Well what staggers me about most people, is your inability to say what you think. What you scared of?
Do you like John Horton Conway, or don't you?
Life, Death and the Monster (John Conway) - Numberphile - YouTube
Enquiring minds want to know.
I have no opinion of John Horton Conway, don`t know him. I have no admiration for mathematicians.
I am reminded of something Dave Kimber (RIP) said on this site a few years ago. He pointed out that on more than one occasion physicists had been proven right about how things worked in reality and mathematicians wrong.
Einstein, and before him Newton, but really a host of famous people started out thinking about a problem, went through thought experiments, and then turned to math in order to encode their ideas in a form that could be tested through the power of prediction as for example in The case of light bending around a massive body like the sun for example.
Currently, the physics world is battling to unite QM and Relativity and it’s not going well. String Theory seems to offer a solution, however it’s not testable in anyway - it remains pure mathematical conjecture despite the best efforts of theorists like Ed Witten and Juan Maldacena.
See Sabina Hossenfelder’s blog for a discussion and why physics is in crises Sabine Hossenfelder: Backreaction
Note this only applies to unification theory - there is good research with predictable, practical, measurable outcomes in most other ranches of physics- one of the areas closer to home of course being solid state physics.
One last thought on this stuff. We have a reasonably good theory for the very big, the very small and EMR. It works otherwise we’d not be having this discussion right now via our devices. We do not have a cure for cancer, Alzheimer’s, Parkinson’s, HIV and a host of other ailments and the people working in these fields are no less smart than the string theorists.
Einstein, and before him Newton, but really a host of famous people started out thinking about a problem, went through thought experiments, and then turned to math in order to encode their ideas in a form that could be tested through the power of prediction as for example in The case of light bending around a massive body like the sun for example.
Currently, the physics world is battling to unite QM and Relativity and it’s not going well. String Theory seems to offer a solution, however it’s not testable in anyway - it remains pure mathematical conjecture despite the best efforts of theorists like Ed Witten and Juan Maldacena.
See Sabina Hossenfelder’s blog for a discussion and why physics is in crises Sabine Hossenfelder: Backreaction
Note this only applies to unification theory - there is good research with predictable, practical, measurable outcomes in most other ranches of physics- one of the areas closer to home of course being solid state physics.
One last thought on this stuff. We have a reasonably good theory for the very big, the very small and EMR. It works otherwise we’d not be having this discussion right now via our devices. We do not have a cure for cancer, Alzheimer’s, Parkinson’s, HIV and a host of other ailments and the people working in these fields are no less smart than the string theorists.
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You should. Even Mr. Albert Einstein said he wished he knew more Maths. 😎
I didn't know about Pinwheel Tilings. But very nice.
Incidentally, was Mr. John Horton Conway in the Standard Model or the String Theory camp?
About LSST | Rubin Observatory
Enough clues in the interview! 😀
I'll resist spelling it out to you.
Aw come on. Have a go at it!
You can tell I am eager to tell you. 😎
What if this calculator is WRONG on a very small Planck scale?
Viktor T. Toth - Hawking radiation calculator
You can tell I am eager to tell you. 😎
What if this calculator is WRONG on a very small Planck scale?
Viktor T. Toth - Hawking radiation calculator
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perhaps the speed of light is lowing down so all observable length scales are shrinking because we perceive the speed as constant and hence, the universe is not expanding and the dark stuff is what causes c to decrease
No. make it simpler:
Life, Death and the Monster (John Conway) - Numberphile - YouTube
Pay attention. Leech lattice - Wikipedia
There's only one theory that uses the beauty of the 24-dimensional Leech Lattice.
Light does slow down when it enters water or other transparent material. In a vacuum it doesn't slow down, color shifts towards the red side of the spectrum.
What logic can cope with the beauty of 24-dimensional space? Linearity is a one dimensional relationship. Algebra cannot even handle dimensionless quantities.
benb,
"theorem" still denotes a proven logical relation, the unpleasant discoveries made in the twentieth century have not changed anything. Life goes on in the mathematical fictional fantasy world as if nothing ever happened.
benb,
"theorem" still denotes a proven logical relation, the unpleasant discoveries made in the twentieth century have not changed anything. Life goes on in the mathematical fictional fantasy world as if nothing ever happened.
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Joined 2009
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You are thinking of light travelling through some medium that was named ether.
