Gravity and the Myth of 0mph

It’s long been an axiom of physics that everything is constantly in motion, due to the cosmic background stretching of the Universe. At least that’s what Brian Greene tells us, and in this case I’m inclined to believe him. No matter that everything he concludes from this fact is not even false.

Yet, al a cartes Thomas Kuhn, we know that old washed up ideas die hard. This is the case with a little gem I was taught in high school physics concerning an object falling toward the Earth, after been thrown away from it. Specifically, if you throw an object straight up, gravity will cause its acceleration/speed to decrease until reaching 0mph, at which point it will begin increasing its acceleration/speed in the opposite vector. Your immediate reaction should be that the phrase “at which point” is inherently ambiguous. Yes it is, and that’s half the problem. Let’s look at a chart provided by a propaganda website.

newton

According to this diagram, an object will be basically at rest right where you see the a= 0 m/s2. Of course, none of these wizards can tell us how long the object will be at rest. That’s because it’s impossible to tell. Why is it impossible to tell? Despite the fantasies of William Tells, the object is never at rest. We know from contemporary science that nothing is ever at rest! Well then, to paraphrase Hume, whence the cognitive dissonance? Basically people have a hard time conceptualizing an instant change in vector – it makes them nervous. As Kant described, the human mind has to impose mental structures on physical perception in order to make sense of it. Well, in the case of “in between time” (the real culprit here), the structure happens to be irrational. It’s what gives us Zeno’s Paradox – the idea that you must be able to always divide time/distance sequences. This idea turns out to be false, as proclaimed loudly and clearly by Bertrand Russell. Well, it’s also false in the case of allegedly negated vectors. There doesn’t have to be a “zero” in between positive and negative opposite vectors. Hard to rap your mind around, but take a look at this adjusted diagram, which should help (although we can’t ever fully understand physical reality, since we play too many language games).

newnewton

Alright. The concept of “0mph” can now be put to rest. No matter what science fiction authors say. Very simply, when you throw up an object into the air, it never stops moving. After all, if it did stop moving, how would it ever get back to you, without something to force it back down? Few people think of the most obvious dilemmas in their allegedly scientific reasoning.

Go ahead and try this one out on your physics friends. Have them tell you how long an object supposedly stays at rest for, at the peak of the falling down curve. They won’t be able to. If pressed, they will tell you that it is an infinitely short moment. And by now my readers can’t fall prey to those shenanigans.

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21 thoughts on “Gravity and the Myth of 0mph

  1. I think by that same argument we can pretty much rule out all motion of any kind. On the face of it this seems utterly preposterous, but it does go a long way toward explaining why I still haven’t assembled that new furniture I brought home two weeks ago, so the idea may have some merit.

  2. Aha – I see the flaw in your argument! What so I win?

    You’re confusing a = 0 (zero acceleration, forces in balance) with v = 0 (zero velocity, object considered at rest).

    So where you say that the object will be at rest when a = 0 on the propaganda chart, you’re confusing “forces in balance” with “object at rest”, and equate it to the “at rest” moment of your throwing example. You make this clear by referring to “acceleration/speed” together increasing and decreasing as the object rises and falls, when obviously only the speed is changing, not the acceleration.

    So the propaganda chart doesn’t apply to your example and doesn’t need to be refuted, since in your example on the surface of the earth, the acceleration is never zero.

    Nor do any of the vectors suddenly change at the top of the arc like you describe – the acceleration is constant (downward, 1g), the vertical velocity is slowly reduced due to that acceleration, and smoothly transitions through the zero point to become downward, and the graph of the position through space traces a smooth parabola, so there’s not even any glitch that needs explainig.

    Yay! Do I get a prize for being the first one to prove that this article is totally bogus?

  3. I cannot figure out how you turned such a simple physics problem (constant acceleration plus some initial conditions) it into your own personal philosophical dilemma.

    Is this supposed to be funny? Am I missing something? I almost believe you are serious. Surely not, right?

  4. I second AngelPlume, and I would like to add a few comments.

    I suppose you could say that nothing is ever at rest on account of the continuing expansion of the Universe, but this is beside the point: I don’t need to write an equation encompassing the entire Universe to calculate how fast a ball will roll down hill.

    The velocity of one thing can only be measured with respect to something else. If you have two books sitting on your desk, the velocity of one of them with respect to the other is most certainly 0 mph.

    Now, for the “infinitely short moment”: These physics equations are not reality, they are simply models of reality. According to the equations, the velocity is zero for an infinitesimal time interval. Does this mean it is true? Who knows?

