Time Moves Forward for Obvious Reason?

[sahmgeek]

sidenote: for some reason, the reference to "clocks measuring time" never sits well with me. it doesn't bother me nearly as much as "rulers measuring distance" which seems slightly more accurate. it's unclear to me what clocks are actually measuring. I find it easier to have a conversation about the nature of time when the whole notion of "clocks" is removed. Perhaps I am just lacking in proper "history of time-keeping" knowledge.

 

[harrylin]

So, are we safe in asserting that "time" itself is no more measurable than "space" itself is measurable? But rather, it is the EVENTS that occur within spacetime, the dynamic nature of physical phenomena, that necessitate measurement. We don't talk about measuring space (or do we?) but rather things in it. The same should be true for time.[..] It's very possible that I am WAY off (my comprehension is mainly conceptual, not technical). If so, please be gentle.

You could be way off, but if so, I don't notice it (yet): for your remark sounds insightful to me.
Early people recorded events by means of positions of Sun and moon, and thus the "time" concept emerged based on observing (and counting in one direction!) the motion of natural clocks.

sidenote: for some reason, the reference to "clocks measuring time" never sits well with me. it doesn't bother me nearly as much as "rulers measuring distance" which seems slightly more accurate. it's unclear to me what clocks are actually measuring. I find it easier to have a conversation about the nature of time when the whole notion of "clocks" is removed. Perhaps I am just lacking in proper "history of time-keeping" knowledge.

Clocks actually are a measure of, as you already hinted at, the progress of natural processes. Thus we have the solar clock, (moon) months, water clocks and "radio clocks" such as C14 as well as "atomic clocks". However, people also have an intuition of a "flow of time" that doesn't exactly correspond to clocks; perhaps that difference in perception is what bugs people. In physics we can only deal with clocks.

 

[petm1]

for some reason, the reference to "clocks measuring time" never sits well with me. it doesn't bother me nearly as much as "rulers measuring distance" which seems slightly more accurate. it's unclear to me what clocks are actually measuring.

Clocks, using a photon for a relative measure of distance, are very accurate at explaining the duration between events at the edge of our universe that we do see.

Anything that happens in time is in the spacetime manifold. The manifold itself is not embedded in another time dimension, hence its complete description (all of space and all of time) is static.

If it were otherwise, spacetime -- all of our space and all of time -- would change along that separate time dimension, and past history would be observed to change continuously.

In the fourth dimension, time, we appear as a solid four dimensional object yet in space we see the same object as 3 dimensional and what do both of these objects have in common but the center of their own separate durations. Past history does change continuously from the future through the present into the past, if the present were the surface, or edge of matter I see, then the solid is inside with the signals from some other present waiting to get in, the future.

 

[James_Harford]

In the fourth dimension, time, we appear as a solid four dimensional object yet in space we see the same object as 3 dimensional and what do both of these objects have in common but the center of their own separate durations. Past history does change continuously from the future through the present into the past, if the present were the surface, or edge of matter I see, then the solid is inside with the signals from some other present waiting to get in, the future.

I have no way to restate that in my own words. Since incomprehension appears to be mutual, adieu.

 

[bobc2]

I have no way to restate that in my own words. Since incomprehension appears to be mutual, adieu.

I don't know how you could have made it more clear, James_Harford. Thanks for the comments.

 

[bobc2]

sidenote: for some reason, the reference to "clocks measuring time" never sits well with me. it doesn't bother me nearly as much as "rulers measuring distance" which seems slightly more accurate. it's unclear to me what clocks are actually measuring. I find it easier to have a conversation about the nature of time when the whole notion of "clocks" is removed. Perhaps I am just lacking in proper "history of time-keeping" knowledge.

That is not an altogether bad thought, sahmgeek. If you think about it, we don't really observe time directly. We are always observing successive points on a 4-dimensional object. Often the 4-dimensional object has a world line that extends for billions or trillions of miles along its 4th dimension. And the periodic squiggles back and forth in the X1 and X2 dimensions (i.e., the tip of a pendulum) offer equally spaced points along the 4-dimensional world line (a 4th dimension ruler) that we can calibrate as time, knowing that dt = dX4/c.

