# Is reverse time dilation posssible?

#### LodeRunner

Hypothetically, if someone built an antigravity generator out of an exotic material that warped spacetime in an opposite way, so that matter was repelled instead of attracted, would the passage of time speed up for that frame of reference?

I'm not a physicist or physics student, though I am a sci-fi writer interested in being as realistic as possible. It occurs to me that if negative energy densities and exotic matter do exist and have inverse gravitational properties, then inverse time dilation must also be a possibility. Given an antigravity generator of sufficient power, one could achieve impressive effects, ex. speeding up the passage of time in a certain region of space so much that for every second that passes outside the region, many years pass on the inside.

Of course, the strong antigravity would make it very difficult for anyone to remain in this region of space for long, but I think I've already figured out a way around this problem. Given a spherical net of antigravity generators connected by filaments made out of another fantastic and nigh-unbreakable form of matter, the region of space at the center of the sphere should experience accelerated time without any harmful effects. The generators would be positioned so that they would cancel each other out, i.e. each object in the region is subjected to very strong antigravity, but from all sides equally. My first instinct was to assume that the objects in the center would be crushed into neutronium, but then I realized that this could only happen due to tidal gravity. If the central region is proportionally small enough (as compared to the entire volume of the sphere) that the strength of antigravity is roughly the same from every direction at every point in the region, then objects or people located in that region of space would feel no gravity at all... yet they would experience the reverse time dilation, because that would not be canceled out.

Comments and objections are very much welcome. I consider myself reasonably well read in relativity and physics, but I wouldn't mind hearing from someone who really knows what they're talking about. Given the existence of these antigravity generators and a cable with incredible tensile strength to keep them from flying apart, would this device really work?

Related Special and General Relativity News on Phys.org

#### russ_watters

Mentor
Time dilation doesn't speed up or slow down time for a given frame of reference, it is what you get when you compare two frames. So to slow your time compared to someone else, move with respect to the other frame. And to speed up your time compared to someone else, have them move with respect to you.

Most of the rest of that is just idle speculation.

#### LodeRunner

russ_watters said:
Time dilation doesn't speed up or slow down time for a given frame of reference, it is what you get when you compare two frames. So to slow your time compared to someone else, move with respect to the other frame. And to speed up your time compared to someone else, have them move with respect to you.
I know that it's only valid when comparing two frames of references, but for sake of brevity one can often shorten it to "it slows down" (or in this case, "it speeds up") time. In the real world there will always been another frame of reference to compare it to.

...move with respect to...
Um, I don't mean to be condescending, but you are aware of the existence of gravitational time dilation, right? That time slows down considerably as one enters a region of space containing a black hole? (Again, this is just shorthand for "as compared to a frame of reference outside of this region of space and outside the influence of any other black holes")

I am not really concerned with velocity time dilation at the moment, and your bringing it up makes me suspect that you are wholly unaware of gravitational time dilation.

Most of the rest of that is just idle speculation.
Speculation, yes, but I take offense at the "idle". Like I said before, I am an aspiring science fiction author; it's my duty to speculate. However, there is a marked difference between wild Star Trek-type speculation made solely for the purpose of advancing the plot, and speculation that is at least somewhat grounded in reality, and could even conceivably lead to an actual scientific theory (emphasis on "could".) I believe that this speculation is the latter, though I'm not yet sure.

There ARE such things as negative energy densities. The Casimir Effect is the only proved example that I know of, but its existence at least makes it plausible that other forms of exotic energy or matter could exist. Given that gravitation increases with mass, a negative mass (to me) implies negative gravitation, which implies negative time dilation.

There are numerous problems with the actual implementation of my idea, but I am concerned only with theory. In a sci fi story, one does not need to know how exactly every single widget works; I just want to know if it is plausible.

So, I'll ask again: Does negative mass imply negative gravitation, and if so does that then imply negative time dilation (speeding up as compared to other frames of reference that lack a source of anti-gravity)?

#### JesseM

russ_watters said:
Time dilation doesn't speed up or slow down time for a given frame of reference, it is what you get when you compare two frames. So to slow your time compared to someone else, move with respect to the other frame. And to speed up your time compared to someone else, have them move with respect to you.
I think LodeRunner was talking about gravitational time dilation, not velocity-based time dilation as seen in inertial frames. Gravitational time dilation is more "objective" in the sense that both observers will agree whose clock is running slower, in terms of what they see using light signals (and I think they'd also agree about whose clock was running slower relative to some 'natural' choice of coordinate systems, like Schwarzschild coordinates). I don't know what would happen if you plug in negative mass/energy into the equations of general relativity (I know you don't get complete nonsense, negative energy is part of the recipe for stable wormholes in GR)--does it lead to any sort of "antigravity"? In Newtonian physics, if you place a negative mass next to a postive one, the positive one is gravitationally repelled by the negative one, while the negative one is gravitationally attracted to the positive one, so something similar should be true in GR. Would the time dilation effects for observers at different distances from a negative-mass planet be the same as if it had positive mass?

