The closer to the speed of light, the more length contraction in the direction of motion (SRT).

[Maartenn100]

According to Einstein's theory of special relativity, when traveling at speeds close to the speed of light, you experience a significant shortening of distances in the direction of your motion. This phenomenon is known as length contraction.

This means that any distance in the universe is reachable as long as we can travel close enough to the speed of light, because as v approaches c, γ\gamma becomes very large, and thus L becomes very small.

For an observer who is stationary relative to your motion (an "outsider"), your clock seems to run slower; this is called time dilation. But from your own perspective inside the spaceship, time proceeds normally, and it is the distance to your destination that becomes shorter.

This can be expressed using the following formulas from special relativity:

L = L₀ / γ
 

Where:

Lo is the rest length (the length measured in the reference frame where the object is at rest),

γ\gamma (gamma) is the Lorentz factor, defined as:

γ = 1 / √(1 - v² / c²)

v is the speed of the moving object,

c is the speed of light.

 

Time Dilation

The dilated time Δt measured by the stationary observer is given by:

Δt = γ * Δt₀
 

Where:

Δt₀ is the proper time (the time measured in the reference frame of the moving observer).

Explanation

• For you in the spaceship: The distance to your destination L is smaller than the rest distance L₀ due to length contraction. Time passes normally for you; you don't notice any difference in the flow of time in your own reference frame.

• For the outsider: Your clock seems to tick slower due to time dilation. The distance between the starting point and the destination remains L₀.

There is no length contraction in their reference frame.

These effects become significant at speeds that are a substantial fraction of the speed of light. They result from the way space and time are interwoven in the theory of relativity.

Conclusion

Any distance becomes reachable once you travel close to the speed of light.

 

 

 

Edited October 3 by Maartenn100

[exchemist]

2 hours ago, Maartenn100 said:

According to Einstein's theory of special relativity, when traveling at speeds close to the speed of light, you experience a significant shortening of distances in the direction of your motion. This phenomenon is known as length contraction.

This means that any distance in the universe is reachable as long as we can travel close enough to the speed of light, because as v approaches c, γ\gamma becomes very large, and thus L becomes very small.

For an observer who is stationary relative to your motion (an "outsider"), your clock seems to run slower; this is called time dilation. But from your own perspective inside the spaceship, time proceeds normally, and it is the distance to your destination that becomes shorter.

This can be expressed using the following formulas from special relativity:

L = L₀ / γ
 

Where:

Lo is the rest length (the length measured in the reference frame where the object is at rest),

γ\gamma (gamma) is the Lorentz factor, defined as:

γ = 1 / √(1 - v² / c²)

v is the speed of the moving object,

c is the speed of light.

 

Time Dilation

The dilated time Δt measured by the stationary observer is given by:

Δt = γ * Δt₀
 

Where:

Δt₀ is the proper time (the time measured in the reference frame of the moving observer).

Explanation

• For you in the spaceship: The distance to your destination L is smaller than the rest distance L₀ due to length contraction. Time passes normally for you; you don't notice any difference in the flow of time in your own reference frame.

• For the outsider: Your clock seems to tick slower due to time dilation. The distance between the starting point and the destination remains L₀.

There is no length contraction in their reference frame.

These effects become significant at speeds that are a substantial fraction of the speed of light. They result from the way space and time are interwoven in the theory of relativity.

Conclusion

Any distance becomes reachable once you travel close to the speed of light.

 

 

 

Surely the problem is you can't get close to the speed of light without incurring a close to infinite energy cost?  

[Endy0816]

4 hours ago, Maartenn100 said:

According to Einstein's theory of special relativity, when traveling at speeds close to the speed of light, you experience a significant shortening of distances in the direction of your motion. This phenomenon is known as length contraction.

This means that any distance in the universe is reachable as long as we can travel close enough to the speed of light, because as v approaches c, γ\gamma becomes very large, and thus L becomes very small.

For an observer who is stationary relative to your motion (an "outsider"), your clock seems to run slower; this is called time dilation. But from your own perspective inside the spaceship, time proceeds normally, and it is the distance to your destination that becomes shorter.

This can be expressed using the following formulas from special relativity:

L = L₀ / γ
 

Where:

Lo is the rest length (the length measured in the reference frame where the object is at rest),

γ\gamma (gamma) is the Lorentz factor, defined as:

γ = 1 / √(1 - v² / c²)

v is the speed of the moving object,

c is the speed of light.

 

Time Dilation

The dilated time Δt measured by the stationary observer is given by:

Δt = γ * Δt₀
 

Where:

Δt₀ is the proper time (the time measured in the reference frame of the moving observer).

Explanation

• For you in the spaceship: The distance to your destination L is smaller than the rest distance L₀ due to length contraction. Time passes normally for you; you don't notice any difference in the flow of time in your own reference frame.