So, in a way, we are using rulers for measuring lengths along dX1, dX2, dX3, and also dX4.

 

[James_Harford]

I don't know how you could have made it more clear, James_Harford. Thanks for the comments.

No problem. Take care.

 

[jfy4]

James,

I was hoping for a more detailed answer before, since I was hoping to have a bit of a discussion... I hope you will come back and talk about this idea you have in more detail, even if apparently you feel there are no more details to talk about.

I will pry a little more at what confuses me with what you are saying...

Your claim is that the spacetime manifold is static, but to me you appear to draw this conclusion from premises that have little to do with your conclusion...

To be dynamic requires a second dimension of time in which it can change...

I'm understanding this to say "dynamics is about evolution in time". And you seem familiar with GR, so I 'm taking this to mean that dynamics is about evolution in time according to an observer (not a global time variable). am I correct?

The manifold itself is not embedded in another time dimension

Like a meta-time?

hence its complete description (all of space and all of time) is static.

This implication from "hence" on-ward I think is unfounded, since we didn't define dynamics as evolution in meta-time to begin with... So even if gravity doesn't evolve in some sort of meta-time, we have never thought of dynamics that way.

If you want to stick to evolution in time, The Einstein equation does say that the gravitational field strength (the observable) changes first order in the time parameter, and that change is proportional to the amount of stress-energy-momentum around it.

If I've mistook something you've said I hope you will come back and explain it again. Sorry if I'm being dense.

Thanks,

 

[nitsuj]

So, are we safe in asserting that "time" itself is no more measurable than "space" itself is measurable?

But rather, it is the EVENTS that occur within spacetime...

We don't talk about measuring space (or do we?) but rather things in it. The same should be true for time.

Very well said!

 

[James_Harford]

I was hoping for a more detailed answer before, since I was hoping to have a bit of a discussion...

No problem. I myself didn't really understand your question which seemed more statement than question. My two-word response was meant to prompt a follow-up, but I guess it was a little too terse.

I will pry a little more at what confuses me with what you are saying...

Your claim is that the spacetime manifold is static, but to me you appear to draw this conclusion from premises that have little to do with your conclusion...

Just to get off to a running start, let me begin with a blatant appeal to authority -- Einstein would love that!

First quote:

People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.

- Albert Einstein​

Letter of condolence to Michele Besso's family (15 Mar 1955). InTabatha Yeatts, Albert Einstein (2007), 116.
Science quotes on: *| *Physicist (53)
​

Second quote:

The four-dimensional structure (Minkowski-space) is thought of as being the carrier of matter and of the field. Inertial spaces, with their associated times, are only privileged four-dimensional coordinate systems that are linked together by the linear Lorentz transformations. Since there exist in this four-dimensional structure no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence.

Relativity and the Problem of Space, from the revised edition of Relativity, the Special and the General Theory: A Popular Exposition. Albert Einstein. Translated by Robert W. Lawson. London: Methuen, 1954
​

I'm understanding this to say "dynamics is about evolution in time". And you seem familiar with GR, so I 'm taking this to mean that dynamics is about evolution in time according to an observer (not a global time variable). am I correct?

Like a meta-time?

Evolution, yes, in the sense that Einstein used it in the quote. The italics are his to contrast "evolution" with mere "existence", which does not evolve and hence "static".

Meta-time, no. That would be outside the physics of the spacetime, wouldn't you agree?

The only way that spacetime can evolve on its own is to be part of the physics of a larger 5-dimensional space with a second dimension of time in which it can evolve. That would be bizarre, since it suggests a past that is not static. But since this is not the case, spacetime merely "exists" and does not "evolve".

Sorry if I'm being dense.

Far from it. Judging from your statements, I can learn more from you.