    There has been speculation over the years that time is not continuous, but is made up of tiny, discrete units, like a movie. If this is true, then your positive to negative vector idea might be valid. However, there is zero experimental evidence for this idea.

    People living in the real world have to stick with what works. Even if discrete time units are one day proven, no one but high-energy physicists would have any need to bother with them. Thus, for good reason, the standard physics curriculum would not change.

    By the way, writing this blog is NOT going to help you meet girls, and isn’t that what’s really important?

  5. Dear Myrmidon,

    Thanks! I believe strongly that some of the best science was actually done in ancient times, and need only be updated with modern data.

    NS

  6. Dear Angela Plume,

    I wasn’t actually confusing acceleration/balance with velocity, so I think you’ll have to rethink your objection!

    I await your correction!

    Cheers,
    NS

  7. Dear Prawn,

    It is not true that nothing is ever at rest – just look at the example proffered by Mr. Tomato Man!

    You write that “Physics is not reality,” and I completely agree!

    As for time being divisible into parts, and that confirming my theory, I would point out that the explanatory elegance is itself empirical confirmation.

    As for girls, fortunately I already have very many always!!

    Cheers,
    NS

  8. The forces in the second diagram are not balanced. Out of curiosity, why do you do this?

  9. Dear NS is a Daft Ninny,

    I don’t know what you mean about the diagram. It says they are balanced.

    I do this because it’s interesting to me; also, I think it’s important to have a counter-voice, as has so often been crucial in the history of science.

    Best,
    NS

  10. Initial velocity is N
    final velocity is -N
    by continuity theorem, velocity RELATIVE to the observer must at some point equal 0! “GASP”

  11. AngelPlume is probably completely correct, but it’s hard to be sure if she really knows where ns went wrong, because his article is so screwed up. Also, NS is a Daft Ninny is correct about the forces being unbalanced. There is a constant, unbalanced force, and therefore a constant acceleration.

    First, remember that whether or not an object is at rest depends on one’s frame of reference, so it’s certainly possible for an object to be at rest, despite what ns might say.

    Now, we have to consider whether quantum effects have to be taken into account. I think that they do, but I’ll consider both possibilities.

    If there are quantum effects, then the object’s trajectory will only approximate the classical trajectory. The velocity may not change smoothly, and the trajectory might even be discontinuous. At the maximum height, various things might happen. The velocity might be zero for a short time (say, a Planck time, or a small multiple thereof). Or the direction of travel might change from up to down, with nothing in between. It could even flip back & forth a few times. In summary, there’s no telling. So, in this case, ns is dead wrong.

    What if we can neglect quantum effects entirely? Well, the acceleration is never zero, so the velocity changes continuously. This means that the object never has the same velocity for a non-zero period of time. For example, approximately 1 sec after reaching maximum height, the object will have a (downward) velocity of exactly 32 ft/sec. It will not have this velocity at ANY OTHER TIME. It will have an infinite number of different velocities, each for an infinitely short period of time. By ns’s logic, this is impossible, right? So, either it’s impossible to throw objects up in the air, or ns is wrong again.

  12. HOLY CRAP! ns, I just took another another look at your 2nd diagram! It’s an object being thrown into the air, and falling back down, right? But by the downward-pointing arrow, it says ‘Stay in Motion (same speed & dir’n)’. SAME SPEED! Are you so damned IGNORANT that you don’t know that a falling body’s speed increases as it falls?!

  13. The point I was trying to make was that the ball’s speed RELATIVE to the ground becomes 0 at the top of the arch.

  14. The diagram does not say that the object will be at rest at the instant its accelleration becomes 0; it may be at rest, or it may be in motion (with a constant speed), depending on what it was doing before the forces are balanced. That is Newton’s Third Law of Motion. This is where AngelPlume believes you confuse acceleration with velocity.

    Next, when an object is in free fall, the forces are NOT balanced, so it has a nonzero acceleration, which means an object tossed upward will slow down until its speed is zero, then speed up in the opposite direction. The moment it is at rest is at the top of its trajectory. Even at rest, the object has a nonzero acceleration, because the net force is nonzero.

    Finally, an object’s speed or velocity cannot be determined without some sort of reference point. Compared to the center of the universe, everything is in motion. However, if I see a table on the ground, if I just stand there, the table’s velocity is zero from my POV.

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  17. This has to be fake. This has to. I cite Poe’s law. Otherwise, this guy really is crazy, thinking his crazy, irrational beliefs to have overturned all of math and science. I hope he doesn’t breed.

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