• For the outsider: Your clock seems to tick slower due to time dilation. The distance between the starting point and the destination remains L₀.

There is no length contraction in their reference frame.

These effects become significant at speeds that are a substantial fraction of the speed of light. They result from the way space and time are interwoven in the theory of relativity.

Conclusion

Any distance becomes reachable once you travel close to the speed of light.

 

 

 

Expansion of spacetime will limit things.

Anywhere can be arbitrarily close, but still remain out of reach.

[Genady]

1 hour ago, Endy0816 said:

Expansion of spacetime

Expansion of spacetime?

[Endy0816]

22 minutes ago, Genady said:

Expansion of spacetime?

Even the hyphen couldn't keep up

[Maartenn100]

5 hours ago, exchemist said:

Surely the problem is you can't get close to the speed of light without incurring a close to infinite energy cost?  

It is true that accelerating an object with mass to the exact speed of light c would require infinite energy, and that this is physically impossible. However, it is not necessary to reach the speed of light to experience significant relativistic effects such as length contraction and time dilation.

Length Contraction: The distance to your destination becomes significantly shorter in your own frame of reference. This makes it possible to bridge enormous cosmic distances within a human lifetime without needing to reach the speed of light.

Energy Requirements: While it is true that the energy needed to get closer to the speed of light increases exponentially, this energy remains finite as long as the velocity is below c. The energy E required for acceleration is given by:

 

E = (γ - 1) * m * c^2

 

where:

• m is the rest mass of the spacecraft.

• γ (gamma) is the Lorentz factor, defined as:

 

γ = 1 / √(1 - v² / c²)
 

Although E becomes large at high γ, it is not infinite as long as v < c .

Practical Approach:

• Constant Acceleration: If we maintain a constant acceleration of, for example, 1g (9.81 m/s²), we can reach very high speeds within a reasonable proper time without overburdening the human body.

• Travel Time to Nearby Stars:

  • To Alpha Centauri (4.37 light-years away): The travel time in proper time (your experienced time) would be only a few years with constant acceleration and deceleration.

• Technological Advancements: Although our current technology does not yet allow for this, it is theoretically possible that future technologies could provide the necessary energy—through means such as antimatter propulsion, nuclear fusion, or other advanced methods.

Conclusion:

• Theoretical Possibility: According to the theory of special relativity, it is possible to traverse enormous distances in the universe within a finite and practical time span in your own frame of reference, without requiring infinite energy.

• Practical Challenges: While there are significant technological and energy challenges remaining, this does not exclude the possibility that such journeys could become feasible in the future.

In summary, while it is physically impossible to reach the speed of light due to the infinite energy that would be required, it is not necessary to reach c to benefit from the relativistic effects that make interstellar travel within a human lifetime possible. By traveling at speeds close to, but below the speed of light, we can theoretically bridge any distance in the universe thanks to length contraction and time dilation, without the need for infinite energy.

 

 

Edited October 3 by Maartenn100

[Genady]

You are talking about a one-way trip, right? One just flies away and gone.

[Maartenn100]

4 minutes ago, Genady said:

You are talking about a one-way trip, right? One just flies away and gone.

Traveling at speeds close to the speed of light does introduce significant time dilation, meaning that while less time passes for the traveler, more time passes for those who remain behind on Earth. However, this doesn't necessarily mean it's only a one-way trip where "one just flies away and gone."

While traveling at relativistic speeds, the astronaut's experienced time (proper time) is much shorter than the time elapsed on Earth. This means that a round trip is possible from the traveler's perspective within their own lifetime.

Example

• Suppose an astronaut travels to a star 10 light-years away at a speed close to c.For the astronaut, due to length contraction and time dilation, the journey might take only a few years each way. However, from Earth's frame of reference, decades might have passed.

:The traveler can return to Earth, but they would find that much more time has passed on Earth than they have experienced. and family may have aged significantly or passed away, and society could have changed drastically.

• Not Just "Gone":

  The traveler isn't lost or unable to return; they can physically come back. The key issue is the asymmetry in experienced time between the traveler and those on Earth.

Practical Considerations:

• Relativity of Simultaneity:

  Events that are simultaneous in one frame of reference are not necessarily simultaneous in another moving at a high relative speed.This affects synchronization of time between Earth and the spacecraft.

• Communication Delays:

  Even at light speed, messages would take years to travel between distant points, complicating real-time communication.

Conclusion:

• Not Necessarily One-Way:

  While the social and personal implications are significant due to time dilation, the journey isn't strictly one-way.The traveler has the ability to return, but must be prepared for the changes that have occurred during their absence.
•  
• Future Possibilities:
• Advances in technology and understanding of physics might offer solutions to mitigate these issues, such as:Cryogenic Sleep: Extending the life of travelers to better align with Earth's time frame.
• Warp Drives or Wormholes: Hypothetical methods that could allow for faster-than-light travel without violating relativity.

