The effect should continue past the point that gravity arrives from the current position—it will be very minute, as distance in time is related to distance in space by the speed of light (where the C in the interval formula comes from—C in m/s, time in s, very short periods of time are very “far away”), but if I’m correct, and gravity propagates through time as well as space, it should be there.
We stop the object very suddenly because otherwise gravity from the future will counter out gravity from the past—for each position in the past, for an object moving in a straight relativistic line, there will be an equidistant position in the future which balances out the gravity from the position in the past. That is, in your model, imagine that gravity is being emitted from every position the particle moving in the line is at, or was ever at, or ever will be at; at the origin, the total gravitic force exerted on some arbitrary point some distance away is centered at the origin. If the particle stops at the origin, the gravity will be distributed only from the side of the origin the particle passed through.
A second, potentially simpler test to visualize is simply that an object in motion, because some of its gravitic force (from the past and from the future) is consumed by vector mathematics (it’s pulling in orthogonal directions to the point of consideration, and these orthogonal directions cancel out), exhibits less apparent gravitational force on another particle than one at rest. (Respective to the point of measurement.)
Drawing a little picture:
.
…..................> (A single particle in motion; breaking time into frames for visualization purposes; the first and the last period, being equidistant and with complimentary vectors, cancel out all but the downward force; the same gravitational force is exerted as in the below picture, but some of it cancels itself out)
versus, over the same time frame:
.
.
The second particle configuration should result in greater apparent gravity, because none of the gravity vectors cancel out.
As for interpreting it, imagine that gravity is a particle (this isn’t necessary, indeed, no particles are necessary in this explanation, but it helps to visualize it). Now imagine a particle of mass M1 moving in a stable orbit. The gravitic particles emitted from M will vary in position over time according to the current position of M1, and indeed will take on a wavelike form. According to my model, this wavelike from -is- light; the variations in the positions of the gravitic particles create varying accelerations in particle M2, another mass particle some distance away, resulting in variable acceleration; insufficient or disoriented acceleration on particle M2 will merely result in it moving in a sinelike wave, propagating the motion forward; sufficient acceleration of the proper orientation may give it enough energy to jump to another stable orbit.
Again, I suspect people will have a much better chance at understanding your ideas if you make your explanations much more concrete and specific—maybe even to the point of using particular numbers. Abstraction and generality and intuitive verbal descriptions are beautiful and great, but they only work if everyone involved has an adequate mental model of exactly what it is that’s being abstracted over.
What do I mean, specifically and concretely, when I speak of specific and concrete explanations? Here’s an example: let’s consider two scenarios (very similar to the one I tried to describe in the grandparent)---
Problem One.
There’s a coordinate system in space with origin [x, y, z] = [0, 0, 0]. Suppose my mass is 80 kg, and that I’m floating in space ten meters away from the origin in the x-direction, so that my position is described as [10, 0, 0]. A 2000 kg object is moving at the constant velocity 10 m/s towards the origin along the negative y-axis, and its position is given as r(t) = [0, −50 + 10t, 0]. Calculate the force acting on me due to the gravity of the object at t=5, the moment the object reaches the origin.
Problem Two.
Everything is the same as in Problem One, except that this time, the object’s position is described by the piecewise-defined function r(t) = [0, −50 + 10t, 0] if t < 5 and r(t) = [0, 0, 0] if t >= 5---that is, the object is stopped at the origin. Again, calculate the force on me when t = 5.
Solutions for Newtonian Physics
The answers are the same for both problems. Two objects with mass m and M exert a force on each other with magnitude GmM/r^2. At t = 5, I’m still at [10, 0, 0], and the object is at the origin, so I should experience a force of magnitude G(80 kg)(2000 kg)/(10 m)^2 = (6.67 10^-11 m^3/(kgs^2))(80 kg)(2000 kg)/(100 m^2) = 1.067 * 10^-7 N directed toward the origin.
Now, you say that “for each position in the past, for an object moving in a straight relativistic line, there will be an equidistant position in the future which balances out the gravity from the position in the past,” which suggests that your theory would compute different answers for Problem One and Problem Two. Can you show me those calculations? Or if the problem statement doesn’t quite make sense (e.g., because it implicitly assumes an absolute space of simultaneity, which doesn’t actually exist), could you solve a similar problem? I realize that this may seem tedious and elementary, but such measures are oftentimes necessary in order to explain technical ideas; if people don’t know how to apply your ideas in very simple specific cases, then they have no hope of understanding the general case.
To use a slightly different problem pair, because it would be easier for me to compute:
Problem one. I have mass of 80kg at point [10,0] (simplifying to two dimensions, as I don’t need Z). A 2,000 KG object is resting at position [0, 0]. The Newtonian force of 1.0687 10^-7 N towards the origin should be accurate. [Edit: 1.06710^-6 N, when I calculated it again. Forgot to update this section]
Problem two. I have mass of 80kg at point [10,0] A 2,000 KG object is moving at 10 m/s along the Y axis, position defined as r(t) = [0, −50 + 10t]. Using strictly the time interval t = 0 → t = 10, where t is in seconds, calculating the force when t=5...
distance(t) = sqrt(10^2 + c^2((5 - t)^2)
Gravity(t) = 6.67 10^-11 sum(802,000distance(t), for t > 0, t < 10) (10 / distance(t)) [Strictly speaking, this should be an integral over the whole of t, not a summation on a limited subset of t, but I’m doing this the faster, slightly less accurate way; the 10 / distance(t) at the end is to take only the y portion of my vectors, as the t portion of the gravitational vectors cancel out.]