 

[petm1]

The only way that spacetime can evolve on its own is to be part of the physics of a larger 5-dimensional space with a second dimension of time in which it can evolve. That would be bizarre, since it suggests a past that is not static. But since this is not the case, spacetime merely "exists" and does not "evolve".

In this view why are photons red shifted? One dimension of time includes all of space and it has been evolving for over thirteen billion light years relative to my present. Hope this makes sense because I see nothing that is static in time nor space.

 

[James_Harford]

In this view why are photons red shifted? One dimension of time includes all of space and it has been evolving for over thirteen billion light years relative to my present. Hope this makes sense because I see nothing that is static in time nor space.

Describe to me, in your own words, the content of Einsteins statements quoted above. If you can show me that you understand them -- not necessarily agree with them -- then maybe I can address your question if you still have it.

- Regards

 

[nitsuj]

Jumping in,

Those comments are referencing the relativity of simultinaity.

The last one, specifically the last sentence; "It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence."

I think illustrates that to an individual (who are always subject to proper time) physical reality "evolves". But, that this is indepent of how others see physical reality "evolve", and they may not agree to the simultinaity of events.

i.e. there is no absolute time, if it were the case (proper) time could be ignored and the "spacetime structure" would only need to be 3 dimensions (EDIT: and a time coordinate) to properly coordinate physical reality in a way all observers agree.


So the content of both those Einstien quotes I think amount to; time is not absolute.

I hope the comment "...concepts of happening and becoming are indeed not completely suspended, but yet complicated." is not being taken as "static".

Clearly he is not saying concepts of becoming & happening are static, but relativity of simultinaity makes this "evolution" of physical "reality" more complicated. That complication is why I think the next comment is qualified with "more natural".

Can you re-word your comment - "The italics are his to contrast "evolution" with mere "existence", which does not evolve and hence "static"." I think I am misunderstanding what is meant.


I really dislke that first Einstien quote, it's misleading for laypeople like myself that happen upon it. Illusions imply "from an individual's perspective", and from an individuals perspective, past, present & future are easily made distinct. The persistent illusion maybe that we (non-physicists) feel that distinction is absolute, which it is not.

 

[Islam Hassan]

Clocks, using a photon for a relative measure of distance, are very accurate at explaining the duration between events at the edge of our universe that we do see.

IMHO, the short, simple yet controversial answer is that clocks measure (relative) movement. Time is not physically measurable outside of movement; it is a derived quantity, derived from a relative movement measurement with respect to that of a standard one (ie, a clock).

For some reason though, this argument does not sit well with many people in the forum for whom time seems to be an absolute, physical given. To my mind , it is a simple derivation.

IH

 

[James_Harford]

Hi nitsuj,

Those comments are referencing the relativity of simultinaity.

Yes, but for what purpose?

The last one, specifically the last sentence; "It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence."

I think illustrates that to an individual (who are always subject to proper time) physical reality "evolves". But, that this is indepent of how others see physical reality "evolve", and they may not agree to the simultinaity of events.

I would say he has moved beyond discussion of observer's relative perceptions, and is now offering a very specific opinion on the objective nature of physical reality that is independent of all observers.

I hope the comment "...concepts of happening and becoming are indeed not completely suspended, but yet complicated." is not being taken as "static".

I agree, the sentence is a little hard to parse, but my own take is that it is these two statements:
1. "Now" has no objective meaning. This idea is echoed in the first quote.
2. Notions of becoming and happening cannot rely upon an objective "now" that moves from past to future.

Can you re-word your comment - "The italics are his to contrast "evolution" with mere "existence", which does not evolve and hence "static"." I think I am misunderstanding what is meant.

How about,

"The italics are his to contrast "evolution" with mere "existence" which does not evolve and hence is `static', or unchanging."

The persistent illusion maybe that we (non-physicists) feel that distinction is absolute, which it is not.