#### Chronos

Gold Member
Traveling forward in time is easy and automatic in this universe. You can adjust your speed of time [relative to the clocks of your target object] by accelerating in it's direction. This will cause your clock to run slower than the target clock. Gravity is the fundamental player here. Gravity is attractive for both matter and anti-matter, but theoretically repulsive for imaginary matter. If you can figure out how to make imaginary matter, you might be able to travel back in time [and most likely lose causal contact with everything in this universe].

#### pervect

Staff Emeritus
The biggest unrealistic story element from the standpoint of pure physics are the anti-gravity genreators (in my opinion, anyway).

If you postulate a negative-mass Schwarzschld solution, it should generate gravitational time acceleration as you suggest. If you make the negative-mass Schwarzschild solution hollow, it should have a field-free region in the interior, as you suggest. In order to get significant time accelerations, though, you would need to generate a black hole-sized negative mass (the amount of mass required depends on the radius you want to enclose in the time acceleration field) AND you'd have to hold it together. This would not be actually practical, but I don't think there's anything wrong with the theory.

This would be one way of meeting a tight schedule at work, though perhaps a trifle expensive :-).

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#### JesseM

Chronos said:
Traveling forward in time is easy and automatic in this universe. You can adjust your speed of time [relative to the clocks of your target object] by accelerating in it's direction. This will cause your clock to run slower than the target clock. Gravity is the fundamental player here. Gravity is attractive for both matter and anti-matter, but theoretically repulsive for imaginary matter. If you can figure out how to make imaginary matter, you might be able to travel back in time [and most likely lose causal contact with everything in this universe].
I dunno if LodeRunner was talking about going backwards in time, I thought he/she was asking if clocks would speed up relative to distant observers when they got close to a negative-mass object, the way they slow down relative to distant observers when they get near a positive-mass object. If I'm understanding pervect's answer correctly, the answer is yes.

#### LodeRunner

pervect said:
The biggest unrealistic story element from the standpoint of pure physics are the anti-gravity genreators (in my opinion, anyway).
I pretty much knew this would be the case from the outset, but I'm quite content with it being theoretically possible, even if it is in all probability impossible to construct. It's a big stretch of the imagination to think that a civilization would ever overcome these technical hurdles, even an very highly advanced civilization, but I think sci-fi was meant to stretch our imaginations. At least this contraption has its theoretical roots based in science fact, which is something you can't say about many of the devices and phenomina found in pop sci-fi.

Many thanks for the replies. I may return later...I've got this idea for an ultimate weapon that I've been toying with...

#### LodeRunner

JesseM said:
I dunno if LodeRunner was talking about going backwards in time, I thought he/she was asking if clocks would speed up relative to distant observers when they got close to a negative-mass object, the way they slow down relative to distant observers when they get near a positive-mass object. If I'm understanding pervect's answer correctly, the answer is yes.
You're quite right of course, but I think Chronos may also be right in saying that negative mass or energy is a key component in being able to travel back in time. I seem to remember Hawking saying that he had mathematically proved this in one of his books, that one needed negative energy (or mass) in order to travel back in time.

#### JesseM

LodeRunner said:
You're quite right of course, but I think Chronos may also be right in saying that negative mass or energy is a key component in being able to travel back in time. I seem to remember Hawking saying that he had mathematically proved this in one of his books, that one needed negative energy (or mass) in order to travel back in time.
Negative energy is a key component in propping a wormhole open, and wormholes could theoretically be used for time travel by moving one mouth at high velocity away from and back towards the other mouth, so the mouth taken on this trip will be "younger" when it returns, like in the twin paradox. But if you looked through the wormhole from one mouth to another during this trip you'd see clocks near both mouths ticking at the same rate, so that time is threaded differently through the wormhole than through normal space--if we are both 30 years old when you depart with one mouth while I stay with the other one, and the trip away and back takes 5 years for you but 10 years for me, then when you return you will meet me as a 40-year old, but if you jump through your mouth you will pop out of my mouth when I was only 35 years old. It's possible that quantum effects will conspire to destroy the wormhole when one mouth enters the other's light cone though (which would be the point where time travel would become possible), and I think it's also not known if negative energy is really possible (it's true that the casimir effect shows you can have energy that's lower than the ground state of the quantum vacuum, but without a theory of quantum gravity I don't think physicists can say for sure that this has the same meaning as negative energy in GR, or if the quantum vacuum should be thought of as having some nonzero energy of its own).

