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Newton's first law of motion states

An object remains with the same velocity, or position of rest unless an external force is exerted.

What if we created a hypothetical universe where

An object in motion tends to accelerate at $0.001\ m/s^2$ in the same direction as its original motion without external force. Objects at rest stay at rest.

In other words, space itself exerts a force on every moving object, without affecting the (space) itself.

All other fundamental principles such as gravity being a force, force being the rate of change in momentum, etc. are the same. All laws that do not rely on this law are the same.

Can the universe exist? Can it exist in a form similar to ours? Suppose some intelligent life forms of that universe were given our technology, which are the most important ones that will still work (or not work)?

And finally, could a Big Bang have created this universe, and can it sustain itself and grow?

Extra Q

Does it matter if I give the acceleration a different value? Or a negative one?

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    $\begingroup$ Isn't the universe already accelerating? $\endgroup$ – Frostfyre May 5 '15 at 16:47
  • $\begingroup$ @Frostfyre First of all, we are accelerating (debatable) from the centre of the universe. And second, space itself is accelerating, along with the matter in it. What I mean is that every object faces an acceleration in the path of motion that does not affect space itself. $\endgroup$ – ghosts_in_the_code May 5 '15 at 16:49
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    $\begingroup$ Which direction does the acceleration come from? If the .001 m/s^2 is being applied from all directions, doesn't it all cancel out? Also, is this acceleration applied upward/downward, or simply in the direction you are already travelling? $\endgroup$ – Twelfth May 5 '15 at 17:27
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    $\begingroup$ Wouldn't your accelerating eliminate or at least greatly shorten the time that any celestial object orbited any other? Since the gravity attraction towards the central mass is unchanging, if the orbiting object is constantly accelerating, it will only remain captured for the time it takes to reach its primary's escape velocity. Likewise, a negative acceleration would make long term orbits impossible. $\endgroup$ – Henry Taylor May 5 '15 at 17:55
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    $\begingroup$ There is no "direction you are already traveling" a person walking is going back words from the perspective of a car passing him, forward according to a person sitting on a bench and standing still relative to themselves. Since kinetic energy is mv squared and velocity is dependent on frame of reference, such a universe could not have conservation of energy. There is no real way to reconcile this. $\endgroup$ – John Meacham May 6 '15 at 2:47
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This is just some speculation on a universe in which object with mass tend to accelerate $.001 \frac{m}{s^2}$ in every reference frame except its own. (You never move in your own reference frame!) To keep with Stack Exchange's "Short Answer" format (short when compared to peer-reviewed publications), I will not justify all claims made here.

Such a universe would:

  • Be much hotter. Since temperature is proportional to the average velocity of a group of particles, and that velocity is always increasing, the average temperature will go up.
  • Thanks to the strong nuclear force, it is very likely that atoms will form at some point. Then those atoms ought to fall apart, since the kinetic energy will always be increasing.
  • As an extension of the previous point, protons and neutrons may not form, or be as stable as they are here, as the quarks within them may have too much energy to maintain their association with each other.
  • Your universe would not have the universal speed limit of $c$. Unless photons (which are massless) are also accelerating at this rate, this "breaks" physics as we know it.

I'm going to stop here. It appears your universe where everything accelerates at $.001 \frac{m}{s^2}$ would just be a plasma of fundamental particles bouncing around at incredible speeds which are physically impossible in our universe. It would be interesting as a young universe, but it would quickly devolve into this super deadly plasma-verse.

I should also add that any value of inherent acceleration, aside from 0, will result in this universe at some point in time. You would merely have more, or less, time before you reach that end-state.

Could a "big bang" have made this universe? Yes, I think so; we have no indication in modern physics as to why fundamental constants are the way they are. It's up to you to figure that one out.

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  • $\begingroup$ Seems as though the plasma-verse would be a near vacuum as well, since particles would be moving faster and faster in random directions, making the "edges" of the universe (that space in which there are particles) expand and expand and expand, without not adding any new mass. density = mass / volume, and since the volume keeps expanding, the density keeps decreasing. $\endgroup$ – BrettFromLA May 5 '15 at 23:47
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    $\begingroup$ @BrettFromLA That's actually a common misconception about the universe expanding. Matter getting further apart by flinging itself around does not expand the size of a universe. Space-time itself needs to expand; this becomes more apparent if you think of a universe which has no edge; going one way will eventually lead you back to where you are. It could still be mostly vacuum, but not for the reasons you mention. $\endgroup$ – PipperChip May 6 '15 at 3:10
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    $\begingroup$ Your universe would not have the universal speed limit of c. There is no reason why c can't be the universal speed limit. There is no upper limit on temperature; the universe would simply wind up with everything approaching increasing number of 9s (e.g. 0.99999c, etc.). $\endgroup$ – Michael May 7 '15 at 1:06
  • $\begingroup$ I'm not sure such a universe will always end up as a plasma. If the expansion of the universe is well synced with the constantly increasing temperature you might even end up with a universe that was totally stable over any amount of time. $\endgroup$ – Vakus Drake Oct 3 '16 at 19:02
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Summary: you break everything.


