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If the speed of light were infinite....


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Ok what about this line of thought , if the speed of light were infinite then what becomes of the value of the vacuum permeability (magnetic constant) and vacuum permittivity (electric constant). These are related to the speed of light - c =1/ (Eo Uo)^1/2,  So do these constants become infinite to and what are the physical implications. Likewise what of the mass energy equivalence (E = mc^2), what would the physical implications be with respect to stellar nuclear processes. I think I read somewhere that if the fundamental constants like G or h etc were slightly different then our universe would not exist in the way it does now :( 

 

Jim 

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7 hours ago, andrew s said:

Doug can you give the formula from the book that justifies the first statement in your quote as I don't have the book. I have not come across such a formulation before.

 

I haven't looked at the book, but I think that this is the way Greene expresses in words the fact that the 4-velocity (or proper velocity) of any massive particle has frame-invariant "length"^2 = c^2.

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On 2/18/2018 at 16:28, George Jones said:

 

I haven't looked at the book, but I think that this is the way Greene expresses in words the fact that the 4-velocity (or proper velocity) of any massive particle has frame-invariant "length"^2 = c^2.

Thanks George that was the prompt I needed.

Looking at the 4 velocity and, as it is invariant under a Lorentz transformation, it means that for us in our frame of reference our time (proper time) just proceeds at one second per second as I said above. It does not mean we have a real velocity c as it is  just part of the formalism where the time component is multiplied by c to convert it to units of distance. If c goes to infinity we would still just move through time in our frame of reference at 1 second per second as c*t/c = t even if c tends to infinity. We don't somehow "speed up" through space time in our own frame of reference.

As c tends to infinity we would see the effects of relativity decrease and we would approach a Newtonian dynamics. Observers would agree which event were simultaneous etc. 

What would a world be like if c were infinite is difficult to tell as you would have incompatibilities between electromagnetism and dynamics... as said before by Jim.

Regards Andrew

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I'd imagine there would be no space and no time. Try plugging infinity into the Lorentz transformation and see where you end up. Things like motion and acceleration would't make any sense, which would do for gravity as well.

Alternatively, we would need to assume all the rest of the laws of physics change too, and possibly admit some kind of ether that serves as an absolute reference frame. But then it wouldn't be "the Universe" at all.

Yep -just had another look at this in light of comments and it is completely wrong - ignore.

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1 hour ago, billyharris72 said:

Try plugging infinity into the Lorentz transformation and see where you end up

You get the Galilean transformations which underpin Newtonian Mechanics. No problems with motion, acceleration etc. 

Regards Andrew

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On ‎18‎/‎02‎/‎2018 at 13:49, saac said:

Ok what about this line of thought , if the speed of light were infinite then what becomes of the value of the vacuum permeability (magnetic constant) and vacuum permittivity (electric constant). These are related to the speed of light - c =1/ (Eo Uo)^1/2,  So do these constants become infinite to and what are the physical implications. Likewise what of the mass energy equivalence (E = mc^2), what would the physical implications be with respect to stellar nuclear processes. I think I read somewhere that if the fundamental constants like G or h etc were slightly different then our universe would not exist in the way it does now :( 

 

Jim 

 

Maxwell's equations and the Lorenz force law describe classical electromagnetism. If the speed of light were infinite then time would collapse and classical electromagnetism would essentially be Coulombs Law. Vacuum permeability would be a meaningless concept and vacuum permittivity would survive insofar as force would need to be redefined. A slight shift in vacuum permittivity would lead to massive consequences for the periodic table as it is closely related to the fine structure constant and stellar nuclear processes.

As for E=mc^2, Special Relativity collapses as the speed of light has no meaning and the theory is lacking a postulate.

 

There is an excellent book called 'Just Six Numbers', by Sir Martin Rees. An easy and fascinating read that marvels at the fortuitous values of certain constants of nature.

 

3 hours ago, billyharris72 said:

 

Alternatively, we would need to assume all the rest of the laws of physics change too, and possibly admit some kind of ether that serves as an absolute reference frame. But then it wouldn't be "the Universe" at all.

It certainly wouldn't.

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Imagine a pool table where all the balls moved at infinite speed.

Each ball would simultaneously be at every point on the pool table. They would not be able to interact meaningfully as each ball would be bouncing off every other ball in every position and every direction at the same time.

In other words you can't have causality in a universe where travel at infinite speed is possible, if such a universe exists, it will be a very boring place because it will be totally isotropic with regard to everything.

It's effectively the same problem as travelling back in time to kill you own grandparents before your parents are born.

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1 hour ago, Tiki said:

If the speed of light were infinite then time would collapse

Can you explain why? I tried to show above it would continue to progress at 1 s per s. 

 

50 minutes ago, Stub Mandrel said:

Imagine a pool table where all the balls moved at infinite speed.

Each ball would simultaneously be at every point on the pool table.

Can you explain why ? 

