Suppose that I am walking down a beach and open a bottle, only to have a genie appear and offer me 3 wishes.
Because I find Newtonian physics much easier to understand than relativity, I ask him to get rid of the speed of light restriction. He explains to me that this can’t be done, but that he can change the speed of light for me.
I say, “Sure. make the speed of light infinite!”
He looks down his nose at me, and says he taking back one wish just for me being a smartass.
So with my two remaining wishes, I ask him to increase the speed of light one million-fold (set c = c*10^6) and to let me observe the effects from within a personal bubble of my current spacetime suspended within the changed universe.
My first thought would be that the universe would at least LOOK very Newtonian, at least at most energies. With big enough engines, I guess we could make fairly quick trips to nearby stars. I guess we would still see relativistic effects within particle colliders.
My second thought was that maybe the universe wouldn’t look much different at all, at least to those who lived in it.
In many “speed of light” posts, I’ve seen comment to the point that the speed of light (“c”) is basically a conversion metric for units of space and time. As I watch from my personal spacetime bubble at the universe as the speed of light grows from c to one million c, will I observe the universe grow around me, so that things that were a millionth of a meter before now look to me to be one meter in size? That is, would the atoms, people, planets, stars, and corresponding distances just grow in proportion to the change in lightspeed? Would I be the only one to see the difference?
This is a common misconception. Nothing that we have now or are likely to have in the near future for propelling a human-sized spaceship reaches high enough velocity that the speed of light is a relevant limit. In purely Newtonian mechanics, simple rocket trips to nearby stars still don’t work - even the most theoretically efficient rockets need something like a 10,000:1 mass ratio for a trip where you accelerate to .2c, coast, decel from .2c, then make a later return trip at the same speed.
The universe would look pretty screwed up depending on exactly how you define changing the speed of light. For example, if the c in E=mc^2 were to go up by a few orders of magnitude, the energy released by fusion in the sun would go up by the square of those orders of magnitude, and you’d likely get a stellar explosion in short order, or at least a crisped cinder of an earth. The speed of light is used in so many places that without a good definition of what you’re changing it’s hard to say, but it very probably makes the universe uninhabitable for life as we know it.
Would this really be a problem? If the atoms and stars and everything grew a million-fold, maybe the extra energy per fusion event would be balanced by the expansion of the space metric?
Okay- I see a flaw in my thinking. By changing c, I change the relationship between time and distance, and a photon should cross a hydrogen atom 1,000,000 times quicker, so no change in the size dimensions of the universe.
Meanwhile any exothermic reaction affected by special relativity (like stellar fusion) becomes 1,000,000,000,000 times more energetic. Pretty much instant supernova in every active star everywhere in the universe all at the same time.
Fusion is an obvious example of matter to energy conversion, but would the same things be true for ordinary chemical reactions? Would humans spontaneously combust and would fireflies explode?
Remember that if you are on the rocket ship going to distant stars you need not increase the speed of light to make the trip assuming you can get to relativistic speeds.
Remember for the astronaut aboard the ship their clocks will move more slowly (compared to here on earth) and distance will be compressed (i.e. they make a shorter trip than we would measure it on earth). These can combine to make it a downright speedy trip to almost anywhere.
I’ll use the Oh My God Particle since they have nicely already done the math:
v = 0.9999999999999999999999951 c
If you are going that fast then according to the astronaut’s watch the following trips would take:
Alpha Centauri: 4.36 light years in 0.43 milliseconds
Galactic nucleus: 32,000 light years in 3.2 seconds
Andromeda galaxy: 2,180,000 light years in 3.5 minutes
Virgo cluster: 42,000,000 light years in 1.15 hours
Quasar 3C273: 2,500,000,000 light years in 3 days
Edge of universe: 17,000,000,000 light years in 19 days
Of course when you come back to earth years to millions or billions of years will have passed. If you did the roundtrip to quasar 3C273 our sun would be in its death throes when you returned. You’d only be a few days older though.
Well c is the speed things travel through space-time. And it is 1. So as discussed in a recent thread it doesn’t make sense to change it. You can re-label the conversions to speed in spatial dimensions, but because c is also in the temporal dimension, all you get is new numbers, not new speeds.
However you could claim that the OP’s allowance that he want to observe from a bubble universe can sort of work. Then you would probably just observe the universe progressing a million times faster. No different to slowing your own bubble universe down. Maybe.
Another interpretation might be that what is asked for is to reduce all the other constants in the universe that relate to c by a factor of a million. E = mc[sup]2[/sup] still, but the fine structure constant would be 1/137000000, and so on. At this point the universe would basically stop working as we know it. Forget stars going nova. Atoms would cease to work.
One way of thinking of it is that objects aren’t distant just in space, they’re distant in time too. The sun for example is about 93,000,000 miles away, which is also about 8 1/3 minutes away in time. You can’t “go faster” because you can’t get there without crossing 8 1/3 minutes.
It’s far, far worse than that. I can’t even directly calculate the propellant-to-payload mass ratio for the scenario you specify (accelerating up to and then down from 0.2c) even the best performance we could expect from a fusion powered rocket specific impulse (I[SUB]sp[/SUB]) ~10,000 s using a 64 bit computer. Just to accelerate up to 0.2c relative to a starting reference frame using a fusion rocket of this kind would result in a propellant mass ratio of about 4.2x10[SUP]265[/SUP]:1, which is greater than the number of atoms in the observable universe. Just to get up to 1% of c (0.01c) would require a mass ratio of 1.91x10[SUP]13[/SUP]:1, and a vessel capable of decelerating from that speed would have a mass ratio of 3.65x10[SUP]26[/SUP]:1. For comparison, the mass of the Earth is 5.97×10[SUP]24[/SUP] kg, so we would need approximately 60 Earth masses to propel one kilogram of payload to and from this speed, notwithstanding the mass of the propulsion system, et cetera. For conventional chemical propulsion (<500 s), it is literally impossible to achieve delta speeds that are even within orders of magnitude of the speed of light, much less fast enough to observe relativistic effects.
You would need to get to I[SUB]sp[/SUB]) >100,000 s (mass ratio is ~453:1) just to accelerate and decelerate a payload to 0.01c, and an I[SUB]sp[/SUB] >10,000,000 at 0.2c. The power density necessary to get the thermal conditions to develop this kind of specific impulse using momentum transfer rocket propulsion are near the same order of magnitude of those seen just after the initial singularity (at the so-called “GUT scale”), and would require unification of the fundamental forces to achieve. We have absolutely no idea how to do this today, although efforts like the Large Hadron Collider give us some vague insight into the properties of fundamental forces and particles that occur at cosmic energies up to 13 TeV but nowhere near the 10[SUP]13[/SUP] TeV level of the GUT scale.
Oh, when I said theoretically most efficient, I wasn’t talking about realistic fusion engines, I meant a perfect photon drive using perfectly mixed matter/antimatter fuel that converts completely to energy. Like you showed, the numbers get really silly if you use an actual drive we’d be able to make and use, but I find that people will weasel out of that with ‘what if I had a REALLY GOOD engine though’. Then again, the OP seemed to ignore the perfect case too - people seem really attached to the idea of ‘c’ as a practical speed limit, but getting anywhere close to that speed using just a drive is a hard task even with no relativistic effects .
