Jesse

Jesse:
But it's just an arbitrary coordinate choice whether you parametrize a worldline with the parameter increasing in the future direction or the past direction. In contrast, remembering the past but not the future is a real physical phenomenon in need of an explanation.

cfgauss:
t could just as well be decreasing. But the thing is, t *is* increasing (or t *is* decreasing).

I think you are completely mistaken about the significance of the coordinates here--whether you parametrize a worldline so that t increases or decreases in the future has jack squat to do with the arrow of time, and it certainly could not be an "explanation" for it. Your profile suggests you're a physics student rather than a professional physicist, I'd suggest asking one of your professors about this if you don't believe me.

Jesse:
I was referring specifically to time-symmetry--if you get into quantum mechanics you have to use CPT symmetry instead, but either way, there is nothing in the fundamental laws of physics that explains why we should see any macroscopic arrows of time.

cfgauss:
But there are violations to many symmetries, too! In fact, there are possibly violations to *every* symmetry!

Huh? Could you give me an example of a violation of CPT symmetry, or of Lorentz invariance, for example?

cfgauss:
Anyway, it's, IMO, that we have some "velocity" through time, just like the velocity through a river, or the progression of t in a parametric equation.

The idea of a "velocity through time" does not make sense, unless you want to propose a second time dimension or something; velocity is just the slope of your worldline in relativity.

Let's put it this way: in the imaginary universe where there is a future low-entropy boundary condition at the big bang, but not at the big crunch, yet we continue to parametrize worldlines in the same way as in our universe, do you think we'd remember events in the +t direction or the -t direction?

Jesse:
I'd still say it's a nitpick, since what he meant by "the structure of the space-time continuum" was the issue of whether there is a preferred reference frame, a question which doesn't really have anything to do with the question of whether space-time is discrete or continuous.

cfgauss:
No, it would be like saying that in order to really understand math you need to understand "the field of integers, which mathematicians ignore." No, it physically hut me to type that.

I don't agree. If one was to propose a new classical theory which modifies SR by adding a preferred reference frame, I think it would be valid to say this proposal involves a change in our understanding of "the structure of the space-time continuum" (i.e., the theory eliminates lorentz invariance). I suppose this is just an aesthetic issue, but I think few physicists would complain if it were phrased that way.

cfgauss

"I think you are completely mistaken about the significance of the coordinates here--whether you parametrize a worldline so that t increases or decreases in the future has jack squat to do with the arrow of time, and it certainly could not be an "explanation" for it. Your profile suggests you're a physics student rather than a professional physicist, I'd suggest asking one of your professors about this if you don't believe me."

Nah, I understand the argument, I just don't agree with it. I think it's just an intrinsic property, rather than a function or result of something else.

Consider a 2-dimensional entity living it's happy life in some plane that exists in 3-space. Now, if I, being its malevolent God, decide to come along and give it a push in a direction perpendicular to its plane it will feel an inexplicable changing in its surroundings! My idea is that time is something like that, but not quite.

"Huh? Could you give me an example of a violation of CPT symmetry, or of Lorentz invariance, for example?"
I remember reading something about CPT violation a while ago, but can't recall off the top of my head now. But quantum mechanics probably provides for some kind of violation of everything (for example, the surprising fact that conservation of energy can be violated for an instant with the spontaneous creation of a particle).

"Let's put it this way: in the imaginary universe where there is a future low-entropy boundary condition at the big bang, but not at the big crunch, yet we continue to parametrize worldlines in the same way as in our universe, do you think we'd remember events in the +t direction or the -t direction?"
I don't follow you.

"I don't agree. If one was to propose a new classical theory which modifies SR by adding a preferred reference frame, I think it would be valid to say this proposal involves a change in our understanding of "the structure of the space-time continuum" (i.e., the theory eliminates lorentz invariance). I suppose this is just an aesthetic issue, but I think few physicists would complain if it were phrased that way."

Lots of physicists and mathematicians are OK with people saying things that are not "quite" right, but I definitely don't agree with this! This can lead to serious problems, like that many people think mass increases with velocity!