#### LodeRunner

JesseM said:
In Newtonian physics, if you place a negative mass next to a postive one, the positive one is gravitationally repelled by the negative one, while the negative one is gravitationally attracted to the positive one, so something similar should be true in GR.
How does that work exactly? Does anyone know if it holds up in GR?

I didn't count on the antimass actually being attracted to matter at the same time that the matter is being repelled. Do the repulsion and attraction cancel each other out exactly? Are they dependant on mass/antimass? Does the antimass repell other antimasses? Would the sphere implode on itself under the attraction of the +mass or be halted by its own repulsion of itself or halted by the repulsion of the +mass? Is any of this at all answerable, theoretically speaking?

#### hellfire

Note that an object with negative mass near another object with poisitive mass would experience a repelling force due to its negative gravitational mass, but would accelerate towards the positive mass due to its negative inertial mass (assuming the validity of the equivalence principle). On the contrary, the positive mass would experience also a repelling force but would accelerate away from the negative mass.

#### russ_watters

Mentor
LodeRunner said:
Um, I don't mean to be condescending, but you are aware of the existence of gravitational time dilation, right?
Yeah, sorry - the same thing can be achieved by having different people move up or down in a gravitational field.

#### Mortimer

I wonder if the assumption that negative gravity will lead to an acceleration of time is logically making sense at all. Think of the time dilation as being a result of the curvature of space-time, regardless of the 'direction' in which this space-time is curved. Total absense of such curvature, i.e. an absolute flat space-time (like in SR) gives the lowest time-dilation, or you could say that this gives timespeed X. Any curvature, caused by gravity or anti-gravity will then lead to timespeeds <X.
Expecting time to speed up with anti-gravity is a bit like expecting that a 'negative' detour will give you a shorter path.

#### nemosum

I think Mortimer has a point. Picture space-time as the classic rubber sheet. if you drop a bowling ball in the middle the sheet will bend down, representing gravity caused by a large body of mass. Likewise we can picture this body of imaginary mass as a bowling ball being shoved up from underneath the sheet, resulting in everything rolling off of it, or "anti-gravity". But either way, the sheet bending down or up, it will take longer for a lightbeam to traverse that area of space due to the warping of the space-time fabric.

#### RandallB

Reverse time - already been observed.

LodeRunner said:
Hypothetically, if someone built an antigravity generator out of .... experience the reverse time dilation, .....
Experiments have already shown time moving backwards no negative mass or energy required. So “reverse time dilation” real yes, but the “antigravity generator” part I don’t thing so -- but you can make up anything in sci-fi.

If you’d like to demonstrate it mathematically plot out ALL the times distances and synchronizations points for two near light speed ‘trains’. One coming towards your base station and one away from you, both passing several base framed stations along the way. (Take your time and be careful with the conversions and charting the observed times for train cars & stations for all). You should find that apparently one of the trains is moving backwards in time.

Can this be proven? I’d say it already has been! No need to spend Mega Bucks to get a couple of near light speed ships flying. Smaller distances and shorter time intervals have already worked in tests at a much lower costs. Just a couple feet with times under nano-seconds, was all that they needed using Particle accelerators. There you find electrons better understood as positrons move backwards in time, plus positrons better explained as electrons moving backwards in time.

For more details on how this has already been observed and explained see some of Richard Feynman’s lectures on Feynman diagrams. Your term of “reverse time dilation” might not be used but “backwards in time” amounts to the same thing.

But for use in sci-fi writing – frankly your better off just “assuming” something like a “Flux Capacitor” if your intent on going back to meet yourself in the past.
Don’t expect a realistic explanation help make a plot believable. Your story has to do the job of getting the reader/audience to ‘suspend their disbelief’.

