The first important thing about spacetime are the transformations mixing space and time. They are called

*Lorentz transformations*because Lorentz figured them out and made them famous before Einstein. Everyone agrees to that. Lorentz even got a Nobel prize in 1902 for related work. See History of Lorentz transformations for details.

Second is combining space and time into a 4-dimension object and giving it a non-Euclidean geometry. Poincare did this in 1905, defining the geometry by the metric and symmetry group. Minkowski elaborated on this with world lines and diagrams, and popularized it in 1908. As a result, spacetime is often called

*Minkowski space*. In the words of a Harvard historian of science:

In sum Minkowski still hoped for the completion of the Electromagnetic World Picture through relativity theory. Moreover, he saw his own work as completing the program of Lorentz, Einstein, Planck, and Poincare. Of these it was Poincare who most directly influenced the mathematics of Minkowski's space-time. As Minkowski acknowledges many times in "The Principle of Relativity," his concept of space-time owes a great deal to Poincare's work.35 [Galison,1979]Third is defining a relativistic theory on spacetime. This means that the observable physical variables and equations must be covariant under the geometric structure. That is, observing from a rotated or moving frame must induce a symmetry in the laws of physics that is a mathematical consequence of the underlying geometry. Poincare proved this for Maxwell's theory of electromagnetism, and constructed a relativistic theory of gravity, in his 1905 paper. Minkowski appears to be the only one who understood Poincare's paper.

While Einstein understood Lorentz's work in step 1, and gave his own presentation of it, he completely missed steps 2 and 3. Even after Minkowski spelled them out clearly in a paper that was accepted all over Europe, Einstein said, "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."

While Poincare and Minkowski explicitly advocated geometric interpretations different from Lorentz's, Einstein denied that he had any differences from what Lorentz published.

While Einstein, in collaboration with Grossmann, Hilbert, and others, eventually built on Minkowski's work for general relativity, he denied the geometric interpretations of special and general relativity that are in textbooks today.

In short, Einstein had almost nothing to do with the development or acceptance of spacetime among physicists.

He started to become a cult figure with the general public when the NY Times published this 1919 story:

LIGHTS ALL ASKEW IN THE HEAVENS;And today, hardly anyone mentions spacetime without also mentioning Einstein's name.

Men of Science More or Less Agog Over Results of Eclipse Observations.

EINSTEIN THEORY TRIUMPHS

Stars Not Where They Seemed or Were Calculated to be, but Nobody Need Worry.

A BOOK FOR 12 WISE MEN

No More in All the World Could Comprehend It, Said Einstein When His Daring Publishers Accepted It.

Great post!

ReplyDeleteWho was the first to write x4=ict. Was it Minkowski? Or Poincare? Or someone else? I think Minkowski did it before Einstein adopted it. But did Poincare do it even earlier?

What year did the concept of x4=ict first appear?

DeleteWhat's your take on the below comment, Roger?

DeleteI think I found the answer to my own question!

https://www.researchgate.net/post/By_dismissing_Minkowskis_notation_x4ict_are_we_not_losing_an_essential_aspect_of_space-time_structure

John Frederick Barrett · University of Southampton

Only recently I became aware of the interesting discussion here and shall try to answer the original question, comments welcome.

Poincaré (1906) introduced the ict coordinate so that Lorentz transformations could be visualized as Euclidean rotations of the sphere

x²+y²+z²+(ict)²= const.

Then Minkowski (1908) took up the idea and made it into a powerful method for calculations in electromagnetic theory but he also applied it generally in SR. Sommerfeld (1909) further developed it for addition of velocity vectors in SR.

The method was often used for many years but gradually went out of use in theoretical discussions largely due to the influential book 'Gravitation' of Misner, Thorne & Archibald (1973) attacking it strongly because of incompatibility with GR.

I think that to understand the situation it is first necessary to understand why the ict method was so successful for SR. My explanation is as follows. The constant in Poincaré's sphere may be positive or negative depending on whether

x²+y²+z²><(ct)².

I think it is correct to make it negative which is the condition for the event (x,y,z,t) to be accessible with a velocity less than that of light either from or to the observer at (0,0,0,0). The sphere then has imaginary radius which means that is a hyperbolic (Lobachevsky) space. This conclusion follows more directly from the differential form when there follows directly using Minkowski's proper time τ (>0)

dx²+dy²+dz²+(icdt)²=(icdτ)²

Consequently the ict method enables us to do calculations in hyperbolic space, which is the correct formulation of SR (though still not generally recognized), by working in more familiar Euclidean space. When written

(cdτ)² = (cdt)²-dx²-dy²-dz²

the equation is in the form to correspond to the GR metric which is known to reduce to the Minkowski metric for linear approximation and weak gravitational fields. So the GR metric is basically the SR form plus nonlinear terms. It is these nonlinear terms which stop the ict method being used although for weak gravitational fields (e.g. for gravitational waves) it could still be used. The GR metric is in no way positive definite although usually represented as such. It is therefore of the type of a space of negative curvature."

https://www.researchgate.net/post/By_dismissing_Minkowskis_notation_x4ict_are_we_not_losing_an_essential_aspect_of_space-time_structure

What's your take on it Roger?

Poincare first wrote x4=ict in his long 1905 paper. Minkowski wrote the same thing in 1907. Minkowski cited Poincare in the references, but does not explicitly say whether he got the concept from Poincare or independenly found it. It seems likely that he got it from Poincare. Einstein did not use it until 1910 or so.