Friar Bellows

Yes, for that object, for this situtation, where we are assuming that the spring's constant k never changes, F and x are equivalent. Why? Because in this restricted sense, x fully determines F. But more generally, the equation F=kx does not imply that x and F are equivalent, because that would be ignoring the variable k.

The universe, eh? That's not very restricted. Therefore, when E=mc^2, E and m are equivalent.

When I measure m for an object at rest in my reference frame, I use E=mc^2 to get the energy of that object in that reference frame. I'm not mixing measurements from different frames.

I think I have been very careful to say that E=mc^2 implies that m and E are equivalent. This equation holds true only in the reference frame of the object of mass m. Of course, more generally, from an arbitrary reference frame, the equation is:

E^2 = p^2 * c^2 + m^2 * c^4

and so in general one can't say that energy and mass are equivalent to each other. This is what I think you've been trying to say. The trouble is, you used a faulty analogy to try to prove your point.

By the way, an easier way to think about mass and energy is to simply note that mass is the magnitude of the four-momentum while energy is the time-component of the four-momentum. But you don't see that often in popular treatments of the subject.

No direct evidence that I know of. One astronomical observation which provides indirect evidence for it, but very weak at this stage. I'm not aware of any experiments, though. Any references to them?

The only people who are always right thump thick fairytale books for a living.

Osm bsm Y.

what about removing time from these equations and replacing all velocities with %c values? do the equations still work?

maybe we could find a way to rewrite ALL of the physics equations without t. in place of t we put known motions. like instead of saying five minutes we say the distance a point on the second hand travels 10 inches from clock's center at whatever percent of c the second hand is traveling 10 inches from the middle.

basically i'm saying this...using v=d/t we replace all t's for d/v where v is a fraction of c. this makes all frames determinable since we are using out percentage of c. time is removed.

if you are using a clock, you would have to know the %c the second hand was travel...thus automatically including relativity into your equation but still excluding time.

is that doable?

and as far as the arrow of time stuff...i agree with guassface again that this is trivial. it's impossible to remember something that hasn't happened yet because of sequence. things happen in order and often with patterns that we can use to make predictions.....the sun rises everyday, i can't remember it rising tomorrow because the sequence hasn't gotten there yet...the causes that will let me perceive the sun rising are still resolving so the sun can't have come up yet. we have to stick to the sequence.

i personally think time is a human concept attributed to the sequences with the most regular patterns. since we see the sun travel throught the sky each day, we can place our sequential events according to one "global" sequential event. basically time is just a globally known sequence of events that has happened and will happen (on earth) at the same rate (rate here being occurence per d/v and v being %c....no time) so we can organize our sequences accordingly and with each other.

if we could stop thinking of velocity as a function of time and give it its own values i think we'd fix a good chunk of the difficulties with relativity. i dunno :banghead:

Hawkingfan

almighty cf,
You still have not excused me? May I PLEASE be excused?

Mr. Sammi

Hey Hawkingfan,

in your last treatment on SR you managed not to mumble. Jolly good old fella. I seem to remember some of what you wrote, and I guess I concur, I am not sure if it is because of what I learned, or what I reflected after learning.

On another note, what do you know about this red-shift found in cosmological spectroscopy. How does this tie in with SR. It seems pretty Newtonion to me. Does this imply the speeds of the systems are Newtonian?


Sammi Na Boodie ()