I've read that the laws of physics can be thought of as non-laws, and the lawlessness naturally gives rise to Newton's laws. That is, there is a lack of special cases and special things. What remains and is self-consistent?

Newton's first law as understood in modern formulations states that there is such a thing as an inertial reference frame where an undisturbed object remains in uniform linear motion. If the universe has no origin coordinate, no absolute positions are possible, as no law can be position dependant. Similarly, all directions are the same.

Relative only (not absolute) motion exists because there is no absolute reference.

In order to impose a rule as you ask, that refers to absolute rest, there must be an absolute coordinate system in space itself, a place that can be identified without regard to anything in space.

You would not have general relativity. So it must be like Galelleo's model and has absolute universal time, too.

The acceleration keeps adding energy, which grows without limit. Energy is not concerved. But isn't conservation of energy a consequence of physics working the same at any given time? We're not varying the rules, so the underlying principles of Noether's Theorm must not apply. That is, the laws cannot be formulated on a principle of least action. There is no such (useful) concept as potential energy, no Hamiltonian, and no way to express the rules using a stricly local infinitesimal patch of space around a particle. Laws must be interpreted using global knowledge of the state.

It would be, essentially, game pieces controled from without, not laws existing within the universe doing the interpretation.

Not elegant.

It would not exist in the same sense as ours. It might be a simulation in a larger universe that does have self-contained rules.

As others have pointed out, everything would get faster and faster and no structures would form. But I point out that without special relativity and with separate space and time, it will behave classicly, not form black holes or approach asymptotes.

You would not get pair-production and annialation as a required outcome of symmetries, either. What stuff exists won't naturally have decay pathways since that happens because of vacuum pair production or annihilation. It won't have quantum spin, since that (one of the triumphs of physics) appears naturally in the equations of motion due to spacetime being one thing. That's what makes matter act like solid stuff. Why is a brick solid and not able to pass through other bricks? Not from any rules introduced for the purpose (lawlessness!) but as an inevitable consequence of a cascade of emergent properties as you work out the details of having no "special" rules.

Everything about that universe needs to be programmed directly, because it's not all snowballed from the most primitive symmetry of spacetime. Good luck getting it all to fit together without contradictions and bugs.


For more on the main breaking point, check out Feynman's Messenger Lectures. It's in book form, and the live presentation is on youtube! He talks about different ways to formulate the same rule, and the 3rd way introduces "least action". That turns out to be the keys to the kingdom.

Not having conservation on energy implies that the "action princple" is not a way to formulate the laws in your proposed universe.

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Everything would reach the speed of light, simultaneously growing to infinite mass, and therefore infinite gravity, causing all matter to collapse into a single ginormous black hole. (The force of gravity would overtake the new acceleration you propose.)

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    $\begingroup$ Without relative (only) motion, you won't get Special Relativity. Everything is different. $\endgroup$ – JDługosz May 5 '15 at 20:32
  • $\begingroup$ Interesting, and a little beyond my current knowledge-base. So if there were also the acceleration proposed by the OP, mass wouldn't increase with speed? $\endgroup$ – BrettFromLA May 5 '15 at 23:17
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    $\begingroup$ Right, @BrettFromLA. That is a compelling consequence of symmetry. If you don't have the symmetry, you don't need all that work to make it work out consistently. For that matter, particle-antiparticle pair production and annialation is forced on us due to spacetime symmetry, so we don't get that either. Also no quantum spin and that's what causes matter to be hard and solid. It's all interwoven, not ad-hoc but must be to fit together. Blow all that away when you remove the first step. $\endgroup$ – JDługosz May 5 '15 at 23:25
  • $\begingroup$ Makes sense, @JDługosz! Based on our chat, I'm going to comment on PipperChip's answer about a "plasma-verse" above. $\endgroup$ – BrettFromLA May 5 '15 at 23:42
  • $\begingroup$ I added the points to my Answer, as well. Maybe I can channel Asimov and write an essay on the row of dominoes behind Newton's First. $\endgroup$ – JDługosz May 5 '15 at 23:49
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You want to read about Emmy Noether, and Noether's Law. What this law states is that for each symmetry, there is a conserved quantity. For example, if a system is symmetric regarding rotations about a point, then the angular momentum about that point must be constant, and must be preserved in all interactions.

The symmetry relevant here is symmetry regarding translations in space. If there is nothing inherently special about one location in space versus another, then momentum must be conserved. This is a mathematical phenomenon, not an empirical observation.

So, in short, no, such a universe cannot exist. The accelerating objects would fail to conserve momentum. It would be mathematically impossible to write down consistent equations of motion for objects in such a universe.

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