#### JesseM

RandallB said:
Experiments have already shown time moving backwards no negative mass or energy required. So “reverse time dilation” real yes, but the “antigravity generator” part I don’t thing so -- but you can make up anything in sci-fi.
If you’d like to demonstrate it mathematically plot out ALL the times distances and synchronizations points for two near light speed ‘trains’. One coming towards your base station and one away from you, both passing several base framed stations along the way. (Take your time and be careful with the conversions and charting the observed times for train cars & stations for all). You should find that apparently one of the trains is moving backwards in time.
Can this be proven? I’d say it already has been! No need to spend Mega Bucks to get a couple of near light speed ships flying. Smaller distances and shorter time intervals have already worked in tests at a much lower costs. Just a couple feet with times under nano-seconds, was all that they needed using Particle accelerators. There you find electrons better understood as positrons move backwards in time, plus positrons better explained as electrons moving backwards in time.
For more details on how this has already been observed and explained see some of Richard Feynman’s lectures on Feynman diagrams. Your term of “reverse time dilation” might not be used but “backwards in time” amounts to the same thing.
Feynman's theories aren't really about time moving backwards in a literal sense. They just show that mathematically a positron moving forward in time can be treated as equivalent to an electron moving backward in time, and likewise an electron moving forward in time can be treated as equivalent to a positron moving backward in time--there is no absolute truth about whether a given particle is moving forward or backward in time. Also, I think "moving forward/backward in time" here is just a verbal description of some mathematical procedure, like whether you evaluate an integral from $$t_0$$ to $$t_1$$ or from $$t_1$$ to $$t_0$$. This FAQ on virtual particles says:
Now, consider a virtual photon that comes from the particle on the right and is absorbed by the particle on the left. Actually calculating the photon's wave function is a little hairy; I have to consider the possibility that the photon was emitted by the other particle at any prior time. (However, I can save myself a little effort later by automatically including the possibility that the photon actually comes from the particle on the left and is absorbed by the particle on the right, with the recoil nudging the left particle: all I have to do is include situations in which the photon is "emitted on the right" in the future and goes "backward in time," and take its momentum to be minus what it really is! As long as I remember what's really going on, this trick is formally OK and saves a lot of trouble; it was introduced by Richard Feynman.)
And here's a Feynman quote from a response to a letter someone sent asking about time travel (found on p. 300 of Perfectly Reasonable Deviations from the Beaten Track):
Dear David:

I was glad to hear from you. I looked at your enclosure "Travelling in Time," but didn't read beyond the second sentence because I, also, believe that time travel cannot be done, and I thought my colleagues agreed with me. The science fiction writers who have interpreted my view of the positron as an electron going backward in time have not realized that that theory is completely consistent with causality principles, and in no way implies that we can travel backward in time.

Sincerely,
Richard P. Feynman

#### RandallB

I never said Feynman claimed "backwards in time" for the macro world.
Feynman Diagrams are about the micro world. Without accepting backwards time movement inside a Feynman diagram; you’re forced to accept photons appearing from nowhere or being guided to just the right location by Magic.
So I guess you can pick one: Magic Photons or Backwards Time inside the diagram.

If you’re just writing fiction what’s it matter? Otherwise, if you like work though a few Feynman Diagram plots and see what you think. Myself “Occam's Razor” suggests to me that (Within the space-time allowed for the micro experiment) “Backwards Time” is most likely real vs. “Magic Photons”.

#### JesseM

JesseM said:
In Newtonian physics, if you place a negative mass next to a postive one, the positive one is gravitationally repelled by the negative one, while the negative one is gravitationally attracted to the positive one, so something similar should be true in GR.
LodeRunner said:
How does that work exactly? Does anyone know if it holds up in GR?
In Newtonian physics, it's just based on the equation for the gravitational force between two objects with masses $$m_1$$ and $$m_2$$, $$F = G m_1 m_2 / r^2$$ along with F = ma for each object. This means that each object will experience acceleration $$G m' / r^2$$ along the vector pointing at the other object, where m' is the mass of the other object. For the positive-mass object, m' is negative, so it experiences the acceleration in the opposite direction as normal gravitational attraction. For the negative-mass object, m' is positive, so it is attracted to the other object in the normal way. This means that if you put two objects of equal and opposite mass next to each other, they will both accelerate continually in the direction of a vector from the negative-mass object to the positive-mass object, maintaining a constant distance between them while their speed increases without bound...this doesn't violate conservation of energy though, because the ever-increasing positive kinetic energy of the positive mass is balanced out by the ever-increasing negative kinetic energy of the negative one.

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#### JesseM

RandallB said:
I never said Feynman claimed "backwards in time" for the macro world.
Feynman Diagrams are about the micro world. Without accepting backwards time movement inside a Feynman diagram; you’re forced to accept photons appearing from nowhere or being guided to just the right location by Magic.
So I guess you can pick one: Magic Photons or Backwards Time inside the diagram.
Particles in feynman diagrams appear from nowhere regardless--if you have a photon that's emitted and absorbed within the diagram, how does the backwards-in-time idea help you avoid it?

And again, I don't think it's really about saying that any given particle in the diagram is objectively moving back in time, it's about having two equally valid ways of describing any given particle, as either a certain particle moving forward in time or its antiparticle moving backward in time.

