Light slows down and speeds up depending on the medium which it travels through. My crystal ball says you're headed towards gravitational lensing. And quite frankly light can care less about an accelerated frame of reference.

 

Does an optical lens bend light
by slowing it down relative to the surroundings ?

You‘ve spotted the index of refraction which is precisely what lenses are about.

 

Light slows down and speeds up depending on the medium which it travels through. My crystal ball says you're headed towards gravitational lensing. And quite frankly light can care less about an accelerated frame of reference.

Gravitational lens was at the back of the mind

been re reading
@dcbingaman

This light stuff is complex,

Thank you guys ,

 

I read that if you have a rocket that can accelerate constantly at 1G (to give a nice, normal gravity environment in the ship) then, due to time dilation, you would be able to get the edge of the know universe in a lifetime (as measured inside the ship).

How much fuel is needed for that travel?
https://www.desy.de/user/projects/Physics/Relativity/SR/rocket.html

How much fuel is this? The next chart shows the amount of fuel needed (M) for every kilogramme of payload (m=1 kg).

d Not stopping, sailing past: M
4.3 ly Nearest star 10 kg
27 ly Vega 57 kg
30,000 ly Center of our galaxy 62 tonnes
2,000,000 ly Andromeda galaxy 4,100 tonnes
This is a lot of fuel—and remember, we are using a motor that is 100% efficient!

What if we prefer to stop at the destination? We accelerate to the half way point at 1g and then immediately switch the direction of our rocket so that we now decelerate at 1g for the rest of second half of the trip. The calculations here are just a little more involved since the trip is now in two distinct halves (and the equations at the top assume a positive acceleration only). Even so, the answer turns out to have exactly the same form: M/m = exp(aT/c) - 1, except that the proper time T is now almost twice as large as for the non-stop case, since the slowing-down rocket is losing the ageing benefits of relativistic speed. This dramatically increases the amount of fuel needed:

d Stopping at: M
4.3 ly Nearest star 38 kg
27 ly Vega 886 kg
30,000 ly Center of our galaxy 955,000 tonnes
2,000,000 ly Andromeda galaxy 4.2 thousand million tonnes

"This fuel-becomes-payload problem is well known in the space programme: part of the reason the Saturn V moon rocket was so big was because it needed yet more fuel just to carry the fuel it was already carrying."

 

How much fuel is needed for that travel?

If its antimatter, not so much.

 

If its antimatter, not so much.

Those calculations were using matter-antimatter annihilation.

How much fuel is needed?
Sadly there are a few technical difficulties you will have to overcome before you can head off into space. One is to create your propulsion system and generate the fuel. The most efficient theoretical way to propel the rocket is to use a "photon drive". It would convert mass to photons or other massless particles which shoot out the back. Perhaps this may even be technically feasible if we ever produce an antimatter-driven "graser" (gamma ray laser).

Remember that energy is equivalent to mass, so provided mass can be converted to 100% radiation by means of matter-antimatter annihilation, we just want to find the mass M of the fuel required to accelerate the payload m. The answer is most easily worked out by conservation of energy and momentum.

 

Gravitational lens was at the back of the mind

been re reading
@dcbingaman

This light stuff is complex,

Thank you guys ,

been re reading @dcbingaman .
A consummate professional. I enjoy his posts.

 

The speed of light is not constant for an accelerating body. If the accelerating body considers itself not moving (perfectly valid viewpoint as any other) the speed of light will be found to vary at least over distances. But it will continue to have speed c when measure locally that is when delta x is small. The x coordinate being the direction of acceleration. So there are some exceptions.

been re reading @dcbingaman .
A consummate professional. I enjoy his posts.

Thanks for the compliment. Though I do not consider special and general relativity to be my specialty it is fascinating stuff.

 

Thanks for the compliment. Though I do not consider special and general relativity to be my specialty it is fascinating stuff.

@dcbingaman

You explanations have amazing,

It has shown me the limits of Newtonian maths,
and the many facets of relativity that I dont know about

Its a bit mind blowing,
but if I drip feed myself
I might get there,

To all of you thank you

 

One interesting thing about the 'speed limit' is that it's not a limit on the speed of change, it's a limit on the speed of information (causality). You can have non-physical things that change FTL without information exchanges being FTL. “Nothing can go faster than light” is a true statement IRT the expansion of empty space or the phase velocity term in Maxwell's equations (Superluminal phase velocity) in some types of transmission media like radio waveguides. The group velocity is how fast the wave travels (the propagation speed), but the phase velocity is just how fast the wave rises and falls.

 

One interesting thing about the 'speed limit' is that it's not a limit on the speed of change, it's a limit on the speed of information (causality). You can have non-physical things that change FTL without information exchanges being FTL. “Nothing can go faster than light” is a true statement IRT the expansion of empty space or the phase velocity term in Maxwell's equations (Superluminal phase velocity) in some types of transmission media like radio waveguides. The group velocity is how fast the wave travels (the propagation speed), but the phase velocity is just how fast the wave rises and falls.

When I was a TA for physics at university, this was a major hangup for many students, especially those who were only superficially familiar with special relativity. It's very important to point out, especially when doing stuff where waves are all the rage.

 

When I was a TA for physics at university, this was a major hangup for many students, especially those who were only superficially familiar with special relativity. It's very important to point out, especially when doing stuff where waves are all the rage.

I was very lucky to have a physics professor as a scoutmaster. He helped me understand all sorts of interesting phenomena. His explanations were so clear and his words always delivered with Socratic eloquence. (Also thanks to him, back in those days my head was invariably buried in pile of sci-fi novels by authors such as Heinlein, Bradbury, Asimov, etc.) Anyway, one day I came up with a thought experiment and presented it to him. I was absolutely elated when he told me that my assessment appeared to be correct! The gist of it is this.

