Godel Meets Einstein : Time Travel in the Godel Universe


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What were Einstein and Gödel talking about?

Bizarre phenomena like negative energy density the Casimir effect lend their strangeness to the already odd character of time travel stories. In this article, we make a distinction between time travel stories that might be possible within the canon of known physical laws and those stories that contravene or go beyond known laws. The former type of stories, which we shall call natural time travel, exploit the features or natural topology of spacetime regions.

Natural time travel tends to severely constrain the activities of a time traveler and entails immense technological challenges. The latter type of stories, which we shall call Wellsian time travel, enable the time traveler more freedom and simplify the technological challenges, but at the expense of the physics.

For example, in H. Wells' story, the narrator is a time traveler who constructs a machine that transports him through time.

1. Introduction

Also, the journey is through some different nonzero duration of time in the world. It is the latter condition that distinguishes the natural time travel story from the Wellsian time travel story. Our laws of physics do not allow travel through a nonzero duration of time in the world in a sense that will be made clearer below. Wellsian time travel stories are mortgaged on our hope or presumption that more fundamental laws of nature are yet to be discovered beyond the current horizon of scientific knowledge.

Natural time travel stories can be analyzed for consistency with known physics while Wellsian time travel stories can be analyzed for consistency with logic. Finally, time travel stories implicate themselves in a constellation of common philosophical problems. Among these philosophically related issues we will address in this article are the metaphysics of time, causality, and personal identity. What is time travel? This definition applies to both natural and Wellsian time travel.

For example, Jane might be a time traveler if she travels for one hour but arrives two hours later in the future or two hours earlier in the past. In both types of time travel, the times experienced by a time traveler are different from the time undergone by their surrounding world. But what do we mean by the "time" in time travel?


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And what do we mean by "travel" in time travel? As the definition for time travel presently stands, we need to clarify what we mean by the word "time" see the next section. While philosophical analysis of time travel has attended mostly to the difficult issue of time, might there also be vagueness in the word "travel"?

Our use of the word "travel" implies two places: an origin and a destination. In truth, how do we conceive of a "when"—as a place, a locale, or a region?

Godel Meets Einstein Time Travel in the Godel Universe

Different scientific ontologies result in different ideas of what travel through time might be like. Also, different metaphysical concepts of time result in different ideas of what kinds of time travel are possible. It is to the issue of time in philosophy that we now turn. How is time related to existence? Philosophy offers three primary answers to this metaphysical question: eternalism, possibilism, and presentism. The names of these views indicate the ontological status given to time.

The eternalist thinks that time, correctly understood, is a fourth dimension essentially constitutive of reality together with space. All times, past, present and future, are actual times just like all points distributed in space are actual points in space. Everything is one; the appearance of things coming to be and ceasing to be, of time passing or flowing, is simply phenomenal, not real.

Objects from the past and future have equal ontological status with present objects.

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Thus, a presently extinct individual dodo bird exists as equably as a presently existing individual house finch, and the dodo bird and the house finch exist as equably as an individual baby sparrow hatched next Saturday. Whether or not the dodo bird and the baby sparrow are present is irrelevant ontologically; they simply aren't in our spacetime region right now. The physicist typically views the relation of time to existence in the way that the eternalist does.

The life of an object in the universe can be properly shown as:. This diagram shows the spatial movement in one dimension of an object through time. The standard depiction of an object's spacetime "worldline" in Special Relativity, the Minkowski diagram see below , privileges this block view of the universe. Many Wellsian time travel stories assume the standpoint of eternalism. The possibilist thinks that the eternalist's picture of the universe is correct except for the status of the future.

The past and the present are fixed and actual; the future is only possible. Or more precisely, the future of an object holds the possibility of many different worldlines, only one of which will become actual for the object. If eternalism seems overly deterministic, eliminating indeterminacies and human free choice, then possibilism seems to retain some indeterminacy and free choice, at least as far as the future is concerned.

For the possibilist, the present takes on a special significance that it does not have for the eternalist. The life of an object according to possibilism might be shown as:. This diagram shows that the object's worldline is not yet fixed or complete. It should be pointed out that the necessity of illustrating the time axis with a beginning and end should not be construed as an implicit claim that time itself has a beginning and end.

Some Wellsian time travel stories make use of possibilism. Stories like Back to the Future and Terminator suggest that we can change the outcome of historical events in our world, including our own personal future, through time travel. The many different possible histories of an object introduce other philosophical problems of causation and personal identity, issues that we will consider in greater depth in later sections of the article.