Exactly. Its a useful illusion to have (which is probably why we have it), but physics works fine without it.

 

[bobc2]

Hi nitsuj,

Yes, but for what purpose?

I would say he has moved beyond discussion of observer's relative perceptions, and is now offering a very specific opinion on the objective nature of physical reality that is independent of all observers.

I agree, the sentence is a little hard to parse, but my own take is that it is these two statements:
1. "Now" has no objective meaning. This idea is echoed in the first quote.
2. Notions of becoming and happening cannot rely upon an objective "now" that moves from past to future.

How about,

"The italics are his to contrast "evolution" with mere "existence" which does not evolve and hence is `static', or unchanging."

Exactly. Its a useful illusion to have (which is probably why we have it), but physics works fine without it.

Good take, James_Harford.

 

[petm1]

People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.
- Albert Einstein

The persistent illusion is the dilating image formed within my eye upon absorption at the end of the photon’s life, or at the end of its duration, appears to be of the beginning of it duration. The duration of a photon always works out to be the length of space/time as measured using the photon as our four dimensional ruler.

The four-dimensional structure (Minkowski-space) is thought of as being the carrier of matter and of the field. Inertial spaces, with their associated times, are only privileged four-dimensional coordinate systems that are linked together by the linear Lorentz transformations. Since there exist in this four-dimensional structure no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence.

I am my own four dimensional object a separate part of space and time, a juxtaposition of one in time with a proper clock to prove it.

The only way that spacetime can evolve on its own is to be part of the physics of a larger 5-dimensional space with a second dimension of time in which it can evolve. That would be bizarre, since it suggests a past that is not static. But since this is not the case, spacetime merely "exists" and does not "evolve".

We change the past in the present all the time, anything you do because of what you see is trying to change the past. Think of a log burning, a rapid chemical chain reaction, as unraveling the log’s past not the space it occupies.

 

[James_Harford]

The persistent illusion is the dilating image formed within my eye upon absorption at the end of the photon’s life, or at the end of its duration, appears to be of the beginning of it duration. The duration of a photon always works out to be the length of space/time as measured using the photon as our four dimensional ruler.

Einstein was saying that in his first quote? I think not.

I am my own four dimensional object a separate part of space and time, a juxtaposition of one in time with a proper clock to prove it.

Is that the point of the second quote? Or are you speaking for yourself? In any case this does not show me that you understand the point he was trying to get across.

We change the past in the present all the time, anything you do because of what you see is trying to change the past. Think of a log burning, a rapid chemical chain reaction, as unraveling the log’s past not the space it occupies.

If this statement is to be taken literally, then when a log is burned, its past is unraveled, and it never existed. If it is to be taken metaphorically, then it doesn't matter what it means, because it isn't physics.

What you are spouting is no theory of Einstein's.

 

[bobc2]

...We change the past in the present all the time, anything you do because of what you see is trying to change the past. Think of a log burning, a rapid chemical chain reaction, as unraveling the log’s past not the space it occupies.

The idea expressed here is in direct contradiction to established relativity theory. If a given observer, A, changed his past events there would be no possibility of all other observers observing the same event, since those events are observed at different times for different observers (moving at different relativistic speeds) within their differing frames. Special relativity theory requires all observers to agree on the fact of the event. If there is a collision, all observers agree that the collision occured.

If an object is moving in a straight line (as opposed to a curved line) in spacetime, then all observers will agree that the path is a straight line, even though their observations may not be observed at the same times in their own frames.

Past events are never altered.

"...unraveling the log’s past..." What does a burning log have to do with the past? That is perhaps a little poetic, but as James_Harford says, it has nothing to do with physics.

 

[nitsuj]

I agree, the sentence is a little hard to parse, but my own take is that it is these two statements:
1. "Now" has no objective meaning. This idea is echoed in the first quote.
2. Notions of becoming and happening cannot rely upon an objective "now" that moves from past to future.

I disagree, "now" has a very very "objective" meaning. The idea echoed in the first quote is this is not absolute; it is relative.

