Revisiting the Definition of Speed: Is Distance/Time Arbitrary?

[honestrosewater]

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

 

[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.

 

[honestrosewater]

Speed is always distance over time and it really has no ther meaning, so we can't define it as time/distance.

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 ?

 

[wave]

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

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

 

[StatusX]

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 ?

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 there's 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.)

 

[dekoi]

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

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

 

[honestrosewater]

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

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.

 

[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.

 

[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.

 

[loseyourname]

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.

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.

 

[Locrian]

I have been wondering if time/space, inverse velocity, would have any physical meaning as well.

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.

Is defining speed as distance/time arbitrary?

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.

 

[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?

 

[Gokul43201]

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.

 

[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

 

[Gokul43201]

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.

 

[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.

 

[FulhamFan3]

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

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.

 

[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.

 

[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 traveled 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.

 

[quantumdude]

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

But v=Δx/Δt doesn't hold for Δt=0. You have to take the limit as Δt-->0, which leads to the derivative.

 

[quantumdude]

How does t/d have no meaning?

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.

 

[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.

 

[chroot]

For t/d to be valid, that would mean that the time elapsed in a given situation would depend on the distance covered.

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.

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,

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

 

[jackle]

Learn relativity before trying to teach it to others.

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 spaceship 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.

 

[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.

 

[UltraPi1]

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.

Perhaps Chroot would like to explain the why of it all. Why doesn't the captain notice any difference? Why does the person on Earth notice a difference?

 

[chroot]

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.

Oh -- you mean, people like yourself. I see.

If you manage to stay around here for a while, you'll discover that very few of us are kids pretending to know things. In fact, we tend to deal pretty harshly with such people. Hint, hint.

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).

You're the one that started trying to shove your misconceptions about relativity down others' throats. I simply corrected you.

When a body moves near the speed of light, time dilates and this is a function of velocity:

You just repeated the exact same errant phrase. Here, I'll correct it for you:

When a body moves near the speed of light with respect to another observer, that observer will measure the body's time elapsing more slowly than his own.

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.

Time dilation exists during the object's movement from A to B. If the object is brought back to the observer, the diffence in elapsed time on their clocks can be measured directly.

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.

Your condescending response was "Time does slow down significantly at relativistic velocities," which is bullcrap. Just admit your mistake and move on.

i don't pretend to know everything about physics.

Could've fooled me, kid.

- Warren

 

[chroot]

Perhaps Chroot would like to explain the why of it all. Why doesn't the captain notice any difference? Why does the person on Earth notice a difference?

Well, imagine you were the captain of a shiny new starship. You take off at 0.9c for the center of the galaxy, and close all the windows so that your passengers can sleep. Every now and then during the trip, you look at your wristwatch. Everything appears normal.

First, let me ask you the question: how could it not appear normal? The only clocks you have are in your starship. Your wristwatch measures time, and so does your brain -- albeit with different mechanisms. If you had a physical experiment, like a pendulum, it would also indirectly measure time.

Even if you'd like to imagine that time did slow down on the starship, you, the captain, would never be able to detect the change. Your wristwatch, brain, and pendulum would all be slowed similarly. To you, everything in your starship would seem to behave the same way, no matter what velocity you're going with respect to anything else.

Also, consider the fact that there are things moving around you all over the universe -- there are distant galaxies moving away from you in different directions all over the sky at very high velocities. There are cosmic rays going very close to the speed of light zipping through your body from all directions. The Sun, the Moon, the other planets, they're all moving at arbitrary velocities. If moving quickly with respect to somethine else changed your perception of time, how could you pick which "something else" to believe? All those other bodies going in different directions at different speeds would imply that your clock should run at many different speeds at once, which can't happen. It doesn't make any sense.

If you're the captain of the starship, your motion with respect to other parts of the universe does not affect your wristwatch.

In relativity theory, people refer to the time on your wristwatch to be your "proper time," assuming that your wristwatch stays fastened to your wrist. No matter how you move through the universe, your wristwatch stays at rest with respect to you, so there is no time dilation.

Now, on to the second part of your question: why does the observer back on Earth measure the starship's clocks running slow?

Well, imagine the starship is equipped with a beacon driven by a simple clock, producing a light that flashes once per second. Someone on Earth measures the time between flashes. As the starship achieves higher and higher velocities, each successive flash of light has a longer and longer trip back to Earth. The result is that the flashes appear to the Earth observer to be not one second apart, but two, or five, or twenty, depending on how fast the starship is going.

