Time Travel/Bootstrap Paradox?

Neogaia777 said:

Not really, from the perspective of both, no one's clocks are moving any faster or slower, but if you took a round trip in a spacecraft (with a clock on board) and you were traveling faster than most everything else around you through the fabric of spacetime the whole time, when you got back, your clock would be shown to have been experiencing the passage of time slower than the ones back on earth the entire time, etc. (Leaving gravitational time dilation effects out of it for the moment of course). But, from the perspective of both looking at their own clocks the entire time, no one's own clock was going any faster or slower the entire time, but that's only because in the ship, both the clock, and the one's looking at the clock on board, were experiencing the passage of time slower the entire time. And, because of this, also when they looked out of their window, or whatever, at everything else outside of them, including the clock on earth, etc, they think they would see them as having been experiencing the passage of time slower the entire time, but it was just only because they were the entire time, etc. (or even slower as they were headed away from Earth, and just a little bit faster as they were headed back) (but that might take a little bit more explaining, and will just only further complicate the issue, so let's just leave that out of it for now) but, point being, when the craft got back to earth, their clock on board would always be behind the one on earth, and that's because they experienced the passage of time slower than those on Earth just simply because of their velocity, or faster movement/travel through spacetime, etc. And while it may have appeared to them that everything else was experiencing the passage of time slower for a time, it actually wasn't, but was just only them experiencing the passage of time slower the entire time, just simply due to their faster velocity, or faster movement/travel through spacetime, etc.

Take Care.

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In the twin paradox the clocks are biological and there is no preferred frame of reference according to special relativity.
Mary travels away from and returns to Frank's location who is stationary is equivalent to Mary being stationary and Frank the travelling twin.
The paradox is that each twin should be young relative to each other on completion of the round trip as there is no preferred frame of reference.

In fact Mary turns out to being the younger twin as during the round trip she changes direction (and undergoes acceleration in the process) which destroys the symmetry of the argument.

The Minkowski space-time diagram for the twin paradox also serves to illustrate the point.
In this case Mary does a 20 year round trip of proper time travelling at v = 0.8c.
Each year Frank sends a signal to Mary who on receiving the signal sends a signal back to Frank.
During this 20 year round trip Frank sends out 20 signals but only receives 12 signals from Mary.

Mathematically this is an example of relativistic Doppler shift, Mary ages at a slower rate than Frank during the round trip, when she returns her biological age is now younger than Frank's.

Neogaia777 said:

Time Travel/Bootstrap Paradox. A reply to somebody.

And that is what is known as the Bootstrap Paradox associated with almost all time travel. You can't go back and change anything if that change will always result in you not going back, or being able to go back, in the first place, etc. So you essentially can't ever go back and change anything ever, is what this theory/paradox amounts to really, etc. Since it will always create a different or alternate future always, etc. But I don't think any of this really matters at all anyway, as I don't think it will ever be possible in the first place, etc. "Time travel", etc. Even faster than light travel can't ever do it, etc. But I also don't know what would or could happen if you could go into a black hole maybe? Or could somehow manage to survive and also escape going into a black hole ever really? But that is only because, right now, nobody can know not one single thing about that right now currently, etc. Because even if that could take you somewhere else in the universe near instantly, the universe still always stays the same age/time equally everywhere really, etc.

Comments?

God Bless.

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If time travel were included in the laws God set up, why not reverse time to when Adam sinned and stop it?

Time travel is a reflection of man's desire to repent of falling short somewhere sometime.

sjastro said:

In the twin paradox the clocks are biological and there is no preferred frame of reference according to special relativity.
Mary travels away from and returns to Frank's location who is stationary is equivalent to Mary being stationary and Frank the travelling twin.
The paradox is that each twin should be young relative to each other on completion of the round trip as there is no preferred frame of reference.

In fact Mary turns out to being the younger twin as during the round trip she changes direction (and undergoes acceleration in the process) which destroys the symmetry of the argument.

The Minkowski space-time diagram for the twin paradox also serves to illustrate the point.
In this case Mary does a 20 year round trip of proper time travelling at v = 0.8c.
Each year Frank sends a signal to Mary who on receiving the signal, sends a signal back to Frank.
During this 20 year round trip, Frank sends out 20 signals but only receives 10 signals from Mary.

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Mathematically this is an example of relativistic Doppler shift, Mary ages at a slower rate than Frank during the round trip, when she returns her biological age is now younger than Frank's.

