Warp Drive Soliton Inertia
Hello All,
In this post I log some thoughts on another proposed challenge to superluminal warp drives: acceleration of the soliton past the speed of light. In their paper published earlier this year, Bobrick and Martire (Introducing Physical Warp Drives) state on page 17 of their pre-print that one cannot accelerate a subluminal warp drive to superluminal speeds for similar reasons as why one cannot accelerate masses moving through space-time to superluminal speeds:
Warp drives can move superluminally only in the same sense as any ordinary inertial mass, test mass, or any other object. Namely, there is no known way of accelerating regular material beyond the speed of light. However, one may postulate a test particle which moves faster than light in relativity, in which case it may continue moving inertially. In the same way, as warp drives are shells of material, there is no known way of accelerating a warp drive beyond the speed of light. However, one may also postulate the warp drive shell to be in superluminal motion, just like the hypothetical test particles, and the shell-like object will continue moving in the same fashion. In this sense, superluminal warp drives are at least as hypothetically possible as any other superluminal objects.
The crux of the above statement is that a warp soliton acts like a point-like massive test body being moved through space-time, having constant non-vanishing inertia (resistance to acceleration) regardless of velocity. In relativity theory, constant inertia implies that a force acting on an object with set mass over a set period of proper time will produce the same change in spatial momentum. However, as a result of the invariance of the speed of light to non-accelerating reference frames, there is an asymptote in momentum and energy as a body approaches the speed of light relative to another time-like observer.
But does a warp drive act in this way? And if it does, what is its inertia?
Recall that the means we are using to create these solitons is intrinsically different as we are not accelerating objects through space-time, but manipulating spacetime itself to alter a ship's separation from an object at some arbitrary speed. As the concept of inertia is rooted in the former (the motion of objects through space-time), we must reconsider what inertia means in the context of warp drives. Since there is no well-defined acceleration mechanism in the literature for a warp drive, and I will not go to the trouble here of solving both the Einstein equation and the stress-energy-momentum conservation law in order to produce one, let us consider the difference between two warp drives at different velocities assuming that there is some acceleration-like process that can connect them.
Let us define inertia for a warp drive soliton as a normalized ratio of the infinitesimal change in momentum over infinitesimal change in energy of a soliton having experienced change in velocity along its original direction of motion
m = r.δp/δE,
where r = v (c/|v|)2 and v is in the velocity. Note that in the limit of a point-like particle moving through space-time, this quantity is the same as the particle mass.
Consider a warp bubble from my paper Breaking the Warp Barrier of a given velocity v. The (Eulerian) energy of that bubble is given by E(|v|) and its (Eulerian) momentum is p = 0, both calculated through the Einstein equation. The zero momentum of the soliton is something of a surprise considering the non-zero energy required to make the bubble. This is a result of the way this warp bubble is constructed, and indicates that the medium sourcing the soliton in net is locally co-moving with the bubble. It does not imply that nothing inside the bubble is moving.
Therefore, a change in soliton velocity would produce no change in momentum. The soliton has zero inertia according to the above definition, and may not be limited to subluminal speeds by that consideration alone. This is not to say that this warp bubble could easily be accelerated to superluminal speeds. There is still a challenge in the form of the dominant energy condition (DEC), which states that sources viewed from any future-pointing reference frame cannot locally move faster than light, which this soliton still violates as it nears the speed of light. I plan to discuss the DEC and the challenge it presents to FTL in more detail in a future post.
Have a good Tuesday,
Erik
Hmmm this is very interesting, I really hope that the challanges will be overcome.
ReplyDeleteHowever I cannot help but wonder something. In the papers related to your research and the counter-papers, it is stated multiple times that the Energy Conditions aren't fundamental physics. If that is true, then why exactly are they so important?
It is true that the energy conditions are not fundamental. Some, like the trace energy condition, can be violated with conventional matter such as a sufficiently hot plasma. I primarily use them as proxies for how the sourcing media is behaving. If I violate one of the conditions, I should think a bit harder about what is going on.
DeleteHmmm, sourcing media? You mean space time?
DeleteI take it that what you are saying is that if some of these conditions are violated there could be unpredictable effects that could be hazardous?
Some...unforseen consequences? (Apologies...I just had to)
Do you have any comments on this paper ?https://link.springer.com/article/10.1140/epjc/s10052-021-09484-z/ I was a bit disappointed by the criticism, I couldn't find any obvious mathematical mistakes, but as an engeneer I might not be the best to say that...any thoughts about?
ReplyDeleteI am still in the process of reading the paper. It looks like the results of the paper are simulation based, which I found confusing given some of the related news articles claiming that a real warp bubble had been created.
DeleteThe same goes for me... some articles really went clickbait on this. Which is pretty disgusting. I just hope that the paper itself holds some merit and that it can be useful to warp drive research.
Delete"But does a warp drive act in this way? And if it does, what is its inertia?
ReplyDeleteAs the concept of inertia is rooted in the former (the motion of objects through space-time), we must reconsider what inertia means in the context of warp drives."
