Time is the fourth dimension in PHYSICS, not our universe

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candyjack
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Post by candyjack »

Sorry for the late response. I haven't had much time, and the few times that I did and I checked the website, there was some server error or another. I will summarize this post in advance by remarking that we indeed seem to be in agreement on most points.
GoldenRishi wrote:
candyjack wrote:First of all, I'd like to correct myself. I'm not sure whether or not Newton believed in determinism, but I meant Laplace. However, while we're at it, Spinoza is probably a way better example. Spinoza's Ethica provides an a priori deduction for determinism. The claim that physics is more fundamental than metaphysics implies that the soundness of even those a priori arguments is altered by empirical data, but this is simply not how philosophy works. Empirical data might inspire arguments, but in order to refute Spinoza, you'll have to tackle his arguments.
That depends on what you mean by "refute." If you mean to "refute" in the sense of providing a counter argument to Spinoza's claim that deductively proves Spinoza wrong with a valid polysyllogism, then no, science isn't going to refute Spinoza. That's not the level at which science would attack Spinoza's thesis. But if you mean to question whether or not science can provide enough empirical data so as to make Spinoza's thesis entirely unreasonable in the sense of almost certainly being wrong, then no, I wouldn't, anymore than I'd need to carefully know the arguments of a Biblical literalist's interpretation of the Bible to refute them with the sole knowledge that evolution is true. However, there's two important issues:

1.) There is a caveat, however, which is important for reading Spinoza before declaring him (or anyone else) to be wrong, and that is the issue of how specific Spinoza's definitions might be or how broadly we construe Spinoza's sense of determinism. If Spinoza used the term "determinism" in a more general sense, then perhaps the deterministic evolution of a wavefunction in QM would be sufficient to make his definition of determinism valid. If that's true, then I don't necessarily have anything to say against his argument.
A deterministic evolution of a wavefunction is indeed be what his metaphysics would translate to. As far as I know, notions of determinism less general than this do not lie in the domain of metaphysics.
GoldenRishi wrote: 2.) I think this gets back to the what you're really trying to get at, but I tend to reject the notion of a priori synthetic statements. Admittedly my readings of metaphysics have been more limited than many other areas of philosophy, but it seems to me that any claim about the nature of reality that comes from pure thought alone is always suspect. For two thousand years people thought that they might make progress in understanding the world around them in this manner, and for two thousand years they failed. Which is not to say that you can't gain insight into the nature of the world by thinking, but the thinking should at least be tethered to corroborated facts of the matter. If this is what is meant by "inspired", then we're in perfect agreement. But if you mean that we can rationally deduce certain synthetic propositions that can never be rendered false by our experience or by an experiment, then I'm all ears on what such a proposition would look like or how one could rationally deduce it with such certainty. I won't go so far as to say such a thing could never done, but I must admit that I'm nonplussed on how anyone could provide such a justification which didn't amount to it actually being an analytic statement.
It is indeed the former that I was talking about. I don't believe we can rationally deduce undeniable synthetic propositions either.
GoldenRishi wrote:
candyjack wrote:
GoldenRishi wrote: [...]

As for the Bell Inequality and the Kochen-Specker theorems, no they are not proofs against determinism, of course, but they add the compounding certainty that determinism is not a tenable position. Technically speaking, there are very old proposals such as Bohmian mechanics which replicates some (it's unknown if it replicates all) of the predictions of QM, but remains deterministic because it contains non-local hidden variables. But it appears to fail to work under any incorporation of relativity, however, and so physicists became very uninterested in it.
In response to the findings of Heisenberg and Bohr and the role of randomness it implied, Einstein hypothesized a hidden variable which could be used to predict the wave-function collapse nonetheless, and of which we simply weren't aware. With this as a possibility, determinism still didn't seem disproven. The reason I brought up the Bell and Kochen-Specker theorems is because they seemed to exclude Einstein's hidden variable.
No, they don't disprove them. All theorems start with assumptions, and the theorems are only as wide-ranging as their assumptions are. In the case of the Bell's Equalities and related theorems, they assume:

There is a deterministic theory with local hidden variables.

If so, then Bell's Inequality cannot hold. Thus, given that the experiments corroborate Bell Inequality to probability P (They aren't entirely experimentally proven yet, but for the sake of argument let's say that they were, so that one can be 99.9999999% sure that Bell's Inequalities hold), then the belief that our universe is deterministic and local holds to .00000001%. In other words, it's a very unreasonable belief.