You climb into a rocket filled with "magical fuel" and lift off, accelerating to say 2 G's. After some time you encounter an exotic cloud of energetic particles and the ships power is knocked out...and so are you, as you have apparently hit your head on something in the process! (Very contrived, I know, but just remember this WAS coming from the mind of a 13-year old.) When you awake you find that you can't remember anything, so you try to assess the situation. The engine is off. You are weightless. How fast are you going? No idea. In fact, according to special relativity, you are effectively stationary!

So here is the really interesting thing about it. You are going some percentage of the speed of light relative to the Earth. Let us say for illustration purposes that is 99%. Well if you were to then restart your engines and commence as planned you could do it ALL OVER AGAIN, all within that tiny sliver of 1%!

And indeed, as judged from planet Earth, travelling just a fraction faster than you were before. From YOUR perspective on the other hand you are starting from zero and accelerating toward a fresh new 99%, so to speak.

So there have it. Time-dilation adheres to Zeno's Paradox!

 

I was very lucky to have a physics professor as a scoutmaster. He helped me understand all sorts of interesting phenomena. His explanations were so clear and his words always delivered with Socratic eloquence. (Also thanks to him, back in those days my head was invariably buried in pile of sci-fi novels by authors such as Heinlein, Bradbury, Asimov, etc.) Anyway, one day I came up with a thought experiment and presented it to him. I was absolutely elated when he told me that my assessment appeared to be correct! The gist of it is this.

You climb into a rocket filled with "magical fuel" and lift off, accelerating to say 2 G's. After some time you encounter an exotic cloud of energetic particles and the ships power is knocked out...and so are you, as you have apparently hit your head on something in the process! (Very contrived, I know, but just remember this WAS coming from the mind of a 13-year old.) When you awake you find that you can't remember anything, so you try to assess the situation. The engine is off. You are weightless. How fast are you going? No idea. In fact, according to special relativity, you are effectively stationary!

So here is the really interesting thing about it. You are going some percentage of the speed of light relative to the Earth. Let us say for illustration purposes that is 99%. Well if you were to then restart your engines and commence as planned you could do it ALL OVER AGAIN, all within that tiny sliver of 1%!

And indeed, as judged from planet Earth, travelling just a fraction faster than you were before. From YOUR perspective on the other hand you are starting from zero and accelerating toward a fresh new 99%, so to speak.

So there have it. Time-dilation adheres to Zeno's Paradox!

Ok, I'll bite

"Fun fact: There are precisely (n - 1)! + 1 = n^2 platonic solids "

Can you expand please ...

 

Ok, I'll bite


"Fun fact: There are precisely (n - 1)! + 1 = n^2 platonic solids "


Can you expand please ...

Oh that? The answer is simply the solution to the equation ((n - 1)! + 1) - n^2 = 0. That number is 5, of course, the number of platonic solids. It also happens to be the actual number of forces in the universe. But that is another conversation entirely!

 

Oh that? The answer is simply the solution to the equation ((n - 1)! + 1) - n^2 = 0. That number is 5, of course, the number of platonic solids. It also happens to be the actual number of forces in the universe. But that is another conversation entirely!

thank you

 

Oh that? The answer is simply the solution to the equation ((n - 1)! + 1) - n^2 = 0. That number is 5, of course, the number of platonic solids. It also happens to be the actual number of forces in the universe. But that is another conversation entirely!

I wonder how you would go about solving that using simple algebra? I have never dealt with equations that contain factorials.

 

I wonder how you would go about solving that using simple algebra? I have never dealt with equations that contain factorials.

I don't think that is possible using only standard algebraic operations. You'd probably need to use some sort of root finding algorithm, like Ridders' method (which doesn't require derivatives).

 

Except little facts kept popping up to poke holes in their balloon.

The assumption that the speed of light is finite and has remained unchanged in all the universe is the single most use of conjecture that I have encountered in the books. Ironically this assumption is used to calculate the timeline and scale of the universe and is the foundation for almost every applied science. Very few academics take this into consideration and most prefer to build on the already known equations which have been placed into the "fact" category. Your statement sums this up nicely..

 

The assumption that the speed of light is finite and has remained unchanged in all the universe is the single most use of conjecture that I have encountered in the books. Ironically this assumption is used to calculate the timeline and scale of the universe and is the foundation for almost every applied science. Very few academics take this into consideration and most prefer to build on the already known equations which have been placed into the "fact" category. Your statement sums this up nicely..

Easy. Prove it's not and win a Nobel for it.

Like Newtonian mechanics, our current understanding is incomplete but it's not wrong. It gets some very fundamental predictions correct when we collect data to check those predictions. Those are facts that any competing theory must also get correct.

 

The assumption that the speed of light is finite and has remained unchanged in all the universe is the single most use of conjecture that I have encountered in the books. Ironically this assumption is used to calculate the timeline and scale of the universe and is the foundation for almost every applied science. Very few academics take this into consideration and most prefer to build on the already known equations which have been placed into the "fact" category. Your statement sums this up nicely..

FAPP (For All Practical Purposes) it appears constant at least where we currently are and when we are. The GPS system must take into account relativity (both Special and General) in order to maintain accuracy. If c was changing nothing could be calculated accurately. But you could be correct in the 'Long Run' who knows. Naturally we have only been measuring it for a rather short period of history.

Technically you are 100% correct. Accelerating frames of reference and or frames of reference under the influence of gravitational fields (bending of space/time) will already show that c is not a constant and will vary with the direction of c with respect to the reference body. The reference body may consider itself stationary within a gravitational field or moving. It does not matter.