Hawkingfan

The only thing I know is that spectroscopy is the breaking down of light from objects in space into its constituent colors (a spectrum) and tells us what an object is composed of, its temperature, its velocity, and other things. It has detected a large amount of helium and hydrogen in the universe and supports the BB theory. When an object moves away from us, the colors in its spectrum get displaced toward longer wavelengths, with the amount of redshift proportional to the object’s velocity. Hubble showed that the spectrum of almost every galaxy is shifted to the red, and that the farther away a galaxy is, the greater the redshift. This relation is called "Hubble's Law"—a galaxy’s speed is directly proportional to its distance. I'm not sure how it ties into SR. It seems more of a theory in tune with QM. But I'll let others who are more informed take it from there.
I don't know. I thought Newton took the Christian viewpoint that the universe is static and finite. But to me, you cannot have a static and finite universe where gravity is attractive.
I don't think so. I think the challenge to the speed of light remaining constant to all observers is that modern scientists believe the speed of light is frequency-dependent and that they have noted differences of arrival times in a detector on earth between photons of varying frequencies. Photons of higher frequencies are expected to come at later times than those of lower frequecies. The frequency-dependent expression of the speed of light depends on the gravitational constant, a quantity that is known since Newton established his law of gravitation. Energetic photons have been noticed coming from Markarian 501. But physicists have not see any of the expected electron-antielectron pairs. It was found that the combined energy of each type of photon was not enough to create an electron-antielectron pair. Therefore, the speed of light is in question.

Mr. Sammi

Hawkingfan,

when light is decomposed, are we speaking another language? no longer light BUT the electro-magnetic spectrum?


Sammi Na Boodie ()

cfgauss

Friar Bellows:
"Yes, for that object, for this situtation, where we are assuming that the spring's constant k never changes, F and x are equivalent. Why? Because in this restricted sense, x fully determines F. But more generally, the equation F=kx does not imply that x and F are equivalent, because that would be ignoring the variable k."
...and again....

"The universe, eh? That's not very restricted. Therefore, when E=mc^2, E and m are equivalent. "
No! They're related, but not equivalent. Looking at it from a more quantum mechanical point of view, matter is "made of" energy, and energy is energy. That's not equivalence though! I mean, the Eiffel Tower and a Buick are both made of the same thing, but are *they* equivalent?

"When I measure m for an object at rest in my reference frame, I use E=mc^2 to get the energy of that object in that reference frame. I'm not mixing measurements from different frames."
Yes, but when you say that mass increases when you add energy *is*!

"I have been very careful to say that E=mc^2 implies that m and E are equivalent."
And they aren't...

"This equation holds true only in the reference frame of the object of mass m."
Yes.

"Of course, more generally, from an arbitrary reference frame, the equation is:
E^2 = p^2 * c^2 + m^2 * c^4"
As I said.

"and so in general one can't say that energy and mass are equivalent to each other. This is what I think you've been trying to say."
What I've been trying to say is that they aren't *ever* equivalent! I mean, you can use kinetic energy to find velocity, but *they* aren't equivalent!

"The trouble is, you used a faulty analogy to try to prove your point."
Not in the way you said it was, no! And *all* analogies are faulty!


Osm bsm Y:

"what about removing time from these equations and replacing all velocities with %c values? do the equations still work?"
As long as you know what you're doing, yeah. We do this in relativity and QM a lot.

We actually do things like measure distance in time and time in distance in relativity, too. It makes some things look nicer.

But you aren't, however, taking out time. c is in meters per *second*, so time's still there. You can also think of it like converting from one unit to another.

Jesse

Jesse:
I think you are completely mistaken about the significance of the coordinates here--whether you parametrize a worldline so that t increases or decreases in the future has jack squat to do with the arrow of time, and it certainly could not be an "explanation" for it. Your profile suggests you're a physics student rather than a professional physicist, I'd suggest asking one of your professors about this if you don't believe me.

cfgauss:
Nah, I understand the argument, I just don't agree with it.

I don't think you fully understand the argument, judging by the fact that you did not seem to understand my last question (see below).

cfgauss:
I think it's just an intrinsic property, rather than a function or result of something else.

Even if the time asymmetry in our memories is somehow built into the fundamental laws of physics, which I guess is what you're arguing, it is still nonsense to "explain" this asymmetry in terms of the fact that we usually make the arbitrary choice to parametrize paths through spacetime with t increasing towards the future rather than towards the past.

Jesse:
Huh? Could you give me an example of a violation of CPT symmetry, or of Lorentz invariance, for example?

cfgauss:
I remember reading something about CPT violation a while ago, but can't recall off the top of my head now. But quantum mechanics probably provides for some kind of violation of everything (for example, the surprising fact that conservation of energy can be violated for an instant with the spontaneous creation of a particle).