We can't be 100% sure through experiments, but for the sake of the argument, let's suppose that we could be. If so, then we can be 100% sure that determinism with local hidden variables is false. So most people who want to play this game, although it hasn't gotten them anywhere, instead rely on something like Bohmian mechanics, which makes use of non-local hidden variables.
This is what I find so deceptive. Since the assumption must clearly be rejected, one might feel seducted to simplify the conclusion to "determinism is not true," but the assumption, specifically, was that there is a deterministic theory i.e. a that it can be described by physics, and the only conclusion that can be made is that whether or not we live in a determined world, lies outside of the domain of physics.

I'm not assuming that you meant to conflate the two, but don't you agree that physicists should (if they make that claim) revise the statement "determinism is untrue" to "whether or not determinism is true, is outside the scope of physics"?
GoldenRishi wrote:
candyjack wrote: And here comes the main issue. If physics is more fundamental than metaphysics, those theorems exclude even the possibility of a variable which remains hidden, and which we'll never be able to measure. In other words: we are to make deductions about the world based on what we can and cannot measure. This relies on the hidden assumption that only that exists which we can measure.
1.) There might be hidden things that we cannot measure that nevertheless are a part of reality, sure. Cro magnon couldn't measure electrons, but electrons certainly existed. The problem is that metaphysicians aren't anymore qualified to talk about them with authority and certainty than physicists are.
Electrons are not a good example, because I'm talking about things which we will never be able to measure.
GoldenRishi wrote:
candyjack wrote:Rather than arguing that this assumption is incorrect, I'm going to take a different approach and say that the very question (i.e. whether or not there can exist more than what we can measure) lies within the boundaries of metaphysics. Thus, in order to argue for how fundamental physics is, one has to rely on metaphysics. It naturally follows that metaphysics is the more fundamental field.
I think you're changing the question. My objection lies mostly with the portion of your claim regarding "even of truth statements", not necessarily with which field is more basic/primitive/fundamental at an assumptions level. The answer to that depends on how you define these things. So if you want to do science, you have to assume a certain kind of metaphysics, then yes you have to assume certain statements about reality. As per above, in order for me to see how it could be true, however, that metaphysics would be more fundamental at a truth-statement level (i.e. metaphysics says X but observation tells us ~X, but we are obliged to conclude X because metaphysics is more fundamental), it seems to hold one-to-one correspondence with providing an a priori synthetic statement. Again, perhaps I'm misunderstanding you and that's not what you mean.
I believe that we're in agreement here. If metaphysics says X and observation tells us ~X, the first question I would ask is whether the two fields really talk about the same thing when they talk about 'X'. This is also the theme of my initial post in this thread: much confusion arises because physicists tend to take words with certain definitions, and attribute incompatible definitions to them. That was my whole issue.
GoldenRishi wrote: Perhaps you mean that philosophy can point out incorrect thinking of scientists, and that this can have important implications, and in this sense philosophy is more fundamental, including truth statements. Certainly, there's a venerable history in the philosophy of science to support this; of course, failures were also made with, e.g., positivism or mechanism. But if so, then I agree with you. One need look no further than David Hume's discussion of the Problem of Induction, which was completely ignored by physicists/natural philosophers for a century until Newton's laws and Euclidean geometry were falsified (Which prior to this were considered a priori synthetic statements) by Einstein's work and the experiments that later corroborated it. Repeating an experiment doesn't prove that the theoretical model that happens to get the prediction correct is deductively correct, and in fact if one wants to do this correctly one introduces probability theory to account for the problem of induction and one modifies their understanding of what to conclude from scientific experiments and theories. However, none of that seems to support the thesis that science cannot correct or disprove metaphysics or philosophical arguments. Philosophical arguments rely on premises just like everyone else's arguments; if science shows that the premise is wrong (or at least worth questioning), then it seems to me that philosophers have to own up to the failure of their ideas to accord with observation and experience, just like every other discipline does when philosophers point out a flawed or incoherent premise.
I'll admit that this is true. In fact, Spinoza made the same mistake of taking Euclid's geometry for unfalsifiable.

