# Proof that Special and General Relativity is Incorrect

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(very rough draft, interested in feedback, just wanted to get these ideas out there)

A Formal Proof that the Theories of Both Special and General Relativity Are Incorrect

followed by

A Comparison of a Turing Machine to the Physical Universe, The Human Concept of Time, and a Critique of Special and General Relativity

by David Ephraim

Formal Proof:

Part 1 (the argument here is nothing new but sets the context for Part 2): The physical universe must consist of discrete space increments because otherwise, according to Xeno's paradoxes, movement would be impossible. To reiterate, the physical universe is not continuous in the Euclidean sense because if it were movement would be impossible.

Part 2: Consider the set U, representing the universe, which is composed of the position data of every particle in the universe. Consider the set O, representing an object in the universe, which is a subset of U. If O is moving very fast relative to other parts of U, then according to the theories of both Special and General Relativity, the time that O experiences must slow down. Given that O is a subset of U, the position data that composes O must be contained in U. Since parts of U will be experiencing fast time compared to O, there will need to be position data for O available even though this position data is being generated at faster rates for different parts of U. In order for O's time to be going slower and in order for O to be a subset of the position data available in U, the position data for O would either need to be null or it would need to sequentially have the same values as other data in U changes due to the differences in the speed of time. If the position data is null, then the object O would not exist which is a contradiction because by definition object O does exist. If the position data is sequentially the same then object O must not be moving which is a contradiction because object O is moving very fast. Thus, by reason of contradiction, Special and General Relativity are an incorrect description of the physical universe.

Discussion:

Imagine observing two theoretical universes. In the first universe, there is no correlation between anything. Observations yield no rules, nothing is predictable, and one moment is totally unconnected to the next. In the second universe, observations yield correlations between aspects of the universe . Predictions can be made and rules can be formulated to describe the universe. From the viewpoint of computer science, the second universe can be considered as a progression of data sets* which can be analyzed to find rules that govern the relationships between these data sets. Physicists have no contribution to make in the first universe. However, in the second universe, where the progression of observable data follows rules (which would be described as algorithms in computer science), physicists are delighted because they have an important role to play. The various rules (aka algorithms) that dictate the progression of the second universe can be compiled and a theory of everything (from the view of computer science, this can be considered a program that operates on the data sets presented by the universe) in the second universe can be established.

Consider that in a very broad sense our physical universe, which is comparable to the second theoretical universe, can be viewed as a computation. Further consider that the simplicity of a Turing machine, which can perform any computation, can help to clarify the fundamental properties necessary to describe the physical universe. Generally, a Turing machine can be summarized with the following parts: there is an array (the physical universe's equivalent of position), there is a set of symbols (the physical universe's equivalent of fundamental particles), there is a state of the machine (the physical universe's equivalent of the positions of all particles in space) and there are rules to be applied (which can be thought of as the laws that physics seeks to learn about the physical universe) which move the machine from one state to the next (the following positions in space of all particles in the physical universe).

Importantly for this conversation, the closest thing there is to time in a Turing machine is the application of next. There are no rules for the "pace" at which next needs to be applied - the results of the Turing machine will always be the same. This should help to clarify that for physics to describe the physical universe, time need not be considered a fundamental property. Indeed, the physical universe can be viewed as a change of states due to the application of the next function independent of the human concept of time. The human concept of time is based upon the relation of observed data to each other (i.e. the position of an hour hand in relation to the position of the sun, etc.). Without the relationships between this observable data, the human concept of time would be meaningless. Furthermore, when considering a Turing machine or the physical universe, the relationship between this observable data is created without any need for time to be a fundamental principle. Instead of the human concept of time, a fundamental property that is necessary to describe the physical universe is sequential observable data.

Given that the human concept of time is not a fundamental property of the physical universe, the Theory of Special Relativity and the Theory of General Relativity are inherently flawed. Consider what would happen to the data set that represents an object moving in space at a very fast velocity such that "time" would have to slow down relative to other objects in space which are experiencing "faster time". Either the data set that represents the slowed down object would have to have null values (i.e. it would cease to exist) or it must have a sequence of the same values (i.e. the object would not be moving at all). Since, by definition, the very fast moving object cannot cease to exist and since it is moving very fast, it is impossible that it is not moving at all.