Again I disagree, they (physics) have to rely upon an objective now, this is how it is defined...right...now. It of course is not an absolute "now". distance across space has an invariant isotropic speed limit.

 

[Paul.Dent]

I think you are on the right track. Independent estimates of the size and mass of our universe place it entirely within its own Schwartzschild radius, where the radial dimension and time switch roles due to a sign change in the metric. My theory is therefore that we are in a humongous Black Hole, and that the inexorable chute towards the central singulaity is the inexorable passage of time, while the unbounded outside time dimension becomes unbounded space inside. An interetsing consequence is that "where" quesions and "when" questions have to be interchanged. So the answer to "Where is the event horizon?" is "13.5 billion years ago", and the answer to "What came before the Big Bang" is "The Outside".

Thus I equate the instant of the Big Bang with the event horizon, "seen" from the inside. From that instant, everything evolved more or less as we know it.
I have done the math and the interior universe is one that exhibts an initial infinite rate of expansion, falling to 70Km/s/Mpc at the plateau phase, and then accelerating towards the Big Rip, and infinite rate expansion which will occur of the order of 10 billion years hence.

Now, such Robertson-Walker-like metrics are normally associated with a uniform density of matter. This matter density has to be an order greater than the visible matter density to explain the observed expansion rate; hence the Dark Matter hypothesis. But I don't need any Dark Matter. I get the expansion due to the mass of the Black Hole, 90% of which is already at the central singulaity, or at least nearer to it than we are - which means it is displaced in time from us to our future, and that is why we can't interact with it.

Now, the orbits of stars around galaxies follow geodesics of the spacetime, and they in turn are totally determined by the metric. So, they will conform to the geodesics of a universe filled with Dark Matter even though it's not, as the math can't tell the difference. Thus anomalous galactic rotation explained.

 

[Paul.Dent]

"The only way that spacetime can evolve on its own is to be part of the physics of a larger 5-dimensional space with a second dimension of time in which it can evolve. That would be bizarre, since it suggests a past that is not static. But since this is not the case, spacetime merely "exists" and does not "evolve". "

I am reminded of Spielberg's SciFi movie "The Langoliers". These were monsters that followed behind us in time to chomp up the spacetime past we left behind us.

Now, with reference to my previous post, where I equate the passage of time with the our inexorable chute along the radial dimension of the interior of a humongous Black Hole, we can place numbers along the radial dimension such as Jan 1 1900, Jan 1 1901, Jan 1 1920 ... Jan 1 2012. Now we ask, if an observer using H.G. Wells' time machine could change his time coodinate from today to Jan 1 1900, what would he see? I say he would not see our universe as it was then, because he did not take our universe back with him. He will see the stuff that is following us 112 years behind in time along the radial dimension. That is a different universe that is now occupying the spacetime coordinates that we once occupied - The Langoliers, no less! So we really do need another dimension along which we can plot the evolution of events in our universe. We occupy a certain 4D region of spacetime at one value of this new axis, and something else occupies the same 4D spacetime at a different value along this axis.


We shouldn't worry about that. Heck, string theorists are into 7 and 11 dimensions and I have also seen suggestions that the number of dimensions must be a large Fermat prime!

 

[James_Harford]

I disagree, "now" has a very very "objective" meaning. The idea echoed in the first quote is this is not absolute; it is relative.

But what objectively distinguishes past from future?

- Regards.

 

[jfy4]

Hi James,

I have been thinking about our exchange, but I have also been very busy, sorry for a late replay. After considering our topic, I do have to agree with you, but unfortunately (and if you can believe it), not for the reason/definitions you give. First off in this quote

Hi nitsuj,
"The italics are his to contrast "evolution" with mere "existence" which does not evolve and hence is `static', or unchanging."

I don't often consider existence and dynamics mutually exclusive things. I tend to think that there are things that exist, and are also dynamic, so I don't interpret that sentence as a point towards the static nature of the universe.