Also, what did you mean when you said "Experiments have already shown time moving backwards no negative mass or energy required"? What experiments have shown this? The virtual particles in Feynman diagrams are never observed experimentally, they're just part of a mathematical procedure for calculating the probability of various results.

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#### JesseM

nemosum said:
I think Mortimer has a point. Picture space-time as the classic rubber sheet. if you drop a bowling ball in the middle the sheet will bend down, representing gravity caused by a large body of mass. Likewise we can picture this body of imaginary mass as a bowling ball being shoved up from underneath the sheet, resulting in everything rolling off of it, or "anti-gravity". But either way, the sheet bending down or up, it will take longer for a lightbeam to traverse that area of space due to the warping of the space-time fabric.
I think you're taking the rubber-sheet metaphor too literally--the orientation of the curved sheet in the higher-dimensional embedding space (a depression pointing 'down' vs. a bump pointing 'up') isn't relevant, it's only the curvature that matters. Also, although on an ordinary curved 2D surface a geodesic would be the shortest path between two points on the surface, in GR a geodesic is the path through curved spacetime with the greatest proper time (time as measured by a clock that travels along the path), which is not captured by the rubber-sheet metaphor. I don't know the details, but I assume when you do the math, negative energy would curve spacetime in a different way from positive energy...stable wormholes are said to require negative energy to hold them open, which wouldn't make sense if negative energy and positive energy curved spacetime in just the same way.

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#### RandallB

JesseM said:
I think you're taking the rubber-sheet metaphor too literally.
That makes sense, but then where does all this negative mass stuff come from? Not anti-matter I hope, it's mass warps space-time (or the rubber-sheet) the same way as "normal" matter so are you just making something up for the fiction guys here or are you basing "negative mass" [repeling but following + mass ??] on something?

#### pervect

Staff Emeritus
RandallB said:
That makes sense, but then where does all this negative mass stuff come from? Not anti-matter I hope, it's mass warps space-time (or the rubber-sheet) the same way as "normal" matter so are you just making something up for the fiction guys here or are you basing "negative mass" [repeling but following + mass ??] on something?
Hermann Bondi, "Negative Mass in General Relativity", Reviews of Modern Physics 29, 423 (1957)

is probably one of the first references in physics.

(This is actually a secondary reference from one of Cramer's Alternate View columns, BTW)

http://www.npl.washington.edu/AV/altvw14.html

Negative mass aka exotic matter is also one of the main requirements to build wormholes. The Casimir effect, a force between a pair of _uncharged_ conducting plates in a vacuum, is an example showing that such negative energy densities are not entirely theoretical and may have some physical basis. Note that the Casimir effect is a quantum effect, while GR is a classical theory.

The wikipedia article on exotic matter isn't very good (I seem to recall it used to be shorter and better). The best article I could find on a popular level was

http://www.physics.hku.hk/~tboyce/sf/topics/wormhole/wormhole.html [Broken]

So far I haven't been able to find anything that refershes my recolleciton on the tie-in between exotic matter and violations of the strong, weak, null, or dominant energy conditions in GR. Basically, I recall that exotic matter and the Casimir effect both violate one of these energy condtions, but not which one it is. Pinning this relationship down, along with an exact statement of the associated energy condition, would make my article a lot less hand-wavy that it has been, but I just can't recall the details anymore :-(.

I thought Cramer had something along these lines in his pop-sci articles about wormholes, but I didn't find anything.

BTW, Cramer's complete collection of old pop-sci articles (not including the last few years) can be found online at

http://www.npl.washington.edu/AV/

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#### RandallB

pervect said:
Hermann Bondi, .. Negative mass aka exotic matter .../QUOTE]Matter and anti-matter vs. exotic matter and I assume anti-exotic matter; OK sounds like good stuff for our fiction writer.

For me, I’ll stick with Occam, since I’m not buying into the “Wormhole” thing anyway.
And if believing the “Backwards Time” is a real thing within a closed microscopic sample, means I consider Anti-gravity, Wormholes and Exotic matter to be fabrications. –-– I’ll take my chances with the negative time till someone can demonstrate one of the others as real.

#### JesseM

RandallB said:
And if believing the “Backwards Time” is a real thing within a closed microscopic sample, means I consider Anti-gravity, Wormholes and Exotic matter to be fabrications.
What does Feynman's backwards-time idea have to do with the question of negative energy in GR? The question of whether or not the second is possible doesn't really have anything to do with whether you accept Feynman's idea (and I don't think anyone disagrees that mathematically Feynman's trick works, whether you interpret this as meaning that some particles are 'really' moving backwards in time seems like more of a philosophical issue).

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