Consider the following thought experiment which will show the inherently flawed contradictions that arise from the concept of length contraction. Suppose two massive spheres are separated by a vast distance. They have a narrow whole drilled through their cores and the wholes are linearly aligned such that a very long string can be pulled through both simultaneously. Further suppose that the string has length increments marked across its entire length. Suppose the string is pulled such that it reaches a very fast velocity - say 99.5% the speed of light. According to the theory of Special Relativity, due to length contraction the space that the string occupies between the two celestial bodies will contract immensely. But this implies that the length between the two celestial bodies would contract immensely. This is quite patently absurd. Given that one can imagine strings of different masses in this thought experiment, the force that needs to be applied to reach 99.5% the velocity of light can vary - and yet somehow any string moving fast enough can contract space and thereby pull the two celestial objects together. Einsteinian Relativity was conceived in an attempt to reconcile Gauss's equations with Classical Relativity. Philosophically, there is no logical reason that it must be possible to apply Classical Relativity to a massively smaller scale such as photons. Philosophically, just because it would be convenient from the view of formulating universal physical laws if our observations of data at one scale applied to all scales does not make it true.

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The physical universe must consist of discrete space increments because otherwise, according to Xeno's paradoxes, movement would be impossible.
Wrong right off the bat. Why should we keep reading if your foundation for your entire argument is incorrect?
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How do you deal with the enormous amount of observational evidence that supports relativity? Even the ionization energy trend of heavy d-block elements is consistent with Lorentz transformations and special relativity due to the relativistic mass of a very fast electron. I'm a chemistry person, I'm sure the physicists around here can come up with a much better example.

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Consider the following thought experiment which will show the inherently flawed contradictions that arise from the concept of length contraction. Suppose two massive spheres are separated by a vast distance. They have a narrow whole drilled through their cores and the wholes are linearly aligned such that a very long string can be pulled through both simultaneously. Further suppose that the string has length increments marked across its entire length. Suppose the string is pulled such that it reaches a very fast velocity - say 99.5% the speed of light. According to the theory of Special Relativity, due to length contraction the space that the string occupies between the two celestial bodies will contract immensely. But this implies that the length between the two celestial bodies would contract immensely. This is quite patently absurd. Given that one can imagine strings of different masses in this thought experiment, the force that needs to be applied to reach 99.5% the velocity of light can vary - and yet somehow any string moving fast enough can contract space and thereby pull the two celestial objects together.

You have misunderstood special relativity, and you achieve absurd results because you apply it incorrectly.

From the perspective of one of the spheres, the string will have gotten very short, and the spheres will still remain exactly the same distance apart. The space between them has not contracted, from the perspective of the spheres.

From the perspective of the string, the spheres have gotten very close together (and are no longer spherical, but contracted in the direction of the string's travel), and the string is exactly the same length as it started out.

At no point does the string pull on the spheres with any amount of force. Space appears contracted, but that does not require any force to be applied on the spheres. It's a matter of perspective.

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Why does there have to be some 1:1 matching of data? Unless that's based on the invalid Xeno paradox premise that ydoaPs already noted.

The only way to falsify a theory is to show that experiment does not match up to the theory. Any contradictions outside of that comparison only show that you have made an argument that is not self-consistent.

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Cap'n Refsmmat,

I am very confused about whether relativity states that space just appears shortened or if space actually is shortened. In general I am very confused about relativity is saying how things appear or whether there is an actual change. In my example with the spheres, if from the perspective of the sphere the length of the string shortens immensely, given that the string goes from one sphere to the other, wouldn't that mean that the spheres must also perceive the space between them as having shortened (given that the string is the physical representation of this space). In the twins paradox, the information I have seen states that for the one twin going fast time really does slowdown which is why when he returns to earth he is younger than the other twin. Is relativity dealing with perception or reality?