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Man I find it sooo difficult to decode @Neogaia777 posts!
I keep coming up with the model of Swiss Cheese whenever I read them .. there are so many concepts just absent in his posts, its hard to figure out where to start. (No offence intended towards @Neogaia777 here either .. its more a comment about me and how I'm visualising, more than it is about him).

One positive about it all though, is that I notice that I must be reading posts looking for evidence of the various fundamental concepts even if they aren't explicitly spelled out in them. That seems to be why I keep visualising the Swiss Cheese mentioned above(?)

SelfSim said:

Man I find it sooo difficult to decode @Neogaia777 posts!
I keep coming up with the model of Swiss Cheese whenever I read them .. there are so many concepts just absent in his posts, its hard to figure out where to start. (No offence intended towards @Neogaia777 here either .. its more a comment about me and how I'm visualising, more than it is about him).

One positive about it all though, is that I notice that I must be reading posts looking for evidence of the various fundamental concepts even if they aren't explicitly spelled out in them. That seems to be why I keep visualising the Swiss Cheese mentioned above(?)

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I gave AI the Swiss Cheese test on summarizing on how the Twin paradox is resolved which it passed with flying colours.

Here's a table summarizing the key elements and evidence that help resolve the twin paradox in special relativity:

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Evidence Table for Resolving the Twin Paradox​

Category	Description	Role in Resolution
1. Time Dilation (Special Relativity)	Moving clocks tick more slowly than stationary ones in inertial frames.	Explains why the traveling twin ages less from the Earth's frame.
2. Asymmetry of Frames	Only the traveling twin changes inertial frames (accelerates during turnaround).	Breaks the symmetry; key to explaining why both twins don't experience the same aging.
3. Relativistic Doppler Effect	Light signals are redshifted when receding, blueshifted when approaching.	Shows how each twin observes the other's clock rate changing during the journey.
4. Shift in Simultaneity	During acceleration, the traveling twin’s concept of "now" on Earth shifts abruptly.	Causes a sudden jump in the Earth twin’s perceived age during turnaround.
5. Spacetime Diagrams (Minkowski Diagrams)	Graphical tool showing worldlines and proper time intervals.	Visual proof: traveling twin's path through spacetime covers less proper time.
6. Proper Time Calculation	Proper time is the actual time experienced by a clock along its worldline:
τ=∫1−v2/c2 dt\tau = \int \sqrt{1 - v^2/c^2} \, dt	The traveling twin's worldline gives less accumulated proper time.
7. Experimental Evidence	Real-life analogs (e.g., Hafele–Keating experiment with atomic clocks on planes).	Confirms that moving clocks tick more slowly — just as the theory predicts.

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Conclusion​

All these pieces together—mathematical, conceptual, graphical, and experimental—confirm that:

• The traveling twin ages less than the stay-at-home twin.
• The paradox is resolved by recognizing the asymmetry in their experiences, especially the acceleration and frame switching of the traveler.

Would you like a diagram or an example calculation to go with this?

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I use AI to generate tables but I am not 100% confident of the results, I carefully read AI's output before posting, in a previous post it made a glaring error which I asked it to revise.
More detail on this in my next post......

sjastro said:

I gave AI the Swiss Cheese test on summarizing on how the Twin paradox is resolved which it passed with flying colours.


I use AI to generate tables but I am not 100% confident of the results, I carefully read AI's output before posting, in a previous post it made a glaring error which I asked it to revise.
More detail on this in my next post......

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In Post #60 AI gave a table comparing muon clocks to galaxy cosmic chronometers.

The original table looked like this.

Here's a comparative table showing the key differences between a muon as a clock and a galaxy as a cosmic chronometer — both are "clocks" in physics, but used in very different contexts:

Aspect	Muon as a Clock	Galaxy as a Cosmic Chronometer
Nature of Clock	Subatomic particle decay clock	Stellar population aging clock
What it measures	Proper time in relativistic contexts	Expansion history of the Universe
Time scale	Microseconds (μs)	Billions of years (Gyr)
Mechanism	Muon decays with a fixed half-life (~2.2 μs at rest)	Galaxies evolve and their stars age in measurable ways
Affected by Time Dilation?	Yes — lifetime extends with increasing velocity (relativity)	No — used in cosmological comoving frame (non-relativistic approximation)
Typical speed	Relativistic (close to speed of light)	Non-relativistic (compared to light speed)
Used to test...	Special relativity	Cosmological models (e.g. Hubble parameter, dark energy)
Measured quantity	Decay time from lab frame	Differential aging between galaxy populations at different redshifts
Example use	Explaining why cosmic ray muons reach Earth's surface	Estimating H(z) (Hubble parameter at redshift z) from galaxy ages
Frame of reference	Usually Earth's frame vs muon's frame	Comoving cosmological frame
Precision constraints	Quantum uncertainty + detector resolution	Stellar population modeling + redshift accuracy