Could your disconnect in the matter of the soliton momentum be found in your own statement? A little commentary on your definitions. Is it possible, in your attempt to reconcile inertia in the context the warp drive you might need to consider not just the energy of the warp bubble itself but of the ship that is creating the soliton? Thus the zero momentum of the soliton is actually a fictitious situation since the energy (and momentum) needed for its creation would stem from the vehicle at its center.
At the moment, this soliton does not contain a ship. Hopefully that will change in future work and I will be able to get back to you on your momentum question. Also, while I did not state it explicitly in the post above, it might be helpful to know that I was considering outside but unspecified influences to be the cause of the soliton's acceleration.
DeleteI don't have much idea of physics, but I have read many times that one of the reasons we can't travel faster than light is that it would violate casualty by allowing time travel. Does your warp drive avoid violating causalty? Thanks.
ReplyDeleteIt seems that if one accepts the relativity of simultaneity, any warp drive would allow time travel and violate causalty. The only case I see you could avoid that is if there were absolute simultaneity as in the Lorentz Ether Theory, although I don't know if in that theory a warp drive would be posible.
DeleteExtremely interesting solution to hyper travel in space.
ReplyDeleteImportant question .
Theoretically, what kind of G-forces if any would the crew of a
vessel travelling inside a Soliton experience ?
Physiologically, would travelling in a rolling plasma bubble create a zero, negative, positive or even a fluctuating gravitational field ?
Ideally, a passenger inside a warp drive soliton would experience no acceleration.
DeleteWhat I always wondered about these warp drives was not so much linear momentum but angular momentum. For example, suppose we start with our two favorite observers, Alice and Bob. Both start out in Minkowski space-time. Alice is (naturally) at the origin of her coordinate system, watching a 100 kg object located at x = 10 m, y = 0, z = 0 and with velocity v = 0. For this system, Alice measures the angular momentum of the object as L = 0.
ReplyDeleteThe object turns on a warp drive at t = 0, warps up to x = 10 m, y = 1,000 m, and z = 0 m, and then turns the warp drive off after an infinitesimal time t = delta. It retains its velocity v = 0. Again, Alice measures the angular momentum as L = 0.
Now lets consider Bob. Bob is moving toward Alice at a velocity v_x = 10 m/s, v_y = 0, v_z = 0 along Alice's x-axis. For convenience, we'll let them both use the same time coordinate system (neglecting relativistic corrections as the speeds are much less than the speed of light). At t= 0, Bob has moved sufficiently that Bob's and Alice's origins of their coordinate systems are coincident. So at t = 0, Bob measures the object at coordinates x = 10 m, y = 0, z = 0 moving at a velocity v_x = -10 m/s, v_y = 0, v_z = 0. At this point, Bob also measures L = 0.
But then the object warps. When it has turned off its warp drive, Bob measures it at x = 10 m, y = 1,000 m, and z = 0 but with V_x = -10 m/s (and all other velocity components 0). At this point, Bob measures the angular momentum as L_z = -1,000,000 kg m^2/s (and all other components zero). From Bob's point of view, the object's angular momentum has changed. If the warping was reactionless, it would appear to Bob that angular momentum conservation ha been violated. Because space-time is Minkowskian both before and after the warp drive was active, and presuming that the geometry deformation of the warp drive was localized, then at all times during this thought experiment space-time should be asymptotically flat and consequently we would expect angular momentum to be conserved.
I am curious to hear about how the particulars of your warp design allow the angular momentum of a warped object to change. What have I overlooked?
Thanks.
A warp drive soliton in GR must obey both the Einstein equation and the stress-energy-momentum conservation law. The later ensures that relativistic momentum (and by extension angular momentum) are conserved, making it difficult for the positive energy warp drives we are considering to be truly reaction-less. My guess is that if we were to create the soliton described in your scenario, the process would create other sources of angular momentum that would leave the net value null.
ReplyDeleteHi Erik, great work. 👏🏽
ReplyDeleteWhat is the effect of the mass of the warp drive on the required energy to accelerate it?
Is it directly proportional?
Hi, Sabine Hossenfelder released a video today that also talked about your paper: https://www.youtube.com/watch?v=YdVIBlyiyBA
ReplyDeleteHi Erik,
ReplyDeleteI am wondering if a dynamically evolving energy distribution can be used to generate and accelerate a soliton from flat spacetime. An error in the original Alcubierre drive was considering v = v(t) as a mechanism for accelerating the bubble which violated energy/mass conservation. A natural consideration is then to evolve the shaping function by considering a family of functions f = f(r,t) that approach Alcubierre's tophat f(r) as t approaches t_0 and hence give the appropriate shift vector B^x = -vf(r) after some time t_0. Could there be such a construction in which the energy distributions for this family of functions evolve in such a way that they do not alter their mass and satisfy the conservation of energy? If so, could a similar construction be used for your soliton by considering a time indexed family of potential functions?
Thank you for your time
Henry