Why Does Jill See Bob's Speed Differently in an Alternate Universe Race?

[Aeoliana]

So I am 100% sure I am missing something here, but can someone explain to me why this doesn't work out?

Say I go to another universe where numbers are easy and photons are observed to travel 100m/s. I decide to capture one to use in my photon race course. This ones name is Bob. Let's also say that I have a very special robot named Jill who can travel 99m/s.

I decide I want them to race one another (still in this alternate universe). So I set up a straight course through a vacuum (of course this wouldn't be physics if it wasn't in a vacuum), the finish line is 1000m from the start. At the firing of the gun both entities speed towards the finish line 1000m away. Herein lies my confusion.

As the outside observer with a fancy stopwatch, I would expect to observe Bob the photon screech across the finish line after 10 seconds. I would also expect to see Jill puffing away at 990m at the moment Bob crossed the finish.

From Jill's perspective, she's sitting there at the line glaring at Bob and as soon as she hears the gun she instantaneously accelerates to her maximum velocity. But lo and behold, Bob is tearing away at 100m/s despite her best efforts. 5.025s later in her frame she sees Bob cross the line and gives up!

In her frame she sees the difference of 1m/s as a difference of 100m/s, does that mean she is experiencing time 100 times more slowly than the observer?

How would she end up in a position where her distance traveled : Bob's distance traveled = 99:100 when in her frame of reference their speeds are 99:199?

I'm probably missing something stupid here.

 

[PeterDonis]

A few things to point out that might help:

(1) In Jill's frame of reference, her speed is zero, not 99 (I'll leave out the units--basically in your scale of speeds a speed of 100 is the speed of light). This is assuming that by "Jill's frame" you mean the frame she is in after she has instantaneously accelerated to speed 99 in the "track frame", the frame in which the start and finish line are at rest. In Jill's frame, the start line is moving away from her at speed 99, and the finish line is moving towards her (at least until she crosses it) at speed 99. You're correct that in Jill's frame the speed of Bob the photon is still 100, so the ratio of (finish line speed) to (Bob's speed) in Jill's frame is 99 / 100. Thus, the ratio of (finish line distance traveled) to (Bob's distance traveled) in Jill's frame is also 99 / 100. This should address the main question you posed.

(2) In Jill's frame, the distance to the finish line at the instant she starts (i.e., the instant where she has just instantaneously accelerated to speed 99 in the track FOR) is *not* 1000; it's 1000 divided by gamma, where gamma is the length contraction/time dilation factor corresponding to a speed of 99. Call that distance X.

(3) In Jill's frame, the finish line is moving towards her at speed 99. So Jill will see Bob cross the finish line at time X / 199 in her frame. She herself will cross the finish line (or rather, the finish line will meet her) at time X / 99 in her frame. Both these times are considerably smaller than the 5.025 seconds you mention.

(4) Note that the latter time, T = X / 99, can be rewritten as T = 1000 / (gamma * 99), meaning that the time T is just the time it takes Jill to reach the finish line in the "track frame", divided by the time dilation factor for Jill's speed. So from the track frame's point of view, yes, Jill is experiencing time more slowly--though not by a factor of 100, only by a factor of gamma, which is considerably smaller than 100 (it's about 7).

 

[Aeoliana]

Is it incorrect to say that the density of space and time surrounding a particle is a function of the energy contained by that particle?

So something of great energy i.e. something moving near the speed of light, would diffuse the time it travels through?

Density of time at low energy
|-----------------------|
-----------> Moving through time at static rate
|- - - - - - - - - - - - - -|
Density of time at high energy

Density of space for particle at high energy, increasing the closer you get to the particle
http://img97.imageshack.us/img97/8068/thingb.png

So would a particle that is massively massive contract the space surrounding it so you have something like black holes trapping light not by gravity but by sheer magnitude of how much space is contracted near it?

Is gravity just the tendency of objects to move with the gradient of space's density?

 

[Dale]

Is it incorrect to say that the density of space and time surrounding a particle is a function of the energy contained by that particle?

