They say: even if our spaceships can go at the speed of light, our spaceship may take many years to reach the other star/ other side of the galaxy/universe.

Fact is: if you go (near) at the speed of light, you will be there in (almost) no time. (according to your own clock)

Thanks to realtivity.

That's our wormhole, right there.

“They” never say who “they” refers to, which is quite convenient for “them” but in science discussion it’s better to actually cite a source because anyone with reasonable competence in physics will know that massive objects can’t travel at the speed of light. So “they” aren’t competent.

The complications you leave out are how you get to the speed near c, and the time dilation effects that will make your elapsed time much less than those you left behind. These are not trivial details.

True, but remember that “energy” and “inertia” are frame-dependent. The astronaut experiences a constant proper acceleration and burns fuel at a steady rate in his own frame.

Not exponentially more energy needed. The apparent exponential energy growth exists only for an external observer, because their clocks run faster and they see his γ increasing. In his own frame, nothing gets harder; it’s the universe that contracts and slows down around him. As far as I understand it.

You're right that from the Earth’s perspective, a ship’s kinetic energy grows without bound as it approaches the speed of light. But that’s a statement about how things look in the Earth’s reference frame, not about what the astronaut actually experiences. From the astronaut’s own frame of reference, his proper acceleration and thrust remain constant. He burns fuel at a steady rate per second of his own proper time.

He can feels a continuous 1 g push in his back, nothing more, nothing less, even as his velocity (measured from Earth) increases. This isn’t a contradiction: energy and inertia are frame-dependent quantities.In the rocket’s frame, the laws of motion stay the same, and the ship doesn’t “get heavier.” What happens instead is that space and time outside the ship distort: distances in the direction of motion contract, and external clocks appear to tick faster.

If we write the relativistic rocket equation in the traveler’s frame,

m(τ) = m₀ * e^(-aτ/u)

where (a) is the proper acceleration, (u) the exhaust velocity, and (\tau) the astronaut’s own time, we find that the fuel consumption per second of proper time is constant. Only when transformed to Earth’s coordinates does this appear to demand exponentially more energy, because the Lorentz factor γ rises as (v -> c). So for the astronaut, the “energy wall” at the speed of light never shows up in his local physics; his engine keeps burning steadily, and it’s the universe that bends around him.

That’s why relativity itself already contains a kind of natural “wormhole effect”:

the traveler doesn’t need to tunnel through space,

because for him, space itself contracts as he continues to accelerate.

It’s not that spatial contraction becomes “harder” for the traveler quite the opposite.
As the ship’s proper acceleration continues, its instantaneous velocity v(τ) increases, and the Lorentz factor γ grows.
The observed length in the direction of motion follows:

L'(τ) = L / γ(τ)

so as γ rises, the contracted distance keeps shrinking more and more rapidly, not more slowly
The “difficulty” exists only in the external frame, where adding energy appears to yield ever smaller gains in velocity.
For the astronaut, space itself keeps folding shorter and shorter ahead of him, while his proper acceleration feels perfectly constant.

Edited October 8Oct 8 by Maartenn100

1 hour ago, Maartenn100 said:

True, but remember that “energy” and “inertia” are frame-dependent. The astronaut experiences a constant proper acceleration and burns fuel at a steady rate in his own frame.

Which aren’t the issues I raised.

1 hour ago, Maartenn100 said:

Not exponentially more energy needed. The apparent exponential energy growth exists only for an external observer, because their clocks run faster and they see his γ increasing. In his own frame, nothing gets harder; it’s the universe that contracts and slows down around him. As far as I understand it.

Again, I didn’t raise “exponential energy” concerns, though energy concerns exist

If you have a target in mind, i.e. the star you mentioned, it will take a certain amount of energy to achieve whatever speed you desire relative to it, in order to make it “(almost) no time” And you have to accelerate the rocket payload, casing, engine and all the fuel. If you want to go faster, that’s even more fuel you have to accelerate.

But it will also take time to accelerate to that speed and to reduce it at the end of the trip, which could be quite restrictive if you have a fragile biological payload like a human.

1 hour ago, Maartenn100 said:

You're right that from the Earth’s perspective, a ship’s kinetic energy grows without bound as it approaches the speed of light. But that’s a statement about how things look in the Earth’s reference frame, not about what the astronaut actually experiences. From the astronaut’s own frame of reference, his proper acceleration and thrust remain constant. He burns fuel at a steady rate per second of his own proper time.

I can’t be right about a point I didn’t make

1 hour ago, Maartenn100 said:

He can feels a continuous 1 g push in his back, nothing more, nothing less, even as his velocity (measured from Earth) increases. This isn’t a contradiction: energy and inertia are frame-dependent quantities.In the rocket’s frame, the laws of motion stay the same, and the ship doesn’t “get heavier.” What happens instead is that space and time outside the ship distort: distances in the direction of motion contract, and external clocks appear to tick faster.

The calculation you need to do is how long it takes to get to .99c (or whatever; you don’t actually specify it) accelerating at 1g (or whatever, since you didn’t specify this in the OP, either)

1 hour ago, Maartenn100 said:

If we write the relativistic rocket equation in the traveler’s frame,

m(τ) = m₀ * e^(-aτ/u)

where (a) is the proper acceleration, (u) the exhaust velocity, and (\tau) the astronaut’s own time, we find that the fuel consumption per second of proper time is constant. Only when transformed to Earth’s coordinates does this appear to demand exponentially more energy, because the Lorentz factor γ rises as (v -> c). So for the astronaut, the “energy wall” at the speed of light never shows up in his local physics; his engine keeps burning steadily, and it’s the universe that bends around him.

That’s why relativity itself already contains a kind of natural “wormhole effect”:

the traveler doesn’t need to tunnel through space,

because for him, space itself contracts as he continues to accelerate.

You’re “rebutting” a straw man

One issue I raised is like this: At v = 0.995c, gamma is ~10. A 10 LY trip takes 1 year at this speed

But it takes about a year to get to that speed at 1g, and another year to get to rest. So your 1 year trip is actually closer to 3 years. And arguably that’s not “almost no time” and those issues are present even if you can increase gamma to 100, or 1000. The trip won’t be shorter than ~2 years.