Which gives, not entirely surprisingly, 1.067 * 10^-6 N directed to the origin. (I think your calculation was off by an order of magnitude, I’m not sure why.)
The difference between Newtonian gravity and gravity with respect to y is 3.38 * 10 ^-33. Which is expected; if the difference in gravitational force were greater, it would have been noticed a long time ago.
I probably messed up somewhere in there, because my brain is mush and it’s been a while since I’ve mucked about with vectors, but this should give you the basic idea.
I must apologize for the delay in replying. Regretfully, I don’t think I can spare any more time for this exchange (and am going to be taking a break from this and some other addicting sites), so this will likely be my final reply.
distance(t) = sqrt(10^2 + c^2((5 - t)^2) Gravity(t) = 6.67 10^-11 sum(802,000distance(t), for t > 0, t < 10) * (10 / distance(t))
Now I think I sort-of see what you’re trying to do here, but I don’t understand what’s motivating that specific expression; it seems to me that if you want to treat space and time symmetrically, then the expression you want is something more like
(80)\,dt}{10%5E2+(-50+10t)%5E2+c%5E2(5%20-%20t)%5E2}), which should be able to be evaluated with the help of a standard integral table.
Please don’t interpret this as hostility (for this is the sort of forum where it’s actually considered polite to tell people this sort of thing), but my subjective impression is that you are confused in some way; I don’t have the time or physics expertise to fully examine all the ideas you’ve mentioned and explain in detail exactly why they fail or why they work, but what you’ve said so far has not impressed me. If you want to learn more about physics, you are of course aware that there are a wide variety of standard textbooks to choose from, and I wish you the best of luck in your future endeavors.
I do not interpret it, or any of your other responses, as hostility. (I’ve been upvoting your responses. I requested feedback, and you’ve provided it.)
I did indicate the integral would be more accurate; I can run a summation in a few seconds, however, where an integral requires breaking out a pencil and paper and skills I haven’t touched since college. It was a rough estimate, which I used strictly to show what it was such a test should be looking for. Since we aren’t running the test itself, accuracy didn’t seem particularly important, since the purpose was strictly demonstrative.
(Neither formula is actually correct for the idea, however. The constant would be be wrong, and would need to be adjusted so the gravitational force would be equivalent to the existing formula for an object at rest.)
The effect should continue past the point that gravity arrives from the current position—it will be very minute, as distance in time is related to distance in space by the speed of light (where the C in the interval formula comes from—C in m/s, time in s, very short periods of time are very “far away”), but if I’m correct, and gravity propagates through time as well as space, it should be there.
We stop the object very suddenly because otherwise gravity from the future will counter out gravity from the past—for each position in the past, for an object moving in a straight relativistic line, there will be an equidistant position in the future which balances out the gravity from the position in the past. That is, in your model, imagine that gravity is being emitted from every position the particle moving in the line is at, or was ever at, or ever will be at; at the origin, the total gravitic force exerted on some arbitrary point some distance away is centered at the origin. If the particle stops at the origin, the gravity will be distributed only from the side of the origin the particle passed through.
A second, potentially simpler test to visualize is simply that an object in motion, because some of its gravitic force (from the past and from the future) is consumed by vector mathematics (it’s pulling in orthogonal directions to the point of consideration, and these orthogonal directions cancel out), exhibits less apparent gravitational force on another particle than one at rest. (Respective to the point of measurement.)
Drawing a little picture: . …..................> (A single particle in motion; breaking time into frames for visualization purposes; the first and the last period, being equidistant and with complimentary vectors, cancel out all but the downward force; the same gravitational force is exerted as in the below picture, but some of it cancels itself out)
versus, over the same time frame: . . The second particle configuration should result in greater apparent gravity, because none of the gravity vectors cancel out.
As for interpreting it, imagine that gravity is a particle (this isn’t necessary, indeed, no particles are necessary in this explanation, but it helps to visualize it). Now imagine a particle of mass M1 moving in a stable orbit. The gravitic particles emitted from M will vary in position over time according to the current position of M1, and indeed will take on a wavelike form. According to my model, this wavelike from -is- light; the variations in the positions of the gravitic particles create varying accelerations in particle M2, another mass particle some distance away, resulting in variable acceleration; insufficient or disoriented acceleration on particle M2 will merely result in it moving in a sinelike wave, propagating the motion forward; sufficient acceleration of the proper orientation may give it enough energy to jump to another stable orbit.
Again, I suspect people will have a much better chance at understanding your ideas if you make your explanations much more concrete and specific—maybe even to the point of using particular numbers. Abstraction and generality and intuitive verbal descriptions are beautiful and great, but they only work if everyone involved has an adequate mental model of exactly what it is that’s being abstracted over.