Every clock on board the spaceship would appear the same way to the Earth observer, not just the beacon. The captain's radio transmissions would appear slowed down, also. If the Earth observer had a very powerful telescope, he could even take pictures of the people moving around inside the cabin of the starship, and he would think the people appeared to be moving very slowly, too.

- Warren

 

[properphysicist]

Everything you just said is exactly what I was trying to say. But I just seem to have upset you more than anything else.

I wasn't trying to be condescending, I'm sorry you couldn't see that.
Perhaps it is time to move on.

Thank-you anyway.

 

[properphysicist]

the above refers to your response to me and not to ultrapi1

 

[UltraPi1]

If the Earth observer had a very powerful telescope, he could even take pictures of the people moving around inside the cabin of the starship, and he would think the people appeared to be moving very slowly, too.

In other words - Why would someone taking a journey from (a) to (b) at very close to the speed of C and returning back to (a) at very close to the speed of C, with a travel distance of 20 light years be younger than the person that stays at A by 20 years? Why does the traveler not age? What mechanism or lack thereof provides for this?

 

[chroot]

UltraPi1,

Because the light comprising their images suffers the same way as the light from the ship's beacon.

- Warren

 

[UltraPi1]

Sorry I edited my words.

 

[chroot]

UltraPi1,

The moving twin will have aged less because the proper time along his world-line is less than that of the stationary twin.

- Warren

 

[UltraPi1]

The moving twin will have aged less because the proper time along his world-line is less than that of the stationary twin.

World line?

There is no mechanical reasoning here?

 

[Enos]

The traveler does age but in days rather than years. But if observed the traveler will move in slow motion with respect to the man on earth. And the man on Earth is moving fast with respect to the traveler. But time continues for both.

 

[UltraPi1]

The traveler does age but in days rather than years. But if observed the traveler will move in slow motion with respect to the man on earth. And the man on Earth is moving fast with respect to the traveler. But time continues for both.

I'm thinking there must be some mechanical reason for this. Otherwise this cannot be explianed through physics.

 

[quantumdude]

In science, a common view of explanation is that of reduction. That is, if predictions for a large collection of phenomena can be derived from a smaller set of postulates, then said phenomena are said to be reduced to those postulates, and the postulates are said to constitue an explanation of the phenomena.

That said: Time dilation is derivable from the postulates of SR, which are:

1. The laws of physics are the same in all inertial frames.
2. The speed of light is the same in all inertial frames.

So you want to know why time dilation occurs? The best and only answer we have is that it is a logical consequence of the above two postulates. That is the explanation, and it is physical.

 

[Enos]

Your seeking an absolute answer in a relative universe. Time isn't absolute so one can live a year and and someone moving slower can live 20 years. The traveler lived a year and wonders why the man he saw last year looks 20 years older while the man can wonder why the man he saw 20 years ago has only aged a year. Both are correct statements and once they meet they now travel at the same speed and age at around the same rate.

 

[UltraPi1]

In science, a common view of explanation is that of reduction. That is, if predictions for a large collection of phenomena can be derived from a smaller set of postulates, then said phenomena are said to be reduced to those postulates, and the postulates are said to constitue an explanation of the phenomena.

That said: Time dilation is derivable from the postulates of SR, which are:

1. The laws of physics are the same in all inertial frames.
2. The speed of light is the same in all inertial frames.

So you want to know why time dilation occurs? The best and only answer we have is that it is a logical consequence of the above two postulates. That is the explanation, and it is physical.

Ok the speed of light and the law of physics are the same in all inertial frames, but obviously this falls way short as to why the traveling twin comes back chipper as the day he left, while the stationary twin is having problems with irregularity. Have there been any attempts to quantify this difference with the two twins?

Are you saying that your explanation is as far as anybody has gone on this subject in the passing decades? No theories? No guesses? No shots in the dark?

Why did the apples fall to the ground?
Because apples grow on trees.
Don't you feel like something is missing here?

 

[quantumdude]

Ok the speed of light and the law of physics are the same in all inertial frames,

Glad you like that bit.

but obviously this falls way short as to why the traveling twin comes back chipper as the day he left, while the stationary twin is having problems with irregularity.

Why? Why is the shortcoming 'obvious'?

Why is the explanation in terms of the postulates of SR not good enough for you?

Have there been any attempts to quantify this difference with the two twins?

Yes, it has been precisely quantified in SR.

Are you saying that your explanation is as far as anybody has gone on this subject in the passing decades? No theories? No guesses? No shots in the dark?

