# What if speed=time/distance?

1. Nov 20, 2004

### honestrosewater

Is defining speed as distance/time arbitrary? Would defining speed as t/d create any irrrecoverable inconsistencies?

2. Nov 20, 2004

### jcsd

Speed is always distance over time and it really has no ther meaning, so we can't define it as time/distance. Howvere we could choose to measure the motio of an object in terms of time/distance, but this quantity is just equal to '1/speed' which would be less intutive. Of course you have problem that when an objects speed is zero the quantity 't/d' is undefined.

3. Nov 20, 2004

### honestrosewater

Thanks, but "We've always done it that way" doesn't answer my question.

How does t/d have no meaning? What is the difference between traveling 1 m/s and 1 s/m? To me, conceptually, both are equally valid.

But, of course, you would have to change all the effected formulas/equations. It is making these changes that may cause problems. For instance, would you define acceleration as (delta)v/(delta)t or (delta)v/(delta)d ?

4. Nov 20, 2004

### wave

What would be your speed (according to your definition) if you're at rest (in terms of the conventional definition)?

5. Nov 20, 2004

### StatusX

He meant that the word "speed" doesn't mean anything but "distance over time." It would be like saying "let's call horses cows from now on." Sure, there's no problem with it, but theres also no reason to do it. This is as opposed to, for example, defining c as the speed of light, because it can be defined in many other ways. (eg, the speed of gravity, 1 over the square root of the product of the permittivity and permeability of free space, etc.)

6. Nov 20, 2004

### dekoi

Defining the word speed as "d/t" is just a standard.

7. Nov 21, 2004

### honestrosewater

Yes, I don't know why I didn't think of that. Your speed would be undefined.

Of course, that isn't necessarily a bad thing. After all, d/t is also undefined for t=0.

Last edited: Nov 21, 2004
8. Nov 26, 2004

### jdm

I have been wondering if time/space, inverse velocity, would have any physical meaning as well. It seems like it could exist in a universe frozen in time where the past, present, and future occur as simultaneous snap shots and time is represented as the distance between the snap shots (check out Julian Barbour's notion of Platonia) In such a set up time/distance might stand for how much time you cover in a particular distance, just as under normal conditions space/time, velocity, stands for how much space you cover in a particular time.

9. Dec 4, 2004

### scienceguy

Isn't this like time travel? t/d would be like the amount of distance needed to travel a specific amount of time, but then it would not equal to speed, meaning the equation cannot exist.

10. Dec 4, 2004

### loseyourname

Staff Emeritus
As long as you knew the average t/d for any motion whatsoever (assuming no object is completely stationary for all of its existence), and could model it with a differentiable function, then you could figure out t/d at any point you wanted to, even when $$\Delta d$$=0, same way you figure out instantaneous velocity.

11. Dec 4, 2004

### Locrian

Yes. It would have physical meaning in that it described the amount that time changes for an object within a certain distance the object travels.

Yes, the definitions of words are arbitrary, though once defined the way they are used is not. The word "speed" does not have any grand significance universally. You can redifine it as you please. You just won't be able to communicate with the rest of us.

12. Dec 4, 2004

### jdm

Does the ability to physically realize time/space suggest anything about the relationship between space and time?

Would it admit a whole new class of physical concepts? i.e. a=t/s^2, F=mt/s^2, E=mt^2/s^2 (mass would have to have an inverse concept as well, energy?), etc.

Would these concepts fit into our current system or require new laws to describe their behavior and relationships to one another?

Last edited: Dec 4, 2004
13. Dec 5, 2004

### Gokul43201

Staff Emeritus
Sure you can go ahead and call something t/d, but I wouldn't name it 'speed' (which is already an english word derived from Germanic and Latin origins meaning prosperity, success, puctuality, ability to complete a given task in time, etc.) : perhaps 'slowness' would be a better name for it. Also, the reciprocal of this slowness will more often end up being used. Speed is also useful for defining accleration, which is a rate of change of speed (velocity). If you wanted to make up a new term for the reciprocal of acceleration too, go ahead by all means. Finally, in Newtonian mechanics, the flow of time is constant, and so, treating time as an independent variable and measuring rates with respect to it, makes sense.