How does your concept of "density of space and time" differ from the modern concept of "curvature of spacetime"?

 

[Aeoliana]

So let's say I define a 'Universe' as an infinite amount of space filled with an infinite amount of energy. Universes have two important constants: One which defines the manner in which energy observes time (like the speed of light), and one which governs how space reacts to energy(?).

Lets look at a universe whose energy is in a purely entropic state, whose energy experiences time proportional to its magnitude and whose space contracts in the presence of energy. In a purely entropic system, the spatial dimensions of this universe would be infinitely contracted about the source of energy within it.

Now let an outside force induce order within this universe. Boom. Now instead of an infinite number of states, there is a finite amount. The force that contracts space no longer has a perfectly equal system to work with and can no longer keep space infinitely contracted. During this expansion, depending on how order was forced into the energy (lets say molecules and nuclear forces) it could be shredded into billions of tiny pieces that travel outwards. Some pieces would be large, large enough to contract space to such a degree that even light gets caught inside it. Surrounding these large pieces are many smaller pieces, far enough from the center of these large contractions to not be swallowed, but not far enough to escape. But even these smaller pieces contain enough energy to surround themselves with even smaller pieces... and so on.

This expansion would continue until the spatial dimension came to equilibrium with the new forces that were introduced and the original energy-space force.

Something that is important to keep in mind is that there is an infinite amount of 'space' contained in the spatial dimensions, but the amount of 'space' at any 'position' in the universe is relative to the amount of energy.

So if the universe were 1000 units across, there would still be an infinite amount of 'space' in that area. Just less than there would be per cubic unit than if it were 100 units across. And the amount of 'space' surrounding an entity of high energy is less than that surrounding an entity of low energy.

The second law of thermodynamics states that the entropy of a closed system tends towards a maximum. This would suggest that once the universe had reached equilibrium with the artificially induced order, it would slowly begin to progress back to the initial state of maximum entropy. As the entropy of the universe increased back towards infinity, it would begin to contract upon itself once more.

Also, if 'space' were expanding in a sense of 'becoming less spatially dense', as opposed to becoming more arbitrary meters across, it would explain the red-shifting of light better than a loss of energy.

Blargh, if the premises were true would this be wrong?

 

[Dale]

Please review the forum rules on overly speculative posts.

 

[Aeoliana]

My apologies.

I was mainly wondering if someone who knew physics better than I could tell me if the reasoning was sound.

 

[PeterDonis]

Is it incorrect to say that the density of space and time surrounding a particle is a function of the energy contained by that particle?

So something of great energy i.e. something moving near the speed of light, would diffuse the time it travels through?

First of all, I want to point out that this question is separate from the one you ask later in the same post. This question can be answered purely within the framework of special relativity, where spacetime is flat and there is no gravity. The answer is that the "energy increase" due to an object's speed is frame-dependent; it depends on the speed of the object relative to you, the observer, not on any invariant physical quantity. So no, that "energy increase" does not affect spacetime itself.

This article from the Usenet Physics FAQ briefly discusses the topic:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

So would a particle that is massively massive contract the space surrounding it so you have something like black holes trapping light not by gravity but by sheer magnitude of how much space is contracted near it?

"Gravity" and "how much space is contracted" are not different things; they're different ways of looking at the same thing. At least, they are in standard general relativity, which is what I assume you're asking about.

 

[JesseM]

Lets look at a universe whose energy is in a purely entropic state, whose energy experiences time proportional to its magnitude and whose space contracts in the presence of energy. In a purely entropic system, the spatial dimensions of this universe would be infinitely contracted about the source of energy within it.

None of this really makes sense in terms of relativity or any other theory of physics. I don't know what it means to say "energy experiences time proportional to its magnitude", and space doesn't automatically "contract in the presence of energy" in relativity (after all our universe is filled with energy and is expanding), nor is it clear why you think a universe at maximum entropy (which I guess is what is meant by "purely entropic state") would be "infinitely contracted, or why you later say that lowering the entropy of the universe should counter the contraction (didn't you claim that space contracts based on energy, not entropy? In any case, as I said before this doesn't really make sense in relativity where the behavior of space and time doesn't depend on entropy).