Summary:

Traveling at relativistic speeds allows for round trips within the traveler's lifetime, but significant time will have passed on Earth due to time dilation. While this presents emotional and social challenges, it's not accurate to say the traveler is simply "gone." The possibility of return exists, but it comes with the understanding that the world they return to may be vastly different from the one they left.

 

[swansont]

1 hour ago, Maartenn100 said:

Practical Approach:

• Constant Acceleration: If we maintain a constant acceleration of, for example, 1g (9.81 m/s²), we can reach very high speeds within a reasonable proper time without overburdening the human body.

How much fuel would one need?

How do you deal with the issues of traveling at high speeds? (collisions, radiation effects)

[MigL]

Even light, moving at c , cannot reach anything beyond a 46 Billion light years radius.
There's s reason they call it the 'observable' universe.

[Janus]

On 10/3/2024 at 8:09 AM, swansont said:

How much fuel would one need?

How do you deal with the issues of traveling at high speeds? (collisions, radiation effects)

Assuming a 100% efficient "Photon drive", you would  need a fuel to mass ratio of 886 to 1 in order to just do a trip to Vega (27ly), stopping there. (this doesn't include a return trip)

The center of the galaxy would require one of 955,000 to 1, and the Andromeda galaxy 4.2e9 to 1.

Since 100% efficiency is not in the cards,  in reality, these would be significantly higher

.

[Halc]

On 10/3/2024 at 11:36 AM, MigL said:

Even light, moving at c , cannot reach anything beyond a 46 Billion light years radius.
There's s reason they call it the 'observable' universe.

Not anything beyond what is now about 16 GLY away, which is where the event horizon currently is, even though we can see it (and they can see our past).

On 10/3/2024 at 11:09 AM, swansont said:

How much fuel would one need?

How do you deal with the issues of traveling at high speeds? (collisions, radiation effects)

I assume the OP was speaking hypothetically, assuming an arbitrarily powerful ship and a totally clear path.  The point wasn't an engineering one.

 

On 10/3/2024 at 1:23 AM, Maartenn100 said:

According to Einstein's theory of special relativity, when traveling at speeds close to the speed of light, you experience a significant shortening of distances in the direction of your motion.

Well actually you experience nothing special, per the first postulate of special relativity.  In the frame that you're experiencing, you're stationary. But yes, all the galaxies and stuff are moving fast past your and, being things in motion, are length contracted. So you're correct that in an inertial frame, there is no limit to the distance (in a given frame) that one can travel in a human lifetime.

Unfortunately the universe is not described by any inertial frame, hence the event horizon limit referenced above.  An infinitely powerful ship cannot reach a star 17 GLY away (proper distance along a line of constant cosmic time), even though one could see it (presuming it was a super long lived star that was visible both now and for as long as the attempt takes). But if the distant star system launched a similar ship in our direction today, the two ships could at least meet.

[MigL]

9 hours ago, Halc said:

Not anything beyond what is now about 16 GLY away, which is where the event horizon currently is, even though we can see it (and they can see our past).

True.
But that is a hypothetical distance, because SR involves space and time.
Any light that traverses that distance will have come from from 46 GLY away; there is no 'now' or 'currently'.

A lot happens during the travel time; like expansion.

Edited October 5 by MigL

[Halc]

On 10/5/2024 at 10:56 AM, MigL said:

But that is a hypothetical distance, because SR involves space and time.

It is a current proper distance measured along a line of constant cosmological time.  Light emitted from here will never ever reach a comoving object 17 GLY away. There's no hypothetical about that. That's what an event horizon is. Communication is not possible across one.

SR does not apply since it only applies to inertial (Minkowskian) frames, and the universe is not Minkowskian.  Under SR and the flat spacetime under which it is relevant, yes, light will eventually get to any coordinate in any given inertial frame given enough time.

But even in SR and flat spacetime, light will never catch up to a sufficiently distant object that undergoes constant proper acceleration (as does said object 17 GLY away), so in a way, SR rules are sufficient to illustrate the effect.  If an object is accelerating away from us at say 1G, it only needs to be a light year away from us and any signal we send will never reach it. A star 16 GLY away (as measured in our inertial frame) need accelerate away at far less than 1G to put us beyond its event horizon.

 

Sorry for slow reply. I don't log on here every day.

[MigL]

The fact remains that whatever is 17 GLY away will take 46 GY to affect us at the speed of causality.
Saying something is 17 GLY away, right now, means nothing, as there is no 'now'.

If it can't affect us, is it really there ?
( that's what hypothetical means )

[KJW]

On 10/10/2024 at 9:11 AM, Halc said:

If an object is accelerating away from us at say 1G, it only needs to be a light year away from us and any signal we send will never reach it.

