Suppose there are two 'universes' (really the equivalent of our known universe) heading towards each other within the empty space around them. A third party observer would see universe A traveling at .4c (c=speed of light) and universe B traveling at .3c. Of course, residents of each universe would perceive their universe as sitting still, and the other one approaching at .7c. What about the effects of speed adding mass though? Would each universe see the other as being super massive due to its .7c speed while seeing its own mass as normal? If so, would they both be right about it, and how does that work?
To further complicate things, suppose there is a space ship in universe A that is completely oblivious of universe B. It tries to accelerate to .8c, which it can normally do. But, it does so in the direction of universe B. Would it succeed in reaching that speed, and from what viewpoints?
(Oh, and I'll stop making new physics posts now, I promise!)
|ocalhoun wrote: |
|A third party observer would see universe A traveling at .4c (c=speed of light) and universe B traveling at .3c. Of course, residents of each universe would perceive their universe as sitting still, and the other one approaching at .7c. |
Velocities don't add!
Don't forget Lorentz. ^_- Off the top of my head, i'd say the residents of each universe would see the other universe approaching at somewhere between .6 and .65 c, not 7 c.
|ocalhoun wrote: |
|What about the effects of speed adding mass though? Would each universe see the other as being super massive due to its .7c speed while seeing its own mass as normal? If so, would they both be right about it, and how does that work? |
Yup, they'd both see the other universe at somewhere between 1.25 and 1.5 times its rest mass while measuring their own mass as the rest mass. And they'd both be right - that's where the relative in relativity comes in. They are both correct within their own frame of reference.
|ocalhoun wrote: |
|To further complicate things, suppose there is a space ship in universe A that is completely oblivious of universe B. It tries to accelerate to .8c, which it can normally do. But, it does so in the direction of universe B. Would it succeed in reaching that speed, and from what viewpoints? |
So it accelerates to .8 c wrt A? In that case you'd have to use the velocity addition formula to see how B would measure it. First you'd have to figure out the velocity of B wrt A, because it's not .7 c, it's somewhere between .6 and .65 c. Then you'd do velocity addition between that value and .8. You'll get .9 something c.
thats the most confusing thing i think i've ever read.
|brainxdead wrote: |
|thats the most confusing thing i think i've ever read. |
Well, relativity is not intuitive - in fact it is largely counter-intuitive. You have to do the sums yourself a few times to see how it works....
Bikerman is right... nothing is going to make sense without the math because it's so far out of our normal experience. You can't add velocities. If a and b are velocities, then v ≠ a + b. Instead, v = (a + b) / (1 + ab/c²).
Let's put that into practice with ocalhoun's example. He said that if there were to universes approaching each other, one moving at 0.4 c and the other at 0.3 c, each would see the other coming at 0.7 c. Makes sense, right? You're in a car at 40 kph, another car is coming at you at 30 kph, that means you're closing in on each other at 70 kph... which is what we know and expect.
Doesn't work though.
v ≠ a + b = 0.4 c + 0.3 c = 0.7 c
v = (a + b) / (1 + ab/c²)
v = (0.4 c + 0.3 c) / (1 + (0.4 c)(0.3 c)/c²)
v = (0.7 c) / (1 + (0.12 c²)/c²)
v = (0.7 c) / (1 + 0.12)
v = (0.7 c) / 1.12
v = 0.625 c
Incidentally, the reason that you can add 30 kph and 40 kph without any trouble is because 30 kph = 2.7797008 × 10⁻⁸ c and 40 kph = 3.7062677 × 10⁻⁸ c, so:
v = (30 kph + 40 kph) / (1 + (2.7797008 × 10⁻⁸ c)(3.7062677 × 10⁻⁸ c)/c²)
v = (70 kph) / (1 + (1.0302315 × 10⁻¹⁵ c²)/c²)
v = (70 kph) / (1 + 1.0302315 × 10⁻¹⁵)
v = (70 kph) / 1.000000000000010302315
v = 69.99999999999993 kph
Which means an error of around 19.7 fm/s or 19.7 × 10⁻¹⁵ m/s... which, speed wise, means it should take about 45 minutes to cross the distance spanned by a hydrogen atom. In other words, 70 kph is close enough. ^_^;
When you crunch the numbers you get an appreciation for why it's ok to add velocities in our normal experience, but not ok at speeds at any appreciable fraction of c. You also get a picture in your head of just how small is small enough before you can't just add anymore, and you have to use the full equation.
As another aside, the last question was about measuring different masses for the universes depending on your relative speed. The key to understanding this is the equation in the other thread (both would work, but the one given by quasar is easier to calculate, and the one i gave makes the picture clearer... so guess which one i'll use ^_^; ): E² = m₀²c⁴ + p²c². Both observers would solve the same equation in the same way... except the ones travelling in the universe would set its momentum to 0, and the ones who see it coming at 0.9 c would give it a large momentum. The ones travelling in the universe would measure its mass as m₀, and the ones who see it coming at 0.9 c would measure its mass as m = m₀ / √(1 - (v² / c²)), where v is 0.9 c (and if they took its speed into account, they could solve for m₀, and get the same value as the people who are travelling in it).
I thin here one needs to mention about the multiverse theory
like the following
|In certain multiverses, where electroweak symmetry breaking occurs only if M is below some critical value, we find that a little hierarchy develops with the value of v2/M2 suppressed by an extra loop factor, as well as by the strength of the distribution. Since the correct theory of electroweak symmetry breaking is unknown, our estimate for PEWSB is theoretical. The LHC will lead to a much more robust determination of PEWSB, and, depending on which theory is indicated by the data, the observer naturalness problem of electroweak symmetry breaking may be removed or strengthened. For each of the three arenas, the discovery of a natural theory would eliminate the evidence for the multiverse; but in the absence of such a theory, the multiverse provides a provisional understanding of the data"
Ref: Lawrence J. Hall and Yasunori Nomura 2008 Evidence for the multiverse in the standard model and beyond ©2008 The American Physical Society
Am I missing something here, or is this a fully philosophical exercise? My first point, that there are two "Universes" moving "Towards" each other surrounded by "Empty Space" defies all observation and logic. The very idea of multiple universes delves into the idea that the rules we know aren't the only ones out there, and that they might not apply or act the way we expect them to in a multiple universe arena. So far as we know, there is only one universe, ours, and having not observed other universes in any form, the idea of multiple ones is just creative thinking. Second, if there are multiple universes, the idea that their relationship would be space based is going in the wrong direction. Space is a feature of our universe, our universe is not a feature of space. This leads me to my third point, that the nature of a "universe" is the entirety of the matter, space, time, and energy in it. Any space outside of a universe, say "Empty space" between two universes, implies that the universes and space around them are part of a larger creation. This construct, not currently having a name, could probably be called the true universe, though I would call it infinity. The idea, however, that there would be a space-based relationship, such as "empty space" between the two, is rather counterintuitive to the idea of a greater multi-verse. I mean, if we can travel between universes I don't want to travel "5 million light-years", I'd rather travel through a "mind-tunnel" or something completely different. Wouldn't you?
I remember reading a hypothesis somewhere, but don't ask me where, that if multiple universes are spawned within a bulk space then each universe would create its own set of dimensions. That means they would not be separated by space as we understand it, but would exist in dimensions unobservable from any other universe. There could, therefore, be no interaction at all between them.
If that is the case, and the dimensions are formed with the creation of each universe, there can be no such thing as an outside observer as he/she/it would be unaware of the newly-created dimensions.