 

[Aeoliana]

I don't know what it means to say "energy experiences time proportional to its magnitude"

That is to say, as the magnitude of energy increases, the less time the energy experiences.

and space doesn't automatically "contract in the presence of energy" in relativity (after all our universe is filled with energy and is expanding)

Two things, one is that this was a premise. 'Assuming there exists a universe where the density of space surrounding energy increases with the magnitude of that energy.

The second is that I addressed the expansion, I will attempt to elaborate:

Take a syringe and place within it a marshmallow. This marshmallow is the infinite space contained in the universe. Stopper the end of the syringe and pull on the plunger. See the mallow expand. The amount of mallow did not change, only the space it occupied, only its density.

Now let us place within this mallow a 'mallow-magnet' which attracts mallow-matter in the same way a magnet does iron. We repeat the experiment and observe that while the mallow expanded as expected, the density of the mallow throughout its entirety was not uniform. Surrounding the mallow-magnet the density increased and elsewhere the density lowered. In fact, the effects of this mallow-magnet reach all extents of the mallow, just incredibly weakly far from the source. We could say for our purposes that the mallow magnet was a high energy entity.

Furthermore, if you induced a wave in the mallow whilst simultaneously expanding it, the wave would traverse the mallow at the same speed it started with Speed as defined as amount of mallow passed through per second, not distance traveled

nor is it clear why you think a universe at maximum entropy (which I guess is what is meant by "purely entropic state") would be "infinitely contracted, or why you later say that lowering the entropy of the universe should counter the contraction

In a system of maximum entropy, the magnitude of energy should be equal throughout yes? If you have a law that contracts space by magnitude of energy, and all magnitudes are equal everywhere, would not it contract completely?

In a state of lowered entropy the magnitude of energy is not uniform throughout and therefore by extension the contraction of space would not be uniform.

It was not the entropy that would cause the expansion but the introduction of forces stronger than the 'space-energy' force in a scenario with non-uniform magnitude of energy.

 

[JesseM]

That is to say, as the magnitude of energy increases, the less time the energy experiences.

Less time relative to what? In relativity there is no objective truth about the rate a clock is ticking, you can only define it relative to time in some coordinate system, or compare how much time elapses on two different clocks that start at the same spot and then move apart and then come together again.

Two things, one is that this was a premise. 'Assuming there exists a universe where the density of space surrounding energy increases with the magnitude of that energy.

I don't know what "density of space" means, do you just mean the amount of space between bits of matter/energy? Anyway there is no rule in relativity that says the space between bits of matter/energy must always contract, and remember the rule about overly speculative posts, you shouldn't be using this forum to discuss your own alternative theories.

The second is that I addressed the expansion, I will attempt to elaborate:

Take a syringe and place within it a marshmallow. This marshmallow is the infinite space contained in the universe. Stopper the end of the syringe and pull on the plunger. See the mallow expand. The amount of mallow did not change, only the space it occupied, only its density.

Even this analogy contradicts your premise that space can only contract in the presence of energy.

In a system of maximum entropy, the magnitude of energy should be equal throughout yes?

Not necessarily, for gravitational systems a clumped state might have a higher entropy than an evenly-distributed one, although I don't think physicists have an agreed-upon definition of gravitational entropy in general relativity (but at least in Newtonian physics, if gravity is significant the maximum-entropy state for a collection of particles in a giant box would not consist of a perfectly even distribution).

Still, we can just substitute "matter/energy is evenly distributed" for "maximum entropy" and continue from there...

If you have a law that contracts space by magnitude of energy, and all magnitudes are equal everywhere, would not it contract completely?

I suppose it would depend on the exact equations relating contraction to energy distribution, but again there is no such law of contraction in relativity (you can have a universe which expands forever despite being filled with a perfectly even distribution of matter) so I don't see the point in discussing this.