You also seem to be saying that the static nature of our universe is a consequence of no apparent outside time variable, which seems weird to me through and through, as I said last time. So before I say I why I interpret the universe as static, I guess I want you to answer me a question, and perhaps we can talk about this question specifically in another thread; If the universe is static, who is it static with respect to?

My understanding of the universe being static comes from the Hamiltonian formulation of GR. In this, GR is a completely constrained system, that is, there is no dynamics term. The whole hamiltonian vanishes. Each constraint lends itself to a geometric meaning, that describes the shape of spacetime.

Talk to you later,

 

[nitsuj]

But what objectively distinguishes past from future?

- Regards.

I don't want to get caught up in semantics.

If instead of the terms "objectively" and "subjectively", I think it would be best to use the words "relative" and "invariant".

If "subjective = relative" & "objective = invariant" then yes I agree with you.

I also feel there is no disputing measurements of time or length with in an FoR, both of which require a "now" (in particular length).

In any case this is silly to interprut such [STRIKE]simple[/STRIKE] comments to such depth, even if they are Einstiens, they are so loosely worded interpretation to this detail is well...subjective :), unlike a ruler or clock.

 

[James_Harford]

Hi James,

I have been thinking about our exchange, but I have also been very busy, sorry for a late replay. After considering our topic, I do have to agree with you, but unfortunately (and if you can believe it), not for the reason/definitions you give.

That is remarkable! Glad to hear from you jfy4.

First off in this [Einstein's second] quote

I don't often consider existence and dynamics mutually exclusive things. I tend to think that there are things that exist, and are also dynamic, so I don't interpret that sentence as a point towards the static nature of the universe.

Then what do you suppose Einstein mean by "exist" vs. "evolve"?

You also seem to be saying that the static nature of our universe is a consequence of no apparent outside time variable, which seems weird to me through and through, as I said last time.

Yes I am, but it seems a tad weirder to postulate an additional outside time variable. Maybe I am mistaken. What function does this variable have?

So before I say I why I interpret the universe as static, I guess I want you to answer me a question, and perhaps we can talk about this question specifically in another thread; If the universe is static, who is it static with respect to?

It's 1+3 dimensional space description is static down to whatever level of detail you wish to take it. It cannot change, except by pencil and eraser, in which case I suppose you could say our physical time is a meta-time of no significance to the physics of that description, or model.

My understanding of the universe being static comes from the Hamiltonian formulation of GR. In this, GR is a completely constrained system, that is, there is no dynamics term. The whole hamiltonian vanishes. Each constraint lends itself to a geometric meaning, that describes the shape of spacetime.

Now that is very interesting! Does H=0 thoroughly weird you as well, then? I wish my physics knowledge was on a par with your own, but it is nowhere near. So, although I very much welcome any conversation in this direction, I am the student and will need to crack open my copy of MTW. (PM me if you think of an appropriate venue.)

It is interesting that you do seem to see this as primarily a GR question.

- Regards.

 

[James_Harford]

I don't want to get caught up in semantics.

Then let's don't.

 

[petm1]

Describe to me, in your own words, the content of Einsteins statements quoted above. If you can show me that you understand them -- not necessarily agree with them -- then maybe I can address your question if you still have it.

I am trying, in my own words, please feel free to address them. Please do not scold I may be slow and simple minded but

If this statement is to be taken literally, then when a log is burned, its past is unraveled, and it never existed.

The temporal image carried within the duration of outgoing photons is the persistence illusion we are all seeing. In my mind the end of the logs duration, as it burned is set, but where is my evidence because now it is as if the log never existed.

But what objectively distinguishes past from future?

Over all I would say matter in the form of atoms, are the most deterministic duration, or maybe dark matter.

 

[James_Harford]

No, I was out of line Petm1. Please do accept my apology. I am new here and trying to find the proper "stance".