ReplyDeleteThanks Roger!

https://www.researchgate.net/post/By_dismissing_Minkowskis_notation_x4ict_are_we_not_losing_an_essential_aspect_of_space-time_structure

DeleteWhat's your take on the below comment, Roger?

I think I found the answer to my own question!

https://www.researchgate.net/post/By_dismissing_Minkowskis_notation_x4ict_are_we_not_losing_an_essential_aspect_of_space-time_structure

John Frederick Barrett · University of Southampton

Only recently I became aware of the interesting discussion here and shall try to answer the original question, comments welcome.

Poincaré (1906) introduced the ict coordinate so that Lorentz transformations could be visualized as Euclidean rotations of the sphere

x²+y²+z²+(ict)²= const.

Then Minkowski (1908) took up the idea and made it into a powerful method for calculations in electromagnetic theory but he also applied it generally in SR. Sommerfeld (1909) further developed it for addition of velocity vectors in SR.

The method was often used for many years but gradually went out of use in theoretical discussions largely due to the influential book 'Gravitation' of Misner, Thorne & Archibald (1973) attacking it strongly because of incompatibility with GR.

I think that to understand the situation it is first necessary to understand why the ict method was so successful for SR. My explanation is as follows. The constant in Poincaré's sphere may be positive or negative depending on whether

x²+y²+z²><(ct)².

I think it is correct to make it negative which is the condition for the event (x,y,z,t) to be accessible with a velocity less than that of light either from or to the observer at (0,0,0,0). The sphere then has imaginary radius which means that is a hyperbolic (Lobachevsky) space. This conclusion follows more directly from the differential form when there follows directly using Minkowski's proper time τ (>0)

dx²+dy²+dz²+(icdt)²=(icdτ)²

Consequently the ict method enables us to do calculations in hyperbolic space, which is the correct formulation of SR (though still not generally recognized), by working in more familiar Euclidean space. When written

(cdτ)² = (cdt)²-dx²-dy²-dz²

the equation is in the form to correspond to the GR metric which is known to reduce to the Minkowski metric for linear approximation and weak gravitational fields. So the GR metric is basically the SR form plus nonlinear terms. It is these nonlinear terms which stop the ict method being used although for weak gravitational fields (e.g. for gravitational waves) it could still be used. The GR metric is in no way positive definite although usually represented as such. It is therefore of the type of a space of negative curvature."

What's your take on it Roger?

Dear Roger--what's your interpretation of the physical meaning of x4=ict? What does it signify? Why does x4=ict? Why the relationship between the fourth dimension, the velocity of light, and time? We don't see this with x1, x2, or x3. Why only x4=ict?

ReplyDeleteUsing ict is a mathematical trick that has some advantages in some formulas, but it is just a trick. Theoretical physics papers still use it sometimes today.

ReplyDeleteWhen Planck first wrote E=hf, he considered it a mathematical trick sans any physical meaning. Would you say that E=hf is a mathematical trick? :)

ReplyDeleteWould you agree with the statement, "Using F=ma is a mathematical trick that has some advantages in some formulas, but it is just a trick. Theoretical physics papers still use it sometimes today."?

ReplyDeleteOr would you agree with the statement, "Using E=hf is a mathematical trick that has some advantages in some formulas, but it is just a trick. Theoretical physics papers still use it sometimes today."?

ReplyDeleteNo, that is not what I mean. You can define the Minkowski metric using ct or ict. Those are just 2 ways of saying the same thing. Using ict instead of ct is the mathematical trick, with no physical significance.

ReplyDeleteYes I know that. But the question remains--"What is the *physical* meaning of x4=ct?"

DeleteOne can write x4=ct instead of x4=ict, as Wheeler et al. did in their text.

But then "What is the *physical* meaning of x4=ct?"

Why does x4=ct, while x1 is not related to the velocity of light nor time?

How is x4 physically different from x1, x2, x3?

A remarkable property of spacetime is that while one can stand still in space (x1, x2, x3) in an inertial frame, there exists no frame in which one can stand still in x4. Why is that? What causes this *foundational* difference between the dimensions?

ReplyDeleteIt looks like you have re-discovered the old distinction between the map and the territory. Imaginary numbers and curved space are just conventions, like Poincare always said. See geometric algebra, for instance. The notion of dimension doesn't have to conform to your notion of "symmetry." The arrow of time and entropy are an assumption. I think your problem is essentialism about physics. Physics doesn't really explain anything and is a rather dull subject. It will always be an infinite regress of whys. Autistic people and people with left-hemisphere lateralization find simple physical things interesting, while most human beings find them quite literal minded and not very interesting.

DeleteDear Roger,

ReplyDeleteYou'll enjoy this one--quantum gravity theorists publish article stating that "quantum gravity" is not really science, and a quantum gravity theorist gets upset for ignoring her non-existent meaningful non-*physical* "research."

http://backreaction.blogspot.com/2017/07/nature-magazine-publishes-comment-on.html

lol!!!

Yes, time coordinates are very different from space coordinates.

ReplyDeleteThe Bee article is amusing. Nature mag publishes an article about speculation on impossible experiment, and she says that 100s of physicists have doing such untestable speculations for years!

Yes, until someone observes a graviton, quantum gravity is a silly subject, guaranteeing tenure, titles, and tax dollars for thousands of "physicists".

Delete"Yes, time coordinates are very different from space coordinates."

DeleteYes! So many "physicists" and "philosophers" are fond of saying "Einstein showed that space and time are the same thing." Wrong.