h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

So if you agree that time is a vector, why don't you agree that speed can also be a vector?

Because vector speed is called velocity. s = |v| means that speed is the magnitude of velocity. Magnitude is the size without a direction. Numbers with an explicit rather than implicit sign are called directed numbers (numbers with a direction on the number line)

I think you're missing the point. Speed is a simplification of velocity. It's there so that people have a practical way of expressing a an easily observable form of movement. No one CARES that time can flow backwards or even (whatever this means mathematically) sideways. It has no bearing on our daily lives. It's nice for all us scientist guys to waltz around with clever little corrections to the nature of the universe, but perhaps the science in this case is losing a wee bit of what the first tenet of the scientific method is: observe. Hence, it's nice to theorize and determine that time is indeed a vector; but no one's ever reliably observed time sidewinding it's way across to the universe next door (in which, according to my research, I am married to Cindy Crawford - but, I have yet to verify that this is the SAME Cindy Crawford ... ). All sarcasm aside for a moment, I find it amusing that it is frequently pointed out amongst forums that our commonly-held beliefs are not TOTALLY correct under all circumstances, because there is a slight tendancy to overstate the importance and relevance of these apparent transgressions in our daily lives. Whew. That was a pompous statement, but I'll stick to my guns.

In summary: Speed is a simple number. It is always positive. It is the measure expressed by the absolute value of the velocity vector of an object moving through space. In fact, here on Earth, with all the gravity around and time moving relatively consistently forward (except on Sunday afternoons, as has been pointed out), speed is a Very Useful Quantity BECAUSE of it's simplicity. It is not a vector, because it was defined not to be such. Going and making time a vector will only lead to re-defining speed to be the absolute value of the velocity in the forward direction of time. That's sort of the point of having speedometers and what not - no one much cares how fast we're moving whatever the temporal equivalent of a non-linearly decreasing-radius left turn off of center into the universe next door is - no one, that is, except those of us who harbor ridiculous ideas of a fantastical relationship with God's gift to men; even if she DOES wind up to be the same Elle MacPhearson.

Time going backwards means we can go faster than light. A VERY important consequence I feel (wanna get to Alpha Centauri sooner than in 50 000 years time, you need reverse time). We are observing time going backwards now. It is important.

Speed isn't positive, it is unsigned. It is *assumed* to be the same as positive since s = |s| but it doesn't have direction as such. Positive is a direction.

Yeah, by THAT definition s = | v | then speed must be a scalar quantity. But by the definition s = d/t then speed is a vector. Who is to say which definition is the right one? They're both accepted.

Speed ISN'T d/t, it is d|x|/dt (the rate of change of the modulus of displacement w.r.t. time)

Very important. We have that drummed into us in maths and physics. If we said the wrong one we could lose many marks.

Hurrah! That is a perfectly valid arguement and consider it accepted.

Now what is your stance on Negative Energy?

Negative energy exists... is required for the symmetry.

Curses! I was hoping for another arguement

I am a mathematician... I think in terms of consistancy and symmetry

It seems there is a fairly ‘logical’ reason not to be able to freeze something to absolute zero.
The only indication of ‘time’s arrow’ (the passage of time) is entropy. Absolute zero would
effectively stop the flow of time for an object and make time’s arrow into time’s period.
This reminds me of what happens to light in a Bose-Einsteinium condensate, it slows to a crawl,
you could literally out walk it.

It also seems that the matter in question would effectively be ‘outside’ our universe (or at least
time space) This seems to be the flip side of the same sort of barriers we run into when trying to
move faster than light. The mass increases unexpectedly as you reach the limit making it
impossible.

These are only thoughts of a layperson, I welcome experts to ripp it to shreds.

I should like to pose the following conjecture as regards the real arrow of time:

just suppose we wanted to travel backwards in time, what would that actually mean?

In order to show that travelling "backwards" in time is possible we need an "Observer" of some sort to make the journey back and leave a message of some sort. Alternatively they could come back (in the "time forwards" direction) with evidence so that we can verify that the "journey" had actually happened.

The Observer must be made of a material object (I can't think of any way of doing it without a material thing)so a person would do.
In order for that person to go back in time they must have a device which is able to put every "particle" in existance back into the same position and with the same momentum it had at that time in the past. In addition it must be able reverse ALL interactions that have occured since that time including, for example, the decay of subatomic particles such as neutrons. These are two of the necessary conditions of what I call a point in time in the past and there may well be others.

This would involve a VERY great deal of energy and a VERY great deal of information. It would also mean that ALL the particles that make up the Observer would also have to be put back into the place that they were in at that time - volunteers can queue here!

In other words: time does have an arrow and the direction is always forwards, at least in this universe.

It is theoretically possible and will, someday, be feasible for us to travel in time at a much faster rate. We simply build a starship with the facility to accelerate at a constant 1G halfway to the Nebula in Andromeda then decelerate for the second half of the distance.
This should take about 35 years as far as the crew is concerned. If they then returned using the same scheme - another 35 years - they would arrive back on earth some 70 years after leaving. Unfortunately, if we assume Andromeda to be 2.5 million light years away then the crew would not recognise earth as the place we left because for those they left behind would be 2.5 million plus 70 years older!

I also note in an earlier thread that someone actually believed that there were such things as Tachyons which could travel backwards in time.

These wave/particles are a result purely of an equation which has two possible MATHEMATICAL solutions. However,this does NOT mean that such particles exist. Mathematics is used in physics because it is one of the best tools we have at our disposal for describing the phenomena in our universe but it is NOT the phenomena.

If you don't believe this just ask yourself if the number TWO, say, actually exists.