What do I mean, specifically and concretely, when I speak of specific and concrete explanations? Here’s an example: let’s consider two scenarios (very similar to the one I tried to describe in the grandparent)---
Problem One. There’s a coordinate system in space with origin [x, y, z] = [0, 0, 0]. Suppose my mass is 80 kg, and that I’m floating in space ten meters away from the origin in the x-direction, so that my position is described as [10, 0, 0]. A 2000 kg object is moving at the constant velocity 10 m/s towards the origin along the negative y-axis, and its position is given as r(t) = [0, −50 + 10t, 0]. Calculate the force acting on me due to the gravity of the object at t=5, the moment the object reaches the origin.
Problem Two. Everything is the same as in Problem One, except that this time, the object’s position is described by the piecewise-defined function r(t) = [0, −50 + 10t, 0] if t < 5 and r(t) = [0, 0, 0] if t >= 5---that is, the object is stopped at the origin. Again, calculate the force on me when t = 5.
Solutions for Newtonian Physics The answers are the same for both problems. Two objects with mass m and M exert a force on each other with magnitude GmM/r^2. At t = 5, I’m still at [10, 0, 0], and the object is at the origin, so I should experience a force of magnitude G(80 kg)(2000 kg)/(10 m)^2 = (6.67 10^-11 m^3/(kgs^2))(80 kg)(2000 kg)/(100 m^2) = 1.067 * 10^-7 N directed toward the origin.
Now, you say that “for each position in the past, for an object moving in a straight relativistic line, there will be an equidistant position in the future which balances out the gravity from the position in the past,” which suggests that your theory would compute different answers for Problem One and Problem Two. Can you show me those calculations? Or if the problem statement doesn’t quite make sense (e.g., because it implicitly assumes an absolute space of simultaneity, which doesn’t actually exist), could you solve a similar problem? I realize that this may seem tedious and elementary, but such measures are oftentimes necessary in order to explain technical ideas; if people don’t know how to apply your ideas in very simple specific cases, then they have no hope of understanding the general case.
To use a slightly different problem pair, because it would be easier for me to compute:
Problem one. I have mass of 80kg at point [10,0] (simplifying to two dimensions, as I don’t need Z). A 2,000 KG object is resting at position [0, 0]. The Newtonian force of 1.0687 10^-7 N towards the origin should be accurate. [Edit: 1.06710^-6 N, when I calculated it again. Forgot to update this section]
Problem two. I have mass of 80kg at point [10,0] A 2,000 KG object is moving at 10 m/s along the Y axis, position defined as r(t) = [0, −50 + 10t]. Using strictly the time interval t = 0 → t = 10, where t is in seconds, calculating the force when t=5...
distance(t) = sqrt(10^2 + c^2((5 - t)^2) Gravity(t) = 6.67 10^-11 sum(802,000distance(t), for t > 0, t < 10) (10 / distance(t)) [Strictly speaking, this should be an integral over the whole of t, not a summation on a limited subset of t, but I’m doing this the faster, slightly less accurate way; the 10 / distance(t) at the end is to take only the y portion of my vectors, as the t portion of the gravitational vectors cancel out.]
Which gives, not entirely surprisingly, 1.067 * 10^-6 N directed to the origin. (I think your calculation was off by an order of magnitude, I’m not sure why.)
The difference between Newtonian gravity and gravity with respect to y is 3.38 * 10 ^-33. Which is expected; if the difference in gravitational force were greater, it would have been noticed a long time ago.
I probably messed up somewhere in there, because my brain is mush and it’s been a while since I’ve mucked about with vectors, but this should give you the basic idea.
I must apologize for the delay in replying. Regretfully, I don’t think I can spare any more time for this exchange (and am going to be taking a break from this and some other addicting sites), so this will likely be my final reply.
Now I think I sort-of see what you’re trying to do here, but I don’t understand what’s motivating that specific expression; it seems to me that if you want to treat space and time symmetrically, then the expression you want is something more like
Please don’t interpret this as hostility (for this is the sort of forum where it’s actually considered polite to tell people this sort of thing), but my subjective impression is that you are confused in some way; I don’t have the time or physics expertise to fully examine all the ideas you’ve mentioned and explain in detail exactly why they fail or why they work, but what you’ve said so far has not impressed me. If you want to learn more about physics, you are of course aware that there are a wide variety of standard textbooks to choose from, and I wish you the best of luck in your future endeavors.
I do not interpret it, or any of your other responses, as hostility. (I’ve been upvoting your responses. I requested feedback, and you’ve provided it.)
I did indicate the integral would be more accurate; I can run a summation in a few seconds, however, where an integral requires breaking out a pencil and paper and skills I haven’t touched since college. It was a rough estimate, which I used strictly to show what it was such a test should be looking for. Since we aren’t running the test itself, accuracy didn’t seem particularly important, since the purpose was strictly demonstrative.
(Neither formula is actually correct for the idea, however. The constant would be be wrong, and would need to be adjusted so the gravitational force would be equivalent to the existing formula for an object at rest.)
Thank you for your time!