​

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The comment in red is clearly incorrect, metric expansion allows galaxies to not only travel at non relativistic speeds, but also at relativistic and superluminal speeds which exceed the speed of light.

On questioning this error, AI responded and corrected the table as shown in Post #60 .

Excellent question — and yes, this is a key point in cosmology that often surprises people:

Yes, galaxies can and do have recession velocities greater than the speed of light, due to the expansion of space itself — and this does not violate special relativity.

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Let’s unpack this, especially in the context of the table we discussed earlier.

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Quick Recap: Recession Velocity vs. Relativistic Motion​

Concept	What it means
Recession velocity	How fast a distant galaxy appears to be receding from us due to expansion of space (not proper motion through space).
Relativistic speed	An object’s speed through space approaching or exceeding 0.1c, where relativistic effects become significant. Governed by special relativity.

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1. Cosmic Expansion ≠ Motion Through Space​

In general relativity and the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, galaxies are mostly at rest in comoving coordinates. The apparent velocity arises from the stretching of space between objects.


The recession velocity is given by:

vrec=H(t)⋅Dv_{\text{rec}} = H(t) \cdot D

• H(t) = Hubble parameter at time t
• DD = proper distance to the galaxy

If the distance DD is large enough, even if H(t) is finite, you get:

vrec>cv_{\text{rec}} > c
This is common for galaxies at high redshift (e.g., z>1.5).

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2. Can We See These Superluminal Galaxies?​

Surprisingly: Yes, some galaxies with recession velocities >c are still observable.


Why? Because the Hubble parameter H(t) was larger in the past, and light from those galaxies was emitted when their recession velocity was less than c, allowing the light to reach us. The observable universe contains galaxies that are currently receding faster than light.

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In the Table Context​

Aspect	Galaxy as a Cosmic Chronometer
Recession velocity	Can be sub-luminal, relativistic, or even superluminal depending on distance
Frame of motion	Not moving through space, but carried with the expansion of space
Special relativity violated?	No — special relativity doesn't apply to the expansion of spacetime itself

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Summary​

• Distant galaxies can recede from us faster than light due to metric expansion of space.
• This is not motion through space and does not violate special relativity.
• Recession speeds span from non-relativistic, to relativistic, to superluminal, depending on the galaxy's distance.
• Galaxies used as cosmic chronometers are usually not considered to be "moving" in the SR sense — they are evolving stellar systems embedded in the expanding universe.

Would you like a diagram or numerical example of how this works with redshift vs recession velocity?

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Neogaia777 said:

@sjastro

Sorry I don't sometimes know all the correct terminology guys, but I thank you for putting up with both it and me though, etc.

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Its not just terminology though .. the terminology is just a label for the concepts. Using them appropriately, denotes recognition of the impact of a given concept. They're also an efficient way for getting to the point of a question.

Getting the concept is the part that matters the most in these discussions however, (IMHO).

Neogaia777 said:

But that's wrong though? One of them is traveling through the fabric of spacetime quicker than the other (Mary), and one of them slower through the fabric of spacetime than the other (Frank) (if he is on earth, for example) otherwise why would there be different time dilation with velocity? There wouldn't be any, because it would wind up meaningless, etc, and it even being said that anyone or anything can even be traveling through space at a particular velocity would all be meaningless also, since there would be no such thing for anything, etc. And I can guarantee you earth is not traveling through the fabric of spacetime @ 0.8c, and that's roughly half the normal speed/rate of time flow at that speed for anyone going that fast, correct? Earth is not experiencing half time flow, I can guarantee you that, but Mary would be, and regardless of whatever direction she was going or heading, as long as she is still traveling at 0.8c, her flow rate of time would be cut roughly in half, but Frank would always be aging somewhat normally the entire time, etc, but Mary wouldn't be, but she would be experiencing her time flow slowed down by half for the entire round trip regardless of which what direction she was going, etc.