An analogy with sound travelling through air.
Michelson experiment shown this model is wrong for light.
Einstein came in to explain what was going on.
An analogy with sound travelling through air.
Michelson experiment shown this model is wrong for light.
Einstein came in to explain what was going on.
I'm not quite sure what you are asking, TNT.
There are three causes of redshift. The movement of a galaxies relative to each other, the universe's expansion and gravitational redshift.
If we are considering the former, the redshift is not a 'problem' of the observer or of the light, but is a consequence of their relative motion.
There are three causes of redshift. The movement of a galaxies relative to each other, the universe's expansion and gravitational redshift.
If we are considering the former, the redshift is not a 'problem' of the observer or of the light, but is a consequence of their relative motion.
Derivation of the Mass-Energy Equivalence:
Momentum = mv .... (where m: mass, v: velocity)
We will consider both v and m as functions as both of them can change with time.
d[mv]/dt = m.dv/dt + v.dm/dt ..... (i) (where t: time, dt: an infinitesimal increase in time)
Relativistic Mass:
m = M/sqrt[1 - (v/c)^2] ..... (ii) (where M: stable mass, sqrt: square root function)
Squaring and rearranging:
m.sqrt[1 - (v/c)^2] = M
m^2.[1 - (v/c)^2] = M^2
Removing c^2 from the denominator:
c^2.m^2 - m^2.v^2 = c^2.M^2
Differentiating with respect to time:
c^2.2m.dm/dt - (m^2.2v.dv/dt + v^2.2m.dm/dt) = 0
Removing redundant terms:
c^2.dm/dt - (mv.dv/dt + v^2.dm/dt) = 0 .... (iii)
Rewriting and inspecting (i):
d[mv]/dt = m.dv/dt + v.dm/dt
The rate of change of momentum is equal to the force producing such a rate of change. The increment of energy is: F.dr, where F is the acting force and dr an increment in displacement.
Therefore:
dE = F.dr
Substituting (i) in the above:
dE = m.(dv/dt).dr + v.(dm/dt).dr
But, dr/dt = v, by definition of velocity:
dE = mv.dv + v^2.dm ..... (iv)
Comparing (iv) with (iii):
dE = c^2.dm
The above, mathematically states, the increment in energy is equal to the square of the velocity of light, multiplied by the increment in mass. In other words, it is telling us, mass and energy are equivalent.
Momentum = mv .... (where m: mass, v: velocity)
We will consider both v and m as functions as both of them can change with time.
d[mv]/dt = m.dv/dt + v.dm/dt ..... (i) (where t: time, dt: an infinitesimal increase in time)
Relativistic Mass:
m = M/sqrt[1 - (v/c)^2] ..... (ii) (where M: stable mass, sqrt: square root function)
Squaring and rearranging:
m.sqrt[1 - (v/c)^2] = M
m^2.[1 - (v/c)^2] = M^2
Removing c^2 from the denominator:
c^2.m^2 - m^2.v^2 = c^2.M^2
Differentiating with respect to time:
c^2.2m.dm/dt - (m^2.2v.dv/dt + v^2.2m.dm/dt) = 0
Removing redundant terms:
c^2.dm/dt - (mv.dv/dt + v^2.dm/dt) = 0 .... (iii)
Rewriting and inspecting (i):
d[mv]/dt = m.dv/dt + v.dm/dt
The rate of change of momentum is equal to the force producing such a rate of change. The increment of energy is: F.dr, where F is the acting force and dr an increment in displacement.
Therefore:
dE = F.dr
Substituting (i) in the above:
dE = m.(dv/dt).dr + v.(dm/dt).dr
But, dr/dt = v, by definition of velocity:
dE = mv.dv + v^2.dm ..... (iv)
Comparing (iv) with (iii):
dE = c^2.dm
The above, mathematically states, the increment in energy is equal to the square of the velocity of light, multiplied by the increment in mass. In other words, it is telling us, mass and energy are equivalent.
Perhaps it is the conflation of refraction (in the first sentence) with redshift (in the second sentence) which is problematical.
When a ray of monochromatic light slows down on entering an optically denser medium it's wavelength decreases, but its frequency does not change.
Since colour is determined by frequency, the colour of the light does not change on slowing down.
This is refraction and is not comparable with redshift.
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