14. Dec 5, 2004

### honestrosewater

Okay, sorry for the confusion. I'm not talking about the word "speed". I'm talking about
$$\frac{d_{1} - d_{0}}{t_{1} - t_{0}}\ \mbox{and}\ \frac{t_{1} - t_{0}}{d_{1} - d_{0}}$$
or
$$\frac{\Delta d}{\Delta t}\ \mbox{and}\ \frac{\Delta t}{\Delta d}$$
I'm asking about the use of these expressions in the physical world. I want to know if one model uses d/t, while another uses t/d, would any differences arise between the models? I can't really clarify what I mean by "differences" since I can't think of any differences that would arise

15. Dec 5, 2004

### Gokul43201

Staff Emeritus
No, there wouldn't be any differences (at least in Newtonian systems), but you'd more often see the inverse of speed being used in equations under the second model, unless you want to redefine a whole bunch of other quantities (acceleration, momnetum, angular velocity, etc.) as well.

16. Dec 24, 2004

### woodysooner

hey honestrosewate i have been working lately with the same notion but not with the idea of speed involved, i have been looking at the idea that instead of always looking at changed is motion over changes in time, dm/dt, maybe we should look at dt/dm, GR shows that time is the result of spacetime curvature do to mass, ie... but i see no way of time ever moving without motion, do a thought experiment, think about a place where there is no motion for heaven sakes think of the def. of a sec.. it requires motion, what if the concept of spacetime is wrong, whatabout a time sheet, in which mass rests on and if there is motion that time intervals can be viewed, then all we deal with is DT/DM, and its so much more grandeur than speed. and with this concept nothing changes with GR you still get all the effects as you do always, i could explain for a while but i has looked at it in many ways and i pans out. slow motion moves lineraly through time whereass speed approaching that of C takes to a bent motion approaching the angle of 180 downward in the time sheet so that no time is seen. think bout it and see what you think.

17. Dec 27, 2004

### FulhamFan3

Actually it is. If you cover any distance in 0 seconds your going at infinite speed.

the point is by your defintion, the bigger the unit the slower you're going. I personally like using bigger numbers the faster I'm going.

18. Dec 28, 2004

### honestrosewater

The question is about the relationship between formal systems and the interpretations applied to them. The point is that "d" and "t" are interpreted as "distance" and "time"; They are not just meaningless symbols, they are given some meaning in the physical world.
I'm working on clarifying some of the terms and concepts involved, but, interpreting my words in the most general way, the question is roughly this:
If your interpretation $I_s$, as applied to formal system $S_i$, works in the physical world, or, I'll say, is a valid interpretation, and you apply some transformation, in this case, inversion, to $S_i$, resulting in $S_j$, and $S_i$ and $S_j$ are still equivalent in some special way (I want to say isomorphic, but I'm not sure that's the right term), is $I_s$ a valid interpretation of $S_j$?
Sorry, that's the best I can do for now. Perhaps someone can clarify it.

19. Feb 2, 2005

### properphysicist

I've been reading these replies and I am dumbfounded at the lack of understanding of our most fundamental principles of physics*.

When an object moves through space it does so as a function of time. That means that distance moved depends on the amount of time elapsed.

Now keeping that in mind, consider the inverse of that statement. For t/d to be valid, that would mean that the time elapsed in a given situation would depend on the distance covered. This is clearly absurd. Time contiues regardless whether you're standing still or running. It does not change depending on how much distance you've covered (notice how I say 'distance covered' and not 'velocity travelled at').

A counter argument from those of you who think you actually understand relativity might go something like this: you'll read the above and say - "Ah yes, but time slows down when moving at relativistic velocities." To them I would shake my head and reply thus:
"You're right. Time does slow down significantly at relativistic velocities, however, the increase of the interval between points in time is dependent on velocity which is itself dependent on time. Time dilation does not depend solely on distance moved. This can be seen clearly from the equations of special relativity which, by the way, are somewhat more complex than d/t."

In conclusion, you may consider t/d if you wish, but it has no significance other than it is the inverse of a fundamental relationship between classical time and space.

*I've not read all the replies. If someone has given a sensible reply, to them I say thank-you and please ignore my opening statement.

Last edited: Feb 2, 2005
20. Feb 2, 2005

### Tom Mattson

Staff Emeritus
But v=&Delta;x/&Delta;t doesn't hold for &Delta;t=0. You have to take the limit as &Delta;t-->0, which leads to the derivative.

21. Feb 2, 2005

### Tom Mattson

Staff Emeritus
He didn't say that t/d has no meaning, he said that the word speed has no meaning other than a distance over a time. Of course, this is a matter of definition, and definitions are always ultimately chosen only because of their usefulness.