During the first part of her (Mary's) journey, as she was headed away from Frank, if Frank sent out ten signals during that time, and Mary was traveling away from him @ 0.8c, then Mary would recieve two signals from him during that time, one mid-way during her trip, and one when she arrived at the point that she was about to turn around and head back, etc. And when she did start to head back, and proceeded with the trip back, and assuming she did this immediately, etc, during that remaining ten years back, she would recieve the remaining 18 signals from Frank over that period of time and travel period, so that she would have all of his messages when she got back, etc. (these signals are not unlike the all of the images generated by light in the universe, but that's a discussion for another time) But, regardless, or irregardless, Mary would have aged half as much as Frank when she got back, etc, but would never, ever, be any younger than the age that both of them were (Mary and Frank) when Mary first started her trip, or first left, but would have aged at half of the rate that Frank did when she did get back if her velocity remained constant the whole entire trip (or almost the whole entire trip) @ 0.8c, etc.

See above.

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Sorry but your post is comprehensively wrong, you need to understand how Minkowski spacetime diagrams and relativistic Doppler shift work.

The 2D Minkowski diagram in my post is composed of a vertical time axis and a horizontal spatial axis.
Frank is stationary spatially but is moving temporally which is represented by his trajectory or worldline being parallel to the time axis. Mary the travelling twin is moving both temporally and spatially at a speed less that c, her worldline is less than 45⁰ to the spatial and time axes on the outward and return journeys respectively.

The relativistic Doppler shift is defined by the formula.

fₒ = fₑ√(1-v/c)/(1+v/c) for a receding observer or fₒ = √(1+v/c)/(1-v/c) for an approaching observer.

fₒ is the frequency of the source in this case Frank sending a signal to Mary at a frequency of 1 signal/year.
fₑ is the frequency of Mary’s return signals to Frank.

In the outbound trip the Doppler factor is √(1-v/c)/(1+v/c) = √(1-0.8)/(1+0.8) = √(0.2)/(1.8) = 1/3, while during the return trip the Doppler factor is √(1+v/c)/(1-v/c) = √(1+0.8)/(1-0.8) = √(1.8)/(0.2) = 3.

In the first ten years in Frank’s frame of reference he sends 10 signals to Mary who is on the outbound journey and receives 3 signals from Mary.
In the next the ten years when Mary is on the return journey Frank receives 3 x 3 = 9 signals, so in total Frank sends 20 signals and receives 3 + 9 = 12 signals from Mary (there was a typo in my post which stated there were 10 signals this has been changed to 12).

Biological clocks are as much subject to relativistic Doppler shift as any other phenomena and Mary has aged at a slower rate than Dave and will be younger when she returns.
If Mary was a light source wavelength would be redshifted during the outward journey resulting in a decrease in frequency, during the return journey blueshift would occur and the frequency would increase.

sjastro said:

I am sure we have had this discussion before, if you were able to travel instantaneously (faster than the speed of light) you will be outside the light cones of the space-time diagram.
Inside the cones in the timelike region causality is preserved, outside in the spacelike region there are no ordering of events, you could be younger, older or both on reaching your destination.

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Why I think perhaps time-travel is impossible

Think about it, if you for example use a strong magnet to speed things up in sort of an attempt to travel in time, people would notice and resist the changes, so only nature would change and speed up or go backwards, but I have the suspicion that the same would happen to nature also, that it...

www.christianforums.com

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Can you explain the ‘no ordering’. If a space ship jumps outside of the light cone wouldn’t there be variables to influence some end of ordering?

Larniavc said:

Can you explain the ‘no ordering’. If a space ship jumps outside of the light cone wouldn’t there be variables to influence some end of ordering?

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Well, there's the small matter of an infinite amount of energy needed to be brought to bear before jumping outside the light cone there.
What effect might that have on the possibility of future effects just before exceeding that threshold?

I don't think we can ignore that the primary purpose of Physics, (and science), is to explain perceptions amongst ourselves, such that they make sense of the universe. That's a good enough 'influencing variable' for me.

Also, what use is a math variable that doesn't make physical sense once it exceeds some conceptual threshold (like infinity)?

Neogaia777 said:

We're going to use Mary again. Mary has a problem, her problem is she needs to measure 25% of a signal, or a beam of light, and have it equal 100%.