It's not my explanation. And as far as shots in the dark go, I could give you mine, buit it wouldn't mean a thing.

 

[cepheid]

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 traveled at').

You've overlooked something. Speed is not "d/t", referring to them as fundamental features of the universe whatever that means. (what is the ratio of space and time? That's meaningless.) (Average) speed is delta d over delta t, where delta d is the distance an object has traveled since it began moving or since we began measuring how far it has traveled from some starting point (we measure it with rulers). Delta t, is the elapsed time since the object began moving or since the instant we began timing it (with clocks) and measuring its motion. So delta t over delta d does have some meaning, because although he passage of time in general is not altered by the motion of the object, the elapsed time measured since an object has begun moving *does* depend on how far it has gone, ie. at what point in its journey you choose to look at the clock. If it could move some distance in zero elapsed time, delta t over delta d would be zero (but it would be more useful to state that as: it would be traveling with infinite speed). That is what people have been trying to say in this thread. They haven't all gone bananas.

 

[jackle]

Have there been any attempts to quantify this difference with the two twins?

I heard that the principle has been well confirmed using "twin" atomic clocks. The traveling clocks do come back younger but it is beyond our technology to make the age difference noticable to ordinary people.

 

[UltraPi1]

Why? Why is the shortcoming 'obvious'?

Why is the explanation in terms of the postulates of SR not good enough for you?

Because the twin returning would appear as if a magic trick took place. Sr only tells you that the twin comes back younger than the twin that stayed. You can quantify by how much this will happen, but not how this will happen. The reason from my estimates is that to do so, would require the understanding of fundamental entities, something we don't have at this juncture. I'm just a bit surprised by the lack of speculation. Surely someone has delved into the minutiae (you'd think).




Why did the apples fall to the ground?
Because apples grow on trees.
Don't you feel like something is missing here?

 

[UltraPi1]

I heard that the principle has been well confirmed using "twin" atomic clocks. The traveling clocks do come back younger but it is beyond our technology to make the age difference noticable to ordinary people.

This is not the bone I'm picking at. I guess I'm looking for details at the fundamental level.

 

[quantumdude]

Because the twin returning would appear as if a magic trick took place.

It's not magic if you understand the connection between the postulates and the consequences thereof.

Sr only tells you that the twin comes back younger than the twin that stayed. You can quantify by how much this will happen, but not how this will happen.

There are 2 ways that I know of to explain it by analogy.

First, consider a meter stick in 3-space. You're looking at it from the side so that it appears 1 m long. When you rotate it, it appears shorter. And if you rotate it 90 degrees, it appears to have a length that is equal to the width of its cross section. Now if you understand SR, then you know that the Lorentz group is an enlargement of the rotation group. That is, SR is a generalization of rotations. Furthermore, SR couples space and time. So when someone is moving relative to you, there is the possibility that their spatial and time coordinates are rotated.

Second, consider a car moving at 30 mph along the positive x-axis, according to an observer standing on the ground. The x-component of its velocity is 30 mph. Now without changing its speed, it turns such that it is moving at a 45 degree angle with respect to the x-axis. Now, the x-component of its velocity is smaller (by a factor of 1/2^1/2). Well, in SR the norm of the 4-velocity of every body is c. If an object is at rest in some frame, then in that frame its velocity is purely timelike. That is, the t-component of its velocity is c. Now if the object starts moving relative to that frame, its "4-speed" (for the lack of a better word) does not change.

Why did the apples fall to the ground?
Because apples grow on trees.
Don't you feel like something is missing here?

Of course. There's always something missing in science. That's what reductionism is for. We can't know about fundamental entities, because we do not have a priori knowledge of the universe.

 

[Canute]

"We can't know about fundamental entities, because we do not have a priori knowledge of the universe."

Are you sure about that?

 

[quantumdude]

"We can't know about fundamental entities, because we do not have a priori knowledge of the universe."

Are you sure about that?

As sure as I can be. If we did have a priori knowledge of the fundamental workings of the unvierse, physics would not be an experimental science.

 

[Canute]

I wasn't suggesting that we had an a priori knowledge of physics, just of the fundamental nature of the universe. That is, perhaps within us, underneath all the clutter, lies a knowledge of reality that we don't normally notice. After all, we are the universe, or at least a part of it, and made out of the same stuff that the universe is made out of. Just a thought.

 

[quantumdude]

I wasn't suggesting that we had an a priori knowledge of physics, just of the fundamental nature of the universe.

What's the difference?