For anyone who is willing to help me understand this, I really appreciate it. I did not come here with an axe to grind - I came here to learn. What I wrote in my "proof" and the following discussion is simply my current understanding. I am asking for help in understanding where I have gone wrong. I sincerely want to learn and did not come here with an assumption that I am right - I just don't get it and am hoping to see where my flaws in thinking about the subject matter are.

David

To the others that replied,

Please note my response to Cap'n. I didn't come here with a notion that I am right. I sincerely want to learn. I just thought the best way to do this would to show my current state of thinking about the subject matter and asking for clarifications on where my reasoning has gone astray. Please understand that I did not come here with an intent to teach, but rather than an intent to learn. Regarding Xeno's paradox, can you please explain to me how it would be possible to get anywhere in the physical universe if you had to progress across a continuous line. To my viewpoint, if this were the case, then Xeno would be correct and getting from point A to point B would be impossible because you would always have to get half-way there first. I took this to mean that since we clearly do move in space that space must be made up of discrete "units." Where have I gone wrong?

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I am very confused about whether relativity states that space just appears shortened or if space actually is shortened.

This question is somewhat deeper than you might think.

We like to think there's some sort of absolute reference frame. By "absolute reference frame," I mean some what of measuring the "real" distance between objects, or the "real" velocity of a rocket, or the "real" time between two events. We like to think there's some correct number for the length of a string or the distance between two stars, and if that number varies because of length contraction, it's some sort of illusion or deviation from the "real" value.

That concept is misguided, because there is no absolute reference frame. And if there's no absolute reference frame, there's no difference between space appearing to be shortened and space actually being shortened, because the only way to tell if space is shortened is to look at it and see if it appears to be shortened.

Relativity inevitably means you will get different values from different observers. One observer will say a distance is one light year, and the other will say it's a half; one observer will say one year has passed, and the other will say 40,000 have passed. It's not that one is right and one is wrong. They're both reporting exactly what the available data tell them.

In my example with the spheres, if from the perspective of the sphere the length of the string shortens immensely, given that the string goes from one sphere to the other, wouldn't that mean that the spheres must also perceive the space between them as having shortened (given that the string is the physical representation of this space).

No; the string will shorten because it is moving. The space between them won't do anything interesting, I don't think.

In the twins paradox, the information I have seen states that for the one twin going fast time really does slowdown which is why when he returns to earth he is younger than the other twin. Is relativity dealing with perception or reality?

In this example, it is indeed reality. The older twin will have aged more than the younger twin according to every atomic clock you can devise, every biological test you can conceive of, and every perception you can ask them about. Relativity isn't just about broken clocks.

For anyone who is willing to help me understand this, I really appreciate it. I did not come here with an axe to grind - I came here to learn. What I wrote in my "proof" and the following discussion is simply my current understanding. I am asking for help in understanding where I have gone wrong. I sincerely want to learn and did not come here with an assumption that I am right - I just don't get it and am hoping to see where my flaws in thinking about the subject matter are.

I certainly appreciate this. We ordinarily get members who don't want to learn at all, but want to argue with us constantly, so we get a bit defensive by reflex.

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Cap'n Refsmmat,

I am very confused about whether relativity states that space just appears shortened or if space actually is shortened. In general I am very confused about relativity is saying how things appear or whether there is an actual change. In my example with the spheres, if from the perspective of the sphere the length of the string shortens immensely, given that the string goes from one sphere to the other, wouldn't that mean that the spheres must also perceive the space between them as having shortened (given that the string is the physical representation of this space). In the twins paradox, the information I have seen states that for the one twin going fast time really does slowdown which is why when he returns to earth he is younger than the other twin. Is relativity dealing with perception or reality?

For anyone who is willing to help me understand this, I really appreciate it. I did not come here with an axe to grind - I came here to learn. What I wrote in my "proof" and the following discussion is simply my current understanding. I am asking for help in understanding where I have gone wrong. I sincerely want to learn and did not come here with an assumption that I am right - I just don't get it and am hoping to see where my flaws in thinking about the subject matter are.