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Huh? Why?
I receive lots of signals at less than 100% of its original form .. Its still a signal I receive though.

SelfSim said:

Well, there's the small matter of an infinite amount of energy needed to be brought to bear before jumping outside the light cone there.

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lol, I totally didn’t think of that. Sounds like I asked a ‘how many angels can dance on a pin’.

I totally get that you cannot go at c with any mass. Where I get snarled up is causality breaking. It confuses the hell out of me (I can just about get my head around the diagram of two space ships where events that are simultaneous in one frame of reference may not be simultaneous in the other) but it does feel like grabbing at weasels, lol.

Larniavc said:

Can you explain the ‘no ordering’. If a space ship jumps outside of the light cone wouldn’t there be variables to influence some end of ordering?

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Here is a basic introduction to Minkowski diagrams and why exceeding the speed of light results in no ordering of events.
A 2D Minkowski diagram is a space-time diagram composed of a vertical time axis ω and horizontal distance axis x.


Although the ω axis is a time axis it is expressed in units of ct which is distance so both axes are dimensionally the same.
For a photon travelling at the speed of light c, the world line or path in space-time forms a 45⁰ angle straight line with the ω and x axis as it undergoes equal displacement in both time and space.

Particles travelling at speeds less than c fall in the region above the world line of the photon since
tan(θ) = dx/dω = (dt/dω)(dx/dt) = 1/c (dx/dt) = v/c.
θ = tan⁻¹(u/c) < 45⁰ when v < c.

The above Minkowski diagram applies to a cone in the first quadrant where ω ≥ 0 and x ≥ 0 but applies to all values of ω and x.

An event is defined as having a position and time coordinate.
If two events occur on the x-axis in the first diagram then each event is only separated in space, there is no temporal displacement as each event occurs at t=0.
This has important consequences as there is no ordering of the events.
This is not a problem for particles travelling at velocities less than c where the world line forms an angle less than 45⁰ with the time axis and any event is both temporally and spatially separated.

So what happens when v > c?

The left hand frame (a) is for an inertial observer while the right hand frame (b) is moving from left to right along the x-axis of (a) at a velocity v and are mathematically related by the Lorentz equations.

x' = (x – βω)/√(1-β²) x = (x’ + βω)/√(1-β²)
ω' = (ω – βx)/√(1-β²) ω = (ω’ + βx)/√(1-β²)
β = v/c

Frame (b) shows the geometrical transformation according to the Lorentz equations, the observer in frame (a) notes the w’ and x’ axes are no longer orthogonal.
If frame (b) is travelling faster than light the angle θ = tan⁻¹(v/c) > 45⁰ since v > c.
All events will fall on the x’ axis which as stated previously are separated in space but not time.

In the diagram in the time like shaded region event O definitely comes before event P, outside this region in the space like region one cannot tell if O comes before Q or Q comes before O since there is no temporal separation between the events as ω’ = 0 along the x’ axis.
From a physics rather than maths perspective what this is amounts to is that O and Q occur in such rapid “succession” that the time difference is less than the time needed for a light ray to traverse the spatial distance between the events.

Hope this helps.

Found a slightly easier to understand Youtube using an animated Minkowski diagram:
(The Minkowski part starts at the 6:55mark).

sjastro said:

If two events occur on the x-axis in the first diagram then each event is only separated in space, there is no temporal displacement as each event occurs at t=0.
This has important consequences as there is no ordering of the events.

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By Jove I think I got it!

Neogaia777 said:

We're going to use Mary again. Mary has a problem, her problem is she needs to measure 25% of a signal, or a beam of light, and have it equal 100%. The only way she can do this is if her time is dilated, and her length contracted, both by 50% each, etc. Now, this is not a problem is she is traveling along at 75% light speed, but the internet tells her that she has to be at 86.6% of c, and that's her problem.

Care to help Mary out?

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Is this question meant to be about the technicalities of receiving signals travelling at c, whilst the receiver is moving at speeds close to c?
If so, then I'd think its also a question about the pre-designed spread of the signal from its source, (ie: the radiation pattern), amplification, re-tuning RF componentry to compensate for redshift .. and message integration times (proper) needed to gather the complete information contained in them(?)
Is it show-stopper that she's travelling too close to c in order to receive them at all? If so, then what is it?
(I mean, its already a physical show-stopper that she can't achieve these speeds anyway .. )