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I am finding Gravity and Special Relativity and General Relativity and all this Metric 4D maths very heavy going, But shall finish the book soon. Already my head is spinning.
Not only do Space and Time have to be combined into a single property, but you have to include all that Lorentz contraction and mass change into it.
Then you have the 4-velocity and 4-momentum. 4-velocity includes the Lorentz factors, but 4-momentum combines Energy, momentum and mass into one thing. So it works for massless photons too.
All this is sort of OK in a flat 4D Minkowski Space in Special relativity, but General Relativity lets mass and energy curve Space, so its really difficult.
Few standard equations here:
rs = 2GM/c^2 (Scwarzschild Radius)
E = m c^2
s^2 = x^2 + y^2 + z^2 - c^2 t^2 ( The distance s between two events in spacetime is the same for all observers, even moving ones)
E^2 = p^2 c^2 + m^2 c^4
Kinetic Energy = p^2 / 2m, which becomes the familiar p = mv and 1/2 mv^2 at low speeds.
Spacetime Coordinates: (x0, x1, x2, x3)
4 momentum coordinates: (p0, p1, p2, p3)
This is without tensors, so it gets worse! It's a lot to take in.
But Tensors are extremely clever and elegant things. They are an extension of vectors. You can add a factor for expanding space quite easliy, for instance.
But it is right. Just a higher level of thought and mathematics required. You have to throw away the Classical Mechanics way of thinking, where you keep variables like space and time, and energy, momentum and mass separate.
Not only do Space and Time have to be combined into a single property, but you have to include all that Lorentz contraction and mass change into it.
Then you have the 4-velocity and 4-momentum. 4-velocity includes the Lorentz factors, but 4-momentum combines Energy, momentum and mass into one thing. So it works for massless photons too.
All this is sort of OK in a flat 4D Minkowski Space in Special relativity, but General Relativity lets mass and energy curve Space, so its really difficult.
Few standard equations here:
rs = 2GM/c^2 (Scwarzschild Radius)
E = m c^2
s^2 = x^2 + y^2 + z^2 - c^2 t^2 ( The distance s between two events in spacetime is the same for all observers, even moving ones)
E^2 = p^2 c^2 + m^2 c^4
Kinetic Energy = p^2 / 2m, which becomes the familiar p = mv and 1/2 mv^2 at low speeds.
Spacetime Coordinates: (x0, x1, x2, x3)
4 momentum coordinates: (p0, p1, p2, p3)
This is without tensors, so it gets worse! It's a lot to take in.
But Tensors are extremely clever and elegant things. They are an extension of vectors. You can add a factor for expanding space quite easliy, for instance.
But it is right. Just a higher level of thought and mathematics required. You have to throw away the Classical Mechanics way of thinking, where you keep variables like space and time, and energy, momentum and mass separate.
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I always get tense at the mention of tensors!
I've found a good description of a tensor: "A tensor represents a physical entity which may be characterized by magnitude and multiple directions simultaneously."
The number of simultaneous directions is called the rank of the tensor in question.
Tensors are ranked thus:
Rank 0 is a scalar
Rank 1 is a vector
Rank 2 is mathematically an N x N matrix and is the tensor involved in Einstein's field equations relating to spacetime.
Rank 3 tensors and above would be stacks of matrices which would relate to spaces of higher dimensions
I can understand the scalar field (when describing energy) and the vector field (when describing force), but I guess I was absent the day the lecturer introduced tensor calculus and differential geometry!
Just as well, as I am led to believe that curvature equations involve 10 partial differential equations and I could never handle that!
There will always be some conjecture concerning red shift and why it occurs. The view will be according to the theory used to explain it.
The math you refer to show the importance of the observers reference frame and nought else.
On special relativity Einstein made some use of Lorenz's work which were actually aimed at sorting out the Aether light theory. In some respects that is somewhat similar to the modern space time idea with gravity tied in. Einstein also chose to accept Maxwell's idea about the speed of electromagnet radiation. The speed of light had been measured as well so why not? It had already been noted that speed did not have any effect on it using the rotational speed of good old planet earth. 1670 kilometres per hour
Then comes General Relativity - the part you seem to be disagreeing with. Space time, gravity, light etc. Not doubt there will be video's about that as well at some point in the series.
Big bang red shift due to that - theory, Different subject,
Aside:
A. Einstein. Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen, Jahrbuch der Radioaktivität 4. (1907/08)
https://www.fisica.net/relatividade...d-die-aus-demselben-gezogenen-Folgerungen.pdf
pdf S. 6, paragraph 2
Einstein originale:
"Daß die hier gemachte Annahme, welche wir 'Prinzip von der Konstanz der Lichtgeschwindigkeit' nennen wollen,
in der Natur wirklich erfüllt sei, ist keineswegs selbsverständlich,
doch wird dies - wenigstens für ein Koordinatensystem von bestimmtem Bewegungszustande - wahrscheinlich gemacht durch die Bestätigungen,
welche die, auf die Voraussetzung eines absolut ruhenden Äthers gegründete Lorentzsche Theorie durch das Experiment erfahren hat."
Translated 1 : 1, step by step (German and English are "dialects" only;-)
"That the here made assumption, which we 'principle of the constancy of the light-velocity' call want,
in the nature really fulfilled would be, is in no way self-evident,
but is this - at least for a coordinate system of a certain motion-state - probable made by the affirmations,
which the, on the presupposition of an absolutely resting ether grounded Lorentz theory by the experiment received has."
