In the Welcome post I mentioned that the time machine could possibly open a "so-called 'gateway' at a fixed point in space". There have been some questions as to what that phrase would mean. One sharp individual notes:

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Of course John is right. I think, though, the problem is just semantic. Where I used the word space, I should have used the more accurate term space-time. To stick with his above example, Let's instead say that the gateway connected two points, a current location and a destination; both of which exist in space-time. It isn't enough to say the location is a hill in Buffalo. A hill in Buffalo in 2012AD is a totally different location in space-time than a hill in Buffalo in 600BC. Typically one would think of the hill in Buffalo as the location and then there is the matter of when (600BC vs. 2012AD), but, as John points out, this model doesn't seem to make sense for time travel as we want it. We have to imagine the fourth dimension as being simultaneous, not sequential; A hill in Buffalo in 2012AD and a hill in Buffalo in 600BC both exist along side each other. It helps me, when thinking about such things, to reduce all the dimensions. See the below diagram:

The three spatial dimensions are reduced down to a zero dimensional point. Therefore, the line, being one dimensional, can represent time because it has one extra dimension than a point. Point A represents a hill in Buffalo in 600BC and Point B represents a hill in Buffalo in 2012AD. Points A and B do not exist in the same "dimension" because in a zero-dimensional universe there can be only one point. The only way to have more than one point is to add at least one more dimension. Think of our three-dimensional universe the same way. Let's use "universe" to mean all that exists at any given present moment. So like the point in zero dimensions, there can only be one "universe" in three dimensions. And in the same way that the distance between two zero-dimensional points can be traversed by traveling on a one dimensional path (line), the distance between two three-dimensional universes can be traversed by traveling on a four-dimensional path (time). Here we are understanding the universe today and the universe tomorrow (or a hill in Buffalo in 600BC and a hill in Buffalo in 2012AD) as two distinct things, in the same way that two points along a line are two different things. So it's important to think of space and time as not being two independent things, but rather think of time as a sort of a fourth spatial measurement. So if we we are on a hill in Buffalo in 2012AD and want to get to what we would think of as that same hill, but in 600BC through some sort of a gateway, I guess it would mean that we'd have to somehow give our time machine coordinates and it would then connect the two "points" in space-time by bending the fourth dimension. Now look at the next diagram:

If we want to get from Point A to Point B we have to travel along the line of time; in other words, we wait. But if time is bent, the two points can be brought together and the "distance" between them made small. This would be where the gateway would happen. This is what I meant by, "a fixed point in space". It's better to say, "a specific location in space-time", or maybe better yet, refer to the gateway as a threshold that connects two specific locations in space-time.

As a footnote, we can infer by this method of thought that if time is to be bent in such a way, there must be a dimension above time for it to be bent into. The two zero-dimensional points on the one-dimensional line are brought closer to each other without affecting other theoretical points along the same line (relative to the line) by using the second dimension. So if the line is time, then the area it is bent into would be a fifth dimension. Thoughts?

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*...if we accept that the Earth rotates and moves and such, doesn't time travel also necessarily involve space travel? I mean, "a fixed point in space" is always relative. You walk into a "gateway" on a hill in Buffalo in 2012AD. Why would you expect to exit on a hill in Buffalo in 600BC (or whenever) and not be left out screaming in the "fixed point in space" where the earth is no longer at? Or caught in solid rock or some such?*"Of course John is right. I think, though, the problem is just semantic. Where I used the word space, I should have used the more accurate term space-time. To stick with his above example, Let's instead say that the gateway connected two points, a current location and a destination; both of which exist in space-time. It isn't enough to say the location is a hill in Buffalo. A hill in Buffalo in 2012AD is a totally different location in space-time than a hill in Buffalo in 600BC. Typically one would think of the hill in Buffalo as the location and then there is the matter of when (600BC vs. 2012AD), but, as John points out, this model doesn't seem to make sense for time travel as we want it. We have to imagine the fourth dimension as being simultaneous, not sequential; A hill in Buffalo in 2012AD and a hill in Buffalo in 600BC both exist along side each other. It helps me, when thinking about such things, to reduce all the dimensions. See the below diagram:

The three spatial dimensions are reduced down to a zero dimensional point. Therefore, the line, being one dimensional, can represent time because it has one extra dimension than a point. Point A represents a hill in Buffalo in 600BC and Point B represents a hill in Buffalo in 2012AD. Points A and B do not exist in the same "dimension" because in a zero-dimensional universe there can be only one point. The only way to have more than one point is to add at least one more dimension. Think of our three-dimensional universe the same way. Let's use "universe" to mean all that exists at any given present moment. So like the point in zero dimensions, there can only be one "universe" in three dimensions. And in the same way that the distance between two zero-dimensional points can be traversed by traveling on a one dimensional path (line), the distance between two three-dimensional universes can be traversed by traveling on a four-dimensional path (time). Here we are understanding the universe today and the universe tomorrow (or a hill in Buffalo in 600BC and a hill in Buffalo in 2012AD) as two distinct things, in the same way that two points along a line are two different things. So it's important to think of space and time as not being two independent things, but rather think of time as a sort of a fourth spatial measurement. So if we we are on a hill in Buffalo in 2012AD and want to get to what we would think of as that same hill, but in 600BC through some sort of a gateway, I guess it would mean that we'd have to somehow give our time machine coordinates and it would then connect the two "points" in space-time by bending the fourth dimension. Now look at the next diagram:

If we want to get from Point A to Point B we have to travel along the line of time; in other words, we wait. But if time is bent, the two points can be brought together and the "distance" between them made small. This would be where the gateway would happen. This is what I meant by, "a fixed point in space". It's better to say, "a specific location in space-time", or maybe better yet, refer to the gateway as a threshold that connects two specific locations in space-time.

As a footnote, we can infer by this method of thought that if time is to be bent in such a way, there must be a dimension above time for it to be bent into. The two zero-dimensional points on the one-dimensional line are brought closer to each other without affecting other theoretical points along the same line (relative to the line) by using the second dimension. So if the line is time, then the area it is bent into would be a fifth dimension. Thoughts?