Anyway, reciprocal speed does in fact have a physical meaning. If you integrate 1/v=dt/dx over a path, you get the time of travel.

22. Feb 2, 2005

### jackle

if you define speed as speed = t/d this implies:

a) it disagrees with the english meaning of speed

or else b) it disagrees with the definition of t=time and the definition of
d=space (which can be reversed for example, to rectify)

or else c) "speed=t/d" disagrees with the conventional mathematical
interpretation, specifically the meaning of the symbols: "=" or "/"

or else d) it disagrees with experiment, specifically any accurate
measurement of speed where d & t are not found to be the same
values in whatever units you choose to accurately measure
them and relate to the same motion of the same object.

Last edited: Feb 2, 2005
23. Feb 2, 2005

### chroot

Staff Emeritus
No, it doesn't. In the definition of speed = d/t, both t and d are independent variables. In the definition of slowness = t/d, both t and d are independent variables.
Many of us here not only think we know relativity, we actually know relativity. In fact, many of us here are paid by various educational institutions to teach relativity to others.

Your comment indicates that you are one of those people who only thinks they understand relativity. The statement that "time slows down at high speed" is a gross misinterpretation of relativity that follows from mixing reference frames -- something "proper physicists" don't do.

If you're the captain of a starship, you never notice time slowing down on your own bridge -- everything looks normal inside your starship, no matter how fast you're going with respect to things outside the starship. Time does not slow down.

On the other hand, to someone on Earth watching your radio transmissions, it would appear that your clocks are slowing down.

Bottom line: time dilation and length contraction are phenomena that occur when comparing measurements made in two different frames. If you are considering only one frame, neither phenomenon occurs.

Learn relativity before trying to teach it to others.

- Warren

Last edited: Feb 2, 2005
24. Feb 3, 2005

### jackle

I think you might be being a bit harsh. I did learn relativity a long time ago and I know that what you have said above is true - Time dilation and length contraction do only occur when comparing measurements in different frames.

Lets try a little thought experiment. I think you can show that if time froze on the bridge for 10 minutes, while the rest of the universe kept ticking, then everything would restart just where it left off, including our brains etc. etc. Nobody on the bridge, nor any measuring device on the bridge would notice time stopping. (Only when the captain left the bridge and compared his watch to his twin who is 2nd in command in engineering, would he notice that he is 10 minutes younger than his twin).

I suggest that if time slowed down, you wouldn't observe this from a detatched ivory tower (this is a meaningless idea if you examine what that would mean). The solution to the twins paradox seems to have similarities to the bridge "freeze". Stella comes home from her space ship and she is, say 10 minutes younger than Terra. Did time slow down for Stella? Not really, but a non-scientist could look at it that way. It isn't too bad.

I am told that something like the "freeze" on the bridge happens near the event horizon of a black hole. The objects near the event horizon do not experience any change in the passage of their time, as expected. When viewed from outside though, you notice "their time has slowed down".

I am suggesting that the common non-scientist's limited undertanding that "time slows down" is OK provided you explain that you can never notice time slow down unless you view it from another time system. And we should say that this is a very simplistic model not the real picture.

Last edited: Feb 3, 2005
25. Feb 3, 2005

### properphysicist

To chroot,

First of all, you are right. I am not an expert on relativity, I was talking to those who appear to be a bunch of kids pretending to know what they're talking about after reading some introductory text rather than studying the subject under a tutor. But I do have some understanding and although what you said about reference frames is clearly true, it is inappropriate here since we are not simply talking experiencing high velocities from some moving frame (as a starship captain). We are in fact talking about making measurements, from a stationary frame, of a moving body within a 'moving' frame. When a body moves near the speed of light, time dilates and this is a function of velocity:

t = t0/sqrt[1-(v/c)^2] as you know.

However, if an object moves from A to B, and is stationary at A and B with respect to your frame, then time dilation does not exist. i.e. time dilation is a function of velocity and not of position.

Furthermore, I did not say time slows down. I said that's what someone else would say in response to what I said. Please take another look at my post to see what was really said.

Thank-you for your input. Please tell me if this makes more sense.

P.S. my username refers to the difference in approach I have to my studies compared to my friends on my course. i don't pretend to know everything about physics. it's a kind of standing joke so there's no need to get all cocky about it. thank-you kindly.

Last edited: Feb 3, 2005