I realize that you have a very poetic way of seeing the universe --a way which the discipline of physics tends to strip away. Yet the magic is always present, albeit unremarked, and that is what to which I suspect you are especially attuned. For sure, the evocative nature of poetic vision is very heady stuff, and the essence of what makes life worth living.

- Regards.

 

[James_Harford]

For anyone reading this thread who hasn't already noticed: The question, "is spacetime static" that this thread morphed into has independently arisen in the "is time mapped out" thread at https://www.physicsforums.com/showthread.php?t=578434.

Perhaps future discussion on this question should be under that thread?

 

[lalbatros]

PMichaud,

When your milch dissolves in your cofee, you see something irreversible that shows a preferential direction of time (for all things of these same kind).

I can't see, however, how milch dissolving in cofee can in any way be related to the assymetric initial conditions of the Big Bang.

This does not mean that specific initial conditions could not, indeed, imply some irreversibility in time. There could be several sources of irreversibility, like also at the particle physics level.

However, the most familiar arrow of time, the one related to the second law of thermodynamics can hardly be related to the big bang.

You might be interrested in this book:

The Physical Basis of The Direction of Time, by H. Dieter Zeh.

 

[yuiop]

I get the impression from this thread that there is a consensus that objects move through time rather than time moving forward and I can agree with that. I think the point that the OP was getting at is that generally things only move in one direction through the time dimension and this makes time special as objects can generally move in either direction, backwards or forwards, through the spatial dimensions. Now the question is, how do we determine this allowed direction for travel through time and is there any sort of "law" that prohibits travel in the negative time direction? Others have already mentioned the thermodynamic arrow of time. This is a statistical probability that systems evolve from a state of low entropy to a state of high entropy and very rarely in the opposite direction. Bahamagreen gave this example:

If you open a bottle of perfume in a still room, the molecules in the bottle will eventually fill the room (and the bottle in the room) with an even balance of distribution.
If you could take a snapshot of the room after this happens, you would have a "configuration" of the molecules' positions and speed directions. Assuming continuity and determinism, there will be an infinite number of these configurations between any two snapshots, and every one of them could be reversed and you would expect that at some point later all the molecules would get back into the bottle. If you took a particular snapshot 4 hours after opening the bottle and reversed all the molecules, you would see the molecules all back in the bottle after four hours...

The point is that though statistically unlikely, it not impossible for all the molecules to end up back in the bottle. Now if we allow the universe to run long enough it is possible (even highly likely) that we will experience events where a system randomly evolves from a state of high entropy to state of low entropy. When this happens, will we declare that "time has run backwards" or that a system has moved backwards through time? Personally I do not think we can claim that. The thermodynamic arrow of time gives a probability of how systems will evolve but it does not prohibit a temporary reversal of the arrow of time. I think there should be some higher principle or law that clearly states that objects can only move forward through the time dimension even though the equations do not that. Most laws are based on observation and if a huge number of observations support a rule and if that rule has NEVER been observed to have been broken then that rule should have the status of being a physical law. Has anyone ever observed a system going backwards through time? The equations of Special Relativity appear to be symmetrical as far as time is concerned, but it has its own "arrow of time" in that for any two causally connected events, the cause always precedes the effect. This could be one way to define the law of time. If the effect is observed to precede the cause of two causally connected events, then that would be a violation of that law. As far as know that condition has never been violated. I know that sometimes antiparticles are considered as ordinary particles going backwards in time, but equally they can be be considered as antiparticles going forward in time and so long as we accept the existence of anti-particles there is no violation of the order of cause and effect. Tachyons would also violate the law of cause and effect but as far as I know they have never been observed. Anyway, the point is that the thermodynamic arrow of time allows the occasional reversal of a system from high entropy to low entropy but in my opinion that does not amount to a reversal of time and there should be (IMHO) a higher law that is much stronger and prohibits the reversal of time. This agrees with everything we have actually observed, but perhaps people are afraid to reach that conclusion for romantic reasons such as closing the door on the possibility of time travel.