Let's say you take the Earth and put a road around the equator of the Earth so that you could drive around it. Now you set your cruise control for say 200mph.
Then let's say we take the Earth and everything on it and copy it and then divide all mass by 1/2 and put it in a parallel dimension; so we have two existing representations of Earth and you are going 200mph in each Earth and each Earth experiences the exact same occurrences. So an observer on both Earths experiences the same things.
Assumption: Time is linear.
Implications of assumption: If time is linear and both Earths have the exact same experience, then you must be going the same speed on both Earths because speed is dependent on time.
Problem: From the bigger Earth's perspective, the car on the smaller Earth is traveling at a smaller speed. And from the smaller Earth's perspective, the car on the bigger Earth is traveling at a greater speed, but they are experiencing the exact same realities from their perspectives, but have different relative speeds, suggesting a distortion between how time is perceived in one versus the other. So how do we interpret this? And is this the basis for Einstein's theory of relativity?
I want to say that this proves that time can't really be linear, or perhaps is relative. What would you say?
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06122010, 08:28 PM #1
How would you solve this problem?

06122010, 08:36 PM #2
If by 1/2 mass you mean that the second earth is smaller in volume (and smaller in circumference), then the two cars (if they indeed circumvent both earths at the same rate due to the fact that observations on each are identical) would have to be traveling at different speeds. The car on the smaller earth would be traveling more slowly that the car on the bigger earth. The only difference would be in the way each earth defines mile, thus leading to a difference in their definitions of mph.

06122010, 09:32 PM #3
There are some mistakes with your problem, but am I right to assume your problem is this?
You have two clocks, both tell time perfectly and are exactly the same.
You put one clock in a fixed point in space you call point A. The move the other clock at high speed, half the speed of light in fact, in a variable point in space (moving) called B.
Point B appears to be moving away from point A. From A's point of view, the clock in point B is ticking slower than the clock in point A. This is a fact, I'll show proof down the post as to why. So if that's a fact you assume that from point B's perspective the opposite is true. (That B sees A ticking faster.)
But let's alter the rules a little bit and assume the previous variable point in space called B. is the fixed point in space, and the previously fixed point in space is actually moving away from point B just in opposite direction. Because relativity is relative like that. :p and what is a fixed and what a variable point of space is entirely up to us to decide.
Then it is true that, clock A is now appearing to go slower to clock B from it's own perspective. And clock B is appearing to go faster than clock A from clock B's perspective. So the exact opposite from our previous assumption. And I assume that is the 'problem' you intend to solve.
Both can't be possible, yet the assumption is that they are simply because they must. So what is at work here?
The problem lies in the assumption that if A sees B moving at a different timespeed, then B would see A at the opposite timespeed. This is however not actually actually happening.
Both A and B see the other's time move at a slower speed. A sees B moving slower. B sees A moving slower. And the opposite is that if they weren't moving apart, but one back to the other at half light speed (or both at quarter of light speed). Then A sees B moving faster and vice versa. Until they are back together and note the exact same times again. Also, both have experienced the exact length of time and experienced and observed the same thing.
The key to understanding is that when we observe an object, we do not observe the object's actual present time and space, but rather the light reflecting from that object which travels at light speed until reaching our observing eyes.
So if an object travels towards you at half light speed, and emits his light at light speed. We observe his light coming in faster than it is actually traveling. As we see more light in a shorter time span.
Time is relative, yes. In fact, time is so relative, that it doesn't even exist other than in the sense we use it to identify and measure. And your 'problem' is not really a problem. You're just imagining it.~Selfdepricating Megalomaniacal Superwolf

06122010, 09:36 PM #4
My question is when did the two Earths become differently sized? Also, when you say smaller and bigger in relation to an object it's best to define what about the object is bigger or smaller: mass or volume.
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06122010, 10:59 PM #5
Yeah, volume. I forget that mass is directly related to gravity and isn't defining the 'existence' of an object in terms of its space. Yeah, I suppose that's the right way to look at it. But I was concerned with how an observer would compare the two in terms of speeds, meaning one definition would have to be used to for both and that they both would then have to have the same speed.
So would an object that is moving away from what we consider a stationary observer be perceived as accelerating no matter what supposed constant positive velocity it has? I hope that makes sense. And now I'm really confused because I'm not sure I was thinking the same thing.
I was trying to imagine if it is true that the smaller an object gets that the faster its time moves relative to an object that is bigger that it comprises of. So it would be like the bigger object is taking 'more time' compared to the smaller object's 'time' if we were to create units of time and compare them against both objects. This would be because both are supposed to be occurring simultaneously, whilst the distances become unimportant because they experience the same occurrences, even though one appears slower to the other. If we apply this to matter...I know what I'll do. I'll draw a picture.
See if we imagine the smaller circle that makes up the bigger circle as experiencing the same onedimensional reality as the bigger circle, then this is what confuses me. They both have exactly the same experiences, but one is moving faster relative to another from an external observer. And the smaller you get, the slower you appear to your larger starting point. If you got to the middle of the circle, it would be like dividing by zero or not having a time to begin with; an unexplainable state in the middle. It just doesn't make sense to me. Does anyone know what I'm talking about? lol.
Yeah, volume.

06132010, 12:15 AM #6ReflecTcelfeRGuest
It's the distance itself that is creating the problem. It is only perceived as slower because of the distance between them.

06132010, 12:19 AM #7ReflecTcelfeRGuest
But your original example only includes two objects that are moving, not the third which is 'stagnant'. It doesn't really change my statement, but excludes it.

06132010, 02:27 AM #8
But the smaller circles are moving slower if they have the same angular velocity as the larger ones. But, slower movement through space does not imply slower movement through time. If both are experiencing the same things, then a person in the inner ring wound age at the same rate as a person on the outer ring (should we consider the circles to actually be earths in orbits). A year is still one rotation, and since both earths make a single rotation in the same amount of time, then both earths experience a "year" within the same timeframe.

06132010, 06:14 AM #9
Clearly not, I don't see how your example would affect time, let alone create the illusion of affecting time. Unless the observers aren't aware of some of the size implications.
Only by assuming all the earths are exactly the same size, would they appear to be moving at different time speeds. But in reality, they are of different size, experience the same time but move at different velocities.~Selfdepricating Megalomaniacal Superwolf

06132010, 06:36 AM #10
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The experience on both earths is not the same. One has more volume, thusly it would invariably take longer.
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