David

To the others that replied,

Please note my response to Cap'n. I didn't come here with a notion that I am right. I sincerely want to learn. I just thought the best way to do this would to show my current state of thinking about the subject matter and asking for clarifications on where my reasoning has gone astray. Please understand that I did not come here with an intent to teach, but rather than an intent to learn. Regarding Xeno's paradox, can you please explain to me how it would be possible to get anywhere in the physical universe if you had to progress across a continuous line. To my viewpoint, if this were the case, then Xeno would be correct and getting from point A to point B would be impossible because you would always have to get half-way there first. I took this to mean that since we clearly do move in space that space must be made up of discrete "units." Where have I gone wrong?

You need to read and study a good book on relativity. There are many. One good one is Wolfgang Rindler's Essential Relativity, Special, General and Cosmological. An Introduction to Special Relativity, also by Rindler is another good one.

Xeno's "paradox" (there are at least three but my comments apply to all of them) is not a paradox at all but simply an example of faulty logic. It is quite possible to add up infinitely many positive quantities and get a finite number. This is exactly what is needed to resolve the usual Xeno's paradox.

1/2 + 1/4 + 1/8 + .... = 1

So if you walk at a speed of 1 ft/sec towards a wall, starting from 1 foot away you cover 1/2 ft in the first 1/2 second, cut the remaining distance in half in the next 1/4 sec cut it in half again in the next 1/8 sec etc. So you reach the wall in 1/2 + 1/4 + 1/8 + ... = 1 seconds just as you would expect.

To see that 1/2 + 1/4 + 1/8 + .... = 1 you note that

$\displaystyle \sum_{n=1}^N x^n = \dfrac {x-x^{N+1}}{1-x}$

For $x=\frac{1}{2}$ this becomes

$\frac {1}{2} + \frac {1}{4} + ... + \frac {1}{2^n}$ $= \dfrac { \frac {1}{2} - \frac {1}{2^{n+1}}}{1-\frac {1}{2}}$

And $\displaystyle \lim_{n \to \infty} \dfrac { \frac {1}{2} - \frac{1}{2^{n+1}}}{1-\frac{1}{2}} = 1$

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Xeno's "paradox" was defeated back in the days of Aristotle. It ignores, well, everything about motion. As the distance decreases, the time need to traverse said distance, given a constant speed, also decreases. It also ignores the mechanics of walking-the gait is more or less constant rather than decreasing by half with each step.

Xeno also didn't know about calculus.

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Are we in a shared universe or are we each in our own universe? And if we are each in our own universe, if each of our perspectives can be both absolutely correct and yet completely different, then what are we to make of the very clear indications that we occupy the same universe - are we not to agree that two objects cannot occupy the same place in space? I read the first several parts of Einstein's paper on Special Relativity and as far as I can tell, my thought experiment involving the spheres and string is very comparable to the types of thought experiments Einstein discussed with rigid rods. Can you please explain in more detail why if the string that goes between and through the two spheres shortens in length, how this can not mean that the two spheres would need to have the length between them shorten (considering the string is a viewable physical representation of the distance between the two spheres). I feel like I sensed the slightest bit of hesitation in your previous reply when you qualified your answer with an "i think" at the end. I sincerely appreciate your patience in helping me to understand this.

ydoaPs,

My point was exactly that Xeno's paradox was incorrect - I was absolutely not saying it is correct. My point was a philosophical one relating to the physical universe and I am certainly not the first to point it out (I mentioned this so as not to claim like it was a new discovery or taking credit for something that was thought of long ago). All I was getting at was the idea that, at least as far as I can tell, the physical universe must consist of discrete units of space because otherwise motion would be impossible. That is assuming you need to get to points in a sequential order along a line, something I assume implicitly - if the line contains infinite points, one can't get very far (technically nowhere) because you need to get between here and there first (a recursive notion that goes on forever). This is why I argue that surely the concept of a line as one made of continuous and infinitely many points could not be a proper representation of the physical universe and therefore that space must consist of discrete units. Regarding the topic of calculus or any other field of mathematics, just because a math can be formulated that is intrinsically consistent and correct does not mean that actually is an exact description of our physical universe.

