Miracles

[seer]

Basically, yes. The closer you get to the speed of light relative to other objects, the shorter the distance between those objects, from your perspective. At the speed of light, you would see no distance between the objects.

But the speed of light is not instant. It would still take time for me to move from the earth to the sun - so I couldn't be standing on both the sun and the earth at the same moment.

[seer]

It would seem so to you.

What would it seem to me? That I was standing on the earth or standing on the sun?

[JonathanL]

What would it seem to me? That I was standing on the earth or standing on the sun?

Yes.

[Boxing Pythagoras]

What would it seem to me? That I was standing on the earth or standing on the sun?

Both, at the same time. And every point in between those two destinations along your trajectory, as well.

As relative velocity increases, the relative experience of distance decreases (length contraction) and the relative experience of time increases (time dilation). In both cases, the speed of light forms an upper boundary-- in fact, it causes a singularity in the case of time dilation. As velocity goes to the speed of light, the relative distance between the object and those points which lie ahead of it along its velocity vector goes to zero. Similarly, as velocity goes to the speed of light, the relative elapse of a tick of time tends towards infinity. Particles which travel at the speed of light follow a null geodesic through 4-Dimensional spacetime. They literally do not experience time or distance.

So, if another observer on the Earth was watching your journey, from her frame of reference it would take 8 minutes for you-- traveling at the speed of light-- to traverse the distance from here to the Sun. However, from your own frame of reference, the journey would be instantaneous, and you would have simultaneously occupied all points along the path of your travel.

[Yttrium]

But the speed of light is not instant. It would still take time for me to move from the earth to the sun - so I couldn't be standing on both the sun and the earth at the same moment.

From the perspective of the Earth and Sun, it would take you time to move from one to the other. But from your own perspective, it would take no time at all. You would experience no time and no distance.

[seer]

So, if another observer on the Earth was watching your journey, from her frame of reference it would take 8 minutes for you-- traveling at the speed of light-- to traverse the distance from here to the Sun. However, from your own frame of reference, the journey would be instantaneous, and you would have simultaneously occupied all points along the path of your travel.

So which frame of reference is actually correct? Mine (the traveler) or the other observer? If it is both, wouldn't that be a contradiction - both A and not A? And wouldn't this make time irrelevant. I mean what is time if it can be so easily dismissed?

[Boxing Pythagoras]

So which frame of reference is actually correct? Mine (the traveler) or the other observer? If it is both, wouldn't that be a contradiction - both A and not A? And wouldn't this make time irrelevant. I mean what is time if it can be so easily dismissed?

Both are correct. It's not a contradiction, though. One case is the time which passes with respect to the observer on Earth. The other case is the time which passes with respect to the observer traveling to the Sun. Neither case involves "dismissing" anything. Time can only be measured with respect to the particular observer performing the measurement.

Incidentally, we have extensive experimental verification of this phenomenon. In fact, every time you use GPS, you make use of this fact of Relativity. GPS satellites determine your position by keeping track of time on very accurate atomic clocks. However, because those clocks are measuring time in a different reference frame than clocks on the face of the Earth, they measure elapsed time differently. Their velocity relative to the surface of the Earth causes a bit of time dilation, while their position in a relatively weak gravitational field causes a significant amount of time contraction. As such, we have to account for the difference in those clocks mathematically in order for them to report the same time as a clock on the surface of the Earth. The contraction due to General Relativity amounts to about 45 microseconds per day, while the dilation from Special Relativity amounts to about 7 microseconds per day. Altogether, GPS clocks run about 38 microseconds faster per day than clocks on the surface of the Earth.

That may not sound like a lot, but it makes a HUGE difference in calculating positions. If left unaccounted for, after a few weeks, your GPS would think you are several miles away from your actual location.

[seer]

Both are correct. It's not a contradiction, though. One case is the time which passes with respect to the observer on Earth. The other case is the time which passes with respect to the observer traveling to the Sun. Neither case involves "dismissing" anything. Time can only be measured with respect to the particular observer performing the measurement.

But this is a contradiction. Either it take 8 minutes to travel to the sun or I do it in an instant. And time would disappear - there is no time for me, the traveler.

[Boxing Pythagoras]

But this is a contradiction. Either it take 8 minutes to travel to the sun or I do it in an instant. And time would disappear - there is no time for me, the traveler.