The third view is presentism. The presentist thinks that only temporally present objects are real. Whatever is, exists now. The past was, but exists no longer; the future will be, but does not exist yet. Objects are scattered throughout space but they are not scattered throughout time. Presentists do not think that time is a dimension in the same sense as the three spatial dimensions; they say the block universe view of the eternalists and the intermediate view of the possibilists gets the metaphysics of time wrong.

If eternalism has its philosophical roots in Parmenides, then presentism can be understood as having its philosophical roots in Heraclitus. Presently existing things are the only actuality and only what is now is real. Many presentists account for the continuity of time, the timelike connection of one moment to the next moment, by appealing to the present intrinsic properties of the world Bigelow.

Kurt Gödel

To fully describe some of these present intrinsic properties of the world, you need past- and future-tensed truths to supervene on those properties. For example, in ordinary language we might make the claim that "George Washington camped at Valley Forge. But, according to presentism, only presently existing things are real. Thus, the proper way to understand the truth of this sentence is to translate it into a more primitive form, where the tense is captured by an operator. It is the basis for their account of persistence through time in issues like causality and personal identity.

Since the use of the term 'time' in our definition of time travel remains ambiguous, we may further distinguish external, or physical time from personal, or inner time again, following Lewis. In the world of the time traveler, they do not. So, with these two senses of time, we may further clarify time travel to occur when the duration of the journey according to the personal time of the time traveler does not equal the duration of the journey in external time.

Most but not all philosophy of time concerns external time see the encyclopedia entry Time. For the purpose of natural time travel, we need to examine the scientific understanding of external time and how it has changed.

Time Bandits

Newton argued that space, time and motion were absolute, that is, that the entire universe was a single, uniform inertial frame and that time passed equably throughout it according to an eternally fixed, immutable and inexorable rate, without relation to anything external. Natural time travel in the Newtonian universe is impossible; there are no attributes or topography of space or time that can be exploited for natural time travel stories.

Only time travel stories that exceed the bounds of Newtonian physics are possible and scenarios described by some Wellsian time travel stories most notably like the one Wells himself wrote are examples of such unscientific time travel. Several philosophers and scientists objected to the notion of absolute space, time and motion, most notably Leibniz, Berkeley and Mach.

Mach rejected Newton's implication that there was anything substantive about time: "It is utterly beyond our power to measure the changes of things by time.

Palle Yourgrau (Brandeis University) - PhilPeople

Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things" The Science of Mechanics, For Mach, change was more fundamental than the concept of time. We find it convenient to talk as if there were some underlying flowing substance like the water of a river that carries these changes along with it.

We abstract time to have a standard measuring tool by which we can quantify change. In , Einstein published his famous paper on Special Relativity. This theory began the transformation of our understanding of space, time and motion. The theory of Special Relativity has two defining principles: the principle of relativity and the invariance of the speed of light. Briefly, the principle of relativity states that the laws of physics are the same for any inertial observer.

An observer is an inertial observer if the observer's trajectory has a constant velocity and therefore is not under the influence of any force. The second principle is the invariance of the speed of light. This second principle profoundly affected the model of the cosmos: the constancy of c was inconsistent with Newtonian physics. The invariance of the speed of light according to Special Relativity replaces the invariance of time and distance in the Newtonian universe. Intervals of space, like length, and intervals of time and hence, motion are no longer absolute quantities.

Instead of speaking of an object in a particular position independently of a particular time, we now speak of an event in which position and time are inseparable. We can relate two events with a new quantity, the spacetime interval. For any pair of events, the spacetime interval is an absolute quantity that is, has the same value for all inertial observers.

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To visualize this new quantity, one constructs spacetime diagrams Minkowski diagrams in which an event is defined by its spatial position usually restricted to one dimension, x and its time ct. The following figure shows a Minkowski diagram depicting the flat spacetime of Special Relativity and three different spacetime intervals, or worldlines.

What are the consequences of Special Relativity for time travel? First, we lose the common sense meaning of simultaneity. Furthermore, an observer in the stationary inertial frame may determine two events to have happened simultaneously, but an observer in the second moving inertial frame would see the same two events happening at different times. The lack of simultaneity across frames of reference means that we might experience the phenomenon of time dilation.

Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the  Godel Universe Godel Meets Einstein : Time Travel in the Godel Universe
Godel Meets Einstein : Time Travel in the Godel Universe

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