A. Einstein. Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen, Jahrbuch der Radioaktivität 4. (1907/08)
https://www.fisica.net/relatividade...d-die-aus-demselben-gezogenen-Folgerungen.pdf
pdf S. 6, paragraph 2
Einstein originale:
"Daß die hier gemachte Annahme, welche wir 'Prinzip von der Konstanz der Lichtgeschwindigkeit' nennen wollen,
in der Natur wirklich erfüllt sei, ist keineswegs selbsverständlich,
doch wird dies - wenigstens für ein Koordinatensystem von bestimmtem Bewegungszustande - wahrscheinlich gemacht durch die Bestätigungen,
welche die, auf die Voraussetzung eines absolut ruhenden Äthers gegründete Lorentzsche Theorie durch das Experiment erfahren hat."
Translated 1 : 1, step by step (German and English are "dialects" only;-)
"That the here made assumption, which we 'principle of the constancy of the light-velocity' call want,
in the nature really fulfilled would be, is in no way self-evident,
but is this - at least for a coordinate system of a certain motion-state - probable made by the affirmations,
which the, on the presupposition of an absolutely resting ether grounded Lorentz theory by the experiment received has."
Dan Fleisch’s video on tensors below and is recommended watching
I have his ‘Students Guide to Electromagnetism’ - highly recommended. Apparently there’s a copy in the CERN library as well, so it must be good. It’s quite a difficult subject, but they way physicists throw the equations around always leaves me in awe to be frank.
This is the book wherein Fleisch says students who want to know what exactly an EM wave is and how it actually propagates through a vacuum should put the question to one side as ‘it’s a deeply philosophical question’. 😳
And for GR doubters, this lecture series remains one of the best intros to the subject
Part 1:
Part 2:
I have his ‘Students Guide to Electromagnetism’ - highly recommended. Apparently there’s a copy in the CERN library as well, so it must be good. It’s quite a difficult subject, but they way physicists throw the equations around always leaves me in awe to be frank.
This is the book wherein Fleisch says students who want to know what exactly an EM wave is and how it actually propagates through a vacuum should put the question to one side as ‘it’s a deeply philosophical question’. 😳
And for GR doubters, this lecture series remains one of the best intros to the subject
Part 1:
Part 2:
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... and people who think the earth is flat, and the moon landings were faked...
On which note - 54 years to the day since Neil Armstrong stepped onto the moon!! (July 21 1969 at 02:56:15 UTC)... I still remember watching it...
For you nothing is bent etc just shows a measured effecthttps://www.britannica.com/video/18...ons-light-gravity-special-relativity-velocity
Pictorial images to show the effects are bent, LOL.
I have read comments post Einstein from people who were educated earlier on based on the aether. One view was that it was something you could pick up and used to show that speed of the source has no effect on the speed of light. ie The aether has no direction. The other view was that it was something light travelled in. That could be replaced with the word dimension, or something that we are not aware of.
Best add the A to the word and then people may realise what is being discussed.Talking gravity an interesting one
https://www.britannica.com/video/22592/Millikan-oil-drop-experiment
Attachments
;-)
"So you hear almost every day how GPS is a practical example of the use of Einstein’s relativity. It must be true, right? Wrong. Just ask Ron Hatch. Ron, a critical thinker, holds of over 30 patents in GPS and one of the most decorated GPS scientists on the planet and he says that GPS doesn’t support relativity, but actually shows flaws in the theory."
GPS and ether and RT and more:
https://beyondmainstream.org/scientist/ron-hatch/
"So you hear almost every day how GPS is a practical example of the use of Einstein’s relativity. It must be true, right? Wrong. Just ask Ron Hatch. Ron, a critical thinker, holds of over 30 patents in GPS and one of the most decorated GPS scientists on the planet and he says that GPS doesn’t support relativity, but actually shows flaws in the theory."
GPS and ether and RT and more:
https://beyondmainstream.org/scientist/ron-hatch/
Or, "for a man" as it was supposed to be, and he said... And "giant leap" for mankind.
Without the "a" it wouldn't really make sense....
From an analysis of the recording I've heard and seen, he did say "for a man" (he later confirmed it) but the "a" was covered with static.Or, "for a man" as it was supposed to be, and he said... And "giant leap" for mankind.
Without the "a" it wouldn't really make sense....
There is an interesting story about this frequency offset. At the time of launch of the NTS-2 satellite (23 June 1977), which contained the first Cesium atomic clock to be placed in orbit, it was recognized that orbiting clocks would require a relativistic correction, but there was uncertainty as to its magnitude as well as its sign. Indeed, there were some who doubted that relativistic effects were truths that would need to be incorporated [5]! A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by general relativity, then the synthesizer could be turned on, bringing the clock to the coordinate rate necessary for operation. After the Cesium clock was turned on in NTS-2, it was operated for about 20 days to measure its clock rate before turning on the synthesizer [11]. The frequency measured during that interval was +442.5 parts in 1012 compared to clocks on the ground, while general relativity predicted +446.5 parts in 1012. The difference was well within the accuracy capabilities of the orbiting clock. This then gave about a 1% verification of the combined second-order Doppler and gravitational frequency shift effects for a clock at 4.2 earth radii.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253894/