Rocket, notice that in your proof you suggest that you start out walking at a pace. If you assume you are walking at a pace, then you are already covering distance and the discussion of how to travel between two points is mute because you already assumed this traveling is possible in the first place simply by providing a pace. I am not an advocate of Xeno's paradox - it certainly does not apply to our physical universe as can be evidenced simply by moving in space. My point is that if our physical universe was constructed of lines in which every line segment has an infinite number of points between them, then Xeno's paradox would apply. The fact that we can move is a philosophical proof that the physical universe must consist of discrete units of space (regardless of how very tiny they are and regardless of how for most practical purposes we can simply consider that for most typical purposes, the concept of a line as described in Euclidean Geometry is all that is needed to perform calculations in physics)

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That is assuming you need to get to points in a sequential order along a line, something I assume implicitly - if the line contains infinite points, one can't get very far (technically nowhere) because you need to get between here and there first (a recursive notion that goes on forever). This is why I argue that surely the concept of a line as one made of continuous and infinitely many points could not be a proper representation of the physical universe and therefore that space must consist of discrete units.

But what if that assumption is wrong? One can restate this: if you need to get to points in a sequential order along a line, and there are an infinite number of points, then you can't get anywhere. Since we do get somewhere, there is a contradiction. But you have assumed the contradiction is in the infinity of points, rather than the need to access them sequentially. Not a valid conclusion.

If one can show independently that having an infinite number of points is OK, then the contradiction must lie in the other assumption.

Regarding the topic of calculus or any other field of mathematics, just because a math can be formulated that is intrinsically consistent and correct does not mean that actually is an exact description of our physical universe.

Quite. That's why you need experiment to disagree with theory in order to falsify it.

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Swansont,

So then, are points on a line accessed in a non-sequential manner by someone who is walking along the line?

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Swansont,

So then, are points on a line accessed in a non-sequential manner by someone who is walking along the line?

That's a false dilemma.

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I am lost. What is a false dilemma? Also, I thought you were suggesting that that if you need to get to points in a sequential order along a line was the part of the initial assumption that was wrong. What part is wrong?

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I am lost. What is a false dilemma? Also, I thought you were suggesting that that if you need to get to points in a sequential order along a line was the part of the initial assumption that was wrong. What part is wrong?

Yeah, I don't know what's going on here either.

Swansont: Is this an equivalent example? "if you need to count using a subset of rational numbers, you need to list the subset sequentially, but there are an infinite number of rational numbers between any distinct 2, so it is impossible to count using a subset of rational numbers". The fault here is only with the final conclusion.

Using rational numbers as an analogy for moving along a line with an infinite number of similarly distributed points, I'd say the following are true:

- Any non-zero movement will require moving through an infinite number of points. Therefore, any movement from one point to any other point will require passing through (infinitely many) other points.

- The points are well-ordered and will be passed through in-order (ie. you'll never pass 2 points in the wrong order).

Obviously then, there is no need to "count" the points you pass through, in order to pass through them. To count "1, 2, 3" or to draw a line with a ruler, I don't need to be aware of all the infinitely many points in-between, to be able to pass over them.

It would be impossible to sequentially list all of the rational numbers between any other 2, I think. Thus it would be impossible to sequentially list all the non-discrete points anything moves through.

But that doesn't mean that all the infinite points in-between don't exist, or similarly that "physical space must consist of discrete units".

I think the main confusion is with the ideas of sequential vs in proper order, which aren't the same.

Edited by md65536
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I am lost. What is a false dilemma? Also, I thought you were suggesting that that if you need to get to points in a sequential order along a line was the part of the initial assumption that was wrong. What part is wrong?

