up a definition and a list of examples including Einsteins Relativity. What is it, exactly, about Relativity that constitutes a paradigm shift?
JM

A "paradigm shift" is simply a radical change in the manner in which people/scientists view a certain issue, concept, or problem. There may be said to several collateral or secondary paradigm shifts in physics created by Einstein, but the fundamental ones in relation to relativity was a shift from Newtonian conception of gravity as an "attractive force" to one of gravity as "curved spacetime," and the shift from the conception of "time" as the universal constant of spacetime to "lightspeed" as the universal constant.

 

[Devils]

There may be said to several collateral or secondary paradigm shifts in physics created by Einstein, but the fundamental ones in relation to relativity was a shift from Newtonian conception of gravity as an "attractive force" to one of gravity as "curved spacetime," and the shift from the conception of "time" as the universal constant of spacetime to "lightspeed" as the universal constant.

Everyone had been thinking the same way as Newton for 200 years & Maxwell for 40 years. There were many "almost made it" moments - Lorentz come up with his transformation in 1895. In 1899 Lorentz assumed that the electrons undergo length contraction. He was almost there in 1904.
http://en.wikisource.org/wiki/Electromagnetic_phenomena

Hints of mass-energy equivalence date from the 1800s too http://en.wikipedia.org/wiki/Electromagnetic_mass

But Einstein put all the ideas together, lined up all the ducks in a row, and had to invent new math too.

Also back in those days they didnt have email & arxiv. Communication crawled along.

 

[WannabeNewton]

But Einstein put all the ideas together, and had to invent new math too.

What new math did Einstein invent?

 

[Devils]

What new math did Einstein invent?

I'm thinking of the Einstein tensor, which is more of an application of math.

 

[WannabeNewton]

I'm thinking of the Einstein tensor, which is more of an application of math.

That isn't even remotely close to "inventing new math".

 

[atyy]

What new math did Einstein invent?

The summation convention

 

[WannabeNewton]

The summation convention

Check and mate my friend. Check and mate. *tips hat*

 

[VeryConfusedP]

The summation convention? Please do explain, someone! If Wannabe is liking it, I'd love to understand it!

 

[atyy]

The summation convention? Please do explain, someone! If Wannabe is liking it, I'd love to understand it!

I was half-kidding. It's analogous to saying writing $\dot{y}$ as $dy/dt$ is "inventing new maths". However, the summation convention was a necessary step to abstract index notation. The Dirac bra-ket notation and the Penrose graphical notation for tensors are two other examples of new notation that one might argue are almost "inventing new maths". As an example of the power of the latter, I'd cite the diagrams in http://arxiv.org/abs/quant-ph/0610099 .

 

[micromass]

The summation convention? Please do explain, someone! If Wannabe is liking it, I'd love to understand it!

The notation convention just says that you can leave out summation signs. For example, let's say you have

$$\sum_{i=1}^n x^iy_i$$

We see that one index i is above and one index i is below. This happens a lot. In that case, we leave out the summation sign and write

$$x^iy_i$$

The genius in Einstein notation is not that we can leave out the signs, of course. That's just useful. The genius in the Einstein notation is knowing which indices come above and which below. Basically, you have vectors and covectors. Vectors are written with a lower index and covectors with an upper index.

The great part is that Einstein notation actually tells you something about geometry. If you succeed in writing something in Einstein notation, then chances are big that it's coordinate invariant. If you don't succeed, then it relies on the coordinates in question. So the good formulas are the ones where you can follow the notation.

 

[JM]

In my opinion though, the great insight of Einstein (which is sort of captured in the above posts, but not quite) is to elevate space and time from passive backdrops upon which physics takes place to actual actors themselves in the game... This is pretty radical in my opinion, since everyone before him just always assumed there was a static background space that was fixed and immutable.

Yes! I agree. I don't disagree with the other ideas, but I think that this idea is at the heart of his SR as presented in the 1905 paper. So, how do we use this idea for better understanding of his analysis? His definition of time seems to be expressed as ' the pointing of the hand on my watch when the train arrives'. Might that be expressed as ' the time of the moving frame is given by the reading on the moving clock when the light ray arrives at x',y',z'? But, if the clocks of both frames are ticking at the same rate, as described by Feynman in 'Six not-so-easy Pieces, then how do they know what they should do?
But I'm just rambling here, trying to figure out how to use this new idea to understand SR. Can anyone point the way?
JM

 

[atyy]

Yes! I agree. I don't disagree with the other ideas, but I think that this idea is at the heart of his SR as presented in the 1905 paper. So, how do we use this idea for better understanding of his analysis? His definition of time seems to be expressed as ' the pointing of the hand on my watch when the train arrives'. Might that be expressed as ' the time of the moving frame is given by the reading on the moving clock when the light ray arrives at x',y',z'? But, if the clocks of both frames are ticking at the same rate, as described by Feynman in 'Six not-so-easy Pieces, then how do they know what they should do?
But I'm just rambling here, trying to figure out how to use this new idea to understand SR. Can anyone point the way?
JM

I think Nabeshin was referring to GR, in which spacetime is affected by matter. In SR, spacetime is not affected by matter.

Actually, SR is revolutionary by being conservative. It takes seriously the Principle of Relativity - ie. the existence of a preferred class of frames called "inertial" and Maxwell's equations.

The key link from SR to GR that Einstein did not make was the identification of the spacetime metric. This was done by Minkowski. His are the famous words, "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

The Principle of Equivalence was known to Newton. However, the idea that the Principle of Equivalence suggests that gravity is geometry was, I believe, Einstein's. Taking this seriously, even Newtonian gravity can be cast as a geometric theory - known as Newton-Cartan theory.