Aditya-L1 will be heading for Earth-Sun Lagrange point 1 which is about 1 million miles away. The journey will take 4 months.
https://www.msn.com/en-us/news/othe...bservatory-its-1st-ever-sun-probe/ar-AA1g8n0c
The mathematicians will surely rule the future if they can sort out the relation between "the math" and reality - i.e. not be to fooled think that everything that is a result of a calculation necessarily has a correspondence in reality. Long live the mathematicians!! The will "save" us.
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We appear to be entering the realms of philosophy!
“Physics is mathematical not because we know so much about the world but because we know so little; it is only its mathematical properties that we can discover” (Bertrand Russell, An Outline of Philosophy, 1927).
There's an examination of mathematics and reality in this link: https://philosophynow.org/issues/102/Mathematics_and_Reality
Nice article here by Ethan Siegel about what constitutes a theory in science. See the comments about ‘mathematical’ theories.
https://bigthink.com/starts-with-a-bang/never-tell-scientist-just-a-theory/?utm_campaign=swab&utm_source=rejoiner&utm_medium=email&utm_content=09/02/23+SWAB&rjnrid=1y4BlkP
https://bigthink.com/starts-with-a-bang/never-tell-scientist-just-a-theory/?utm_campaign=swab&utm_source=rejoiner&utm_medium=email&utm_content=09/02/23+SWAB&rjnrid=1y4BlkP
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I was day analyst at Goddard SFC for ISEE-3 International Sun Earth Explorer satellite, kept in a holding location at Lagrange point until end of mission, at which time ISEE-3 was commanded to execute a slingshot maneuver around sun and rendezvous with comet, Giacobini-Zinner. The “slingshot maneuver” was an important plot device in the movie, The Martian.
Nobody would doubt that mathematics underpins quantum physics. The mathematics involved has a correspondence with reality by way of computers, smartphones, the Internet, GPS, and MRI.
However, as Bonsai's link points out, some mathematical physics, e.g. string "theory", is purely speculative and may never correspond with reality.
I am interested in dimensionless constants of the universe.
I do not understand the bit about G over c^3/he. It doesn’t look dimensionless to me. How come the unit of the electron charge disapear ?
Could it be that e stands not for the electron charge, but for the electric constant?
Cosmology and general relativity adopt natural units whereby c, h and e (the electric constant) are set to unity.
In natural units c^3/he would equal 1, making G = 1 and thus dimensionless.
I'm not a mathematician, so perhaps our resident mathematics expert has more to offer in relation to your question?
What do you perceive as the similarity?
The former expression is the kinetic energy of a mass m moving with speed v, while the latter expression is the energy stored up inside the mass.
The full form of the equation E = mc^2 is E squared equals mc squared squared plus p times c squared, where p represents the momentum of the object in question.
"Constant" means not depending on some variable; not changing as that variable changes. In the first case above, it means not depending on h; in the second, it means not depending on x. A constant in a narrower context could be regarded as a variable in a broader context.
The part in bold is a similar idea. Variables set to 1, Used to spot trends in some equation.
I think what Sir Michael Atiyah was saying there is the RATIO of the Gravitational Constant G to the Electric Constant (1 over 4 pi Epsilon nought IIRC) can be made dimensionless for given particles of particular charge and mass:
https://en.wikipedia.org/wiki/Dimensionless_physical_constant#Martin_Rees's_Six_Numbers
Neither are dimensionless in themselves, but both constants describe inverse square force laws traditionally. The Electric force is monstrously stronger overall, at least locally. It's always fun to describe constants in terms of the speed of light, Planck's Constant, the electron charge an all that.
Proper Physicists start with Einstein's FULL Energy equation! E=mc^2 is the more limited bomb equation for particles of mass m. The Proper jobbie is this one:
https://www.wondriumdaily.com/theory-of-special-relativity-simplifying-einsteins-equation/
This one works for everything, including massless photons and includes all that Lorentz stuff. E= hv for a photon, so you can work out the linear momentum.
I have to admit it has never been obvious to me that a car at 60mph has 4 times the energy of one at 30mph. But this is how it is.
A low velocity car with kinetic energy of 1/2 mv^2 can also be described as having an energy of p^2 / 2m where p =mv.
In a way, momentum is more important than velocity, but we don't think that way.
Hope that clears it up.
A dimensionless constant, as mentioned by mchambin, is a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.
G is certainly not dimensionless in the SI system of units, having the dimensional formula of L^3 / [M] [T^2].
E = ɣ m c^2, where ɣ is the Lorentz factor.
For low speeds, E = ɣ m c^2 may be approximated to E = m c^2 + 1/2 m v^2.
This approximation is pretty good for speeds even as high as 20% of the speed of light.
I am genuinely Autistic. This means I am excellent at Maths and Physics, but useless at Relationships. Such is my lot:
My Ma always admired this quality in me. She would brag about it to her friends,
Special Relativity Puzzle for You:
WHO WILL COME OFF WORSE?
An Easy One, IMO. For a Physicist.
My Ma always admired this quality in me. She would brag about it to her friends,
Special Relativity Puzzle for You:
WHO WILL COME OFF WORSE?
An Easy One, IMO. For a Physicist.
Anybody that has fallen off a bicycle knows about kinetic energy proportional to velocity squared. At 10 mph, no pain in abrasion resistant clothes (dickies long pants long sleeves, + cotton+poly gloves). At 25 mph, broke my chin. Don't ride down hills onto a gravel berm. (was dark).
Situation 1: Total kinetic energy is proportional to 60 squared or 3600 units.
Situation 2: Total kinetic energy is proportional to 30 squared plus 30 squared or 1800 units.
Question, how is the top right astronaut travelling at 0 mph when his rocket motor is on?
Is that where special relativity and frames of reference come in, Steve?