Now, I'd like to bring up the issue of time one more time. I appreciate the clarification on special relativity you gave in your other post, but I still have a problem with the idea of time as 'the fourth dimension'. First of all: it still isn't clear to me whether or not special and general relativity lead physicists to believe that it's the fourth dimension. If additional dimensions are discovered, would time necessarily come between them and the third dimension? Or can it still be separate?

If physicists do treat it as the fourth dimension, I will agree that, once again, the physical definition of 'dimension' has diverged from what we intuitively mean by the word. Here are some examples of how time seems to function in a way fundamentally different from the three << regular >> (for lack of a better word) dimensions:
  • In the << regular >> dimensions, we can freely move in any direction, or stand still, but we can only move in one way when it comes to time (namely forward), and we necessarily move that way. In addition, we can (under normal circumstances) only move through time with a certain... << velocity >> (This seems like an incorrect term, but I hope you know what I mean). This seems to have a simple explanation, namely that we as three-dimensional beings only have control over our movement in those dimensions, and not others. However, if time really works in the same way as the other dimensions, wouldn't that lead to the possibility of four-dimensional objects which can freely move through time as well?
  • The velocity with which we move in the x, y, or z directions are independent of each other (i.e. when steering perfectly, a spaceship may move as fast as he wishes in a certain direction, without it affecting his movement in other directions), but when we approach the velocity c in any direction, it necessarily leads to an increase in the << velocity >> with which we move through time. With the << regular >> dimensions, the axes are perpendicular to each other, but this behaviour leads one to suspect that time's axis has some overlap with the axes of the other dimensions.
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Post by GoldenRishi »

candyjack wrote:Sorry for the late response. I haven't had much time, and the few times that I did and I checked the website, there was some server error or another. I will summarize this post in advance by remarking that we indeed seem to be in agreement on most points.
I think so, yes.
candyjack wrote:
GoldenRishi wrote: No, they don't disprove them. All theorems start with assumptions, and the theorems are only as wide-ranging as their assumptions are. In the case of the Bell's Equalities and related theorems, they assume:

There is a deterministic theory with local hidden variables.

If so, then Bell's Inequality cannot hold. Thus, given that the experiments corroborate Bell Inequality to probability P (They aren't entirely experimentally proven yet, but for the sake of argument let's say that they were, so that one can be 99.9999999% sure that Bell's Inequalities hold), then the belief that our universe is deterministic and local holds to .00000001%. In other words, it's a very unreasonable belief.

We can't be 100% sure through experiments, but for the sake of the argument, let's suppose that we could be. If so, then we can be 100% sure that determinism with local hidden variables is false. So most people who want to play this game, although it hasn't gotten them anywhere, instead rely on something like Bohmian mechanics, which makes use of non-local hidden variables.
This is what I find so deceptive. Since the assumption must clearly be rejected, one might feel seducted to simplify the conclusion to "determinism is not true," but the assumption, specifically, was that there is a deterministic theory i.e. a that it can be described by physics, and the only conclusion that can be made is that whether or not we live in a determined world, lies outside of the domain of physics.

I'm not assuming that you meant to conflate the two, but don't you agree that physicists should (if they make that claim) revise the statement "determinism is untrue" to "whether or not determinism is true, is outside the scope of physics"?
Could you clarify what you mean by a "deterministic theory" v. "determinism"? To me that means the same thing. Do you mean that metaphysics can transcend physics in that it doesn't have to conform to any laws? That would be a most curious assertion, as this essentially is the statement that metaphysics cannot be described with propositions or otherwise.
candyjack wrote: I believe that we're in agreement here. If metaphysics says X and observation tells us ~X, the first question I would ask is whether the two fields really talk about the same thing when they talk about 'X'. This is also the theme of my initial post in this thread: much confusion arises because physicists tend to take words with certain definitions, and attribute incompatible definitions to them. That was my whole issue.
Every field in academia has highly technical set of definitions for what words mean in their field and almost without exception that deviates strongly from the colloquial usage of these words. For instance, philosophy distinguishes between a valid argument and a sound argument, between logic and reason, etc, which in everyday language we would say that they meant the same thing. One always has to translate their own personal (or their own field's) conception of words into the precise framing before anyone outside of their context will understand what they're talking about. Often times, people are lazy in how they do this (e.g. Lawrence Krauss v. philosophers on a universe that comes from "nothing"), but one should dispense with the notion that there's a preferred set of definitions attached to placeholders (words) that everyone should be subject to, least of all colloquial understandings (which are usually not incredibly imprecise but also often self-refuting).