I'm not sure, but I don't think physicists would call quantum fluctuations in energy "violations of conservation of energy" and I’m pretty sure they wouldn’t call it a violation of time translation symmetry, which is where this conservation law comes from (see this table of conservation laws and their associated symmetries, which I think someone posted on another thread—might have been you, actually). This is really more of a semantic issue, though.

Jesse:
Let's put it this way: in the imaginary universe where there is a future low-entropy boundary condition at the big bang, but not at the big crunch, yet we continue to parametrize worldlines in the same way as in our universe, do you think we'd remember events in the +t direction or the -t direction?

cfgauss:
I don't follow you.

This is why I suggested above that you don’t fully understand the argument, since most physicists would explain the arrow of time in terms of a low-entropy boundary condition at the big bang (and would also say that the arrow of time would be reversed if the boundary condition was at the big crunch instead). For example, Hawking mentions it in the same section of his book which I posted earlier:

A Brief History of Time, pp. 145-146

Roger Penrose also devotes a whole chapter to the arrow-of-time problem, and how it is probably traceable to a low-entropy boundary condition at the big bang but not the big crunch in The Emperor’s New Mind, a book which has a lot of interesting stuff about physics even if, like me, you don’t agree with his ideas about A.I. or about the interpretation of quantum mechanics. Here is a paragraph where he wraps up a discussion about how the low entropy of the big bang cannot be explained solely in terms of the smaller size of the universe, by showing that the entropy would be much higher at the big crunch in a closed universe:

The Emperor’s New Mind, p. 339

It may be helpful to think about the ‘arrow of time’ problem in terms of a simple toy model. Consider a computer simulation involving a bunch of billiard balls bouncing around on a table, using classical physics with elastic collisions and no friction. These laws are time-reversible. Suppose you simulate the balls bouncing around for 10 seconds, and then look at the state of the system at that time; if you reverse all the momentum vectors (which is equivalent to replacing t by –t in all the dynamical equations, the basic test of time-symmetry) and then use that state as your new set of initial conditions, then run the simulation forward for another 10 seconds, it will behave like a perfectly reversed version of the original 10-second simulation. In this world, reversing momentum vectors and simulating forward is equivalent to reversing time.

To make things a little more interesting, suppose our first simulation involved low-entropy initial conditions, like all the balls but one sitting neatly in the center of the table with the extra ball barreling towards them with high momentum. As the ball hit the cluster and scattered them the balls would spread out more over the table, increasing the entropy. This is the sort of behavior we expect. On the other hand, if we start out with an initial condition where all the balls are distributed randomly throughout the table, we expect that after 10 seconds of bouncing around they will still be in a distributed, high-entropy state. However, one could confound this expectation by running the simulation that started off with all the balls in the center for 10 seconds, then taking the state of the balls after 10 seconds and reversing all the momentum vectors, and using it as a new set of initial conditions. If you gave this set of initial conditions to a friend but lied and said you’d picked them randomly, he’d be very surprised to find that when he ran these conditions forward, the balls would appear to spontaneously organize themselves into a neat arrangement at the center of the table!

Indeed, such a spontaneous decrease in entropy would be incredibly unlikely if the initial conditions had been picked randomly—only a tiny subset of all possible initial conditions will happen to lead to reductions in entropy when played forward. On the other hand, only a tiny subset of random initial conditions happen to start out in a low-entropy state. Most randomly chosen initial conditions start out high-entropy, with the balls spread out all over the table, and will stay at high entropy as the balls bounce around for 10 seconds. In fact, because of the time-symmetry here, we know that if you choose the initial conditions randomly, the chance that you will happen to get a run that goes high-->low entropy is exactly equal to the chance you will happen to get a run that goes low-->high enropy.