You're presenting two alternatives: that we progress either sequentially or nonsequentially along an infinite series of points. The crux of the argument appears to be that you can't move along an infinite number of points. What if that isn't a good model of motion? The motion also requires an infinite number of "instants" of time. The infinities do not matter — they will cancel out.

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Baryon, Swanson, and anyone else who will help,

Alright, this is quite fascinating for me and I really appreciate your help. I accept the idea that there may indeed be infinite points in space and that it may be essentially possible to jump from one point to another (part 1 of the proof is flawed), but doesn't part 2 hold water anyways. If time is going slower for object A than for object B (because object A is moving fast relative to B), both of which are part of universe U, doesn't this mean that there must be positional data sets available for object B at which object A would be forced to have either null values or sequentially the same values? And aren't the inherent contradictions of both of these possibilities, that object A either does not exist (contradiction is object A does exist) or object A is not moving (contradiction is that object A is moving fast relative to B which is why it's time is slower) still proof that Special and General Relativity are incorrect?

Edited by SeekingToUnderstand
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AFAIK it's not a problem. Infinities are weird; even though there are an infinite number of point in one meter and an infinite number in ten meters, one can still map them one-to-one. It's only an issue of you have infinities of different sizes (e.g. the real numbers vs natural numbers)

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swansont and anyone else who might be of assistance,

I have been considering this point you make about the mathematical definitions that Cantor developed for comparing different types of infinity, specifically as it relates to line segments. In a deep sense, Cantor is correct that any two line segments have equivalent amounts of infinity, for if you zoom in or zoom out on a line segment, one can see that any line segment of any proposed length has the same internal relationships of all of its parts to itself (in this sense, when thinking about infinity in this relational way, the specific values for the endpoints are quite irrelevant and quite meaningless). However, if one does not have the option to zoom in or zoom out on the line segment, say because there is another line segment to be considered because both are measured in the same units. In this case, a line segment of length one clearly cannot contain an exactly equal amount of points as a line segment of length 10 (Since one could place the small line segment on top of the long line segment which necessitates a one-to-one mapping and the long line segment would still have a length of 9 which is not covered by the small segment). In the physical universe (which is not just a single line segment), but deals with line segments of a set unit and the relationship between line segments and everything else in the universe, I would argue that Cantor's notion of comparing infinity is not adequate. In physics, I believe the values of the end points of a line segment are crucial in comparing the number of data points contained therein explicitly because physics has the inherent practical purpose of comparing things in the universe. Just as the values of the end points matter, I would argue that the density of data points contained therein matter as well. So, if time slows for one object relative to another, then there cannot be pragmatic (for comparison in the physical universe) one-to-one mapping unless the second part of my proof holds true. And if one asks why it matters if there is a one-to-one mapping of data points (what does it matter if the object going slower in time has a null value for some data points), I would argue that the very ability of physics to make comparisons at a very fundamental level is attacked if one accepts null data. This is a very real shortcoming of Special and General Relativity because a primary goal of physics is to make comparisons at any level and an acceptance of null data muddies the waters in which to make those comparisons. In this sense, Special and General Relativity is at the very least contains major shortcomings (and at the most is simple incorrect).

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I think you might be caught up in some cyclical reasoning.

Yes, if space is quantized, you probably can't divide an arbitrarily small length into an infinite number of parts, which implies that space is quantized.

But if space is continuous, you can divide it so, which doesn't imply that space is quantized.

I think you're taking aspects of your conclusion, putting it into your assumption.

Also... (not sure if I got this right but...) does your Turing machine require that you can record the state of the entire universe at a single time? I don't think this makes sense or is possible, because there is no universal instants of time (due to relativity of simultaneity). If GR says the machine is impossible, then explaining its working function won't disprove GR; proving that the machine is possible would.