If anything, I think that the correct argument that Lawrence should have made is that the notion of "nothing" is incoherent from the standpoint of Quantum Field Theory.
candyjack wrote:Now, I'd like to bring up the issue of time one more time. I appreciate the clarification on special relativity you gave in your other post, but I still have a problem with the idea of time as 'the fourth dimension'. First of all: it still isn't clear to me whether or not special and general relativity lead physicists to believe that it's the fourth dimension.
It does. Although traditionally we don't call it "the fourth dimension." It's one of the four dimensions, there's no special ordering for each of the dimensions. In modern notation, it's assigned zeroeth slot, so to speak, so time would be the zeroeth dimension. (i.e. the zeroeth entry of a list, then the first, second, third, etc). There's nothing deep about that, it's just nomenclature.

candyjack wrote:If additional dimensions are discovered, would time necessarily come between them and the third dimension? Or can it still be separate?
No, again, I think that's taking the statement a little too literally. Time is one of the four dimensions, there's no special ordering.

Let's take spatial dimensions as an analogy. Suppose that I have a two-dimensional surface, let's say a sheet of paper, and I draw a y-axis on the piece of paper and an x-axis on the paper. Then I have two dimensions, but there's nothing special about their naming. For instance, I could call the x-axis the first or second dimension, and vice-versa for the y-axis, It wouldn't make any difference. Also, I could tilt the paper, and now what I would call the up-down axis would be different from the paper's y-axis, it'd be a combination of the paper's x-axis and y-axis. They'd get mixed into each other because of the rotation.

Spacetime is the same general idea. Yes, you can hold a clock out and measure time rather than using a ruler like you would for spatial dimensions, and this is different, but it's much less different than you'd think. Setting aside the fact that you're using a clock to measure how much you've moved along the time-axis, the same basic facts hold. If you're moving away from me (the spacetime equivalent of a rotation, it turns out), my time and space get mixed into each other according to you. So what you call "time" and how you experience time is actually a mix of what I'm calling space and time, and the same is true for what you're calling space, it's a mix up of my time and my space. There's no "correct" time direction, it's all relative just like what you call left and right or what you call up and down.

candyjack wrote: If physicists do treat it as the fourth dimension, I will agree that, once again, the physical definition of 'dimension' has diverged from what we intuitively mean by the word.
Yes, but intuitions are deceptive and almost always wrong at a fundamental level. There's a reason why academic fields have to carefully hone their technical language, and it holds a one-to-one correspondence with the vagueness, ambiguity, and often self-refuting nature of colloquial understandings and how naively we use language on a day-to-day basis.

Mathematicians and physicists have thought about what a "dimension" is for a very long time. The notion of a "dimension" has been broadened (although in mathematics, the generalization of a dimension to include time looks quite paltry in comparison to the kinds of abstractions that physicists would call a "dimension"). Time is not exactly like spatial dimensions in every single sense, but it is exactly like spatial dimensions in the sense that it's a dimension. I think people are confused over this point, being a dimension is surprisingly trivial. The conversation that's actually interesting is what makes the temporal dimension different than the spatial dimensions, and what the implications are (as you mention below).
candyjack wrote:Here are some examples of how time seems to function in a way fundamentally different from the three << regular >> (for lack of a better word) dimensions:
  • In the << regular >> dimensions, we can freely move in any direction, or stand still, but we can only move in one way when it comes to time (namely forward), and we necessarily move that way. In addition, we can (under normal circumstances) only move through time with a certain... << velocity >> (This seems like an incorrect term, but I hope you know what I mean). This seems to have a simple explanation, namely that we as three-dimensional beings only have control over our movement in those dimensions, and not others. However, if time really works in the same way as the other dimensions, wouldn't that lead to the possibility of four-dimensional objects which can freely move through time as well?
This isn't a bad observation, in fact it's quite an important one. If we analyze the statement "What if we have four dimensions, only the sign in front of one of the terms in the Pythagorean theorem is negative, i.e. d^2 = -t^2 + x^2 + y^2 + z^2, will this extra dimension be special?", then the answer will be "Yes." After much work, you will actually derive as a consequence that if an object has mass, then it must move forward in time. In fact, all particles are "moving" at the speed of light, if you account for their "temporal velocity" (or temporal motion) in addition to their spatial velocity. By this I mean that -(time velocity)^2 + (spatial velocity)^2 = (speed of light)^2. However, massive particles have a certain amount of that momentum which is stuck in the time direction, so there's no way to make it stop traveling in time.
candyjack wrote: [*] The velocity with which we move in the x, y, or z directions are independent of each other (i.e. when steering perfectly, a spaceship may move as fast as he wishes in a certain direction, without it affecting his movement in other directions), but when we approach the velocity c in any direction, it necessarily leads to an increase in the << velocity >> with which we move through time. With the << regular >> dimensions, the axes are perpendicular to each other, but this behaviour leads one to suspect that time's axis has some overlap with the axes of the other dimensions.[/list]
This is also not a bad question, however the full answer is a bit technical. The long and the short of it is what I said before about massive particles being forced to travel in time. This means that particles momentum in space and their "momentum in time" (turns out this is their energy), are related, and it's precisely has to do with this statement about their mass (although it turns out that the relation also works for massless particles, too).
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Post by candyjack »