Regards Andrew

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29 minutes ago, andrew s said:

Can you explain why ? 

Regards Andrew

Imagine a ball that moves constantly on a pool table, never stopping. Given enough time it will eventually pass through every point on the table.

If it is speeded up to go infinitely fast it will do that journey instantaneously and therefore be everywhere on the billiard table simultaneously.

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48 minutes ago, andrew s said:

Can you explain why? I tried to show above it would continue to progress at 1 s per s. 

 

 

No-one really knows what light is. It is defined as a disturbance in space that carries information about charges and their motion (or acceleration). If 'everything happened at once', then the wave equation would lose it's time dependence. 'Space-time' would become 'space'.

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4 hours ago, Tiki said:

There is an excellent book called 'Just Six Numbers', by Sir Martin Rees. An easy and fascinating read that marvels at the fortuitous values of certain constants of nature.

 

 

Tiki, that is where I read about it, Just Six Numbers. It was a holiday read on my Kindle, I read it a few years ago and forgot about it. Thanks for the reminder, I'm going to pick it up again.

Jim 

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9 hours ago, Tiki said:

Maxwell's equations and the Lorenz force law describe classical electromagnetism. There is an excellent book called 'Just Six Numbers', by Sir Martin Rees.

:thumbsup:

Maxwell etc gave me a lot of grief some 1/2 a century ago (or thereabouts+!, when - I suspect my mentors had not a total grasp on it all either  ?! ) when I was last required to study it formally.

Not just six numbers, somewhere near here someone mentioned the Fine Structure Constant which is probably the one amongst those the special numbers that most deposits one's thinking into anthropic principles and reaching for turgid books by R.Dawkins Esq. ,, , err Penrose is a good read tho' :)

But it is all good stuff !

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Sorry about my last post not sure what happened.

I thought I would have one last go at trying to explain that you can have a perfectly good dynamics if the speed of light were infinite. 
Nothing silly happens to time or causality. It repeats I hope more clearly what has been said before.

The diagram below shows the Lorentz transformation which describe the transformation of coordinated when c is finite in Special Relativity (SR).

LT.png.46e55198acc73856b1458b17281dd2f8.png

As you can see if you let c-> infinity then as c is always in the denominator nothing bad happens and you get
x' = x - vt, t'= t etc. These are the Galilean transformation that transform coordinates in Galiliean / Newtonian dynamics.

What happens as c gets larger is that coupling of time and space diminishes and eventually disappears as c -> infinity. This means that the invariant 4 vectors of SR no longer apply and the simpler rules of Galilian / Newtonian dynamic hold sway. You can't pug c = infinity into the SR equations and expect a sensible answer. You can't derive them if c is infinite.

If you look at a standard SR space-time diagram you normally get a ct axis and an x axis obviously this is problematic if c= infinity.

spacetime.png.12dcb8e9702c45caddd0e77c6e418792.png

But you don't need to do this you can perfectly well use SI units and plot t and x. If you do this on graph paper with 1s to the cm and 1m to the cm then the light-line would in effect be along the x axis. You would have to go 3x10^8 cm before it when up to the 1 second line. ( Which is why professional physicists set c = 1 so the light-line is at 45 degees.)

So what about causality. The diagram shows the region of causality in standard SR as c -> infinity the light-lines tilt towards the x axis and the region of causality gets larger! We can influence all event in our future if c= infinity. 

causal-diamond.jpg.2f7f4d95f217c50629a76167af4d5f75.jpg

In addition our past light cone opens out and we see all events at a particularly time as simultaneous however close or far away in space they are.

None of this means all events happen at once. We still progress along our world lines at one second per second and every thing looks as it does to us in our everyday life where the distances and speeds are too small to show up relativistic effects.

Regards Andrew

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39 minutes ago, johnfosteruk said:

Surely if the speed of light (that is to say the speed at which photons travel) were infinite (Can anyone actually comprehend such a speed?) surely Maxwell and Lorentz would be broken. Just sayin'

In our Universe the speed of light is finite and it needs to be for Maxwell's equations to be valid. Indeed you are right if it were infinite then Maxwell's  equations and the Lorentz transformations don't work.

However, before SR was developed the Galilean transformations were used for dynamics even when it was known that Maxwell's equations were Lorentz invariant and not Galilean invariant.

We still use the Galilean transformations in everyday calculations in dynamics when speeds are low and distances short.

Regards Andrew 

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  • 2 weeks later...

hi 

the speed of light like all things has a beging and an end.i think the light made of photons cant run infiniely its anti natural.

like the universe has a beginig and a end.the big Crunch.

from dark comes light and from light comes dark.

thanks:icon_biggrin:.

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Is a brief digression allowed now?  What if c = 30mph?  You'd see passing cars shrunk in the direction of travel - or maybe not, because it would take a huge amount of fuel to overcome inertia to get anywhere near 30mph.  I think.......

Doug.

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