The answers already posted answer probably your question. I just will add a little about what physics says about time reversibility. It does say that macroscopically past and future are distinguishable, but microscopically they are almost the same, but also not identical.

You saw in the other answers that thermodynamics, the science of large numbers of particles that then must be described macroscopically, can distinguish between past and future because disorder (entropy in physics) goes up with time, for any irreversible process (of which there are many, macroscopically, such as your vase breaking). Too many pieces to put them back together.

Still, there is cause and effect, you just know which came first

Microscopically it is different. The physics for all particle and radiation interactions are also causal, but in this case they are all almost completely reversible. Almost in a minute. But ignoring the almost, that means that if you ran a movie of particle interactions forwards or backwards they both would look legitimate, and you could not distinguish past and future.

The alsmot comes about because time reversibility, called T symmetry, is not an exact symmetry of nature. The weak interaction in physics. (One of the 4 forces of nature) is not T symmetric. We see some weak interactions with particles that do not go the same way forward and backward. The same is true with another so called discrete symmetry (discrete: only two ways it can be), the mirror symmetry, called the parity P. There are right handed interactions and left handed ones, and they are sometimes not the same. Finally there is a charge symmetry (positive and negative), called C, which is also sometimes broken. But CPT as the combination of the 3 seems to be always symmetric.

There still some uncertainty whether there might be some strong force interaction with also slightly breaks P and T, and why there is more matter than antimatter in the universe, which is probably due to some C, P and or T breaking early in the universe history.

But we do know that Each of,those, and particularly for your question, T is anot a symmetry of nature. Google and look at the Wikipedia article and others for time symmetry. See the wiki article at https://en.m.wikipedia.org/wiki/T-symmetry

The answers already posted answer probably your question. I just will add a little about what physics says about time reversibility. It does say that macroscopically past and future are distinguishable, but microscopically they are almost the same, but also not identical.

You saw in the other answers that thermodynamics, the science of large numbers of particles that then must be described macroscopically, can distinguish between past and future because disorder (entropy in physics) goes up with time, for any irreversible process (of which there are many, macroscopically, such as your vase breaking). Too many pieces to put them back together.

Still, there is cause and effect, you just know which came first

Microscopically it is different. The physics for all particle and radiation interactions are also causal, but in this case they are all almost completely reversible. Almost in a minute. But ignoring the almost, that means that if you ran a movie of particle interactions forwards or backwards they both would look legitimate, and you could not distinguish past and future.

The alsmot comes about because time reversibility, called T symmetry, is not an exact symmetry of nature. The weak interaction in physics (One of the 4 forces of nature) is not T symmetric. We see some weak interactions with particles that do not go the same way forward and backward. The same is true with another so called discrete symmetry (discrete: only two ways it can be), the mirror symmetry, called the parity P. There are right handed interactions and left handed ones, and they are sometimes not the same. Finally there is a charge symmetry (positive and negative), called C, which is also sometimes broken. But CPT as the combination of the 3 seems to be always symmetric.

There still some uncertainty whether there might be some strong force interaction with also slightly breaks P and T, and why there is more matter than antimatter in the universe, which is probably due to some C, P and or T breaking early in the universe history.

But we do know that each of,those, and particularly for your question, T is not a symmetry of nature. Google and look at the Wikipedia article and others for time symmetry. See the wiki article at https://en.m.wikipedia.org/wiki/T-symmetry