Are you sure about this? The relevant formula is:

[math]d = \dfrac{c^2}{a}[/math]

I haven't evaluated this formula, but it seems an unlikely coincidence of units for an acceleration of 1 g to lead to a distance of 1 light-year.

 

[swansont]

8 hours ago, KJW said:

Are you sure about this? The relevant formula is:

d=c2a

I haven't evaluated this formula, but it seems an unlikely coincidence of units for an acceleration of 1 g to lead to a distance of 1 light-year.

 

1 LY is 9.461 × 10^15 meters

By inspection, the number seem to at least approximately match

[joigus]

On 10/3/2024 at 7:23 AM, Maartenn100 said:

Conclusion

Any distance becomes reachable once you travel close to the speed of light.

 

What do you mean by a distance becoming "reachable"?

In the sense of being able to probe it? In the sense of making it fit through some kind of physical system in the perpendicular direction playing the role of a slit (like a couple of high-energy photons, etc...)?

Or perhaps in the purely kinematical sense of it being proven that short by means of telemetry of some kind?

[zapatos]

On 10/3/2024 at 12:23 AM, Maartenn100 said:

Conclusion

Any distance becomes reachable once you travel close to the speed of light.

If any distance is 'reachable' at close to c, then any distance is 'reachable' at any speed at all. You just need more time.

[KJW]

9 hours ago, swansont said:

1 LY is 9.461 × 10^15 meters

By inspection, the number seem to at least approximately match

I have to see for myself:

 

[math]d = \dfrac{c^2}{a}
\\
= \dfrac{(299792458 \text{ m s}^{-1})^2}{9.80665 \text{ m s}^{-2}}
\\
= 9.16475 \times 10^{15} \text{ m}
\\
= \dfrac{9.16475 \times 10^{15} \text{ m}}{9.4607304725808 \times 10^{15} \text{ m ly}^{-1}}
\\
= 0.9687 \text{ ly}[/math]

 

That's remarkably close!

[Halc]

On 10/10/2024 at 11:14 PM, KJW said:

I haven't evaluated this formula, but it seems an unlikely coincidence of units for an acceleration of 1 g to lead to [an event horizon] distance of 1 light-year.

Yes, it's a neat coincidence, and memorized since it's a useful fact for such discussions.

 

On 10/11/2024 at 10:16 AM, joigus said:

What do you mean by a distance becoming "reachable"?

I imagine it means: Reachable before you die.  In an inertial frame, any distance is reachable in finite proper time given enough speed, so with a speedy ship, I can get to the other side of the galaxy (where the dinosaurs were) before I die.  I say dinosaurs because some of the most popular ones were around when our solar system was half a galactic orbit prior.

 

In a universe with dark energy, the event horizon is the limit and there is no reaching that or anything beyond, regardless of the power of your ship or your life expectancy.

[joigus]

5 hours ago, Halc said:

I imagine it means: Reachable before you die.  In an inertial frame, any distance is reachable in finite proper time given enough speed, so with a speedy ship, I can get to the other side of the galaxy (where the dinosaurs were) before I die.  I say dinosaurs because some of the most popular ones were around when our solar system was half a galactic orbit prior.

 

Oh, I see. I was thinking more of short distances rather than longer ones, as Lorentz contraction makes the accelerated body shorter and shorter. But the OP, as well as other members have been talking about cosmological distances too, now that you mention it. I must confess I haven't figured out how both are related. It seems like some combination of length contraction and time dilation (contraction relative to the traveller relative to the observers tied to the planets?). What I fail to see is how one is supposed to use these effects to achieve interstellar space travel. It could be that OP is trying to combine effects happening in different frames... This happens often.

[Endy0816]

6 hours ago, joigus said:

Oh, I see. I was thinking more of short distances rather than longer ones, as Lorentz contraction makes the accelerated body shorter and shorter. But the OP, as well as other members have been talking about cosmological distances too, now that you mention it. I must confess I haven't figured out how both are related. It seems like some combination of length contraction and time dilation (contraction relative to the traveller relative to the observers tied to the planets?). What I fail to see is how one is supposed to use these effects to achieve interstellar space travel. It could be that OP is trying to combine effects happening in different frames... This happens often.

For person onboard the ship, the distance between them and their destination is also shortened due to length contraction.

 

Edited October 14 by Endy0816

[zapatos]

43 minutes ago, Endy0816 said:

For person onboard the ship, the distance between them and their destination is also shortened due to length contraction.

 

I thought length contraction was the shortening of the object traveling at light speeds. Did I get that wrong?

[Genady]

20 minutes ago, zapatos said:

I thought length contraction was the shortening of the object traveling at light speeds. Did I get that wrong?

It is shortening of a distance between two spatial points. It happens at any speed and does not depend on what is there between the points.