Edited by md65536
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md65536,

I need to think about the cyclical reasoning, but regarding the Turing machine recording the state of the entire universe at a single time - yes this is definitely a fundamental part of the machine I am describing. Choose any observer's point of view (irregardless of whether one observer's view is any more correct than any other observer's point of view). For a randomly chosen observer, shouldn't there be a complete set of data describing the positional state of the universe because at that moment for that observer isn't his position compared to every other particle in the universe fixed, thus providing a complete positional data set for said observer. Philosophically restated, from the point of view of any observer (pick whatever one you want) doesn't the entire universe exist at once? If so, let this observer's position data about the universe be provided to the Turing machine for the current state. And if there is not a complete set of data for any particular observer, exactly what does this imply about the universe - doesn't the very idea of the existence of a universe for any given observer imply a complete data set for that observer?

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md65536,

I need to think about the cyclical reasoning, but regarding the Turing machine recording the state of the entire universe at a single time - yes this is definitely a fundamental part of the machine I am describing. Choose any observer's point of view (irregardless of whether one observer's view is any more correct than any other observer's point of view). For a randomly chosen observer, shouldn't there be a complete set of data describing the positional state of the universe because at that moment for that observer isn't his position compared to every other particle in the universe fixed, thus providing a complete positional data set for said observer. Philosophically restated, from the point of view of any observer (pick whatever one you want) doesn't the entire universe exist at once? If so, let this observer's position data about the universe be provided to the Turing machine for the current state. And if there is not a complete set of data for any particular observer, exactly what does this imply about the universe - doesn't the very idea of the existence of a universe for any given observer imply a complete data set for that observer?

I see. I'd misunderstood.

But then why don't you record time using the specific observer's clock? It doesn't matter what rate other clocks are ticking at. If the observer has a working clock -- whether or not it is physically quantized -- it should provide a fixed rate at which to record location data for everything else.

Why would timing and position data be "according to an arbitrary observer" and yet "position data is being generated" according to another object's modified clock? It seems to me that if you're talking about data that is specific to an observer, the position data of other objects is specific to and valid for that observer, according to the observer's timing.

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Yes, as you stated, the arbitrary observer should have their set of the universe's position data generated according to their own clock - I didn't intend to suggest otherwise. So what exactly then is meant by SR and GR when it states that when an object moves fast relative to the arbitrarily observer, the arbitrary observer (who has his own valid clock) sees that the fast moving objects time has slowed down? To the arbitrary observer, his own time is the time, and the position of the fast moving object exists for each moment at his time. Does this mean the arbitrary observer views the fast moving object's atoms as jiggling slowly - would this mean the arbitrary observer would view the fast moving object as having a low thermal energy?

Part of my difficulty in discussing the subject matter with clarity is that Einstein in my opinion really never gave a definition of time - to me, he basically sidestepped the issue by discussing clocks. Therefore, I am trying to understand the meaning of SR/GR when it states that the arbitrary observer sees a fast moving object as having slower time. To the arbitrary observer we have been discussing, his time using his clock is the time and the notion that he views an object of having a slower time is something I need clarification on.

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To quote swansont: Time is what clocks measure.

Suppose there is an observer with a clock and a spaceship with a giant clock on its outside, so the observer can watch it. The spaceship blasts past at near the speed of light, and the observer notes how fast the clock moves. He will note that the clock on the spaceship appears to be ticking rather slowly.

That's what SR means when it talks about time dilation.

An example: The Hafele-Keating experiment loaded atomic clocks on airliners and flew them around the world a few times. When they returned, they were compared with a stationary clock at the US Naval Observatory, and it was discovered that the clocks were no longer synchronized. Time had elapsed differently for the clocks on the airplanes.

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment

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There are many clocks that tick slowly. How do you decide when this means that time is moving slowly and how do you decide when this means that the clock is broken?

In the context of the previous conversation regarding an arbitrary (randomly chosen) observer. If the observer has his own clock and sees that the clock on the spaceship is slow, shouldn't the observer come to the determination that the spaceship's clock is broken? And if the observer suspects that this is not a "typical" case of a broken clock, shouldn't the observer be able to look to the underlying mechanics of the clock to determine what is going on? Isn't it vital to be able to determine if a clock is only representative of itself or if it is representative of the system in which it is in. This is the deeper meaning of time that I am trying to understand and am asking for help in understanding.

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