Thank you for your time, this has been very educative to me, and I am especially glad to learn that the seeming contradictions with the idea of time as a dimension, are all accounted for in physics. It seems that the only point on which we still differ is whether or not a theory of physics can lead to conclusions about whether or not other fields can describe a certain phenomenon (determinism, in our example). Beside that, I'm pretty content about the discussion, and I hope we can agree to disagree on that point. The problem also very quickly intermingles with the problem of definitions, as we have seen before. Maybe I'll get back to it some other time.
GoldenRishi wrote:d^2 = -t^2 + x^2 + y^2 + z^2
Are you sure that this is the correct formula, and that it shouldn't be d² = -(t * v)² + x² + y² + z² ? Otherwise, it seems that the formula can be falsified through dimensional analysis. No pun intended. :dopefish
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Post by GoldenRishi »

candyjack wrote:Thank you for your time, this has been very educative to me, and I am especially glad to learn that the seeming contradictions with the idea of time as a dimension, are all accounted for in physics.
No problem, happy to educate. 'Tis what I do for a living. =P

And yes, it's true that there are many things that you think could be a serious problem when trying to say that time is a dimension, in fact there's many more outside of this conversation that would lead a person to scratch their heads. (For instance, how does causality work if there's a relativity of simultaneity? That's a serious question that has a really intricate answer, but yes, causality still operates in SR.)
candyjack wrote:It seems that the only point on which we still differ is whether or not a theory of physics can lead to conclusions about whether or not other fields can describe a certain phenomenon (determinism, in our example). Beside that, I'm pretty content about the discussion, and I hope we can agree to disagree on that point. The problem also very quickly intermingles with the problem of definitions, as we have seen before. Maybe I'll get back to it some other time.
Yes. I still think that when a theory of physics, which has a preponderance of evidence supporting it, has the implication "X is true", then even if it's been held for a very long time that "X isn't true", one should probably accept that X is true or that it is reasonable to believe that X is true.
candyjack wrote:
GoldenRishi wrote:d^2 = -t^2 + x^2 + y^2 + z^2
Are you sure that this is the correct formula, and that it shouldn't be d² = -(t * v)² + x² + y² + z² ? Otherwise, it seems that the formula can be falsified through dimensional analysis. No pun intended. :dopefish
Well, if we insist on measuring time and space as different quantities, then yes, the formula will look like:

d² = -(c t)² + x² + y² + z²

where c is the speed of light. But what's the philosophical implication of a constant (the speed of light) that everyone can agree upon and which has units [distance]/[time]? It means that if you give me a quantity in distance, I can multiply it by this physical constant and turn it into units of time, and vice versa. What that is telling us is that intervals of distance and periods of time are basically the same thing. This tells us that there's nothing special about the speed of light, it's simply a conversion between the units we read off of a clock and the units we read off of a ruler. But that's just an accident of how we defined seconds and how we defined meters; c just acts as a conversion between these two equivalent units.