Suppose we had a "supercomputer of the gods" that could quickly run through all possible 10-second simulations with all possible initial conditions, and then throw away all but those that matched some criteria we gave it, like "the simulation should start off high-entropy but be in a state of low entropy by the end of the simulation". This would be an example of imposing "boundary conditions" on the simulated history. Again, note that it would be just as easy to impose a low-entropy boundary condition on the final state as on the initial state; both would be represented by an equally tiny fraction of all possible 10-second histories, because of the time-symmetry in the laws. We could even impose a low-entropy boundary condition on both the initial and final state—in this case, the number of runs that would satisfy this boundary condition would be a much smaller fraction of all possible hsitories. The few that did satisfy this condition would tend to start off in an organized state, then gradually disorganize, and then probably around the midpoint of the simulation they would start to reorganize again.

Now imagine we have a more complicated simulation with more complicated laws than just billiard balls bouncing around on a table for 10 seconds. In fact, imagine we have a set of time-symmetric laws which are complicated enough to allow for the emergence of simulated-life forms, even intelligent ones, given a large enough simulation running for a few billion simulated years. Say you started off such a simulation with low-entropy initial conditions—assuming these laws include something like gravity dominating at long ranges, "low entropy" would involve all particles about equally distributed through space while "high entropy" would involve particles being clumped up, which is the reverse of how we usually think of entropy in a case like a box of gas particles where there is no strong attractive force. So, you’d start off with all the particles smoothly distributed through space, then after a while you might have stars and planets form under the influence of gravity, and on some of these planets life might arise, and occasionally you might even find that life evolved into intelligent life (assuming you agree that ‘intelligence’ can arise from matter obeying simple laws, rather than requiring the infusion of a supernatural soul of some kind). Of course, in such a universe you’d expect the psychological arrow of time to run just like ours does, with the beings remembering the past but not the future.

But assuming the laws of this universe really are time-symmetric, you should be able to do the same trick of taking some set of final conditions, doing the equivalent of reversing all the momentum vectors (ie replacing every t by –t), and then using this reversed final condition as a new initial condition. If you run this initial condition forward using the exact same laws, everything will play out in reverse—life will devolve and then dissapear, planets and stars will dissipate, etc. In this simulated run, any intelligent beings would appear to remember events that, from your point of view watching the simulation unfold, haven’t happened yet.

The important thing to realize here is that, from the point of view of randomly-chosen initial conditions with no boundary conditions, you are equally likely to get this sort of high-entropy-to-low-entropy as you are to get a low-to-high entropy history. The vast majority of all possible histories will start in a state of maximum entropy and stay that way, displaying no "arrow of time" at all. Only if you impose a low-entropy boundary condition on either the beginning or the end of the simulation will you have the possibility of life and intelligence, with its associated "arrow of time", appearing at some point during the simulation, and the arrow of time will be wholly dependent on whether you choose low-entropy initial or final conditions. And again, if you just pick your initial conditions at random, and use the "supercomputer of the gods" to keep doing so until you find a universe which satisfies the boundary condition of a low-entropy beginning or end, neither one is more likely than the other—a priori they are both equally unlikely, assuming a "random universe". Any intelligent beings that arise in such a universe will refer to the low-entropy end as "the past" and the high-entropy end as "the future", so from their P.O.V. they will always remember the past but not the future, but from your P.O.V. watching the simulation you are equally likely to get beings who seem to remember what you call the future of the simulated world as you are to get ones who remember the past.

As the Hawking and Penrose quotes above indicate, most physicists think that the arrow of time in our universe, including the psychological arrow of time, is due entirely to the fact that the universe started off in a state of low entropy and has been increasing ever since. Correspondingly, most physicists imagine that if we lived in a universe with a low-entropy boundary condition at the big crunch but none at the big bang, then we’d refer to the direction of the big crunch as "the past" and that our psychological arrow of time would be reversed. So, to return to my original question which started this all, do you disagree with this idea? Do you think that even in a universe with a low-entropy boundary condition on the big crunch but not the big bang, we’d continue to refer to the direction of the big bang as "the past" and that we’d remember events in that direction but not remember events on our worldlines which lie closer to the big crunch?