It's really not a contradiction. Once again, Time is not a single, monolithic thing which affects everything equally. It's not like the whole universe ticks forward, uniformly, by the same clock. Time is a dimension of measurement, and the particulars of its measurement depend on the path of the observer through spacetime. We can translate measurements of time from one reference frame into their equivalent measurement in another frame, but no single frame can be said to be "correct" while others are "wrong."

Here's an analogy. Let's say a guy in New York is talking to his sister in LA. The guy in New York says he plans on visiting Philadelphia, since it is only 100 miles away. His sister says, "Actually, Philadelphia is 2400 miles away." Who is right and who is wrong?

[seer]

It's really not a contradiction. Once again, Time is not a single, monolithic thing which affects everything equally. It's not like the whole universe ticks forward, uniformly, by the same clock. Time is a dimension of measurement, and the particulars of its measurement depend on the path of the observer through spacetime. We can translate measurements of time from one reference frame into their equivalent measurement in another frame, but no single frame can be said to be "correct" while others are "wrong."

Here's an analogy. Let's say a guy in New York is talking to his sister in LA. The guy in New York says he plans on visiting Philadelphia, since it is only 100 miles away. His sister says, "Actually, Philadelphia is 2400 miles away." Who is right and who is wrong?

But that is apples and oranges. You are saying that both the sister and the brother live in NY and to the sister Philadelphia is 2400 miles away, and to the brother it is 100 miles away. And if I am am standing both on the sun and the earth at the same moment then time, in this example, no longer exists.

[Boxing Pythagoras]

But that is apples and oranges. You are saying that both the sister and the brother live in NY and to the sister Philadelphia is 2400 miles away, and to the brother it is 100 miles away. And if I am am standing both on the sun and the earth at the same moment then time, in this example, no longer exists.

It's actually not apples and oranges. In both cases, it's simply geometry. In the case of the brother and the sister, it's a matter of two-dimensional geometry, measuring the displacement of each observer to a specific position in the spatial plane. In the case of traveling to the sun, it's a matter of four-dimensional geometry, measuring the displacement of each observer to a specific position in the spacetime manifold.

[seer]

It's actually not apples and oranges. In both cases, it's simply geometry. In the case of the brother and the sister, it's a matter of two-dimensional geometry, measuring the displacement of each observer to a specific position in the spatial plane. In the case of traveling to the sun, it's a matter of four-dimensional geometry, measuring the displacement of each observer to a specific position in the spacetime manifold.

This still does not make sense. How can I be at two places at the same moment? On the sun and on the earth? And again, if I am at both positions at the same moment, time, at least for me, no longer exists.

[Boxing Pythagoras]

This still does not make sense. How can I be at two places at the same moment?

Because position in spacetime is a function of four variables-- let's call them x, y, z, and t. So, position (0,0,0,0) is an entirely different position than (1,1,1,0) even though there's no time difference between them.

And again, if I am at both positions at the same moment, time, at least for me, no longer exists.

Time exists. It is simply that there is no displacement of time between your different positions in spacetime for that particular journey. As soon as you are at rest relative to the sun, your clock will measure time as the Sun's clock does.

[seer]

Because position in spacetime is a function of four variables-- let's call them x, y, z, and t. So, position (0,0,0,0) is an entirely different position than (1,1,1,0) even though there's no time difference between them.

I'm not sure what this means, but you still have me occupying two different positions (millions of miles apart) to the same moment. I am literally in two places at once.

Time exists. It is simply that there is no displacement of time between your different positions in spacetime for that particular journey. As soon as you are at rest relative to the sun, your clock will measure time as the Sun's clock does.

Yes, time may exist when I am again at rest, but it certainly did not exist for me as I traveled. It is not merely the displacement of time, time has no relevance, force, or influence as I travel. It may exist somewhere - but it doesn't exist for the traveler.

[Boxing Pythagoras]

I'm not sure what this means, but you still have me occupying two different positions (millions of miles apart) to the same moment. I am literally in two places at once.

Yes. In fact, in that particular situation, you would be occupying an infinite number of positions at the same moment: your position on Earth, your position on the Sun, and every position along the trajectory between these two points.

Yes, time may exist when I am again at rest, but it certainly did not exist for me as I traveled.

Yes, it did.

It is not merely the displacement of time, time has no relevance, force, or influence as I travel.

Time has no "force" or "influence," regardless of whether you are traveling at light speed or not. Time doesn't act upon anything. It does not exert any causal influence over anything.

It is no more peculiar that you can exist in many different spatial positions at the same time than that you can exist in many different temporal moments at the same position in space.