Let's take an analogous example. Suppose that we demanded that we measured the x-axis on our sheet of papers in inches and the y-axis in centimeters (Maybe for some reason we only have two rulers, one in metric and the other in imperial). Well, the formula for computing distances would now include a conversation factor between inches and cm --let's call this conversion factor "b", so b ~ .39 cm/in-- which would now take the form:

d² = (bx)² + y²


There's nothing fundamental about "b", it's just that you're using two different units in your measurements of the two axes, and Nature will remind you of that inconsistency. (If you didn't know that distances are best measured in the same units, you could do an experiment and determine b from it.) Likewise, if you demand that time is different, you're not discovering that the speed of light is anything special, per se, you're discovering that:

1.) 1 second == 299,792,458 meters

2.) Then the conversation factor in front of time, now where we use the same units for time as we do distance, then the speed of light is "1", just like b = 1 when we use the same units to measure the x-axis and the y-axis.


So then, viola, the natural form of the equation is:

d² = -t² + x² + y² + z²

Just now with the understanding that I'm not demanding that I measure time in different units than I measure distances. This is what physicists mean when they say "The speed of light is really 1".
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Post by GoldenRishi »

GoldenRishi wrote:Yes. I still think that when a theory of physics, which has a preponderance of evidence supporting it, has the implication "X is true", then even if it's been held for a very long time that "X isn't true", one should probably accept that X is true or that it is reasonable to believe that X is true.
Just to further clarify this point, I understand that there may be very complex issues regarding definitions. However I think that metaphysics is inherently limited in its ability to make claims. The only statements which it can firmly claim are ones that are analytic (e.g. "Something cannot both exist and not exist at the same time") and statements tethered to physical observations (e.g. "Time appears to exist"). Physics only makes the latter more precise. There aren't a priori synthetic statements, so we're sort of left with extrapolations from a posteriori synthetic statements and analytic statements.
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Post by KeenEmpire »

I need to get back into physics, I think.
GoldenRishi wrote:1.) 1 second == 299,792,458 meters

2.) Then the conversation factor in front of time, now where we use the same units for time as we do distance, then the speed of light is "1", just like b = 1 when we use the same units to measure the x-axis and the y-axis.


So then, viola, the natural form of the equation is:

d² = -t² + x² + y² + z²

Just now with the understanding that I'm not demanding that I measure time in different units than I measure distances. This is what physicists mean when they say "The speed of light is really 1".
The way I'm reading this, time literally is just another spatial dimension (thus, distinguishing between spatial and temporal dimensions is wrong as a matter of fact). Does that sound accurate?
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Post by GoldenRishi »

KeenEmpire wrote:I need to get back into physics, I think.
GoldenRishi wrote:1.) 1 second == 299,792,458 meters

2.) Then the conversation factor in front of time, now where we use the same units for time as we do distance, then the speed of light is "1", just like b = 1 when we use the same units to measure the x-axis and the y-axis.


So then, viola, the natural form of the equation is:

d² = -t² + x² + y² + z²

Just now with the understanding that I'm not demanding that I measure time in different units than I measure distances. This is what physicists mean when they say "The speed of light is really 1".
The way I'm reading this, time literally is just another spatial dimension (thus, distinguishing between spatial and temporal dimensions is wrong as a matter of fact). Does that sound accurate?
Yes, except that it's not a "spatial dimension." It's a temporal dimension, which means that it comes into the Pythagorean theorem with a minus sign, hence:

d² = -t² + x² + y² + z²

Otherwise, yes. Spatial dimensions only come in with a plus sign, temporal dimensions only come in with a minus sign, and this minus sign is not without consequences. Rotations mix up the spatial dimensions, as is known, and you can prove that the form that rotations take preserves the Pythagorean theorem (the all plus parts). But there's a set of "rotations" (Not angular rotations, but "hyperbolic rotations") that mix spatial dimensions and the temporal dimension, which is called a "boost." This is just a fancy name for two frames which are offset by a constant velocity, in other words one appears to be "boosted" with respect to the other.



N.B.1: General Relativity corrects all of this. Gravity, it turns out, modifies the spacetime Pythagorean theorem, which changes the notion of distance and time around massive bodies. (Well, bodies that generate a large stress-energy tensor). Which, by the way, GPS satellites actually have to account for gravitational corrections to time in order to correctly calibrate themselves.

N.B.2: Quantum Field Theory forbids the existence of a second time dimension. This relates to a property called "unitarity", which means that all probabilities of all possible outcomes must sum to 100%. If you add an extra time dimension, it violates this principle.
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